Multilevel ensemble Kalman filter
Chernov, Alexey
2016-01-06
This work embeds a multilevel Monte Carlo (MLMC) sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF). In terms of computational cost vs. approximation error the asymptotic performance of the multilevel ensemble Kalman filter (MLEnKF) is superior to the EnKF s.
Multilevel ensemble Kalman filtering
Hoel, Haakon
2016-01-08
The ensemble Kalman filter (EnKF) is a sequential filtering method that uses an ensemble of particle paths to estimate the means and covariances required by the Kalman filter by the use of sample moments, i.e., the Monte Carlo method. EnKF is often both robust and efficient, but its performance may suffer in settings where the computational cost of accurate simulations of particles is high. The multilevel Monte Carlo method (MLMC) is an extension of classical Monte Carlo methods which by sampling stochastic realizations on a hierarchy of resolutions may reduce the computational cost of moment approximations by orders of magnitude. In this work we have combined the ideas of MLMC and EnKF to construct the multilevel ensemble Kalman filter (MLEnKF) for the setting of finite dimensional state and observation spaces. The main ideas of this method is to compute particle paths on a hierarchy of resolutions and to apply multilevel estimators on the ensemble hierarchy of particles to compute Kalman filter means and covariances. Theoretical results and a numerical study of the performance gains of MLEnKF over EnKF will be presented. Some ideas on the extension of MLEnKF to settings with infinite dimensional state spaces will also be presented.
Multilevel ensemble Kalman filtering
Hoel, Hakon
2016-06-14
This work embeds a multilevel Monte Carlo sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF) in the setting of finite dimensional signal evolution and noisy discrete-time observations. The signal dynamics is assumed to be governed by a stochastic differential equation (SDE), and a hierarchy of time grids is introduced for multilevel numerical integration of that SDE. The resulting multilevel EnKF is proved to asymptotically outperform EnKF in terms of computational cost versus approximation accuracy. The theoretical results are illustrated numerically.
On Ensemble Nonlinear Kalman Filtering with Symmetric Analysis Ensembles
Luo, Xiaodong
2010-09-19
The ensemble square root filter (EnSRF) [1, 2, 3, 4] is a popular method for data assimilation in high dimensional systems (e.g., geophysics models). Essentially the EnSRF is a Monte Carlo implementation of the conventional Kalman filter (KF) [5, 6]. It is mainly different from the KF at the prediction steps, where it is some ensembles, rather then the means and covariance matrices, of the system state that are propagated forward. In doing this, the EnSRF is computationally more efficient than the KF, since propagating a covariance matrix forward in high dimensional systems is prohibitively expensive. In addition, the EnSRF is also very convenient in implementation. By propagating the ensembles of the system state, the EnSRF can be directly applied to nonlinear systems without any change in comparison to the assimilation procedures in linear systems. However, by adopting the Monte Carlo method, the EnSRF also incurs certain sampling errors. One way to alleviate this problem is to introduce certain symmetry to the ensembles, which can reduce the sampling errors and spurious modes in evaluation of the means and covariances of the ensembles [7]. In this contribution, we present two methods to produce symmetric ensembles. One is based on the unscented transform [8, 9], which leads to the unscented Kalman filter (UKF) [8, 9] and its variant, the ensemble unscented Kalman filter (EnUKF) [7]. The other is based on Stirling’s interpolation formula (SIF), which results in the divided difference filter (DDF) [10]. Here we propose a simplified divided difference filter (sDDF) in the context of ensemble filtering. The similarity and difference between the sDDF and the EnUKF will be discussed. Numerical experiments will also be conducted to investigate the performance of the sDDF and the EnUKF, and compare them to a well‐established EnSRF, the ensemble transform Kalman filter (ETKF) [2].
Ensemble Kalman filter with the unscented transform
Luo, X.; Moroz, I. M.
2009-03-01
A modification scheme to the ensemble Kalman filter (EnKF) is introduced based on the concept of the unscented transform [S. Julier, J. Uhlmann, H. Durrant-Whyte, A new method for the nonlinear transformation of means and covariances in filters and estimators, IEEE Trans. Automat. Control. 45 (2000) 477-482; S.J. Julier, J.K. Uhlmann, Unscented filtering and nonlinear estimation, Proc. IEEE 92 (2004) 401-422], which therefore will be called the ensemble unscented Kalman filter (EnUKF) in this work. When the error distribution of the analysis is symmetric (not necessarily Gaussian), it can be shown that, compared with the ordinary EnKF, the EnUKF has more accurate estimations of the ensemble mean and covariance of the background by examining the multidimensional Taylor series expansion term by term. This implies that, the EnUKF may have better performance in state estimation than the ordinary EnKF in the sense that the deviations from the true states are smaller. For verification, some numerical experiments are conducted on a 40-dimensional system due to Lorenz and Emanuel [E.N. Lorenz, K.A. Emanuel, Optimal sites for supplementary weather observations: Simulation with a small model, J. Atmos. Sci. 55 (1998) 399-414]. Simulation results support our argument.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Particle Kalman Filtering: A Nonlinear Framework for Ensemble Kalman Filters
Hoteit, Ibrahim
2010-09-19
Optimal nonlinear filtering consists of sequentially determining the conditional probability distribution functions (pdf) of the system state, given the information of the dynamical and measurement processes and the previous measurements. Once the pdfs are obtained, one can determine different estimates, for instance, the minimum variance estimate, or the maximum a posteriori estimate, of the system state. It can be shown that, many filters, including the Kalman filter (KF) and the particle filter (PF), can be derived based on this sequential Bayesian estimation framework. In this contribution, we present a Gaussian mixture‐based framework, called the particle Kalman filter (PKF), and discuss how the different EnKF methods can be derived as simplified variants of the PKF. We also discuss approaches to reducing the computational burden of the PKF in order to make it suitable for complex geosciences applications. We use the strongly nonlinear Lorenz‐96 model to illustrate the performance of the PKF.
An iterative ensemble Kalman filter for reservoir engineering applications
Krymskaya, M.V.; Hanea, R.G.; Verlaan, M.
2009-01-01
The study has been focused on examining the usage and the applicability of ensemble Kalman filtering techniques to the history matching procedures. The ensemble Kalman filter (EnKF) is often applied nowadays to solving such a problem. Meanwhile, traditional EnKF requires assumption of the
Observation bias correction with an ensemble Kalman filter
Fertig, Elana J.; Baek, Seung-Jong; Hunt, Brian R.; Ott, Edward; Szunyogh, Istvan; Aravéquia, José A.; Kalnay, Eugenia; Li, Hong; Liu, Junjie
2009-01-01
This paper considers the use of an ensemble Kalman filter to correct satellite radiance observations for state dependent biases. Our approach is to use state-space augmentation to estimate satellite biases as part of the ensemble data assimilation procedure. We illustrate our approach by applying it to a particular ensemble scheme—the local ensemble transform Kalman filter (LETKF)—to assimilate simulated biased atmospheric infrared sounder brightness temperature observations from 15 channels ...
Reservoir History Matching Using Ensemble Kalman Filters with Anamorphosis Transforms
Aman, Beshir M.
2012-12-01
This work aims to enhance the Ensemble Kalman Filter performance by transforming the non-Gaussian state variables into Gaussian variables to be a step closer to optimality. This is done by using univariate and multivariate Box-Cox transformation. Some History matching methods such as Kalman filter, particle filter and the ensemble Kalman filter are reviewed and applied to a test case in the reservoir application. The key idea is to apply the transformation before the update step and then transform back after applying the Kalman correction. In general, the results of the multivariate method was promising, despite the fact it over-estimated some variables.
Multivariate localization methods for ensemble Kalman filtering
Roh, S.
2015-12-03
In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performance of EnKF, is the localization of the estimates of the covariances. One family of localization techniques is based on taking the Schur (element-wise) product of the ensemble-based sample covariance matrix and a correlation matrix whose entries are obtained by the discretization of a distance-dependent correlation function. While the proper definition of the localization function for a single state variable has been extensively investigated, a rigorous definition of the localization function for multiple state variables that exist at the same locations has been seldom considered. This paper introduces two strategies for the construction of localization functions for multiple state variables. The proposed localization functions are tested by assimilating simulated observations experiments into the bivariate Lorenz 95 model with their help.
Multivariate localization methods for ensemble Kalman filtering
Roh, S.
2015-05-08
In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performance of EnKF, is the localization of the estimates of the covariances. One family of localization techniques is based on taking the Schur (entry-wise) product of the ensemble-based sample covariance matrix and a correlation matrix whose entries are obtained by the discretization of a distance-dependent correlation function. While the proper definition of the localization function for a single state variable has been extensively investigated, a rigorous definition of the localization function for multiple state variables has been seldom considered. This paper introduces two strategies for the construction of localization functions for multiple state variables. The proposed localization functions are tested by assimilating simulated observations experiments into the bivariate Lorenz 95 model with their help.
Ensemble Kalman filtering with residual nudging
Luo, X.
2012-10-03
Covariance inflation and localisation are two important techniques that are used to improve the performance of the ensemble Kalman filter (EnKF) by (in effect) adjusting the sample covariances of the estimates in the state space. In this work, an additional auxiliary technique, called residual nudging, is proposed to monitor and, if necessary, adjust the residual norms of state estimates in the observation space. In an EnKF with residual nudging, if the residual norm of an analysis is larger than a pre-specified value, then the analysis is replaced by a new one whose residual norm is no larger than a pre-specified value. Otherwise, the analysis is considered as a reasonable estimate and no change is made. A rule for choosing the pre-specified value is suggested. Based on this rule, the corresponding new state estimates are explicitly derived in case of linear observations. Numerical experiments in the 40-dimensional Lorenz 96 model show that introducing residual nudging to an EnKF may improve its accuracy and/or enhance its stability against filter divergence, especially in the small ensemble scenario.
Ensemble Kalman filtering with residual nudging
Directory of Open Access Journals (Sweden)
Xiaodong Luo
2012-10-01
Full Text Available Covariance inflation and localisation are two important techniques that are used to improve the performance of the ensemble Kalman filter (EnKF by (in effect adjusting the sample covariances of the estimates in the state space. In this work, an additional auxiliary technique, called residual nudging, is proposed to monitor and, if necessary, adjust the residual norms of state estimates in the observation space. In an EnKF with residual nudging, if the residual norm of an analysis is larger than a pre-specified value, then the analysis is replaced by a new one whose residual norm is no larger than a pre-specified value. Otherwise, the analysis is considered as a reasonable estimate and no change is made. A rule for choosing the pre-specified value is suggested. Based on this rule, the corresponding new state estimates are explicitly derived in case of linear observations. Numerical experiments in the 40-dimensional Lorenz 96 model show that introducing residual nudging to an EnKF may improve its accuracy and/or enhance its stability against filter divergence, especially in the small ensemble scenario.
Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters*
Hoteit, Ibrahim
2012-02-01
This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture. The authors show that this filter is an algorithm in between the Kalman filter and the particle filter, and therefore is referred to as the particle Kalman filter (PKF). In the PKF, the solution of a nonlinear filtering problem is expressed as the weighted average of an “ensemble of Kalman filters” operating in parallel. Running an ensemble of Kalman filters is, however, computationally prohibitive for realistic atmospheric and oceanic data assimilation problems. For this reason, the authors consider the construction of the PKF through an “ensemble” of ensemble Kalman filters (EnKFs) instead, and call the implementation the particle EnKF (PEnKF). It is shown that different types of the EnKFs can be considered as special cases of the PEnKF. Similar to the situation in the particle filter, the authors also introduce a resampling step to the PEnKF in order to reduce the risk of weights collapse and improve the performance of the filter. Numerical experiments with the strongly nonlinear Lorenz-96 model are presented and discussed.
Bridging the ensemble Kalman filter and particle filters
Energy Technology Data Exchange (ETDEWEB)
Stordal, Andreas Stoerksen; Karlsen, Hans A.; Naevdal, Geir; Skaug, Hans J.; Valles, Brice
2009-12-15
The nonlinear filtering problem occurs in many scientific areas. Sequential Monte Carlo solutions with the correct asymptotic behavior such as particle filters exist but they are computationally too expensive when working with high-dimensional systems. The ensemble Kalman filter is a more robust method that has shown promising results with a small sample size but the samples are not guaranteed to come from the true posterior distribution. By approximating the model error with Gaussian kernels we get the advantage of both a Kalman correction and a weighting step. The resulting Gaussian mixture filter has the advantage of both a local Kalman type correction and the weighting/re sampling step of a particle filter. The Gaussian mixture approximation relies on a tunable bandwidth parameter which often has to be kept quite large in order to avoid weight collapse in high dimensions. As a result, the Kalman correction is too large to capture highly non-Gaussian posterior distributions. In this paper we have extended the Gaussian mixture filter (Hoteit et al., 2008b) and also made the connection to particle filters more transparent. In particular we introduce a tuning parameter for the importance weights. In the last part of the paper we have performed a simulation experiment with the Lorenz40 model where our method has been compared to the EnKF and a full implementation of a particle filter. The results clearly indicate that the new method has advantages compared to the standard EnKF. (Author)
A Comparison of Ensemble Kalman Filters for Storm Surge Assimilation
Altaf, Muhammad
2014-08-01
This study evaluates and compares the performances of several variants of the popular ensembleKalman filter for the assimilation of storm surge data with the advanced circulation (ADCIRC) model. Using meteorological data from Hurricane Ike to force the ADCIRC model on a domain including the Gulf ofMexico coastline, the authors implement and compare the standard stochastic ensembleKalman filter (EnKF) and three deterministic square root EnKFs: the singular evolutive interpolated Kalman (SEIK) filter, the ensemble transform Kalman filter (ETKF), and the ensemble adjustment Kalman filter (EAKF). Covariance inflation and localization are implemented in all of these filters. The results from twin experiments suggest that the square root ensemble filters could lead to very comparable performances with appropriate tuning of inflation and localization, suggesting that practical implementation details are at least as important as the choice of the square root ensemble filter itself. These filters also perform reasonably well with a relatively small ensemble size, whereas the stochastic EnKF requires larger ensemble sizes to provide similar accuracy for forecasts of storm surge.
A review of issues in ensemble-based Kalman filtering
Energy Technology Data Exchange (ETDEWEB)
Ehrendorfer, M. [Dept. of Meteorology and Geophysics, The Univ. of Reading (United Kingdom)
2007-12-15
Ensemble-based data assimilation methods related to the fundamental theory of Kalman filtering have been explored in a variety of mostly non-operational data assimilation contexts over the past decade with increasing intensity. While promising properties have been reported, a number of issues that arise in the development and application of ensemble-based data assimilation techniques, such as in the basic form of the ensemble Kalman filter (EnKF), still deserve particular attention. The necessity of employing an ensemble of small size represents a fundamental issue which in turn leads to several related points that must be carefully considered. In particular, the need to correct for sampling noise in the covariance structure estimated from the finite ensemble must be mentioned. Covariance inflation, localization through a Schur/Hadamard product, preventing the occurrence of filter divergence and inbreeding, as well as the loss of dynamical balances, are all issues directly related to the use of small ensemble sizes. Attempts to reduce effectively the sampling error due to small ensembles and at the same time maintaining an ensemble spread that realistically describes error structures have given rise to the development of variants of the basic form of the EnKF. These include, for example, the Ensemble Adjustment Kalman Filter (EAKF), the Ensemble Transform Kalman Filter (ETKF), the Ensemble Square-Root Filter (EnSRF), and the Local Ensemble Kalman Filter (LEKF). Further important considerations within ensemble-based Kalman filtering concern issues such as the treatment of model error, stochastic versus deterministic updating algorithms, the case of implementation and computational cost, serial processing of observations, avoiding the appearance of undesired dynamic imbalances, and the treatment of non-Gaussianity and nonlinearity. The discussion of the above issues within ensemble-based Kalman filtering forms the central topic of this article, that starts out with a
Reduced Kalman Filters for Clock Ensembles
Greenhall, Charles A.
2011-01-01
This paper summarizes the author's work ontimescales based on Kalman filters that act upon the clock comparisons. The natural Kalman timescale algorithm tends to optimize long-term timescale stability at the expense of short-term stability. By subjecting each post-measurement error covariance matrix to a non-transparent reduction operation, one obtains corrected clocks with improved short-term stability and little sacrifice of long-term stability.
A modified iterative ensemble Kalman filter data assimilation method
Xu, Baoxiong; Bai, Yulong; Wang, Yizhao; Li, Zhe; Ma, Boyang
2017-08-01
High nonlinearity is a typical characteristic associated with data assimilation systems. Additionally, iterative ensemble based methods have attracted a large amount of research attention, which has been focused on dealing with nonlinearity problems. To solve the local convergence problem of the iterative ensemble Kalman filter, a modified iterative ensemble Kalman filter algorithm was put forward, which was based on a global convergence strategy from the perspective of a Gauss-Newton iteration. Through self-adaption, the step factor was adjusted to enable every iteration to approach expected values during the process of the data assimilation. A sensitivity experiment was carried out in a low dimensional Lorenz-63 chaotic system, as well as a Lorenz-96 model. The new method was tested via ensemble size, observation variance, and inflation factor changes, along with other aspects. Meanwhile, comparative research was conducted with both a traditional ensemble Kalman filter and an iterative ensemble Kalman filter. The results showed that the modified iterative ensemble Kalman filter algorithm was a data assimilation method that was able to effectively estimate a strongly nonlinear system state.
Ensemble Kalman filtering without the intrinsic need for inflation
Directory of Open Access Journals (Sweden)
M. Bocquet
2011-10-01
Full Text Available The main intrinsic source of error in the ensemble Kalman filter (EnKF is sampling error. External sources of error, such as model error or deviations from Gaussianity, depend on the dynamical properties of the model. Sampling errors can lead to instability of the filter which, as a consequence, often requires inflation and localization. The goal of this article is to derive an ensemble Kalman filter which is less sensitive to sampling errors. A prior probability density function conditional on the forecast ensemble is derived using Bayesian principles. Even though this prior is built upon the assumption that the ensemble is Gaussian-distributed, it is different from the Gaussian probability density function defined by the empirical mean and the empirical error covariance matrix of the ensemble, which is implicitly used in traditional EnKFs. This new prior generates a new class of ensemble Kalman filters, called finite-size ensemble Kalman filter (EnKF-N. One deterministic variant, the finite-size ensemble transform Kalman filter (ETKF-N, is derived. It is tested on the Lorenz '63 and Lorenz '95 models. In this context, ETKF-N is shown to be stable without inflation for ensemble size greater than the model unstable subspace dimension, at the same numerical cost as the ensemble transform Kalman filter (ETKF. One variant of ETKF-N seems to systematically outperform the ETKF with optimally tuned inflation. However it is shown that ETKF-N does not account for all sampling errors, and necessitates localization like any EnKF, whenever the ensemble size is too small. In order to explore the need for inflation in this small ensemble size regime, a local version of the new class of filters is defined (LETKF-N and tested on the Lorenz '95 toy model. Whatever the size of the ensemble, the filter is stable. Its performance without inflation is slightly inferior to that of LETKF with optimally tuned inflation for small interval between updates, and
Robust Ensemble Filtering and Its Relation to Covariance Inflation in the Ensemble Kalman Filter
Luo, Xiaodong
2011-12-01
A robust ensemble filtering scheme based on the H∞ filtering theory is proposed. The optimal H∞ filter is derived by minimizing the supremum (or maximum) of a predefined cost function, a criterion different from the minimum variance used in the Kalman filter. By design, the H∞ filter is more robust than the Kalman filter, in the sense that the estimation error in the H∞ filter in general has a finite growth rate with respect to the uncertainties in assimilation, except for a special case that corresponds to the Kalman filter. The original form of the H∞ filter contains global constraints in time, which may be inconvenient for sequential data assimilation problems. Therefore a variant is introduced that solves some time-local constraints instead, and hence it is called the time-local H∞ filter (TLHF). By analogy to the ensemble Kalman filter (EnKF), the concept of ensemble time-local H∞ filter (EnTLHF) is also proposed. The general form of the EnTLHF is outlined, and some of its special cases are discussed. In particular, it is shown that an EnKF with certain covariance inflation is essentially an EnTLHF. In this sense, the EnTLHF provides a general framework for conducting covariance inflation in the EnKF-based methods. Some numerical examples are used to assess the relative robustness of the TLHF–EnTLHF in comparison with the corresponding KF–EnKF method.
Data assimilation in integrated hydrological modeling using ensemble Kalman filtering
DEFF Research Database (Denmark)
Rasmussen, Jørn; Madsen, H.; Jensen, Karsten Høgh
2015-01-01
Groundwater head and stream discharge is assimilated using the ensemble transform Kalman filter in an integrated hydrological model with the aim of studying the relationship between the filter performance and the ensemble size. In an attempt to reduce the required number of ensemble members...... numbers and spatial distributions of groundwater head observations and with or without discharge assimilation and parameter estimation. The study shows that (1) more ensemble members are needed when fewer groundwater head observations are assimilated, and (2) assimilating discharge observations...... and estimating parameters requires a much larger ensemble size than just assimilating groundwater head observations. However, the required ensemble size can be greatly reduced with the use of adaptive localization, which by far outperforms distance-based localization. The study is conducted using synthetic data...
Data assimilation the ensemble Kalman filter
Evensen, Geir
2007-01-01
Data Assimilation comprehensively covers data assimilation and inverse methods, including both traditional state estimation and parameter estimation. This text and reference focuses on various popular data assimilation methods, such as weak and strong constraint variational methods and ensemble filters and smoothers. It is demonstrated how the different methods can be derived from a common theoretical basis, as well as how they differ and/or are related to each other, and which properties characterize them, using several examples. Rather than emphasize a particular discipline such as oceanography or meteorology, it presents the mathematical framework and derivations in a way which is common for any discipline where dynamics is merged with measurements. The mathematics level is modest, although it requires knowledge of basic spatial statistics, Bayesian statistics, and calculus of variations. Readers will also appreciate the introduction to the mathematical methods used and detailed derivations, which should b...
Weighted ensemble transform Kalman filter for image assimilation
Directory of Open Access Journals (Sweden)
Sebastien Beyou
2013-01-01
Full Text Available This study proposes an extension of the Weighted Ensemble Kalman filter (WEnKF proposed by Papadakis et al. (2010 for the assimilation of image observations. The main focus of this study is on a novel formulation of the Weighted filter with the Ensemble Transform Kalman filter (WETKF, incorporating directly as a measurement model a non-linear image reconstruction criterion. This technique has been compared to the original WEnKF on numerical and real world data of 2-D turbulence observed through the transport of a passive scalar. In particular, it has been applied for the reconstruction of oceanic surface current vorticity fields from sea surface temperature (SST satellite data. This latter technique enables a consistent recovery along time of oceanic surface currents and vorticity maps in presence of large missing data areas and strong noise.
Observation Quality Control with a Robust Ensemble Kalman Filter
Roh, Soojin
2013-12-01
Current ensemble-based Kalman filter (EnKF) algorithms are not robust to gross observation errors caused by technical or human errors during the data collection process. In this paper, the authors consider two types of gross observational errors, additive statistical outliers and innovation outliers, and introduce a method to make EnKF robust to gross observation errors. Using both a one-dimensional linear system of dynamics and a 40-variable Lorenz model, the performance of the proposed robust ensemble Kalman filter (REnKF) was tested and it was found that the new approach greatly improves the performance of the filter in the presence of gross observation errors and leads to only a modest loss of accuracy with clean, outlier-free, observations.
Ensemble Kalman filtering with one-step-ahead smoothing
Raboudi, Naila F.
2018-01-11
The ensemble Kalman filter (EnKF) is widely used for sequential data assimilation. It operates as a succession of forecast and analysis steps. In realistic large-scale applications, EnKFs are implemented with small ensembles and poorly known model error statistics. This limits their representativeness of the background error covariances and, thus, their performance. This work explores the efficiency of the one-step-ahead (OSA) smoothing formulation of the Bayesian filtering problem to enhance the data assimilation performance of EnKFs. Filtering with OSA smoothing introduces an updated step with future observations, conditioning the ensemble sampling with more information. This should provide an improved background ensemble in the analysis step, which may help to mitigate the suboptimal character of EnKF-based methods. Here, the authors demonstrate the efficiency of a stochastic EnKF with OSA smoothing for state estimation. They then introduce a deterministic-like EnKF-OSA based on the singular evolutive interpolated ensemble Kalman (SEIK) filter. The authors show that the proposed SEIK-OSA outperforms both SEIK, as it efficiently exploits the data twice, and the stochastic EnKF-OSA, as it avoids observational error undersampling. They present extensive assimilation results from numerical experiments conducted with the Lorenz-96 model to demonstrate SEIK-OSA’s capabilities.
Adaptive ensemble Kalman filtering of non-linear systems
Directory of Open Access Journals (Sweden)
Tyrus Berry
2013-07-01
Full Text Available A necessary ingredient of an ensemble Kalman filter (EnKF is covariance inflation, used to control filter divergence and compensate for model error. There is an on-going search for inflation tunings that can be learned adaptively. Early in the development of Kalman filtering, Mehra (1970, 1972 enabled adaptivity in the context of linear dynamics with white noise model errors by showing how to estimate the model error and observation covariances. We propose an adaptive scheme, based on lifting Mehra's idea to the non-linear case, that recovers the model error and observation noise covariances in simple cases, and in more complicated cases, results in a natural additive inflation that improves state estimation. It can be incorporated into non-linear filters such as the extended Kalman filter (EKF, the EnKF and their localised versions. We test the adaptive EnKF on a 40-dimensional Lorenz96 model and show the significant improvements in state estimation that are possible. We also discuss the extent to which such an adaptive filter can compensate for model error, and demonstrate the use of localisation to reduce ensemble sizes for large problems.
Local Ensemble Kalman Particle Filters for efficient data assimilation
Robert, Sylvain
2016-01-01
Ensemble methods such as the Ensemble Kalman Filter (EnKF) are widely used for data assimilation in large-scale geophysical applications, as for example in numerical weather prediction (NWP). There is a growing interest for physical models with higher and higher resolution, which brings new challenges for data assimilation techniques because of the presence of non-linear and non-Gaussian features that are not adequately treated by the EnKF. We propose two new localized algorithms based on the Ensemble Kalman Particle Filter (EnKPF), a hybrid method combining the EnKF and the Particle Filter (PF) in a way that maintains scalability and sample diversity. Localization is a key element of the success of EnKFs in practice, but it is much more challenging to apply to PFs. The algorithms that we introduce in the present paper provide a compromise between the EnKF and the PF while avoiding some of the problems of localization for pure PFs. Numerical experiments with a simplified model of cumulus convection based on a...
Mean-field Ensemble Kalman Filter
Law, Kody
2015-01-07
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d < 2 . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Estimation of Human Heart Activity Using Ensemble Kalman Filter
Directory of Open Access Journals (Sweden)
Pradhnya Arun Priyadarshi
2017-02-01
Full Text Available Heart beat measurement techniques come across various challenges. Electrocardiogram (ECG obtained sometimes does not reveal complete information about electrochemical activity of human heart, because of which functioning of heart cannot be studied properly. In this paper Ensemble Kalman Filter (EnKF is used to generate ECG signal efficiently with better accuracy such that the drawbacks of current techniques are eliminated. Here EnKF is applied to second order mathematical model of human heart, input applied to this mathematical model is a pacemaker signal. The initial values of heart muscle movements and electrochemical activity as a discrete data set are used and prediction steps are commenced. EnKF uses ensemble integration technique to model error statistics which helps obtaining more precise output. The results are obtained with negligible sum squared error, therefore the ECG obtained using EnKF can diagnose the disease related to heart with better accuracy.
Ensemble Kalman filter data assimilation for the MPAS system
Ha, Soyoung; Snyder, Chris
2015-04-01
The Model for Prediction Across Scales (MPAS; http://mpas-dev.github.io/) is a global non-hydrostatic numerical atmospheric model based on unstructured centroidal Voronoi meshes that allow both uniform and variable resolutions. The variable resolution allows locally high-resolution meshes that transition smoothly to coarser resolution over the rest of the globe, avoiding the need to drive a limited-area model with lateral boundary conditions from a separate global model. The nonhydrostatic MPAS solver (for both atmospheric and oceanic components) is now coupled to the Data Assimilation Research Testbed (DART; http://www.image.ucar.edu/ DAReS/DART) system with a full capability of ensemble Kalman filter data assimilation. The analysis/forecast cycling experiments using MPAS/DART is successfully tested with real observations for different retrospective cases. Assimilated observations are all conventional data as well as satellite winds and GPS radio occultation refractivity data. Testing on different grid mesh, we examine issues specific to the MPAS grid, such as smoothing in the interpolation and the update of horizontal wind fields, and show their impact on the Ensemble Kalman Filter (EnKF) analysis and the following short-range forecast. Up to 5-day forecasts for a month-long cycle period are verified against observations and compared to the NCEP GFS (Global Forecast System) forecasts.
The Ensemble Kalman filter: a signal processing perspective
Roth, Michael; Hendeby, Gustaf; Fritsche, Carsten; Gustafsson, Fredrik
2017-12-01
The ensemble Kalman filter (EnKF) is a Monte Carlo-based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear, and non-Gaussian state estimation problems. Its ability to handle state dimensions in the order of millions has made the EnKF a popular algorithm in different geoscientific disciplines. Despite a similarly vital need for scalable algorithms in signal processing, e.g., to make sense of the ever increasing amount of sensor data, the EnKF is hardly discussed in our field. This self-contained review is aimed at signal processing researchers and provides all the knowledge to get started with the EnKF. The algorithm is derived in a KF framework, without the often encountered geoscientific terminology. Algorithmic challenges and required extensions of the EnKF are provided, as well as relations to sigma point KF and particle filters. The relevant EnKF literature is summarized in an extensive survey and unique simulation examples, including popular benchmark problems, complement the theory with practical insights. The signal processing perspective highlights new directions of research and facilitates the exchange of potentially beneficial ideas, both for the EnKF and high-dimensional nonlinear and non-Gaussian filtering in general.
Quantifying Monte Carlo uncertainty in ensemble Kalman filter
Energy Technology Data Exchange (ETDEWEB)
Thulin, Kristian; Naevdal, Geir; Skaug, Hans Julius; Aanonsen, Sigurd Ivar
2009-01-15
This report is presenting results obtained during Kristian Thulin PhD study, and is a slightly modified form of a paper submitted to SPE Journal. Kristian Thulin did most of his portion of the work while being a PhD student at CIPR, University of Bergen. The ensemble Kalman filter (EnKF) is currently considered one of the most promising methods for conditioning reservoir simulation models to production data. The EnKF is a sequential Monte Carlo method based on a low rank approximation of the system covariance matrix. The posterior probability distribution of model variables may be estimated fram the updated ensemble, but because of the low rank covariance approximation, the updated ensemble members become correlated samples from the posterior distribution. We suggest using multiple EnKF runs, each with smaller ensemble size to obtain truly independent samples from the posterior distribution. This allows a point-wise confidence interval for the posterior cumulative distribution function (CDF) to be constructed. We present a methodology for finding an optimal combination of ensemble batch size (n) and number of EnKF runs (m) while keeping the total number of ensemble members ( m x n) constant. The optimal combination of n and m is found through minimizing the integrated mean square error (MSE) for the CDFs and we choose to define an EnKF run with 10.000 ensemble members as having zero Monte Carlo error. The methodology is tested on a simplistic, synthetic 2D model, but should be applicable also to larger, more realistic models. (author). 12 refs., figs.,tabs
Parameter Estimation for Observation Bias with an Ensemble Kalman Filter
Lorente-Plazas, R.; Hacker, J.
2015-12-01
In this work we evaluate a method to estimate systematic errors of individual in-situ observations. The approach is based on parameter estimation using an augmented state in an ensemble adjustment Kalman filter. Biased observations are assimilated in the highly chaotic Lorenz (2005) model that combines small and large scales. For this purpose, synthetic observations are created by introducing a grid-point dependent bias and random errors to a nature run (truth). The sensitivity of the methodology to model error, the number of ensemble members, the number of parameters, and the parameter variance is evaluated. Results demonstrate that the methodology is able to estimate observation bias for a both a perfect model and an imperfect model if the model error is estimated. The parameter estimation and the rms errors are significantly deteriorated if model error is ignored. Errors are qualitatively independent of model forcing when model error is estimated. By contrast, parameter estimation depends on model error when model error is not estimated, especially if observation biases are estimated. Errors increase with the number of estimated parameters, but they are independent of ensemble size as long as the number of ensembles members is large enough. There is an optimum value of parameter variance that minimizes the errors and improves the parameter estimation, but this value depends on observation bias and model error. Overall, the results suggest more accuracy in observation bias estimates than model error estimates.
The PV Corrosion Fault Prognosis Based on Ensemble Kalman Filter
Directory of Open Access Journals (Sweden)
Radouane Ouladsine
2017-01-01
Full Text Available The degradation of photovoltaic (PV modules remains a major concern on the control and the development of the photovoltaic field, particularly, in regions with difficult climatic conditions. The main degradation modes of the PV modules are corrosion, discoloration, glass breaks, and cracks of cells. However, corrosion and discoloration remain the predominant degradation modes that still require further investigations. In this paper, a model-based PV corrosion prognostic approach, based on an ensemble Kalman filter (EnKF, is introduced to identify the PV corrosion parameters and then estimate the remaining useful life (RUL. Simulations have been conducted using measured data set, and results are reported to show the efficiency of the proposed approach.
Directory of Open Access Journals (Sweden)
Tong-chao Nan
2017-01-01
Full Text Available Though the ensemble Kalman filter (EnKF has been successfully applied in many areas, it requires explicit and accurate model and measurement error information, leading to difficulties in practice when only limited information on error mechanisms of observational instruments for subsurface systems is accessible. To handle the uncertain errors, we applied a robust data assimilation algorithm, the ensemble H-infinity filter (EnHF, to estimation of aquifer hydraulic heads and conductivities in a flow model with uncertain/correlated observational errors. The impacts of spatial and temporal correlations in measurements were analyzed, and the performance of EnHF was compared with that of the EnKF. The results show that both EnHF and EnKF are able to estimate hydraulic conductivities properly when observations are free of error; EnHF can provide robust estimates of hydraulic conductivities even when no observational error information is provided. In contrast, the estimates of EnKF seem noticeably undermined because of correlated errors and inaccurate error statistics, and filter divergence was observed. It is concluded that EnHF is an efficient assimilation algorithm when observational errors are unknown or error statistics are inaccurate.
IASI Radiance Data Assimilation in Local Ensemble Transform Kalman Filter
Cho, K.; Hyoung-Wook, C.; Jo, Y.
2016-12-01
Korea institute of Atmospheric Prediction Systems (KIAPS) is developing NWP model with data assimilation systems. Local Ensemble Transform Kalman Filter (LETKF) system, one of the data assimilation systems, has been developed for KIAPS Integrated Model (KIM) based on cubed-sphere grid and has successfully assimilated real data. LETKF data assimilation system has been extended to 4D- LETKF which considers time-evolving error covariance within assimilation window and IASI radiance data assimilation using KPOP (KIAPS package for observation processing) with RTTOV (Radiative Transfer for TOVS). The LETKF system is implementing semi operational prediction including conventional (sonde, aircraft) observation and AMSU-A (Advanced Microwave Sounding Unit-A) radiance data from April. Recently, the semi operational prediction system updated radiance observations including GPS-RO, AMV, IASI (Infrared Atmospheric Sounding Interferometer) data at July. A set of simulation of KIM with ne30np4 and 50 vertical levels (of top 0.3hPa) were carried out for short range forecast (10days) within semi operation prediction LETKF system with ensemble forecast 50 members. In order to only IASI impact, our experiments used only conventional and IAIS radiance data to same semi operational prediction set. We carried out sensitivity test for IAIS thinning method (3D and 4D). IASI observation number was increased by temporal (4D) thinning and the improvement of IASI radiance data impact on the forecast skill of model will expect.
An Adjoint-Based Adaptive Ensemble Kalman Filter
Song, Hajoon
2013-10-01
A new hybrid ensemble Kalman filter/four-dimensional variational data assimilation (EnKF/4D-VAR) approach is introduced to mitigate background covariance limitations in the EnKF. The work is based on the adaptive EnKF (AEnKF) method, which bears a strong resemblance to the hybrid EnKF/three-dimensional variational data assimilation (3D-VAR) method. In the AEnKF, the representativeness of the EnKF ensemble is regularly enhanced with new members generated after back projection of the EnKF analysis residuals to state space using a 3D-VAR [or optimal interpolation (OI)] scheme with a preselected background covariance matrix. The idea here is to reformulate the transformation of the residuals as a 4D-VAR problem, constraining the new member with model dynamics and the previous observations. This should provide more information for the estimation of the new member and reduce dependence of the AEnKF on the assumed stationary background covariance matrix. This is done by integrating the analysis residuals backward in time with the adjoint model. Numerical experiments are performed with the Lorenz-96 model under different scenarios to test the new approach and to evaluate its performance with respect to the EnKF and the hybrid EnKF/3D-VAR. The new method leads to the least root-mean-square estimation errors as long as the linear assumption guaranteeing the stability of the adjoint model holds. It is also found to be less sensitive to choices of the assimilation system inputs and parameters.
ASSIMILATION OF COARSE-SCALEDATAUSINGTHE ENSEMBLE KALMAN FILTER
Efendiev, Yalchin
2011-01-01
Reservoir data is usually scale dependent and exhibits multiscale features. In this paper we use the ensemble Kalman filter (EnKF) to integrate data at different spatial scales for estimating reservoir fine-scale characteristics. Relationships between the various scales is modeled via upscaling techniques. We propose two versions of the EnKF to assimilate the multiscale data, (i) where all the data are assimilated together and (ii) the data are assimilated sequentially in batches. Ensemble members obtained after assimilating one set of data are used as a prior to assimilate the next set of data. Both of these versions are easily implementable with any other upscaling which links the fine to the coarse scales. The numerical results with different methods are presented in a twin experiment setup using a two-dimensional, two-phase (oil and water) flow model. Results are shown with coarse-scale permeability and coarse-scale saturation data. They indicate that additional data provides better fine-scale estimates and fractional flow predictions. We observed that the two versions of the EnKF differed in their estimates when coarse-scale permeability is provided, whereas their results are similar when coarse-scale saturation is used. This behavior is thought to be due to the nonlinearity of the upscaling operator in the case of the former data. We also tested our procedures with various precisions of the coarse-scale data to account for the inexact relationship between the fine and coarse scale data. As expected, the results show that higher precision in the coarse-scale data yielded improved estimates. With better coarse-scale modeling and inversion techniques as more data at multiple coarse scales is made available, the proposed modification to the EnKF could be relevant in future studies.
Optimal initial perturbations for El Nino ensemble prediction with ensemble Kalman filter
Energy Technology Data Exchange (ETDEWEB)
Ham, Yoo-Geun; Kang, In-Sik [Seoul National University, School of Earth and Environment Sciences, Seoul (Korea); Kug, Jong-Seong [Korea Ocean Research and Development Institute, Ansan (Korea)
2009-12-15
A method for selecting optimal initial perturbations is developed within the framework of an ensemble Kalman filter (EnKF). Among the initial conditions generated by EnKF, ensemble members with fast growing perturbations are selected to optimize the ENSO seasonal forecast skills. Seasonal forecast experiments show that the forecast skills with the selected ensemble members are significantly improved compared with other ensemble members for up to 1-year lead forecasts. In addition, it is found that there is a strong relationship between the forecast skill improvements and flow-dependent instability. That is, correlation skills are significantly improved over the region where the predictable signal is relatively small (i.e. an inverse relationship). It is also shown that forecast skills are significantly improved during ENSO onset and decay phases, which are the most unpredictable periods among the ENSO events. (orig.)
Directory of Open Access Journals (Sweden)
E. Crestani
2013-04-01
Full Text Available Estimating the spatial variability of hydraulic conductivity K in natural aquifers is important for predicting the transport of dissolved compounds. Especially in the nonreactive case, the plume evolution is mainly controlled by the heterogeneity of K. At the local scale, the spatial distribution of K can be inferred by combining the Lagrangian formulation of the transport with a Kalman-filter-based technique and assimilating a sequence of time-lapse concentration C measurements, which, for example, can be evaluated on site through the application of a geophysical method. The objective of this work is to compare the ensemble Kalman filter (EnKF and the ensemble smoother (ES capabilities to retrieve the hydraulic conductivity spatial distribution in a groundwater flow and transport modeling framework. The application refers to a two-dimensional synthetic aquifer in which a tracer test is simulated. Moreover, since Kalman-filter-based methods are optimal only if each of the involved variables fit to a Gaussian probability density function (pdf and since this condition may not be met by some of the flow and transport state variables, issues related to the non-Gaussianity of the variables are analyzed and different transformation of the pdfs are considered in order to evaluate their influence on the performance of the methods. The results show that the EnKF reproduces with good accuracy the hydraulic conductivity field, outperforming the ES regardless of the pdf of the concentrations.
Reservoir structural model updating using the Ensemble Kalman Filter
Energy Technology Data Exchange (ETDEWEB)
Seiler, Alexandra
2010-09-15
In reservoir characterization, a large emphasis is placed on risk management and uncertainty assessment, and the dangers of basing decisions on a single base-case reservoir model are widely recognized. In the last years, statistical methods for assisted history matching have gained popularity for providing integrated models with quantified uncertainty, conditioned on all available data. Structural modeling is the first step in a reservoir modeling work flow and consists in defining the geometrical framework of the reservoir, based on the information from seismic surveys and well data. Large uncertainties are typically associated with the processing and interpretation of seismic data. However, the structural model is often fixed to a single interpretation in history-matching work flows due to the complexity of updating the structural model and related reservoir grid. This thesis present a method that allows to account for the uncertainties in the structural model and continuously update the model and related uncertainties by assimilation of production data using the Ensemble Kalman Filter (EnKF). We consider uncertainties in the depth of the reservoir horizons and in the fault geometry, and assimilate production data, such as oil production rate, gas-oil ratio and water-cut. In the EnKF model-updating work flow, an ensemble of reservoir models, expressing explicitly the model uncertainty, is created. We present a parameterization that allows to generate different realizations of the structural model to account for the uncertainties in faults and horizons and that maintains the consistency throughout the reservoir characterization project, from the structural model to the prediction of production profiles. The uncertainty in the depth of the horizons is parameterized as simulated depth surfaces, the fault position as a displacement vector and the fault throw as a throw-scaling factor. In the EnKF, the model parameters and state variables are updated sequentially in
Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms
Janjic, Tijana; Mclaughlin, Dennis; Cohn, Stephen E.; Verlaan, Martin
2014-01-01
This paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate non-negativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a non-negativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.
Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms
Janjic, Tijana; McLaughlin, Dennis B.; Cohn, Stephen E.; Verlaan, Martin
2013-01-01
Maintaining conservative physical laws numerically has long been recognized as being important in the development of numerical weather prediction (NWP) models. In the broader context of data assimilation, concerted efforts to maintain conservation laws numerically and to understand the significance of doing so have begun only recently. In order to enforce physically based conservation laws of total mass and positivity in the ensemble Kalman filter, we incorporate constraints to ensure that the filter ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. We show that the analysis steps of ensemble transform Kalman filter (ETKF) algorithm and ensemble Kalman filter algorithm (EnKF) can conserve the mass integral, but do not preserve positivity. Further, if localization is applied or if negative values are simply set to zero, then the total mass is not conserved either. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct a data assimilation algorithms based on quadratic programming and ensemble Kalman filtering. Mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate constraints. Some simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features. Behavior of the algorithm is also tested in presence of model error.
Hydrologic data assimilation has become an important tool for improving hydrologic model predictions by utilizing observations from ground, aircraft, and satellite sensors. Among existing data assimilation methods, the ensemble Kalman filter (EnKF) provides a robust framework for optimally updating ...
Assimilating Remotely Sensed Surface Soil Moisture into SWAT using Ensemble Kalman Filter
In this study, a 1-D Ensemble Kalman Filter has been used to update the soil moisture states of the Soil and Water Assessment Tool (SWAT) model. Experiments were conducted for the Cobb Creek Watershed in southeastern Oklahoma for 2006-2008. Assimilation of in situ data proved limited success in the ...
Performance of the ensemble Kalman filter outside of existing wells for a channelized reservoir
Peters, E.
2010-01-01
The ensemble Kalman filter (EnKF) appears to give good results for matching production data at existing wells. However, the predictive power of these models outside of the existing wells is much more uncertain. In this paper, for a channelized reservoir for five different cases with different levels
Distance parameterization for efficient seismic history matching the ensemble Kalman Filters
Leeuwenburgh, O.; Arts, R.J.
2014-01-01
The availability of multiple history matched models is essential for proper handling of uncertainty in determining the optimal development of producing hydrocarbon fields. The ensemble Kalman Filter in particular is becoming recognized as an efficient method for quantitative conditioning of multiple
Wit, de A.J.W.; Diepen, van C.A.
2007-01-01
Uncertainty in spatial and temporal distribution of rainfall in regional crop yield simulations comprises a major fraction of the error on crop model simulation results. In this paper we used an Ensemble Kalman filter (EnKF) to assimilate coarse resolution satellite microwave sensor derived soil
Distance parameterization for efficient seismic history matching with the ensemble Kalman Filter
Leeuwenburgh, O.; Arts, R.
2012-01-01
The Ensemble Kalman Filter (EnKF), in combination with travel-time parameterization, provides a robust and flexible method for quantitative multi-model history matching to time-lapse seismic data. A disadvantage of the parameterization in terms of travel-times is that it requires simulation of
Sebacher, B.; Hanea, R.G.; Heemink, A.
2013-01-01
In the past years, many applications of historymatching methods in general and ensemble Kalman filter in particular have been proposed, especially in order to estimate fields that provide uncertainty in the stochastic process defined by the dynamical system of hydrocarbon recovery. Such fields can
Directory of Open Access Journals (Sweden)
Elias D. Nino-Ruiz
2017-07-01
Full Text Available In this paper, a matrix-free posterior ensemble Kalman filter implementation based on a modified Cholesky decomposition is proposed. The method works as follows: the precision matrix of the background error distribution is estimated based on a modified Cholesky decomposition. The resulting estimator can be expressed in terms of Cholesky factors which can be updated based on a series of rank-one matrices in order to approximate the precision matrix of the analysis distribution. By using this matrix, the posterior ensemble can be built by either sampling from the posterior distribution or using synthetic observations. Furthermore, the computational effort of the proposed method is linear with regard to the model dimension and the number of observed components from the model domain. Experimental tests are performed making use of the Lorenz-96 model. The results reveal that, the accuracy of the proposed implementation in terms of root-mean-square-error is similar, and in some cases better, to that of a well-known ensemble Kalman filter (EnKF implementation: the local ensemble transform Kalman filter. In addition, the results are comparable to those obtained by the EnKF with large ensemble sizes.
An estimate of the inflation factor and analysis sensitivity in the ensemble Kalman filter
Directory of Open Access Journals (Sweden)
G. Wu
2017-07-01
Full Text Available The ensemble Kalman filter (EnKF is a widely used ensemble-based assimilation method, which estimates the forecast error covariance matrix using a Monte Carlo approach that involves an ensemble of short-term forecasts. While the accuracy of the forecast error covariance matrix is crucial for achieving accurate forecasts, the estimate given by the EnKF needs to be improved using inflation techniques. Otherwise, the sampling covariance matrix of perturbed forecast states will underestimate the true forecast error covariance matrix because of the limited ensemble size and large model errors, which may eventually result in the divergence of the filter. In this study, the forecast error covariance inflation factor is estimated using a generalized cross-validation technique. The improved EnKF assimilation scheme is tested on the atmosphere-like Lorenz-96 model with spatially correlated observations, and is shown to reduce the analysis error and increase its sensitivity to the observations.
The effect of sampling noise in ensemble-based Kalman filters
Sacher, William
Ensemble-based Kalman filters have drawn a lot of attention in the atmospheric and ocean scientific community because of their potential to be used as a data assimilation tool for numerical prediction in a strongly nonlinear context at an affordable cost. However, many studies have noted practical problems in their implementation. Indeed, being Monte-Carlo methods, the useful parameters are estimated from a sample of limited size of independent realizations of the process. As a consequence, the unavoidable sampling noise impacts the quality of the analysis. An idealized perfect model context is considered in which the analytical expression for the analysis accuracy and reliability as a function of the ensemble size is established, from a second-order moment perspective. It is proved that one can analytically explain the general tendency for ensemble-based Kalman filters to underestimate, on average, the analysis variance and therefore the likeliness for these filters to diverge. Performance of alternative methods, designed to reduce or eliminate sampling error effects, such as the double ensemble Kalman filter or covariance inflation are also analytically explored. For methods using perturbed observations, it is shown that the covariance inflation is the easiest and least expensive method to obtain the most accurate and reliable analysis. These analytical results agreed well with means over a large number of experiments using a perfect, low-resolution, and quasi-geostrophic barotropic model, in a series of observation system simulation experiments of single analysis cycles as well as in a simulated forecast system. In one-analysis cycle experiments with rank histograms, non-perturbed-observation methods show a lack of reliability regardless of the number of members. For small ensemble sizes, sampling error effects are dominant but have a smaller impact than in the perturbed observation method, making non-perturbed-observation method filters much less subject to
Data assimilation using a climatologically augmented local ensemble transform Kalman filter
Directory of Open Access Journals (Sweden)
Matthew Kretschmer
2015-05-01
Full Text Available Ensemble data assimilation methods are potentially attractive because they provide a computationally affordable (and computationally parallel means of obtaining flow-dependent background-error statistics. However, a limitation of these methods is that the rank of their flow-dependent background-error covariance estimate, and hence the space of possible analysis increments, is limited by the number of forecast ensemble members. To overcome this deficiency ensemble methods typically use empirical localisation, which allows more degrees of freedom for the analysis increment by suppressing spatially distant background correlations. The method presented here improves the performance of an Ensemble Kalman filter by increasing the size of the ensemble at analysis time in order to boost the rank of its background-error covariance estimate. The additional ensemble members added to the forecast ensemble at analysis time are created by adding a collection of ‘climatological’ perturbations to the forecast ensemble mean. These perturbations are constant in time and provide state space directions, possibly missed by the dynamically forecasted background ensemble, in which the analysis increment can correct the forecast mean based on observations. As the climatological perturbations are calculated once, there is negligible computational cost in obtaining the additional ensemble members at each analysis cycle. Included here are a formulation of the method, results of numerical experiments conducted with a spatiotemporally chaotic model in one spatial dimension and discussion of possible future extensions and applications. The numerical tests indicate that the method presented here has significant potential for improving analyses and forecasts.
A new deterministic Ensemble Kalman Filter with one-step-ahead smoothing for storm surge forecasting
Raboudi, Naila
2016-11-01
The Ensemble Kalman Filter (EnKF) is a popular data assimilation method for state-parameter estimation. Following a sequential assimilation strategy, it breaks the problem into alternating cycles of forecast and analysis steps. In the forecast step, the dynamical model is used to integrate a stochastic sample approximating the state analysis distribution (called analysis ensemble) to obtain a forecast ensemble. In the analysis step, the forecast ensemble is updated with the incoming observation using a Kalman-like correction, which is then used for the next forecast step. In realistic large-scale applications, EnKFs are implemented with limited ensembles, and often poorly known model errors statistics, leading to a crude approximation of the forecast covariance. This strongly limits the filter performance. Recently, a new EnKF was proposed in [1] following a one-step-ahead smoothing strategy (EnKF-OSA), which involves an OSA smoothing of the state between two successive analysis. At each time step, EnKF-OSA exploits the observation twice. The incoming observation is first used to smooth the ensemble at the previous time step. The resulting smoothed ensemble is then integrated forward to compute a "pseudo forecast" ensemble, which is again updated with the same observation. The idea of constraining the state with future observations is to add more information in the estimation process in order to mitigate for the sub-optimal character of EnKF-like methods. The second EnKF-OSA "forecast" is computed from the smoothed ensemble and should therefore provide an improved background. In this work, we propose a deterministic variant of the EnKF-OSA, based on the Singular Evolutive Interpolated Ensemble Kalman (SEIK) filter. The motivation behind this is to avoid the observations perturbations of the EnKF in order to improve the scheme\\'s behavior when assimilating big data sets with small ensembles. The new SEIK-OSA scheme is implemented and its efficiency is demonstrated
The role of model dynamics in ensemble Kalman filter performance for chaotic systems
Ng, G.-H.C.; McLaughlin, D.; Entekhabi, D.; Ahanin, A.
2011-01-01
The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or 'diverging', when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter's update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short-term growth and Lyapunov vectors, corresponding to long-term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long-term unstable subspace is spanned. However, short-term dynamics also become important as non-linearity in the system increases. Non-linear movement prevents errors in the long-term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short-term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics. ?? 2011 The Authors Tellus A ?? 2011 John Wiley & Sons A/S.
Ocean state and uncertainty forecasts using HYCOM with Local Ensemble Transfer Kalman Filter (LETKF)
Wei, Mozheng; Hogan, Pat; Rowley, Clark; Smedstad, Ole-Martin; Wallcraft, Alan; Penny, Steve
2017-04-01
An ensemble forecast system based on the US Navy's operational HYCOM using Local Ensemble Transfer Kalman Filter (LETKF) technology has been developed for ocean state and uncertainty forecasts. One of the advantages is that the best possible initial analysis states for the HYCOM forecasts are provided by the LETKF which assimilates the operational observations using ensemble method. The background covariance during this assimilation process is supplied with the ensemble, thus it avoids the difficulty of developing tangent linear and adjoint models for 4D-VAR from the complicated hybrid isopycnal vertical coordinate in HYCOM. Another advantage is that the ensemble system provides the valuable uncertainty estimate corresponding to every state forecast from HYCOM. Uncertainty forecasts have been proven to be critical for the downstream users and managers to make more scientifically sound decisions in numerical prediction community. In addition, ensemble mean is generally more accurate and skilful than the single traditional deterministic forecast with the same resolution. We will introduce the ensemble system design and setup, present some results from 30-member ensemble experiment, and discuss scientific, technical and computational issues and challenges, such as covariance localization, inflation, model related uncertainties and sensitivity to the ensemble size.
An Adaptive Approach to Mitigate Background Covariance Limitations in the Ensemble Kalman Filter
Song, Hajoon
2010-07-01
A new approach is proposed to address the background covariance limitations arising from undersampled ensembles and unaccounted model errors in the ensemble Kalman filter (EnKF). The method enhances the representativeness of the EnKF ensemble by augmenting it with new members chosen adaptively to add missing information that prevents the EnKF from fully fitting the data to the ensemble. The vectors to be added are obtained by back projecting the residuals of the observation misfits from the EnKF analysis step onto the state space. The back projection is done using an optimal interpolation (OI) scheme based on an estimated covariance of the subspace missing from the ensemble. In the experiments reported here, the OI uses a preselected stationary background covariance matrix, as in the hybrid EnKF–three-dimensional variational data assimilation (3DVAR) approach, but the resulting correction is included as a new ensemble member instead of being added to all existing ensemble members. The adaptive approach is tested with the Lorenz-96 model. The hybrid EnKF–3DVAR is used as a benchmark to evaluate the performance of the adaptive approach. Assimilation experiments suggest that the new adaptive scheme significantly improves the EnKF behavior when it suffers from small size ensembles and neglected model errors. It was further found to be competitive with the hybrid EnKF–3DVAR approach, depending on ensemble size and data coverage.
Directory of Open Access Journals (Sweden)
Kazuo Saito
2012-01-01
Full Text Available The effect of lateral boundary perturbations (LBPs on the mesoscale breeding (MBD method and the local ensemble transform Kalman filter (LETKF as the initial perturbations generators for mesoscale ensemble prediction systems (EPSs was examined. A LBPs method using the Japan Meteorological Agency's (JMA's operational one-week global ensemble prediction was developed and applied to the mesoscale EPS of the Meteorological Research Institute for the World Weather Research Programme, Beijing 2008 Olympics Research and Development Project. The amplitude of the LBPs was adjusted based on the ensemble spread statistics considering the difference of the forecast times of the JMA's one-week EPS and the associated breeding/ensemble Kalman filter (EnKF cycles. LBPs in the ensemble forecast increase the ensemble spread and improve the accuracy of the ensemble mean forecast. In the MBD method, if LBPs were introduced in its breeding cycles, the growth rate of the generated bred vectors is increased, and the ensemble spread and the root mean square errors (RMSEs of the ensemble mean are further improved in the ensemble forecast. With LBPs in the breeding cycles, positional correspondences to the meteorological disturbances and the orthogonality of the bred vectors are improved. Brier Skill Scores (BSSs also showed a remarkable effect of LBPs in the breeding cycles. LBPs showed a similar effect with the LETKF. If LBPs were introduced in the EnKF data assimilation cycles, the ensemble spread, ensemble mean accuracy, and BSSs for precipitation were improved, although the relative advantage of LETKF as the initial perturbations generator against MDB was not necessarily clear. LBPs in the EnKF cycles contribute not to the orthogonalisation but to prevent the underestimation of the forecast error near the lateral boundary.The accuracy of the LETKF analyses was compared with that of the mesoscale 4D-VAR analyses. With LBPs in the LETKF cycles, the RMSEs of the
A square root ensemble Kalman filter application to a motor-imagery brain-computer interface.
Kamrunnahar, M; Schiff, S J
2011-01-01
We here investigated a non-linear ensemble Kalman filter (SPKF) application to a motor imagery brain computer interface (BCI). A square root central difference Kalman filter (SR-CDKF) was used as an approach for brain state estimation in motor imagery task performance, using scalp electroencephalography (EEG) signals. Healthy human subjects imagined left vs. right hand movements and tongue vs. bilateral toe movements while scalp EEG signals were recorded. Offline data analysis was conducted for training the model as well as for decoding the imagery movements. Preliminary results indicate the feasibility of this approach with a decoding accuracy of 78%-90% for the hand movements and 70%-90% for the tongue-toes movements. Ongoing research includes online BCI applications of this approach as well as combined state and parameter estimation using this algorithm with different system dynamic models.
