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
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.
Stubberud, Allen R.
2017-01-01
When considering problems of linear sequential estimation, two versions of the Kalman filter, the continuous-time version and the discrete-time version, are often used. (A hybrid filter also exists.) In many applications in which the Kalman filter is used, the system to which the filter is applied is a linear continuous-time system, but the Kalman filter is implemented on a digital computer, a discrete-time device. The two general approaches for developing a discrete-time filter for implementation on a digital computer are: (1) approximate the continuous-time system by a discrete-time system (called discretization of the continuous-time system) and develop a filter for the discrete-time approximation; and (2) develop a continuous-time filter for the system and then discretize the continuous-time filter. Generally, the two discrete-time filters will be different, that is, it can be said that discretization and filter generation are not, in general, commutative operations. As a result, any relationship between the discrete-time and continuous-time versions of the filter for the same continuous-time system is often obfuscated. This is particularly true when an attempt is made to generate the continuous-time version of the Kalman filter through a simple limiting process (the sample period going to zero) applied to the discrete-time version. The correct result is, generally, not obtained. In a 1961 research report, Kalman showed that the continuous-time Kalman filter can be obtained from the discrete-time Kalman filter by taking limits as the sample period goes to zero if the white noise process for the continuous-time version is appropriately defined. Using this basic concept, a discrete-time Kalman filter can be developed for a continuous-time system as follows: (1) discretize the continuous-time system using Kalman's technique; and (2) develop a discrete-time Kalman filter for that discrete-time system. Kalman's results show that the discrete-time filter generated in
Brad Baxter; Liam Graham; Stephen Wright
2007-01-01
We relax the assumption of full information that underlies most dynamic general equilibrium models, and instead assume agents optimally form estimates of the states from an incomplete information set. We derive a version of the Kalman filter that is endogenous to agents' optimising decisions, and state conditions for its convergence. We show the (restrictive) conditions under which the endogenous Kalman filter will at least asymptotically reveal the true states. In general we show that incomp...
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.
DEFF Research Database (Denmark)
Drecourt, J.-P.; Madsen, H.; Rosbjerg, Dan
2006-01-01
. The colored noise filter formulation is extended to correct both time correlated and uncorrelated model error components. A more stable version of the separate filter without feedback is presented. The filters are implemented in an ensemble framework using Latin hypercube sampling. The techniques...... are illustrated on a simple one-dimensional groundwater problem. The results show that the presented filters outperform the standard Kalman filter and that the implementations with bias feedback work in more general conditions than the implementations without feedback. 2005 Elsevier Ltd. All rights reserved....
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.
Tracking speckle displacement by double Kalman filtering
Institute of Scientific and Technical Information of China (English)
Donghui Li; Li Guo
2006-01-01
@@ A tracking technique using two sequentially-connected Kalman filter for tracking laser speckle displacement is presented. One Kalman filter tracks temporal speckle displacement, while another Kalman filter tracks spatial speckle displacement. The temporal Kalman filter provides a prior for the spatial Kalman filter, and the spatial Kalman filter provides measurements for the temporal Kalman filter. The contribution of a prior to estimations of the spatial Kalman filter is analyzed. An optical analysis system was set up to verify the double-Kalman-filter tracker's ability of tracking laser speckle's constant displacement.
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.
Robust Kriged Kalman Filtering
Energy Technology Data Exchange (ETDEWEB)
Baingana, Brian; Dall' Anese, Emiliano; Mateos, Gonzalo; Giannakis, Georgios B.
2015-11-11
Although the kriged Kalman filter (KKF) has well-documented merits for prediction of spatial-temporal processes, its performance degrades in the presence of outliers due to anomalous events, or measurement equipment failures. This paper proposes a robust KKF model that explicitly accounts for presence of measurement outliers. Exploiting outlier sparsity, a novel l1-regularized estimator that jointly predicts the spatial-temporal process at unmonitored locations, while identifying measurement outliers is put forth. Numerical tests are conducted on a synthetic Internet protocol (IP) network, and real transformer load data. Test results corroborate the effectiveness of the novel estimator in joint spatial prediction and outlier identification.
Kalman filtering implementation with Matlab
Kleinbauer, Rachel
2004-01-01
1960 und 1961 veröffentlichte Rudolf Emil Kalmen seine Arbeiten über einen rekursiven prädiktiven Filter, der auf dem Gebrauch von rekursiven Algorithmen basiert. Damit revolutionierte er das Feld der Schätzverfahren. Seitdem ist der sogenannte Kalman Filter Gegenstand ausführlicher Forschung und findet bis heute Anwendung in zahlreichen Gebieten. Der Kalman Filter schätzt den Zustand eines dynamischen Systems, auch wenn die exakte Form dieses Systems unbekannt ist. Der Filter ist sehr lei...
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.
A mollified Ensemble Kalman filter
Bergemann, Kay
2010-01-01
It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high frequency adjustment processes in the model dynamics. Various methods have been devised to continuously spread out the analysis increments over a fixed time interval centered about analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow-fast extension of the popular Lorenz-96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter.