Application of the Multimodel Ensemble Kalman Filter Method in Groundwater System
Directory of Open Access Journals (Sweden)
Liang Xue
2015-02-01
Full Text Available With the development of in-situ monitoring techniques, the ensemble Kalman filter (EnKF has become a popular data assimilation method due to its capability to jointly update model parameters and state variables in a sequential way, and to assess the uncertainty associated with estimation and prediction. To take the conceptual model uncertainty into account during the data assimilation process, a novel multimodel ensemble Kalman filter method has been proposed by incorporating the standard EnKF with Bayesian model averaging framework. In this paper, this method is applied to analyze the dataset obtained from the Hailiutu River Basin located in the northwest part of China. Multiple conceptual models are created by considering two important factors that control groundwater dynamics in semi-arid areas: the zonation pattern of the hydraulic conductivity field and the relationship between evapotranspiration and groundwater level. The results show that the posterior model weights of the postulated models can be dynamically adjusted according to the mismatch between the measurements and the ensemble predictions, and the multimodel ensemble estimation and the corresponding uncertainty can be quantified.
Energy Technology Data Exchange (ETDEWEB)
Chitralekha, S.B.; Trivedi, J.J.; Shah, S.L. [Alberta Univ., Edmonton, AB (Canada)
2010-07-01
The ensemble Kalman filter (EnKF) was used to continuously update and history match the petroleum reservoir characteristics of 2 unconventional oil reservoir models, notably (1) a highly heterogenous black oil reservoir model, and (2) a heterogenous steam assisted gravity drainage (SAGD) reservoir model. The method was used to sequentially update the spatial properties of the reservoir models through the integration of dynamic production data. Monte Carlo simulations of the model ensembles were used. The method considered production uncertainty by using error covariance matrices for measurement and state vectors. Results of the study demonstrated the advantages of using a localized EnKF for effective history matching. Significant computational time was saved by running the ensemble simulations on independent processors in a parallel mode. 28 refs., 16 figs.
Lenartz, F.; Raick, C.; Soetaert, K.E.R.; Grégoire, M.
2007-01-01
The Ensemble Kalman filter (EnKF) has been applied to a 1-D complex ecosystem model coupled with a hydrodynamic model of the Ligurian Sea. In order to improve the performance of the EnKF, an ensemble subsampling strategy has been used to better represent the covariance matrices and a pre-analysis
Markov models and the ensemble Kalman filter for estimation of sorption rates.
Energy Technology Data Exchange (ETDEWEB)
Vugrin, Eric D.; McKenna, Sean Andrew (Sandia National Laboratories, Albuquerque, NM); Vugrin, Kay White
2007-09-01
Non-equilibrium sorption of contaminants in ground water systems is examined from the perspective of sorption rate estimation. A previously developed Markov transition probability model for solute transport is used in conjunction with a new conditional probability-based model of the sorption and desorption rates based on breakthrough curve data. Two models for prediction of spatially varying sorption and desorption rates along a one-dimensional streamline are developed. These models are a Markov model that utilizes conditional probabilities to determine the rates and an ensemble Kalman filter (EnKF) applied to the conditional probability method. Both approaches rely on a previously developed Markov-model of mass transfer, and both models assimilate the observed concentration data into the rate estimation at each observation time. Initial values of the rates are perturbed from the true values to form ensembles of rates and the ability of both estimation approaches to recover the true rates is examined over three different sets of perturbations. The models accurately estimate the rates when the mean of the perturbations are zero, the unbiased case. For the cases containing some bias, addition of the ensemble Kalman filter is shown to improve accuracy of the rate estimation by as much as an order of magnitude.
Application of Ensemble Kalman Filter in Power System State Tracking and Sensitivity
Energy Technology Data Exchange (ETDEWEB)
Li, Yulan; Huang, Zhenyu; Zhou, Ning; Lee, Barry; Diao, Ruisheng; Du, Pengwei
2012-05-01
Ensemble Kalman Filter (EnKF) is proposed to track dynamic states of generators. The algorithm of EnKF and its application to generator state tracking are presented in detail. The accuracy and sensitivity of the method are analyzed with respect to initial state errors, measurement noise, unknown fault locations, time steps and parameter errors. It is demonstrated through simulation studies that even with some errors in the parameters, the developed EnKF can effectively track generator dynamic states using disturbance data.
Ensemble-Type Kalman Filter Algorithm conserving mass, total energy and enstrophy
Zeng, Yuefei; Janjic, Tijana; Ruckstuhl, Yvonne; Verlaan, Martin
2017-04-01
In a recent study (Zeng and Janjic 2016), we explored the effect on conservation properties of data assimilation using perfect model experiments with a 2D shallow water model preserving important properties of the true nonlinear flow. It was found that during the assimilation with the ensemble Kalman filter algorithm, the total energy of the analysis ensemble mean converges towards the nature run value with time. However, the enstrophy, divergence and energy spectra were strongly affected by the data assimilation settings. We tested the effects on the prediction depending on the type of error in the initial condition and showed that the accumulated noise during assimilation and the error of analysis are good indicators of the quality of the prediction. Having in mind that the conservation of both the kinetic energy and enstrophy by momentum advection schemes in the case of non-divergent flow prevents a systematic and unrealistic energy cascade towards the high wave numbers, we constructed the ensemble data assimilation algorithm that conserves both energy and enstrophy. This is done by extending QPEns (Janjic et al. 2014) to allow for nonlinear constraints using, instead of quadratic programming, the sequential quadratic programming algorithm. Experiments with the 2D shallow water model show similar RMSEs of the algorithm without constraints and the algorithm with only the total energy constrained. The algorithm which constraints enstrophy as well as energy and enstrophy during data assimilation showed smaller RMSE to the one without the constraint on enstrophy. Similar behavior can be seen in the energy spectrum where algorithms which include the constraint on enstrophy are closer to the true spectrum, in particular for wavelengths between 200 km and 1000 km. The enstrophy constraint resulted in a reduction of noise during data assimilation. Finally, the algorithm, with both energy and enstrophy constraint showed the smallest error growth during the two weeks
Godinez, Humberto C; Fierro, Alexandre O; Guimond, Stephen R; Kao, Jim
2011-01-01
In this work we present the assimilation of dual-Doppler radar observations for rapidly intensifying hurricane Guillermo (1997) using the Ensemble Kalman Filter (EnKF) to determine key model parameters. A unique aspect of Guillermo was that during the period of radar observations strong convective bursts, attributable to wind shear, formed primarily within the eastern semicircle of the eyewall. To reproduce this observed structure within a hurricane model, background wind shear of some magnitude must be specified; as well as turbulence and surface parameters appropriately specified so that the impact of the shear on the simulated hurricane vortex can be realized. To first illustrate the complex nonlinear interactions induced by changes in these parameters, an ensemble of 120 simulations have been conducted in which individual members were formulated by sampling the parameters within a certain range via a Latin hypercube approach. Next, data from the 120 simulations and two distinct derived fields of observati...
A partial ensemble Kalman filtering approach to enable use of range limited observations
DEFF Research Database (Denmark)
Borup, Morten; Grum, Morten; Madsen, Henrik
2015-01-01
The ensemble Kalman filter (EnKF) relies on the assumption that an observed quantity can be regarded as a stochastic variable that is Gaussian distributed with mean and variance that equals the measurement and the measurement noise, respectively. When a gauge has a minimum and/or maximum detection...... limit and the observed quantity is outside this range, the signal from the gauge can, however, not be related to the observed quantity in this way. The current study proposes a method for utilizing this kind of out-of-range observations with the EnKF by explicitly treating the out-of-range observations...... the same model and noise descriptions are used for the truth simulation and for the EnKF. The results show that the positive impact of the method in case of range-limited observations can exceed that of increasing the ensemble size from 10 to 100 and that the method makes it possible to improve model...
Directory of Open Access Journals (Sweden)
Eugenia Kalnay
2012-10-01
Full Text Available We introduce a new formulation of the ensemble forecast sensitivity developed by Liu and Kalnay with a small correction from Li et al. The new formulation, like the original one, is tested on the simple Lorenz 40-variable model. We find that, except for short-range forecasts, the use of localization in the analysis, necessary in ensemble Kalman filter (EnKF when the number of ensemble members is much smaller than the model's degrees of freedom, has a negative impact on the accuracy of the sensitivity. This is because the impact of an observation during the analysis (i.e. the analysis increment associated with the observation is transported by the flow during the integration, and this is ignored when the ensemble sensitivity uses a fixed localization. To address this problem, we introduce two approaches that could be adapted to evolve the localization during the estimation of forecast sensitivity to the observations. The first one estimates the non-linear evolution of the initial localization but is computationally expensive. The second one moves the localization with a constant estimation of the group velocity. Both methods succeed in improving the ensemble estimations for longer forecasts.Overall, the adjoint and ensemble forecast impact estimations give similarly accurate results for short-range forecasts, except that the new formulation gives an estimation of the fraction of observations that improve the forecast closer to that obtained by data denial (Observing System Experiments. For longer-range forecasts, they both deteriorate for different reasons. The adjoint sensitivity becomes noisy due to the forecast non-linearities not captured in the linear tangent model and the adjoint. The ensemble sensitivity becomes less accurate due to the use of a fixed localization, a problem that could be ameliorated with an evolving adaptive localization. Advantages of the new formulation include it being simpler than the original formulation and
Wang, S.; Huang, G. H.; Baetz, B. W.; Cai, X. M.; Ancell, B. C.; Fan, Y. R.
2017-11-01
The ensemble Kalman filter (EnKF) is recognized as a powerful data assimilation technique that generates an ensemble of model variables through stochastic perturbations of forcing data and observations. However, relatively little guidance exists with regard to the proper specification of the magnitude of the perturbation and the ensemble size, posing a significant challenge in optimally implementing the EnKF. This paper presents a robust data assimilation system (RDAS), in which a multi-factorial design of the EnKF experiments is first proposed for hydrologic ensemble predictions. A multi-way analysis of variance is then used to examine potential interactions among factors affecting the EnKF experiments, achieving optimality of the RDAS with maximized performance of hydrologic predictions. The RDAS is applied to the Xiangxi River watershed which is the most representative watershed in China's Three Gorges Reservoir region to demonstrate its validity and applicability. Results reveal that the pairwise interaction between perturbed precipitation and streamflow observations has the most significant impact on the performance of the EnKF system, and their interactions vary dynamically across different settings of the ensemble size and the evapotranspiration perturbation. In addition, the interactions among experimental factors vary greatly in magnitude and direction depending on different statistical metrics for model evaluation including the Nash-Sutcliffe efficiency and the Box-Cox transformed root-mean-square error. It is thus necessary to test various evaluation metrics in order to enhance the robustness of hydrologic prediction systems.
Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time
Kelly, D. T B
2014-09-22
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations associated with the filter, which are required to make a useable algorithm in practice, are derived in an ad hoc fashion. The aim of this paper is to initiate the development of a systematic analysis of the EnKF, in particular to do so for small ensemble size. The perspective is to view the method as a state estimator, and not as an algorithm which approximates the true filtering distribution. The perturbed observation version of the algorithm is studied, without and with variance inflation. Without variance inflation well-posedness of the filter is established; with variance inflation accuracy of the filter, with respect to the true signal underlying the data, is established. The algorithm is considered in discrete time, and also for a continuous time limit arising when observations are frequent and subject to large noise. The underlying dynamical model, and assumptions about it, is sufficiently general to include the Lorenz \\'63 and \\'96 models, together with the incompressible Navier-Stokes equation on a two-dimensional torus. The analysis is limited to the case of complete observation of the signal with additive white noise. Numerical results are presented for the Navier-Stokes equation on a two-dimensional torus for both complete and partial observations of the signal with additive white noise.
Continuous updating of a coupled reservoir-seismic model using an ensemble Kalman filter technique
Energy Technology Data Exchange (ETDEWEB)
Skjervheim, Jan-Arild
2007-07-01
This work presents the development of a method based on the ensemble Kalman filter (EnKF) for continuous reservoir model updating with respect to the combination of production data, 3D seismic data and time-lapse seismic data. The reservoir-seismic model system consists of a commercial reservoir simulator coupled to existing rock physics and seismic modelling software. The EnKF provides an ideal-setting for real time updating and prediction in reservoir simulation models, and has been applied to synthetic models and real field cases from the North Sea. In the EnKF method, static parameters as the porosity and permeability, and dynamic variables, as fluid saturations and pressure, are updated in the reservoir model at each step data become available. In addition, we have updated a lithology parameter (clay ratio) which is linked to the rock physics model, and the fracture density in a synthetic fractured reservoir. In the EnKF experiments we have assimilated various types of production and seismic data. Gas oil ratio (GOR), water cut (WCT) and bottom-hole pressure (BHP) are used in the data assimilation. Furthermore, inverted seismic data, such as Poisson's ratio and acoustic impedance, and seismic waveform data have been assimilated. In reservoir applications seismic data may introduce a large amount of data in the assimilation schemes, and the computational time becomes expensive. In this project efficient EnKF schemes are used to handle such large datasets, where challenging aspects such as the inversion of a large covariance matrix and potential loss of rank are considered. Time-lapse seismic data may be difficult to assimilate since they are time difference data, i.e. data which are related to the model variable at two or more time instances. Here we have presented a general sequential Bayesian formulation which incorporates time difference data, and we show that the posterior distribution includes both a filter and a smoother solution. Further, we show
2015-09-30
1 Approved for public release; distribution is unlimited. Toward the Development of a Coupled COAMPS-ROMS Ensemble Kalman Filter and Adjoint...system at NCAR. (2) Compare the performance of the Ensemble Kalman Filter (EnKF) using the Data Assimilation Research Testbed (DART) and 4
Wilschut, F.; Peters, E.; Visser, K.; Fokker, P.A.; Hooff, P.M.E. van
2011-01-01
The number of reported applications of the Ensemble Kalman Filter (EnKF) for history matching reservoir models is increasing steadily for various reasons. Here, we report on exploiting the capability of EnKF to handle observations from different sources simultaneously. While traditionally only well
[Simulation of cropland soil moisture based on an ensemble Kalman filter].
Liu, Zhao; Zhou, Yan-Lian; Ju, Wei-Min; Gao, Ping
2011-11-01
By using an ensemble Kalman filter (EnKF) to assimilate the observed soil moisture data, the modified boreal ecosystem productivity simulator (BEPS) model was adopted to simulate the dynamics of soil moisture in winter wheat root zones at Xuzhou Agro-meteorological Station, Jiangsu Province of China during the growth seasons in 2000-2004. After the assimilation of observed data, the determination coefficient, root mean square error, and average absolute error of simulated soil moisture were in the ranges of 0.626-0.943, 0.018-0.042, and 0.021-0.041, respectively, with the simulation precision improved significantly, as compared with that before assimilation, indicating the applicability of data assimilation in improving the simulation of soil moisture. The experimental results at single point showed that the errors in the forcing data and observations and the frequency and soil depth of the assimilation of observed data all had obvious effects on the simulated soil moisture.
Brandhorst, N.; Erdal, D.; Neuweiler, I.
2017-12-01
For predicting flow in the unsaturated zone, an adequate choice of the model parameters, especially the soil hydraulic parameters, is essential. It is difficult to determine these parameters, as the parameter estimation problem easily becomes ill-posed, e.g. due to pseudo-correlations among two or more of the unknown parameters. In the field, this problem is strongly related to the available observations which, in monitoring networks, are not optimized to be used for parameter estimation. In this paper, we investigate the potential of data assimilation using the ensemble Kalman filter (EnKF) with unsaturated zone models under conditions where model parameters are highly uncertain and not identifiable. Different ways of dealing with the parameter uncertainty, such as parameter updates and bias correction, are discussed and compared. It is shown that jointly updating all uncertain parameters and states is the best method to account for the error induced by parameter uncertainty.
Chen, Zi; Zanini, Andrea; Gómez-Hernández, J. Jaime; Xu, Teng; Cupola, Fausto
2017-04-01
In this work , the ensemble Kalman filter(EnKF) is employed to identify the contaminant source and barrier information in a laboratory sandbox experiment. A typical single point pollution experiment was performed in the sandbox with a barrier by using sodium fluorescein as the tracer.The movement of the contaminant was recorded by a digital camera and the contaminant concentration was obtained by the analysis of the luminosity of the pictures. The capability of the EnKF is tested through the experiment data. With a vague prior speculation of the contaminant source and barrier information, EnKF is applied to simultaneously identify these parameters through assimilating the concentration observations. The updated parameters match the actually sandbox parameters quite well implying that EnKF is an effective approach to identify the source location, barrier position, contaminant concentration and releasing history.
Dynamic State Estimation and Parameter Calibration of DFIG based on Ensemble Kalman Filter
Energy Technology Data Exchange (ETDEWEB)
Fan, Rui; Huang, Zhenyu; Wang, Shaobu; Diao, Ruisheng; Meng, Da
2015-07-30
With the growing interest in the application of wind energy, doubly fed induction generator (DFIG) plays an essential role in the industry nowadays. To deal with the increasing stochastic variations introduced by intermittent wind resource and responsive loads, dynamic state estimation (DSE) are introduced in any power system associated with DFIGs. However, sometimes this dynamic analysis canould not work because the parameters of DFIGs are not accurate enough. To solve the problem, an ensemble Kalman filter (EnKF) method is proposed for the state estimation and parameter calibration tasks. In this paper, a DFIG is modeled and implemented with the EnKF method. Sensitivity analysis is demonstrated regarding the measurement noise, initial state errors and parameter errors. The results indicate this EnKF method has a robust performance on the state estimation and parameter calibration of DFIGs.
Calibration of a Land Subsidence Model Using InSAR Data via the Ensemble Kalman Filter.
Li, Liangping; Zhang, Meijing; Katzenstein, Kurt
2017-05-23
The application of interferometric synthetic aperture radar (InSAR) has been increasingly used to improve capabilities to model land subsidence in hydrogeologic studies. A number of investigations over the last decade show how spatially detailed time-lapse images of ground displacements could be utilized to advance our understanding for better predictions. In this work, we use simulated land subsidences as observed measurements, mimicking InSAR data to inversely infer inelastic specific storage in a stochastic framework. The inelastic specific storage is assumed as a random variable and modeled using a geostatistical method such that the detailed variations in space could be represented and also that the uncertainties of both characterization of specific storage and prediction of land subsidence can be assessed. The ensemble Kalman filter (EnKF), a real-time data assimilation algorithm, is used to inversely calibrate a land subsidence model by matching simulated subsidences with InSAR data. The performance of the EnKF is demonstrated in a synthetic example in which simulated surface deformations using a reference field are assumed as InSAR data for inverse modeling. The results indicate: (1) the EnKF can be used successfully to calibrate a land subsidence model with InSAR data; the estimation of inelastic specific storage is improved, and uncertainty of prediction is reduced, when all the data are accounted for; and (2) if the same ensemble is used to estimate Kalman gain, the analysis errors could cause filter divergence; thus, it is essential to include localization in the EnKF for InSAR data assimilation. © 2017, National Ground Water Association.
Ensemble Kalman filter for the reconstruction of the Earth's mantle circulation
Directory of Open Access Journals (Sweden)
M. Bocher
2018-02-01
Full Text Available Recent advances in mantle convection modeling led to the release of a new generation of convection codes, able to self-consistently generate plate-like tectonics at their surface. Those models physically link mantle dynamics to surface tectonics. Combined with plate tectonic reconstructions, they have the potential to produce a new generation of mantle circulation models that use data assimilation methods and where uncertainties in plate tectonic reconstructions are taken into account. We provided a proof of this concept by applying a suboptimal Kalman filter to the reconstruction of mantle circulation (Bocher et al., 2016. Here, we propose to go one step further and apply the ensemble Kalman filter (EnKF to this problem. The EnKF is a sequential Monte Carlo method particularly adapted to solve high-dimensional data assimilation problems with nonlinear dynamics. We tested the EnKF using synthetic observations consisting of surface velocity and heat flow measurements on a 2-D-spherical annulus model and compared it with the method developed previously. The EnKF performs on average better and is more stable than the former method. Less than 300 ensemble members are sufficient to reconstruct an evolution. We use covariance adaptive inflation and localization to correct for sampling errors. We show that the EnKF results are robust over a wide range of covariance localization parameters. The reconstruction is associated with an estimation of the error, and provides valuable information on where the reconstruction is to be trusted or not.
An Ensemble Kalman Filter for severe dust storm data assimilation over China
Directory of Open Access Journals (Sweden)
C. Lin
2008-06-01
Full Text Available An Ensemble Kalman Filter (EnKF data assimilation system was developed for a regional dust transport model. This paper applied the EnKF method to investigate modeling of severe dust storm episodes occurring in March 2002 over China based on surface observations of dust concentrations to explore the impact of the EnKF data assimilation systems on forecast improvement. A series of sensitivity experiments using our system demonstrates the ability of the advanced EnKF assimilation method using surface observed PM_{10} in North China to correct initial conditions, which leads to improved forecasts of dust storms. However, large errors in the forecast may arise from model errors (uncertainties in meteorological fields, dust emissions, dry deposition velocity, etc.. This result illustrates that the EnKF requires identification and correction model errors during the assimilation procedure in order to significantly improve forecasts. Results also show that the EnKF should use a large inflation parameter to obtain better model performance and forecast potential. Furthermore, the ensemble perturbations generated at the initial time should include enough ensemble spreads to represent the background error after several assimilation cycles.
2011-09-01
several in- dependent, locally stationary processes with simple parametric stationary (or isotropic) covariance func- tions ( Fuentes 2001). Parametric...230, 99–111. ——, and S. L. Anderson, 1999: A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimi- lations and...Q. Yao, 2003: Nonlinear Time Series: Nonparametric and Parametric Methods. Springer-Verlag, 552 pp. Fuentes , M., 2001: A high frequency kriging
Luo, Xiaodong
2014-10-01
The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an observation-space-based strategy, called residual nudging, to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor and, if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In the present study, residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that, under suitable conditions, is able to achieve the objective of residual nudging for data assimilation problems with nonlinear observation operators. The 40-dimensional Lorenz-96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge with nonlinear observation operators, the proposed iterative filter remains stable and leads to reasonable estimation accuracy under various experimental settings.
Directory of Open Access Journals (Sweden)
X. Yang
2009-07-01
Full Text Available A new class of ensemble filters, called the Diffuse Ensemble Filter (DEnF, is proposed in this paper. The DEnF assumes that the forecast errors orthogonal to the first guess ensemble are uncorrelated with the latter ensemble and have infinite variance. The assumption of infinite variance corresponds to the limit of "complete lack of knowledge" and differs dramatically from the implicit assumption made in most other ensemble filters, which is that the forecast errors orthogonal to the first guess ensemble have vanishing errors. The DEnF is independent of the detailed covariances assumed in the space orthogonal to the ensemble space, and reduces to conventional ensemble square root filters when the number of ensembles exceeds the model dimension. The DEnF is well defined only in data rich regimes and involves the inversion of relatively large matrices, although this barrier might be circumvented by variational methods. Two algorithms for solving the DEnF, namely the Diffuse Ensemble Kalman Filter (DEnKF and the Diffuse Ensemble Transform Kalman Filter (DETKF, are proposed and found to give comparable results. These filters generally converge to the traditional EnKF and ETKF, respectively, when the ensemble size exceeds the model dimension. Numerical experiments demonstrate that the DEnF eliminates filter collapse, which occurs in ensemble Kalman filters for small ensemble sizes. Also, the use of the DEnF to initialize a conventional square root filter dramatically accelerates the spin-up time for convergence. However, in a perfect model scenario, the DEnF produces larger errors than ensemble square root filters that have covariance localization and inflation. For imperfect forecast models, the DEnF produces smaller errors than the ensemble square root filter with inflation. These experiments suggest that the DEnF has some advantages relative to the ensemble square root filters in the regime of small ensemble size, imperfect model, and copious
Directory of Open Access Journals (Sweden)
D. Fairbairn
2015-12-01
Full Text Available Two data assimilation (DA methods are compared for their ability to produce an accurate soil moisture analysis using the Météo-France land surface model: (i SEKF, a simplified extended Kalman filter, which uses a climatological background-error covariance, and (ii EnSRF, the ensemble square root filter, which uses an ensemble background-error covariance and approximates random rainfall errors stochastically. In situ soil moisture observations at 5 cm depth are assimilated into the surface layer and 30 cm deep observations are used to evaluate the root-zone analysis on 12 sites in south-western France (SMOSMANIA network. These sites differ in terms of climate and soil texture. The two methods perform similarly and improve on the open loop. Both methods suffer from incorrect linear assumptions which are particularly degrading to the analysis during water-stressed conditions: the EnSRF by a dry bias and the SEKF by an over-sensitivity of the model Jacobian between the surface and the root-zone layers. These problems are less severe for the sites with wetter climates. A simple bias correction technique is tested on the EnSRF. Although this reduces the bias, it modifies the soil moisture fluxes and suppresses the ensemble spread, which degrades the analysis performance. However, the EnSRF flow-dependent background-error covariance evidently captures seasonal variability in the soil moisture errors and should exploit planned improvements in the model physics. Synthetic twin experiments demonstrate that when there is only a random component in the precipitation forcing errors, the correct stochastic representation of these errors enables the EnSRF to perform better than the SEKF. It might therefore be possible for the EnSRF to perform better than the SEKF with real data, if the rainfall uncertainty was accurately captured. However, the simple rainfall error model is not advantageous in our real experiments. More realistic rainfall error models are
Energy Technology Data Exchange (ETDEWEB)
Monache, L D; Grell, G A; McKeen, S; Wilczak, J; Pagowski, M O; Peckham, S; Stull, R; McHenry, J; McQueen, J
2006-03-20
Kalman filtering (KF) is used to postprocess numerical-model output to estimate systematic errors in surface ozone forecasts. It is implemented with a recursive algorithm that updates its estimate of future ozone-concentration bias by using past forecasts and observations. KF performance is tested for three types of ozone forecasts: deterministic, ensemble-averaged, and probabilistic forecasts. Eight photochemical models were run for 56 days during summer 2004 over northeastern USA and southern Canada as part of the International Consortium for Atmospheric Research on Transport and Transformation New England Air Quality (AQ) Study. The raw and KF-corrected predictions are compared with ozone measurements from the Aerometric Information Retrieval Now data set, which includes roughly 360 surface stations. The completeness of the data set allowed a thorough sensitivity test of key KF parameters. It is found that the KF improves forecasts of ozone-concentration magnitude and the ability to predict rare events, both for deterministic and ensemble-averaged forecasts. It also improves the ability to predict the daily maximum ozone concentration, and reduces the time lag between the forecast and observed maxima. For this case study, KF considerably improves the predictive skill of probabilistic forecasts of ozone concentration greater than thresholds of 10 to 50 ppbv, but it degrades it for thresholds of 70 to 90 ppbv. Moreover, KF considerably reduces probabilistic forecast bias. The significance of KF postprocessing and ensemble-averaging is that they are both effective for real-time AQ forecasting. KF reduces systematic errors, whereas ensemble-averaging reduces random errors. When combined they produce the best overall forecast.
Yan, Y.; Barth, A.; Beckers, J. M.; Brankart, J. M.; Brasseur, P.; Candille, G.
2017-07-01
In this paper, three incremental analysis update schemes (IAU 0, IAU 50 and IAU 100) are compared in the same assimilation experiments with a realistic eddy permitting primitive equation model of the North Atlantic Ocean using the Ensemble Kalman Filter. The difference between the three IAU schemes lies on the position of the increment update window. The relevance of each IAU scheme is evaluated through analyses on both thermohaline and dynamical variables. The validation of the assimilation results is performed according to both deterministic and probabilistic metrics against different sources of observations. For deterministic validation, the ensemble mean and the ensemble spread are compared to the observations. For probabilistic validation, the continuous ranked probability score (CRPS) is used to evaluate the ensemble forecast system according to reliability and resolution. The reliability is further decomposed into bias and dispersion by the reduced centred random variable (RCRV) score. The obtained results show that 1) the IAU 50 scheme has the same performance as the IAU 100 scheme 2) the IAU 50/100 schemes outperform the IAU 0 scheme in error covariance propagation for thermohaline variables in relatively stable region, while the IAU 0 scheme outperforms the IAU 50/100 schemes in dynamical variables estimation in dynamically active region 3) in case with sufficient number of observations and good error specification, the impact of IAU schemes is negligible. The differences between the IAU 0 scheme and the IAU 50/100 schemes are mainly due to different model integration time and different instability (density inversion, large vertical velocity, etc.) induced by the increment update. The longer model integration time with the IAU 50/100 schemes, especially the free model integration, on one hand, allows for better re-establishment of the equilibrium model state, on the other hand, smooths the strong gradients in dynamically active region.
Ensemble Kalman Filter data assimilation and storm surge experiments of tropical cyclone Nargis
Directory of Open Access Journals (Sweden)
Le Duc
2015-07-01
Full Text Available Data assimilation experiments on Myanmar tropical cyclone (TC, Nargis, using the Local Ensemble Transform Kalman Filter (LETKF method and the Japan Meteorological Agency (JMA non-hydrostatic model (NHM were performed to examine the impact of LETKF on analysis performance in real cases. Although the LETKF control experiment using NHM as its driving model (NHM–LETKF produced a weak vortex, the subsequent 3-day forecast predicted Nargis’ track and intensity better than downscaling from JMA's global analysis. Some strategies to further improve the final analysis were considered. They were sea surface temperature (SST perturbations and assimilation of TC advisories. To address SST uncertainty, SST analyses issued by operational forecast centres were used in the assimilation window. The use of a fixed source of SST analysis for each ensemble member was more effective in practice. SST perturbations were found to have slightly positive impact on the track forecasts. Assimilation of TC advisories could have a positive impact with a reasonable choice of its free parameters. However, the TC track forecasts exhibited northward displacements, when the observation error of intensities was underestimated in assimilation of TC advisories. The use of assimilation of TC advisories was considered in the final NHM–LETKF by choosing an appropriate set of free parameters. The extended forecast based on the final analysis provided meteorological forcings for a storm surge simulation using the Princeton Ocean Model. Probabilistic forecasts of the water levels at Irrawaddy and Yangon significantly improved the results in the previous studies.
Lorente-Plazas, Raquel; Hacker, Josua P.; Collins, Nancy; Lee, Jared A.
2017-04-01
The impact of assimilating surface observations has been shown in several publications, for improving weather prediction inside of the boundary layer as well as the flow aloft. However, the assimilation of surface observations is often far from optimal due to the presence of both model and observation biases. The sources of these biases can be diverse: an instrumental offset, errors associated to the comparison of point-based observations and grid-cell average, etc. To overcome this challenge, a method was developed using the ensemble Kalman filter. The approach consists on representing each observation bias as a parameter. These bias parameters are added to the forward operator and they extend the state vector. As opposed to the observation bias estimation approaches most common in operational systems (e.g. for satellite radiances), the state vector and parameters are simultaneously updated by applying the Kalman filter equations to the augmented state. The method to estimate and correct the observation bias is evaluated using observing system simulation experiments (OSSEs) with the Weather Research and Forecasting (WRF) model. OSSEs are constructed for the conventional observation network including radiosondes, aircraft observations, atmospheric motion vectors, and surface observations. Three different kinds of biases are added to 2-meter temperature for synthetic METARs. From the simplest to more sophisticated, imposed biases are: (1) a spatially invariant bias, (2) a spatially varying bias proportional to topographic height differences between the model and the observations, and (3) bias that is proportional to the temperature. The target region characterized by complex terrain is the western U.S. on a domain with 30-km grid spacing. Observations are assimilated every 3 hours using an 80-member ensemble during September 2012. Results demonstrate that the approach is able to estimate and correct the bias when it is spatially invariant (experiment 1). More
Ait-El-Fquih, Boujemaa
2016-08-12
Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface ground-water models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model\\'s state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The joint EnKF directly updates the augmented state-parameter vector, whereas the dual EnKF empirically employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. To develop a Bayesian consistent dual approach and improve the state-parameter estimates and their consistency, we propose in this paper a one-step-ahead (OSA) smoothing formulation of the state-parameter Bayesian filtering problem from which we derive a new dual-type EnKF, the dual EnKF(OSA). Compared with the standard dual EnKF, it imposes a new update step to the state, which is shown to enhance the performance of the dual approach with almost no increase in the computational cost. Numerical experiments are conducted with a two-dimensional (2-D) synthetic groundwater aquifer model to investigate the performance and robustness of the proposed dual EnKFOSA, and to evaluate its results against those of the joint and dual EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, providing further reliable estimates of their uncertainties. Furthermore, it is found to be more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25% more accurate state and parameter estimations than the joint and dual approaches.
Briseño, Jessica; Herrera, Graciela S.
2010-05-01
Herrera (1998) proposed a method for the optimal design of groundwater quality monitoring networks that involves space and time in a combined form. The method was applied later by Herrera et al (2001) and by Herrera and Pinder (2005). To get the estimates of the contaminant concentration being analyzed, this method uses a space-time ensemble Kalman filter, based on a stochastic flow and transport model. When the method is applied, it is important that the characteristics of the stochastic model be congruent with field data, but, in general, it is laborious to manually achieve a good match between them. For this reason, the main objective of this work is to extend the space-time ensemble Kalman filter proposed by Herrera, to estimate the hydraulic conductivity, together with hydraulic head and contaminant concentration, and its application in a synthetic example. The method has three steps: 1) Given the mean and the semivariogram of the natural logarithm of hydraulic conductivity (ln K), random realizations of this parameter are obtained through two alternatives: Gaussian simulation (SGSim) and Latin Hypercube Sampling method (LHC). 2) The stochastic model is used to produce hydraulic head (h) and contaminant (C) realizations, for each one of the conductivity realizations. With these realization the mean of ln K, h and C are obtained, for h and C, the mean is calculated in space and time, and also the cross covariance matrix h-ln K-C in space and time. The covariance matrix is obtained averaging products of the ln K, h and C realizations on the estimation points and times, and the positions and times with data of the analyzed variables. The estimation points are the positions at which estimates of ln K, h or C are gathered. In an analogous way, the estimation times are those at which estimates of any of the three variables are gathered. 3) Finally the ln K, h and C estimate are obtained using the space-time ensemble Kalman filter. The realization mean for each one
Sana, Furrukh
2015-07-26
Recovering information on subsurface geological features, such as flow channels, holds significant importance for optimizing the productivity of oil reservoirs. The flow channels exhibit high permeability in contrast to low permeability rock formations in their surroundings, enabling formulation of a sparse field recovery problem. The Ensemble Kalman filter (EnKF) is a widely used technique for the estimation of subsurface parameters, such as permeability. However, the EnKF often fails to recover and preserve the channel structures during the estimation process. Compressed Sensing (CS) has shown to significantly improve the reconstruction quality when dealing with such problems. We propose a new scheme based on CS principles to enhance the reconstruction of subsurface geological features by transforming the EnKF estimation process to a sparse domain representing diverse geological structures. Numerical experiments suggest that the proposed scheme provides an efficient mechanism to incorporate and preserve structural information in the estimation process and results in significant enhancement in the recovery of flow channel structures.
Ensemble Kalman Filtering with a Divided State-Space Strategy for Coupled Data Assimilation Problems
Luo, Xiaodong
2014-12-01
This study considers the data assimilation problem in coupled systems, which consists of two components (subsystems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in such systems is to concatenate the states of the subsystems into one augmented state vector, so that a standard ensemble Kalman filter (EnKF) can be directly applied. This work presents a divided state-space estimation strategy, in which data assimilation is carried out with respect to each individual subsystem, involving quantities from the subsystem itself and correlated quantities from other coupled subsystems. On top of the divided state-space estimation strategy, the authors also consider the possibility of running the subsystems separately. Combining these two ideas, a few variants of the EnKF are derived. The introduction of these variants is mainly inspired by the current status and challenges in coupled data assimilation problems and thus might be of interest from a practical point of view. Numerical experiments with a multiscale Lorenz 96 model are conducted to evaluate the performance of these variants against that of the conventional EnKF. In addition, specific for coupled data assimilation problems, two prototypes of extensions of the presented methods are also developed in order to achieve a trade-offbetween efficiency and accuracy.
An operational high resolution ensemble kalman filter data assimilation cycle over South America
Cossetin, Camila; Goncalves, Luis; Silveira, Bruna; Vendrasco, Eder; Khamis, Eduardo; Sapucci, Luiz
2016-04-01
The brazilian Center for Weather Forecast and Climate Studies (CPTEC/INPE) has recently initiated an effort to develop operationally a high resolution probabilistic mesoscale analysis over the continental South America and portions of the surrounding south Pacific and Atlantic oceans. This work presents a high resolution regional ensemble Kalman filter (EnKF) system with the WRF model. It uses the gridpoint statistical interpolation (GSI) mantained by the Developmental Testbed Center (DTC) for observational data processing and observation operators. The initial tests were run at approximately 9 Km of spatial resolution and 20 members with 6-hourly data assimilation cycles using all regional observations and selected satellite radiances (AMSU-A, MHS and HIRS). The impact of the choice of covariance localization and covariance inflation in the model performance is assessed to demonstrate the sensitive to the tunning. A two-weeks simulation is performed to illustrate the system adjustment (spin up) and how the model errors and innovation respond during the first days of run. Furthermore, the relative contribution of satellite brightness temperature assimilation to the analysis increments is also evaluated.
Development of an ensemble Kalman filter data assimilation system for the Venusian atmosphere.
Sugimoto, Norihiko; Yamazaki, Akira; Kouyama, Toru; Kashimura, Hiroki; Enomoto, Takeshi; Takagi, Masahiro
2017-08-24
The size and mass of Venus is similar to those of the Earth; however, its atmospheric dynamics are considerably different and they are poorly understood due to limited observations and computational difficulties. Here, we developed a data assimilation system based on the local ensemble transform Kalman filter (LETKF) for a Venusian Atmospheric GCM for the Earth Simulator (VAFES), to make full use of the observational data. To examine the validity of the system, two datasets were assimilated separately into the VAFES forecasts forced with solar heating that excludes the diurnal component Qz; one was created from a VAFES run forced with solar heating that includes the diurnal component Qt, whereas the other was based on observations made by the Venus Monitoring Camera (VMC) onboard the Venus Express. The VAFES-LETKF system rapidly reduced the errors between the analysis and forecasts. In addition, the VAFES-LETKF system successfully reproduced the thermal tide excited by the diurnal component of solar heating, even though the second datasets only included horizontal winds at a single altitude on the dayside with a long interval of approximately one Earth day. This advanced system could be useful in the analysis of future datasets from the Venus Climate Orbiter 'Akatsuki'.
An ensemble Kalman filter for atmospheric data assimilation: Application to wind tunnel data
Zheng, D. Q.; Leung, J. K. C.; Lee, B. Y.
2010-05-01
In the previous work ( Zheng et al., 2007, 2009), a data assimilation method, based on ensemble Kalman filter, has been applied to a Monte Carlo Dispersion Model (MCDM). The results were encouraging when the method was tested by the twin experiment and a short-range field experiment. In this technical note, the measured data collected in a wind tunnel experiment have been assimilated into the Monte Carlo dispersion model. The uncertain parameters in the dispersion model, including source term, release height, turbulence intensity and wind direction have been considered. The 3D parameters, i.e. the turbulence intensity and wind direction, have been perturbed by 3D random fields. In order to find the factors which may influence the assimilation results, eight tests with different specifications were carried out. Two strategies of constructing the 3D perturbation field of wind direction were proposed, and the result shows that the two level strategy performs better than the one level strategy. It is also found that proper standard deviation and the correlation radius of the perturbation field play an important role for the data assimilation results.
Sana, Furrukh
2016-02-23
Estimating the locations and the structures of subsurface channels holds significant importance for forecasting the subsurface flow and reservoir productivity. These channels exhibit high permeability and are easily contrasted from the low-permeability rock formations in their surroundings. This enables formulating the flow channels estimation problem as a sparse field recovery problem. The ensemble Kalman filter (EnKF) is a widely used technique for the estimation and calibration of subsurface reservoir model parameters, such as permeability. However, the conventional EnKF framework does not provide an efficient mechanism to incorporate prior information on the wide varieties of subsurface geological structures, and often fails to recover and preserve flow channel structures. Recent works in the area of compressed sensing (CS) have shown that estimating in a sparse domain, using algorithms such as the orthogonal matching pursuit (OMP), may significantly improve the estimation quality when dealing with such problems. We propose two new, and computationally efficient, algorithms combining OMP with the EnKF to improve the estimation and recovery of the subsurface geological channels. Numerical experiments suggest that the proposed algorithms provide efficient mechanisms to incorporate and preserve structural information in the EnKF and result in significant improvements in recovering flow channel structures.
Ping, Jing
2017-05-19
Optimal management of subsurface processes requires the characterization of the uncertainty in reservoir description and reservoir performance prediction. For fractured reservoirs, the location and orientation of fractures are crucial for predicting production characteristics. With the help of accurate and comprehensive knowledge of fracture distributions, early water/CO 2 breakthrough can be prevented and sweep efficiency can be improved. However, since the rock property fields are highly non-Gaussian in this case, it is a challenge to estimate fracture distributions by conventional history matching approaches. In this work, a method that combines vector-based level-set parameterization technique and ensemble Kalman filter (EnKF) for estimating fracture distributions is presented. Performing the necessary forward modeling is particularly challenging. In addition to the large number of forward models needed, each model is used for sampling of randomly located fractures. Conventional mesh generation for such systems would be time consuming if possible at all. For these reasons, we rely on a novel polyhedral mesh method using the mimetic finite difference (MFD) method. A discrete fracture model is adopted that maintains the full geometry of the fracture network. By using a cut-cell paradigm, a computational mesh for the matrix can be generated quickly and reliably. In this research, we apply this workflow on 2D two-phase fractured reservoirs. The combination of MFD approach, level-set parameterization, and EnKF provides an effective solution to address the challenges in the history matching problem of highly non-Gaussian fractured reservoirs.
Dual states estimation of a subsurface flow-transport coupled model using ensemble Kalman filtering
El Gharamti, Mohamad
2013-10-01
Modeling the spread of subsurface contaminants requires coupling a groundwater flow model with a contaminant transport model. Such coupling may provide accurate estimates of future subsurface hydrologic states if essential flow and contaminant data are assimilated in the model. Assuming perfect flow, an ensemble Kalman filter (EnKF) can be used for direct data assimilation into the transport model. This is, however, a crude assumption as flow models can be subject to many sources of uncertainty. If the flow is not accurately simulated, contaminant predictions will likely be inaccurate even after successive Kalman updates of the contaminant model with the data. The problem is better handled when both flow and contaminant states are concurrently estimated using the traditional joint state augmentation approach. In this paper, we introduce a dual estimation strategy for data assimilation into a one-way coupled system by treating the flow and the contaminant models separately while intertwining a pair of distinct EnKFs, one for each model. The presented strategy only deals with the estimation of state variables but it can also be used for state and parameter estimation problems. This EnKF-based dual state-state estimation procedure presents a number of novel features: (i) it allows for simultaneous estimation of both flow and contaminant states in parallel; (ii) it provides a time consistent sequential updating scheme between the two models (first flow, then transport); (iii) it simplifies the implementation of the filtering system; and (iv) it yields more stable and accurate solutions than does the standard joint approach. We conducted synthetic numerical experiments based on various time stepping and observation strategies to evaluate the dual EnKF approach and compare its performance with the joint state augmentation approach. Experimental results show that on average, the dual strategy could reduce the estimation error of the coupled states by 15% compared with the
Keppenne, Christian L.
2013-01-01
A two-step ensemble recentering Kalman filter (ERKF) analysis scheme is introduced. The algorithm consists of a recentering step followed by an ensemble Kalman filter (EnKF) analysis step. The recentering step is formulated such as to adjust the prior distribution of an ensemble of model states so that the deviations of individual samples from the sample mean are unchanged but the original sample mean is shifted to the prior position of the most likely particle, where the likelihood of each particle is measured in terms of closeness to a chosen subset of the observations. The computational cost of the ERKF is essentially the same as that of a same size EnKF. The ERKF is applied to the assimilation of Argo temperature profiles into the OGCM component of an ensemble of NASA GEOS-5 coupled models. Unassimilated Argo salt data are used for validation. A surprisingly small number (16) of model trajectories is sufficient to significantly improve model estimates of salinity over estimates from an ensemble run without assimilation. The two-step algorithm also performs better than the EnKF although its performance is degraded in poorly observed regions.
Directory of Open Access Journals (Sweden)
Lili Lei
2012-05-01
Full Text Available A hybrid nudging-ensemble Kalman filter (HNEnKF data assimilation approach, explored in the Lorenz three-variable system in Part I, is tested in a two-dimensional shallow-water model for dynamic analysis and numerical weather prediction. The HNEnKF effectively combines the advantages of the ensemble Kalman filter (EnKF and the observation nudging to achieve more gradual and continuous data assimilation by computing the nudging coefficients from the flow-dependent, time-varying error covariances of the EnKF. It can also transform the gain matrix of the EnKF into additional terms in the model's predictive equations to assist the data assimilation process. The HNEnKF is tested for both a wave case and a vortex case with different observation frequencies and observation networks. The HNEnKF generally produces smaller root mean square (RMS errors than either nudging or EnKF alone. It also has better temporal smoothness than the EnKF and lagged ensemble Kalman smoother (EnKS. The HNEnKF allows the gain matrix of the EnKF to be applied gradually in time, reducing the error spikes commonly found around the analysis times when using intermittent data assimilation methods. Therefore, the HNEnKF produces a seamless analysis with better inter-variable consistency and dynamic balance than the intermittent EnKF.
Investigation of flow and transport processes at the MADE site using ensemble Kalman filter
Liu, Gaisheng; Chen, Y.; Zhang, Dongxiao
2008-01-01
In this work the ensemble Kalman filter (EnKF) is applied to investigate the flow and transport processes at the macro-dispersion experiment (MADE) site in Columbus, MS. The EnKF is a sequential data assimilation approach that adjusts the unknown model parameter values based on the observed data with time. The classic advection-dispersion (AD) and the dual-domain mass transfer (DDMT) models are employed to analyze the tritium plume during the second MADE tracer experiment. The hydraulic conductivity (K), longitudinal dispersivity in the AD model, and mass transfer rate coefficient and mobile porosity ratio in the DDMT model, are estimated in this investigation. Because of its sequential feature, the EnKF allows for the temporal scaling of transport parameters during the tritium concentration analysis. Inverse simulation results indicate that for the AD model to reproduce the extensive spatial spreading of the tritium observed in the field, the K in the downgradient area needs to be increased significantly. The estimated K in the AD model becomes an order of magnitude higher than the in situ flowmeter measurements over a large portion of media. On the other hand, the DDMT model gives an estimation of K that is much more comparable with the flowmeter values. In addition, the simulated concentrations by the DDMT model show a better agreement with the observed values. The root mean square (RMS) between the observed and simulated tritium plumes is 0.77 for the AD model and 0.45 for the DDMT model at 328 days. Unlike the AD model, which gives inconsistent K estimates at different times, the DDMT model is able to invert the K values that consistently reproduce the observed tritium concentrations through all times. ?? 2008 Elsevier Ltd. All rights reserved.
Khaki, M.
2017-10-25
Assimilating Gravity Recovery And Climate Experiment (GRACE) data into land hydrological models provides a valuable opportunity to improve the models’ forecasts and increases our knowledge of terrestrial water storages (TWS). The assimilation, however, may harm the consistency between hydrological water fluxes, namely precipitation, evaporation, discharge, and water storage changes. To address this issue, we propose a weak constrained ensemble Kalman filter (WCEnKF) that maintains estimated water budgets in balance with other water fluxes. Therefore, in this study, GRACE terrestrial water storages data are assimilated into the World-Wide Water Resources Assessment (W3RA) hydrological model over the Earth’s land areas covering 2002 – 2012. Multi-mission remotely sensed precipitation measurements from the Tropical Rainfall Measuring Mission (TRMM) and evaporation products from the Moderate Resolution Imaging Spectroradiometer (MODIS), as well as ground-based water discharge measurements are applied to close the water balance equation. The proposed WCEnKF contains two update steps; first, it incorporates observations from GRACE to improve model simulations of water storages, and second, uses the additional observations of precipitation, evaporation, and water discharge to establish the water budget closure. These steps are designed to account for error information associated with the included observation sets during the assimilation process. In order to evaluate the assimilation results, in addition to monitoring the water budget closure errors, in-situ groundwater measurements over the Mississippi River Basin in the US and the Murray-Darling Basin in Australia are used. Our results indicate approximately 24% improvement in the WCEnKF groundwater estimates over both basins compared to the use of (constraint-free) EnKF. WCEnKF also further reduces imbalance errors by approximately 82.53% (on average) and at the same time increases the correlations between the
Khaki, M.; Ait-El-Fquih, B.; Hoteit, I.; Forootan, E.; Awange, J.; Kuhn, M.
2017-12-01
Assimilating Gravity Recovery And Climate Experiment (GRACE) data into land hydrological models provides a valuable opportunity to improve the models' forecasts and increases our knowledge of terrestrial water storages (TWS). The assimilation, however, may harm the consistency between hydrological water fluxes, namely precipitation, evaporation, discharge, and water storage changes. To address this issue, we propose a weak constrained ensemble Kalman filter (WCEnKF) that maintains estimated water budgets in balance with other water fluxes. Therefore, in this study, GRACE terrestrial water storages data are assimilated into the World-Wide Water Resources Assessment (W3RA) hydrological model over the Earth's land areas covering 2002-2012. Multi-mission remotely sensed precipitation measurements from the Tropical Rainfall Measuring Mission (TRMM) and evaporation products from the Moderate Resolution Imaging Spectroradiometer (MODIS), as well as ground-based water discharge measurements are applied to close the water balance equation. The proposed WCEnKF contains two update steps; first, it incorporates observations from GRACE to improve model simulations of water storages, and second, uses the additional observations of precipitation, evaporation, and water discharge to establish the water budget closure. These steps are designed to account for error information associated with the included observation sets during the assimilation process. In order to evaluate the assimilation results, in addition to monitoring the water budget closure errors, in situ groundwater measurements over the Mississippi River Basin in the US and the Murray-Darling Basin in Australia are used. Our results indicate approximately 24% improvement in the WCEnKF groundwater estimates over both basins compared to the use of (constraint-free) EnKF. WCEnKF also further reduces imbalance errors by approximately 82.53% (on average) and at the same time increases the correlations between the
3D soil water nowcasting using electromagnetic conductivity imaging and the ensemble Kalman filter
Huang, Jingyi; McBratney, Alex B.; Minasny, Budiman; Triantafilis, John
2017-06-01
Mapping and immediate forecasting of soil water content (θ) and its movement can be challenging. Although inversion of apparent electrical conductivity (ECa) measured by electromagnetic induction to calculate depth-specific electrical conductivity (σ) has been used, it is difficult to apply it across a field. In this paper we use a calibration established along a transect, across a 3.94-ha field with varying soil texture, using an ensemble Kalman filter (EnKF) to monitor and nowcast the 3-dimensional θ dynamics on 16 separate days over a period of 38 days. The EnKF combined a physical model fitted with θ measured by soil moisture sensors and an Artificial Neural Network model comprising σ generated by quasi-3d inversions of DUALEM-421S ECa data. Results showed that the distribution of θ was controlled by soil texture, topography, and vegetation. Soil water dried fastest at the beginning after the initial irrigation event and decreased with time and soil depth, which was consistent with classical soil drying theory and experiments. It was also found that the soil dried fastest in the loamy and duplex soils present in the field, which was attributable to deep drainage and preferential flow. It was concluded that the EnKF approach can be used to improve the irrigation efficiency by applying variable irrigation rates across the field. In addition, soil water status can be nowcasted across large spatial extents using this method with weather forecast information, which will provide guidance to farmers for real-time irrigation management.
Energy Technology Data Exchange (ETDEWEB)
Zhang, X.L.; Su, G.F.; Chen, J.G. [Institute of Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing 100084 (China); Raskob, W. [Institute for Nuclear and Energy Technologies, Karlsruhe Institute of Technology, Karlsruhe, D-76021 (Germany); Yuan, H.Y., E-mail: hy-yuan@outlook.com [Institute of Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing 100084 (China); Huang, Q.Y. [Institute of Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing 100084 (China)
2015-10-30
Highlights: • We integrate the iterative EnKF method into the POLYPHEMUS platform. • We thoroughly evaluate the data assimilation system against the Kincaid dataset. • The data assimilation system substantially improves the model predictions. • More than 60% of the retrieved emissions are within a factor two of actual values. • The results reveal that the boundary layer height is the key influential factor. - Abstract: Information about atmospheric dispersion of radionuclides is vitally important for planning effective countermeasures during nuclear accidents. Results of dispersion models have high spatial and temporal resolutions, but they are not accurate enough due to the uncertain source term and the errors in meteorological data. Environmental measurements are more reliable, but they are scarce and unable to give forecasts. In this study, our newly proposed iterative ensemble Kalman filter (EnKF) data assimilation scheme is used to combine model results and environmental measurements. The system is thoroughly validated against the observations in the Kincaid tracer experiment. The initial first-guess emissions are assumed to be six magnitudes underestimated. The iterative EnKF system rapidly corrects the errors in the emission rate and wind data, thereby significantly improving the model results (>80% reduction of the normalized mean square error, r = 0.71). Sensitivity tests are conducted to investigate the influence of meteorological parameters. The results indicate that the system is sensitive to boundary layer height. When the heights from the numerical weather prediction model are used, only 62.5% of reconstructed emission rates are within a factor two of the actual emissions. This increases to 87.5% when the heights derived from the on-site observations are used.
Fan, Y. R.; Huang, G. H.; Baetz, B. W.; Li, Y. P.; Huang, K.; Chen, X.; Gao, M.
2017-07-01
This study improved hydrologic data assimilation through integrating the capabilities of particle filter (PF) and ensemble Kalman filter (EnKF) methods, leading to two integrated data assimilation schemes: the coupled EnKF and PF (CEnPF) and parallelized EnKF and PF (PEnPF) approaches. The applicability and usefulness of CEnPF and PEnPF were demonstrated using a conceptual rainfall-runoff model. The performance of two new developed data assimilation methods and traditional EnKF and PF approaches was tested through a synthetic experiment and two real-world cases with one located in the Jing River basin and one located in the Yangtze River basin. The results show that both PEnPF and CEnPF approaches have more opportunities to provide better results for both deterministic and probabilistic predictions than traditional EnKF and PF approaches. Moreover, the computational time of the two integrated methods is manageable. But the proposed PEnPF may need much more time for some large-scale or time-consuming hydrologic models since it generally needs three times of model runs used by EnKF, PF and CEnPF.
Final Technical Report [Carbon Data Assimilation with a Coupled Ensemble Kalman Filter
Energy Technology Data Exchange (ETDEWEB)
Kalnay, Eugenia
2013-08-30
We proposed (and accomplished) the development of an Ensemble Kalman Filter (EnKF) approach for the estimation of surface carbon fluxes as if they were parameters, augmenting the model with them. Our system is quite different from previous approaches, such as carbon flux inversions, 4D-Var, and EnKF with approximate background error covariance (Peters et al., 2008). We showed (using observing system simulation experiments, OSSEs) that these differences lead to a more accurate estimation of the evolving surface carbon fluxes at model grid-scale resolution. The main properties of the LETKF-C are: a) The carbon cycle LETKF is coupled with the simultaneous assimilation of the standard atmospheric variables, so that the ensemble wind transport of the CO2 provides an estimation of the carbon transport uncertainty. b) The use of an assimilation window (6hr) much shorter than the months-long windows used in other methods. This avoids the inevitable “blurring” of the signal that takes place in long windows due to turbulent mixing since the CO2 does not have time to mix before the next window. In this development we introduced new, advanced techniques that have since been adopted by the EnKF community (Kang, 2009, Kang et al., 2011, Kang et al. 2012). These advances include “variable localization” that reduces sampling errors in the estimation of the forecast error covariance, more advanced adaptive multiplicative and additive inflations, and vertical localization based on the time scale of the processes. The main result has been obtained using the LETKF-C with all these advances, and assimilating simulated atmospheric CO2 observations from different observing systems (surface flask observations of CO2 but no surface carbon fluxes observations, total column CO2 from GoSAT/OCO-2, and upper troposphere AIRS retrievals). After a spin-up of about one month, the LETKF-C succeeded in reconstructing the true evolving surface fluxes of carbon at a model grid
Final report on "Carbon Data Assimilation with a Coupled Ensemble Kalman Filter"
Energy Technology Data Exchange (ETDEWEB)
Kalnay, Eugenia; Kang, Ji-Sun; Fung, Inez
2014-07-23
We proposed (and accomplished) the development of an Ensemble Kalman Filter (EnKF) approach for the estimation of surface carbon fluxes as if they were parameters, augmenting the model with them. Our system is quite different from previous approaches, such as carbon flux inversions, 4D-Var, and EnKF with approximate background error covariance (Peters et al., 2008). We showed (using observing system simulation experiments, OSSEs) that these differences lead to a more accurate estimation of the evolving surface carbon fluxes at model grid-scale resolution. The main properties of the LETKF-C are: a) The carbon cycle LETKF is coupled with the simultaneous assimilation of the standard atmospheric variables, so that the ensemble wind transport of the CO2 provides an estimation of the carbon transport uncertainty. b) The use of an assimilation window (6hr) much shorter than the months-long windows used in other methods. This avoids the inevitable “blurring” of the signal that takes place in long windows due to turbulent mixing since the CO2 does not have time to mix before the next window. In this development we introduced new, advanced techniques that have since been adopted by the EnKF community (Kang, 2009, Kang et al., 2011, Kang et al. 2012). These advances include “variable localization” that reduces sampling errors in the estimation of the forecast error covariance, more advanced adaptive multiplicative and additive inflations, and vertical localization based on the time scale of the processes. The main result has been obtained using the LETKF-C with all these advances, and assimilating simulated atmospheric CO2 observations from different observing systems (surface flask observations of CO2 but no surface carbon fluxes observations, total column CO2 from GoSAT/OCO-2, and upper troposphere AIRS retrievals). After a spin-up of about one month, the LETKF-C succeeded in reconstructing the true evolving surface fluxes of carbon at a model grid resolution. When
Ensemble unscented Kalman filter for state inference in continuous–discrete systems
Directory of Open Access Journals (Sweden)
Bin Liu
2014-05-01
Full Text Available The authors consider non-linear state filtering problem in continuous–discrete systems, where the system dynamics is modelled by a stochastic differential equation, and noisy measurements of the system are obtained at discrete time instances. A novel particle method is proposed based on sequential importance sampling. This approach uses a bank of the continuous–discrete unscented Kalman filters (CDUKFs to obtain the importance proposal distribution, retaining the advantage of the CDUKF in continuous–discrete systems as well as the accuracy of particle filter in highly non-linear systems. Simulation results show that the algorithm outperforms some other benchmarks substantially in estimation accuracy.
Triantafyllou, George N.
2013-09-01
An application of an ensemble-based robust filter for data assimilation into an ecosystem model of the Cretan Sea is presented and discussed. The ecosystem model comprises two on-line coupled sub-models: the Princeton Ocean Model (POM) and the European Regional Seas Ecosystem Model (ERSEM). The filtering scheme is based on the Singular Evolutive Interpolated Kalman (SEIK) filter which is implemented with a time-local H∞ filtering strategy to enhance robustness and performances during periods of strong ecosystem variability. Assimilation experiments in the Cretan Sea indicate that robustness can be achieved in the SEIK filter by introducing an adaptive inflation scheme of the modes of the filter error covariance matrix. Twin-experiments are performed to evaluate the performance of the assimilation system and to study the benefits of using robust filtering in an ensemble filtering framework. Pseudo-observations of surface chlorophyll, extracted from a model reference run, were assimilated every two days. Simulation results suggest that the adaptive inflation scheme significantly improves the behavior of the SEIK filter during periods of strong ecosystem variability. © 2012 Elsevier B.V.
El Gharamti, Mohamad
2015-11-26
The ensemble Kalman filter (EnKF) recursively integrates field data into simulation models to obtain a better characterization of the model’s state and parameters. These are generally estimated following a state-parameters joint augmentation strategy. In this study, we introduce a new smoothing-based joint EnKF scheme, in which we introduce a one-step-ahead smoothing of the state before updating the parameters. Numerical experiments are performed with a two-dimensional synthetic subsurface contaminant transport model. The improved performance of the proposed joint EnKF scheme compared to the standard joint EnKF compensates for the modest increase in the computational cost.
History Matching of 4D Seismic Data Attributes using the Ensemble Kalman Filter
Ravanelli, Fabio M.
2013-05-01
One of the most challenging tasks in the oil industry is the production of reliable reservoir forecast models. Because of different sources of uncertainties the numerical models employed are often only crude approximations of the reality. This problem is tackled by the conditioning of the model with production data through data assimilation. This process is known in the oil industry as history matching. Several recent advances are being used to improve history matching reliability, notably the use of time-lapse seismic data and automated history matching software tools. One of the most promising data assimilation techniques employed in the oil industry is the ensemble Kalman filter (EnKF) because its ability to deal with highly non-linear models, low computational cost and easy computational implementation when compared with other methods. A synthetic reservoir model was used in a history matching study designed to predict the peak production allowing decision makers to properly plan field development actions. If only production data is assimilated, a total of 12 years of historical data is required to properly characterize the production uncertainty and consequently the correct moment to take actions and decommission the field. However if time-lapse seismic data is available this conclusion can be reached 4 years in advance due to the additional fluid displacement information obtained with the seismic data. Production data provides geographically sparse data in contrast with seismic data which are sparse in time. Several types of seismic attributes were tested in this study. Poisson’s ratio proved to be the most sensitive attribute to fluid displacement. In practical applications, however the use of this attribute is usually avoided due to poor quality of the data. Seismic impedance tends to be more reliable. Finally, a new conceptual idea was proposed to obtain time-lapse information for a history matching study. The use of crosswell time-lapse seismic
Assimilation of IASI partial tropospheric columns with an Ensemble Kalman Filter over Europe
Directory of Open Access Journals (Sweden)
A. Coman
2012-03-01
Full Text Available Partial lower tropospheric ozone columns provided by the IASI (Infrared Atmospheric Sounding Interferometer instrument have been assimilated into a chemistry-transport model at continental scale (CHIMERE using an Ensemble Square Root Kalman Filter (EnSRF. Analyses are made for the month of July 2007 over the European domain. Launched in 2006, aboard the MetOp-A satellite, IASI shows high sensitivity for ozone in the free troposphere and low sensitivity at the ground; therefore it is important to evaluate if assimilation of these observations can improve free tropospheric ozone, and possibly surface ozone. The analyses are validated against independent ozone observations from sondes, MOZAIC^{1} aircraft and ground based stations (AIRBASE – the European Air quality dataBase and compared with respect to the free run of CHIMERE. These comparisons show a decrease in error of 6 parts-per-billion (ppb in the free troposphere over the Frankfurt area, and also a reduction of the root mean square error (respectively bias at the surface of 19% (33% for more than 90% of existing ground stations. This provides evidence of the potential of data assimilation of tropospheric IASI columns to better describe the tropospheric ozone distribution, including surface ozone, despite the lower sensitivity.
The changes in concentration resulting from the observational constraints were quantified and several geophysical explanations for the findings of this study were drawn. The corrections were most pronounced over Italy and the Mediterranean region, we noted an average reduction of 8–9 ppb in the free troposphere with respect to the free run, and still a reduction of 5.5 ppb at ground, likely due to a longer residence time of air masses in this part associated to the general circulation pattern (i.e. dominant western circulation and to persistent anticyclonic conditions over the Mediterranean basin. This is an important geophysical result, since the
Directory of Open Access Journals (Sweden)
J. H. Lee
2012-11-01
Full Text Available Aerodynamic roughness height (Z_{om} is a key parameter required in several land surface hydrological models, since errors in heat flux estimation are largely dependent on optimization of this input. Despite its significance, it remains an uncertain parameter which is not readily determined. This is mostly because of non-linear relationship in Monin-Obukhov similarity (MOS equations and uncertainty of vertical characteristic of vegetation in a large scale. Previous studies often determined aerodynamic roughness using a minimization of cost function over MOS relationship or linear regression over it, traditional wind profile method, or remotely sensed vegetation index. However, these are complicated procedures that require a high accuracy for several other related parameters embedded in serveral equations including MOS. In order to simplify this procedure and reduce the number of parameters in need, this study suggests a new approach to extract aerodynamic roughness parameter from single or two heat flux measurements analyzed via Ensemble Kalman Filter (EnKF that affords non-linearity. So far, to our knowledge, no previous study has applied EnKF to aerodynamic roughness estimation, while the majority of data assimilation study have paid attention to updates of other land surface state variables such as soil moisture or land surface temperature. The approach of this study was applied to grassland in semi-arid Tibetan Plateau and maize on moderately wet condition in Italy. It was demonstrated that aerodynamic roughness parameter can be inversely tracked from heat flux EnKF final analysis. The aerodynamic roughness height estimated in this approach was consistent with eddy covariance method and literature value. Through a calibration of this parameter, this adjusted the sensible heat previously overestimated and latent heat flux previously underestimated by the original Surface Energy Balance System (SEBS model. It was considered that
Directory of Open Access Journals (Sweden)
L. Li
2012-02-01
Full Text Available The normal-score ensemble Kalman filter (NS-EnKF is tested on a synthetic aquifer characterized by the presence of channels with a bimodal distribution of its hydraulic conductivities. This is a clear example of an aquifer that cannot be characterized by a multiGaussian distribution. Fourteen scenarios are analyzed which differ among them in one or various of the following aspects: the prior random function model, the boundary conditions of the flow problem, the number of piezometers used in the assimilation process, or the use of covariance localization in the implementation of the Kalman filter. The performance of the NS-EnKF is evaluated through the ensemble mean and variance maps, the connectivity patterns of the individual conductivity realizations and the degree of reproduction of the piezometric heads. The results show that (i the localized NS-EnKF can characterize the non-multiGaussian underlying hydraulic distribution even when an erroneous prior random function model is used, (ii localization plays an important role to prevent filter inbreeding and results in a better logconductivity characterization, and (iii the NS-EnKF works equally well under very different flow configurations.
Directory of Open Access Journals (Sweden)
Lili Lei
2012-05-01
Full Text Available A hybrid data assimilation approach combining nudging and the ensemble Kalman filter (EnKF for dynamic analysis and numerical weather prediction is explored here using the non-linear Lorenz three-variable model system with the goal of a smooth, continuous and accurate data assimilation. The hybrid nudging-EnKF (HNEnKF computes the hybrid nudging coefficients from the flow-dependent, time-varying error covariance matrix from the EnKF's ensemble forecasts. It extends the standard diagonal nudging terms to additional off-diagonal statistical correlation terms for greater inter-variable influence of the innovations in the model's predictive equations to assist in the data assimilation process. The HNEnKF promotes a better fit of an analysis to data compared to that achieved by either nudging or incremental analysis update (IAU. When model error is introduced, it produces similar or better root mean square errors compared to the EnKF while minimising the error spikes/discontinuities created by the intermittent EnKF. It provides a continuous data assimilation with better inter-variable consistency and improved temporal smoothness than that of the EnKF. Data assimilation experiments are also compared to the ensemble Kalman smoother (EnKS. The HNEnKF has similar or better temporal smoothness than that of the EnKS, and with much smaller central processing unit (CPU time and data storage requirements.
Generic Kalman Filter Software
Lisano, Michael E., II; Crues, Edwin Z.
2005-01-01
The Generic Kalman Filter (GKF) software provides a standard basis for the development of application-specific Kalman-filter programs. Historically, Kalman filters have been implemented by customized programs that must be written, coded, and debugged anew for each unique application, then tested and tuned with simulated or actual measurement data. Total development times for typical Kalman-filter application programs have ranged from months to weeks. The GKF software can simplify the development process and reduce the development time by eliminating the need to re-create the fundamental implementation of the Kalman filter for each new application. The GKF software is written in the ANSI C programming language. It contains a generic Kalman-filter-development directory that, in turn, contains a code for a generic Kalman filter function; more specifically, it contains a generically designed and generically coded implementation of linear, linearized, and extended Kalman filtering algorithms, including algorithms for state- and covariance-update and -propagation functions. The mathematical theory that underlies the algorithms is well known and has been reported extensively in the open technical literature. Also contained in the directory are a header file that defines generic Kalman-filter data structures and prototype functions and template versions of application-specific subfunction and calling navigation/estimation routine code and headers. Once the user has provided a calling routine and the required application-specific subfunctions, the application-specific Kalman-filter software can be compiled and executed immediately. During execution, the generic Kalman-filter function is called from a higher-level navigation or estimation routine that preprocesses measurement data and post-processes output data. The generic Kalman-filter function uses the aforementioned data structures and five implementation- specific subfunctions, which have been developed by the user on
Iglesias, Marco
2017-11-26
In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analogous to our previously proposed approach [1,2], for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary value problems when the boundary data are noisy. We apply EnMKF to infer the thermal properties of building walls and to estimate the corresponding heat flux from real and synthetic data. Compared with a modified Ensemble Kalman Filter (EnKF) that is not marginalized, EnMKF reduces the bias error, avoids the collapse of the ensemble without needing to add inflation, and converges to the mean field posterior using $50\\\\%$ or less of the ensemble size required by EnKF. According to our results, the marginalization technique in EnMKF is key to performance improvement with smaller ensembles at any fixed time.
Directory of Open Access Journals (Sweden)
J. I. Allen
2003-01-01
Full Text Available The purpose of this paper is to examine the use of a complex ecosystem model along with near real-time in situ data and a sequential data assimilation method for state estimation. The ecosystem model used is the European Regional Seas Ecosystem Model (ERSEM; Baretta et al., 1995 and the assimilation method chosen is the Ensemble Kalman Filer (EnKF. Previously, it has been shown that this method captures the nonlinear error evolution in time and is capable of both tracking the observations and providing realistic error estimates for the estimated state. This system has been used to assimilate long time series of in situ chlorophyll taken from a data buoy in the Cretan Sea. The assimilation of this data using the EnKF method results in a marked improvement in the ability of ERSEM to hindcast chlorophyll. The sensitivity of this system to the type of data used for assimilation, the frequency of assimilation, ensemble size and model errors is discussed. The predictability window of the EnKF appears to be at least 2 days. This is an indication that the methodology might be suitable for future operational data assimilation systems using more complex three-dimensional models. Key words. Oceanography: general (numerical modelling; ocean prediction – Oceanography: biological and chemical (plankton
Directory of Open Access Journals (Sweden)
J. I. Allen
Full Text Available The purpose of this paper is to examine the use of a complex ecosystem model along with near real-time in situ data and a sequential data assimilation method for state estimation. The ecosystem model used is the European Regional Seas Ecosystem Model (ERSEM; Baretta et al., 1995 and the assimilation method chosen is the Ensemble Kalman Filer (EnKF. Previously, it has been shown that this method captures the nonlinear error evolution in time and is capable of both tracking the observations and providing realistic error estimates for the estimated state. This system has been used to assimilate long time series of in situ chlorophyll taken from a data buoy in the Cretan Sea. The assimilation of this data using the EnKF method results in a marked improvement in the ability of ERSEM to hindcast chlorophyll. The sensitivity of this system to the type of data used for assimilation, the frequency of assimilation, ensemble size and model errors is discussed. The predictability window of the EnKF appears to be at least 2 days. This is an indication that the methodology might be suitable for future operational data assimilation systems using more complex three-dimensional models.
Key words. Oceanography: general (numerical modelling; ocean prediction – Oceanography: biological and chemical (plankton
Energy Technology Data Exchange (ETDEWEB)
Moreno, David Leonardo
2009-04-15
In the present work a coupling methodology between level set methods and the ensemble Kalman filter (EnKF) for modeling and conditioning geological facies with respect to production and, well data is presented. The modeling of the facies is based on the concept of implicit interfaces where level set methods are used to add dynamics to the implicit interfaces. The conditioning of the facies models is done through the application of the ensemble Kalman filter (EnKF), a sequential Bayesian inversion technique completely automatic that does not require the calculation of gradients or uses the information of previous states. The EnKF has been presented as an evolution of the extended Kalman filter (EKF) that solves the problem of the unbounded error growth of the covariance of a non-linear dynamical system by extending the traditional Kalman filter(KF) to a Monte Carlo ensemble type filter where the covariance representation is centered on the first moment of an ensemble distribution instead of the unknown true model, however, for the problem to be well defined, the parameters to be estimated should still be Gaussian or approximately Gaussian. For updating facies models defined as highly non-Gaussian systems the EnKF fails at first, since if facies types with different petrophysical properties are mixed, the generated petrophysical model will have some average properties that do not behave like any of the original facies types. The methodology presented in this work is designed to avoid the problem of the non-Gaussianity provided by facies models by applying a transformation of the facies into implicit interfaces and uses a more Gaussian variable to perturb and move the implicit representations of the facies. The result is a methodology that conditions Gaussian random fields (GRFs) to production and well data with the EnKF, later used as velocity fields in the level set equations for moving boundaries between facies systems with the purpose of obtaining good topological
Data from modern soil water contents probes can be used for data assimilation in soil water flow modeling, i.e. continual correction of the flow model performance based on observations. The ensemble Kalman filter appears to be an appropriate method for that. The method requires estimates of the unce...
Calibration of sea ice dynamic parameters in an ocean-sea ice model using an ensemble Kalman filter
Massonnet, F.; Goosse, H.; Fichefet, T.; Counillon, F.
2014-07-01
The choice of parameter values is crucial in the course of sea ice model development, since parameters largely affect the modeled mean sea ice state. Manual tuning of parameters will soon become impractical, as sea ice models will likely include more parameters to calibrate, leading to an exponential increase of the number of possible combinations to test. Objective and automatic methods for parameter calibration are thus progressively called on to replace the traditional heuristic, "trial-and-error" recipes. Here a method for calibration of parameters based on the ensemble Kalman filter is implemented, tested and validated in the ocean-sea ice model NEMO-LIM3. Three dynamic parameters are calibrated: the ice strength parameter P*, the ocean-sea ice drag parameter Cw, and the atmosphere-sea ice drag parameter Ca. In twin, perfect-model experiments, the default parameter values are retrieved within 1 year of simulation. Using 2007-2012 real sea ice drift data, the calibration of the ice strength parameter P* and the oceanic drag parameter Cw improves clearly the Arctic sea ice drift properties. It is found that the estimation of the atmospheric drag Ca is not necessary if P* and Cw are already estimated. The large reduction in the sea ice speed bias with calibrated parameters comes with a slight overestimation of the winter sea ice areal export through Fram Strait and a slight improvement in the sea ice thickness distribution. Overall, the estimation of parameters with the ensemble Kalman filter represents an encouraging alternative to manual tuning for ocean-sea ice models.
Gharamti, M. E.
2014-03-01
Isothermal compositional flow models require coupling transient compressible flows and advective transport systems of various chemical species in subsurface porous media. Building such numerical models is quite challenging and may be subject to many sources of uncertainties because of possible incomplete representation of some geological parameters that characterize the system\\'s processes. Advanced data assimilation methods, such as the ensemble Kalman filter (EnKF), can be used to calibrate these models by incorporating available data. In this work, we consider the problem of estimating reservoir permeability using information about phase pressure as well as the chemical properties of fluid components. We carry out state-parameter estimation experiments using joint and dual updating schemes in the context of the EnKF with a two-dimensional single-phase compositional flow model (CFM). Quantitative and statistical analyses are performed to evaluate and compare the performance of the assimilation schemes. Our results indicate that including chemical composition data significantly enhances the accuracy of the permeability estimates. In addition, composition data provide more information to estimate system states and parameters than do standard pressure data. The dual state-parameter estimation scheme provides about 10% more accurate permeability estimates on average than the joint scheme when implemented with the same ensemble members, at the cost of twice more forward model integrations. At similar computational cost, the dual approach becomes only beneficial after using large enough ensembles.
DEFF Research Database (Denmark)
Drecourt, J.-P.; Madsen, H.; Rosbjerg, Dan
2006-01-01
This paper reviews two different approaches that have been proposed to tackle the problems of model bias with the Kalman filter: the use of a colored noise model and the implementation of a separate bias filter. Both filters are implemented with and without feedback of the bias into the model sta...
Fu, Guangliang; Lin, Hai Xiang; Heemink, Arnold; Segers, Arjo; Verlaan, Martin; Lu, Tongchao; Lu, Sha
2017-04-01
After the eruption of volcano Eyjafjallajökull in 2010, which had a huge impact to aviation and economy, improvements of volcanic ash forecasts have been put onto the research agenda. Data assimilation uses observations to improve the forecast accuracy. Among the data assimilation approaches, the ensemble Kalman filter (EnKF) is a well-known and popular method. A proper covariance localization strategy in the analysis step of EnKF is essential for reducing spurious covariances caused by the finite ensemble size, as shown for this application for assimilation of aircraft in situ measurements. After analyzing the characteristics of the physical forecast error covariances, we present a two-way tracking approach to define the localization matrix for covariance localization. The result shows that the Two-way-tracking Localized EnKF (TL-EnKF) effectively maintains the correctly specified physical covariances and largely reduces the spurious ones. The computational cost of TL-EnKF is also evaluated and is shown to be advantageous for both serial and parallel implementations. Compared to the commonly used distance-based covariance localization, the two-way tracking approach is shown to be more suitable. In addition, the covariance inflation approach is verified as an additional improvement to TL-EnKF to achieve more accurate results.
Directory of Open Access Journals (Sweden)
Chih-Chien Tsai
2014-03-01
Full Text Available This study develops a Doppler radar data assimilation system, which couples the local ensemble transform Kalman filter with the Weather Research and Forecasting model. The benefits of this system to quantitative precipitation nowcasting (QPN are evaluated with observing system simulation experiments on Typhoon Morakot (2009, which brought record-breaking rainfall and extensive damage to central and southern Taiwan. The results indicate that the assimilation of radial velocity and reflectivity observations improves the three-dimensional winds and rain-mixing ratio most significantly because of the direct relations in the observation operator. The patterns of spiral rainbands become more consistent between different ensemble members after radar data assimilation. The rainfall intensity and distribution during the 6-hour deterministic nowcast are also improved, especially for the first 3 hours. The nowcasts with and without radar data assimilation have similar evolution trends driven by synoptic-scale conditions. Furthermore, we carry out a series of sensitivity experiments to develop proper assimilation strategies, in which a mixed localisation method is proposed for the first time and found to give further QPN improvement in this typhoon case.
Energy Technology Data Exchange (ETDEWEB)
Ham, Yoo-Geun [NASA/GSFC Code 610.1, Global Modeling and Assimilation Office, Greenbelt, MD (United States); Universities Space Research Association, Goddard Earth Sciences Technology and Research Studies and Investigations, Baltimore, MD (United States); Rienecker, Michele M. [NASA/GSFC Code 610.1, Global Modeling and Assimilation Office, Greenbelt, MD (United States)
2012-10-15
In this study, a new approach for extracting flow-dependent empirical singular vectors (FESVs) for seasonal prediction using ensemble perturbations obtained from an ensemble Kalman filter (EnKF) assimilation is presented. Due to the short interval between analyses, EnKF perturbations primarily contain instabilities related to fast weather variability. To isolate slower, coupled instabilities that would be more suitable for seasonal prediction, an empirical linear operator for seasonal time-scales (i.e. several months) is formulated using a causality hypothesis; then, the most unstable mode from the linear operator is extracted for seasonal time-scales. It is shown that the flow-dependent operator represents nonlinear integration results better than a conventional empirical linear operator static in time. Through 20 years of retrospective seasonal predictions, it is shown that the skill of forecasting equatorial SST anomalies using the FESV is systematically improved over that using Conventional ESV (CESV). For example, the correlation skill of the NINO3 SST index using FESV is higher, by about 0.1, than that of CESV at 8-month leads. In addition, the forecast skill improvement is significant over the locations where the correlation skill of conventional methods is relatively low, indicating that the FESV is effective where the initial uncertainty is large. (orig.)
Gharamti, M. E.
2015-05-11
The ensemble Kalman filter (EnKF) is a popular method for state-parameters estimation of subsurface flow and transport models based on field measurements. The common filtering procedure is to directly update the state and parameters as one single vector, which is known as the Joint-EnKF. In this study, we follow the one-step-ahead smoothing formulation of the filtering problem, to derive a new joint-based EnKF which involves a smoothing step of the state between two successive analysis steps. The new state-parameters estimation scheme is derived in a consistent Bayesian filtering framework and results in separate update steps for the state and the parameters. This new algorithm bears strong resemblance with the Dual-EnKF, but unlike the latter which first propagates the state with the model then updates it with the new observation, the proposed scheme starts by an update step, followed by a model integration step. We exploit this new formulation of the joint filtering problem and propose an efficient model-integration-free iterative procedure on the update step of the parameters only for further improved performances. Numerical experiments are conducted with a two-dimensional synthetic subsurface transport model simulating the migration of a contaminant plume in a heterogenous aquifer domain. Contaminant concentration data are assimilated to estimate both the contaminant state and the hydraulic conductivity field. Assimilation runs are performed under imperfect modeling conditions and various observational scenarios. Simulation results suggest that the proposed scheme efficiently recovers both the contaminant state and the aquifer conductivity, providing more accurate estimates than the standard Joint and Dual EnKFs in all tested scenarios. Iterating on the update step of the new scheme further enhances the proposed filter’s behavior. In term of computational cost, the new Joint-EnKF is almost equivalent to that of the Dual-EnKF, but requires twice more model
Multilevel Mixture Kalman Filter
Directory of Open Access Journals (Sweden)
Xiaodong Wang
2004-11-01
Full Text Available The mixture Kalman filter is a general sequential Monte Carlo technique for conditional linear dynamic systems. It generates samples of some indicator variables recursively based on sequential importance sampling (SIS and integrates out the linear and Gaussian state variables conditioned on these indicators. Due to the marginalization process, the complexity of the mixture Kalman filter is quite high if the dimension of the indicator sampling space is high. In this paper, we address this difficulty by developing a new Monte Carlo sampling scheme, namely, the multilevel mixture Kalman filter. The basic idea is to make use of the multilevel or hierarchical structure of the space from which the indicator variables take values. That is, we draw samples in a multilevel fashion, beginning with sampling from the highest-level sampling space and then draw samples from the associate subspace of the newly drawn samples in a lower-level sampling space, until reaching the desired sampling space. Such a multilevel sampling scheme can be used in conjunction with the delayed estimation method, such as the delayed-sample method, resulting in delayed multilevel mixture Kalman filter. Examples in wireless communication, specifically the coherent and noncoherent 16-QAM over flat-fading channels, are provided to demonstrate the performance of the proposed multilevel mixture Kalman filter.
Energy Technology Data Exchange (ETDEWEB)
Juxiu Tong; Bill X. Hu; Hai Huang; Luanjin Guo; Jinzhong Yang
2014-03-01
With growing importance of water resources in the world, remediations of anthropogenic contaminations due to reactive solute transport become even more important. A good understanding of reactive rate parameters such as kinetic parameters is the key to accurately predicting reactive solute transport processes and designing corresponding remediation schemes. For modeling reactive solute transport, it is very difficult to estimate chemical reaction rate parameters due to complex processes of chemical reactions and limited available data. To find a method to get the reactive rate parameters for the reactive urea hydrolysis transport modeling and obtain more accurate prediction for the chemical concentrations, we developed a data assimilation method based on an ensemble Kalman filter (EnKF) method to calibrate reactive rate parameters for modeling urea hydrolysis transport in a synthetic one-dimensional column at laboratory scale and to update modeling prediction. We applied a constrained EnKF method to pose constraints to the updated reactive rate parameters and the predicted solute concentrations based on their physical meanings after the data assimilation calibration. From the study results we concluded that we could efficiently improve the chemical reactive rate parameters with the data assimilation method via the EnKF, and at the same time we could improve solute concentration prediction. The more data we assimilated, the more accurate the reactive rate parameters and concentration prediction. The filter divergence problem was also solved in this study.
Directory of Open Access Journals (Sweden)
C. L. Keppenne
2005-01-01
Full Text Available To compensate for a poorly known geoid, satellite altimeter data is usually analyzed in terms of anomalies from the time mean record. When such anomalies are assimilated into an ocean model, the bias between the climatologies of the model and data is problematic. An ensemble Kalman filter (EnKF is modified to account for the presence of a forecast-model bias and applied to the assimilation of TOPEX/Poseidon (T/P altimeter data. The online bias correction (OBC algorithm uses the same ensemble of model state vectors to estimate biased-error and unbiased-error covariance matrices. Covariance localization is used but the bias covariances have different localization scales from the unbiased-error covariances, thereby accounting for the fact that the bias in a global ocean model could have much larger spatial scales than the random error.The method is applied to a 27-layer version of the Poseidon global ocean general circulation model with about 30-million state variables. Experiments in which T/P altimeter anomalies are assimilated show that the OBC reduces the RMS observation minus forecast difference for sea-surface height (SSH over a similar EnKF run in which OBC is not used. Independent in situ temperature observations show that the temperature field is also improved. When the T/P data and in situ temperature data are assimilated in the same run and the configuration of the ensemble at the end of the run is used to initialize the ocean component of the GMAO coupled forecast model, seasonal SSH hindcasts made with the coupled model are generally better than those initialized with optimal interpolation of temperature observations without altimeter data. The analysis of the corresponding sea-surface temperature hindcasts is not as conclusive.
Camporese, Matteo; Cassiani, Giorgio; Deiana, Rita; Salandin, Paolo; Binley, Andrew
2015-05-01
Recent advances in geophysical methods have been increasingly exploited as inverse modeling tools in groundwater hydrology. In particular, several attempts to constrain the hydrogeophysical inverse problem to reduce inversion errors have been made using time-lapse geophysical measurements through both coupled and uncoupled (also known as sequential) inversion approaches. Despite the appeal and popularity of coupled inversion approaches, their superiority over uncoupled methods has not been proved conclusively; the goal of this work is to provide an objective comparison between the two approaches within a specific inversion modeling framework based on the ensemble Kalman filter (EnKF). Using EnKF and a model of Lagrangian transport, we compare the performance of a fully coupled and uncoupled inversion method for the reconstruction of heterogeneous saturated hydraulic conductivity fields through the assimilation of ERT-monitored tracer test data. The two inversion approaches are tested in a number of different scenarios, including isotropic and anisotropic synthetic aquifers, where we change the geostatistical parameters used to generate the prior ensemble of hydraulic conductivity fields. Our results show that the coupled approach outperforms the uncoupled when the prior statistics are close to the ones used to generate the true field. Otherwise, the coupled approach is heavily affected by "filter inbreeding" (an undesired effect of variance underestimation typical of EnKF), while the uncoupled approach is more robust, being able to correct biased prior information, thanks to its capability of capturing the solute travel times even in presence of inversion artifacts such as the violation of mass balance. Furthermore, the coupled approach is more computationally intensive than the uncoupled, due to the much larger number of forward runs required by the electrical model. Overall, we conclude that the relative merit of the coupled versus the uncoupled approach cannot
Hut, Rolf; Amisigo, Barnabas A.; Steele-Dunne, Susan; van de Giesen, Nick
2015-12-01
Reduction of Used Memory Ensemble Kalman Filtering (RumEnKF) is introduced as a variant on the Ensemble Kalman Filter (EnKF). RumEnKF differs from EnKF in that it does not store the entire ensemble, but rather only saves the first two moments of the ensemble distribution. In this way, the number of ensemble members that can be calculated is less dependent on available memory, and mainly on available computing power (CPU). RumEnKF is developed to make optimal use of current generation super computer architecture, where the number of available floating point operations (flops) increases more rapidly than the available memory and where inter-node communication can quickly become a bottleneck. RumEnKF reduces the used memory compared to the EnKF when the number of ensemble members is greater than half the number of state variables. In this paper, three simple models are used (auto-regressive, low dimensional Lorenz and high dimensional Lorenz) to show that RumEnKF performs similarly to the EnKF. Furthermore, it is also shown that increasing the ensemble size has a similar impact on the estimation error from the three algorithms.
Durazo, Juan A.; Kostelich, Eric J.; Mahalov, Alex
2017-09-01
We propose a targeted observation strategy, based on the influence matrix diagnostic, that optimally selects where additional observations may be placed to improve ionospheric forecasts. This strategy is applied in data assimilation observing system experiments, where synthetic electron density vertical profiles, which represent those of Constellation Observing System for Meteorology, Ionosphere, and Climate/Formosa satellite 3, are assimilated into the Thermosphere-Ionosphere-Electrodynamics General Circulation Model using the local ensemble transform Kalman filter during the 26 September 2011 geomagnetic storm. During each analysis step, the observation vector is augmented with five synthetic vertical profiles optimally placed to target electron density errors, using our targeted observation strategy. Forecast improvement due to assimilation of augmented vertical profiles is measured with the root-mean-square error (RMSE) of analyzed electron density, averaged over 600 km regions centered around the augmented vertical profile locations. Assimilating vertical profiles with targeted locations yields about 60%-80% reduction in electron density RMSE, compared to a 15% average reduction when assimilating randomly placed vertical profiles. Assimilating vertical profiles whose locations target the zonal component of neutral winds (Un) yields on average a 25% RMSE reduction in Un estimates, compared to a 2% average improvement obtained with randomly placed vertical profiles. These results demonstrate that our targeted strategy can improve data assimilation efforts during extreme events by detecting regions where additional observations would provide the largest benefit to the forecast.
Directory of Open Access Journals (Sweden)
Masahiro Sawada
2015-03-01
Full Text Available Monitoring severe weather, including wind shear and clear air turbulence, is important for aviation safety. To provide accurate information for nowcasts and very short-range forecasts up to an hour, a rapid-update prediction system has been developed, with a particular focus on lateral boundary adjustment (LBA using the local ensemble transform Kalman filter (LETKF. Due to the small forecast domain, limited-area forecasts are dominated by the lateral boundary conditions from coarse-resolution global forecasts. To effectively extend the forecast lead time for the small domain, a new LBA scheme using the LETKF has been developed and assessed with three sea-breeze front cases. Observing system simulation experiments for high-resolution winds from a simulated Doppler lidar were performed with the Japan Meteorological Agency Nonhydrostatic Mesoscale Model at a horizontal resolution of 400 m and 15-minute update cycle. The results indicate that the LBA improved the forecast significantly. In particular, the 1-hour wind-speed forecast with the LBA is as accurate as the 15-minute forecast without the LBA. The assimilation of Doppler lidar high-resolution wind data with the LBA is a promising approach for very short-range forecasts up to an hour with a small domain, such as for aviation weather.
Jones, Thomas A.; Stensrud, David; Wicker, Louis; Minnis, Patrick; Palikonda, Rabindra
2015-01-01
Assimilating high-resolution radar reflectivity and radial velocity into convection-permitting numerical weather prediction models has proven to be an important tool for improving forecast skill of convection. The use of satellite data for the application is much less well understood, only recently receiving significant attention. Since both radar and satellite data provide independent information, combing these two sources of data in a robust manner potentially represents the future of high-resolution data assimilation. This research combines Geostationary Operational Environmental Satellite 13 (GOES-13) cloud water path (CWP) retrievals with Weather Surveillance Radar-1988 Doppler (WSR-88D) reflectivity and radial velocity to examine the impacts of assimilating each for a severe weather event occurring in Oklahoma on 24 May 2011. Data are assimilated into a 3-km model using an ensemble adjustment Kalman filter approach with 36 members over a 2-h assimilation window between 1800 and 2000 UTC. Forecasts are then generated for 90 min at 5-min intervals starting at 1930 and 2000 UTC. Results show that both satellite and radar data are able to initiate convection, but that assimilating both spins up a storm much faster. Assimilating CWP also performs well at suppressing spurious precipitation and cloud cover in the model as well as capturing the anvil characteristics of developed storms. Radar data are most effective at resolving the 3D characteristics of the core convection. Assimilating both satellite and radar data generally resulted in the best model analysis and most skillful forecast for this event.
Maki, T.; Sekiyama, T. T.; Shibata, K.; Miyazaki, K.; Miyoshi, T.; Yamada, K.; Yokoo, Y.; Iwasaki, T.
2011-12-01
In the current carbon cycle analysis, inverse modeling plays an important role. However, it requires enormous computational resources when we deal with more flux regions and more observations. The local ensemble transform Kalman filter (LETKF) is an alternative approach to reduce such problems. We constructed a carbon cycle analysis system with the LETKF and MRI (Meteorological Research Institute) online transport model (MJ98-CDTM). In MJ98-CDTM, an off-line transport model (CDTM) is directly coupled with the MRI/JMA GCM (MJ98). We further improved vertical transport processes in MJ98-CDTM from previous study. The LETKF includes enhanced features such as smoother to assimilate future observations, adaptive inflation and bias correction scheme. In this study, we use CO2 observations of surface data (continuous and flask), aircraft data (CONTRAIL) and satellite data (GOSAT), although we plan to assimilate AIRS tropospheric CO2 data. We developed a quality control system. We estimated 3-day-mean CO2 flux at a resolution of T42. Here, only CO2 concentrations and fluxes are analyzed whereas meteorological fields are nudged by the Japanese reanalysis (JCDAS). The horizontal localization length scale and assimilation window are chosen to be 1000 km and 3 days, respectively. The results indicate that the assimilation system works properly, better than free transport model run when we validate with independent CO2 concentration observational data and CO2 analysis data.
Directory of Open Access Journals (Sweden)
Di Liu
2010-12-01
Full Text Available Hybrid data assimilation (DA is a method seeing more use in recent hydrology and water resources research. In this study, a DA method coupled with the support vector machines (SVMs and the ensemble Kalman filter (EnKF technology was used for the prediction of soil moisture in different soil layers: 0–5 cm, 30 cm, 50 cm, 100 cm, 200 cm, and 300 cm. The SVM methodology was first used to train the ground measurements of soil moisture and meteorological parameters from the Meilin study area, in East China, to construct soil moisture statistical prediction models. Subsequent observations and their statistics were used for predictions, with two approaches: the SVM predictor and the SVM-EnKF model made by coupling the SVM model with the EnKF technique using the DA method. Validation results showed that the proposed SVM-EnKF model can improve the prediction results of soil moisture in different layers, from the surface to the root zone.
Thiboult, A.; Anctil, F.
2015-10-01
Forecast reliability and accuracy is a prerequisite for successful hydrological applications. This aim may be attained by using data assimilation techniques such as the popular Ensemble Kalman filter (EnKF). Despite its recognized capacity to enhance forecasting by creating a new set of initial conditions, implementation tests have been mostly carried out with a single model and few catchments leading to case specific conclusions. This paper performs an extensive testing to assess ensemble bias and reliability on 20 conceptual lumped models and 38 catchments in the Province of Québec with perfect meteorological forecast forcing. The study confirms that EnKF is a powerful tool for short range forecasting but also that it requires a more subtle setting than it is frequently recommended. The success of the updating procedure depends to a great extent on the specification of the hyper-parameters. In the implementation of the EnKF, the identification of the hyper-parameters is very unintuitive if the model error is not explicitly accounted for and best estimates of forcing and observation error lead to overconfident forecasts. It is shown that performance are also related to the choice of updated state variables and that all states variables should not systematically be updated. Additionally, the improvement over the open loop scheme depends on the watershed and hydrological model structure, as some models exhibit a poor compatibility with EnKF updating. Thus, it is not possible to conclude in detail on a single ideal manner to identify an optimal implementation; conclusions drawn from a unique event, catchment, or model are likely to be misleading since transferring hyper-parameters from a case to another may be hazardous. Finally, achieving reliability and bias jointly is a daunting challenge as the optimization of one score is done at the cost of the other.
Directory of Open Access Journals (Sweden)
S. Nie
2011-08-01
Full Text Available The performance of the ensemble Kalman filter (EnKF in soil moisture assimilation applications is investigated in the context of simultaneous state-parameter estimation in the presence of uncertainties from model parameters, soil moisture initial condition and atmospheric forcing. A physically based land surface model is used for this purpose. Using a series of identical twin experiments in two kinds of initial parameter distribution (IPD scenarios, the narrow IPD (NIPD scenario and the wide IPD (WIPD scenario, model-generated near surface soil moisture observations are assimilated to estimate soil moisture state and three hydraulic parameters (the saturated hydraulic conductivity, the saturated soil moisture suction and a soil texture empirical parameter in the model. The estimation of single imperfect parameter is successful with the ensemble mean value of all three estimated parameters converging to their true values respectively in both NIPD and WIPD scenarios. Increasing the number of imperfect parameters leads to a decline in the estimation performance. A wide initial distribution of estimated parameters can produce improved simultaneous multi-parameter estimation performances compared to that of the NIPD scenario. However, when the number of estimated parameters increased to three, not all parameters were estimated successfully for both NIPD and WIPD scenarios. By introducing constraints between estimated hydraulic parameters, the performance of the constrained three-parameter estimation was successful, even if temporally sparse observations were available for assimilation. The constrained estimation method can reduce RMSE much more in soil moisture forecasting compared to the non-constrained estimation method and traditional non-parameter-estimation assimilation method. The benefit of this method in estimating all imperfect parameters simultaneously can be fully demonstrated when the corresponding non-constrained estimation method
Du, Tien Duc; Ngo-Duc, Thanh; Kieu, Chanh
2017-07-01
This study presents an approach to assimilate tropical cyclone (TC) real-time reports and the University of Wisconsin-Cooperative Institute for Meteorological Satellite Studies (CIMSS) Atmospheric Motion Vectors (AMV) data into the Weather Research and Forecasting (WRF) model for TC forecast applications. Unlike current methods in which TC real-time reports are used to either generate a bogus vortex or spin up a model initial vortex, the proposed approach ingests the TC real-time reports through blending a dynamically consistent synthetic vortex structure with the CIMSS-AMV data. The blended dataset is then assimilated into the WRF initial condition, using the local ensemble transform Kalman filter (LETKF) algorithm. Retrospective experiments for a number of TC cases in the northwestern Pacific basin during 2013-2014 demonstrate that this approach could effectively increase both the TC circulation and enhance the large-scale environment that the TCs are embedded in. Further evaluation of track and intensity forecast errors shows that track forecasts benefit more from improvement in the large-scale flow at 4-5-day lead times, whereas the intensity improvement is minimal. While the difference between the track and intensity improvement could be due to a specific model configuration, this result appears to be consistent with the recent reports of insignificant impacts of inner core data assimilation in operational TC models at the long range of 4-5 days. The new approach will be most beneficial for future regional TC models that are directly initialized from very high-resolution global models whose storm initial locations are sufficiently accurate at the initial analysis that there is no need to carry out any artificial vortex removal or filtering steps.
Kollat, J. B.; Reed, P. M.
2009-12-01
This study contributes the ASSIST (Adaptive Strategies for Sampling in Space and Time) framework for improving long-term groundwater monitoring decisions across space and time while accounting for the influences of systematic model errors (or predictive bias). The ASSIST framework combines contaminant flow-and-transport modeling, bias-aware ensemble Kalman filtering (EnKF) and many-objective evolutionary optimization. Our goal in this work is to provide decision makers with a fuller understanding of the information tradeoffs they must confront when performing long-term groundwater monitoring network design. Our many-objective analysis considers up to 6 design objectives simultaneously and consequently synthesizes prior monitoring network design methodologies into a single, flexible framework. This study demonstrates the ASSIST framework using a tracer study conducted within a physical aquifer transport experimental tank located at the University of Vermont. The tank tracer experiment was extensively sampled to provide high resolution estimates of tracer plume behavior. The simulation component of the ASSIST framework consists of stochastic ensemble flow-and-transport predictions using ParFlow coupled with the Lagrangian SLIM transport model. The ParFlow and SLIM ensemble predictions are conditioned with tracer observations using a bias-aware EnKF. The EnKF allows decision makers to enhance plume transport predictions in space and time in the presence of uncertain and biased model predictions by conditioning them on uncertain measurement data. In this initial demonstration, the position and frequency of sampling were optimized to: (i) minimize monitoring cost, (ii) maximize information provided to the EnKF, (iii) minimize failure to detect the tracer, (iv) maximize the detection of tracer flux, (v) minimize error in quantifying tracer mass, and (vi) minimize error in quantifying the moment of the tracer plume. The results demonstrate that the many-objective problem
Directory of Open Access Journals (Sweden)
Francois Counillon
2014-03-01
Full Text Available Here, we firstly demonstrate the potential of an advanced flow dependent data assimilation method for performing seasonal-to-decadal prediction and secondly, reassess the use of sea surface temperature (SST for initialisation of these forecasts. We use the Norwegian Climate Prediction Model (NorCPM, which is based on the Norwegian Earth System Model (NorESM and uses the deterministic ensemble Kalman filter to assimilate observations. NorESM is a fully coupled system based on the Community Earth System Model version 1, which includes an ocean, an atmosphere, a sea ice and a land model. A numerically efficient coarse resolution version of NorESM is used. We employ a twin experiment methodology to provide an upper estimate of predictability in our model framework (i.e. without considering model bias of NorCPM that assimilates synthetic monthly SST data (EnKF-SST. The accuracy of EnKF-SST is compared to an unconstrained ensemble run (FREE and ensemble predictions made with near perfect (i.e. microscopic SST perturbation initial conditions (PERFECT. We perform 10 cycles, each consisting of a 10-yr assimilation phase, followed by a 10-yr prediction. The results indicate that EnKF-SST improves sea level, ice concentration, 2 m atmospheric temperature, precipitation and 3-D hydrography compared to FREE. Improvements for the hydrography are largest near the surface and are retained for longer periods at depth. Benefits in salinity are retained for longer periods compared to temperature. Near-surface improvements are largest in the tropics, while improvements at intermediate depths are found in regions of large-scale currents, regions of deep convection, and at the Mediterranean Sea outflow. However, the benefits are often small compared to PERFECT, in particular, at depth suggesting that more observations should be assimilated in addition to SST. The EnKF-SST system is also tested for standard ocean circulation indices and demonstrates decadal
A Gaussian mixture ensemble transform filter
Reich, Sebastian
2011-01-01
We generalize the popular ensemble Kalman filter to an ensemble transform filter where the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions, ...
Zhu, Penghui; Shi, Liangsheng; Zhu, Yan; Zhang, Qiuru; Huang, Kai; Williams, Mathew
2017-12-01
This paper assesses the value of multi-scale near-surface (0∼5 cm) soil moisture observations to improve state-only or state-parameter estimation based on the ensemble Kalman filter (EnKF). To the best of our knowledge, studies on assimilating multi-scale soil moisture data into a distributed hydrological model with a series of detailed vertical soil moisture profiles are rare. Our analysis factors include spatial measurement scales, soil spatial heterogeneity, multi-scale data with contrasting information and systematic measurement errors. Results show that coarse-scale soil moisture data are also very useful for identifying finer-scale parameters and states given biased initial parameter fields, but it becomes increasingly difficult to recover the finer-scale spatial heterogeneity of soil property as the observation grids become coarser. In state-only estimation, near-surface soil moisture data result in improvement for shallow soil moisture profiles and degradation for deeper soil moisture profiles, with stronger influences from finer-scale data. With the decrease of background spatial heterogeneity of soil property, the value of coarse-scale data increases notably. Soil moisture data at two scales with contrasting information are found to be both useful. By updating spatially correlated soil hydraulic parameters, deviated observations still contain considerably useful information for finer-scale state-parameter estimation. Eventually, by presenting a difference information assimilation method based on EnKF we successfully extract useful information from soil moisture data containing systematic measurement errors. The current study can be extended to consider more complex atmosphere input and topography, etc.
Xu, Teng; Gómez-Hernández, J. Jaime
2018-02-01
Detecting where and when a contaminant entered an aquifer from observations downgradient of the source is a difficult task; this identification becomes more challenging when the uncertainty about the spatial distribution of hydraulic conductivity is accounted for. In this paper, we have implemented an application of the restart normal-score ensemble Kalman filter (NS-EnKF) for the simultaneous identification of a contaminant source and the spatially variable hydraulic conductivity in an aquifer. The method is capable of providing estimates of the spatial location, initial release time, the duration of the release and the mass load of a point-contamination event, plus the spatial distribution of hydraulic conductivity together with an assessment of the estimation uncertainty of all the parameters. The method has been applied in synthetic aquifers exhibiting both Gaussian and non-Gaussian patterns. The identification is made possible by assimilating in time both piezometric head and concentration observations from an array of observation wells. The method is demonstrated in three different synthetic scenarios that combine hydraulic conductivities with unimodal and bimodal histograms, and releases in high and low conductivity zones. The results prove that the specific implementation of the EnKF is capable of recovering the source parameters with some uncertainty and of recovering the main patterns of heterogeneity of the hydraulic conductivity fields by assimilating a sufficient number of state variable observations. The proposed approach is an important step towards contaminant source identification in real aquifers, which may have logconductivity spatial distributions with either Gaussian or non-Gaussian features, yet, it is still far from practical applications since the transport parameters, the external sinks and sources and the initial and boundary conditions are assumed known.
Camporese, Matteo; Binley, Andrew; Cassiani, Giorgio; Deiana, Rita; Salandin, Paolo
2013-04-01
Recent advances in geophysical methods have been increasingly exploited as inverse modeling tools in groundwater hydrology. In particular, several attempts to constrain the hydrogeophysical inverse problem to reduce inversion error have been made using time-lapse geophysical measurements through both coupled and uncoupled inversion approaches. The main advantage of coupled approaches is that the numerical models for the geophysical and hydrological processes are linked together such that the geophysical data are inverted directly for the hydrological properties of interest. On the other hand, uncoupled approaches allow assessing in advance the reliability of the data, thanks to the geophysical inversion that is carried out before estimating the hydrological variable of interest. In spite of the recent popularity of fully coupled inversion approaches, we argue that their superiority over uncoupled methods still needs to be proven. The objective of this work is to shed some light on this debate. An approach based on the Lagrangian formulation of transport and the ensemble Kalman filter (EnKF) is here applied to assess the spatial distribution of hydraulic conductivity (K) by assimilating ERT data generated for a synthetic tracer test in a heterogeneous aquifer. In the coupled version of our inverse modeling tool, the K distribution is retrieved by assimilating raw ERT voltage data without the need for a preliminary electrical inversion. In the uncoupled version, K is estimated by assimilating time-lapse cross-hole electrical resistivity tomography (ERT) images derived by an electrical inversion. We compare the performance of the two approaches in a number of simulation scenarios and assess the impact on the inversions of the choice of the prior statistics of K.
Siripatana, Adil
2017-06-08
Bayesian estimation/inversion is commonly used to quantify and reduce modeling uncertainties in coastal ocean model, especially in the framework of parameter estimation. Based on Bayes rule, the posterior probability distribution function (pdf) of the estimated quantities is obtained conditioned on available data. It can be computed either directly, using a Markov chain Monte Carlo (MCMC) approach, or by sequentially processing the data following a data assimilation approach, which is heavily exploited in large dimensional state estimation problems. The advantage of data assimilation schemes over MCMC-type methods arises from the ability to algorithmically accommodate a large number of uncertain quantities without significant increase in the computational requirements. However, only approximate estimates are generally obtained by this approach due to the restricted Gaussian prior and noise assumptions that are generally imposed in these methods. This contribution aims at evaluating the effectiveness of utilizing an ensemble Kalman-based data assimilation method for parameter estimation of a coastal ocean model against an MCMC polynomial chaos (PC)-based scheme. We focus on quantifying the uncertainties of a coastal ocean ADvanced CIRCulation (ADCIRC) model with respect to the Manning’s n coefficients. Based on a realistic framework of observation system simulation experiments (OSSEs), we apply an ensemble Kalman filter and the MCMC method employing a surrogate of ADCIRC constructed by a non-intrusive PC expansion for evaluating the likelihood, and test both approaches under identical scenarios. We study the sensitivity of the estimated posteriors with respect to the parameters of the inference methods, including ensemble size, inflation factor, and PC order. A full analysis of both methods, in the context of coastal ocean model, suggests that an ensemble Kalman filter with appropriate ensemble size and well-tuned inflation provides reliable mean estimates and
Siripatana, Adil; Mayo, Talea; Sraj, Ihab; Knio, Omar; Dawson, Clint; Le Maitre, Olivier; Hoteit, Ibrahim
2017-08-01
Bayesian estimation/inversion is commonly used to quantify and reduce modeling uncertainties in coastal ocean model, especially in the framework of parameter estimation. Based on Bayes rule, the posterior probability distribution function (pdf) of the estimated quantities is obtained conditioned on available data. It can be computed either directly, using a Markov chain Monte Carlo (MCMC) approach, or by sequentially processing the data following a data assimilation approach, which is heavily exploited in large dimensional state estimation problems. The advantage of data assimilation schemes over MCMC-type methods arises from the ability to algorithmically accommodate a large number of uncertain quantities without significant increase in the computational requirements. However, only approximate estimates are generally obtained by this approach due to the restricted Gaussian prior and noise assumptions that are generally imposed in these methods. This contribution aims at evaluating the effectiveness of utilizing an ensemble Kalman-based data assimilation method for parameter estimation of a coastal ocean model against an MCMC polynomial chaos (PC)-based scheme. We focus on quantifying the uncertainties of a coastal ocean ADvanced CIRCulation (ADCIRC) model with respect to the Manning's n coefficients. Based on a realistic framework of observation system simulation experiments (OSSEs), we apply an ensemble Kalman filter and the MCMC method employing a surrogate of ADCIRC constructed by a non-intrusive PC expansion for evaluating the likelihood, and test both approaches under identical scenarios. We study the sensitivity of the estimated posteriors with respect to the parameters of the inference methods, including ensemble size, inflation factor, and PC order. A full analysis of both methods, in the context of coastal ocean model, suggests that an ensemble Kalman filter with appropriate ensemble size and well-tuned inflation provides reliable mean estimates and
Botto, Anna; Camporese, Matteo
2017-04-01
Hydrological models allow scientists to predict the response of water systems under varying forcing conditions. In particular, many physically-based integrated models were recently developed in order to understand the fundamental hydrological processes occurring at the catchment scale. However, the use of this class of hydrological models is still relatively limited, as their prediction skills heavily depend on reliable parameter estimation, an operation that is never trivial, being normally affected by large uncertainty and requiring huge computational effort. The objective of this work is to test the potential of data assimilation to be used as an inverse modeling procedure for the broad class of integrated hydrological models. To pursue this goal, a Bayesian data assimilation (DA) algorithm based on a Monte Carlo approach, namely the ensemble Kalman filter (EnKF), is combined with the CATchment HYdrology (CATHY) model. In this approach, input variables (atmospheric forcing, soil parameters, initial conditions) are statistically perturbed providing an ensemble of realizations aimed at taking into account the uncertainty involved in the process. Each realization is propagated forward by the CATHY hydrological model within a parallel R framework, developed to reduce the computational effort. When measurements are available, the EnKF is used to update both the system state and soil parameters. In particular, four different assimilation scenarios are applied to test the capability of the modeling framework: first only pressure head or water content are assimilated, then, the combination of both, and finally both pressure head and water content together with the subsurface outflow. To demonstrate the effectiveness of the approach in a real-world scenario, an artificial hillslope was designed and built to provide real measurements for the DA analyses. The experimental facility, located in the Department of Civil, Environmental and Architectural Engineering of the
A Localized Ensemble Kalman Smoother
Butala, Mark D.
2012-01-01
Numerous geophysical inverse problems prove difficult because the available measurements are indirectly related to the underlying unknown dynamic state and the physics governing the system may involve imperfect models or unobserved parameters. Data assimilation addresses these difficulties by combining the measurements and physical knowledge. The main challenge in such problems usually involves their high dimensionality and the standard statistical methods prove computationally intractable. This paper develops and addresses the theoretical convergence of a new high-dimensional Monte-Carlo approach called the localized ensemble Kalman smoother.
Zovi, Francesco; Camporese, Matteo; Hendricks Franssen, Harrie-Jan; Huisman, Johan Alexander; Salandin, Paolo
2017-05-01
Alluvial aquifers are often characterized by the presence of braided high-permeable paleo-riverbeds, which constitute an interconnected preferential flow network whose localization is of fundamental importance to predict flow and transport dynamics. Classic geostatistical approaches based on two-point correlation (i.e., the variogram) cannot describe such particular shapes. In contrast, multiple point geostatistics can describe almost any kind of shape using the empirical probability distribution derived from a training image. However, even with a correct training image the exact positions of the channels are uncertain. State information like groundwater levels can constrain the channel positions using inverse modeling or data assimilation, but the method should be able to handle non-Gaussianity of the parameter distribution. Here the normal score ensemble Kalman filter (NS-EnKF) was chosen as the inverse conditioning algorithm to tackle this issue. Multiple point geostatistics and NS-EnKF have already been tested in synthetic examples, but in this study they are used for the first time in a real-world case study. The test site is an alluvial unconfined aquifer in northeastern Italy with an extension of approximately 3 km2. A satellite training image showing the braid shapes of the nearby river and electrical resistivity tomography (ERT) images were used as conditioning data to provide information on channel shape, size, and position. Measured groundwater levels were assimilated with the NS-EnKF to update the spatially distributed groundwater parameters (hydraulic conductivity and storage coefficients). Results from the study show that the inversion based on multiple point geostatistics does not outperform the one with a multiGaussian model and that the information from the ERT images did not improve site characterization. These results were further evaluated with a synthetic study that mimics the experimental site. The synthetic results showed that only for a much
Improving short-range ensemble Kalman storm surge forecasting using robust adaptive inflation
Altaf, M.U.; Butler, T.; Luo, X.; Dawson, C.; Mayo, T.; Hoteit, I.
2013-01-01
This paper presents a robust ensemble filtering methodology for storm surge forecasting based on the singular evolutive interpolated Kalman (SEIK) filter, which has been implemented in the framework of the H? filter. By design, an H? filter is more robust than the common Kalman filter in the sense
Kalman Filter Desing, Smoothing and Analysis
Cederkvist, Henrik Rene
2001-01-01
Thesis is based on three different aspects of Kalman filtering. >Kalman filters for navigation. Investigate the difference between a Extended Kalman Filter and a Linearized Kalman Filter with feedback. And show how different system models relate to these Kalman Filters when implemented in a filter. >Smoothing. Investigate how much there is to be gained from smoothing. We will only look at the fixed-interval smoother, using the method of forward and backward filtering. ...
Tsiaras, Kostas P.; Hoteit, Ibrahim; Kalaroni, Sofia; Petihakis, George; Triantafyllou, George
2017-06-01
A hybrid ensemble data assimilation scheme (HYBRID), combining a flow-dependent with a static background covariance, was developed and implemented for assimilating satellite (SeaWiFS) Chl-a data into a marine ecosystem model of the Mediterranean. The performance of HYBRID was assessed against a model free-run, the ensemble-based singular evolutive interpolated Kalman (SEIK) and its variant with static covariance (SFEK), with regard to the assimilated variable (Chl-a) and non-assimilated variables (dissolved inorganic nutrients). HYBRID was found more efficient than both SEIK and SFEK, reducing the Chl-a error by more than 40% in most areas, as compared to the free-run. Data assimilation had a positive overall impact on nutrients, except for a deterioration of nitrates simulation by SEIK in the most productive area (Adriatic). This was related to SEIK pronounced update in this area and the phytoplankton limitation on phosphate that lead to a built up of excess nitrates. SEIK was found more efficient in productive and variable areas, where its ensemble exhibited important spread. SFEK had an effect mostly on Chl-a, performing better than SEIK in less dynamic areas, adequately described by the dominant modes of its static covariance. HYBRID performed well in all areas, due to its "blended" covariance. Its flow-dependent component appears to track changes in the system dynamics, while its static covariance helps maintaining sufficient spread in the forecast. HYBRID sensitivity experiments showed that an increased contribution from the flow-dependent covariance results in a deterioration of nitrates, similar to SEIK, while the improvement of HYBRID with increasing flow-dependent ensemble size quickly levels off.
Tsiaras, Kostas P.