Indirect Kalman Filter in Mobile Robot Application
Directory of Open Access Journals (Sweden)
Surachai Panich
2010-01-01
Full Text Available Problem statement: The most successful applications of Kalman filtering are to linearize about some nominal trajectory in state space that does not depend on the measurement data. The resulting filter is usually referred to as simply a linearized Kalman filter. Approach: This study introduced mainly indirect Kalman filter to estimate robots position. A developed differential encoder system integrated accelerometer is experimental tested in square shape. Results: Experimental results confirmed that indirect Kalman filter improves the accuracy and confidence of position estimation. Conclusion: In summary, we concluded that indirect Kalman filter has good potential to reduce error of measurement data.
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.
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
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 distributi
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...
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.
A Recursive Kalman Filter Forecasting Approach
Douglas R. Kahl; Johannes Ledolter
1983-01-01
This paper examines the forecasting accuracy and the cost effectiveness of time series models with time-varying coefficients. A simulation study investigates the potential forecasting benefits of a proposed Kalman filter type adaptive estimation and forecasting approach. It is found that: (1) When appropriate, the time-varying coefficient approach leads to better forecasts than the constant coefficient procedures. (2) A simple decision rule, which indicates whether time-varying coefficient mo...
Implementation of Kalman Filter with Python Language
Laaraiedh, Mohamed
2012-01-01
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.
Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters
Hoteit, Ibrahim; Pham, Dinh-Tuan
2011-01-01
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. We 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, we consider the construction of the PKF through an "ensemble" of ensemble Kalman filters (EnKFs) instead, ...
Kullback-Leibler Divergence Approach to Partitioned Update Kalman Filter
Raitoharju, Matti; García-Fernández, Ángel F.; Piché, Robert
2016-01-01
Kalman filtering is a widely used framework for Bayesian estimation. The partitioned update Kalman filter applies a Kalman filter update in parts so that the most linear parts of measurements are applied first. In this paper, we generalize partitioned update Kalman filter, which requires the use oft the second order extended Kalman filter, so that it can be used with any Kalman filter extension. To do so, we use a Kullback-Leibler divergence approach to measure the nonlinearity of the measure...
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.
Motion estimation using point cluster method and Kalman filter.
Senesh, M; Wolf, A
2009-05-01
The most frequently used method in a three dimensional human gait analysis involves placing markers on the skin of the analyzed segment. This introduces a significant artifact, which strongly influences the bone position and orientation and joint kinematic estimates. In this study, we tested and evaluated the effect of adding a Kalman filter procedure to the previously reported point cluster technique (PCT) in the estimation of a rigid body motion. We demonstrated the procedures by motion analysis of a compound planar pendulum from indirect opto-electronic measurements of markers attached to an elastic appendage that is restrained to slide along the rigid body long axis. The elastic frequency is close to the pendulum frequency, as in the biomechanical problem, where the soft tissue frequency content is similar to the actual movement of the bones. Comparison of the real pendulum angle to that obtained by several estimation procedures--PCT, Kalman filter followed by PCT, and low pass filter followed by PCT--enables evaluation of the accuracy of the procedures. When comparing the maximal amplitude, no effect was noted by adding the Kalman filter; however, a closer look at the signal revealed that the estimated angle based only on the PCT method was very noisy with fluctuation, while the estimated angle based on the Kalman filter followed by the PCT was a smooth signal. It was also noted that the instantaneous frequencies obtained from the estimated angle based on the PCT method is more dispersed than those obtained from the estimated angle based on Kalman filter followed by the PCT method. Addition of a Kalman filter to the PCT method in the estimation procedure of rigid body motion results in a smoother signal that better represents the real motion, with less signal distortion than when using a digital low pass filter. Furthermore, it can be concluded that adding a Kalman filter to the PCT procedure substantially reduces the dispersion of the maximal and minimal
Estimation of Kalman filter gain from output residuals
Juang, Jer-Nan; Chen, Chung-Wen; Phan, Minh
1993-01-01
This paper presents a procedure to estimate the Kalman filter gain from input-output measurement data with a given system model. The system model can be a finite element model or an experimental model from any identification method. The procedure consists of three basic steps. First, the stochastic portion related to the residuals of the response is computed. Second, the coefficients of a linear difference model for the stochastic portion are estimated by a least-squares solution that minimizes the filter residual. Third, the Kalman filter gain is computed from these model coefficients. Experimental results are presented to illustrate the usefulness of the developed procedure.
Kalman-Takens filtering in the presence of dynamical noise
Hamilton, Franz; Sauer, Timothy
2016-01-01
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. We find that this hybrid approach results in comparable efficiency to parametric methods in identifying underlying dynamics, even in the presence of dynamical noise. 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 w...