2017-04-20
A hybrid ensemble data assimilation scheme (HYBRID), combining a flow-dependent with a static background covariance, was developed and implemented for assimilating satellite (SeaWiFS) Chl-a data into a marine ecosystem model of the Mediterranean. The performance of HYBRID was assessed against a model free-run, the ensemble-based singular evolutive interpolated Kalman (SEIK) and its variant with static covariance (SFEK), with regard to the assimilated variable (Chl-a) and non-assimilated variables (dissolved inorganic nutrients). HYBRID was found more efficient than both SEIK and SFEK, reducing the Chl-a error by more than 40% in most areas, as compared to the free-run. Data assimilation had a positive overall impact on nutrients, except for a deterioration of nitrates simulation by SEIK in the most productive area (Adriatic). This was related to SEIK pronounced update in this area and the phytoplankton limitation on phosphate that lead to a built up of excess nitrates. SEIK was found more efficient in productive and variable areas, where its ensemble exhibited important spread. SFEK had an effect mostly on Chl-a, performing better than SEIK in less dynamic areas, adequately described by the dominant modes of its static covariance. HYBRID performed well in all areas, due to its “blended” covariance. Its flow-dependent component appears to track changes in the system dynamics, while its static covariance helps maintaining sufficient spread in the forecast. HYBRID sensitivity experiments showed that an increased contribution from the flow-dependent covariance results in a deterioration of nitrates, similar to SEIK, while the improvement of HYBRID with increasing flow-dependent ensemble size quickly levels off.
He, L.; Chen, J. M.; Liu, J.; Mo, G.; Zhen, T.; Chen, B.; Wang, R.; Arain, M.
2013-12-01
Terrestrial ecosystem models have been widely used to simulate carbon, water and energy fluxes and climate-ecosystem interactions. In these models, some vegetation and soil parameters are determined based on limited studies from literatures without consideration of their seasonal variations. Data assimilation (DA) provides an effective way to optimize these parameters at different time scales . In this study, an ensemble Kalman filter (EnKF) is developed and applied to optimize two key parameters of an ecosystem model, namely the Boreal Ecosystem Productivity Simulator (BEPS): (1) the maximum photosynthetic carboxylation rate (Vcmax) at 25 °C, and (2) the soil water stress factor (fw) for stomatal conductance formulation. These parameters are optimized through assimilating observations of gross primary productivity (GPP) and latent heat (LE) fluxes measured in a 74 year-old pine forest, which is part of the Turkey Point Flux Station's age-sequence sites. Vcmax is related to leaf nitrogen concentration and varies slowly over the season and from year to year. In contrast, fw varies rapidly in response to soil moisture dynamics in the root-zone. Earlier studies suggested that DA of vegetation parameters at daily time steps leads to Vcmax values that are unrealistic. To overcome the problem, we developed a three-step scheme to optimize Vcmax and fw. First, the EnKF is applied daily to obtain precursor estimates of Vcmax and fw. Then Vcmax is optimized at different time scales assuming fw is unchanged from first step. The best temporal period or window size is then determined by analyzing the magnitude of the minimized cost-function, and the coefficient of determination (R2) and Root-mean-square deviation (RMSE) of GPP and LE between simulation and observation. Finally, the daily fw value is optimized for rain free days corresponding to the Vcmax curve from the best window size. The optimized fw is then used to model its relationship with soil moisture. We found that
DEFF Research Database (Denmark)
Sørensen, Jacob Viborg Tornfeldt; Madsen, Henrik; Madsen, H.
2006-01-01
sensitivity study of three well known Kalman filter approaches for the assimilation of water levels in a three dimensional hydrodynamic modelling system. The filters considered are the ensemble Kalman filter (EnKF), the reduced rank square root Kalman filter (RRSQRT) and the steady Kalman filter...
Kalman filter data assimilation: targeting observations and parameter estimation.
Bellsky, Thomas; Kostelich, Eric J; Mahalov, Alex
2014-06-01
This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation.
Energy Technology Data Exchange (ETDEWEB)
Deng, Ziwang; Tang, Youmin; Zhou, Xiaobing [University of Northern British Columbia, Environmental Science and Engineering, Prince George, BC (Canada)
2009-02-15
In this study, we assimilated sea surface temperature (SST) data of the past 120 years into an oceanic general circulation model (OGCM) for El Nino-southern oscillation (ENSO) retrospective predictions using ensemble Kalman filter (EnKF). It was found that the ensemble covariance matrix in EnKF can act as a time-variant transfer operator to project the SST corrections onto the subsurface temperatures effectively when initial perturbations of ensemble were constructed using vertically coherent random fields. As such the increments of subsurface temperatures can be obtained via the transfer operator during assimilation cycles. The results show that the SST assimilation improves the model simulation skills significantly, not only for the SST anomalies over the whole assimilated domain, but also for the subsurface temperature anomalies of the upper 100 m over the tropical Pacific off the equator. Along the equator, the improvement of the assimilation is confined within the mixing layer because strong upwelling motions there prevent the downward transfer of SST information. The retrospective prediction skills of ENSO over the past 120 years from 1881 to 2000 were significantly improved by the SST assimilation at all leads of 1-12 months, especially for the 3-6 months leads, compared with those initialized by the control run without assimilation. The skilful predictions by the assimilation allow us to further study ENSO predictability using this coupled model. (orig.)
Directory of Open Access Journals (Sweden)
BYoung-Joo Jung
2012-01-01
Full Text Available During August and September 2008, The Observing System Research and Predictability Experiment (THORPEX – Pacific Asian Regional Campaign (T-PARC was conducted to investigate the formation, structure, targeted observation, extratropical transition (ET and downstream effects of tropical cyclones (TCs in the Western North Pacific (WNP region. This study investigates the effect of targeted dropsonde observations from T-PARC and the TC best track data on the track forecast of Typhoon Sinlaku (2008. A WRF-based ensemble Kalman filter (EnKF is used for a series of observation system experiments (OSEs. From the innovation statistics and rank histograms, the EnKF behaves well in terms of ensemble spread, despite some spread deficiency in low-tropospheric winds and warm and moist biases. Assimilation of targeted dropsonde observations leads to improved initial position and subsequent track forecast compared with experiments that only assimilate conventional observations. In the meantime, assimilation of TC position reduces the initial position error, whereas assimilation of minimum sea level pressure (SLP information is efficient to analyse the strong vortex structures of TC and reduces track forecast errors. Assimilation of TC position and minimum SLP information is particularly beneficial when dropsonde observations do not exist.
Directory of Open Access Journals (Sweden)
O. Rakovec
2012-09-01
Full Text Available This paper presents a study on the optimal setup for discharge assimilation within a spatially distributed hydrological model. The Ensemble Kalman filter (EnKF is employed to update the grid-based distributed states of such an hourly spatially distributed version of the HBV-96 model. By using a physically based model for the routing, the time delay and attenuation are modelled more realistically. The discharge and states at a given time step are assumed to be dependent on the previous time step only (Markov property.
Synthetic and real world experiments are carried out for the Upper Ourthe (1600 km^{2}, a relatively quickly responding catchment in the Belgian Ardennes. We assess the impact on the forecasted discharge of (1 various sets of the spatially distributed discharge gauges and (2 the filtering frequency. The results show that the hydrological forecast at the catchment outlet is improved by assimilating interior gauges. This augmentation of the observation vector improves the forecast more than increasing the updating frequency. In terms of the model states, the EnKF procedure is found to mainly change the pdfs of the two routing model storages, even when the uncertainty in the discharge simulations is smaller than the defined observation uncertainty.
Bei, Naifang; Li, Guohui; Meng, Zhiyong; Weng, Yonghui; Zavala, Miguel; Molina, L T
2014-11-15
The purpose of this study is to investigate the impact of using an ensemble Kalman filter (EnKF) on air quality simulations in the California-Mexico border region on two days (May 30 and June 04, 2010) during Cal-Mex 2010. The uncertainties in ozone (O3) and aerosol simulations in the border area due to the meteorological initial uncertainties were examined through ensemble simulations. The ensemble spread of surface O3 averaged over the coastal region was less than 10ppb. The spreads in the nitrate and ammonium aerosols are substantial on both days, mostly caused by the large uncertainties in the surface temperature and humidity simulations. In general, the forecast initialized with the EnKF analysis (EnKF) improved the simulation of meteorological fields to some degree in the border region compared to the reference forecast initialized with NCEP analysis data (FCST) and the simulation with observation nudging (FDDA), which in turn leading to reasonable air quality simulations. The simulated surface O3 distributions by EnKF were consistently better than FCST and FDDA on both days. EnKF usually produced more reasonable simulations of nitrate and ammonium aerosols compared to the observations, but still have difficulties in improving the simulations of organic and sulfate aerosols. However, discrepancies between the EnKF simulations and the measurements were still considerably large, particularly for sulfate and organic aerosols, indicating that there are still ample rooms for improvement in the present data assimilation and/or the modeling systems. Copyright © 2014 Elsevier B.V. All rights reserved.
Kalman Filtering with Real-Time Applications
Chui, Charles K
2009-01-01
Kalman Filtering with Real-Time Applications presents a thorough discussion of the mathematical theory and computational schemes of Kalman filtering. The filtering algorithms are derived via different approaches, including a direct method consisting of a series of elementary steps, and an indirect method based on innovation projection. Other topics include Kalman filtering for systems with correlated noise or colored noise, limiting Kalman filtering for time-invariant systems, extended Kalman filtering for nonlinear systems, interval Kalman filtering for uncertain systems, and wavelet Kalman filtering for multiresolution analysis of random signals. Most filtering algorithms are illustrated by using simplified radar tracking examples. The style of the book is informal, and the mathematics is elementary but rigorous. The text is self-contained, suitable for self-study, and accessible to all readers with a minimum knowledge of linear algebra, probability theory, and system engineering.
Cavaglieri, Daniele; Bewley, Thomas; Previsic, Mirko
2014-11-01
In recent years, there has been a growing interest in renewable energy. Among all the available possibilities, wave energy conversion, due to the huge availability of energy that the ocean could provide, represents nowadays one of the most promising solutions. However, the efficiency of a wave energy converter for ocean wave energy harvesting is still far from making it competitive with more mature fields of renewable energy, such as solar and wind energy. One of the main problems is related to the difficulty to increase the power take-off through the implementation of an active controller without a precise knowledge of the oncoming wavefield. This work represents the first attempt at defining a realistic control framework for optimal power take-off of a wave energy converter where the ocean wavefield is predicted through a nonlinear Ensemble Kalman filter which assimilates data from a wave measurement device, such as a Doppler radar or a measurement buoy. Knowledge of the future wave profile is then leveraged in a nonlinear direct multiple shooting model predictive control framework allowing the online optimization of the energy absorption under motion and machinery constraints of the device.
Li, Bailing; Toll, David; Zhan, Xiwu; Cosgrove, Brian
2011-01-01
Model simulated soil moisture fields are often biased due to errors in input parameters and deficiencies in model physics. Satellite derived soil moisture estimates, if retrieved appropriately, represent the spatial mean of soil moisture in a footprint area, and can be used to reduce model bias (at locations near the surface) through data assimilation techniques. While assimilating the retrievals can reduce model bias, it can also destroy the mass balance enforced by the model governing equation because water is removed from or added to the soil by the assimilation algorithm. In addition, studies have shown that assimilation of surface observations can adversely impact soil moisture estimates in the lower soil layers due to imperfect model physics, even though the bias near the surface is decreased. In this study, an ensemble Kalman filter (EnKF) with a mass conservation updating scheme was developed to assimilate the actual value of Advanced Microwave Scanning Radiometer (AMSR-E) soil moisture retrievals to improve the mean of simulated soil moisture fields by the Noah land surface model. Assimilation results using the conventional and the mass conservation updating scheme in the Little Washita watershed of Oklahoma showed that, while both updating schemes reduced the bias in the shallow root zone, the mass conservation scheme provided better estimates in the deeper profile. The mass conservation scheme also yielded physically consistent estimates of fluxes and maintained the water budget. Impacts of model physics on the assimilation results are discussed.
Directory of Open Access Journals (Sweden)
B. Li
2012-01-01
Full Text Available Model simulated soil moisture fields are often biased due to errors in input parameters and deficiencies in model physics. Satellite derived soil moisture estimates, if retrieved appropriately, represent the spatial mean of near surface soil moisture in a footprint area, and can be used to reduce bias of model estimates (at locations near the surface through data assimilation techniques. While assimilating the retrievals can reduce bias, it can also destroy the mass balance enforced by the model governing equation because water is removed from or added to the soil by the assimilation algorithm. In addition, studies have shown that assimilation of surface observations can adversely impact soil moisture estimates in the lower soil layers due to imperfect model physics, even though the bias near the surface is decreased. In this study, an ensemble Kalman filter (EnKF with a mass conservation updating scheme was developed to assimilate Advanced Microwave Scanning Radiometer (AMSR-E soil moisture retrievals, as they are without any scaling or pre-processing, to improve the estimated soil moisture fields by the Noah land surface model. Assimilation results using the conventional and the mass conservation updating scheme in the Little Washita watershed of Oklahoma showed that, while both updating schemes reduced the bias in the shallow root zone, the mass conservation scheme provided better estimates in the deeper profile. The mass conservation scheme also yielded physically consistent estimates of fluxes and maintained the water budget. Impacts of model physics on the assimilation results are discussed.
Directory of Open Access Journals (Sweden)
Yongwei Liu
2016-01-01
Full Text Available This study investigates the capability of improving the distributed hydrological model performance by assimilating the streamflow observations. Incorrectly estimated model states will lead to discrepancies between the observed and estimated streamflow. Consequently, streamflow observations can be used to update the model states, and the improved model states will eventually benefit the streamflow predictions. This study tests this concept in upper Huai River basin. We assimilate the streamflow observations sequentially into the Soil and Water Assessment Tool (SWAT using the ensemble Kalman filter (EnKF to update the model states. Both synthetic experiments and real data application are used to demonstrate the benefit of this data assimilation scheme. The experiment shows that assimilating the streamflow observations at interior sites significantly improves the streamflow predictions for the whole basin. Assimilating the catchment outlet streamflow improves the streamflow predictions near the catchment outlet. In real data case, the estimated streamflow at the catchment outlet is significantly improved by assimilating the in situ streamflow measurements at interior gauges. Assimilating the in situ catchment outlet streamflow also improves the streamflow prediction of one interior location on the main reach. This may demonstrate that updating model states using streamflow observations can constrain the flux estimates in distributed hydrological modeling.
Mixtures of skewed Kalman filters
Kim, Hyoungmoon
2014-01-01
Normal state-space models are prevalent, but to increase the applicability of the Kalman filter, we propose mixtures of skewed, and extended skewed, Kalman filters. To do so, the closed skew-normal distribution is extended to a scale mixture class of closed skew-normal distributions. Some basic properties are derived and a class of closed skew. t distributions is obtained. Our suggested family of distributions is skewed and has heavy tails too, so it is appropriate for robust analysis. Our proposed special sequential Monte Carlo methods use a random mixture of the closed skew-normal distributions to approximate a target distribution. Hence it is possible to handle skewed and heavy tailed data simultaneously. These methods are illustrated with numerical experiments. © 2013 Elsevier Inc.
Kalman filtering with real-time applications
Chui, Charles K
2017-01-01
This new edition presents a thorough discussion of the mathematical theory and computational schemes of Kalman filtering. The filtering algorithms are derived via different approaches, including a direct method consisting of a series of elementary steps, and an indirect method based on innovation projection. Other topics include Kalman filtering for systems with correlated noise or colored noise, limiting Kalman filtering for time-invariant systems, extended Kalman filtering for nonlinear systems, interval Kalman filtering for uncertain systems, and wavelet Kalman filtering for multiresolution analysis of random signals. Most filtering algorithms are illustrated by using simplified radar tracking examples. The style of the book is informal, and the mathematics is elementary but rigorous. The text is self-contained, suitable for self-study, and accessible to all readers with a minimum knowledge of linear algebra, probability theory, and system engineering. Over 100 exercises and problems with solutions help de...
A quantum extended Kalman filter
Emzir, Muhammad F.; Woolley, Matthew J.; Petersen, Ian R.
2017-06-01
In quantum physics, a stochastic master equation (SME) estimates the state (density operator) of a quantum system in the Schrödinger picture based on a record of measurements made on the system. In the Heisenberg picture, the SME is a quantum filter. For a linear quantum system subject to linear measurements and Gaussian noise, the dynamics may be described by quantum stochastic differential equations (QSDEs), also known as quantum Langevin equations, and the quantum filter reduces to a so-called quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to systems of nonlinear QSDEs. We will show that there are conditions under which a filter similar to a classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problem with ‘state-dependent’ covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems that involve multiple modes, nonlinear Hamiltonians, and simultaneous jump-diffusive measurements.
Keppenne, Christian; Vernieres, Guillaume; Rienecker, Michele; Jacob, Jossy; Kovach, Robin
2011-01-01
Satellite altimetry measurements have provided global, evenly distributed observations of the ocean surface since 1993. However, the difficulties introduced by the presence of model biases and the requirement that data assimilation systems extrapolate the sea surface height (SSH) information to the subsurface in order to estimate the temperature, salinity and currents make it difficult to optimally exploit these measurements. This talk investigates the potential of the altimetry data assimilation once the biases are accounted for with an ad hoc bias estimation scheme. Either steady-state or state-dependent multivariate background-error covariances from an ensemble of model integrations are used to address the problem of extrapolating the information to the sub-surface. The GMAO ocean data assimilation system applied to an ensemble of coupled model instances using the GEOS-5 AGCM coupled to MOM4 is used in the investigation. To model the background error covariances, the system relies on a hybrid ensemble approach in which a small number of dynamically evolved model trajectories is augmented on the one hand with past instances of the state vector along each trajectory and, on the other, with a steady state ensemble of error estimates from a time series of short-term model forecasts. A state-dependent adaptive error-covariance localization and inflation algorithm controls how the SSH information is extrapolated to the sub-surface. A two-step predictor corrector approach is used to assimilate future information. Independent (not-assimilated) temperature and salinity observations from Argo floats are used to validate the assimilation. A two-step projection method in which the system first calculates a SSH increment and then projects this increment vertically onto the temperature, salt and current fields is found to be most effective in reconstructing the sub-surface information. The performance of the system in reconstructing the sub-surface fields is particularly
Directory of Open Access Journals (Sweden)
S. Dance
2009-04-01
Full Text Available We have developed an ensemble Kalman Filter (EnKF to estimate 8-day regional surface fluxes of CO2 from space-borne CO2 dry-air mole fraction observations (XCO2 and evaluate the approach using a series of synthetic experiments, in preparation for data from the NASA Orbiting Carbon Observatory (OCO. The 32-day duty cycle of OCO alternates every 16 days between nadir and glint measurements of backscattered solar radiation at short-wave infrared wavelengths. The EnKF uses an ensemble of states to represent the error covariances to estimate 8-day CO2 surface fluxes over 144 geographical regions. We use a 12×8-day lag window, recognising that XCO2 measurements include surface flux information from prior time windows. The observation operator that relates surface CO2 fluxes to atmospheric distributions of XCO2 includes: a the GEOS-Chem transport model that relates surface fluxes to global 3-D distributions of CO2 concentrations, which are sampled at the time and location of OCO measurements that are cloud-free and have aerosol optical depths 2 profiles to XCO2, accounting for differences between nadir and glint measurements, and the associated scene-dependent observation errors. We show that OCO XCO2 measurements significantly reduce the uncertainties of surface CO2 flux estimates. Glint measurements are generally better at constraining ocean CO2 flux estimates. Nadir XCO2 measurements over the terrestrial tropics are sparse throughout the year because of either clouds or smoke. Glint measurements provide the most effective constraint for estimating tropical terrestrial CO2 fluxes by accurately sampling fresh continental outflow over neighbouring oceans. We also present results from sensitivity experiments that investigate how flux estimates change with 1 bias and unbiased errors, 2 alternative duty cycles, 3 measurement density and correlations, 4 the spatial resolution of estimated flux estimates, and 5 reducing the length of the lag window and the
Implementation of Kalman Filter with Python Language
Laaraiedh, Mohamed
2009-01-01
International audience; In this paper, we investigate the implementation of a Python code for a Kalman Filter using the Numpy package. A Kalman Filtering is carried out in two steps: Prediction and Update. Each step is investigated and coded as a function with matrix input and output. These different functions are explained and an example of a Kalman Filter application for the localization of mobile in wireless networks is given.
Li, Xuejian; Mao, Fangjie; Du, Huaqiang; Zhou, Guomo; Xu, Xiaojun; Han, Ning; Sun, Shaobo; Gao, Guolong; Chen, Liang
2017-04-01
Subtropical forest ecosystems play essential roles in the global carbon cycle and in carbon sequestration functions, which challenge the traditional understanding of the main functional areas of carbon sequestration in the temperate forests of Europe and America. The leaf area index (LAI) is an important biological parameter in the spatiotemporal simulation of the carbon cycle, and it has considerable significance in carbon cycle research. Dynamic retrieval based on remote sensing data is an important method with which to obtain large-scale high-accuracy assessments of LAI. This study developed an algorithm for assimilating LAI dynamics based on an integrated ensemble Kalman filter using MODIS LAI data, MODIS reflectance data, and canopy reflectance data modeled by PROSAIL, for three typical types of subtropical forest (Moso bamboo forest, Lei bamboo forest, and evergreen and deciduous broadleaf forest) in China during 2014-2015. There were some errors of assimilation in winter, because of the bad data quality of the MODIS product. Overall, the assimilated LAI well matched the observed LAI, with R2 of 0.82, 0.93, and 0.87, RMSE of 0.73, 0.49, and 0.42, and aBIAS of 0.50, 0.23, and 0.03 for Moso bamboo forest, Lei bamboo forest, and evergreen and deciduous broadleaf forest, respectively. The algorithm greatly decreased the uncertainty of the MODIS LAI in the growing season and it improved the accuracy of the MODIS LAI. The advantage of the algorithm is its use of biophysical parameters (e.g., measured LAI) in the LAI assimilation, which makes it possible to assimilate long-term MODIS LAI time series data, and to provide high-accuracy LAI data for the study of carbon cycle characteristics in subtropical forest ecosystems.
Vogt, C.; Marquart, G.; Kosack, C.; Wolf, A.; Clauser, C.
2012-08-01
We present an estimation of the permeability fields of the reservoir at the Enhanced Geothermal System (EGS) at Soultz-sous-Forêts, France, based on the data assimilation technique Ensemble Kalman Filter (EnKF). To this end, we assimilate data from a tracer circulation experiment performed in 2005. Using a 3-D numerical simulation of fluid transport and chemical tracer dispersion, we advance the tracer in time and control the concentration. With the EnKF we obtain reliable fits for concentration data recorded in both existing production boreholes, GPK2 and GPK4. As an alternative to discrete fracture networks, our heterogeneous equivalent porous medium approach thus can also characterize the hydraulically fractured zone of the engineered geothermal system. We present best estimates for permeabilities (10-14 m2-10-12 m2for the fracture zone) and the corresponding uncertainty which is about one order of magnitude. After comparing our results to results from a massive Monte Carlo and from a gradient-based Bayesian approach, it becomes clear that only the EnKF of this three approaches is able to fit concentrations at GPK2 and GPK4 simultaneously. Based on the EnKF estimates obtained, a long-term performance prediction including an uncertainty analysis for the reservoir (as it was in 2005) yields no thermal breakthrough in the system within at least 50 years of operation. Our study demonstrates the efficiency of the EnKF when estimating the permeability distribution in an EGS reservoir even with sparse data available.
Hain, Christopher R.; Crow, Wade T.; Anderson, Martha C.; Mecikalski, John R.
2012-11-01
Studies that have assimilated remotely sensed soil moisture (SM) into land surface models (LSMs) have generally focused on retrievals from microwave (MW) sensors. However, retrievals from thermal infrared (TIR) sensors have also been shown to add unique information, especially where MW sensors are not able to provide accurate retrievals (due to, e.g., dense vegetation). In this study, we examine the assimilation of a TIR product based on surface evaporative flux estimates from the Atmosphere Land Exchange Inverse (ALEXI) model and the MW-based VU Amsterdam NASA surface SM product generated with the Land Parameter Retrieval Model (LPRM). A set of data assimilation experiments using an ensemble Kalman filter are performed over the contiguous United States to assess the impact of assimilating ALEXI and LPRM SM retrievals in isolation and together in a dual-assimilation case. The relative skill of each assimilation case is assessed through a data denial approach where a LSM is forced with an inferior precipitation data set. The ability of each assimilation case to correct for precipitation errors is quantified by comparing with a simulation forced with a higher-quality precipitation data set. All three assimilation cases (ALEXI, LPRM, and Dual assimilation) show relative improvements versus the open loop (i.e., reduced RMSD) for surface and root zone SM. In the surface zone, the dual assimilation case provides the largest improvements, followed by the LPRM case. However, the ALEXI case performs best in the root zone. Results from the data denial experiment are supported by comparisons between assimilation results and ground-based SM observations from the Soil Climate Analysis Network.
Directory of Open Access Journals (Sweden)
W. Ju
2010-03-01
Full Text Available Soil and atmospheric water deficits have significant influences on CO_{2} and energy exchanges between the atmosphere and terrestrial ecosystems. Model parameterization significantly affects the ability of a model to simulate carbon, water, and energy fluxes. In this study, an ensemble Kalman filter (EnKF and observations of gross primary productivity (GPP and latent heat (LE fluxes were used to optimize model parameters significantly affecting the calculation of these fluxes for a subtropical coniferous plantation in southeastern China. The optimized parameters include the maximum carboxylation rate (Vc_{max}, the slope in the modified Ball-Berry model (M and the coefficient determining the sensitivity of stomatal conductance to atmospheric water vapor deficit (D_{0}. Optimized Vc_{max} and M showed larger variations than D_{0}. Seasonal variations of Vc_{max} and M were more pronounced than the variations between the two years. Vc_{max} and M were associated with soil water content (SWC. During dry periods, SWC at the 20 cm depth explained 61% and 64% of variations of Vc_{max} and M, respectively. EnKF parameter optimization improved the simulations of GPP, LE and SH, mainly during dry periods. After parameter optimization using EnKF, the variations of GPP, LE and SH explained by the model increased by 1% to 4% at half-hourly steps and by 3% to 5% at daily time steps. Further efforts are needed to differentiate the real causes of parameter variations and improve the ability of models to describe the change of stomatal conductance with net photosynthesis rate and the sensitivity of photosynthesis capacity to soil water stress under different environmental conditions.
Camporese, M.; Cassiani, G.; Deiana, R.; Salandin, P.; Binley, A. M.
2013-12-01
Recent advances in geophysical methods have been increasingly exploited as inverse modeling tools in groundwater hydrology. In particular, several attempts to constrain the hydrogeophysical inverse problem to reduce inversion error have been made using time-lapse geophysical measurements through both coupled and uncoupled inversion approaches. On one hand, the main advantage of coupled approaches is that the numerical models for the geophysical and hydrological processes are linked together such that the geophysical data are inverted directly for the hydrological properties of interest, avoiding artifacts related to the classical geophysical inversions. On the other hand, uncoupled approaches, relying upon a geophysical inversion that is carried out before estimating the hydrological variable of interest, could reveal something about the process that is not accounted for in a model, i.e., they are not constrained by the conceptualization of the hydrological model. In spite of the appeal and popularity of fully coupled inversion approaches, their superiority over more traditional uncoupled methods still needs to be objectively proven; the aim of this work is to shed some light on this debate. An approach based on the Lagrangian formulation of transport and the ensemble Kalman filter (EnKF) is here applied to assess the spatial distribution of hydraulic conductivity (K) by assimilating time-lapse cross-hole electrical resistivity tomography (ERT) data generated for a synthetic tracer test in a heterogeneous aquifer. In the coupled version of the proposed inverse modeling approach, the K distribution is retrieved by assimilating raw ERT resistance data without the need for a preliminary geoelectrical inversion. In the uncoupled version, K is estimated by assimilating electrical conductivity data derived from a previously performed classical geophysical inversion of the same resistance dataset. We compare the performance of the two approaches in a number of simulation
Adaptable Iterative and Recursive Kalman Filter Schemes
Zanetti, Renato
2014-01-01
Nonlinear filters are often very computationally expensive and usually not suitable for real-time applications. Real-time navigation algorithms are typically based on linear estimators, such as the extended Kalman filter (EKF) and, to a much lesser extent, the unscented Kalman filter. The Iterated Kalman filter (IKF) and the Recursive Update Filter (RUF) are two algorithms that reduce the consequences of the linearization assumption of the EKF by performing N updates for each new measurement, where N is the number of recursions, a tuning parameter. This paper introduces an adaptable RUF algorithm to calculate N on the go, a similar technique can be used for the IKF as well.
Gray, Morgan; Petit, Cyril; Rodionov, Sergey; Bocquet, Marc; Bertino, Laurent; Ferrari, Marc; Fusco, Thierry
2014-08-25
We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).
A Tool for Kalman Filter Tuning
DEFF Research Database (Denmark)
Åkesson, Bernt Magnus; Jørgensen, John Bagterp; Poulsen, Niels Kjølstad
2007-01-01
The Kalman filter requires knowledge about the noise statistics. In practical applications, however, the noise covariances are generally not known. A method for estimating noise covariances from process data has been investigated. The method gives a least-squares estimate of the noise covariances......, which can be used to compute the Kalman filter gain....
Harmonic Detection at Initialization With Kalman Filter
DEFF Research Database (Denmark)
Hussain, Dil Muhammad Akbar; Imran, Raja Muhammad; Shoro, Ghulam Mustafa
2014-01-01
the affect of harmonics on the supply. For the detection of these harmonics various techniques are available and one of that technique is the Kalman filter. In this paper we investigate that what are the consequences when harmonic detection system based on Kalman Filtering is initialized...
A new martingale approach to Kalman Filtering
Bagchi, Arunabha
1976-01-01
A new derivation of continuous-time Kalman Filter equations is presented. The underlying idea has been previously used to derive the smoothing equations. A unified approach to filtering and smoothing problems has thus been achieved.
Boundary Value Problems Arising in Kalman Filtering
Directory of Open Access Journals (Sweden)
Bashirov Agamirza
2008-01-01
Full Text Available The classic Kalman filtering equations for independent and correlated white noises are ordinary differential equations (deterministic or stochastic with the respective initial conditions. Changing the noise processes by taking them to be more realistic wide band noises or delayed white noises creates challenging partial differential equations with initial and boundary conditions. In this paper, we are aimed to give a survey of this connection between Kalman filtering and boundary value problems, bringing them into the attention of mathematicians as well as engineers dealing with Kalman filtering and boundary value problems.
Boundary Value Problems Arising in Kalman Filtering
Directory of Open Access Journals (Sweden)
Sinem Ertürk
2009-01-01
Full Text Available The classic Kalman filtering equations for independent and correlated white noises are ordinary differential equations (deterministic or stochastic with the respective initial conditions. Changing the noise processes by taking them to be more realistic wide band noises or delayed white noises creates challenging partial differential equations with initial and boundary conditions. In this paper, we are aimed to give a survey of this connection between Kalman filtering and boundary value problems, bringing them into the attention of mathematicians as well as engineers dealing with Kalman filtering and boundary value problems.
Kalman filtering theory and practice with MATLAB
Grewal, M
2015-01-01
The definitive textbook and professional reference on Kalman Filtering fully updated, revised, and expanded This book contains the latest developments in the implementation and application of Kalman filtering. Authors Grewal and Andrews draw upon their decades of experience to offer an in-depth examination of the subtleties, common pitfalls, and limitations of estimation theory as it applies to real-world situations. They present many illustrative examples including adaptations for nonlinear filtering, global navigation satellite systems, the error modeling of gyros and accelerometers, inertial navigation systems, and freeway traffic control. Kalman Filtering: Theory and Practice Using MATLAB, Fourth Edition is an ideal textbook in advanced undergraduate and beginning graduate courses in stochastic processes and Kalman filtering. It is also appropriate for self-instruction or review by practicing engineers and scientists who want to learn more about this important topic.
Kalman filter to update forest cover estimates
Raymond L. Czaplewski
1990-01-01
The Kalman filter is a statistical estimator that combines a time-series of independent estimates, using a prediction model that describes expected changes in the state of a system over time. An expensive inventory can be updated using model predictions that are adjusted with more recent, but less expensive and precise, monitoring data. The concepts of the Kalman...
Industrial applications of the Kalman filter
DEFF Research Database (Denmark)
Auger, François; Hilairet, Mickael; Guerrero, Josep M.
2013-01-01
The Kalman filter has received a huge interest from the industrial electronics community and has played a key role in many engineering fields since the 70s, ranging, without being exhaustive, trajectory estimation, state and parameter estimation for control or diagnosis, data merging, signal...... processing and so on. This paper provides a brief overview of the industrial applications and implementation issues of the Kalman filter in six topics of the industrial electronics community, highlighting some relevant reference papers and giving future research trends....
Nonlinear Kalman Filtering With Divergence Minimization
Gultekin, San; Paisley, John
2017-12-01
We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper we propose novel algorithms to optimize the forward and reverse forms of the KL divergence, as well as the alpha-divergence which contains these two as limiting cases. Unlike previous approaches, our algorithms do not make approximations to the divergences being optimized, but use Monte Carlo integration techniques to derive unbiased algorithms for direct optimization. We assess performance on radar and sensor tracking, and options pricing problems, showing general improvement over the UKF and EKF, as well as competitive performance with particle filtering.
Deterministic Kalman filtering in a behavioral framework
Fagnani, F; Willems, JC
1997-01-01
The purpose of this paper is to obtain a deterministic version of the Kalman filtering equations. We will use a behavioral description of the plant, specifically, an image representation. The resulting algorithm requires a matrix spectral factorization. We also show that the filter can be
MR fingerprinting reconstruction with Kalman filter.
Zhang, Xiaodi; Zhou, Zechen; Chen, Shiyang; Chen, Shuo; Li, Rui; Hu, Xiaoping
2017-09-01
Magnetic resonance fingerprinting (MR fingerprinting or MRF) is a newly introduced quantitative magnetic resonance imaging technique, which enables simultaneous multi-parameter mapping in a single acquisition with improved time efficiency. The current MRF reconstruction method is based on dictionary matching, which may be limited by the discrete and finite nature of the dictionary and the computational cost associated with dictionary construction, storage and matching. In this paper, we describe a reconstruction method based on Kalman filter for MRF, which avoids the use of dictionary to obtain continuous MR parameter measurements. With this Kalman filter framework, the Bloch equation of inversion-recovery balanced steady state free-precession (IR-bSSFP) MRF sequence was derived to predict signal evolution, and acquired signal was entered to update the prediction. The algorithm can gradually estimate the accurate MR parameters during the recursive calculation. Single pixel and numeric brain phantom simulation were implemented with Kalman filter and the results were compared with those from dictionary matching reconstruction algorithm to demonstrate the feasibility and assess the performance of Kalman filter algorithm. The results demonstrated that Kalman filter algorithm is applicable for MRF reconstruction, eliminating the need for a pre-define dictionary and obtaining continuous MR parameter in contrast to the dictionary matching algorithm. Copyright © 2017 Elsevier Inc. All rights reserved.
A class of quaternion Kalman filters.
Jahanchahi, Cyrus; Mandic, Danilo P
2014-03-01
The existing Kalman filters for quaternion-valued signals do not operate fully in the quaternion domain, and are combined with the real Kalman filter to enable the tracking in 3-D spaces. Using the recently introduced HR-calculus, we develop the fully quaternion-valued Kalman filter (QKF) and quaternion-extended Kalman filter (QEKF), allowing for the tracking of 3-D and 4-D signals directly in the quaternion domain. To consider the second-order noncircularity of signals, we employ the recently developed augmented quaternion statistics to derive the widely linear QKF (WL-QKF) and widely linear QEKF (WL-QEKF). To reduce computational requirements of the widely linear algorithms, their efficient implementation are proposed and it is shown that the quaternion widely linear model can be simplified when processing 3-D data, further reducing the computational requirements. Simulations using both synthetic and real-world circular and noncircular signals illustrate the advantages offered by widely linear over strictly linear quaternion Kalman filters.
Improving Short-Range Ensemble Kalman Storm Surge Forecasting Using Robust Adaptive Inflation
Altaf, Muhammad
2013-08-01
This paper presents a robust ensemble filtering methodology for storm surge forecasting based on the singular evolutive interpolated Kalman (SEIK) filter, which has been implemented in the framework of the H∞ filter. By design, an H∞ filter is more robust than the common Kalman filter in the sense that the estimation error in the H∞ filter has, in general, a finite growth rate with respect to the uncertainties in assimilation. The computational hydrodynamical model used in this study is the Advanced Circulation (ADCIRC) model. The authors assimilate data obtained from Hurricanes Katrina and Ike as test cases. The results clearly show that the H∞-based SEIK filter provides more accurate short-range forecasts of storm surge compared to recently reported data assimilation results resulting from the standard SEIK filter.
Nonlinear Kalman filtering in affine term structure models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris
2014-01-01
The extended Kalman filter, which linearizes the relationship between security prices and state variables, is widely used in fixed-income applications. We investigate whether the unscented Kalman filter should be used to capture nonlinearities and compare the performance of the Kalman filter with...... performs well when compared with the much more computationally intensive particle filter. These findings suggest that the unscented Kalman filter may be a good approach for a variety of problems in fixed-income pricing....
Target detection by way of Kalman filtering
Sipe, Gary A.
1993-03-01
A simple, time domain method is used to analyze moderate to high PRF radar signals. The quantities of interest are the signal's PRF, SNR, and time of arrival. The time of arrival problem is important because it can be used, with multiple sensors, to determine the position of the emitting target. An algorithm is described which will produce these values using Kalman filtering. Individual pulses in a pulsed type radar are measured against a threshold using a two sample detection scheme to provide some glitch rejection. Results of individual time domain measurements of the signal parameter are smoothed with a Kalman filter. Integrating the pulse train envelope during the radar dwell time provides the energy centroid for a scan cycle. This centroid, time differenced with multiple sensors, provides observables for an Extended Kalman Filter for emitter localization. The work here simulates all data. Tests of the algorithms developed were conducted on real, classified data in addition to the work presented here.
Restricted Kalman Filtering Theory, Methods, and Application
Pizzinga, Adrian
2012-01-01
In statistics, the Kalman filter is a mathematical method whose purpose is to use a series of measurements observed over time, containing random variations and other inaccuracies, and produce estimates that tend to be closer to the true unknown values than those that would be based on a single measurement alone. This Brief offers developments on Kalman filtering subject to general linear constraints. There are essentially three types of contributions: new proofs for results already established; new results within the subject; and applications in investment analysis and macroeconomics, where th
Kalman Filter Predictor and Initialization Algorithm for PRI Tracking
National Research Council Canada - National Science Library
Hock, Melinda
1998-01-01
.... The algorithm uses a Kalman filter for prediction combined with a preprocessing routine to determine the period of the stagger sequence and to construct an uncorrupted data set for Kalman filter initialization...
On a nonlinear Kalman filter with simplified divided difference approximation
Luo, Xiaodong
2012-03-01
We present a new ensemble-based approach that handles nonlinearity based on a simplified divided difference approximation through Stirling\\'s interpolation formula, which is hence called the simplified divided difference filter (sDDF). The sDDF uses Stirling\\'s interpolation formula to evaluate the statistics of the background ensemble during the prediction step, while at the filtering step the sDDF employs the formulae in an ensemble square root filter (EnSRF) to update the background to the analysis. In this sense, the sDDF is a hybrid of Stirling\\'s interpolation formula and the EnSRF method, while the computational cost of the sDDF is less than that of the EnSRF. Numerical comparison between the sDDF and the EnSRF, with the ensemble transform Kalman filter (ETKF) as the representative, is conducted. The experiment results suggest that the sDDF outperforms the ETKF with a relatively large ensemble size, and thus is a good candidate for data assimilation in systems with moderate dimensions. © 2011 Elsevier B.V. All rights reserved.
Kalman Filter Application to Symmetrical Fault Detection during Power Swing
DEFF Research Database (Denmark)
Khodaparast, Jalal; Silva, Filipe Miguel Faria da; Khederzadeh, M.
2016-01-01
capability of Kalman Filter. The proposed index is calculated by assessing the difference between predicted and actual samples of impedance. The predicted impedance samples are obtained using Kalman filter and Taylor expansion, which is used in this paper to track the phasor precisely. Second order of Taylor...... expansion is used to decrease corrugation effect of impedance estimation and increase the reliability of proposed method. The instantaneous estimation and prediction capability of Kalman filter are two reasons for proposing utilizing Kalman filter....
Cubature/ Unscented/ Sigma Point Kalman Filtering with Angular Measurement Models
2015-07-06
Cubature/ Unscented/ Sigma Point Kalman Filtering with Angular Measurement Models David Frederic Crouse Naval Research Laboratory 4555 Overlook Ave...measurement and process non- linearities, such as the cubature Kalman filter, can perform ex- tremely poorly in many applications involving angular... Kalman filtering is a realization of the best linear unbiased estimator (BLUE) that evaluates certain integrals for expected values using different forms
Q-Method Extended Kalman Filter
Zanetti, Renato; Ainscough, Thomas; Christian, John; Spanos, Pol D.
2012-01-01
A new algorithm is proposed that smoothly integrates non-linear estimation of the attitude quaternion using Davenport s q-method and estimation of non-attitude states through an extended Kalman filter. The new method is compared to a similar existing algorithm showing its similarities and differences. The validity of the proposed approach is confirmed through numerical simulations.
Towards self-organizing Kalman filters
Sijs, J.; Papp, Z.
2012-01-01
Distributed Kalman filtering is an important signal processing method for state estimation in large-scale sensor networks. However, existing solutions do not account for unforeseen events that are likely to occur and thus dramatically changing the operational conditions (e.g. node failure,
A distributed Kalman filter with global covariance
Sijs, J.; Lazar, M.
2011-01-01
Most distributed Kalman filtering (DKF) algorithms for sensor networks calculate a local estimate of the global state-vector in each node. An important challenge within distributed estimation is that all sensors in the network contribute to the local estimate in each node. In this paper, a novel DKF
Detection of Harmonic Occurring using Kalman Filtering
DEFF Research Database (Denmark)
Hussain, Dil Muhammad Akbar; Shoro, Ghulam Mustafa; Imran, Raja Muhammed
2014-01-01
As long as the load to a power system is linear which has been the case before 80's, typically no harmonics are produced. However, the modern power electronic equipment for controlled power consumption produces harmonic disturbances, these devices/equipment possess nonlinear voltage/current chara...... using Kalman filter. This may be very useful for example to quickly switching on certain filters based on the harmonic present. We are using a unique technique to detect the occurrence of harmonics....
Peng, Zhen; Liu, Zhiquan; Chen, Dan; Ban, Junmei
2017-04-01
In an attempt to improve the forecasting of atmospheric aerosols, the ensemble square root filter algorithm was extended to simultaneously optimize the chemical initial conditions (ICs) and emission input. The forecast model, which was expanded by combining the Weather Research and Forecasting with Chemistry (WRF-Chem) model and a forecast model of emission scaling factors, generated both chemical concentration fields and emission scaling factors. The forecast model of emission scaling factors was developed by using the ensemble concentration ratios of the WRF-Chem forecast chemical concentrations and also the time smoothing operator. Hourly surface fine particulate matter (PM2. 5) observations were assimilated in this system over China from 5 to 16 October 2014. A series of 48 h forecasts was then carried out with the optimized initial conditions and emissions on each day at 00:00 UTC and a control experiment was performed without data assimilation. In addition, we also performed an experiment of pure assimilation chemical ICs and the corresponding 48 h forecasts experiment for comparison. The results showed that the forecasts with the optimized initial conditions and emissions typically outperformed those from the control experiment. In the Yangtze River delta (YRD) and the Pearl River delta (PRD) regions, large reduction of the root-mean-square errors (RMSEs) was obtained for almost the entire 48 h forecast range attributed to assimilation. In particular, the relative reduction in RMSE due to assimilation was about 37.5 % at nighttime when WRF-Chem performed comparatively worse. In the Beijing-Tianjin-Hebei (JJJ) region, relatively smaller improvements were achieved in the first 24 h forecast but then no improvements were achieved afterwards. Comparing to the forecasts with only the optimized ICs, the forecasts with the joint adjustment were always much better during the night in the PRD and YRD regions. However, they were very similar during daytime in both
LHCb Kalman Filter cross architecture studies
Hugo, Daniel; Pérez, Cámpora
2017-10-01
The 2020 upgrade of the LHCb detector will vastly increase the rate of collisions the Online system needs to process in software, in order to filter events in real time. 30 million collisions per second will pass through a selection chain, where each step is executed conditional to its prior acceptance. The Kalman Filter is a fit applied to all reconstructed tracks which, due to its time characteristics and early execution in the selection chain, consumes 40% of the whole reconstruction time in the current trigger software. This makes the Kalman Filter a time-critical component as the LHCb trigger evolves into a full software trigger in the Upgrade. I present a new Kalman Filter algorithm for LHCb that can efficiently make use of any kind of SIMD processor, and its design is explained in depth. Performance benchmarks are compared between a variety of hardware architectures, including x86_64 and Power8, and the Intel Xeon Phi accelerator, and the suitability of said architectures to efficiently perform the LHCb Reconstruction process is determined.
Design of Kalman filters for mobile robots
DEFF Research Database (Denmark)
Larsen, Thomas Dall; Hansen, Karsten L.; Andersen, Nils Axel
1999-01-01
the mobile robot is equipped with a dual encoder system supported by some additional absolute measurements. A common filter type for this setup is the odometric filter, where readings from the odometry system on the robot are used together with the geometry of the robot movement as a model of the robot....... If additional kinematic assumptions are made, for instance regarding the velocity of the robot, an augmented model can be used instead. This kinematic filter has some advantages when used intelligently, and it is shown how this type of filter can be used to suppress noise on encoder readings and velocity...... estimates. The Kalman filter normally consists of a time update followed by one or more data updates. However, it is shown that when using the kinematic filter, the encoder measurements should be fused prior to the time update for better performance....
Estimasi Variabel Dinamik Menggunakan Metode Kalman Filter
Directory of Open Access Journals (Sweden)
Nathanael Leon Gozali
2013-09-01
Full Text Available Sebuah sistem pengendalian kapal dituntut untuk memiliki akurasi yang tinggi. Hal ini dituntut dengan adanya sistem pengendalian otomatis yang dibuat dengan menjadikan feedback dari alat ukur sebagai nilai yang mempengaruhi pengendali. Dengan alat ukur yang memiliki noise dan sistem yang memiliki noise sehingga tidak sesuai dengan perancangan sistem tersebut menjadi penyebab ketidaktepatan dalam pengendalian kapal. Meskipun noise bernilai kecil namun dalam waktu yang lama dan terus menerus terakumulasi sehingga pengendalian tidak berjalan dengan baik. Tujuan dari penelitian ini adalah untuk merancang sebuah estimator Kalman Filter pada kondisi noise dari alat ukur, noise dari sistem kapal dan ketidaktepatan dalam pemodelan. Metode Kalman Filter yang digunakan adalah metode Kalman Filter diskrit linier karena model dinamika kapal telah dilinierisai dan didiskritisasi terlebih dahulu. Variabel dinamik kapal yang diestimasi untuk keperluan steering adalah dinamika sway-yaw dengan variabel kecepatan sudut, posisi sudut dan kecepatan arah sway. Perancangan sistem berdasarkan spesifikasi kapal perang kelas SIGMA Extended. Berdasarkan hasil simulasi, estimator yang dirancang mampu memberikan nilai estimasi pada ketiga variabel dinamika kapal dengan persentase integral absolute error dari sistem dengan noise sistem dan noise pengukuran sebesar 0,41% untuk variabel yaw, 4,30% untuk yaw-rate dan 6,78% untuk sway-rate.
A GPU-accelerated extended Kalman filter
Wei, Shih-Chieh; Huang, Bormin
2011-11-01
The extended Kalman filter is one of the most widely used techniques for state estimation of nonlinear systems. In its two steps of forecast and data assimilation, many matrix operations including multiplication and inversion are involved. As recent graphic processor units (GPU) have shown to provide much speedup in matrix operations, we will explore in this work a GPU-based implementation of the extended Kalman filter. The Compute Unified Device Architecture (CUDA) on the Nvidia GeForce GTX 590 GPU hardware will be used for comparison with a single threaded CPU counterpart. Experiments were conducted on typical large-scale over-determined systems with thousands of components in states and measurements. Within the GPU memory limit, a speedup of 1386x is achieved for a system with measurements having 5000 components and states having 3750 components. The speedup profile for various combinations of measurement and state sizes will serve as good reference for future implementation of extended Kalman filter on real large-scale applications.
Ahrens, H.; Argin, F.; Klinkenbusch, L.
2013-07-01
The non-invasive and radiation-free imaging of the electrical activity of the heart with Electrocardiography (ECG) or Magnetocardiography (MCG) can be helpful for physicians for instance in the localization of the origin of cardiac arrhythmia. In this paper we compare two Kalman Filter algorithms for the solution of a nonlinear state-space model and for the subsequent imaging of the activation/depolarization times of the heart muscle: the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). The algorithms are compared for simulations of a (6×6) magnetometer array, a torso model with piecewise homogeneous conductivities, 946 current dipoles located in a small part of the heart (apex), and several noise levels. It is found that for all tested noise levels the convergence of the activation times is faster for the UKF.
A Kalman Filtering Perspective for Multiatlas Segmentation.
Gao, Yi; Zhu, Liangjia; Cates, Joshua; MacLeod, Rob S; Bouix, Sylvain; Tannenbaum, Allen
In multiatlas segmentation, one typically registers several atlases to the novel image, and their respective segmented label images are transformed and fused to form the final segmentation. In this work, we provide a new dynamical system perspective for multiatlas segmentation, inspired by the following fact: The transformation that aligns the current atlas to the novel image can be not only computed by direct registration but also inferred from the transformation that aligns the previous atlas to the image together with the transformation between the two atlases. This process is similar to the global positioning system on a vehicle, which gets position by inquiring from the satellite and by employing the previous location and velocity-neither answer in isolation being perfect. To solve this problem, a dynamical system scheme is crucial to combine the two pieces of information; for example, a Kalman filtering scheme is used. Accordingly, in this work, a Kalman multiatlas segmentation is proposed to stabilize the global/affine registration step. The contributions of this work are twofold. First, it provides a new dynamical systematic perspective for standard independent multiatlas registrations, and it is solved by Kalman filtering. Second, with very little extra computation, it can be combined with most existing multiatlas segmentation schemes for better registration/segmentation accuracy.
Kalman filter tracking on parallel architectures
Cerati, G.; Elmer, P.; Krutelyov, S.; Lantz, S.; Lefebvre, M.; McDermott, K.; Riley, D.; Tadel, M.; Wittich, P.; Wurthwein, F.; Yagil, A.
2017-10-01
We report on the progress of our studies towards a Kalman filter track reconstruction algorithm with optimal performance on manycore architectures. The combinatorial structure of these algorithms is not immediately compatible with an efficient SIMD (or SIMT) implementation; the challenge for us is to recast the existing software so it can readily generate hundreds of shared-memory threads that exploit the underlying instruction set of modern processors. We show how the data and associated tasks can be organized in a way that is conducive to both multithreading and vectorization. We demonstrate very good performance on Intel Xeon and Xeon Phi architectures, as well as promising first results on Nvidia GPUs.
Radio Channel State Prediction by Kalman Filter
Directory of Open Access Journals (Sweden)
Peter Ziacik
2005-01-01
Full Text Available In this article there is the description Kalman filter using as a radio channel state predictor. Simulator of prediction has been created in MATLAB environment and it is capable to simulate the prediction of radio signal envelope by Clark’s model of radio channel, which is implemented to the simulator. Simulations were realized for prediction range 0.41 ms and 6.24 ms and as comparing criterion we used the prediction error. It is clear from simulations, that with the duration of prediction the prediction error is enlarging, which may cause the erroneous decision of adaptation algorithms.
Vehicle Sideslip Angle Estimation Based on Hybrid Kalman Filter
Directory of Open Access Journals (Sweden)
Jing Li
2016-01-01
Full Text Available Vehicle sideslip angle is essential for active safety control systems. This paper presents a new hybrid Kalman filter to estimate vehicle sideslip angle based on the 3-DoF nonlinear vehicle dynamic model combined with Magic Formula tire model. The hybrid Kalman filter is realized by combining square-root cubature Kalman filter (SCKF, which has quick convergence and numerical stability, with square-root cubature based receding horizon Kalman FIR filter (SCRHKF, which has robustness against model uncertainty and temporary noise. Moreover, SCKF and SCRHKF work in parallel, and the estimation outputs of two filters are merged by interacting multiple model (IMM approach. Experimental results show the accuracy and robustness of the hybrid Kalman filter.
Kalman Filter Tracking on Parallel Architectures
Directory of Open Access Journals (Sweden)
Cerati Giuseppe
2016-01-01
Full Text Available Power density constraints are limiting the performance improvements of modern CPUs. To address this we have seen the introduction of lower-power, multi-core processors such as GPGPU, ARM and Intel MIC. In order to achieve the theoretical performance gains of these processors, it will be necessary to parallelize algorithms to exploit larger numbers of lightweight cores and specialized functions like large vector units. Track finding and fitting is one of the most computationally challenging problems for event reconstruction in particle physics. At the High-Luminosity Large Hadron Collider (HL-LHC, for example, this will be by far the dominant problem. The need for greater parallelism has driven investigations of very different track finding techniques such as Cellular Automata or Hough Transforms. The most common track finding techniques in use today, however, are those based on a Kalman filter approach. Significant experience has been accumulated with these techniques on real tracking detector systems, both in the trigger and offline. They are known to provide high physics performance, are robust, and are in use today at the LHC. Given the utility of the Kalman filter in track finding, we have begun to port these algorithms to parallel architectures, namely Intel Xeon and Xeon Phi. We report here on our progress towards an end-to-end track reconstruction algorithm fully exploiting vectorization and parallelization techniques in a simplified experimental environment.
Kalman Filter Tracking on Parallel Architectures
Cerati, Giuseppe; Elmer, Peter; Lantz, Steven; McDermott, Kevin; Riley, Dan; Tadel, Matevž; Wittich, Peter; Würthwein, Frank; Yagil, Avi
2015-12-01
Power density constraints are limiting the performance improvements of modern CPUs. To address this we have seen the introduction of lower-power, multi-core processors, but the future will be even more exciting. In order to stay within the power density limits but still obtain Moore's Law performance/price gains, it will be necessary to parallelize algorithms to exploit larger numbers of lightweight cores and specialized functions like large vector units. Example technologies today include Intel's Xeon Phi and GPGPUs. Track finding and fitting is one of the most computationally challenging problems for event reconstruction in particle physics. At the High Luminosity LHC, for example, this will be by far the dominant problem. The need for greater parallelism has driven investigations of very different track finding techniques including Cellular Automata or returning to Hough Transform. The most common track finding techniques in use today are however those based on the Kalman Filter [2]. Significant experience has been accumulated with these techniques on real tracking detector systems, both in the trigger and offline. They are known to provide high physics performance, are robust and are exactly those being used today for the design of the tracking system for HL-LHC. Our previous investigations showed that, using optimized data structures, track fitting with Kalman Filter can achieve large speedup both with Intel Xeon and Xeon Phi. We report here our further progress towards an end-to-end track reconstruction algorithm fully exploiting vectorization and parallelization techniques in a realistic simulation setup.
Kalman filter applied in underwater integrated navigation system
Directory of Open Access Journals (Sweden)
Yan Xincun
2013-02-01
Full Text Available For the underwater integrated navigation system, information fusion is an important technology. This paper introduces the Kalman filter as the most useful information fusion technology, and then gives a summary of the Kalman filter applied in underwater integrated navigation system at present, and points out the further research directions in this field.
Improving Artificial Neural Network Forecasts with Kalman Filtering ...
African Journals Online (AJOL)
... used to compare the two models over different set of data from different companies over a period of 750 trading days. In all the cases we find that the Kalman filter algorithm significantly adds value to the forecasting process. Keywords: Artificial Neural Networks, Kalman filter, Stock prices, Forecasting, Back propagation ...
Kalman filter estimation of RLC parameters for UMP transmission line
Directory of Open Access Journals (Sweden)
Mohd Amin Siti Nur Aishah
2018-01-01
Full Text Available This paper present the development of Kalman filter that allows evaluation in the estimation of resistance (R, inductance (L, and capacitance (C values for Universiti Malaysia Pahang (UMP short transmission line. To overcome the weaknesses of existing system such as power losses in the transmission line, Kalman Filter can be a better solution to estimate the parameters. The aim of this paper is to estimate RLC values by using Kalman filter that in the end can increase the system efficiency in UMP. In this research, matlab simulink model is developed to analyse the UMP short transmission line by considering different noise conditions to reprint certain unknown parameters which are difficult to predict. The data is then used for comparison purposes between calculated and estimated values. The results have illustrated that the Kalman Filter estimate accurately the RLC parameters with less error. The comparison of accuracy between Kalman Filter and Least Square method is also presented to evaluate their performances.
Kalman Filter for Spinning Spacecraft Attitude Estimation
Markley, F. Landis; Sedlak, Joseph E.
2008-01-01
This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames by employing a reduced six-component error state. Four variants of the filter, defined by different choices for the reduced error state, are tested against a quaternion-based filter using simulated data for the THEMIS mission. Three of these variants choose three of the components of the error state to be the infinitesimal attitude error angles, facilitating the computation of measurement sensitivity matrices and causing the usual 3x3 attitude covariance matrix to be a submatrix of the 6x6 covariance of the error state. These variants differ in their choice for the other three components of the error state. The variant employing the infinitesimal attitude error angles and the angular momentum components in an inertial reference frame as the error state shows the best combination of robustness and efficiency in the simulations. Attitude estimation results using THEMIS flight data are also presented.
DEFF Research Database (Denmark)
Khazraj, Hesam; Silva, Filipe Miguel Faria da; Bak, Claus Leth
2016-01-01
Dynamic State Estimation (DSE) is a critical tool for analysis, monitoring and planning of a power system. The concept of DSE involves designing state estimation with Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF) methods, which can be used by wide area monitoring to improve the st...
Nonlinear Kalman Filtering in Affine Term Structure Models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris
the potential of the unscented Kalman …filter to properly capture nonlinearities. To illustrate the advantages of the unscented Kalman …filter, we analyze the cross section of swap rates, which are relatively simple non-linear instruments, and cap prices, which are highly nonlinear in the states. An extensive...... Monte Carlo experiment demonstrates that the unscented Kalman fi…lter is much more accurate than its extended counterpart in fi…ltering the states and forecasting swap rates and caps. Our fi…ndings suggest that the unscented Kalman fi…lter may prove to be a good approach for a number of other problems...
Distributed Kalman-Consensus Filtering for Sparse Signal Estimation
Directory of Open Access Journals (Sweden)
Yisha Liu
2014-01-01
Full Text Available A Kalman filtering-based distributed algorithm is proposed to deal with the sparse signal estimation problem. The pseudomeasurement-embedded Kalman filter is rebuilt in the information form, and an improved parameter selection approach is discussed. By introducing the pseudomeasurement technology into Kalman-consensus filter, a distributed estimation algorithm is developed to fuse the measurements from different nodes in the network, such that all filters can reach a consensus on the estimate of sparse signals. Some numerical examples are provided to demonstrate the effectiveness of the proposed approach.
Weighted Ensemble Square Root Filters for Non-linear, Non-Gaussian, Data Assimilation
Livings, D. M.; van Leeuwen, P.
2012-12-01
In recent years the Ensemble Kalman Filter (EnKF) has become widely-used in both operational and research data assimilation systems. The particle filter is an alternative ensemble-based algorithm that offers the possibility of improved performance in non-linear and non-Gaussian problems. Papadakis et al (2010) introduced the Weighted Ensemble Kalman Filter (WEnKF) as a combination of the best features of the EnKF and the particle filter. Published work on the WEnKF has so far concentrated on the formulation of the EnKF in which observations are perturbed; no satisfactory general framework has been given for particle filters based on the alternative formulation of the EnKF known as the ensemble square root filter. This presentation will provide such a framework and show how several popular ensemble square root filters fit into it. No linear or Gaussian assumptions about the dynamical or observational models will be necessary. By examining the algorithms closely, shortcuts will be identified that increase both the simplicity and the efficiency of the resulting particle filter in comparison with a naive implementation. A procedure will be given for simply converting an existing ensemble square root filter into a particle filter. The procedure will not be limited to basic ensemble square root filters, but will be able to incorporate common variations such as covariance inflation without making any approximations.
RSSI based indoor tracking in sensor networks using Kalman filters
DEFF Research Database (Denmark)
Tøgersen, Frede Aakmann; Skjøth, Flemming; Munksgaard, Lene
2010-01-01
We propose an algorithm for estimating positions of devices in a sensor network using Kalman filtering techniques. The specific area of application is monitoring the movements of cows in a barn. The algorithm consists of two filters. The first filter enhances the signal-to-noise ratio of the obse......We propose an algorithm for estimating positions of devices in a sensor network using Kalman filtering techniques. The specific area of application is monitoring the movements of cows in a barn. The algorithm consists of two filters. The first filter enhances the signal-to-noise ratio...
Autonomous mobile robot localization using Kalman filter
Directory of Open Access Journals (Sweden)
Mohd Nasir Nabil Zhafri
2017-01-01
Full Text Available Autonomous mobile robot field has gain interest among researchers in recent years. The ability of a mobile robot to locate its current position and surrounding environment is the fundamental in order for it to operate autonomously, which commonly known as localization. Localization of mobile robot are commonly affected by the inaccuracy of the sensors. These inaccuracies are caused by various factors which includes internal interferences of the sensor and external environment noises. In order to overcome these noises, a filtering method is required in order to improve the mobile robot’s localization. In this research, a 2- wheeled-drive (2WD mobile robot will be used as platform. The odometers, inertial measurement unit (IMU, and ultrasonic sensors are used for data collection. Data collected is processed using Kalman filter to predict and correct the error from these sensors reading. The differential drive model and measurement model which estimates the environmental noises and predict a correction are used in this research. Based on the simulation and experimental results, the x, y and heading was corrected by converging the error to10 mm, 10 mm and 0.06 rad respectively.
Kalman Filtering with Inequality Constraints for Turbofan Engine Health Estimation
Simon, Dan; Simon, Donald L.
2003-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops two analytic methods of incorporating state variable inequality constraints in the Kalman filter. The first method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satisfied rather than exactly satisfied.) The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results. The use of the algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate health parameters. The turbofan engine model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.
Kalman Filter Constraint Tuning for Turbofan Engine Health Estimation
Simon, Dan; Simon, Donald L.
2005-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter, which has been shown to generally improve the filter s estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy as the Kalman filter is theoretically optimal. This paper proposes a way to tune the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.
A LBL Positioning Method Based on Feedback Kalman Filter
Jucheng Zhang; Dajun Sun; Changlin Ji
2014-01-01
LBL (Long Basic Line) positioning is an important and high-precision method for underwater vehicle navigation. Due to its narrow work frequency-band, system would be easily affected by external factors and gave wrong results. A new Kalman filter model based on the feedback from travel time and position information was presented in this paper. By combining travel time with positioning in the Kalman filter, the navigation state of underwater vehicle was accurately estimated. Experimental result...
DEFF Research Database (Denmark)
Khazraj, Hesam; Silva, Filipe Miguel Faria da; Bak, Claus Leth
2016-01-01
Dynamic State Estimation (DSE) is a critical tool for analysis, monitoring and planning of a power system. The concept of DSE involves designing state estimation with Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF) methods, which can be used by wide area monitoring to improve the st...... and studying the advantages and disadvantages of both methods under transient conditions. It is demonstrated that UKF is easier to implement and accurate in estimation....
Kalman-Takens filtering in the presence of dynamical noise
Hamilton, Franz; Berry, Tyrus; Sauer, Timothy
2017-12-01
The use of data assimilation for the merging of observed data with dynamical models is becoming standard in modern physics. If a parametric model is known, methods such as Kalman filtering have been developed for this purpose. If no model is known, a hybrid Kalman-Takens method has been recently introduced, in order to exploit the advantages of optimal filtering in a nonparametric setting. This procedure replaces the parametric model with dynamics reconstructed from delay coordinates, while using the Kalman update formulation to assimilate new observations. In this article, we study the efficacy of this method for identifying underlying dynamics in the presence of dynamical noise. Furthermore, by combining the Kalman-Takens method with an adaptive filtering procedure we are able to estimate the statistics of the observational and dynamical noise. This solves a long-standing problem of separating dynamical and observational noise in time series data, which is especially challenging when no dynamical model is specified.
Power system static state estimation using Kalman filter algorithm
Directory of Open Access Journals (Sweden)
Saikia Anupam
2016-01-01
Full Text Available State estimation of power system is an important tool for operation, analysis and forecasting of electric power system. In this paper, a Kalman filter algorithm is presented for static estimation of power system state variables. IEEE 14 bus system is employed to check the accuracy of this method. Newton Raphson load flow study is first carried out on our test system and a set of data from the output of load flow program is taken as measurement input. Measurement inputs are simulated by adding Gaussian noise of zero mean. The results of Kalman estimation are compared with traditional Weight Least Square (WLS method and it is observed that Kalman filter algorithm is numerically more efficient than traditional WLS method. Estimation accuracy is also tested for presence of parametric error in the system. In addition, numerical stability of Kalman filter algorithm is tested by considering inclusion of zero mean errors in the initial estimates.
Impulse control in Kalman-like filtering problems
Directory of Open Access Journals (Sweden)
Michael V. Basin
1998-01-01
Full Text Available This paper develops the impulse control approach to the observation process in Kalman-like filtering problems, which is based on impulsive modeling of the transition matrix in an observation equation. The impulse control generates the jumps of the estimate variance from its current position down to zero and, as a result, enables us to obtain the filtering equations for the Kalman estimate with zero variance for all post-jump time moments. The filtering equations for the estimates with zero variances are obtained in the conventional linear filtering problem and in the case of scalar nonlinear state and nonlinear observation equations.
Efficient Kernel-Based Ensemble Gaussian Mixture Filtering
Liu, Bo
2015-11-11
We consider the Bayesian filtering problem for data assimilation following the kernel-based ensemble Gaussian-mixture filtering (EnGMF) approach introduced by Anderson and Anderson (1999). In this approach, the posterior distribution of the system state is propagated with the model using the ensemble Monte Carlo method, providing a forecast ensemble that is then used to construct a prior Gaussian-mixture (GM) based on the kernel density estimator. This results in two update steps: a Kalman filter (KF)-like update of the ensemble members and a particle filter (PF)-like update of the weights, followed by a resampling step to start a new forecast cycle. After formulating EnGMF for any observational operator, we analyze the influence of the bandwidth parameter of the kernel function on the covariance of the posterior distribution. We then focus on two aspects: i) the efficient implementation of EnGMF with (relatively) small ensembles, where we propose a new deterministic resampling strategy preserving the first two moments of the posterior GM to limit the sampling error; and ii) the analysis of the effect of the bandwidth parameter on contributions of KF and PF updates and on the weights variance. Numerical results using the Lorenz-96 model are presented to assess the behavior of EnGMF with deterministic resampling, study its sensitivity to different parameters and settings, and evaluate its performance against ensemble KFs. The proposed EnGMF approach with deterministic resampling suggests improved estimates in all tested scenarios, and is shown to require less localization and to be less sensitive to the choice of filtering parameters.
Reduced-Order Kalman Filtering for Processing Relative Measurements
Bayard, David S.
2008-01-01
A study in Kalman-filter theory has led to a method of processing relative measurements to estimate the current state of a physical system, using less computation than has previously been thought necessary. As used here, relative measurements signifies measurements that yield information on the relationship between a later and an earlier state of the system. An important example of relative measurements arises in computer vision: Information on relative motion is extracted by comparing images taken at two different times. Relative measurements do not directly fit into standard Kalman filter theory, in which measurements are restricted to those indicative of only the current state of the system. One approach heretofore followed in utilizing relative measurements in Kalman filtering, denoted state augmentation, involves augmenting the state of the system at the earlier of two time instants and then propagating the state to the later time instant.While state augmentation is conceptually simple, it can also be computationally prohibitive because it doubles the number of states in the Kalman filter. When processing a relative measurement, if one were to follow the state-augmentation approach as practiced heretofore, one would find it necessary to propagate the full augmented state Kalman filter from the earlier time to the later time and then select out the reduced-order components. The main result of the study reported here is proof of a property called reduced-order equivalence (ROE). The main consequence of ROE is that it is not necessary to augment with the full state, but, rather, only the portion of the state that is explicitly used in the partial relative measurement. In other words, it suffices to select the reduced-order components first and then propagate the partial augmented state Kalman filter from the earlier time to the later time; the amount of computation needed to do this can be substantially less than that needed for propagating the full augmented
Restoration of nuclear medicine images using a Kalman filtering approach
Schmitt, Thomas; Gebauer, Heinz-Dieter; Freyer, Richard; Oehme, Liane; Franke, Wolf-Gunter
1995-03-01
The discrepancy between diagnostic importance of nuclear medicine images and their quality and the predominating visual interpretation of the images demand quality improvements. Digital image restoration procedures are known for being capable to solve this problem considering both noise and blurring. In this paper we propose the application of a modified 2D Kalman filter for nuclear medicine images (SPECT). In addition to the special capability of processing instationary signals the Kalman filter offers a possibility for controlling the filtering effect in a convenient way. The Kalman filter is based on a state space approach subdividing the imaging process into image generation and image degradation processes. The tested filter operates adaptively by permanent identification of the image generation model. For adaptation to the human visual system the filtering effect is modified depending on image quality represented by the mean information density and the local image contents represented by a structure information. The appropriate filtering effect is determined by modifying filter parameters with a predefined piecewise linear characteristic curve. The both smoothing and structure enhancing effect of our Kalman filtering approach is demonstrated in numerous tests performed with SPECT phantom images and brain SPECT studies.
Mobile indoor localization using Kalman filter and trilateration technique
Wahid, Abdul; Kim, Su Mi; Choi, Jaeho
2015-12-01
In this paper, an indoor localization method based on Kalman filtered RSSI is presented. The indoor communications environment however is rather harsh to the mobiles since there is a substantial number of objects distorting the RSSI signals; fading and interference are main sources of the distortion. In this paper, a Kalman filter is adopted to filter the RSSI signals and the trilateration method is applied to obtain the robust and accurate coordinates of the mobile station. From the indoor experiments using the WiFi stations, we have found that the proposed algorithm can provide a higher accuracy with relatively lower power consumption in comparison to a conventional method.
Estimation of Sideslip Angle Based on Extended Kalman Filter
Directory of Open Access Journals (Sweden)
Yupeng Huang
2017-01-01
Full Text Available The sideslip angle plays an extremely important role in vehicle stability control, but the sideslip angle in production car cannot be obtained from sensor directly in consideration of the cost of the sensor; it is essential to estimate the sideslip angle indirectly by means of other vehicle motion parameters; therefore, an estimation algorithm with real-time performance and accuracy is critical. Traditional estimation method based on Kalman filter algorithm is correct in vehicle linear control area; however, on low adhesion road, vehicles have obvious nonlinear characteristics. In this paper, extended Kalman filtering algorithm had been put forward in consideration of the nonlinear characteristic of the tire and was verified by the Carsim and Simulink joint simulation, such as the simulation on the wet cement road and the ice and snow road with double lane change. To test and verify the effect of extended Kalman filtering estimation algorithm, the real vehicle test was carried out on the limit test field. The experimental results show that the accuracy of vehicle sideslip angle acquired by extended Kalman filtering algorithm is obviously higher than that acquired by Kalman filtering in the area of the nonlinearity.
The ensemble particle filter (EnPF) in rainfall-runoff models
Van Delft, G.; El Serafy, G.Y.; Heemink, A.W.
2009-01-01
Rainfall-runoff models play a very important role in flood forecasting. However, these models contain large uncertainties caused by errors in both the model itself and the input data. Data assimilation techniques are being used to reduce these uncertainties. The ensemble Kalman filter (EnKF) and the
A probabilistic collocation based iterative Kalman filter for landfill data assimilation
Zheng, Qiang; Xu, Wenjie; Man, Jun; Zeng, Lingzao; Wu, Laosheng
2017-11-01
Accurate forecast of landfill gas (LFG) transport has remained as an active research area, due to the safety and environmental concerns, as well as the green energy potential. The iterative ensemble Kalman filter (IEnKF) has been used to characterize the heterogeneous permeability field of landfills. As a Monte Carlo-based method, IEnKF requires a sufficiently large ensemble size to guarantee its accuracy, which may result in a huge computational cost, especially for large-scale problems. In this study, an efficient probabilistic collocation based iterative Kalman filter (PCIKF) is developed. The polynomial chaos expansion (PCE) is employed to represent and propagate the uncertainties, and an iterative form of Kalman filter is used to assimilate the measurements. To further reduce the computational cost, only the zeroth and first-order ANOVA (analysis of variance) components are kept in the PCE approximation. As demonstrated by two numerical case studies, PCIKF shows significant superiority over IEnKF in terms of accuracy and efficiency. The developed method has the potential to reliably predict and develop best management practices for landfill gas production.
Energy Technology Data Exchange (ETDEWEB)
Man, Jun; Li, Weixuan; Zeng, Lingzao; Wu, Laosheng
2016-06-01
The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a relatively large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the polynomial chaos to approximate the original system. In this way, the sampling error can be reduced. However, PCKF suffers from the so-called "curse of dimensionality". When the system nonlinearity is strong and number of parameters is large, PCKF could be even more computationally expensive than EnKF. Motivated by most recent developments in uncertainty quantification, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problems. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected. The "restart" technology is used to eliminate the inconsistency between model parameters and states. The performance of RAPCKF is tested with numerical cases of unsaturated flow models. It is shown that RAPCKF is more efficient than EnKF with the same computational cost. Compared with the traditional PCKF, the RAPCKF is more applicable in strongly nonlinear and high dimensional problems.
Iterated unscented Kalman filter for phase unwrapping of interferometric fringes.
Xie, Xianming
2016-08-22
A fresh phase unwrapping algorithm based on iterated unscented Kalman filter is proposed to estimate unambiguous unwrapped phase of interferometric fringes. This method is the result of combining an iterated unscented Kalman filter with a robust phase gradient estimator based on amended matrix pencil model, and an efficient quality-guided strategy based on heap sort. The iterated unscented Kalman filter that is one of the most robust methods under the Bayesian theorem frame in non-linear signal processing so far, is applied to perform simultaneously noise suppression and phase unwrapping of interferometric fringes for the first time, which can simplify the complexity and the difficulty of pre-filtering procedure followed by phase unwrapping procedure, and even can remove the pre-filtering procedure. The robust phase gradient estimator is used to efficiently and accurately obtain phase gradient information from interferometric fringes, which is needed for the iterated unscented Kalman filtering phase unwrapping model. The efficient quality-guided strategy is able to ensure that the proposed method fast unwraps wrapped pixels along the path from the high-quality area to the low-quality area of wrapped phase images, which can greatly improve the efficiency of phase unwrapping. Results obtained from synthetic data and real data show that the proposed method can obtain better solutions with an acceptable time consumption, with respect to some of the most used algorithms.
Low-Rank Kalman Filtering in Subsurface Contaminant Transport Models
El Gharamti, Mohamad
2010-12-01
Understanding the geology and the hydrology of the subsurface is important to model the fluid flow and the behavior of the contaminant. It is essential to have an accurate knowledge of the movement of the contaminants in the porous media in order to track them and later extract them from the aquifer. A two-dimensional flow model is studied and then applied on a linear contaminant transport model in the same porous medium. Because of possible different sources of uncertainties, the deterministic model by itself cannot give exact estimations for the future contaminant state. Incorporating observations in the model can guide it to the true state. This is usually done using the Kalman filter (KF) when the system is linear and the extended Kalman filter (EKF) when the system is nonlinear. To overcome the high computational cost required by the KF, we use the singular evolutive Kalman filter (SEKF) and the singular evolutive extended Kalman filter (SEEKF) approximations of the KF operating with low-rank covariance matrices. The SEKF can be implemented on large dimensional contaminant problems while the usage of the KF is not possible. Experimental results show that with perfect and imperfect models, the low rank filters can provide as much accurate estimates as the full KF but at much less computational cost. Localization can help the filter analysis as long as there are enough neighborhood data to the point being analyzed. Estimating the permeabilities of the aquifer is successfully tackled using both the EKF and the SEEKF.
A new iterative speech enhancement scheme based on Kalman filtering
DEFF Research Database (Denmark)
Li, Chunjian; Andersen, Søren Vang
2005-01-01
A new iterative speech enhancement scheme that can be seen as an approximation to the Expectation-Maximization (EM) algorithm is proposed. The algorithm employs a Kalman filter that models the excitation source as a spectrally white process with a rapidly time-varying variance, which calls...... for a high temporal resolution estimation of this variance. A Local Variance Estimator based on a Prediction Error Kalman Filter is designed for this high temporal resolution variance estimation. To achieve fast convergence and avoid local maxima of the likelihood function, a Weighted Power Spectral...
A LBL Positioning Method Based on Feedback Kalman Filter
Directory of Open Access Journals (Sweden)
Jucheng Zhang
2014-01-01
Full Text Available LBL (Long Basic Line positioning is an important and high-precision method for underwater vehicle navigation. Due to its narrow work frequency-band, system would be easily affected by external factors and gave wrong results. A new Kalman filter model based on the feedback from travel time and position information was presented in this paper. By combining travel time with positioning in the Kalman filter, the navigation state of underwater vehicle was accurately estimated. Experimental results show that the influence of random high-frequency measurement noise on positioning results was effectively solved and the navigation precision was improved.
Potential of an ensemble Kalman smoother for stratospheric chemical-dynamical data assimilation
Directory of Open Access Journals (Sweden)
Thomas Milewski
2013-02-01
Full Text Available A new stratospheric ensemble Kalman smoother (EnKS system is introduced, and the potential of assimilating posterior stratospheric observations to better constrain the whole model state at analysis time is investigated. A set of idealised perfect-model Observation System Simulation Experiments (OSSE assimilating synthetic limb-sounding temperature or ozone retrievals are performed with a chemistry–climate model. The impact during the analysis step is characterised in terms of the root mean square error reduction between the forecast state and the analysis state. The performances of (1 a fixed-lag EnKS assimilating observations spread over 48 hours and (2 an ensemble Kalman Filter (EnKF assimilating a denser network of observations are compared with a reference EnKF. The ozone assimilation with EnKS shows a significant additional reduction of analysis error of the order of 10% for dynamical and chemical variables in the extratropical upper troposphere lower stratosphere (UTLS and Polar Vortex regions when compared to the reference EnKF. This reduction has similar magnitude to the one achieved by the denser-network EnKF assimilation. Similarly, the temperature assimilation with EnKS significantly decreases the error in the UTLS for the wind variables like the denser-network EnKF assimilation. However, the temperature assimilation with EnKS has little or no significant impact on the temperature and ozone analyses, whereas the denser-network EnKF shows improvement with respect to the reference EnKF. The different analysis impacts from the assimilation of current and posterior ozone observations indicate the capacity of time-lagged background-error covariances to represent temporal interactions up to 48 hours between variables during the ensemble data assimilation analysis step, and the possibility to use posterior observations whenever additional current observations are unavailable. The possible application of the EnKS for reanalyses is
Fuzzy Adaptive Cubature Kalman Filter for Integrated Navigation Systems
Directory of Open Access Journals (Sweden)
Chien-Hao Tseng
2016-07-01
Full Text Available This paper presents a sensor fusion method based on the combination of cubature Kalman filter (CKF and fuzzy logic adaptive system (FLAS for the integrated navigation systems, such as the GPS/INS (Global Positioning System/inertial navigation system integration. The third-degree spherical-radial cubature rule applied in the CKF has been employed to avoid the numerically instability in the system model. In processing navigation integration, the performance of nonlinear filter based estimation of the position and velocity states may severely degrade caused by modeling errors due to dynamics uncertainties of the vehicle. In order to resolve the shortcoming for selecting the process noise covariance through personal experience or numerical simulation, a scheme called the fuzzy adaptive cubature Kalman filter (FACKF is presented by introducing the FLAS to adjust the weighting factor of the process noise covariance matrix. The FLAS is incorporated into the CKF framework as a mechanism for timely implementing the tuning of process noise covariance matrix based on the information of degree of divergence (DOD parameter. The proposed FACKF algorithm shows promising accuracy improvement as compared to the extended Kalman filter (EKF, unscented Kalman filter (UKF, and CKF approaches.
Fuzzy Adaptive Cubature Kalman Filter for Integrated Navigation Systems.
Tseng, Chien-Hao; Lin, Sheng-Fuu; Jwo, Dah-Jing
2016-07-26
This paper presents a sensor fusion method based on the combination of cubature Kalman filter (CKF) and fuzzy logic adaptive system (FLAS) for the integrated navigation systems, such as the GPS/INS (Global Positioning System/inertial navigation system) integration. The third-degree spherical-radial cubature rule applied in the CKF has been employed to avoid the numerically instability in the system model. In processing navigation integration, the performance of nonlinear filter based estimation of the position and velocity states may severely degrade caused by modeling errors due to dynamics uncertainties of the vehicle. In order to resolve the shortcoming for selecting the process noise covariance through personal experience or numerical simulation, a scheme called the fuzzy adaptive cubature Kalman filter (FACKF) is presented by introducing the FLAS to adjust the weighting factor of the process noise covariance matrix. The FLAS is incorporated into the CKF framework as a mechanism for timely implementing the tuning of process noise covariance matrix based on the information of degree of divergence (DOD) parameter. The proposed FACKF algorithm shows promising accuracy improvement as compared to the extended Kalman filter (EKF), unscented Kalman filter (UKF), and CKF approaches.
Parallelized unscented Kalman filters for carrier recovery in coherent optical communication.
Jignesh, Jokhakar; Corcoran, Bill; Lowery, Arthur
2016-07-15
We show that unscented Kalman filters can be used to mitigate local oscillator phase noise and to compensate carrier frequency offset in coherent single-carrier optical communication systems. A parallel processing architecture implementing the unscented Kalman filter is proposed, improving upon a previous parallelized linear Kalman filter (LKF) implementation.
Improving Artificial eural etwork Forecasts with Kalman Filtering
African Journals Online (AJOL)
Nafiisah
In this paper, we show that the post-processing of forecasts produced by an artificial neural networks (ANN) model ... model and the numerical method used for fitting the model and computing the forecasts. Faraway et al. (1998) ..... linear Kalman filters to numerical weather predictions', Annales Geophysicae, Vol. 24, pp.
Improving Artificial Neural Network Forecasts with Kalman Filtering ...
African Journals Online (AJOL)
In this paper, we examine the use of the artificial neural network method as a forecasting technique in financial time series and the application of a Kalman filter algorithm to improve the accuracy of the model. Forecasting accuracy criteria are used to compare the two models over different set of data from different companies ...
Implementation of extended Kalman filter-based simultaneous ...
Indian Academy of Sciences (India)
Manigandan Nagarajan Santhanakrishnan
2017-07-03
Jul 3, 2017 ... Abstract. The implementation of extended Kalman filter-based simultaneous localization and mapping is challenging as the associated system state and covariance matrices along with the memory requirements become significantly large as the information space increases. Unique and consistent point ...
HOKF: High Order Kalman Filter for Epilepsy Forecasting Modeling.
Nguyen, Ngoc Anh Thi; Yang, Hyung-Jeong; Kim, Sunhee
2017-08-01
Epilepsy forecasting has been extensively studied using high-order time series obtained from scalp-recorded electroencephalography (EEG). An accurate seizure prediction system would not only help significantly improve patients' quality of life, but would also facilitate new therapeutic strategies to manage epilepsy. This paper thus proposes an improved Kalman Filter (KF) algorithm to mine seizure forecasts from neural activity by modeling three properties in the high-order EEG time series: noise, temporal smoothness, and tensor structure. The proposed High-Order Kalman Filter (HOKF) is an extension of the standard Kalman filter, for which higher-order modeling is limited. The efficient dynamic of HOKF system preserves the tensor structure of the observations and latent states. As such, the proposed method offers two main advantages: (i) effectiveness with HOKF results in hidden variables that capture major evolving trends suitable to predict neural activity, even in the presence of missing values; and (ii) scalability in that the wall clock time of the HOKF is linear with respect to the number of time-slices of the sequence. The HOKF algorithm is examined in terms of its effectiveness and scalability by conducting forecasting and scalability experiments with a real epilepsy EEG dataset. The results of the simulation demonstrate the superiority of the proposed method over the original Kalman Filter and other existing methods. Copyright © 2017 Elsevier B.V. All rights reserved.
Predicting breeding values in animals by kalman filter
DEFF Research Database (Denmark)
Karacaören, Burak; Janss, Luc; Kadarmideen, Haja
2012-01-01
The aim of this study was to investigate usefulness of Kalman Filter (KF) Random Walk methodology (KF-RW) for prediction of breeding values in animals. We used body condition score (BCS) from dairy cattle for illustrating use of KF-RW. BCS was measured by Swiss Holstein Breeding Association during...
Adaptive Unscented Kalman Filter using Maximum Likelihood Estimation
DEFF Research Database (Denmark)
Mahmoudi, Zeinab; Poulsen, Niels Kjølstad; Madsen, Henrik
2017-01-01
The purpose of this study is to develop an adaptive unscented Kalman filter (UKF) by tuning the measurement noise covariance. We use the maximum likelihood estimation (MLE) and the covariance matching (CM) method to estimate the noise covariance. The multi-step prediction errors generated...
Forecasting with the Standardized Self-Perturbed Kalman Filter
DEFF Research Database (Denmark)
Grassi, Stefano; Nonejad, Nima; Santucci de Magistris, Paolo
We propose and study the finite-sample properties of a modified version of the self-perturbed Kalman filter of Park and Jun (1992) for the on-line estimation of models subject to parameter instability. The perturbation term in the updating equation of the state covariance matrix is now weighted b...
Ramchandani, Varun; Pamarthi, Kranthi; Chowdhury, Shubhajit Roy
2012-01-01
The paper proposes comparative study of Field Programmable Gate Array implementation of 2 closely related approaches to track maximum power point of a solar photovoltaic array. The current work uses 2 versions of kalman filter viz. linear kalman filter and unscented kalman filter to track maximum power point. Using either of these approach the maximum power point tracking (MPPT) becomes much faster than using the conventional Perturb & Observe approach specifically in case of sudden weather c...
Maximum Correntropy Unscented Kalman Filter for Spacecraft Relative State Estimation.
Liu, Xi; Qu, Hua; Zhao, Jihong; Yue, Pengcheng; Wang, Meng
2016-09-20
A new algorithm called maximum correntropy unscented Kalman filter (MCUKF) is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF) provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC), the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT) is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm.
Star spot location estimation using Kalman filter for star tracker.
Liu, Hai-bo; Yang, Jian-kun; Wang, Jiong-qi; Tan, Ji-chun; Li, Xiu-jian
2011-04-20
Star pattern recognition and attitude determination accuracy is highly dependent on star spot location accuracy for the star tracker. A star spot location estimation approach with the Kalman filter for a star tracker has been proposed, which consists of three steps. In the proposed approach, the approximate locations of the star spots in successive frames are predicted first; then the measurement star spot locations are achieved by defining a series of small windows around each predictive star spot location. Finally, the star spot locations are updated by the designed Kalman filter. To confirm the proposed star spot location estimation approach, the simulations based on the orbit data of the CHAMP satellite and the real guide star catalog are performed. The simulation results indicate that the proposed approach can filter out noises from the measurements remarkably if the sampling frequency is sufficient. © 2011 Optical Society of America
A Novel Robust Interval Kalman Filter Algorithm for GPS/INS Integrated Navigation
Directory of Open Access Journals (Sweden)
Chen Jiang
2016-01-01
Full Text Available Kalman filter is widely applied in data fusion of dynamic systems under the assumption that the system and measurement noises are Gaussian distributed. In literature, the interval Kalman filter was proposed aiming at controlling the influences of the system model uncertainties. The robust Kalman filter has also been proposed to control the effects of outliers. In this paper, a new interval Kalman filter algorithm is proposed by integrating the robust estimation and the interval Kalman filter in which the system noise and the observation noise terms are considered simultaneously. The noise data reduction and the robust estimation methods are both introduced into the proposed interval Kalman filter algorithm. The new algorithm is equal to the standard Kalman filter in terms of computation, but superior for managing with outliers. The advantage of the proposed algorithm is demonstrated experimentally using the integrated navigation of Global Positioning System (GPS and the Inertial Navigation System (INS.
Orchard navigation using derivative free Kalman filtering
DEFF Research Database (Denmark)
Hansen, Søren; Bayramoglu, Enis; Andersen, Jens Christian
2011-01-01
This paper describes the use of derivative free filters for mobile robot localization and navigation in an orchard. The localization algorithm fuses odometry and gyro measurements with line features representing the surrounding fruit trees of the orchard. The line features are created on basis of 2......D laser scanner data by a least square algorithm. The three derivative free filters are compared to an EKF based localization method on a typical run covering four rows in the orchard. The Matlab R toolbox Kalmtool is used for easy switching between different filter implementations without the need...
Ohkubo, Jun
2015-10-01
An alternative application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, here I employ numerical solutions of the dual processes and investigate the usefulness. As a demonstration, estimation problems of hidden variables in stochastic differential equations are discussed. Employing algebraic probability theory, a little complicated birth-death process is derived from the stochastic differential equations, and an estimation method based on the ensemble Kalman filter is proposed. As a result, the possibility for making faster computational algorithms based on the duality concepts is shown.
Series load induction heating inverter state estimator using Kalman filter
Directory of Open Access Journals (Sweden)
Szelitzky T.
2011-12-01
Full Text Available LQR and H2 controllers require access to the states of the controlled system. The method based on description function with Fourier series results in a model with immeasurable states. For this reason, we proposed a Kalman filter based state estimator, which not only filters the input signals, but also computes the unobservable states of the system. The algorithm of the filter was implemented in LabVIEW v8.6 and tested on recorded data obtained from a 10-40 kHz series load frequency controlled induction heating inverter.
Pauwels, V. R. N.; DeLannoy, G. J. M.; Hendricks Franssen, H.-J.; Vereecken, H.
2013-01-01
In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the discrete Kalman filter, and the state variables using the ensemble Kalman filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware ensemble Kalman filter. Furthermore, minimal code modification in existing data assimilation software is needed to implement the method. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.
Spacecraft Dynamics Should be Considered in Kalman Filter Attitude Estimation
Yang, Yaguang; Zhou, Zhiqiang
2016-01-01
Kalman filter based spacecraft attitude estimation has been used in some high-profile missions and has been widely discussed in literature. While some models in spacecraft attitude estimation include spacecraft dynamics, most do not. To our best knowledge, there is no comparison on which model is a better choice. In this paper, we discuss the reasons why spacecraft dynamics should be considered in the Kalman filter based spacecraft attitude estimation problem. We also propose a reduced quaternion spacecraft dynamics model which admits additive noise. Geometry of the reduced quaternion model and the additive noise are discussed. This treatment is more elegant in mathematics and easier in computation. We use some simulation example to verify our claims.
Bayesian fault detection and isolation using Field Kalman Filter
Baranowski, Jerzy; Bania, Piotr; Prasad, Indrajeet; Cong, Tian
2017-12-01
Fault detection and isolation is crucial for the efficient operation and safety of any industrial process. There is a variety of methods from all areas of data analysis employed to solve this kind of task, such as Bayesian reasoning and Kalman filter. In this paper, the authors use a discrete Field Kalman Filter (FKF) to detect and recognize faulty conditions in a system. The proposed approach, devised for stochastic linear systems, allows for analysis of faults that can be expressed both as parameter and disturbance variations. This approach is formulated for the situations when the fault catalog is known, resulting in the algorithm allowing estimation of probability values. Additionally, a variant of algorithm with greater numerical robustness is presented, based on computation of logarithmic odds. Proposed algorithm operation is illustrated with numerical examples, and both its merits and limitations are critically discussed and compared with traditional EKF.
On Kalman Filtering With Nonlinear Equality Constraints
2007-06-01
1)). The filter is updated with the observation to give the unconstrained estimate x̂ ( kjk ). The constraint is applied to give the final estimate x̂... kjk ). II. PROBLEM STATEMENT We seek the minimum-mean squared error estimate of the state vector of the nonlinear discrete time system where is the
Localization of Wheeled Mobile Robot Based on Extended Kalman Filtering
Directory of Open Access Journals (Sweden)
Li Guangxu
2015-01-01
Full Text Available A mobile robot localization method which combines relative positioning with absolute orientation is presented. The code salver and gyroscope are used for relative positioning, and the laser radar is used to detect absolute orientation. In this paper, we established environmental map, multi-sensor information fusion model, sensors and robot motion model. The Extended Kalman Filtering (EKF is adopted as multi-sensor data fusion technology to realize the precise localization of wheeled mobile robot.
SUBSTANTIATION OF THE PUBLIC DEBT SUSTAINABILITY USING KALMAN FILTER
Directory of Open Access Journals (Sweden)
Bolos Marcel
2011-12-01
Full Text Available Global economic conditions have pushed many countries into the delicate situation of contracting foreign loans, leading overnight at alarming volumes of public debt. The need for control and relevant analysis for the sustainability of a country's public debt has led us to use the Kalman filter in predicting future values of the key indicators of public debt. The development of a mathematical model of analysis for public services and the budget deficit was necessary to objectively assess the level of the public debt sustainability.Knowing future values of the public debt or the future evolutions of the revenues for the operational budget, offers the posibility of a better handling of the operational expenditures and finally a better balance for the public budget deficit.Using the mathematical mechanism of Kalman filters implemented in Matlab programming language, we generated the estimated future values of the proposed model proposed and key indicators, the results confirming the fears of a low public debt sustainability for Romania.We predicted the future values for the debt service, the public external debt and the operational public revenues,expenditures and deficit, and compared them, to obtain an image of the future evolution and position of the sustainability of the public debt. The work in this paper is an innovative one for the public science sector, and the results obtained are promising for future researches. The values estimated by the Kalman filter are an orientation for the future public policies, and indicate a rather stable but negative evolution for the public debt service. The sustainability of the public debt depends on the decisions taken for the correction of the estimated values, in changing the negative evolution of the budgetary indicators into a positive one.Taking all this into consideration we will conclude that the mathematical mecanism of the Kalman filters offers valuable informations for Government and future
Relationship between Allan variances and Kalman Filter parameters
Vandierendonck, A. J.; Mcgraw, J. B.; Brown, R. G.
1984-01-01
A relationship was constructed between the Allan variance parameters (H sub z, H sub 1, H sub 0, H sub -1 and H sub -2) and a Kalman Filter model that would be used to estimate and predict clock phase, frequency and frequency drift. To start with the meaning of those Allan Variance parameters and how they are arrived at for a given frequency source is reviewed. Although a subset of these parameters is arrived at by measuring phase as a function of time rather than as a spectral density, they all represent phase noise spectral density coefficients, though not necessarily that of a rational spectral density. The phase noise spectral density is then transformed into a time domain covariance model which can then be used to derive the Kalman Filter model parameters. Simulation results of that covariance model are presented and compared to clock uncertainties predicted by Allan variance parameters. A two state Kalman Filter model is then derived and the significance of each state is explained.
Directory of Open Access Journals (Sweden)
Cahit Tağı ÇELİK
2004-01-01
Full Text Available Monitoring the Crustal Movement in Geodesy is performed by the deformation survey and analysis. If monitoring the crustal movements involves more than two epochs of survey campaign then from the plate tectonic theory, stations do not move randomly from one epoch to the other, therefore Kalman Filter may be suitable to use. However, if sudden movements happened in the crust in particular earthquake happened, the crust moves very fast in a very short period of time. When Kalman Filter used for monitoring these movements, from associated epoch, for a number of epochs the results may be biased. In the paper, comparison of two methods for elimination of the above mentioned biases have been performed. These methods are Fading Memory Filter and Adaptive Kalman Filter for an unknown bias.
Energy Technology Data Exchange (ETDEWEB)
Pike, D.H.; Morrison, G.W.; Westley, G.W.
1977-10-01
The feasibility of using modern state estimation techniques (specifically Kalman Filtering and Linear Smoothing) to detect losses of material from material balance areas is evaluated. It is shown that state estimation techniques are not only feasible but in most situations are superior to existing methods of analysis. The various techniques compared include Kalman Filtering, linear smoothing, standard control charts, and average cumulative summation (CUSUM) charts. Analysis results indicated that the standard control chart is the least effective method for detecting regularly occurring losses. An improvement in the detection capability over the standard control chart can be realized by use of the CUSUM chart. Even more sensitivity in the ability to detect losses can be realized by use of the Kalman Filter and the linear smoother. It was found that the error-covariance matrix can be used to establish limits of error for state estimates. It is shown that state estimation techniques represent a feasible and desirable method of theft detection. The technique is usually more sensitive than the CUSUM chart in detecting losses. One kind of loss which is difficult to detect using state estimation techniques is a single isolated loss. State estimation procedures are predicated on dynamic models and are well-suited for detecting losses which occur regularly over several accounting periods. A single isolated loss does not conform to this basic assumption and is more difficult to detect.
Gossip and Distributed Kalman Filtering: Weak Consensus Under Weak Detectability
Kar, Soummya; Moura, José M. F.
2011-04-01
The paper presents the gossip interactive Kalman filter (GIKF) for distributed Kalman filtering for networked systems and sensor networks, where inter-sensor communication and observations occur at the same time-scale. The communication among sensors is random; each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link. We show that under a weak distributed detectability condition: 1. the GIKF error process remains stochastically bounded, irrespective of the instability properties of the random process dynamics; and 2. the network achieves \\emph{weak consensus}, i.e., the conditional estimation error covariance at a (uniformly) randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semi-definite matrices (independent of the initial state.) To prove these results, we interpret the filtered states (estimates and error covariances) at each node in the GIKF as stochastic particles with local interactions. We analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched (random) Riccati equation, the switching being dictated by a non-stationary Markov chain on the network graph.
Unscented Kalman filters for polarization state tracking and phase noise mitigation.
Jignesh, Jokhakar; Corcoran, Bill; Zhu, Chen; Lowery, Arthur
2016-09-19
Simultaneous polarization and phase noise tracking and compensation is proposed based on an unscented Kalman filter (UKF). We experimentally demonstrate the tracking under noise-loading and after 800-km single-mode fiber transmission with 20-Gbaud QPSK and 16-QAM signals. These experiments show that the proposed UKF outperforms both conventional blind tracing algorithms and a previously proposed extended Kalman filter, at the cost of higher complexity. Additionally, we propose and test modified Kalman filter algorithms to reduce computational complexity.
Gerasimos G. Rigatos; Pierluigi Siano
2011-01-01
The paper studies sensorless control for DC and induction motors, using Kalman Filtering techniques. First the case of a DC motor is considered and Kalman Filter-based control is implemented. Next the nonlinear model of a field-oriented induction motor is examined and the motor's angular velocity is estimated by an Extended Kalman Filter which processes measurements of the rotor's angle. Sensorless control of the induction motor is again implemented through feedback of the estimated state vec...
Applying Kalman filtering to investigate tropospheric effects in VLBI
Soja, Benedikt; Nilsson, Tobias; Karbon, Maria; Heinkelmann, Robert; Liu, Li; Lu, Cuixian; Andres Mora-Diaz, Julian; Raposo-Pulido, Virginia; Xu, Minghui; Schuh, Harald
2014-05-01
Very Long Baseline Interferometry (VLBI) currently provides results, e.g., estimates of the tropospheric delays, with a delay of more than two weeks. In the future, with the coming VLBI2010 Global Observing System (VGOS) and increased usage of electronic data transfer, it is planned that the time between observations and results is decreased. This may, for instance, allow the integration of VLBI-derived tropospheric delays into numerical weather prediction models. Therefore, future VLBI analysis software packages need to be able to process the observational data autonomously in near real-time. For this purpose, we have extended the Vienna VLBI Software (VieVS) by a Kalman filter module. This presentation describes the filter and discusses its application for tropospheric studies. Instead of estimating zenith wet delays as piece-wise linear functions in a least-squares adjustment, the Kalman filter allows for more sophisticated stochastic modeling. We start with a random walk process to model the time-dependent behavior of the zenith wet delays. Other possible approaches include the stochastic model described by turbulence theory, e.g. the model by Treuhaft and Lanyi (1987). Different variance-covariance matrices of the prediction error, depending on the time of the year and the geographic latitude, have been tested. In winter and closer to the poles, lower variances and covariances are appropriate. The horizontal variations in tropospheric delays have been investigated by comparing three different strategies: assumption of a horizontally stratified troposphere, using north and south gradients modeled, e.g., as Gauss-Markov processes, and applying a turbulence model assuming correlations between observations in different azimuths. By conducting Monte-Carlo simulations of current standard VLBI networks and of future VGOS networks, the different tropospheric modeling strategies are investigated. For this purpose, we use the simulator module of VieVS which takes into
Enhancement of Spanish Oesophageal Speech vowels using coherent subband modulator Kalman filtering.
Ishaq, Rizwan; Zapirain, Begoña García
2016-01-01
This paper proposes an Oesophageal Speech (OES) enhancement method, based on Kalman filtering. The Kalman filter is applied to modulators of OES frequency subbands instead of the fullband signal. The OES frequency subbands are decomposed into modulators and carriers components using coherent demodulation. In comparison with fullband Kalman filtering and pole stabilization, the proposed technique shows better results. The system performance is evaluated objectively and subjectively using the Harmonic to Noise Ratio (HNR) and Mean Opinion Score (MOS) respectively. Results have shown that Kalman filter in subband modulators processing is robust and efficient, improving the HNR by 4 to 5 dB for all Spanish vowels.
El Gharamti, Mohamad
2014-02-01
The accuracy of groundwater flow and transport model predictions highly depends on our knowledge of subsurface physical parameters. Assimilation of contaminant concentration data from shallow dug wells could help improving model behavior, eventually resulting in better forecasts. In this paper, we propose a joint state-parameter estimation scheme which efficiently integrates a low-rank extended Kalman filtering technique, namely the Singular Evolutive Extended Kalman (SEEK) filter, with the prominent complex-step method (CSM). The SEEK filter avoids the prohibitive computational burden of the Extended Kalman filter by updating the forecast along the directions of error growth only, called filter correction directions. CSM is used within the SEEK filter to efficiently compute model derivatives with respect to the state and parameters along the filter correction directions. CSM is derived using complex Taylor expansion and is second order accurate. It is proven to guarantee accurate gradient computations with zero numerical round-off errors, but requires complexifying the numerical code. We perform twin-experiments to test the performance of the CSM-based SEEK for estimating the state and parameters of a subsurface contaminant transport model. We compare the efficiency and the accuracy of the proposed scheme with two standard finite difference-based SEEK filters as well as with the ensemble Kalman filter (EnKF). Assimilation results suggest that the use of the CSM in the context of the SEEK filter may provide up to 80% more accurate solutions when compared to standard finite difference schemes and is competitive with the EnKF, even providing more accurate results in certain situations. We analyze the results based on two different observation strategies. We also discuss the complexification of the numerical code and show that this could be efficiently implemented in the context of subsurface flow models. © 2013 Elsevier B.V.
Kalman filtering to suppress spurious signals in Adaptive Optics control
Energy Technology Data Exchange (ETDEWEB)
Poyneer, L; Veran, J P
2010-03-29
In many scenarios, an Adaptive Optics (AO) control system operates in the presence of temporally non-white noise. We use a Kalman filter with a state space formulation that allows suppression of this colored noise, hence improving residual error over the case where the noise is assumed to be white. We demonstrate the effectiveness of this new filter in the case of the estimated Gemini Planet Imager tip-tilt environment, where there are both common-path and non-common path vibrations. We discuss how this same framework can also be used to suppress spatial aliasing during predictive wavefront control assuming frozen flow in a low-order AO system without a spatially filtered wavefront sensor, and present experimental measurements from Altair that clearly reveal these aliased components.
Kalman Filter Estimation of Spinning Spacecraft Attitude using Markley Variables
Sedlak, Joseph E.; Harman, Richard
2004-01-01
There are several different ways to represent spacecraft attitude and its time rate of change. For spinning or momentum-biased spacecraft, one particular representation has been put forward as a superior parameterization for numerical integration. Markley has demonstrated that these new variables have fewer rapidly varying elements for spinning spacecraft than other commonly used representations and provide advantages when integrating the equations of motion. The current work demonstrates how a Kalman filter can be devised to estimate the attitude using these new variables. The seven Markley variables are subject to one constraint condition, making the error covariance matrix singular. The filter design presented here explicitly accounts for this constraint by using a six-component error state in the filter update step. The reduced dimension error state is unconstrained and its covariance matrix is nonsingular.
Maximum Correntropy Unscented Kalman Filter for Spacecraft Relative State Estimation
Directory of Open Access Journals (Sweden)
Xi Liu
2016-09-01
Full Text Available A new algorithm called maximum correntropy unscented Kalman filter (MCUKF is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC, the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm.
Extracting Steady State Components from Synchrophasor Data Using Kalman Filters
Directory of Open Access Journals (Sweden)
Farhan Mahmood
2016-04-01
Full Text Available Data from phasor measurement units (PMUs may be exploited to provide steady state information to the applications which require it. As PMU measurements may contain errors and missing data, the paper presents the application of a Kalman Filter technique for real-time data processing. PMU data captures the power system’s response at different time-scales, which are generated by different types of power system events; the presented Kalman Filter methods have been applied to extract the steady state components of PMU measurements that can be fed to steady state applications. Two KF-based methods have been proposed, i.e., a windowing-based KF method and “the modified KF”. Both methods are capable of reducing noise, compensating for missing data and filtering outliers from input PMU signals. A comparison of proposed methods has been carried out using the PMU data generated from a hardware-in-the-loop (HIL experimental setup. In addition, a performance analysis of the proposed methods is performed using an evaluation metric.
Data assimilation in the early phase: Kalman filtering RIMPUFF
DEFF Research Database (Denmark)
Astrup, P.; Turcanu, C.; Puch, R.O.
2004-01-01
In the framework of the DAONEM project (Data Assimilation for Off-site Nuclear Emergency Management), a data assimilation module, ADUM (Atmospheric Dispersion Updating Module), for the mesoscale atmospheric dispersion program RIMPUFF (Risø Mesoscale Puffmodel) – part of the early-phase programs...... of RODOS (Realtime Online DecisiOn Support system for nuclear emergencies) – has been developed. It is built on the Kalman filtering algorithm and it assimilates 10-minute averaged gamma dose rates measured atground level stations. Since the gamma rates are non-linear functions of the state vector...
Adaptive training of feedforward neural networks by Kalman filtering
Energy Technology Data Exchange (ETDEWEB)
Ciftcioglu, Oe. [Istanbul Technical Univ. (Turkey). Dept. of Electrical Engineering; Tuerkcan, E. [Netherlands Energy Research Foundation (ECN), Petten (Netherlands)
1995-02-01
Adaptive training of feedforward neural networks by Kalman filtering is described. Adaptive training is particularly important in estimation by neural network in real-time environmental where the trained network is used for system estimation while the network is further trained by means of the information provided by the experienced/exercised ongoing operation. As result of this, neural network adapts itself to a changing environment to perform its mission without recourse to re-training. The performance of the training method is demonstrated by means of actual process signals from a nuclear power plant. (orig.).
Comparison of Sigma-Point and Extended Kalman Filters on a Realistic Orbit Determination Scenario
Gaebler, John; Hur-Diaz. Sun; Carpenter, Russell
2010-01-01
Sigma-point filters have received a lot of attention in recent years as a better alternative to extended Kalman filters for highly nonlinear problems. In this paper, we compare the performance of the additive divided difference sigma-point filter to the extended Kalman filter when applied to orbit determination of a realistic operational scenario based on the Interstellar Boundary Explorer mission. For the scenario studied, both filters provided equivalent results. The performance of each is discussed in detail.
Marginalized Particle Filtering Framework for Tuning of Ensemble Filters
Czech Academy of Sciences Publication Activity Database
Šmídl, Václav; Hofman, Radek
2011-01-01
Roč. 139, č. 11 (2011), s. 3589-3599 ISSN 0027-0644 R&D Projects: GA MV VG20102013018; GA ČR GP102/08/P250 Institutional research plan: CEZ:AV0Z10750506 Keywords : ensemble finter * marginalized particle filter * data assimilation Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.688, year: 2011 http://library.utia.cas.cz/separaty/2011/AS/smidl-0367533.pdf
A balanced Kalman filter ocean data assimilation system with application to the South Australian Sea
Li, Yi; Toumi, Ralf
2017-08-01
In this paper, an Ensemble Kalman Filter (EnKF) based regional ocean data assimilation system has been developed and applied to the South Australian Sea. This system consists of the data assimilation algorithm provided by the NCAR Data Assimilation Research Testbed (DART) and the Regional Ocean Modelling System (ROMS). We describe the first implementation of the physical balance operator (temperature-salinity, hydrostatic and geostrophic balance) to DART, to reduce the spurious waves which may be introduced during the data assimilation process. The effect of the balance operator is validated in both an idealised shallow water model and the ROMS model real case study. In the shallow water model, the geostrophic balance operator eliminates spurious ageostrophic waves and produces a better sea surface height (SSH) and velocity analysis and forecast. Its impact increases as the sea surface height and wind stress increase. In the real case, satellite-observed sea surface temperature (SST) and SSH are assimilated in the South Australian Sea with 50 ensembles using the Ensemble Adjustment Kalman Filter (EAKF). Assimilating SSH and SST enhances the estimation of SSH and SST in the entire domain, respectively. Assimilation with the balance operator produces a more realistic simulation of surface currents and subsurface temperature profile. The best improvement is obtained when only SSH is assimilated with the balance operator. A case study with a storm suggests that the benefit of the balance operator is of particular importance under high wind stress conditions. Implementing the balance operator could be a general benefit to ocean data assimilation systems.
Directory of Open Access Journals (Sweden)
Hassana Maigary Georges
2015-01-01
Full Text Available Among the inertial navigation system (INS devices used in land vehicle navigation (LVN, low-cost microelectromechanical systems (MEMS inertial sensors have received more interest for bridging global navigation satellites systems (GNSS signal failures because of their price and portability. Kalman filter (KF based GNSS/INS integration has been widely used to provide a robust solution to the navigation. However, its prediction model cannot give satisfactory results in the presence of colored and variational noise. In order to achieve reliable and accurate positional solution for LVN in urban areas surrounded by skyscrapers or under dense foliage and tunnels, a novel model combining variational Bayesian adaptive Kalman smoother (VB-ACKS as an alternative of KF and ensemble regularized extreme learning machine (ERELM for bridging global positioning systems outages is proposed. The ERELM is applied to reduce the fluctuating performance of GNSS during an outage. We show that a well-organized collection of predictors using ensemble learning yields a more accurate positional result when compared with conventional artificial neural network (ANN predictors. Experimental results show that the performance of VB-ACKS is more robust compared with KF solution, and the prediction of ERELM contains the smallest error compared with other ANN solutions.
Non-linear DSGE Models, The Central Difference Kalman Filter, and The Mean Shifted Particle Filter
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper shows how non-linear DSGE models with potential non-normal shocks can be estimated by Quasi-Maximum Likelihood based on the Central Difference Kalman Filter (CDKF). The advantage of this estimator is that evaluating the quasi log-likelihood function only takes a fraction of a second...
Direct and accelerated parameter mapping using the unscented Kalman filter.
Zhao, Li; Feng, Xue; Meyer, Craig H
2016-05-01
To accelerate parameter mapping using a new paradigm that combines image reconstruction and model regression as a parameter state-tracking problem. In T2 mapping, the T2 map is first encoded in parameter space by multi-TE measurements and then encoded by Fourier transformation with readout/phase encoding gradients. Using a state transition function and a measurement function, the unscented Kalman filter can describe T2 mapping as a dynamic system and directly estimate the T2 map from the k-space data. The proposed method was validated with a numerical brain phantom and volunteer experiments with a multiple-contrast spin echo sequence. Its performance was compared with a conjugate-gradient nonlinear inversion method at undersampling factors of 2 to 8. An accelerated pulse sequence was developed based on this method to achieve prospective undersampling. Compared with the nonlinear inversion reconstruction, the proposed method had higher precision, improved structural similarity and reduced normalized root mean squared error, with acceleration factors up to 8 in numerical phantom and volunteer studies. This work describes a new perspective on parameter mapping by state tracking. The unscented Kalman filter provides a highly accelerated and efficient paradigm for T2 mapping. © 2015 Wiley Periodicals, Inc.
ERP Estimation using a Kalman Filter in VLBI
Karbon, M.; Soja, B.; Nilsson, T.; Heinkelmann, R.; Liu, L.; Lu, C.; Mora-Diaz, J. A.; Raposo-Pulido, V.; Xu, M.; Schuh, H.
2014-12-01
Geodetic Very Long Baseline Interferometry (VLBI) is one of the primary space geodetic techniques, providing the full set of Earth Orientation Parameters (EOP), and it is unique for observing long term Universal Time (UT1). For applications such as satellite-based navigation and positioning, accurate and continuous ERP obtained in near real-time are essential. They also allow the precise tracking of interplanetary spacecraft. One of the goals of VGOS (VLBI Global Observing System) is to provide such near real-time ERP. With the launch of this next generation VLBI system, the International VLBI Service for Geodesy and Astrometry (IVS) increased its efforts not only to reach 1 mm accuracy on a global scale but also to reduce the time span between the collection of VLBI observations and the availability of the final results substantially. Project VLBI-ART contributes to these objectives by implementing an elaborate Kalman filter, which represents a perfect tool for analyzing VLBI data in quasi real-time. The goal is to implement it in the GFZ version of the Vienna VLBI Software (VieVS) as a completely automated tool, i.e., with no need for human interaction. Here we present the methodology and first results of Kalman filtered EOP from VLBI data.
Method for Improving Indoor Positioning Accuracy Using Extended Kalman Filter
Directory of Open Access Journals (Sweden)
Seoung-Hyeon Lee
2016-01-01
Full Text Available Beacons using bluetooth low-energy (BLE technology have emerged as a new paradigm of indoor positioning service (IPS because of their advantages such as low power consumption, miniaturization, wide signal range, and low cost. However, the beacon performance is poor in terms of the indoor positioning accuracy because of noise, motion, and fading, all of which are characteristics of a bluetooth signal and depend on the installation location. Therefore, it is necessary to improve the accuracy of beacon-based indoor positioning technology by fusing it with existing indoor positioning technology, which uses Wi-Fi, ZigBee, and so forth. This study proposes a beacon-based indoor positioning method using an extended Kalman filter that recursively processes input data including noise. After defining the movement of a smartphone on a flat two-dimensional surface, it was assumed that the beacon signal is nonlinear. Then, the standard deviation and properties of the beacon signal were analyzed. According to the analysis results, an extended Kalman filter was designed and the accuracy of the smartphone’s indoor position was analyzed through simulations and tests. The proposed technique achieved good indoor positioning accuracy, with errors of 0.26 m and 0.28 m from the average x- and y-coordinates, respectively, based solely on the beacon signal.
Autonomous underwater vehicle motion tracking using a Kalman Filter for sensor fusion
CSIR Research Space (South Africa)
Holtzhausen, S
2008-01-01
Full Text Available it will be shown how a Kalman Filter is used to estimate the position of an autonomous vehicle in a three dimensional space. The Kalman filter is used to estimate movement and position using measurements from multiple sensors...
Autonomous underwater vehicle motion tracking using a Kalman filter for sensor fusion
CSIR Research Space (South Africa)
Holtzhausen, S
2008-11-01
Full Text Available it will be shown how a Kalman Filter is used to estimate the position of an autonomous vehicle in a three dimensional space. The Kalman filter is used to estimate movement and position using measurements from multiple sensors...
Improved Kalman filter method for measurement noise reduction in multi sensor RFID systems.
Eom, Ki Hwan; Lee, Seung Joon; Kyung, Yeo Sun; Lee, Chang Won; Kim, Min Chul; Jung, Kyung Kwon
2011-01-01
Recently, the range of available radio frequency identification (RFID) tags has been widened to include smart RFID tags which can monitor their varying surroundings. One of the most important factors for better performance of smart RFID system is accurate measurement from various sensors. In the multi-sensing environment, some noisy signals are obtained because of the changing surroundings. We propose in this paper an improved Kalman filter method to reduce noise and obtain correct data. Performance of Kalman filter is determined by a measurement and system noise covariance which are usually called the R and Q variables in the Kalman filter algorithm. Choosing a correct R and Q variable is one of the most important design factors for better performance of the Kalman filter. For this reason, we proposed an improved Kalman filter to advance an ability of noise reduction of the Kalman filter. The measurement noise covariance was only considered because the system architecture is simple and can be adjusted by the neural network. With this method, more accurate data can be obtained with smart RFID tags. In a simulation the proposed improved Kalman filter has 40.1%, 60.4% and 87.5% less mean squared error (MSE) than the conventional Kalman filter method for a temperature sensor, humidity sensor and oxygen sensor, respectively. The performance of the proposed method was also verified with some experiments.
Kalman filter for statistical monitoring of forest cover across sub-continental regions
Raymond L. Czaplewski
1991-01-01
The Kalman filter is a multivariate generalization of the composite estimator which recursively combines a current direct estimate with a past estimate that is updated for expected change over time with a prediction model. The Kalman filter can estimate proportions of different cover types for sub-continental regions each year. A random sample of high-resolution...
Directory of Open Access Journals (Sweden)
Gerasimos G. Rigatos
2011-12-01
Full Text Available The paper studies sensorless control for DC and induction motors, using Kalman Filtering techniques. First the case of a DC motor is considered and Kalman Filter-based control is implemented. Next the nonlinear model of a field-oriented induction motor is examined and the motor
Improved Kalman Filter Method for Measurement Noise Reduction in Multi Sensor RFID Systems
Directory of Open Access Journals (Sweden)
Min Chul Kim
2011-10-01
Full Text Available Recently, the range of available Radio Frequency Identification (RFID tags has been widened to include smart RFID tags which can monitor their varying surroundings. One of the most important factors for better performance of smart RFID system is accurate measurement from various sensors. In the multi-sensing environment, some noisy signals are obtained because of the changing surroundings. We propose in this paper an improved Kalman filter method to reduce noise and obtain correct data. Performance of Kalman filter is determined by a measurement and system noise covariance which are usually called the R and Q variables in the Kalman filter algorithm. Choosing a correct R and Q variable is one of the most important design factors for better performance of the Kalman filter. For this reason, we proposed an improved Kalman filter to advance an ability of noise reduction of the Kalman filter. The measurement noise covariance was only considered because the system architecture is simple and can be adjusted by the neural network. With this method, more accurate data can be obtained with smart RFID tags. In a simulation the proposed improved Kalman filter has 40.1%, 60.4% and 87.5% less Mean Squared Error (MSE than the conventional Kalman filter method for a temperature sensor, humidity sensor and oxygen sensor, respectively. The performance of the proposed method was also verified with some experiments.
A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems
Iglesias, Marco A.
2016-02-01
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The general aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference to develop a derivative-free stable method easy to implement in applications where the PDE (forward) model is only accessible as a black box (e.g. with commercial software). The proposed regularizing ensemble Kalman method can be derived as an approximation of the regularizing Levenberg-Marquardt (LM) scheme (Hanke 1997 Inverse Problems 13 79-95) in which the derivative of the forward operator and its adjoint are replaced with empirical covariances from an ensemble of elements from the admissible space of solutions. The resulting ensemble method consists of an update formula that is applied to each ensemble member and that has a regularization parameter selected in a similar fashion to the one in the LM scheme. Moreover, an early termination of the scheme is proposed according to a discrepancy principle-type of criterion. The proposed method can be also viewed as a regularizing version of standard Kalman approaches which are often unstable unless ad hoc fixes, such as covariance localization, are implemented. The aim of this paper is to provide a detailed numerical investigation of the regularizing and convergence properties of the proposed regularizing ensemble Kalman scheme; the proof of these properties is an open problem. By means of numerical experiments, we investigate the conditions under which the proposed method inherits the regularizing properties of the LM scheme of (Hanke 1997 Inverse Problems 13 79-95) and is thus stable and suitable for its application in problems where the computation of the Fréchet derivative is not computationally feasible. More concretely, we study the effect of ensemble size, number of measurements, selection of initial ensemble and tunable parameters on the performance of the method
Kalman Filter for Calibrating a Telescope Focal Plane
Kang, Bryan; Bayard, David
2006-01-01
The instrument-pointing frame (IPF) Kalman filter, and an algorithm that implements this filter, have been devised for calibrating the focal plane of a telescope. As used here, calibration signifies, more specifically, a combination of measurements and calculations directed toward ensuring accuracy in aiming the telescope and determining the locations of objects imaged in various arrays of photodetectors in instruments located on the focal plane. The IPF Kalman filter was originally intended for application to a spaceborne infrared astronomical telescope, but can also be applied to other spaceborne and ground-based telescopes. In the traditional approach to calibration of a telescope, (1) one team of experts concentrates on estimating parameters (e.g., pointing alignments and gyroscope drifts) that are classified as being of primarily an engineering nature, (2) another team of experts concentrates on estimating calibration parameters (e.g., plate scales and optical distortions) that are classified as being primarily of a scientific nature, and (3) the two teams repeatedly exchange data in an iterative process in which each team refines its estimates with the help of the data provided by the other team. This iterative process is inefficient and uneconomical because it is time-consuming and entails the maintenance of two survey teams and the development of computer programs specific to the requirements of each team. Moreover, theoretical analysis reveals that the engineering/ science iterative approach is not optimal in that it does not yield the best estimates of focal-plane parameters and, depending on the application, may not even enable convergence toward a set of estimates.
Using Kalman Filters to Reduce Noise from RFID Location System
Directory of Open Access Journals (Sweden)
Pedro Henriques Abreu
2014-01-01
Full Text Available Nowadays, there are many technologies that support location systems involving intrusive and nonintrusive equipment and also varying in terms of precision, range, and cost. However, the developers some time neglect the noise introduced by these systems, which prevents these systems from reaching their full potential. Focused on this problem, in this research work a comparison study between three different filters was performed in order to reduce the noise introduced by a location system based on RFID UWB technology with an associated error of approximately 18 cm. To achieve this goal, a set of experiments was devised and executed using a miniature train moving at constant velocity in a scenario with two distinct shapes—linear and oval. Also, this train was equipped with a varying number of active tags. The obtained results proved that the Kalman Filter achieved better results when compared to the other two filters. Also, this filter increases the performance of the location system by 15% and 12% for the linear and oval paths respectively, when using one tag. For a multiple tags and oval shape similar results were obtained (11–13% of improvement.
Kalman Filter Techniques for Control of Repeated Economic Surveys.
1980-09-30
jlk) , for T=1,2,...,T m~ max ho tweoen aurvco, (k+jjk) =x( kjk ) , for k=T,2T,... , and j=l,...,T (4) (:(k+jlk) = C(klk) + jQ at EUrveyr’ x( kjk ) = x...klk-T) + K(k) [y(k)- ( kjk -T)] (5) C(klk) = [I- K(k)] C( kjk -T) where K(k) is the Kalman gain K(k) = C( kjk -T) [C(klk-T)+B(k)]- (6) and B(k) is the sample...the error variance equations in the optimal filter theorem for the scalar case of Model A: N (k+jlk) = N 0 ( kjk ) [1 + jQR -I N (klk)]- N0 (kfk) = nd(k
Dynamic Mode Decomposition based on Kalman Filter for Parameter Estimation
Shibata, Hisaichi; Nonomura, Taku; Takaki, Ryoji
2017-11-01
With the development of computational fluid dynamics, large-scale data can now be obtained. In order to model physical phenomena from such data, it is required to extract features of flow field. Dynamic mode decomposition (DMD) is a method which meets the request. DMD can compute dominant eigenmodes of flow field by approximating system matrix. From this point of view, DMD can be considered as parameter estimation of system matrix. To estimate such parameters, we propose a novel method based on Kalman filter. Our numerical experiments indicated that the proposed method can estimate the parameters more accurately if it is compared with standard DMD methods. With this method, it is also possible to improve the parameter estimation accuracy if characteristics of noise acting on the system is given.
Kalman Filter Track Fits and Track Breakpoint Analysis
Astier, Pierre; Cousins, R D; Letessier-Selvon, A A; Popov, B A; Vinogradova, T G; Astier, Pierre; Cardini, Alessandro; Cousins, Robert D.; Letessier-Selvon, Antoine; Popov, Boris A.; Vinogradova, Tatiana
2000-01-01
We give an overview of track fitting using the Kalman filter method in the NOMAD detector at CERN, and emphasize how the wealth of by-product information can be used to analyze track breakpoints (discontinuities in track parameters caused by scattering, decay, etc.). After reviewing how this information has been previously exploited by others, we describe extensions which add power to breakpoint detection and characterization. We show how complete fits to the entire track, with breakpoint parameters added, can be easily obtained from the information from unbroken fits. Tests inspired by the Fisher F-test can then be used to judge breakpoints. Signed quantities (such as change in momentum at the breakpoint) can supplement unsigned quantities such as the various chisquares. We illustrate the method with electrons from real data, and with Monte Carlo simulations of pion decays.
Kalman Filter for Mass Property and Thrust Identification (MMS)
Queen, Steven
2015-01-01
The Magnetospheric Multiscale (MMS) mission consists of four identically instrumented, spin-stabilized observatories, elliptically orbiting the Earth in a tetrahedron formation. For the operational success of the mission, on-board systems must be able to deliver high-precision orbital adjustment maneuvers. On MMS, this is accomplished using feedback from on-board star sensors in tandem with accelerometers whose measurements are dynamically corrected for errors associated with a spinning platform. In order to determine the required corrections to the measured acceleration, precise estimates of attitude, rate, and mass-properties is necessary. To this end, both an on-board and ground-based Multiplicative Extended Kalman Filter (MEKF) were formulated and implemented in order to estimate the dynamic and quasi-static properties of the spacecraft.
A Study about Kalman Filters Applied to Embedded Sensors.
Valade, Aurélien; Acco, Pascal; Grabolosa, Pierre; Fourniols, Jean-Yves
2017-12-05
Over the last decade, smart sensors have grown in complexity and can now handle multiple measurement sources. This work establishes a methodology to achieve better estimates of physical values by processing raw measurements within a sensor using multi-physical models and Kalman filters for data fusion. A driving constraint being production cost and power consumption, this methodology focuses on algorithmic complexity while meeting real-time constraints and improving both precision and reliability despite low power processors limitations. Consequently, processing time available for other tasks is maximized. The known problem of estimating a 2D orientation using an inertial measurement unit with automatic gyroscope bias compensation will be used to illustrate the proposed methodology applied to a low power STM32L053 microcontroller. This application shows promising results with a processing time of 1.18 ms at 32 MHz with a 3.8% CPU usage due to the computation at a 26 Hz measurement and estimation rate.
Alignment of the LHCb detector with Kalman filter fitted tracks
Amoraal, J M
2009-01-01
The LHCb detector, operating at the Large Hadron Collider at CERN, is a single arm spectrometer optimised for the detection of forward b and anti-b production for b physics studies. The reconstruction of vertices and tracks is done by silicon micro-strip and gaseous straw-tube based detectors. To obtain excellent momentum, mass and vertex resolutions, the detectors need to be aligned well within the hit resolution for a given detector. We present a general and easy to configure alignment framework which uses the closed from method of alignment with Kalman filter fitted tracks to determine the alignment parameters. This allows us to use the standard LHCb track model and fit, and correctly take complexities such as multiple scattering and energy loss corrections into account. With this framework it is possible to align any detector for any degree of freedom.
Energy Technology Data Exchange (ETDEWEB)
Lall, Pradeep; Wei, Junchao; Davis, Lynn
2013-08-08
Solid-state lighting (SSL) luminaires containing light emitting diodes (LEDs) have the potential of seeing excessive temperatures when being transported across country or being stored in non-climate controlled warehouses. They are also being used in outdoor applications in desert environments that see little or no humidity but will experience extremely high temperatures during the day. This makes it important to increase our understanding of what effects high temperature exposure for a prolonged period of time will have on the usability and survivability of these devices. Traditional light sources “burn out” at end-of-life. For an incandescent bulb, the lamp life is defined by B50 life. However, the LEDs have no filament to “burn”. The LEDs continually degrade and the light output decreases eventually below useful levels causing failure. Presently, the TM-21 test standard is used to predict the L70 life of LEDs from LM-80 test data. Several failure mechanisms may be active in a LED at a single time causing lumen depreciation. The underlying TM-21 Model may not capture the failure physics in presence of multiple failure mechanisms. Correlation of lumen maintenance with underlying physics of degradation at system-level is needed. In this paper, Kalman Filter (KF) and Extended Kalman Filters (EKF) have been used to develop a 70-percent Lumen Maintenance Life Prediction Model for LEDs used in SSL luminaires. Ten-thousand hour LM-80 test data for various LEDs have been used for model development. System state at each future time has been computed based on the state space at preceding time step, system dynamics matrix, control vector, control matrix, measurement matrix, measured vector, process noise and measurement noise. The future state of the lumen depreciation has been estimated based on a second order Kalman Filter model and a Bayesian Framework. The measured state variable has been related to the underlying damage using physics-based models. Life
Energy Technology Data Exchange (ETDEWEB)
Lall, Pradeep; Wei, Junchao; Davis, J Lynn
2014-06-24
Abstract— Solid-state lighting (SSL) luminaires containing light emitting diodes (LEDs) have the potential of seeing excessive temperatures when being transported across country or being stored in non-climate controlled warehouses. They are also being used in outdoor applications in desert environments that see little or no humidity but will experience extremely high temperatures during the day. This makes it important to increase our understanding of what effects high temperature exposure for a prolonged period of time will have on the usability and survivability of these devices. Traditional light sources “burn out” at end-of-life. For an incandescent bulb, the lamp life is defined by B50 life. However, the LEDs have no filament to “burn”. The LEDs continually degrade and the light output decreases eventually below useful levels causing failure. Presently, the TM-21 test standard is used to predict the L70 life of LEDs from LM-80 test data. Several failure mechanisms may be active in a LED at a single time causing lumen depreciation. The underlying TM-21 Model may not capture the failure physics in presence of multiple failure mechanisms. Correlation of lumen maintenance with underlying physics of degradation at system-level is needed. In this paper, Kalman Filter (KF) and Extended Kalman Filters (EKF) have been used to develop a 70-percent Lumen Maintenance Life Prediction Model for LEDs used in SSL luminaires. Ten-thousand hour LM-80 test data for various LEDs have been used for model development. System state at each future time has been computed based on the state space at preceding time step, system dynamics matrix, control vector, control matrix, measurement matrix, measured vector, process noise and measurement noise. The future state of the lumen depreciation has been estimated based on a second order Kalman Filter model and a Bayesian Framework. Life prediction of L70 life for the LEDs used in SSL luminaires from KF and EKF based models have
Fast Kalman-like filtering for large-dimensional linear and Gaussian state-space models
Ait-El-Fquih, Boujemaa
2015-08-13
This paper considers the filtering problem for linear and Gaussian state-space models with large dimensions, a setup in which the optimal Kalman Filter (KF) might not be applicable owing to the excessive cost of manipulating huge covariance matrices. Among the most popular alternatives that enable cheaper and reasonable computation is the Ensemble KF (EnKF), a Monte Carlo-based approximation. In this paper, we consider a class of a posteriori distributions with diagonal covariance matrices and propose fast approximate deterministic-based algorithms based on the Variational Bayesian (VB) approach. More specifically, we derive two iterative KF-like algorithms that differ in the way they operate between two successive filtering estimates; one involves a smoothing estimate and the other involves a prediction estimate. Despite its iterative nature, the prediction-based algorithm provides a computational cost that is, on the one hand, independent of the number of iterations in the limit of very large state dimensions, and on the other hand, always much smaller than the cost of the EnKF. The cost of the smoothing-based algorithm depends on the number of iterations that may, in some situations, make this algorithm slower than the EnKF. The performances of the proposed filters are studied and compared to those of the KF and EnKF through a numerical example.
Kalman plus weights: a time scale algorithm
Greenhall, C. A.
2001-01-01
KPW is a time scale algorithm that combines Kalman filtering with the basic time scale equation (BTSE). A single Kalman filter that estimates all clocks simultaneously is used to generate the BTSE frequency estimates, while the BTSE weights are inversely proportional to the white FM variances of the clocks. Results from simulated clock ensembles are compared to previous simulation results from other algorithms.
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Thomsen, Per Grove; Madsen, Henrik
2007-01-01
We present a novel numerically robust and computationally efficient extended Kalman filter for state estimation in nonlinear continuous-discrete stochastic systems. The resulting differential equations for the mean-covariance evolution of the nonlinear stochastic continuous-discrete time systems...... differential equations....... are solved efficiently using an ESDIRK integrator with sensitivity analysis capabilities. This ESDIRK integrator for the mean- covariance evolution is implemented as part of an extended Kalman filter and tested on a PDE system. For moderate to large sized systems, the ESDIRK based extended Kalman filter...
Kalman filtering techniques for focal plane electric field estimation.
Groff, Tyler D; Jeremy Kasdin, N
2013-01-01
For a coronagraph to detect faint exoplanets, it will require focal plane wavefront control techniques to continue reaching smaller angular separations and higher contrast levels. These correction algorithms are iterative and the control methods need an estimate of the electric field at the science camera, which requires nearly all of the images taken for the correction. The best way to make such algorithms the least disruptive to science exposures is to reduce the number required to estimate the field. We demonstrate a Kalman filter estimator that uses prior knowledge to create the estimate of the electric field, dramatically reducing the number of exposures required to estimate the image plane electric field while stabilizing the suppression against poor signal-to-noise. In addition to a significant reduction in exposures, we discuss the relative merit of this algorithm to estimation schemes that do not incorporate prior state estimate history, particularly in regard to estimate error and covariance. Ultimately the filter will lead to an adaptive algorithm which can estimate physical parameters in the laboratory for robustness to variance in the optical train.
Data Sketching for Large-Scale Kalman Filtering
Berberidis, Dimitris; Giannakis, Georgios B.
2017-07-01
In an age of exponentially increasing data generation, performing inference tasks by utilizing the available information in its entirety is not always an affordable option. The present paper puts forth approaches to render tracking of large-scale dynamic processes via a Kalman filter affordable, by processing a reduced number of data. Three distinct methods are introduced for reducing the number of data involved in the correction step of the filter. Towards this goal, the first two methods employ random projections and innovation-based censoring to effect dimensionality reduction and measurement selection respectively. The third method achieves reduced complexity by leveraging sequential processing of observations and selecting a few informative updates based on an information-theoretic metric. Simulations on synthetic data, compare the proposed methods with competing alternatives, and corroborate their efficacy in terms of estimation accuracy over complexity reduction. Finally, monitoring large networks is considered as an application domain, with the proposed methods tested on Kronecker graphs to evaluate their efficiency in tracking traffic matrices and time-varying link costs.
Zhu, Wei; Wang, Wei; Yuan, Gannan
2016-06-01
In order to improve the tracking accuracy, model estimation accuracy and quick response of multiple model maneuvering target tracking, the interacting multiple models five degree cubature Kalman filter (IMM5CKF) is proposed in this paper. In the proposed algorithm, the interacting multiple models (IMM) algorithm processes all the models through a Markov Chain to simultaneously enhance the model tracking accuracy of target tracking. Then a five degree cubature Kalman filter (5CKF) evaluates the surface integral by a higher but deterministic odd ordered spherical cubature rule to improve the tracking accuracy and the model switch sensitivity of the IMM algorithm. Finally, the simulation results demonstrate that the proposed algorithm exhibits quick and smooth switching when disposing different maneuver models, and it also performs better than the interacting multiple models cubature Kalman filter (IMMCKF), interacting multiple models unscented Kalman filter (IMMUKF), 5CKF and the optimal mode transition matrix IMM (OMTM-IMM).
Application of Kalman Filter for Estimating a Process Disturbance in a Building Space
Directory of Open Access Journals (Sweden)
Deuk-Woo Kim
2017-10-01
Full Text Available This paper addresses an application of the Kalman filter for estimating a time-varying process disturbance in a building space. The process disturbance means a synthetic composite of heat gains and losses caused by internal heat sources e.g., people, lights, equipment, and airflows. It is difficult to measure and quantify the internal heat sources and airflows due to their dynamic nature and time-lag impact on indoor environment. To address this issue, a Kalman filter estimation method was used in this study. The Kalman filtering is well suited for situations when state variables of interest cannot be measured. Based on virtual and real experiments conducted in this study, it was found that the Kalman filter can be used to estimate the time-varying process disturbance in a building space.
Ledsham, W. H.; Staelin, D. H.
1978-01-01
An extended Kalman-Bucy filter has been implemented for atmospheric temperature profile retrievals from observations made using the Scanned Microwave Spectrometer (SCAMS) instrument carried on the Nimbus 6 satellite. This filter has the advantage that it requires neither stationary statistics in the underlying processes nor linear production of the observed variables from the variables to be estimated. This extended Kalman-Bucy filter has yielded significant performance improvement relative to multiple regression retrieval methods. A multi-spot extended Kalman-Bucy filter has also been developed in which the temperature profiles at a number of scan angles in a scanning instrument are retrieved simultaneously. These multi-spot retrievals are shown to outperform the single-spot Kalman retrievals.
Ghumare, Eshwar; Schrooten, Maarten; Vandenberghe, Rik; Dupont, Patrick
2015-08-01
Kalman filter approaches are widely applied to derive time varying effective connectivity from electroencephalographic (EEG) data. For multi-trial data, a classical Kalman filter (CKF) designed for the estimation of single trial data, can be implemented by trial-averaging the data or by averaging single trial estimates. A general linear Kalman filter (GLKF) provides an extension for multi-trial data. In this work, we studied the performance of the different Kalman filtering approaches for different values of signal-to-noise ratio (SNR), number of trials and number of EEG channels. We used a simulated model from which we calculated scalp recordings. From these recordings, we estimated cortical sources. Multivariate autoregressive model parameters and partial directed coherence was calculated for these estimated sources and compared with the ground-truth. The results showed an overall superior performance of GLKF except for low levels of SNR and number of trials.
Wang, Rui; Li, Yanxiao; Sun, Hui; Chen, Zengqiang
2017-11-01
The modern civil aircrafts use air ventilation pressurized cabins subject to the limited space. In order to monitor multiple contaminants and overcome the hypersensitivity of the single sensor, the paper constructs an output correction integrated sensor configuration using sensors with different measurement theories after comparing to other two different configurations. This proposed configuration works as a node in the contaminant distributed wireless sensor monitoring network. The corresponding measurement error models of integrated sensors are also proposed by using the Kalman consensus filter to estimate states and conduct data fusion in order to regulate the single sensor measurement results. The paper develops the sufficient proof of the Kalman consensus filter stability when considering the system and the observation noises and compares the mean estimation and the mean consensus errors between Kalman consensus filter and local Kalman filter. The numerical example analyses show the effectiveness of the algorithm. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Jue Huang
2015-01-01
Full Text Available We propose a robust method for tracking nonlinear target with the fusion unscented Kalman filter (FUKF. We noticed that when some outliers exist in the measurements of the sensors, they cannot track the target accurately by using the standard Kalman filters. The robust statistics theory is used in this paper to solve this problem. The measurement noise variance which is at the time of the outlier is restructured through minimizing the designed cost function. Then, the standard fusion unscented Kalman filter is used to track the target in order to avoid the bias brought by the linear approximation. Compared to the traditional tracking method and Huber robust method (HFUKF, this method has a more accurate performance and can track the target efficiently while the outliers exist. Last, simulation examples in three different conditions are given and the simulation results show the advantages of the proposed method over the fusion unscented Kalman filter (FUKF and the Huber robust method (HFUKF.
Analysis of Video-Based Microscopic Particle Trajectories Using Kalman Filtering
Wu, Pei-Hsun; Agarwal, Ashutosh; Hess, Henry; Khargonekar, Pramod P.; Tseng, Yiider
2010-01-01
Abstract The fidelity of the trajectories obtained from video-based particle tracking determines the success of a variety of biophysical techniques, including in situ single cell particle tracking and in vitro motility assays. However, the image acquisition process is complicated by system noise, which causes positioning error in the trajectories derived from image analysis. Here, we explore the possibility of reducing the positioning error by the application of a Kalman filter, a powerful algorithm to estimate the state of a linear dynamic system from noisy measurements. We show that the optimal Kalman filter parameters can be determined in an appropriate experimental setting, and that the Kalman filter can markedly reduce the positioning error while retaining the intrinsic fluctuations of the dynamic process. We believe the Kalman filter can potentially serve as a powerful tool to infer a trajectory of ultra-high fidelity from noisy images, revealing the details of dynamic cellular processes. PMID:20550894
National Research Council Canada - National Science Library
Xiaoping Wu; Claudio Abbondanza; Zuheir Altamimi; T Mike Chin; Xavier Collilieux; Richard S Gross; Michael B Heflin; Yan Jiang; Jay W Parker
2015-01-01
...) quasi-instantaneously. Here, we use a Kalman filter and smoother approach to combine time series from four space geodetic techniques to realize an experimental TRF through weekly time series of geocentric coordinates...
National Research Council Canada - National Science Library
Wu, Xiaoping; Abbondanza, Claudio; Altamimi, Zuheir; Chin, T. Mike; Collilieux, Xavier; Gross, Richard S; Heflin, Michael B; Jiang, Yan; Parker, Jay W
2015-01-01
.... Here, we use a Kalman filter and smoother approach to combine time series from four space geodetic techniques to realize an experimental TRF through weekly time series of geocentric coordinates...
Determination of High-Speed Multiple Threat Using Kalman Filter Analysis of Maritime Movement
2015-06-01
and W. Kazimierski, “A concept of decentralized fusion of maritime radar targets with multisensor Kalman filter,” Vilnius, Lithuania, 16–18 June 2010...reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of...feeding data into the Kalman filtering algorithm, which is used in the tracking of moving targets based on simulated radar position measurements
Modified iterated extended Kalman particle filter for single satellite passive tracking
WU, Panlong; KONG, Jianshou; BO, Yuming
2013-01-01
Single satellite-to-satellite passive tracking techniques have great significance in space surveillance systems. A new passive modified iterated extended Kalman particle filter (MIEKPF) using bearings-only measurements in the Earth-Centered Inertial Coordinate System is proposed. The modified iterated extended Kalman filter (MIEKF), with a new maximum likelihood iteration termination criterion, is used to generate the proposal distribution of the MIEKPF. Moreover, a new measurement u...
Application of a Kalman Filter with Augmented Measurement Model in Non-Invasive Cardiac Imaging
Elies Henar, Francesc
2011-01-01
This work will focus on improving the Kalman filter by use of an extended measurement model [Kaipio et Somersalo, 1999] which introduces spatial regularization terms into the filter. This model has been applied in solvers of the inverse problem of electrical impedance tomography [Hiltunen et al., 2010], though this tomography inverse problem is non-linear, it is mathematically very similar to the imaging of electric sources in the heart. Trabajo trata sobre la mejora de un filtro de Kalman...
Application of a Strong Tracking Finite-Difference Extended Kalman Filter to Eye Tracking
Zhang, Zutao; Zhang, Jiashu
2010-01-01
This paper proposes a new eye tracking method using strong finite-difference Kalman filter. Firstly, strong tracking factor is introduced to modify priori covariance matrix to improve the accuracy of the eye tracking algorithm. Secondly, the finite-difference method is proposed to replace partial derivatives of nonlinear functions to eye tracking. From above deduction, the new strong finite-difference Kalman filter becomes very simple because of replacing partial derivatives calculation using...
Fuzzy Logic Based Autonomous Parallel Parking System with Kalman Filtering
Panomruttanarug, Benjamas; Higuchi, Kohji
This paper presents an emulation of fuzzy logic control schemes for an autonomous parallel parking system in a backward maneuver. There are four infrared sensors sending the distance data to a microcontroller for generating an obstacle-free parking path. Two of them mounted on the front and rear wheels on the parking side are used as the inputs to the fuzzy rules to calculate a proper steering angle while backing. The other two attached to the front and rear ends serve for avoiding collision with other cars along the parking space. At the end of parking processes, the vehicle will be in line with other parked cars and positioned in the middle of the free space. Fuzzy rules are designed based upon a wall following process. Performance of the infrared sensors is improved using Kalman filtering. The design method needs extra information from ultrasonic sensors. Starting from modeling the ultrasonic sensor in 1-D state space forms, one makes use of the infrared sensor as a measurement to update the predicted values. Experimental results demonstrate the effectiveness of sensor improvement.
Estimating short-period dynamics using an extended Kalman filter
Bauer, Jeffrey E.; Andrisani, Dominick
1990-01-01
An extended Kalman filter (EKF) is used to estimate the parameters of a low-order model from aircraft transient response data. The low-order model is a state space model derived from the short-period approximation of the longitudinal aircraft dynamics. The model corresponds to the pitch rate to stick force transfer function currently used in flying qualities analysis. Because of the model chosen, handling qualities information is also obtained. The parameters are estimated from flight data as well as from a six-degree-of-freedom, nonlinear simulation of the aircraft. These two estimates are then compared and the discrepancies noted. The low-order model is able to satisfactorily match both flight data and simulation data from a high-order computer simulation. The parameters obtained from the EKF analysis of flight data are compared to those obtained using frequency response analysis of the flight data. Time delays and damping ratios are compared and are in agreement. This technique demonstrates the potential to determine, in near real time, the extent of differences between computer models and the actual aircraft. Precise knowledge of these differences can help to determine the flying qualities of a test aircraft and lead to more efficient envelope expansion.
Dynamics of Electricity Demand in Lesotho: A Kalman Filter Approach
Directory of Open Access Journals (Sweden)
Thamae Retselisitsoe Isaiah
2015-04-01
Full Text Available This study provides an empirical analysis of the time-varying price and income elasticities of electricity demand in Lesotho for the period 1995-2012 using the Kalman filter approach. The results reveal that economic growth has been one of the main drivers of electricity consumption in Lesotho while electricity prices are found to play a less significant role since they are monopoly-driven and relatively low when compared to international standards. These findings imply that increases in electricity prices in Lesotho might not have a significant impact on consumption in the short-run. However, if the real electricity prices become too high over time, consumers might change their behavior and sensitivity to price and hence, energy policymakers will need to reconsider their impact in the long-run. Furthermore, several exogenous shocks seem to have affected the sensitivity of electricity demand during the period prior to regulation, which made individuals, businesses and agencies to be more sensitive to electricity costs. On the other hand, the period after regulation has been characterized by more stable and declining sensitivity of electricity demand. Therefore, factors such as regulation and changes in the country’s economic activities appear to have affected both price and income elasticities of electricity demand in Lesotho.
A Study about Kalman Filters Applied to Embedded Sensors
Directory of Open Access Journals (Sweden)
Aurélien Valade
2017-12-01
Full Text Available Over the last decade, smart sensors have grown in complexity and can now handle multiple measurement sources. This work establishes a methodology to achieve better estimates of physical values by processing raw measurements within a sensor using multi-physical models and Kalman filters for data fusion. A driving constraint being production cost and power consumption, this methodology focuses on algorithmic complexity while meeting real-time constraints and improving both precision and reliability despite low power processors limitations. Consequently, processing time available for other tasks is maximized. The known problem of estimating a 2D orientation using an inertial measurement unit with automatic gyroscope bias compensation will be used to illustrate the proposed methodology applied to a low power STM32L053 microcontroller. This application shows promising results with a processing time of 1.18 ms at 32 MHz with a 3.8% CPU usage due to the computation at a 26 Hz measurement and estimation rate.
Directory of Open Access Journals (Sweden)
Gerasimos G. Rigatos
2011-12-01
Full Text Available The paper studies sensorless control for DC and induction motors, using Kalman Filtering techniques. First the case of a DC motor is considered and Kalman Filter-based control is implemented. Next the nonlinear model of a field-oriented induction motor is examined and the motor's angular velocity is estimated by an Extended Kalman Filter which processes measurements of the rotor's angle. Sensorless control of the induction motor is again implemented through feedback of the estimated state vector. Additionally, a state estimation-based control loop is implemented using the Unscented Kalman Filter. Moreover, state estimation-based control is developed for the induction motor model using a nonlinear flatness-based controller and the state estimation that is provided by the Extended Kalman Filter. Unlike field oriented control, in the latter approach there is no assumption about decoupling between the rotor speed dynamics and the magnetic flux dynamics. The efficiency of the Kalman Filter-based control schemes, for both the DC and induction motor models, is evaluated through simulation experiments.
A Fixed-Lag Kalman Smoother to Filter Power Line Interference in Electrocardiogram Recordings.
Warmerdam, G J J; Vullings, R; Schmitt, L; Van Laar, J O E H; Bergmans, J W M
2017-08-01
Filtering power line interference (PLI) from electrocardiogram (ECG) recordings can lead to significant distortions of the ECG and mask clinically relevant features in ECG waveform morphology. The objective of this study is to filter PLI from ECG recordings with minimal distortion of the ECG waveform. In this paper, we propose a fixed-lag Kalman smoother with adaptive noise estimation. The performance of this Kalman smoother in filtering PLI is compared to that of a fixed-bandwidth notch filter and several adaptive PLI filters that have been proposed in the literature. To evaluate the performance, we corrupted clean neonatal ECG recordings with various simulated PLI. Furthermore, examples are shown of filtering real PLI from an adult and a fetal ECG recording. The fixed-lag Kalman smoother outperforms other PLI filters in terms of step response settling time (improvements that range from 0.1 to 1 s) and signal-to-noise ratio (improvements that range from 17 to 23 dB). Our fixed-lag Kalman smoother can be used for semi real-time applications with a limited delay of 0.4 s. The fixed-lag Kalman smoother presented in this study outperforms other methods for filtering PLI and leads to minimal distortion of the ECG waveform.
Carbon flux bias estimation employing Maximum Likelihood Ensemble Filter (MLEF)
Zupanski, Dusanka; Denning, A. Scott; Uliasz, Marek; Zupanski, Milija; Schuh, Andrew E.; Rayner, Peter J.; Peters, Wouter; Corbin, Katherine D.
2007-01-01
We evaluate the capability of an ensemble based data assimilation approach, referred to as Maximum Likelihood Ensemble Filter (MLEF), to estimate biases in the CO2 photosynthesis and respiration fluxes. We employ an off-line Lagrangian Particle Dispersion Model (LPDM), which is driven by the carbon
Toward the application of the Kalman filter to regional open ocean modeling
Miller, R. N.
1986-01-01
A partial differential equation model is defined for ocean meteorological prediction and synoptic analysis. The Kalman filter used for data assimilation is described and applied to the one-dimensional linear barotropic quasi-geostrophic model with periodic and open boundary conditions. The model accounts for eddy scale dynamics in the ocean. The assumptions made in the forecast model are discussed, along with comparisons of the error variances expected with the filter and from an objective analysis method. The effectiveness of the Kalman filter is demonstrated and subsequent efforts to extend the filter to two dimensions are indicated.
Dynamic Mode Decomposition based on Bootstrapping Extended Kalman Filter Application to Noisy data
Nonomura, Taku; Shibata, Hisaichi; Takaki, Ryoji
2017-11-01
In this study, dynamic mode decomposition (DMD) based on bootstrapping extended Kalman filter is proposed for time-series data. In this framework, state variables (x and y) are filtered as well as the parameter estimation (aij) which is conducted in the conventional DMD and the standard Kalman-filter-based DMD. The filtering process of state variables enables us to obtain highly accurate eigenvalue of the system with strong noise. In the presentation, formulation, advantages and disadvantages are discussed. This research is partially supported by Presto, JST (JPMJPR1678).
Directory of Open Access Journals (Sweden)
Nataliya Chukhrova
2017-05-01
Full Text Available This paper gives a detailed overview of the current state of research in relation to the use of state space models and the Kalman-filter in the field of stochastic claims reserving. Most of these state space representations are matrix-based, which complicates their applications. Therefore, to facilitate the implementation of state space models in practice, we present a scalar state space model for cumulative payments, which is an extension of the well-known chain ladder (CL method. The presented model is distribution-free, forms a basis for determining the entire unobservable lower and upper run-off triangles and can easily be applied in practice using the Kalman-filter for prediction, filtering and smoothing of cumulative payments. In addition, the model provides an easy way to find outliers in the data and to determine outlier effects. Finally, an empirical comparison of the scalar state space model, promising prior state space models and some popular stochastic claims reserving methods is performed.
Vertical Covariance Localization for Satellite Radiances in Ensemble Kalman Filters
2010-01-01
applied to the JMA global model (GSM). SOLA, 3, 37–40. NOAA, 2009: KLM user’s guide with NOAA-N,-N’ supplement. [Available online at http://www2...ncdc.noaa.gov/docs/ klm / index.htm.] Saunders, R. W., 1993: Note on the Advanced Microwave Sound- ing Unit. Bull. Amer. Meteor. Soc., 74, 2211–2212. Whitaker
Multi Data Reservoir History Matching using the Ensemble Kalman Filter
Katterbauer, Klemens
2015-05-01
Reservoir history matching is becoming increasingly important with the growing demand for higher quality formation characterization and forecasting and the increased complexity and expenses for modern hydrocarbon exploration projects. History matching has long been dominated by adjusting reservoir parameters based solely on well data whose spatial sparse sampling has been a challenge for characterizing the flow properties in areas away from the wells. Geophysical data are widely collected nowadays for reservoir monitoring purposes, but has not yet been fully integrated into history matching and forecasting fluid flow. In this thesis, I present a pioneering approach towards incorporating different time-lapse geophysical data together for enhancing reservoir history matching and uncertainty quantification. The thesis provides several approaches to efficiently integrate multiple geophysical data, analyze the sensitivity of the history matches to observation noise, and examine the framework’s performance in several settings, such as the Norne field in Norway. The results demonstrate the significant improvements in reservoir forecasting and characterization and the synergy effects encountered between the different geophysical data. In particular, the joint use of electromagnetic and seismic data improves the accuracy of forecasting fluid properties, and the usage of electromagnetic data has led to considerably better estimates of hydrocarbon fluid components. For volatile oil and gas reservoirs the joint integration of gravimetric and InSAR data has shown to be beneficial in detecting the influx of water and thereby improving the recovery rate. Summarizing, this thesis makes an important contribution towards integrated reservoir management and multiphysics integration for reservoir history matching.
Enhanced Ocean Prediction using Ensemble Kalman Filter Techniques
2006-09-30
that is currently undergoing operational trials at the Australian Bureau of Meteorology . Under this project we have developed an EnKF version of...bluelink/) is a partnership between the CSIRO Wealth from Oceans Flagship Program, the Australian Bureau of Meteorology and the Royal Australian Navy. An
A Greedy Approach for Placement of Subsurface Aquifer Wells in an Ensemble Filtering Framework
El Gharamti, Mohamad
2015-11-26
Optimizing wells placement may help in better understanding subsurface solute transport and detecting contaminant plumes. In this work, we use the ensemble Kalman filter (EnKF) as a data assimilation tool and propose a greedy observational design algorithm to optimally select aquifer wells locations for updating the prior contaminant ensemble. The algorithm is greedy in the sense that it operates sequentially, without taking into account expected future gains. The selection criteria is based on maximizing the information gain that the EnKF carries during the update of the prior uncertainties. We test the efficiency of this algorithm in a synthetic aquifer system where a contaminant plume is set to migrate over a 30 years period across a heterogenous domain.
The extended Kalman filter for forecast of algal bloom dynamics.
Mao, J Q; Lee, Joseph H W; Choi, K W
2009-09-01
A deterministic ecosystem model is combined with an extended Kalman filter (EKF) to produce short term forecasts of algal bloom and dissolved oxygen dynamics in a marine fish culture zone (FCZ). The weakly flushed FCZ is modelled as a well-mixed system; the tidal exchange with the outer bay is lumped into a flushing rate that is numerically determined from a three-dimensional hydrodynamic model. The ecosystem model incorporates phytoplankton growth kinetics, nutrient uptake, photosynthetic production, nutrient sources from organic fish farm loads, and nutrient exchange with a sediment bed layer. High frequency field observations of chlorophyll, dissolved oxygen (DO) and hydro-meteorological parameters (sampling interval Deltat=1 day, 2h, 1h, respectively) and bi-weekly nutrient data are assimilated into the model to produce the combined state estimate accounting for the uncertainties. In addition to the water quality state variables, the EKF incorporates dynamic estimation of algal growth rate and settling velocity. The effectiveness of the EKF data assimilation is studied for a wide range of sampling intervals and prediction lead-times. The chlorophyll and dissolved oxygen estimated by the EKF are compared with field data of seven algal bloom events observed at Lamma Island, Hong Kong. The results show that the EKF estimate well captures the nonlinear error evolution in time; the chlorophyll level can be satisfactorily predicted by the filtered model estimate with a mean absolute error of around 1-2 microg/L. Predictions with 1-2 day lead-time are highly correlated with the observations (r=0.7-0.9); the correlation stays at a high level for a lead-time of 3 days (r=0.6-0.7). Estimated algal growth and settling rates are in accord with field observations; the more frequent DO data can compensate for less frequent algal biomass measurements. The present study is the first time the EKF is successfully applied to forecast an entire algal bloom cycle, suggesting the
Schmidt, S. F.; Flanagan, P. F.; Sorenson, J. A.
1978-01-01
A Kalman filter for aircraft terminal area and landing navigation was implemented and flight tested in the NASA Ames STOLAND avionics computer onboard a Twin Otter aircraft. This system combines navaid measurements from TACAN, MODILS, air data, radar altimeter sensors along with measurements from strap-down accelerometer and attitude angle sensors. The flight test results demonstrate that the Kalman filter provides improved estimates of the aircraft position and velocity as compared with estimates from the more standard complementary filter. The onboard computer implementation requirements to achieve this improved performance are discussed.
Square Root Unscented Kalman Filters for State Estimation of Induction Motor Drives
DEFF Research Database (Denmark)
Lascu, Cristian; Jafarzadeh, Saeed; Fadali, M.Sami
2013-01-01
This paper investigates the application, design, and implementation of the square root unscented Kalman filter (UKF) (SRUKF) for induction motor (IM) sensorless drives. The UKF uses nonlinear unscented transforms (UTs) in the prediction step in order to preserve the stochastic characteristics...... of a nonlinear system. The advantage of using the UT is its ability to capture the nonlinear behavior of the system, unlike the extended Kalman filter (EKF) that uses linearized models. The SRUKF implements the UKF using square root filtering to reduce computational errors. We discuss the theoretical aspects...
Directory of Open Access Journals (Sweden)
Chuanxue Song
2017-05-01
Full Text Available To improve the accuracy of insulation monitoring between the battery pack and chassis of electric vehicles, we established a serial battery pack model composed of first-order resistor-capacitor (RC circuit battery cells. We then designed a low-voltage, low-frequency insulation monitoring model based on this serial battery pack model. An extended Kalman filter (EKF was designed for this non-linear system to filter the measured results, thus mitigating the influence of noise. Experimental and simulation results show that the proposed monitoring model and extended Kalman filtering algorithm for insulation resistance monitoring present satisfactory estimation accuracy and robustness.
Directory of Open Access Journals (Sweden)
Dongyan Chen
2015-01-01
Full Text Available This paper is concerned with the optimal Kalman filtering problem for a class of discrete stochastic systems with multiplicative noises and random two-step sensor delays. Three Bernoulli distributed random variables with known conditional probabilities are introduced to characterize the phenomena of the random two-step sensor delays which may happen during the data transmission. By using the state augmentation approach and innovation analysis technique, an optimal Kalman filter is constructed for the augmented system in the sense of the minimum mean square error (MMSE. Subsequently, the optimal Kalman filtering is derived for corresponding augmented system in initial instants. Finally, a simulation example is provided to demonstrate the feasibility and effectiveness of the proposed filtering method.
DEFF Research Database (Denmark)
Høilund, Carsten; Moeslund, Thomas B.; Madsen, Claus B.
2010-01-01
This paper presents a method for determining the free space in a scene as viewed by a vehicle-mounted camera. Using disparity maps from a stereo camera and known camera motion, the disparity maps are first filtered by an iconic Kalman filter, operating on each pixel individually, thereby reducing...
A new Approach for Kalman filtering on Mobile Robots in the presence of uncertainties
DEFF Research Database (Denmark)
Larsen, Thomas Dall; Andersen, Nils Axel; Ravn, Ole
1999-01-01
In many practical Kalman filter applications, the quantity of most significance for the estimation error is the process noise matrix. When filters are stabilized or performance is sought to be improved, tuning of this matrix is the most common method. This tuning process cannot be done before the...
Feedback Robust Cubature Kalman Filter for Target Tracking Using an Angle Sensor.
Wu, Hao; Chen, Shuxin; Yang, Binfeng; Chen, Kun
2016-05-09
The direction of arrival (DOA) tracking problem based on an angle sensor is an important topic in many fields. In this paper, a nonlinear filter named the feedback M-estimation based robust cubature Kalman filter (FMR-CKF) is proposed to deal with measurement outliers from the angle sensor. The filter designs a new equivalent weight function with the Mahalanobis distance to combine the cubature Kalman filter (CKF) with the M-estimation method. Moreover, by embedding a feedback strategy which consists of a splitting and merging procedure, the proper sub-filter (the standard CKF or the robust CKF) can be chosen in each time index. Hence, the probability of the outliers' misjudgment can be reduced. Numerical experiments show that the FMR-CKF performs better than the CKF and conventional robust filters in terms of accuracy and robustness with good computational efficiency. Additionally, the filter can be extended to the nonlinear applications using other types of sensors.
Foussier, Jerome; Teichmann, Daniel; Jia, Jing; Misgeld, Berno; Leonhardt, Steffen
2014-05-09
Extracting cardiorespiratory signals from non-invasive and non-contacting sensor arrangements, i.e. magnetic induction sensors, is a challenging task. The respiratory and cardiac signals are mixed on top of a large and time-varying offset and are likely to be disturbed by measurement noise. Basic filtering techniques fail to extract relevant information for monitoring purposes. We present a real-time filtering system based on an adaptive Kalman filter approach that separates signal offsets, respiratory and heart signals from three different sensor channels. It continuously estimates respiration and heart rates, which are fed back into the system model to enhance performance. Sensor and system noise covariance matrices are automatically adapted to the aimed application, thus improving the signal separation capabilities. We apply the filtering to two different subjects with different heart rates and sensor properties and compare the results to the non-adaptive version of the same Kalman filter. Also, the performance, depending on the initialization of the filters, is analyzed using three different configurations ranging from best to worst case. Extracted data are compared with reference heart rates derived from a standard pulse-photoplethysmographic sensor and respiration rates from a flowmeter. In the worst case for one of the subjects the adaptive filter obtains mean errors (standard deviations) of -0.2 min(-1) (0.3 min(-1)) and -0.7 bpm (1.7 bpm) (compared to -0.2 min(-1) (0.4 min(-1)) and 42.0 bpm (6.1 bpm) for the non-adaptive filter) for respiration and heart rate, respectively. In bad conditions the heart rate is only correctly measurable when the Kalman matrices are adapted to the target sensor signals. Also, the reduced mean error between the extracted offset and the raw sensor signal shows that adapting the Kalman filter continuously improves the ability to separate the desired signals from the raw sensor data. The average total computational time needed
Three Revised Kalman Filtering Models for Short-Term Rail Transit Passenger Flow Prediction
Directory of Open Access Journals (Sweden)
Pengpeng Jiao
2016-01-01
Full Text Available Short-term prediction of passenger flow is very important for the operation and management of a rail transit system. Based on the traditional Kalman filtering method, this paper puts forward three revised models for real-time passenger flow forecasting. First, the paper introduces the historical prediction error into the measurement equation and formulates a revised Kalman filtering model based on error correction coefficient (KF-ECC. Second, this paper employs the deviation between real-time passenger flow and corresponding historical data as state variable and presents a revised Kalman filtering model based on Historical Deviation (KF-HD. Third, the paper integrates nonparametric regression forecast into the traditional Kalman filtering method using a Bayesian combined technique and puts forward a revised Kalman filtering model based on Bayesian combination and nonparametric regression (KF-BCNR. A case study is implemented using statistical passenger flow data of rail transit line 13 in Beijing during a one-month period. The reported prediction results show that KF-ECC improves the applicability to historical trend, KF-HD achieves excellent accuracy and stability, and KF-BCNR yields the best performances. Comparisons among different periods further indicate that results during peak periods outperform those during nonpeak periods. All three revised models are accurate and stable enough for on-line predictions, especially during the peak periods.
Directory of Open Access Journals (Sweden)
Shujie Yang
2016-01-01
Full Text Available Network virtualization has become pervasive and is used in many applications. Through the combination of network virtualization and wireless sensor networks, it can greatly improve the multiple applications of traditional wireless sensor networks. However, because of the dynamic reconfiguration of topologies in the physical layer of virtualized sensor networks (VSNs, it requires a mechanism to guarantee the accuracy of estimate values by sensors. In this paper, we focus on the distributed Kalman filter algorithm with dynamic topologies to support this requirement. As one strategy of distributed Kalman filter algorithms, diffusion Kalman filter algorithm has a better performance on the state estimation. However, the existing diffusion Kalman filter algorithms all focus on the fixed topologies. Considering the dynamic topologies in the physical layer of VSNs mentioned above, we present a diffusion Kalman filter algorithm with dynamic topologies (DKFdt. Then, we emphatically derive the theoretical expressions of the mean and mean-square performance. From the expressions, the feasibility of the algorithm is verified. Finally, simulations confirm that the proposed algorithm achieves a greatly improved performance as compared with a noncooperative manner.
Directory of Open Access Journals (Sweden)
Segundo Esteban
2016-10-01
Full Text Available Most satellites use an on-board attitude estimation system, based on available sensors. In the case of low-cost satellites, which are of increasing interest, it is usual to use magnetometers and Sun sensors. A Kalman filter is commonly recommended for the estimation, to simultaneously exploit the information from sensors and from a mathematical model of the satellite motion. It would be also convenient to adhere to a quaternion representation. This article focuses on some problems linked to this context. The state of the system should be represented in observable form. Singularities due to alignment of measured vectors cause estimation problems. Accommodation of the Kalman filter originates convergence difficulties. The article includes a new proposal that solves these problems, not needing changes in the Kalman filter algorithm. In addition, the article includes assessment of different errors, initialization values for the Kalman filter; and considers the influence of the magnetic dipole moment perturbation, showing how to handle it as part of the Kalman filter framework.
Esteban, Segundo; Girón-Sierra, Jose M; Polo, Óscar R; Angulo, Manuel
2016-10-31
Most satellites use an on-board attitude estimation system, based on available sensors. In the case of low-cost satellites, which are of increasing interest, it is usual to use magnetometers and Sun sensors. A Kalman filter is commonly recommended for the estimation, to simultaneously exploit the information from sensors and from a mathematical model of the satellite motion. It would be also convenient to adhere to a quaternion representation. This article focuses on some problems linked to this context. The state of the system should be represented in observable form. Singularities due to alignment of measured vectors cause estimation problems. Accommodation of the Kalman filter originates convergence difficulties. The article includes a new proposal that solves these problems, not needing changes in the Kalman filter algorithm. In addition, the article includes assessment of different errors, initialization values for the Kalman filter; and considers the influence of the magnetic dipole moment perturbation, showing how to handle it as part of the Kalman filter framework.
Gaussian Process Kalman Filter for Focal Plane Wavefront Correction and Exoplanet Signal Extraction
Sun, He; Kasdin, N. Jeremy
2018-01-01
Currently, the ultimate limitation of space-based coronagraphy is the ability to subtract the residual PSF after wavefront correction to reveal the planet. Called reference difference imaging (RDI), the technique consists of conducting wavefront control to collect the reference point spread function (PSF) by observing a bright star, and then extracting target planet signals by subtracting a weighted sum of reference PSFs. Unfortunately, this technique is inherently inefficient because it spends a significant fraction of the observing time on the reference star rather than the target star with the planet. Recent progress in model based wavefront estimation suggests an alternative approach. A Kalman filter can be used to estimate the stellar PSF for correction by the wavefront control system while simultaneously estimating the planet signal. Without observing the reference star, the (extended) Kalman filter directly utilizes the wavefront correction data and combines the time series observations and model predictions to estimate the stellar PSF and planet signals. Because wavefront correction is used during the entire observation with no slewing, the system has inherently better stability. In this poster we show our results aimed at further improving our Kalman filter estimation accuracy by including not only temporal correlations but also spatial correlations among neighboring pixels in the images. This technique is known as a Gaussian process Kalman filter (GPKF). We also demonstrate the advantages of using a Kalman filter rather than RDI by simulating a real space exoplanet detection mission.
The Joint Adaptive Kalman Filter (JAKF) for Vehicle Motion State Estimation.
Gao, Siwei; Liu, Yanheng; Wang, Jian; Deng, Weiwen; Oh, Heekuck
2016-07-16
This paper proposes a multi-sensory Joint Adaptive Kalman Filter (JAKF) through extending innovation-based adaptive estimation (IAE) to estimate the motion state of the moving vehicles ahead. JAKF views Lidar and Radar data as the source of the local filters, which aims to adaptively adjust the measurement noise variance-covariance (V-C) matrix 'R' and the system noise V-C matrix 'Q'. Then, the global filter uses R to calculate the information allocation factor 'β' for data fusion. Finally, the global filter completes optimal data fusion and feeds back to the local filters to improve the measurement accuracy of the local filters. Extensive simulation and experimental results show that the JAKF has better adaptive ability and fault tolerance. JAKF enables one to bridge the gap of the accuracy difference of various sensors to improve the integral filtering effectivity. If any sensor breaks down, the filtered results of JAKF still can maintain a stable convergence rate. Moreover, the JAKF outperforms the conventional Kalman filter (CKF) and the innovation-based adaptive Kalman filter (IAKF) with respect to the accuracy of displacement, velocity, and acceleration, respectively.
Applications of Kalman filters based on non-linear functions to numerical weather predictions
Directory of Open Access Journals (Sweden)
G. Galanis
2006-10-01
Full Text Available This paper investigates the use of non-linear functions in classical Kalman filter algorithms on the improvement of regional weather forecasts. The main aim is the implementation of non linear polynomial mappings in a usual linear Kalman filter in order to simulate better non linear problems in numerical weather prediction. In addition, the optimal order of the polynomials applied for such a filter is identified. This work is based on observations and corresponding numerical weather predictions of two meteorological parameters characterized by essential differences in their evolution in time, namely, air temperature and wind speed. It is shown that in both cases, a polynomial of low order is adequate for eliminating any systematic error, while higher order functions lead to instabilities in the filtered results having, at the same time, trivial contribution to the sensitivity of the filter. It is further demonstrated that the filter is independent of the time period and the geographic location of application.
Kalman Filters for Time Delay of Arrival-Based Source Localization
Directory of Open Access Journals (Sweden)
Klee Ulrich
2006-01-01
Full Text Available In this work, we propose an algorithm for acoustic source localization based on time delay of arrival (TDOA estimation. In earlier work by other authors, an initial closed-form approximation was first used to estimate the true position of the speaker followed by a Kalman filtering stage to smooth the time series of estimates. In the proposed algorithm, this closed-form approximation is eliminated by employing a Kalman filter to directly update the speaker's position estimate based on the observed TDOAs. In particular, the TDOAs comprise the observation associated with an extended Kalman filter whose state corresponds to the speaker's position. We tested our algorithm on a data set consisting of seminars held by actual speakers. Our experiments revealed that the proposed algorithm provides source localization accuracy superior to the standard spherical and linear intersection techniques. Moreover, the proposed algorithm, although relying on an iterative optimization scheme, proved efficient enough for real-time operation.
Incorporation of Time Delayed Measurements in a Discrete-time Kalman Filter
DEFF Research Database (Denmark)
Larsen, Thomas Dall; Andersen, Nils Axel; Ravn, Ole
1998-01-01
In many practical systems there is a delay in some of the sensor devices, for instance vision measurements that may have a long processing time. How to fuse these measurements in a Kalman filter is not a trivial problem if the computational delay is critical. Depending on how much time there is a......In many practical systems there is a delay in some of the sensor devices, for instance vision measurements that may have a long processing time. How to fuse these measurements in a Kalman filter is not a trivial problem if the computational delay is critical. Depending on how much time...... using past and present estimates of the Kalman filter and calculating an optimal gain for this extrapolated measurement...
Event-triggered Kalman-consensus filter for two-target tracking sensor networks.
Su, Housheng; Li, Zhenghao; Ye, Yanyan
2017-11-01
This paper is concerned with the problem of event-triggered Kalman-consensus filter for two-target tracking sensor networks. According to the event-triggered protocol and the mean-square analysis, a suboptimal Kalman gain matrix is derived and a suboptimal event-triggered distributed filter is obtained. Based on the Kalman-consensus filter protocol, all sensors which only depend on its neighbors' information can track their corresponding targets. Furthermore, utilizing Lyapunov method and matrix theory, some sufficient conditions are presented for ensuring the stability of the system. Finally, a simulation example is presented to verify the effectiveness of the proposed event-triggered protocol. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Direct Torque Control of Sensorless Induction Machine Drives: A Two-Stage Kalman Filter Approach
Directory of Open Access Journals (Sweden)
Jinliang Zhang
2015-01-01
Full Text Available Extended Kalman filter (EKF has been widely applied for sensorless direct torque control (DTC in induction machines (IMs. One key problem associated with EKF is that the estimator suffers from computational burden and numerical problems resulting from high order mathematical models. To reduce the computational cost, a two-stage extended Kalman filter (TEKF based solution is presented for closed-loop stator flux, speed, and torque estimation of IM to achieve sensorless DTC-SVM operations in this paper. The novel observer can be similarly derived as the optimal two-stage Kalman filter (TKF which has been proposed by several researchers. Compared to a straightforward implementation of a conventional EKF, the TEKF estimator can reduce the number of arithmetic operations. Simulation and experimental results verify the performance of the proposed TEKF estimator for DTC of IMs.
On the equivalence of Kalman filtering and least-squares estimation
Mysen, E.
2017-01-01
The Kalman filter is derived directly from the least-squares estimator, and generalized to accommodate stochastic processes with time variable memory. To complete the link between least-squares estimation and Kalman filtering of first-order Markov processes, a recursive algorithm is presented for the computation of the off-diagonal elements of the a posteriori least-squares error covariance. As a result of the algebraic equivalence of the two estimators, both approaches can fully benefit from the advantages implied by their individual perspectives. In particular, it is shown how Kalman filter solutions can be integrated into the normal equation formalism that is used for intra- and inter-technique combination of space geodetic data.
Kalman filtering for neural prediction of response spectra from mining tremors
Energy Technology Data Exchange (ETDEWEB)
Krok, A.; Waszczyszyn, Z. [Cracow University of Technology, Krakow (Poland)
2007-08-15
Acceleration response spectra (ARS) for mining tremors in the Upper Silesian Coalfield, Poland are generated using neural networks trained by means of Kalman filtering. The target ARS were computed on the base of measured accelerograms. It was proved that the standard feed-forward, layered neural network, trained by the DEFK (decoupled extended Kalman filter) algorithm is numerically much less efficient than the standard recurrent NN learnt by Recurrent DEKF, cf. (Haykin S, (editor). Kalman filtering and neural networks. New York: John Wiley & Sons; 2001). It is also shown that the studied KF algorithms are better than the traditional Resilient-Propagation learning method. The improvement of the training process and neural prediction due to introduction of an autoregressive input is also discussed in the paper.
Huang, Chunlin; Chen, Weijin; Wang, Weizhen; Gu, Juan
2017-04-01
Uncertainties in model parameters can easily cause systematic differences between model states and observations from ground or satellites, which significantly affect the accuracy of soil moisture estimation in data assimilation systems. In this paper, a novel soil moisture assimilation scheme is developed to simultaneously assimilate AMSR-E brightness temperature (TB) and MODIS Land Surface Temperature (LST), which can correct model bias by simultaneously updating model states and parameters with dual ensemble Kalman filter (DEnKS). The Common Land Model (CoLM) and a Q-h Radiative Transfer Model (RTM) are adopted as model operator and observation operator, respectively. The assimilation experiment is conducted in Naqu, Tibet Plateau, from May 31 to September 27, 2011. Compared with in-situ measurements, the accuracy of soil moisture estimation is tremendously improved in terms of a variety of scales. The updated soil temperature by assimilating MODIS LST as input of RTM can reduce the differences between the simulated and observed brightness temperatures to a certain degree, which helps to improve the estimation of soil moisture and model parameters. The updated parameters show large discrepancy with the default ones and the former effectively reduces the states bias of CoLM. Results demonstrate the potential of assimilating both microwave TB and MODIS LST to improve the estimation of soil moisture and related parameters. Furthermore, this study also indicates that the developed scheme is an effective soil moisture downscaling approach for coarse-scale microwave TB.
Barber, Jared; Tanase, Roxana; Yotov, Ivan
2016-06-01
Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion. Copyright © 2016 Elsevier Inc. All rights reserved.
Decadal climate predictions improved by ocean ensemble dispersion filtering
Kadow, C.; Illing, S.; Kröner, I.; Ulbrich, U.; Cubasch, U.
2017-06-01
Decadal predictions by Earth system models aim to capture the state and phase of the climate several years in advance. Atmosphere-ocean interaction plays an important role for such climate forecasts. While short-term weather forecasts represent an initial value problem and long-term climate projections represent a boundary condition problem, the decadal climate prediction falls in-between these two time scales. In recent years, more precise initialization techniques of coupled Earth system models and increased ensemble sizes have improved decadal predictions. However, climate models in general start losing the initialized signal and its predictive skill from one forecast year to the next. Here we show that the climate prediction skill of an Earth system model can be improved by a shift of the ocean state toward the ensemble mean of its individual members at seasonal intervals. We found that this procedure, called ensemble dispersion filter, results in more accurate results than the standard decadal prediction. Global mean and regional temperature, precipitation, and winter cyclone predictions show an increased skill up to 5 years ahead. Furthermore, the novel technique outperforms predictions with larger ensembles and higher resolution. Our results demonstrate how decadal climate predictions benefit from ocean ensemble dispersion filtering toward the ensemble mean.Plain Language SummaryDecadal predictions aim to predict the climate several years in advance. Atmosphere-ocean interaction plays an important role for such climate forecasts. The ocean memory due to its heat capacity holds big potential skill. In recent years, more precise initialization techniques of coupled Earth system models (incl. atmosphere and ocean) have improved decadal predictions. Ensembles are another important aspect. Applying slightly perturbed predictions to trigger the famous butterfly effect results in an ensemble. Instead of evaluating one prediction, but the whole ensemble with its
Attitude Estimation Based on the Spherical Simplex Transformation Modified Unscented Kalman Filter
Directory of Open Access Journals (Sweden)
Jianwei Zhao
2014-01-01
Full Text Available An antenna attitude estimation algorithm is proposed to improve the antenna pointing accuracy for the satellite communication on-the-move. The extrapolated angular acceleration is adopted to improve the performance of the time response. The states of the system are modified according to the modification rules. The spherical simplex transformation unscented Kalman filter is used to improve the precision of the estimated attitude and decrease the calculation of the unscented Kalman filter. The experiment results show that the proposed algorithm can improve the instantaneity of the estimated attitude and the precision of the antenna pointing, which meets the requirement of the antenna pointing.
Inexpensive CubeSat attitude estimation using COTS components and Unscented Kalman Filtering
DEFF Research Database (Denmark)
Larsen, Jesper Abildgaard; Vinther, Kasper
2011-01-01
This paper describes a quaternion implementation of an Unscented Kalman Filter for attitude estimation on CubeSats using measurements of a sun vector, a magnetic field vector and angular velocity. Using unit quaternions provides a singularity free attitude parameterization. However, the unity...... constraint requires a redesign of the Unscented Kalman Filter. Therefore, a quaternion error state is introduced. Emphasis has been put in making the implementation accessible to other CubeSat by using realistic models of COTS components used for attitude sensing and simulations have shown that the extra...
Modeling of HVDC in Dynamic State Estimation Using Unscented Kalman Filter Method
DEFF Research Database (Denmark)
Khazraj, Hesam; Silva, Filipe Miguel Faria da; Bak, Claus Leth
2016-01-01
HVDC transmission is an integral part of various power system networks. This article presents an Unscented Kalman Filter dynamic state estimator algorithm that considers the presence of HVDC links. The AC - DC power flow analysis, which is implemented as power flow solver for Dynamic State...... Estimation (DSE), creates an updated admittance matrix. First, a hybrid AC/DC network model is developed to combine the AC network and DC links. Then a non-linear state estimator can solve for hybrid AC/DC states by applying the unscented Kalman filter (UKF) algorithm. It is demonstrated that UKF is easy...
An improved TLD algorithm based on Kalman filter and SURF feature matching
Zhao, Linlin; Chen, Yimin; Ye, Qingqun
2017-05-01
The TLD algorithm can achieve a better performance on single target tracking. However, it still has some defects in respects of real-time computing and target rotation. In this paper, an improved TLD algorithm based on Kalman filter and SURF feature matching is proposed. In order to reduce the number of invalid sliding windows and improve the real-time performance of TLD, the Kalman filter is introduced to improve the detection module. Meanwhile, in order to solve the problem of target rotation, the SURF feature matching is introduced to improve the reliability of tracking module. The experiment results demonstrate that our method improves the accuracy and robustness of TLD algorithm.
Application Of Kalman Filter In Navigation Process Of Automated Guided Vehicles
Directory of Open Access Journals (Sweden)
Śmieszek Mirosław
2015-09-01
Full Text Available In the paper an example of application of the Kalman filtering in the navigation process of automatically guided vehicles was presented. The basis for determining the position of automatically guided vehicles is odometry – the navigation calculation. This method of determining the position of a vehicle is affected by many errors. In order to eliminate these errors, in modern vehicles additional systems to increase accuracy in determining the position of a vehicle are used. In the latest navigation systems during route and position adjustments the probabilistic methods are used. The most frequently applied are Kalman filters.
Kim, S.; Riazi, H.; Shin, C.; Seo, D.
2013-12-01
Due to the large dimensionality of the state vector and sparsity of observations, the initial conditions (IC) of water quality models are subject to large uncertainties. To reduce the IC uncertainties in operational water quality forecasting, an ensemble data assimilation (DA) procedure for the Hydrologic Simulation Program - Fortran (HSPF) model has been developed and evaluated for the Kumho River Subcatchment of the Nakdong River Basin in Korea. The procedure, referred to herein as MLEF-HSPF, uses maximum likelihood ensemble filter (MLEF) which combines strengths of variational assimilation (VAR) and ensemble Kalman filter (EnKF). The Control variables involved in the DA procedure include the bias correction factors for mean areal precipitation and mean areal potential evaporation, the hydrologic state variables, and the water quality state variables such as water temperature, dissolved oxygen (DO), biochemical oxygen demand (BOD), ammonium (NH4), nitrate (NO3), phosphate (PO4) and chlorophyll a (CHL-a). Due to the very large dimensionality of the inverse problem, accurately specifying the parameters for the DA procdedure is a challenge. Systematic sensitivity analysis is carried out for identifying the optimal parameter settings. To evaluate the robustness of MLEF-HSPF, we use multiple subcatchments of the Nakdong River Basin. In evaluation, we focus on the performance of MLEF-HSPF on prediction of extreme water quality events.
Rucci, Michael; Hardie, Russell C; Barnard, Kenneth J
2014-05-01
In this paper, we present a computationally efficient video restoration algorithm to address both blur and noise for a Nyquist sampled imaging system. The proposed method utilizes a temporal Kalman filter followed by a correlation-model based spatial adaptive Wiener filter (AWF). The Kalman filter employs an affine background motion model and novel process-noise variance estimate. We also propose and demonstrate a new multidelay temporal Kalman filter designed to more robustly treat local motion. The AWF is a spatial operation that performs deconvolution and adapts to the spatially varying residual noise left in the Kalman filter stage. In image areas where the temporal Kalman filter is able to provide significant noise reduction, the AWF can be aggressive in its deconvolution. In other areas, where less noise reduction is achieved with the Kalman filter, the AWF balances the deconvolution with spatial noise reduction. In this way, the Kalman filter and AWF work together effectively, but without the computational burden of full joint spatiotemporal processing. We also propose a novel hybrid system that combines a temporal Kalman filter and BM3D processing. To illustrate the efficacy of the proposed methods, we test the algorithms on both simulated imagery and video collected with a visible camera.
Detecting Power Voltage Dips using Tracking Filters - A Comparison against Kalman
Directory of Open Access Journals (Sweden)
STANCIU, I.-R.
2012-11-01
Full Text Available Due of its significant economical impact, Power-Quality (PQ analysis is an important domain today. Severe voltage distortions affect the consumers and disturb their activity. They may be caused by short circuits (in this case the voltage drops significantly or by varying loads (with a smaller drop. These two types are the PQ currently issues. Monitoring these phenomena (called dips or sags require powerful techniques. Digital Signal Processing (DSP algorithms are currently employed to fulfill this task. Discrete Wavelet Transforms, (and variants, Kalman filters, and S-Transform are currently proposed by researchers to detect voltage dips. This paper introduces and examines a new tool to detect voltage dips: the so-called tracking filters. Discovered and tested during the cold war, they can estimate a parameter of interest one-step-ahead based on the previously observed values. Two filters are implemented. Their performance is assessed by comparison against the Kalman filter?s results.
GPS/UWB/MEMS-IMU tightly coupled navigation with improved robust Kalman filter
Li, Zengke; Chang, Guobin; Gao, Jingxiang; Wang, Jian; Hernandez, Alberto
2016-12-01
The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been very intensively developed and widely applied in multiple areas. To further enhance the reliability and availability of GPS/INS integrated navigation in GPS challenging environment, range observation through ultra-wideband (UWB) is introduced in GPS/INS tightly coupled navigation. An improved robust Kalman filter is proposed and used to resist the influence of gross error from UWB observation in GPS/UWB/IMU tightly coupled navigation. The variance of the squared Mahalanobis distance in moving window is calculated, which brings as new judgement factor for gross errors in order to decrease the rate of false outlier identification. A simulation analysis shows that the improved robust Kalman filter is able to correctly identify gross errors and the rate of false judgment as zero. In order to validate the new robust filter, a real experiment is conducted. The results indicate that the improved robust Kalman filter used in GPS/UWB/INS tightly coupled navigation is able to remove the harmful effect of gross error in UWB observation. It clearly illustrates that the improved robust Kalman filter is very effective, and all the simulated small and large gross errors added to UWB distance observation are successfully identified.
Adaptive distributed Kalman filtering with wind estimation for astronomical adaptive optics.
Massioni, Paolo; Gilles, Luc; Ellerbroek, Brent
2015-12-01
In the framework of adaptive optics (AO) for astronomy, it is a common assumption to consider the atmospheric turbulent layers as "frozen flows" sliding according to the wind velocity profile. For this reason, having knowledge of such a velocity profile is beneficial in terms of AO control system performance. In this paper we show that it is possible to exploit the phase estimate from a Kalman filter running on an AO system in order to estimate wind velocity. This allows the update of the Kalman filter itself with such knowledge, making it adaptive. We have implemented such an adaptive controller based on the distributed version of the Kalman filter, for a realistic simulation of a multi-conjugate AO system with laser guide stars on a 30 m telescope. Simulation results show that this approach is effective and promising and the additional computational cost with respect to the distributed filter is negligible. Comparisons with a previously published slope detection and ranging wind profiler are made and the impact of turbulence profile quantization is assessed. One of the main findings of the paper is that all flavors of the adaptive distributed Kalman filter are impacted more significantly by turbulence profile quantization than the static minimum mean square estimator which does not incorporate wind profile information.
Unscented Kalman Filter Applied to the Spacecraft Attitude Estimation with Euler Angles
Directory of Open Access Journals (Sweden)
Roberta Veloso Garcia
2012-01-01
Full Text Available The aim of this work is to test an algorithm to estimate, in real time, the attitude of an artificial satellite using real data supplied by attitude sensors that are on board of the CBERS-2 satellite (China Brazil Earth Resources Satellite. The real-time estimator used in this work for attitude determination is the Unscented Kalman Filter. This filter is a new alternative to the extended Kalman filter usually applied to the estimation and control problems of attitude and orbit. This algorithm is capable of carrying out estimation of the states of nonlinear systems, without the necessity of linearization of the nonlinear functions present in the model. This estimation is possible due to a transformation that generates a set of vectors that, suffering a nonlinear transformation, preserves the same mean and covariance of the random variables before the transformation. The performance will be evaluated and analyzed through the comparison between the Unscented Kalman filter and the extended Kalman filter results, by using real onboard data.
Directory of Open Access Journals (Sweden)
Lijun Song
2018-01-01
Full Text Available The centralized Kalman filter is always applied in the velocity and attitude matching of Transfer Alignment (TA. But the centralized Kalman has many disadvantages, such as large amount of calculation, poor real-time performance, and low reliability. In the paper, the federal Kalman filter (FKF based on neural networks is used in the velocity and attitude matching of TA, the Kalman filter is adjusted by the neural networks in the two subfilters, the federal filter is used to fuse the information of the two subfilters, and the global suboptimal state estimation is obtained. The result of simulation shows that the federal Kalman filter based on neural networks is better in estimating the initial attitude misalignment angle of inertial navigation system (INS when the system dynamic model and noise statistics characteristics of inertial navigation system are unclear, and the estimation error is smaller and the accuracy is higher.
Djalalova, Irina; Delle Monache, Luca; Wilczak, James
2015-10-01
A new post-processing method for surface particulate matter (PM2.5) predictions from the National Oceanic and Atmospheric Administration (NOAA) developmental air quality forecasting system using the Community Multiscale Air Quality (CMAQ) model is described. It includes three main components: A real-time quality control procedure for surface PM2.5 observations; Model post-processing at each observational site using historical forecast analogs and Kalman filtering; Spreading the forecast corrections from the observation locations to the entire gridded domain. The methodology is tested using 12 months of CMAQ forecasts of hourly PM2.5, from December 01, 2009 through November 30, 2010. The model domain covers the contiguous USA, and model data are verified against U.S. Environmental Prediction Agency AIRNow PM2.5 observations measured at 716 stations over the CMAQ domain. The model bias is found to have a strong seasonal dependency, with a large positive bias in winter and a small bias in the summer months, and also to have a strong diurnal cycle. Five different post-processing techniques are compared, including a seven-day running mean subtraction, Kalman-filtering, analogs, and combinations of analogs and Kalman filtering. The most accurate PM2.5 forecasts have been found to be produced when applying the Kalman filter correction to the analog ensemble weighted mean, referred to as KFAN. The choice of analog predictors used in the analog search is also found to have a significant effect. A monthly error analysis is computed, in each case using the remaining 11 months of the data set for the analog searches. The improvement of KFAN errors over the raw CMAQ model errors ranges from 44 to 52% for MAE and 13-30% for the correlation coefficient. Since the post-processing analysis is only done at the locations where observations are available, the spreading of post-processing correction information over nearby model grid points is necessary to make forecast contour maps
A Two-stage Kalman Filter for Sensorless Direct Torque Controlled PM Synchronous Motor Drive
Directory of Open Access Journals (Sweden)
Boyu Yi
2013-01-01
Full Text Available This paper presents an optimal two-stage extended Kalman filter (OTSEKF for closed-loop flux, torque, and speed estimation of a permanent magnet synchronous motor (PMSM to achieve sensorless DTC-SVPWM operation of drive system. The novel observer is obtained by using the same transformation as in a linear Kalman observer, which is proposed by C.-S. Hsieh and F.-C. Chen in 1999. The OTSEKF is an effective implementation of the extended Kalman filter (EKF and provides a recursive optimum state estimation for PMSMs using terminal signals that may be polluted by noise. Compared to a conventional EKF, the OTSEKF reduces the number of arithmetic operations. Simulation and experimental results verify the effectiveness of the proposed OTSEKF observer for DTC of PMSMs.
An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models
Chow, Sy-Miin; Ferrer, Emilio; Nesselroade, John R.
2007-01-01
In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways:…
State Estimation of Induction Motor Drives Using the Unscented Kalman Filter
DEFF Research Database (Denmark)
Lascu, Cristian; Jafarzadeh, Saeed; Fadali, M.Sami
2012-01-01
This paper investigates the application, design, and implementation of unscented Kalman filters (KFs) (UKFs) for induction motor (IM) sensorless drives. UKFs use nonlinear unscented transforms (UTs) in the prediction step in order to preserve the stochastic characteristics of a nonlinear system...
Target Centroid Position Estimation of Phase-Path Volume Kalman Filtering
Directory of Open Access Journals (Sweden)
Fengjun Hu
2016-01-01
Full Text Available For the problem of easily losing track target when obstacles appear in intelligent robot target tracking, this paper proposes a target tracking algorithm integrating reduced dimension optimal Kalman filtering algorithm based on phase-path volume integral with Camshift algorithm. After analyzing the defects of Camshift algorithm, compare the performance with the SIFT algorithm and Mean Shift algorithm, and Kalman filtering algorithm is used for fusion optimization aiming at the defects. Then aiming at the increasing amount of calculation in integrated algorithm, reduce dimension with the phase-path volume integral instead of the Gaussian integral in Kalman algorithm and reduce the number of sampling points in the filtering process without influencing the operational precision of the original algorithm. Finally set the target centroid position from the Camshift algorithm iteration as the observation value of the improved Kalman filtering algorithm to fix predictive value; thus to make optimal estimation of target centroid position and keep the target tracking so that the robot can understand the environmental scene and react in time correctly according to the changes. The experiments show that the improved algorithm proposed in this paper shows good performance in target tracking with obstructions and reduces the computational complexity of the algorithm through the dimension reduction.
Advantages of Square-Root Extended Kalman Filter for Sensorless Control of AC Drives
Czech Academy of Sciences Publication Activity Database
Šmídl, Václav; Peroutka, Z.
2012-01-01
Roč. 59, č. 11 (2012), s. 4189-4196 ISSN 0278-0046 Institutional research plan: CEZ:AV0Z10750506 Institutional support: RVO:67985556 Keywords : Kalman filters * Mathematical model * AC motors Subject RIV: BC - Control Systems Theory Impact factor: 5.165, year: 2012 http://library.utia.cas.cz/separaty/2012/AS/smidl-0436868.pdf
An Adaptive Object Tracking Using Kalman Filter and Probability Product Kernel
Directory of Open Access Journals (Sweden)
Hamd Ait Abdelali
2016-01-01
Full Text Available We present a new method for object tracking; we use an efficient local search scheme based on the Kalman filter and the probability product kernel (KFPPK to find the image region with a histogram most similar to the histogram of the tracked target. Experimental results verify the effectiveness of this proposed system.
FPGA Realization of Sensorless PMSM Speed Controller Based on Extended Kalman Filter
National Research Council Canada - National Science Library
Kung, Ying-Shieh; Quynh, Nguyen Vu; Hieu, Nguyen Trung; Lin, Jin-Mu
2013-01-01
...]. Those sensorless control strategies have sliding mode observer (SMO), extended Kalman filter (EKF), reduced-order EKF, and so forth. The EKF is basically a full-order stochastic observer for the recursive optimum state estimation of a nonlinear dynamic system in real time by using signals that are in noisy environment [7]. Comparing with SMO, EKF ca...
A Bolus Calculator Based on Continuous-Discrete Unscented Kalman Filtering for Type 1 Diabetics
DEFF Research Database (Denmark)
Boiroux, Dimitri; Aradóttir, Tinna Björk; Hagdrup, Morten
2015-01-01
after or 30 minutes after the beginning of the meal). We implement a continuous-discrete unscented Kalman filter to estimate the states and insulin sensitivity. These estimates are used in a bolus calculator. The numerical results demonstrate that administering the meal bolus 15 minutes after mealtime...
CONSISTENT USE OF THE KALMAN FILTER IN CHEMICAL TRANSPORT MODELS (CTMS) FOR DEDUCING EMISSIONS
Past research has shown that emissions can be deduced using observed concentrations of a chemical, a Chemical Transport Model (CTM), and the Kalman filter in an inverse modeling application. An expression was derived for the relationship between the "observable" (i.e., the con...
Rigatos, Gerasimos G; Rigatou, Efthymia G; Djida, Jean Daniel
2015-10-01
A method for early diagnosis of parametric changes in intracellular protein synthesis models (e.g. the p53 protein - mdm2 inhibitor model) is developed with the use of a nonlinear Kalman Filtering approach (Derivative-free nonlinear Kalman Filter) and of statistical change detection methods. The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. For the linearized equivalent of the dynamical system, state estimation can be performed using the Kalman Filter recursion. Moreover, by applying an inverse transformation based on the previous diffeomorphism it becomes also possible to obtain estimates of the state variables of the initial nonlinear model. By comparing the output of the Kalman Filter (which is assumed to correspond to the undistorted dynamical model) with measurements obtained from the monitored protein synthesis system, a sequence of differences (residuals) is obtained. The statistical processing of the residuals with the use of x2 change detection tests, can provide indication within specific confidence intervals about parametric changes in the considered biological system and consequently indications about the appearance of specific diseases (e.g. malignancies).
Model-Based Engine Control Architecture with an Extended Kalman Filter
Csank, Jeffrey T.; Connolly, Joseph W.
2016-01-01
This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The nonlinear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.
Wang, Li-Qi; Ge, Hui-Fang; Li, Gui-Bin; Yu, Dian-Yu; Hu, Li-Zhi; Jiang, Lian-Zhou
2014-04-01
Combining classical Kalman filter with NIR analysis technology, a new method of characteristic wavelength variable selection, namely Kalman filtering method, is presented. The principle of Kalman filter for selecting optimal wavelength variable was analyzed. The wavelength selection algorithm was designed and applied to NIR detection of soybean oil acid value. First, the PLS (partial leastsquares) models were established by using different absorption bands of oil. The 4 472-5 000 cm(-1) characteristic band of oil acid value, including 132 wavelengths, was selected preliminarily. Then the Kalman filter was used to select characteristic wavelengths further. The PLS calibration model was established using selected 22 characteristic wavelength variables, the determination coefficient R2 of prediction set and RMSEP (root mean squared error of prediction) are 0.970 8 and 0.125 4 respectively, equivalent to that of 132 wavelengths, however, the number of wavelength variables was reduced to 16.67%. This algorithm is deterministic iteration, without complex parameters setting and randomicity of variable selection, and its physical significance was well defined. The modeling using a few selected characteristic wavelength variables which affected modeling effect heavily, instead of total spectrum, can make the complexity of model decreased, meanwhile the robustness of model improved. The research offered important reference for developing special oil near infrared spectroscopy analysis instruments on next step.
Tracking and convergence of multi-channel Kalman filters for active noise control
Berkhoff, Arthur P.; van Ophem, S.
2013-01-01
The feed-forward broadband active noise control problem can be formulated as a state estimation problem to achieve a faster rate of convergence than the filtered reference least mean squares algorithm and possibly also a better tracking performance. A multiple input/multiple output Kalman algorithm
Kalman Filter Based Data Fusion for Bi-Axial Neutral Axis Tracking in Wind Turbine Towers
DEFF Research Database (Denmark)
Soman, Rohan; Malinowski, Pawel; Schmidt Paulsen, Uwe
2015-01-01
demonstrates a methodology for the selection of threshold for damage detection based on qualitative data acquired from several damage scenarios of a 10 MW wind turbine. The damage indicator is the change of neutral axis (NA) which is tracked using Kalman Filter (KF). Based on the level of damage to be detected...
Nonlinear Kalman Filtering for acoustic emission source localization in anisotropic panels.
Dehghan Niri, E; Farhidzadeh, A; Salamone, S
2014-02-01
Nonlinear Kalman Filtering is an established field in applied probability and control systems, which plays an important role in many practical applications from target tracking to weather and climate prediction. However, its application for acoustic emission (AE) source localization has been very limited. In this paper, two well-known nonlinear Kalman Filtering algorithms are presented to estimate the location of AE sources in anisotropic panels: the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). These algorithms are applied to two cases: velocity profile known (CASE I) and velocity profile unknown (CASE II). The algorithms are compared with a more traditional nonlinear least squares method. Experimental tests are carried out on a carbon-fiber reinforced polymer (CFRP) composite panel instrumented with a sparse array of piezoelectric transducers to validate the proposed approaches. AE sources are simulated using an instrumented miniature impulse hammer. In order to evaluate the performance of the algorithms, two metrics are used: (1) accuracy of the AE source localization and (2) computational cost. Furthermore, it is shown that both EKF and UKF can provide a confidence interval of the estimated AE source location and can account for uncertainty in time of flight measurements. Copyright © 2013 Elsevier B.V. All rights reserved.
Kalman filter for speech enhancement in cocktail party scenarios using a codebook-based approach
DEFF Research Database (Denmark)
Kavalekalam, Mathew Shaji; Christensen, Mads Græsbøll; Gran, Fredrik
2016-01-01
Enhancement of speech in non-stationary background noise is a challenging task, and conventional single channel speech enhancement algorithms have not been able to improve the speech intelligibility in such scenarios. The work proposed in this paper investigates a single channel Kalman filter based...
Detecting land cover change using an extended Kalman filter on MODIS NDVI time-series data
CSIR Research Space (South Africa)
Kleynhans, W
2011-05-01
Full Text Available . The NDVI time series for each of these pixels was modeled as a triply (mean, phase, and amplitude) modulated cosine function, and an extended Kalman filter was used to estimate the parameters of the modulated cosine function through time. A spatial...
DEFF Research Database (Denmark)
Wang, Yunlong; Soltani, Mohsen; Hussain, Dil muhammed Akbar
2016-01-01
, an adaptive Multiplicative Extended Kalman Filter (MEKF) for attitude estimation of Marine Satellite Tracking Antenna (MSTA) is presented with the measurement noise covariance matrix adjusted according to the norm of accelerometer measurements, which can significantly reduce the slamming influence from waves...
Non-linear DSGE Models and The Central Difference Kalman Filter
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper introduces a Quasi Maximum Likelihood (QML) approach based on the Cen- tral Difference Kalman Filter (CDKF) to estimate non-linear DSGE models with potentially non-Gaussian shocks. We argue that this estimator can be expected to be consistent and asymptotically normal for DSGE models...
Kalman filter for statistical monitoring of forest cover across sub-continental regions [Symposium
Raymond L. Czaplewski
1991-01-01
The Kalman filter is a generalization of the composite estimator. The univariate composite estimate combines 2 prior estimates of population parameter with a weighted average where the scalar weight is inversely proportional to the variances. The composite estimator is a minimum variance estimator that requires no distributional assumptions other than estimates of the...
Upper Atmosphere Research Satellite (UARS) onboard attitude determination using a Kalman filter
Garrick, Joseph
1993-01-01
The Upper Atmospheric Research Satellite (UARS) requires a highly accurate knowledge of its attitude to accomplish its mission. Propagation of the attitude state using gyro measurements is not sufficient to meet the accuracy requirements, and must be supplemented by a observer/compensation process to correct for dynamics and observation anomalies. The process of amending the attitude state utilizes a well known method, the discrete Kalman Filter. This study is a sensitivity analysis of the discrete Kalman Filter as implemented in the UARS Onboard Computer (OBC). The stability of the Kalman Filter used in the normal on-orbit control mode within the OBC, is investigated for the effects of corrupted observations and nonlinear errors. Also, a statistical analysis on the residuals of the Kalman Filter is performed. These analysis is based on simulations using the UARS Dynamics Simulator (UARSDSIM) and compared against attitude requirements as defined by General Electric (GE). An independent verification of expected accuracies is performed using the Attitude Determination Error Analysis System (ADEAS).
The use of the Kalman filter in the automated segmentation of EIT lung images.
Zifan, A; Liatsis, P; Chapman, B E
2013-06-01
In this paper, we present a new pipeline for the fast and accurate segmentation of impedance images of the lungs using electrical impedance tomography (EIT). EIT is an emerging, promising, non-invasive imaging modality that produces real-time, low spatial but high temporal resolution images of impedance inside a body. Recovering impedance itself constitutes a nonlinear ill-posed inverse problem, therefore the problem is usually linearized, which produces impedance-change images, rather than static impedance ones. Such images are highly blurry and fuzzy along object boundaries. We provide a mathematical reasoning behind the high suitability of the Kalman filter when it comes to segmenting and tracking conductivity changes in EIT lung images. Next, we use a two-fold approach to tackle the segmentation problem. First, we construct a global lung shape to restrict the search region of the Kalman filter. Next, we proceed with augmenting the Kalman filter by incorporating an adaptive foreground detection system to provide the boundary contours for the Kalman filter to carry out the tracking of the conductivity changes as the lungs undergo deformation in a respiratory cycle. The proposed method has been validated by using performance statistics such as misclassified area, and false positive rate, and compared to previous approaches. The results show that the proposed automated method can be a fast and reliable segmentation tool for EIT imaging.
State of Charge Estimation of Lithium-Ion Batteries Using an Adaptive Cubature Kalman Filter
Directory of Open Access Journals (Sweden)
Bizhong Xia
2015-06-01
Full Text Available Accurate state of charge (SOC estimation is of great significance for a lithium-ion battery to ensure its safe operation and to prevent it from over-charging or over-discharging. However, it is difficult to get an accurate value of SOC since it is an inner sate of a battery cell, which cannot be directly measured. This paper presents an Adaptive Cubature Kalman filter (ACKF-based SOC estimation algorithm for lithium-ion batteries in electric vehicles. Firstly, the lithium-ion battery is modeled using the second-order resistor-capacitor (RC equivalent circuit and parameters of the battery model are determined by the forgetting factor least-squares method. Then, the Adaptive Cubature Kalman filter for battery SOC estimation is introduced and the estimated process is presented. Finally, two typical driving cycles, including the Dynamic Stress Test (DST and New European Driving Cycle (NEDC are applied to evaluate the performance of the proposed method by comparing with the traditional extended Kalman filter (EKF and cubature Kalman filter (CKF algorithms. Experimental results show that the ACKF algorithm has better performance in terms of SOC estimation accuracy, convergence to different initial SOC errors and robustness against voltage measurement noise as compared with the traditional EKF and CKF algorithms.
A Kalman filter approach to realize the lowest astronomical tide surface
Slobbe, D.C.; Sumihar, JH; Frederikse, T.; Verlaan, M.; Klees, R.; Zijl, F; Hashemi Farahani, H.; Broekman, R
2017-01-01
In this paper, we present a novel Kalman filter approach to combine a hydrodynamic model-derived lowest astronomical tide (LAT) surface with tide gauge record-derived LAT values. In the approach, tidal water levels are assimilated into the model. As such, the combination is guided by the model
Raymond L. Czaplewski
2015-01-01
Wall-to-wall remotely sensed data are increasingly available to monitor landscape dynamics over large geographic areas. However, statistical monitoring programs that use post-stratification cannot fully utilize those sensor data. The Kalman filter (KF) is an alternative statistical estimator. I develop a new KF algorithm that is numerically robust with large numbers of...
Modified temporal approach to meta-optimizing an extended Kalman filter's parameters
CSIR Research Space (South Africa)
Salmon, BP
2014-07-01
Full Text Available meta-optimization approach has been proposed in the literature for setting the parameters of the non-linear Extended Kalman Filter (EKF) to rapidly and efficiently estimate the features for these triply modulated cosine functions using spatial...
In-situ estimation of MOCVD growth rate via a modified Kalman filter
Energy Technology Data Exchange (ETDEWEB)
Woo, W.W.; Svoronos, S.A. [Univ. of Florida, Gainesville, FL (United States). Dept. of Chemical Engineering; Sankur, H.O.; Bajaj, J. [Rockwell International Corp., Thousand Oaks, CA (United States); Irvine, S.J.C. [North East Wales Inst. Plas Coch, Wrexham (United Kingdom)
1996-05-01
In-situ laser reflectance monitoring of metal-organic chemical vapor deposition (MOCVD) is an effective way to monitor growth rate and epitaxial layer thickness of a variety of III-V and II-VI semiconductors. Materials with low optical extinction coefficients, such as ZnTe/GaAs and AlAs/GaAs for a 6,328 {angstrom} HeNe laser, are ideal for such an application. An extended Kalman filter modified to include a variable forgetting factor was applied to the MOCVD systems. The filter was able to accurately estimate thickness and growth rate while filtering out process noise and cope with sudden changes in growth rate, reflectance drift, and bias. Due to the forgetting factor, the Kalman filter was successful, even when based on very simple process models.
Chuanxue Song; Yulong Shao; Shixin Song; Silun Peng; Fang Zhou; Cheng Chang; Da Wang
2017-01-01
To improve the accuracy of insulation monitoring between the battery pack and chassis of electric vehicles, we established a serial battery pack model composed of first-order resistor-capacitor (RC) circuit battery cells. We then designed a low-voltage, low-frequency insulation monitoring model based on this serial battery pack model. An extended Kalman filter (EKF) was designed for this non-linear system to filter the measured results, thus mitigating the influence of noise. Experimental and...
Strong Tracking Spherical Simplex-Radial Cubature Kalman Filter for Maneuvering Target Tracking.
Liu, Hua; Wu, Wen
2017-03-31
Conventional spherical simplex-radial cubature Kalman filter (SSRCKF) for maneuvering target tracking may decline in accuracy and even diverge when a target makes abrupt state changes. To overcome this problem, a novel algorithm named strong tracking spherical simplex-radial cubature Kalman filter (STSSRCKF) is proposed in this paper. The proposed algorithm uses the spherical simplex-radial (SSR) rule to obtain a higher accuracy than cubature Kalman filter (CKF) algorithm. Meanwhile, by introducing strong tracking filter (STF) into SSRCKF and modifying the predicted states' error covariance with a time-varying fading factor, the gain matrix is adjusted on line so that the robustness of the filter and the capability of dealing with uncertainty factors is improved. In this way, the proposed algorithm has the advantages of both STF's strong robustness and SSRCKF's high accuracy. Finally, a maneuvering target tracking problem with abrupt state changes is used to test the performance of the proposed filter. Simulation results show that the STSSRCKF algorithm can get better estimation accuracy and greater robustness for maneuvering target tracking.
Directory of Open Access Journals (Sweden)
Biçer Cenker
2016-01-01
Full Text Available In this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable.
Parallelized Kalman-Filter-Based Reconstruction of Particle Tracks on Many-Core Processors and GPUs
Cerati, Giuseppe; Elmer, Peter; Krutelyov, Slava; Lantz, Steven; Lefebvre, Matthieu; Masciovecchio, Mario; McDermott, Kevin; Riley, Daniel; Tadel, Matevž; Wittich, Peter; Würthwein, Frank; Yagil, Avi
2017-08-01
For over a decade now, physical and energy constraints have limited clock speed improvements in commodity microprocessors. Instead, chipmakers have been pushed into producing lower-power, multi-core processors such as Graphical Processing Units (GPU), ARM CPUs, and Intel MICs. Broad-based efforts from manufacturers and developers have been devoted to making these processors user-friendly enough to perform general computations. However, extracting performance from a larger number of cores, as well as specialized vector or SIMD units, requires special care in algorithm design and code optimization. One of the most computationally challenging problems in high-energy particle experiments is finding and fitting the charged-particle tracks during event reconstruction. This is expected to become by far the dominant problem at the High-Luminosity Large Hadron Collider (HL-LHC), for example. Today the most common track finding methods are those based on the Kalman filter. Experience with Kalman techniques on real tracking detector systems has shown that they are robust and provide high physics performance. This is why they are currently in use at the LHC, both in the trigger and offine. Previously we reported on the significant parallel speedups that resulted from our investigations to adapt Kalman filters to track fitting and track building on Intel Xeon and Xeon Phi. Here, we discuss our progresses toward the understanding of these processors and the new developments to port the Kalman filter to NVIDIA GPUs.
Parallelized Kalman-Filter-Based Reconstruction of Particle Tracks on Many-Core Processors and GPUs
Directory of Open Access Journals (Sweden)
Cerati Giuseppe
2017-01-01
Full Text Available For over a decade now, physical and energy constraints have limited clock speed improvements in commodity microprocessors. Instead, chipmakers have been pushed into producing lower-power, multi-core processors such as Graphical Processing Units (GPU, ARM CPUs, and Intel MICs. Broad-based efforts from manufacturers and developers have been devoted to making these processors user-friendly enough to perform general computations. However, extracting performance from a larger number of cores, as well as specialized vector or SIMD units, requires special care in algorithm design and code optimization. One of the most computationally challenging problems in high-energy particle experiments is finding and fitting the charged-particle tracks during event reconstruction. This is expected to become by far the dominant problem at the High-Luminosity Large Hadron Collider (HL-LHC, for example. Today the most common track finding methods are those based on the Kalman filter. Experience with Kalman techniques on real tracking detector systems has shown that they are robust and provide high physics performance. This is why they are currently in use at the LHC, both in the trigger and offine. Previously we reported on the significant parallel speedups that resulted from our investigations to adapt Kalman filters to track fitting and track building on Intel Xeon and Xeon Phi. Here, we discuss our progresses toward the understanding of these processors and the new developments to port the Kalman filter to NVIDIA GPUs.
Application of a Bank of Kalman Filters for Aircraft Engine Fault Diagnostics
Kobayashi, Takahisa; Simon, Donald L.
2003-01-01
In this paper, a bank of Kalman filters is applied to aircraft gas turbine engine sensor and actuator fault detection and isolation (FDI) in conjunction with the detection of component faults. This approach uses multiple Kalman filters, each of which is designed for detecting a specific sensor or actuator fault. In the event that a fault does occur, all filters except the one using the correct hypothesis will produce large estimation errors, thereby isolating the specific fault. In the meantime, a set of parameters that indicate engine component performance is estimated for the detection of abrupt degradation. The proposed FDI approach is applied to a nonlinear engine simulation at nominal and aged conditions, and the evaluation results for various engine faults at cruise operating conditions are given. The ability of the proposed approach to reliably detect and isolate sensor and actuator faults is demonstrated.
Derivative free Kalman filtering used for orchard navigation
DEFF Research Database (Denmark)
Hansen, Søren; Bayramoglu, Enis; Andersen, Jens Christian
2010-01-01
In this paper the use of derivative free filters for mobile robot localisation is investigated. Three different filters are tested on real life data from an autonomous tractor running in an orchard environment. The localisation algorithm fuses odometry and gyro measurements with line features...
El Gharamti, Mohamad
2012-04-01
Accurate knowledge of the movement of contaminants in porous media is essential to track their trajectory and later extract them from the aquifer. A two-dimensional flow model is implemented and then applied on a linear contaminant transport model in the same porous medium. Because of different sources of uncertainties, this coupled model might not be able to accurately track the contaminant state. Incorporating observations through the process of data assimilation can guide the model toward the true trajectory of the system. The Kalman filter (KF), or its nonlinear invariants, can be used to tackle this problem. To overcome the prohibitive computational cost of the KF, the singular evolutive Kalman filter (SEKF) and the singular fixed Kalman filter (SFKF) are used, which are variants of the KF operating with low-rank covariance matrices. Experimental results suggest that under perfect and imperfect model setups, the low-rank filters can provide estimates as accurate as the full KF but at much lower computational effort. Low-rank filters are demonstrated to significantly reduce the computational effort of the KF to almost 3%. © 2012 American Society of Civil Engineers.
Directory of Open Access Journals (Sweden)
Ming Liu
2015-01-01
Full Text Available This paper is concerned with the topic of gravity matching aided inertial navigation technology using Kalman filter. The dynamic state space model for Kalman filter is constructed as follows: the error equation of the inertial navigation system is employed as the process equation while the local gravity model based on 9-point surface interpolation is employed as the observation equation. The unscented Kalman filter is employed to address the nonlinearity of the observation equation. The filter is refined in two ways as follows. The marginalization technique is employed to explore the conditionally linear substructure to reduce the computational load; specifically, the number of the needed sigma points is reduced from 15 to 5 after this technique is used. A robust technique based on Chi-square test is employed to make the filter insensitive to the uncertainties in the above constructed observation model. Numerical simulation is carried out, and the efficacy of the proposed method is validated by the simulation results.
Directory of Open Access Journals (Sweden)
E. L. Dmitrieva
2016-05-01
Full Text Available Basic peculiarities of nonlinear Kalman filtering algorithm applied to processing of interferometric signals are considered. Analytical estimates determining statistical characteristics of signal values prediction errors were obtained and analysis of errors histograms taking into account variations of different parameters of interferometric signal was carried out. Modeling of the signal prediction procedure with known fixed parameters and variable parameters of signal in the algorithm of nonlinear Kalman filtering was performed. Numerical estimates of prediction errors for interferometric signal values were obtained by formation and analysis of the errors histograms under the influence of additive noise and random variations of amplitude and frequency of interferometric signal. Nonlinear Kalman filter is shown to provide processing of signals with randomly variable parameters, however, it does not take into account directly the linearization error of harmonic function representing interferometric signal that is a filtering error source. The main drawback of the linear prediction consists in non-Gaussian statistics of prediction errors including cases of random deviations of signal amplitude and/or frequency. When implementing stochastic filtering of interferometric signals, it is reasonable to use prediction procedures based on local statistics of a signal and its parameters taken into account.
A nonlinear Kalman filtering approach to embedded control of turbocharged diesel engines
Rigatos, Gerasimos; Siano, Pierluigi; Arsie, Ivan
2014-10-01
The development of efficient embedded control for turbocharged Diesel engines, requires the programming of elaborated nonlinear control and filtering methods. To this end, in this paper nonlinear control for turbocharged Diesel engines is developed with the use of Differential flatness theory and the Derivative-free nonlinear Kalman Filter. It is shown that the dynamic model of the turbocharged Diesel engine is differentially flat and admits dynamic feedback linearization. It is also shown that the dynamic model can be written in the linear Brunovsky canonical form for which a state feedback controller can be easily designed. To compensate for modeling errors and external disturbances the Derivative-free nonlinear Kalman Filter is used and redesigned as a disturbance observer. The filter consists of the Kalman Filter recursion on the linearized equivalent of the Diesel engine model and of an inverse transformation based on differential flatness theory which enables to obtain estimates for the state variables of the initial nonlinear model. Once the disturbances variables are identified it is possible to compensate them by including an additional control term in the feedback loop. The efficiency of the proposed control method is tested through simulation experiments.
Dynamic Inverse Problem Solution Using a Kalman Filter Smoother for Neuronal Activity Estimation
Directory of Open Access Journals (Sweden)
Eduardo Giraldo-Suárez
2011-12-01
Full Text Available This article presents an estimation method of neuronal activity into the brain using a Kalman smoother approach that takes into account in the solution of the inverse problem the dynamic variability of the time series. This method is applied over a realistic head model calculated with the boundary element method. A comparative analysis for the dynamic estimation methods is made up from simulated EEG signals for several noise conditions. The solution of the inverse problem is achieved by using high performance computing techniques and an evaluation of the computational cost is performed for each method. As a result, the Kalman smoother approach presents better performance in the estimation task than the regularized static solution, and the direct Kalman filter.
Dynamic electrical impedance imaging of a chest phantom using the Kalman filter.
Kim, Bong Seok; Kim, Kyung Youn; Kao, Tzu-Jen; Newell, Jonathan C; Isaacson, David; Saulnier, Gary J
2006-05-01
A dynamic complex impedance imaging technique is developed with the aid of the linearized Kalman filter (LKF) for real-time reconstruction of the human chest. The forward problem is solved by an analytical method based on the separation of variables and Fourier series. The inverse problem is treated as a state estimation problem. The nonlinear measurement equation is linearized about the best homogeneous impedivity value as an initial guess, and the impedivity distribution is estimated with the aid of the Kalman estimator. The Kalman gain matrix is pre-computed and stored off-line to minimize the on-line computational time. Simulation and phantom experiment are reported to illustrate the reconstruction performances in the sense of spatio-temporal resolution in a simplified geometry of the human chest.
Dual Extended Kalman Filter for the Identification of Time-Varying Human Manual Control Behavior
Popovici, Alexandru; Zaal, Peter M. T.; Pool, Daan M.
2017-01-01
A Dual Extended Kalman Filter was implemented for the identification of time-varying human manual control behavior. Two filters that run concurrently were used, a state filter that estimates the equalization dynamics, and a parameter filter that estimates the neuromuscular parameters and time delay. Time-varying parameters were modeled as a random walk. The filter successfully estimated time-varying human control behavior in both simulated and experimental data. Simple guidelines are proposed for the tuning of the process and measurement covariance matrices and the initial parameter estimates. The tuning was performed on simulation data, and when applied on experimental data, only an increase in measurement process noise power was required in order for the filter to converge and estimate all parameters. A sensitivity analysis to initial parameter estimates showed that the filter is more sensitive to poor initial choices of neuromuscular parameters than equalization parameters, and bad choices for initial parameters can result in divergence, slow convergence, or parameter estimates that do not have a real physical interpretation. The promising results when applied to experimental data, together with its simple tuning and low dimension of the state-space, make the use of the Dual Extended Kalman Filter a viable option for identifying time-varying human control parameters in manual tracking tasks, which could be used in real-time human state monitoring and adaptive human-vehicle haptic interfaces.
Kalman Filter for Estimation of Sensor Acceleration Using Six - axis Inertial Sensor
Energy Technology Data Exchange (ETDEWEB)
Lee, Jung Keun [Hankyong National University, Anseong (Korea, Republic of)
2015-02-15
Although an accelerometer is a sensor that measures acceleration, it cannot be used by itself to measure the acceleration when the orientation of the sensor changes. This paper introduces a Kalman filter for the estimation of a sensor acceleration based on a six-axis inertial sensor (i.e., a three-axis accelerometer and three-axis gyroscope). The novelty of the proposed Kalman filter lies in the fact that its state vector includes not only the tilt angle variable but also the sensor acceleration. Thus, the filter can explicitly estimate the latter with a high accuracy. The accuracy of acceleration estimates were validated experimentally under three different dynamic conditions, using an optical motion capture system. It could be concluded that the performance of the proposed Kalman filter was comparable to that of the state-of-the-art estimation algorithm employed by the Xsens MTw. The proposed algorithm may be more suitable than inertial/magnetic sensor-based algorithms for various applications adopting six-axis inertial sensors.
A Novel Kalman Filter for Human Motion Tracking With an Inertial-Based Dynamic Inclinometer.
Ligorio, Gabriele; Sabatini, Angelo M
2015-08-01
Design and development of a linear Kalman filter to create an inertial-based inclinometer targeted to dynamic conditions of motion. The estimation of the body attitude (i.e., the inclination with respect to the vertical) was treated as a source separation problem to discriminate the gravity and the body acceleration from the specific force measured by a triaxial accelerometer. The sensor fusion between triaxial gyroscope and triaxial accelerometer data was performed using a linear Kalman filter. Wrist-worn inertial measurement unit data from ten participants were acquired while performing two dynamic tasks: 60-s sequence of seven manual activities and 90 s of walking at natural speed. Stereophotogrammetric data were used as a reference. A statistical analysis was performed to assess the significance of the accuracy improvement over state-of-the-art approaches. The proposed method achieved, on an average, a root mean square attitude error of 3.6° and 1.8° in manual activities and locomotion tasks (respectively). The statistical analysis showed that, when compared to few competing methods, the proposed method improved the attitude estimation accuracy. A novel Kalman filter for inertial-based attitude estimation was presented in this study. A significant accuracy improvement was achieved over state-of-the-art approaches, due to a filter design that better matched the basic optimality assumptions of Kalman filtering. Human motion tracking is the main application field of the proposed method. Accurately discriminating the two components present in the triaxial accelerometer signal is well suited for studying both the rotational and the linear body kinematics.
Directory of Open Access Journals (Sweden)
Yunsick Sung
2016-11-01
Full Text Available Given that location information is the key to providing a variety of services in sustainable indoor computing environments, it is required to obtain accurate locations. Locations can be estimated by three distances from three fixed points. Therefore, if the distance between two points can be measured or estimated accurately, the location in indoor environments can be estimated. To increase the accuracy of the measured distance, noise filtering, signal revision, and distance estimation processes are generally performed. This paper proposes a novel framework for estimating the distance between a beacon and an access point (AP in a sustainable indoor computing environment. Diverse types of received strength signal indications (RSSIs are used for WiFi, Bluetooth, and radio signals, and the proposed distance estimation framework is unique in that it is independent of the specific wireless signal involved, being based on the Bluetooth signal of the beacon. Generally, RSSI measurement, noise filtering, and revision are required for distance estimation using RSSIs. The employed RSSIs are first measured from an AP, with multiple APs sometimes used to increase the accuracy of the distance estimation. Owing to the inevitable presence of noise in the measured RSSIs, the application of noise filtering is essential, and further revision is used to address the inaccuracy and instability that characterizes RSSIs measured in an indoor environment. The revised RSSIs are then used to estimate the distance. The proposed distance estimation framework uses one AP to measure the RSSIs, a Kalman filter to eliminate noise, and a log-distance path loss model to revise the measured RSSIs. In the experimental implementation of the framework, both a RSSI filter and a Kalman filter were respectively used for noise elimination to comparatively evaluate the performance of the latter for the specific application. The Kalman filter was found to reduce the accumulated errors by 8
Ermolaev, Petr A.; Volynsky, Maxim A.
2017-06-01
The paper deals with the machine learning approach to automatic tuning of extended Kalman filter in application to interferometric signals processing. The representation of interferometric signals as output of dynamic systems with varying state vector is presented. It is shown that the challenge of the extended Kalman filter application to interferometric data processing is selection of initial parameters for the filter. The complex tuning problem is described in a formal form. The machine learning approach to the automatic filter tuning is proposed. The combination of Monte Carlo optimization and the gradient descent are implemented for initial filter parameters selection. The optimization criterion in the form of sum differences between measured and estimated signal value is presented and discussed. The results of simulated and experimental interferometric signals processing are presented and analyzed. The quality of amplitude and phase estimation by the automatically tuned filter is at the same level as hand tuned filter. It is shown, that proposed approach allows to obtain robust results of experimental data processing.
Optimal Tuner Selection for Kalman-Filter-Based Aircraft Engine Performance Estimation
Simon, Donald L.; Garg, Sanjay
2011-01-01
An emerging approach in the field of aircraft engine controls and system health management is the inclusion of real-time, onboard models for the inflight estimation of engine performance variations. This technology, typically based on Kalman-filter concepts, enables the estimation of unmeasured engine performance parameters that can be directly utilized by controls, prognostics, and health-management applications. A challenge that complicates this practice is the fact that an aircraft engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters such as efficiencies and flow capacities related to each major engine module. Through Kalman-filter-based estimation techniques, the level of engine performance degradation can be estimated, given that there are at least as many sensors as health parameters to be estimated. However, in an aircraft engine, the number of sensors available is typically less than the number of health parameters, presenting an under-determined estimation problem. A common approach to address this shortcoming is to estimate a subset of the health parameters, referred to as model tuning parameters. The problem/objective is to optimally select the model tuning parameters to minimize Kalman-filterbased estimation error. A tuner selection technique has been developed that specifically addresses the under-determined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine that seeks to minimize the theoretical mean-squared estimation error of the Kalman filter. This approach can significantly reduce the error in onboard aircraft engine parameter estimation
National Research Council Canada - National Science Library
Sallberg, Scott A
2007-01-01
Kalman filtering and multiple model adaptive estimation (MMAE) methods have been applied by researchers in several engineering disciplines to a multitude of problems featuring a linear (or mildly nonlinear...
Sky-Hook Control and Kalman Filtering in Nonlinear Model of Tracked Vehicle Suspension System
Directory of Open Access Journals (Sweden)
Jurkiewicz Andrzej
2017-09-01
Full Text Available The essence of the undertaken topic is application of the continuous sky-hook control strategy and the Extended Kalman Filter as the state observer in the 2S1 tracked vehicle suspension system. The half-car model of this suspension system consists of seven logarithmic spiral springs and two magnetorheological dampers which has been described by the Bingham model. The applied continuous sky-hook control strategy considers nonlinear stiffness characteristic of the logarithmic spiral springs. The control is determined on estimates generated by the Extended Kalman Filter. Improve of ride comfort is verified by comparing simulation results, under the same driving conditions, of controlled and passive vehicle suspension systems.
Flatness-based control and Kalman filtering for a continuous-time macroeconomic model
Rigatos, G.; Siano, P.; Ghosh, T.; Busawon, K.; Binns, R.
2017-11-01
The article proposes flatness-based control for a nonlinear macro-economic model of the UK economy. The differential flatness properties of the model are proven. This enables to introduce a transformation (diffeomorphism) of the system's state variables and to express the state-space description of the model in the linear canonical (Brunowsky) form in which both the feedback control and the state estimation problem can be solved. For the linearized equivalent model of the macroeconomic system, stabilizing feedback control can be achieved using pole placement methods. Moreover, to implement stabilizing feedback control of the system by measuring only a subset of its state vector elements the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized equivalent model of the financial system and of an inverse transformation that is based again on differential flatness theory. The asymptotic stability properties of the control scheme are confirmed.
Huang, Lei
2015-09-30
To solve the problem in which the conventional ARMA modeling methods for gyro random noise require a large number of samples and converge slowly, an ARMA modeling method using a robust Kalman filtering is developed. The ARMA model parameters are employed as state arguments. Unknown time-varying estimators of observation noise are used to achieve the estimated mean and variance of the observation noise. Using the robust Kalman filtering, the ARMA model parameters are estimated accurately. The developed ARMA modeling method has the advantages of a rapid convergence and high accuracy. Thus, the required sample size is reduced. It can be applied to modeling applications for gyro random noise in which a fast and accurate ARMA modeling method is required.
Rapid Transfer Alignment of MEMS SINS Based on Adaptive Incremental Kalman Filter.
Chu, Hairong; Sun, Tingting; Zhang, Baiqiang; Zhang, Hongwei; Chen, Yang
2017-01-14
In airborne MEMS SINS transfer alignment, the error of MEMS IMU is highly environment-dependent and the parameters of the system model are also uncertain, which may lead to large error and bad convergence of the Kalman filter. In order to solve this problem, an improved adaptive incremental Kalman filter (AIKF) algorithm is proposed. First, the model of SINS transfer alignment is defined based on the "Velocity and Attitude" matching method. Then the detailed algorithm progress of AIKF and its recurrence formulas are presented. The performance and calculation amount of AKF and AIKF are also compared. Finally, a simulation test is designed to verify the accuracy and the rapidity of the AIKF algorithm by comparing it with KF and AKF. The results show that the AIKF algorithm has better estimation accuracy and shorter convergence time, especially for the bias of the gyroscope and the accelerometer, which can meet the accuracy and rapidity requirement of transfer alignment.
Riggs, A. J. Eldorado; Cady, Eric J.; Prada, Camilo M.; Kern, Brian D.; Zhou, Hanying; Kasdin, N. Jeremy; Groff, Tyler D.
2016-07-01
For direct imaging and spectral characterization of cold exoplanets in reflected light, the proposed Wide-Field Infrared Survey Telescope (WFIRST) Coronagraph Instrument (CGI) will carry two types of coronagraphs. The High Contrast Imaging Testbed (HCIT) at the Jet Propulsion Laboratory has been testing both coronagraph types and demonstrated their abilities to achieve high contrast. Focal plane wavefront correction is used to estimate and mitigate aberrations. As the most time-consuming part of correction during a space mission, the acquisition of probed images for electric field estimation needs to be as short as possible. We present results from the HCIT of narrowband, low-signal wavefront estimation tests using a shaped pupil Lyot coronagraph (SPLC) designed for the WFIRST CGI. In the low-flux regime, the Kalman filter and iterated extended Kalman filter provide faster correction, better achievable contrast, and more accurate estimates than batch process estimation.
Li, Jing; Song, Ningfang; Yang, Gongliu; Jiang, Rui
2016-07-01
In the initial alignment process of strapdown inertial navigation system (SINS), large misalignment angles always bring nonlinear problem, which can usually be processed using the scaled unscented Kalman filter (SUKF). In this paper, the problem of large misalignment angles in SINS alignment is further investigated, and the strong tracking scaled unscented Kalman filter (STSUKF) is proposed with fixed parameters to improve convergence speed, while these parameters are artificially constructed and uncertain in real application. To further improve the alignment stability and reduce the parameters selection, this paper proposes a fuzzy adaptive strategy combined with STSUKF (FUZZY-STSUKF). As a result, initial alignment scheme of large misalignment angles based on FUZZY-STSUKF is designed and verified by simulations and turntable experiment. The results show that the scheme improves the accuracy and convergence speed of SINS initial alignment compared with those based on SUKF and STSUKF.
Lepine, Nicholas N; Tajima, Takuro; Ogasawara, Takayuki; Kasahara, Ryoichi; Koizumi, Hiroshi
2016-08-01
An adaptive Kalman filter-based fusion algorithm capable of estimating respiration rate for unobtrusive respiratory monitoring is proposed. Using both signal characteristics and a priori information, the Kalman filter is adaptively optimized to improve accuracy. Furthermore, the system is able to combine the respiration-related signals extracted from a textile ECG sensor and an accelerometer to create a single robust measurement. We measured derived respiratory rates and, when compared to a reference, found root-mean-square error of 2.11 breaths-per-minute (BrPM) while lying down, 2.30 BrPM while sitting, 5.97 BrPM while walking, and 5.98 BrPM while running. These results demonstrate that the proposed system is applicable to unobtrusive monitoring for various applications.
Model Predictive Control Based on Kalman Filter for Constrained Hammerstein-Wiener Systems
Directory of Open Access Journals (Sweden)
Man Hong
2013-01-01
Full Text Available To precisely track the reactor temperature in the entire working condition, the constrained Hammerstein-Wiener model describing nonlinear chemical processes such as in the continuous stirred tank reactor (CSTR is proposed. A predictive control algorithm based on the Kalman filter for constrained Hammerstein-Wiener systems is designed. An output feedback control law regarding the linear subsystem is derived by state observation. The size of reaction heat produced and its influence on the output are evaluated by the Kalman filter. The observation and evaluation results are calculated by the multistep predictive approach. Actual control variables are computed while considering the constraints of the optimal control problem in a finite horizon through the receding horizon. The simulation example of the CSTR tester shows the effectiveness and feasibility of the proposed algorithm.
Thermal Error Modeling of the CNC Machine Tool Based on Data Fusion Method of Kalman Filter
Directory of Open Access Journals (Sweden)
Haitong Wang
2017-01-01
Full Text Available This paper presents a modeling methodology for the thermal error of machine tool. The temperatures predicted by modified lumped-mass method and the temperatures measured by sensors are fused by the data fusion method of Kalman filter. The fused temperatures, instead of the measured temperatures used in traditional methods, are applied to predict the thermal error. The genetic algorithm is implemented to optimize the parameters in modified lumped-mass method and the covariances in Kalman filter. The simulations indicate that the proposed method performs much better compared with the traditional method of MRA, in terms of prediction accuracy and robustness under a variety of operating conditions. A compensation system is developed based on the controlling system of Siemens 840D. Validated by the compensation experiment, the thermal error after compensation has been reduced dramatically.
Identification of parameters in nonlinear geotechnical models using extenden Kalman filter
Directory of Open Access Journals (Sweden)
Nestorović Tamara
2014-01-01
Full Text Available Direct measurement of relevant system parameters often represents a problem due to different limitations. In geomechanics, measurement of geotechnical material constants which constitute a material model is usually a very diffcult task even with modern test equipment. Back-analysis has proved to be a more effcient and more economic method for identifying material constants because it needs measurement data such as settlements, pore pressures, etc., which are directly measurable, as inputs. Among many model parameter identification methods, the Kalman filter method has been applied very effectively in recent years. In this paper, the extended Kalman filter – local iteration procedure incorporated with finite element analysis (FEA software has been implemented. In order to prove the effciency of the method, parameter identification has been performed for a nonlinear geotechnical model.
Bar-Itzhack, I. Y.; Deutschmann, J.; Markley, F. L.
1991-01-01
This work introduces, examines and compares several quaternion normalization algorithms, which are shown to be an effective stage in the application of the additive extended Kalman filter to spacecraft attitude determination, which is based on vector measurements. Three new normalization schemes are introduced. They are compared with one another and with the known brute force normalization scheme, and their efficiency is examined. Simulated satellite data are used to demonstate the performance of all four schemes.
Kalman Filter Chemical Data Assimilation: A Case Study in January 1992
Lary, D. J.; Khattatov, B.; Atlas, Robert; Mussa, H.
2002-01-01
This paper describes a Kalman filter chemical data assimilation system and its use for analysing a vertical atmospheric profile during January 1992. The vertical profile was at an equivalent PV latitude (phi(sub e)) of 55 deg S and consisted of 21 potential temperature (theta) levels spaced equally in log(theta) between 400 K and 2000 K. This equivalent latitude was chosen as it was well observed during January 1992 by instruments on board the Upper Atmosphere Research Satellite (UARS).
Distributed Estimation of Oscillations in Power Systems: an Extended Kalman Filtering Approach
Yu, Zhe; Shi, Di; Wang, Zhiwei; Zhang, Qibing; Huang, Junhui; Pan, Sen
2017-01-01
Online estimation of electromechanical oscillation parameters provides essential information to prevent system instability and blackout and helps to identify event categories and locations. We formulate the problem as a state space model and employ the extended Kalman filter to estimate oscillation frequencies and damping factors directly based on data from phasor measurement units. Due to considerations of communication burdens and privacy concerns, a fully distributed algorithm is proposed ...
Environment reconstruction and navigation with electric sense based on a Kalman filter
Lebastard, Vincent; Chevallereau, Christine; Girin, Alexis; Servagent, Noël; Gossiaux, Pol-Bernard; Boyer, Frédéric
2013-01-01
International audience; Electric fish sense the perturbations of a self generated electric field through their electro- receptive skin. This sense allows them to navigate and reconstruct their environment in conditions where vision and sonar cannot work. In this article, we use a sensor inspired by this sense to address the problem of locating and reconstructing small objects (electrolocation) and navigating in a tank. Based on a Kalman filter, any small object in the surroundings of the moti...
Localization of small objects with electric sense based on kalman filter
Lebastard, Vincent; Chevallereau, C; Girin, A; Boyer, Frédéric; Gossiaux, P.
2012-01-01
International audience; — Electric fish feel the perturbations of a self-generated electric field through their electro-receptive skin. This sense allows them to navigate and reconstruct their environment in conditions where vision and sonar cannot work. In this article, we use a sensor bio-inspired from this active sense to address the problem of small objects reconstruction and electrolocation. Based on a Kalman filter, any small object in the surrounding of the motion controlled sensor can...
van der Wal, J. T.; Janssen, L. H. J. M.
The spatial and temporal variations of PM10 concentrations in the Netherlands as measured by the National Air Quality Monitoring Network in the period of 1993-1994 have been analysed using descriptive statistics, principal component analysis (PCA) and Kalman filtering. Spatial differences in PM10 concentrations in the Netherlands are rather small. PM10 concentrations may be elevated by about 10-20% with respect to the yearly average, which is about 40 μg/m 3, in areas with local sources such as traffic or other urban, industrial or agricultural sources. Actual PM10 concentrations vary between 20 and 50 μg/m 3 throughout the year. During episodes, PM10 concentrations may increase to 4 to 5 times the annual average (>200 μg/m 3). The large amount of variance explained by the first component of PCA, i.e. 85%, shows that all measuring stations observe the same pattern of daily variations which is mainly governed by large-scale weather systems.The daily variations are analysed using multiple-linear regression and Kalman filtering; the latter employed as a time-varying linear regression technique. The results of the both methods are compared and show that using wind direction, temperature and duration of precipitation as variables, ordinary linear regression explains about 25% of the variance of PM10 concentrations, while the application of the Kalman filter explains about 45% of the variance. The improvement using the Kalman filter is primarily obtained by making the explaining variables time dependent. This shows a significant effect of seasonal variation on temperature and wind direction at PM10 levels.
Forecasting optimal duration of a beer main fermentation process using the Kalman filter
Niyonsaba T.; Pavlov V. A.
2016-01-01
One of the most important processes of beer production is the main process of fermentation. In this process, the wort transforms into beer. The quality of beer depends on the dynamics of wort parameters. The main fermentation process continues for 10 days and requires high costs. Therefore, the main purpose of this article is to forecast the optimal duration of the beer main fermentation process and provide its optimal control. The Kalman filter can provide optimal control of the main ferment...
Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering
Directory of Open Access Journals (Sweden)
Xiu Kan
2012-01-01
Full Text Available The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameter θ:dXt=(θα(t+β(tXtdt+σ(tdWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameter θ based on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.
On-chip implementation of Extended Kalman Filter for adaptive battery states monitoring
Nejad, S.; Gladwin, D.T.; Stone, D. A.
2016-01-01
This paper reports the development and implementation of an adaptive lithium-ion battery monitoring system. The monitoring algorithm is based on the nonlinear Dual Extended Kalman Filter (DEKF), which allows for simultaneous states and parameters estimation. The hardware platform consists of an ARM cortex-M0 processor with six embedded analogue-to-digital converters (ADCs) for data acquisition. Two definitions for online state-of-health (SOH) characterisation are presented; one energy-based a...
Application of Kalman filter in detecting pre-earthquake ionospheric TEC anomaly
Directory of Open Access Journals (Sweden)
Zhu Fuying
2011-05-01
Full Text Available : As an attempt, the Kalman filter was used to study the anomalous variations of ionospheric Total Electron Content (TEC before and after Wenchuan Ms8.0 earthquake, these TEC data were calculated from the GPS data observed by the Crustal Movement Observation Network of China. The result indicates that this method is reasonable and reliable in detecting TEC anomalies associated with large earthquakes.
Quaternion-Based Kalman Filter for AHRS Using an Adaptive-Step Gradient Descent Algorithm
Directory of Open Access Journals (Sweden)
Li Wang
2015-09-01
Full Text Available This paper presents a quaternion-based Kalman filter for real-time estimation of the orientation of a quadrotor. Quaternions are used to represent rotation relationship between navigation frame and body frame. Processing of a 3-axis accelerometer using Adaptive-Step Gradient Descent (ASGD produces a computed quaternion input to the Kalman filter. The step-size in GD is set in direct proportion to the physical orientation rate. Kalman filter combines 3-axis gyroscope and computed quaternion to determine pitch and roll angles. This combination overcomes linearization error of the measurement equations and reduces the calculation cost. 3-axis magnetometer is separated from ASGD to independently calculate yaw angle for Attitude Heading Reference System (AHRS. This AHRS algorithm is able to remove the magnetic distortion impact. Experiments are carried out in the small-size flight controller and the real world flying test shows the proposed AHRS algorithm is adequate for the real-time estimation of the orientation of a quadrotor.
Low-dimensional recurrent neural network-based Kalman filter for speech enhancement.
Xia, Youshen; Wang, Jun
2015-07-01
This paper proposes a new recurrent neural network-based Kalman filter for speech enhancement, based on a noise-constrained least squares estimate. The parameters of speech signal modeled as autoregressive process are first estimated by using the proposed recurrent neural network and the speech signal is then recovered from Kalman filtering. The proposed recurrent neural network is globally asymptomatically stable to the noise-constrained estimate. Because the noise-constrained estimate has a robust performance against non-Gaussian noise, the proposed recurrent neural network-based speech enhancement algorithm can minimize the estimation error of Kalman filter parameters in non-Gaussian noise. Furthermore, having a low-dimensional model feature, the proposed neural network-based speech enhancement algorithm has a much faster speed than two existing recurrent neural networks-based speech enhancement algorithms. Simulation results show that the proposed recurrent neural network-based speech enhancement algorithm can produce a good performance with fast computation and noise reduction. Copyright © 2015 Elsevier Ltd. All rights reserved.
Optimal Tuner Selection for Kalman Filter-Based Aircraft Engine Performance Estimation
Simon, Donald L.; Garg, Sanjay
2010-01-01
A linear point design methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented. This technique specifically addresses the underdetermined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine which seeks to minimize the theoretical mean-squared estimation error. This paper derives theoretical Kalman filter estimation error bias and variance values at steady-state operating conditions, and presents the tuner selection routine applied to minimize these values. Results from the application of the technique to an aircraft engine simulation are presented and compared to the conventional approach of tuner selection. Experimental simulation results are found to be in agreement with theoretical predictions. The new methodology is shown to yield a significant improvement in on-line engine performance estimation accuracy
Robust cubature Kalman filter for GNSS/INS with missing observations and colored measurement noise.
Cui, Bingbo; Chen, Xiyuan; Tang, Xihua; Huang, Haoqian; Liu, Xiao
2017-10-10
In order to improve the accuracy of GNSS/INS working in GNSS-denied environment, a robust cubature Kalman filter (RCKF) is developed by considering colored measurement noise and missing observations. First, an improved cubature Kalman filter (CKF) is derived by considering colored measurement noise, where the time-differencing approach is applied to yield new observations. Then, after analyzing the disadvantages of existing methods, the measurement augment in processing colored noise is translated into processing the uncertainties of CKF, and new sigma point update framework is utilized to account for the bounded model uncertainties. By reusing the diffused sigma points and approximation residual in the prediction stage of CKF, the RCKF is developed and its error performance is analyzed theoretically. Results of numerical experiment and field test reveal that RCKF is more robust than CKF and extended Kalman filter (EKF), and compared with EKF, the heading error of land vehicle is reduced by about 72.4%. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Rajabioun, Mehdi; Nasrabadi, Ali Motie; Shamsollahi, Mohammad Bagher
2017-09-01
Effective connectivity is one of the most important considerations in brain functional mapping via EEG. It demonstrates the effects of a particular active brain region on others. In this paper, a new method is proposed which is based on dual Kalman filter. In this method, firstly by using a brain active localization method (standardized low resolution brain electromagnetic tomography) and applying it to EEG signal, active regions are extracted, and appropriate time model (multivariate autoregressive model) is fitted to extracted brain active sources for evaluating the activity and time dependence between sources. Then, dual Kalman filter is used to estimate model parameters or effective connectivity between active regions. The advantage of this method is the estimation of different brain parts activity simultaneously with the calculation of effective connectivity between active regions. By combining dual Kalman filter with brain source localization methods, in addition to the connectivity estimation between parts, source activity is updated during the time. The proposed method performance has been evaluated firstly by applying it to simulated EEG signals with interacting connectivity simulation between active parts. Noisy simulated signals with different signal to noise ratios are used for evaluating method sensitivity to noise and comparing proposed method performance with other methods. Then the method is applied to real signals and the estimation error during a sweeping window is calculated. By comparing proposed method results in different simulation (simulated and real signals), proposed method gives acceptable results with least mean square error in noisy or real conditions.
Parallelized Kalman-Filter-Based Reconstruction of Particle Tracks on Many-Core Architectures
Energy Technology Data Exchange (ETDEWEB)
Cerati, Giuseppe [Fermilab; Elmer, Peter [Princeton U.; Krutelyov, Slava [UC, San Diego; Lantz, Steven [Cornell U., Phys. Dept.; Lefebvre, Matthieu [Princeton U.; Masciovecchio, Mario [UC, San Diego; McDermott, Kevin [Cornell U., Phys. Dept.; Riley, Daniel [Cornell U., Phys. Dept.; Tadel, Matevž [UC, San Diego; Wittich, Peter [Cornell U., Phys. Dept.; Würthwein, Frank [UC, San Diego; Yagil, Avi [UC, San Diego
2017-11-16
Faced with physical and energy density limitations on clock speed, contemporary microprocessor designers have increasingly turned to on-chip parallelism for performance gains. Examples include the Intel Xeon Phi, GPGPUs, and similar technologies. Algorithms should accordingly be designed with ample amounts of fine-grained parallelism if they are to realize the full performance of the hardware. This requirement can be challenging for algorithms that are naturally expressed as a sequence of small-matrix operations, such as the Kalman filter methods widely in use in high-energy physics experiments. In the High-Luminosity Large Hadron Collider (HL-LHC), for example, one of the dominant computational problems is expected to be finding and fitting charged-particle tracks during event reconstruction; today, the most common track-finding methods are those based on the Kalman filter. Experience at the LHC, both in the trigger and offline, has shown that these methods are robust and provide high physics performance. Previously we reported the significant parallel speedups that resulted from our efforts to adapt Kalman-filter-based tracking to many-core architectures such as Intel Xeon Phi. Here we report on how effectively those techniques can be applied to more realistic detector configurations and event complexity.
Real-time MR diffusion tensor and Q-ball imaging using Kalman filtering.
Poupon, Cyril; Roche, Alexis; Dubois, Jessica; Mangin, Jean-François; Poupon, Fabrice
2008-10-01
Diffusion magnetic resonance imaging (dMRI) has become an established research tool for the investigation of tissue structure and orientation. In this paper, we present a method for real-time processing of diffusion tensor and Q-ball imaging. The basic idea is to use Kalman filtering framework to fit either the linear tensor or Q-ball model. Because the Kalman filter is designed to be an incremental algorithm, it naturally enables updating the model estimate after the acquisition of any new diffusion-weighted volume. Processing diffusion models and maps during ongoing scans provides a new useful tool for clinicians, especially when it is not possible to predict how long a subject may remain still in the magnet. First, we introduce the general linear models corresponding to the two diffusion tensor and analytical Q-ball models of interest. Then, we present the Kalman filtering framework and we focus on the optimization of the diffusion orientation sets in order to speed up the convergence of the online processing. Last, we give some results on a healthy volunteer for the online tensor and the Q-ball model, and we make some comparisons with the conventional offline techniques used in the literature. We could achieve full real-time for diffusion tensor imaging and deferred time for Q-ball imaging, using a single workstation.
Detection of Sensor Faults in Small Helicopter UAVs Using Observer/Kalman Filter Identification
Directory of Open Access Journals (Sweden)
Guillermo Heredia
2011-01-01
Full Text Available Reliability is a critical issue in navigation of unmanned aerial vehicles (UAVs since there is no human pilot that can react to any abnormal situation. Due to size and cost limitations, redundant sensor schemes and aeronautical-grade navigation sensors used in large aircrafts cannot be installed in small UAVs. Therefore, other approaches like analytical redundancy should be used to detect faults in navigation sensors and increase reliability. This paper presents a sensor fault detection and diagnosis system for small autonomous helicopters based on analytical redundancy. Fault detection is accomplished by evaluating any significant change in the behaviour of the vehicle with respect to the fault-free behaviour, which is estimated by using an observer. The observer is obtained from input-output experimental data with the Observer/Kalman Filter Identification (OKID method. The OKID method is able to identify the system and an observer with properties similar to a Kalman filter, directly from input-output experimental data. Results are similar to the Kalman filter, but, with the proposed method, there is no need to estimate neither system matrices nor sensor and process noise covariance matrices. The system has been tested with real helicopter flight data, and the results compared with other methods.
The Kalman Filter and High Performance Computing at NASA's Data Assimilation Office (DAO)
Lyster, Peter M.
1999-01-01
Atmospheric data assimilation is a method of combining actual observations with model simulations to produce a more accurate description of the earth system than the observations alone provide. The output of data assimilation, sometimes called "the analysis", are accurate regular, gridded datasets of observed and unobserved variables. This is used not only for weather forecasting but is becoming increasingly important for climate research. For example, these datasets may be used to assess retrospectively energy budgets or the effects of trace gases such as ozone. This allows researchers to understand processes driving weather and climate, which have important scientific and policy implications. The primary goal of the NASA's Data Assimilation Office (DAO) is to provide datasets for climate research and to support NASA satellite and aircraft missions. This presentation will: (1) describe ongoing work on the advanced Kalman/Lagrangian filter parallel algorithm for the assimilation of trace gases in the stratosphere; and (2) discuss the Kalman filter in relation to other presentations from the DAO on Four Dimensional Data Assimilation at this meeting. Although the designation "Kalman filter" is often used to describe the overarching work, the series of talks will show that the scientific software and the kind of parallelization techniques that are being developed at the DAO are very different depending on the type of problem being considered, the extent to which the problem is mission critical, and the degree of Software Engineering that has to be applied.
Miao, Zhiyong; Shi, Hongyang; Zhang, Yi; Xu, Fan
2017-10-01
In this paper, a new variational Bayesian adaptive cubature Kalman filter (VBACKF) is proposed for nonlinear state estimation. Although the conventional VBACKF performs better than cubature Kalman filtering (CKF) in solving nonlinear systems with time-varying measurement noise, its performance may degrade due to the uncertainty of the system model. To overcome this drawback, a multilayer feed-forward neural network (MFNN) is used to aid the conventional VBACKF, generalizing it to attain higher estimation accuracy and robustness. In the proposed neural-network-aided variational Bayesian adaptive cubature Kalman filter (NN-VBACKF), the MFNN is used to turn the state estimation of the VBACKF adaptively, and it is used for both state estimation and in the online training paradigm simultaneously. To evaluate the performance of the proposed method, it is compared with CKF and VBACKF via target tracking problems. The simulation results demonstrate that the estimation accuracy and robustness of the proposed method are better than those of the CKF and VBACKF.
A Quantum Kalman Filter-Based PID Controller
Gough, John E.
2017-01-01
We give a concrete description of a controlled quantum stochastic dynamical model corresponding to a quantum system (a cavity mode) under going continual quadrature measurements, with a PID controller acting on the filtered estimate for the mode operator. Central use is made of the input and output pictures when constructing the model: these unitarily equivalent pictures are presented in the paper, and used to transfer concepts relating to the controlled internal dynamics to those relating to...
Liu, Hua; Wu, Wen
2017-06-13
For improving the tracking accuracy and model switching speed of maneuvering target tracking in nonlinear systems, a new algorithm named the interacting multiple model fifth-degree spherical simplex-radial cubature Kalman filter (IMM5thSSRCKF) is proposed in this paper. The new algorithm is a combination of the interacting multiple model (IMM) filter and the fifth-degree spherical simplex-radial cubature Kalman filter (5thSSRCKF). The proposed algorithm makes use of Markov process to describe the switching probability among the models, and uses 5thSSRCKF to deal with the state estimation of each model. The 5thSSRCKF is an improved filter algorithm, which utilizes the fifth-degree spherical simplex-radial rule to improve the filtering accuracy. Finally, the tracking performance of the IMM5thSSRCKF is evaluated by simulation in a typical maneuvering target tracking scenario. Simulation results show that the proposed algorithm has better tracking performance and quicker model switching speed when disposing maneuver models compared with the interacting multiple model unscented Kalman filter (IMMUKF), the interacting multiple model cubature Kalman filter (IMMCKF) and the interacting multiple model fifth-degree cubature Kalman filter (IMM5thCKF).
Extended and Unscented Kalman Filtering Applied to a Flexible-Joint Robot with Jerk Estimation
Directory of Open Access Journals (Sweden)
Mohammad Ali Badamchizadeh
2010-01-01
Full Text Available Robust nonlinear control of flexible-joint robots requires that the link position, velocity, acceleration, and jerk be available. In this paper, we derive the dynamic model of a nonlinear flexible-joint robot based on the governing Euler-Lagrange equations and propose extended and unscented Kalman filters to estimate the link acceleration and jerk from position and velocity measurements. Both observers are designed for the same model and run with the same covariance matrices under the same initial conditions. A five-bar linkage robot with revolute flexible joints is considered as a case study. Simulation results verify the effectiveness of the proposed filters.
An Improved Unscented Kalman Filter Based Decoder for Cortical Brain-Machine Interfaces.
Li, Simin; Li, Jie; Li, Zheng
2016-01-01
Brain-machine interfaces (BMIs) seek to connect brains with machines or computers directly, for application in areas such as prosthesis control. For this application, the accuracy of the decoding of movement intentions is crucial. We aim to improve accuracy by designing a better encoding model of primary motor cortical activity during hand movements and combining this with decoder engineering refinements, resulting in a new unscented Kalman filter based decoder, UKF2, which improves upon our previous unscented Kalman filter decoder, UKF1. The new encoding model includes novel acceleration magnitude, position-velocity interaction, and target-cursor-distance features (the decoder does not require target position as input, it is decoded). We add a novel probabilistic velocity threshold to better determine the user's intent to move. We combine these improvements with several other refinements suggested by others in the field. Data from two Rhesus monkeys indicate that the UKF2 generates offline reconstructions of hand movements (mean CC 0.851) significantly more accurately than the UKF1 (0.833) and the popular position-velocity Kalman filter (0.812). The encoding model of the UKF2 could predict the instantaneous firing rate of neurons (mean CC 0.210), given kinematic variables and past spiking, better than the encoding models of these two decoders (UKF1: 0.138, p-v Kalman: 0.098). In closed-loop experiments where each monkey controlled a computer cursor with each decoder in turn, the UKF2 facilitated faster task completion (mean 1.56 s vs. 2.05 s) and higher Fitts's Law bit rate (mean 0.738 bit/s vs. 0.584 bit/s) than the UKF1. These results suggest that the modeling and decoder engineering refinements of the UKF2 improve decoding performance. We believe they can be used to enhance other decoders as well.
Tuning the Solar Dynamics Observatory Onboard Kalman Filter
Halverson, Julie Kay; Harman, Rick; Carpenter, Russell; Poland, Devin
2017-01-01
The Solar Dynamics Observatory (SDO) was launched in 2010. SDO is a sun pointing semi-autonomous spacecraft in a geosynchronous orbit that allows nearly continuous observations of the sun. SDO is equipped with coarse sun sensors, two star trackers, a digital sun sensor, and three two-axis inertial reference units (IRU). The IRUs are temperature sensitive and were designed to operate in a stable thermal environment. Due to battery degradation concerns the IRU heaters were not used on SDO and the onboard filter was tuned to accommodate the noisier IRU data. Since launch currents have increased on two IRUs, one had to eventually be powered off. Recent ground tests on a battery similar to SDO indicated the heaters would have negligible impact on battery degradation, so in 2016 a decision was made to turn the heaters on. This paper presents the analysis and results of updating the filter tuning parameters onboard SDO with the IRUs now operating in their intended thermal environment.
Performance analysis of improved iterated cubature Kalman filter and its application to GNSS/INS.
Cui, Bingbo; Chen, Xiyuan; Xu, Yuan; Huang, Haoqian; Liu, Xiao
2017-01-01
In order to improve the accuracy and robustness of GNSS/INS navigation system, an improved iterated cubature Kalman filter (IICKF) is proposed by considering the state-dependent noise and system uncertainty. First, a simplified framework of iterated Gaussian filter is derived by using damped Newton-Raphson algorithm and online noise estimator. Then the effect of state-dependent noise coming from iterated update is analyzed theoretically, and an augmented form of CKF algorithm is applied to improve the estimation accuracy. The performance of IICKF is verified by field test and numerical simulation, and results reveal that, compared with non-iterated filter, iterated filter is less sensitive to the system uncertainty, and IICKF improves the accuracy of yaw, roll and pitch by 48.9%, 73.1% and 83.3%, respectively, compared with traditional iterated KF. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
DEFF Research Database (Denmark)
Larsen, Thomas Dall; Bak, Martin; Andersen, Nils Axel
1998-01-01
A Kalman filter using encoder readings as inputs and vision measurements as observations is designed as a location estimator for an autonomously guided vehicle (AGV). To reduce the effect of modelling errors an augmented filter that estimates the true system parameters is designed. The traditional...... way of reducing these errors is by fictitious noise injection in the filter model. The main problem with that approach however is that the filter does not learn about its bad model, it just puts more confidence in incoming measurements and less in the model. As a result the estimates will drift...... and the covariance grow rapidly between measurements causing these to be fused at a very high gain. This not only leads to a very ``bumpy'' behavior of the estimates and a high sensitivity to measurement noise but will also lead to large estimation errors in the absence of measurements. The taken approach offers...
A Kalman filter for a two-dimensional shallow-water model
Parrish, D. F.; Cohn, S. E.
1985-01-01
A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.
Multi-Sensor Optimal Data Fusion Based on the Adaptive Fading Unscented Kalman Filter
Directory of Open Access Journals (Sweden)
Bingbing Gao
2018-02-01
Full Text Available This paper presents a new optimal data fusion methodology based on the adaptive fading unscented Kalman filter for multi-sensor nonlinear stochastic systems. This methodology has a two-level fusion structure: at the bottom level, an adaptive fading unscented Kalman filter based on the Mahalanobis distance is developed and serves as local filters to improve the adaptability and robustness of local state estimations against process-modeling error; at the top level, an unscented transformation-based multi-sensor optimal data fusion for the case of N local filters is established according to the principle of linear minimum variance to calculate globally optimal state estimation by fusion of local estimations. The proposed methodology effectively refrains from the influence of process-modeling error on the fusion solution, leading to improved adaptability and robustness of data fusion for multi-sensor nonlinear stochastic systems. It also achieves globally optimal fusion results based on the principle of linear minimum variance. Simulation and experimental results demonstrate the efficacy of the proposed methodology for INS/GNSS/CNS (inertial navigation system/global navigation satellite system/celestial navigation system integrated navigation.
Hu, Shaoxing; Xu, Shike; Wang, Duhu; Zhang, Aiwu
2015-11-11
Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted "useful" data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency.
Directory of Open Access Journals (Sweden)
Shaoxing Hu
2015-11-01
Full Text Available Aiming at addressing the problem of high computational cost of the traditional Kalman filter in SINS/GPS, a practical optimization algorithm with offline-derivation and parallel processing methods based on the numerical characteristics of the system is presented in this paper. The algorithm exploits the sparseness and/or symmetry of matrices to simplify the computational procedure. Thus plenty of invalid operations can be avoided by offline derivation using a block matrix technique. For enhanced efficiency, a new parallel computational mechanism is established by subdividing and restructuring calculation processes after analyzing the extracted “useful” data. As a result, the algorithm saves about 90% of the CPU processing time and 66% of the memory usage needed in a classical Kalman filter. Meanwhile, the method as a numerical approach needs no precise-loss transformation/approximation of system modules and the accuracy suffers little in comparison with the filter before computational optimization. Furthermore, since no complicated matrix theories are needed, the algorithm can be easily transplanted into other modified filters as a secondary optimization method to achieve further efficiency.
Kobayashi, Takahisa; Simon, Donald L.
2004-01-01
In this paper, an approach for in-flight fault detection and isolation (FDI) of aircraft engine sensors based on a bank of Kalman filters is developed. This approach utilizes multiple Kalman filters, each of which is designed based on a specific fault hypothesis. When the propulsion system experiences a fault, only one Kalman filter with the correct hypothesis is able to maintain the nominal estimation performance. Based on this knowledge, the isolation of faults is achieved. Since the propulsion system may experience component and actuator faults as well, a sensor FDI system must be robust in terms of avoiding misclassifications of any anomalies. The proposed approach utilizes a bank of (m+1) Kalman filters where m is the number of sensors being monitored. One Kalman filter is used for the detection of component and actuator faults while each of the other m filters detects a fault in a specific sensor. With this setup, the overall robustness of the sensor FDI system to anomalies is enhanced. Moreover, numerous component fault events can be accounted for by the FDI system. The sensor FDI system is applied to a commercial aircraft engine simulation, and its performance is evaluated at multiple power settings at a cruise operating point using various fault scenarios.
Hesar, Hamed Danandeh; Mohebbi, Maryam
2017-05-01
In this paper, a model-based Bayesian filtering framework called the "marginalized particle-extended Kalman filter (MP-EKF) algorithm" is proposed for electrocardiogram (ECG) denoising. This algorithm does not have the extended Kalman filter (EKF) shortcoming in handling non-Gaussian nonstationary situations because of its nonlinear framework. In addition, it has less computational complexity compared with particle filter. This filter improves ECG denoising performance by implementing marginalized particle filter framework while reducing its computational complexity using EKF framework. An automatic particle weighting strategy is also proposed here that controls the reliance of our framework to the acquired measurements. We evaluated the proposed filter on several normal ECGs selected from MIT-BIH normal sinus rhythm database. To do so, artificial white Gaussian and colored noises as well as nonstationary real muscle artifact (MA) noise over a range of low SNRs from 10 to -5 dB were added to these normal ECG segments. The benchmark methods were the EKF and extended Kalman smoother (EKS) algorithms which are the first model-based Bayesian algorithms introduced in the field of ECG denoising. From SNR viewpoint, the experiments showed that in the presence of Gaussian white noise, the proposed framework outperforms the EKF and EKS algorithms in lower input SNRs where the measurements and state model are not reliable. Owing to its nonlinear framework and particle weighting strategy, the proposed algorithm attained better results at all input SNRs in non-Gaussian nonstationary situations (such as presence of pink noise, brown noise, and real MA). In addition, the impact of the proposed filtering method on the distortion of diagnostic features of the ECG was investigated and compared with EKF/EKS methods using an ECG diagnostic distortion measure called the "Multi-Scale Entropy Based Weighted Distortion Measure" or MSEWPRD. The results revealed that our proposed
A cascaded two-step Kalman filter for estimation of human body segment orientation using MEMS-IMU.
Zihajehzadeh, S; Loh, D; Lee, M; Hoskinson, R; Park, E J
2014-01-01
Orientation of human body segments is an important quantity in many biomechanical analyses. To get robust and drift-free 3-D orientation, raw data from miniature body worn MEMS-based inertial measurement units (IMU) should be blended in a Kalman filter. Aiming at less computational cost, this work presents a novel cascaded two-step Kalman filter orientation estimation algorithm. Tilt angles are estimated in the first step of the proposed cascaded Kalman filter. The estimated tilt angles are passed to the second step of the filter for yaw angle calculation. The orientation results are benchmarked against the ones from a highly accurate tactical grade IMU. Experimental results reveal that the proposed algorithm provides robust orientation estimation in both kinematically and magnetically disturbed conditions.
LIDAR-Aided Inertial Navigation with Extended Kalman Filtering for Pinpoint Landing
Busnardo, David M.; Aitken, Matthew L.; Tolson, Robert H.; Pierrottet, Diego; Amzajerdian, Farzin
2011-01-01
In support of NASA s Autonomous Landing and Hazard Avoidance Technology (ALHAT) project, an extended Kalman filter routine has been developed for estimating the position, velocity, and attitude of a spacecraft during the landing phase of a planetary mission. The proposed filter combines measurements of acceleration and angular velocity from an inertial measurement unit (IMU) with range and Doppler velocity observations from an onboard light detection and ranging (LIDAR) system. These high-precision LIDAR measurements of distance to the ground and approach velocity will enable both robotic and manned vehicles to land safely and precisely at scientifically interesting sites. The filter has been extensively tested using a lunar landing simulation and shown to improve navigation over flat surfaces or rough terrain. Experimental results from a helicopter flight test performed at NASA Dryden in August 2008 demonstrate that LIDAR can be employed to significantly improve navigation based exclusively on IMU integration.
Islam, Tariqul; Islam, Md. Saiful; Shajid-Ul-Mahmud, Md.; Hossam-E-Haider, Md
2017-12-01
An Attitude Heading Reference System (AHRS) provides 3D orientation of an aircraft (roll, pitch, and yaw) with instantaneous position and also heading information. For implementation of a low cost AHRS system Micro-electrical-Mechanical system (MEMS) based sensors are used such as accelerometer, gyroscope, and magnetometer. Accelerometers suffer from errors caused by external accelerations that sums to gravity and make accelerometers based rotation inaccurate. Gyroscopes can remove such errors but create drifting problems. So for getting the precise data additionally two very common and well known filters Complementary and Kalman are introduced to the system. In this paper a comparison of system performance using these two filters is shown separately so that one would be able to select filter with better performance for his/her system.
Kokkinaki, A.; Li, J. Y.; Zhou, Q.; Birkholzer, J. T.; Kitanidis, P. K.
2014-12-01
Carbon dioxide (CO2) storage in deep geologic formations is gaining ground as a potential measure for climate change mitigation. Such storage projects typically operate at large scales (~km), but their performance is often governed by smaller-scale (~m) heterogeneities. The large domain sizes prohibit detailed site characterization and dense monitoring networks, leading to predictions of CO2 migration and trapping based on rough geologic models that cannot capture preferential flow. Kalman Filtering can be used to improve these prior models by assimilating available monitoring data, thereby tracking system performance and reducing prediction uncertainty. However, for large systems with fine discretization, the number of unknowns is in the order of tens of thousands or more, in which case the textbook version of the Kalman Filter has prohibitively expensive computation and storage costs. We present the Compressed State Kalman Filter (CSKF) that can be effectively used for systems with a large number of unknowns to estimate the underlying heterogeneity and to predict the state of interest (e.g., pressure and CO2 saturation). The algorithm's computational efficiency is achieved by using a low-rank approximation of the covariance matrix, as well as a Jacobian-free approach. We demonstrate the estimation and computational performance of our method in a typical CO2 storage scenario with a spatially sparse monitoring network, but with multiple datasets obtained before and during CO2 injection. Our data assimilation framework provides an efficient and practical way to characterize geological formations intended for CO2 injection and storage using monitoring data commonly collected in field applications, as well as to quantify the reduction in uncertainty brought by different types of monitoring data.
Application of unscented Kalman filter for robust pose estimation in image-guided surgery
Vaccarella, Alberto; De Momi, Elena; Valenti, Marta; Ferrigno, Giancarlo; Enquobahrie, Andinet
2012-02-01
Image-guided surgery (IGS) allows clinicians to view current, intra-operative scenes superimposed on preoperative images (typically MRI or CT scans). IGS systems use localization systems to track and visualize surgical tools overlaid on top of preoperative images of the patient during surgery. The most commonly used localization systems in the Operating Rooms (OR) are optical tracking systems (OTS) due to their ease of use and cost effectiveness. However, OTS' suffer from the major drawback of line-of-sight requirements. State space approaches based on different implementations of the Kalman filter have recently been investigated in order to compensate for short line-of-sight occlusion. However, the proposed parameterizations for the rigid body orientation suffer from singularities at certain values of rotation angles. The purpose of this work is to develop a quaternion-based Unscented Kalman Filter (UKF) for robust optical tracking of both position and orientation of surgical tools in order to compensate marker occlusion issues. This paper presents preliminary results towards a Kalman-based Sensor Management Engine (SME). The engine will filter and fuse multimodal tracking streams of data. This work was motivated by our experience working in robot-based applications for keyhole neurosurgery (ROBOCAST project). The algorithm was evaluated using real data from NDI Polaris tracker. The results show that our estimation technique is able to compensate for marker occlusion with a maximum error of 2.5° for orientation and 2.36 mm for position. The proposed approach will be useful in over-crowded state-of-the-art ORs where achieving continuous visibility of all tracked objects will be difficult.
A Novel Fifth-Degree Cubature Kalman Filter for Real-Time Orbit Determination by Radar
Directory of Open Access Journals (Sweden)
Zhaoming Li
2017-01-01
Full Text Available A novel fifth-degree cubature Kalman filter is proposed to improve the accuracy of real-time orbit determination by ground-based radar. A fully symmetric cubature rule, approaching the Gaussian weighted integral of a nonlinear function in general form, is introduced, and the specific points and weights are calculated by matching the monomials of degree not greater than five with the exact values. On the basis of the above rule, a novel fifth-degree cubature Kalman filter, which can achieve a higher accuracy than UKF and CKF, is derived under the Bayesian filtering framework. Then, to describe the nonlinear system more accurately, the orbital dynamics equation with J2 perturbation is used as the state equation, and the nonlinear relationship between the radar measurement elements and orbital states is built as the measurement equation. The simulation results show that, compared with the traditional third-degree algorithm, the proposed fifth-degree algorithm has a higher accuracy of orbit determination.
Sadaghzadeh N, Nargess; Poshtan, Javad; Wagner, Achim; Nordheimer, Eugen; Badreddin, Essameddin
2014-03-01
Based on a cascaded Kalman-Particle Filtering, gyroscope drift and robot attitude estimation method is proposed in this paper. Due to noisy and erroneous measurements of MEMS gyroscope, it is combined with Photogrammetry based vision navigation scenario. Quaternions kinematics and robot angular velocity dynamics with augmented drift dynamics of gyroscope are employed as system state space model. Nonlinear attitude kinematics, drift and robot angular movement dynamics each in 3 dimensions result in a nonlinear high dimensional system. To reduce the complexity, we propose a decomposition of system to cascaded subsystems and then design separate cascaded observers. This design leads to an easier tuning and more precise debugging from the perspective of programming and such a setting is well suited for a cooperative modular system with noticeably reduced computation time. Kalman Filtering (KF) is employed for the linear and Gaussian subsystem consisting of angular velocity and drift dynamics together with gyroscope measurement. The estimated angular velocity is utilized as input of the second Particle Filtering (PF) based observer in two scenarios of stochastic and deterministic inputs. Simulation results are provided to show the efficiency of the proposed method. Moreover, the experimental results based on data from a 3D MEMS IMU and a 3D camera system are used to demonstrate the efficiency of the method. © 2013 ISA Published by ISA All rights reserved.
Delay Kalman Filter to Estimate the Attitude of a Mobile Object with Indoor Magnetic Field Gradients
Directory of Open Access Journals (Sweden)
Christophe Combettes
2016-05-01
Full Text Available More and more services are based on knowing the location of pedestrians equipped with connected objects (smartphones, smartwatches, etc.. One part of the location estimation process is attitude estimation. Many algorithms have been proposed but they principally target open space areas where the local magnetic field equals the Earth’s field. Unfortunately, this approach is impossible indoors, where the use of magnetometer arrays or magnetic field gradients has been proposed. However, current approaches omit the impact of past state estimates on the current orientation estimate, especially when a reference field is computed over a sliding window. A novel Delay Kalman filter is proposed in this paper to integrate this time correlation: the Delay MAGYQ. Experimental assessment, conducted in a motion lab with a handheld inertial and magnetic mobile unit, shows that the novel filter better estimates the Euler angles of the handheld device with an 11.7° mean error on the yaw angle as compared to 16.4° with a common Additive Extended Kalman filter.
GPS Interference Mitigation Using Derivative-free Kalman Filter-based RNN
Directory of Open Access Journals (Sweden)
W. L. Mao
2016-09-01
Full Text Available The global positioning system (GPS with accurate positioning and timing properties has become integral part of all applications around the world. Radio frequency interference can significantly decrease the performance of GPS receivers or even completely prohibit the acquisition or tracking of satellites. The approaches of system performances that can be further enhanced by preprocessing to reject the jamming signal will be investigated. A recurrent neural network (RNN predictor for the GPS anti-jamming applications will be proposed. The adaptive RNN predictor is utilized to accurately predict the narrowband waveform based on an unscented Kalman filter (UKF-based algorithm. The UKF algorithm as a derivative-free alternative to the extended Kalman filter (EKF in the framework of state-estimation is adopted to achieve better performance in terms of convergence rate and quality of solution. The adaptive RNN filter can be successfully applied for the suppression of interference with a number of different narrowband formats, i.e. continuous wave interference (CWI, multi-tone CWI, swept CWI and pulsed CWI, to emulate realistic circumstances. Simulation results show that the proposed UKF-based scheme can offer the superior performances to suppress the interference over the conventional methods by computing mean squared prediction error (MSPE and signal-to-noise ratio (SNR improvements.
Tracking and Data Relay Satellite (TDRS) Orbit Estimation Using an Extended Kalman Filter
Ward, Douglas T.; Dang, Ket D.; Slojkowski, Steve; Blizzard, Mike; Jenkins, Greg
2007-01-01
Alternatives to the Tracking and Data Relay Satellite (TDRS) orbit estimation procedure were studied to develop a technique that both produces more reliable results and is more amenable to automation than the prior procedure. The Earth Observing System (EOS) Terra mission has TDRS ephemeris prediction 3(sigma) requirements of 75 meters in position and 5.5 millimeters per second in velocity over a 1.5-day prediction span. Meeting these requirements sometimes required reruns of the prior orbit determination (OD) process, with manual editing of tracking data to get an acceptable solution. After a study of the available alternatives, the Flight Dynamics Facility (FDF) began using the Real-Time Orbit Determination (RTOD(Registered TradeMark)) Kalman filter program for operational support of TDRSs in February 2007. This extended Kalman filter (EKF) is used for daily support, including within hours after most thrusting, to estimate the spacecraft position, velocity, and solar radiation coefficient of reflectivity (C(sub R)). The tracking data used are from the Bilateration Ranging Transponder System (BRTS), selected TDRS System (TDRSS) User satellite tracking data, and Telemetry, Tracking, and Command (TT&C) data. Degraded filter results right after maneuvers and some momentum unloads provided incentive for a hybrid OD technique. The results of combining EKF strengths with the Goddard Trajectory Determination System (GTDS) Differential Correction (DC) program batch-least-squares solutions, as recommended in a 2005 paper on the chain-bias technique, are also presented.
Aircraft Engine Sensor/Actuator/Component Fault Diagnosis Using a Bank of Kalman Filters
Kobayashi, Takahisa; Simon, Donald L. (Technical Monitor)
2003-01-01
In this report, a fault detection and isolation (FDI) system which utilizes a bank of Kalman filters is developed for aircraft engine sensor and actuator FDI in conjunction with the detection of component faults. This FDI approach uses multiple Kalman filters, each of which is designed based on a specific hypothesis for detecting a specific sensor or actuator fault. In the event that a fault does occur, all filters except the one using the correct hypothesis will produce large estimation errors, from which a specific fault is isolated. In the meantime, a set of parameters that indicate engine component performance is estimated for the detection of abrupt degradation. The performance of the FDI system is evaluated against a nonlinear engine simulation for various engine faults at cruise operating conditions. In order to mimic the real engine environment, the nonlinear simulation is executed not only at the nominal, or healthy, condition but also at aged conditions. When the FDI system designed at the healthy condition is applied to an aged engine, the effectiveness of the FDI system is impacted by the mismatch in the engine health condition. Depending on its severity, this mismatch can cause the FDI system to generate incorrect diagnostic results, such as false alarms and missed detections. To partially recover the nominal performance, two approaches, which incorporate information regarding the engine s aging condition in the FDI system, will be discussed and evaluated. The results indicate that the proposed FDI system is promising for reliable diagnostics of aircraft engines.
Wavefront correction with Kalman filtering for the WFIRST-AFTA coronagraph instrument
Riggs, A. J. Eldorado; Kasdin, N. Jeremy; Groff, Tyler D.
2015-09-01
The only way to characterize most exoplanets spectrally is via direct imaging. For example, the Coronagraph Instrument (CGI) on the proposed Wide-Field Infrared Survey Telescope-Astrophysics Focused Telescope Assets (WFIRST-AFTA) mission plans to image and characterize several cool gas giants around nearby stars. The integration time on these faint exoplanets will be many hours to days. A crucial assumption for mission planning is that the time required to dig a dark hole (a region of high star-to-planet contrast) with deformable mirrors is small compared to science integration time. The science camera must be used as the wavefront sensor to avoid non-common path aberrations, but this approach can be quite time intensive. Several estimation images are required to build an estimate of the starlight electric field before it can be partially corrected, and this process is repeated iteratively until high contrast is reached. Here we present simulated results of batch process and recursive wavefront estimation schemes. In particular, we test a Kalman filter and an iterative extended Kalman filter (IEKF) to reduce the total exposure time and improve the robustness of wavefront correction for the WFIRST-AFTA CGI. An IEKF or other nonlinear filter also allows recursive, real-time estimation of sources incoherent with the star, such as exoplanets and disks, and may therefore reduce detection uncertainty.
Directory of Open Access Journals (Sweden)
Carlos D. Zuluaga-Ríos
2015-01-01
Full Text Available Heart rate variability (HRV has received considerable attention for many years, since it provides a quantitative marker for examining the sinus rhythm modulated by the autonomic nervous system (ANS. The ANS plays an important role in clinical and physiological fields. HRV analysis can be performed by computing several time and frequency domain measurements. However, the computation of such measurements can be affected by the presence of artifacts or ectopic beats in the electrocardiogram (ECG recording. This is particularly true for ECG recordings from Holter monitors. The aim of this work was to study the performance of several robust Kalman filters for artifact correction in Inter-beat (RR interval time series. For our experiments, two data sets were used: the first data set included 10 RR interval time series from a realistic RR interval time series generator. The second database contains 10 sets of RR interval series from five healthy patients and five patients suffering from congestive heart failure. The standard deviation of the RR interval was computed over the filtered signals. Results were compared with a state of the art processing software, showing similar values and behavior. In addition, the proposed methods offer satisfactory results in contrast to standard Kalman filtering.
Directory of Open Access Journals (Sweden)
P. A. Ermolaev
2014-03-01
Full Text Available Data processing in the interferometer systems requires high-resolution and high-speed algorithms. Recurrence algorithms based on parametric representation of signals execute consequent processing of signal samples. In some cases recurrence algorithms make it possible to increase speed and quality of data processing as compared with classic processing methods. Dependence of the measured interferometer signal on parameters of its model and stochastic nature of noise formation in the system is, in general, nonlinear. The usage of nonlinear stochastic filtering algorithms is expedient for such signals processing. Extended Kalman filter with linearization of state and output equations by the first vector parameters derivatives is an example of these algorithms. To decrease approximation error of this method the second order extended Kalman filtering is suggested with additionally usage of the second vector parameters derivatives of model equations. Examples of algorithm implementation with the different sets of estimated parameters are described. The proposed algorithm gives the possibility to increase the quality of data processing in interferometer systems in which signals are forming according to considered models. Obtained standard deviation of estimated amplitude envelope does not exceed 4% of the maximum. It is shown that signal-to-noise ratio of reconstructed signal is increased by 60%.
A New Adaptive Square-Root Unscented Kalman Filter for Nonlinear Systems with Additive Noise
Directory of Open Access Journals (Sweden)
Yong Zhou
2015-01-01
Full Text Available The Kalman filter (KF, extended KF, and unscented KF all lack a self-adaptive capacity to deal with system noise. This paper describes a new adaptive filtering approach for nonlinear systems with additive noise. Based on the square-root unscented KF (SRUKF, traditional Maybeck’s estimator is modified and extended to nonlinear systems. The square root of the process noise covariance matrix Q or that of the measurement noise covariance matrix R is estimated straightforwardly. Because positive semidefiniteness of Q or R is guaranteed, several shortcomings of traditional Maybeck’s algorithm are overcome. Thus, the stability and accuracy of the filter are greatly improved. In addition, based on three different nonlinear systems, a new adaptive filtering technique is described in detail. Specifically, simulation results are presented, where the new filter was applied to a highly nonlinear model (i.e., the univariate nonstationary growth model (UNGM. The UNGM is compared with the standard SRUKF to demonstrate its superior filtering performance. The adaptive SRUKF (ASRUKF algorithm can complete direct recursion and calculate the square roots of the variance matrixes of the system state and noise, which ensures the symmetry and nonnegative definiteness of the matrixes and greatly improves the accuracy, stability, and self-adaptability of the filter.
A Quantised State Systems Approach for Jacobian Free Extended Kalman Filtering
DEFF Research Database (Denmark)
Alminde, Lars; Bendtsen, Jan Dimon; Stoustrup, Jakob
2007-01-01
Model based methods for control of intelligent autonomous systems rely on a state estimate being available. One of the most common methods to obtain a state estimate for non-linear systems is the Extended Kalman Filter (EKF) algorithm. In order to apply the EKF an expression must be available...... for the Jacobian of the driving function; for complex systems this can be difficult to obtain. This paper presents an EKF variation that makes use of integrated quantised state simulation to propagate the state and obtain a backward difference estimate of the Jacobian at a small computational cost. A simulation...... case study involving a deep space probe is presented....
On Convergence of the Unscented Kalman-Bucy Filter using Contraction Theory
DEFF Research Database (Denmark)
Maree, J.P.; Imsland, Lars; Jouffroy, Jerome
2016-01-01
Contraction theory entails a theoretical framework in which convergence of a nonlinear system can be analysed differentially in an appropriate contraction metric. This paper is concerned with utilizing stochastic contraction theory to conclude on exponential convergence of the Unscented Kalman......-Bucy Filter. The underlying process and measurement models of interest are Itô-type stochastic differential equations. In particular, statistical linearisation techniques are employed in a virtual-actual systems framework to establish deterministic contraction of the estimated expected mean of process values...
Galvan, Jose Ramon; Saxena, Abhinav; Goebel, Kai Frank
2012-01-01
This article discusses several aspects of uncertainty representation and management for model-based prognostics methodologies based on our experience with Kalman Filters when applied to prognostics for electronics components. In particular, it explores the implications of modeling remaining useful life prediction as a stochastic process, and how it relates to uncertainty representation, management and the role of prognostics in decision-making. A distinction between the interpretations of estimated remaining useful life probability density function is explained and a cautionary argument is provided against mixing interpretations for two while considering prognostics in making critical decisions.
Directory of Open Access Journals (Sweden)
Meherdad Jafarboland
2010-07-01
Full Text Available Permanent Magnet Synchronous Machines (PMSM are increasingly used because of their advantages over other machines, which include compactness, high efficiency, and well developed drives.. The substitution of the position sensors by advanced algorithms embedded in the controls hardware and software has been investigated for the last couple of decades. This Paper presents the modeling, analysis, design and experimental validation of a robust sensor less control method for PMSM based on Extended Kalman Filter. The position/speed sensor less control scheme along with the power electronic circuitry is modeled. The performance of the proposed control is assessed and verified for different types of dynamic and static torque loads.
The Performance of A Sampled Data Delay Lock Loop Implemented with a Kalman Loop Filter.
1980-01-01
terms to yield nearly zero determinants result in a loss of significant bits in the computation. If the machine precision (i.e., word length) is not...STEADY (Appendix V) is structured to make extensive use of subroutines. Because the input signal to the Kalman filters is the difference between the time...P 19 SET I z/ JSOP I t A [J 1-7 EP " I SOT HE!’ AI LG OP SST rk SIP(E. ASTP 82 Appendix VI The Computer Program TRNS L’ **~~ * ***,&**PP0C’iA-! TkA
Fast Bayesian reconstruction of chaotic dynamical systems via extended Kalman filtering
Meyer, Renate; Christensen, Nelson
2002-01-01
We present an improved Markov chain Monte Carlo (MCMC) algorithm for posterior computation in chaotic dynamical systems. Recent Bayesian approaches to estimate the parameters of chaotic maps have used the Gibbs sampler which exhibits slow convergence due to high posterior correlations. Using the extended Kalman filter to compute the likelihood function by integrating out all unknown system states, we obtain a very efficient MCMC technique. We compare the new algorithm to the Gibbs sampler using the logistic, the tent, and the Moran-Ricker maps as applications, measuring the performance in terms of CPU and integrated autocorrelation time.
Removal of jitter noise in 3D shape recovery from image focus by using Kalman filter.
Jang, Hoon-Seok; Muhammad, Mannan Saeed; Choi, Tae-Sun
2018-02-01
In regard to Shape from Focus, one critical factor impacting system application is mechanical vibration of the translational stage causing jitter noise along the optical axis. This noise is not detectable by simply observing the image. However, when focus measures are applied, inaccuracies in the depth occur. In this article, jitter noise and focus curves are modeled by Gaussian distribution and quadratic function, respectively. Then Kalman filter is designed and applied to eliminate this noise in the focus curves, as a post-processing step after the focus measure application. Experiments are implemented with simulated objects and real objects to show usefulness of proposed algorithm. © 2017 Wiley Periodicals, Inc.
Bonnet, V; Dumas, R; Cappozzo, A; Joukov, V; Daune, G; Kulić, D; Fraisse, P; Andary, S; Venture, G
2017-09-06
This paper presents a method for real-time estimation of the kinematics and kinetics of a human body performing a sagittal symmetric motor task, which would minimize the impact of the stereophotogrammetric soft tissue artefacts (STA). The method is based on a bi-dimensional mechanical model of the locomotor apparatus the state variables of which (joint angles, velocities and accelerations, and the segments lengths and inertial parameters) are estimated by a constrained extended Kalman filter (CEKF) that fuses input information made of both stereophotogrammetric and dynamometric measurement data. Filter gains are made to saturate in order to obtain plausible state variables and the measurement covariance matrix of the filter accounts for the expected STA maximal amplitudes. We hypothesised that the ensemble of constraints and input redundant information would allow the method to attenuate the STA propagation to the end results. The method was evaluated in ten human subjects performing a squat exercise. The CEKF estimated and measured skin marker trajectories exhibited a RMS difference lower than 4mm, thus in the range of STAs. The RMS differences between the measured ground reaction force and moment and those estimated using the proposed method (9N and 10Nm) were much lower than obtained using a classical inverse dynamics approach (22N and 30Nm). From the latter results it may be inferred that the presented method allows for a significant improvement of the accuracy with which kinematic variables and relevant time derivatives, model parameters and, therefore, intersegmental moments are estimated. Copyright © 2016 Elsevier Ltd. All rights reserved.
National Research Council Canada - National Science Library
Salman, H
2008-01-01
.... To illustrate the main advantages of our formulation over existing filters, we compare our method to the perturbed observation Ensemble Kalman filter and a particle filter with Gaussian resampling...
Leroux, Romain; Chatellier, Ludovic; David, Laurent
2018-01-01
This article is devoted to the estimation of time-resolved particle image velocimetry (TR-PIV) flow fields using a time-resolved point measurements of a voltage signal obtained by hot-film anemometry. A multiple linear regression model is first defined to map the TR-PIV flow fields onto the voltage signal. Due to the high temporal resolution of the signal acquired by the hot-film sensor, the estimates of the TR-PIV flow fields are obtained with a multiple linear regression method called orthonormalized partial least squares regression (OPLSR). Subsequently, this model is incorporated as the observation equation in an ensemble Kalman filter (EnKF) applied on a proper orthogonal decomposition reduced-order model to stabilize it while reducing the effects of the hot-film sensor noise. This method is assessed for the reconstruction of the flow around a NACA0012 airfoil at a Reynolds number of 1000 and an angle of attack of {20}°. Comparisons with multi-time delay-modified linear stochastic estimation show that both the OPLSR and EnKF combined with OPLSR are more accurate as they produce a much lower relative estimation error, and provide a faithful reconstruction of the time evolution of the velocity flow fields.
Dreano, Denis
2015-04-27
A statistical model is proposed to filter satellite-derived chlorophyll concentration from the Red Sea, and to predict future chlorophyll concentrations. The seasonal trend is first estimated after filling missing chlorophyll data using an Empirical Orthogonal Function (EOF)-based algorithm (Data Interpolation EOF). The anomalies are then modeled as a stationary Gaussian process. A method proposed by Gneiting (2002) is used to construct positive-definite space-time covariance models for this process. After choosing an appropriate statistical model and identifying its parameters, Kriging is applied in the space-time domain to make a one step ahead prediction of the anomalies. The latter serves as the prediction model of a reduced-order Kalman filter, which is applied to assimilate and predict future chlorophyll concentrations. The proposed method decreases the root mean square (RMS) prediction error by about 11% compared with the seasonal average.