Spectral diagonal ensemble Kalman filters
Kasanický, Ivan; Vejmelka, Martin
2015-01-01
A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields, which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT) and discrete wavelet transform (DWT) are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles.
Unscented Kalman filter for SINS alignment
Institute of Scientific and Technical Information of China (English)
Zhou Zhanxin; Gao Yanan; Chen Jiabin
2007-01-01
In order to improve the filter accuracy for the nonlinear error model of strapdown inertial navigation system (SINS) alignment, Unscented Kalman Filter (UKF) is presented for simulation with stationary base and moving base of SINS alignment.Simulation results show the superior performance of this approach when compared with classical suboptimal techniques such as extended Kalman filter in cases of large initial misalignment.The UKF has good performance in case of small initial misalignment.
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.
Hierarchical Bayes Ensemble Kalman Filtering
Tsyrulnikov, Michael
2015-01-01
Ensemble Kalman filtering (EnKF), when applied to high-dimensional systems, suffers from an inevitably small affordable ensemble size, which results in poor estimates of the background error covariance matrix ${\\bf B}$. The common remedy is a kind of regularization, usually an ad-hoc spatial covariance localization (tapering) combined with artificial covariance inflation. Instead of using an ad-hoc regularization, we adopt the idea by Myrseth and Omre (2010) and explicitly admit that the ${\\bf B}$ matrix is unknown and random and estimate it along with the state (${\\bf x}$) in an optimal hierarchical Bayes analysis scheme. We separate forecast errors into predictability errors (i.e. forecast errors due to uncertainties in the initial data) and model errors (forecast errors due to imperfections in the forecast model) and include the two respective components ${\\bf P}$ and ${\\bf Q}$ of the ${\\bf B}$ matrix into the extended control vector $({\\bf x},{\\bf P},{\\bf Q})$. Similarly, we break the traditional backgrou...
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......Most power electronic equipment these days generate harmonic disturbances, these devices hold nonlinear voltage/current characteristic. The harmonics generated can potentially be harmful to the consumer supply. Typically, filters are integrated at the power source or utility location to filter out...
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.
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.
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 implemente
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 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.
Deconvolution Kalman filtering for force measurements of revolving wings
Vester, R.; Percin, M.; van Oudheusden, B.
2016-09-01
The applicability of a deconvolution Kalman filtering approach is assessed for the force measurements on a flat plate undergoing a revolving motion, as an alternative procedure to correct for test setup vibrations. The system identification process required for the correct implementation of the deconvolution Kalman filter is explained in detail. It is found that in the presence of a relatively complex forcing history, the DK filter is better suited to filter out structural test rig vibrations than conventional filtering techniques that are based on, for example, low-pass or moving-average filtering. The improvement is especially found in the characterization of the generated force peaks. Consequently, more reliable force data is obtained, which is vital to validate semi-empirical estimation models, but is also relevant to correlate identified flow phenomena to the force production.
A numerical storm surge forecast model with Kalman filter
Institute of Scientific and Technical Information of China (English)
Yu Fujiang; Zhang Zhanhai; Lin Yihua
2001-01-01
Kalman filter data assimilation technique is incorporated into a standard two-dimensional linear storm surge model. Imperfect model equation and imperfect meteorological forcimg are accounted for by adding noise terms to the momentum equations. The deterministic model output is corrected by using the available tidal gauge station data. The stationary Kalman filter algorithm for the model domain is calculated by an iterative procedure using specified information on the inaccuracies in the momentum equations and specified error information for the observations. An application to a real storm surge that occurred in the summer of 1956 in the East China Sea is performed by means of this data assimilation technique. The result shows that Kalman filter is useful for storm surge forecast and hindcast.
Design of Kalman filters for mobile robots
DEFF Research Database (Denmark)
Larsen, Thomas Dall; Hansen, Karsten L.; Andersen, Nils Axel
1999-01-01
Kalman filters have for a long time been widely used on mobile robots as a location estimator. Many different Kalman filter designs have been proposed, using models of various complexity. In this paper, two different design methods are evaluated and compared. Focus is put on the common setup where...... 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...
Distributed Kalman Filter via Gaussian Belief Propagation
Bickson, Danny; Dolev, Danny
2008-01-01
Recent result shows how to compute distributively and efficiently the linear MMSE for the multiuser detection problem, using the Gaussian BP algorithm. In the current work, we extend this construction, and show that operating this algorithm twice on the matching inputs, has several interesting interpretations. First, we show equivalence to computing one iteration of the Kalman filter. Second, we show that the Kalman filter is a special case of the Gaussian information bottleneck algorithm, when the weight parameter $\\beta = 1$. Third, we discuss the relation to the Affine-scaling interior-point method and show it is a special case of Kalman filter. Besides of the theoretical interest of this linking estimation, compression/clustering and optimization, we allow a single distributed implementation of those algorithms, which is a highly practical and important task in sensor and mobile ad-hoc networks. Application to numerous problem domains includes collaborative signal processing and distributed allocation of ...
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 estimation model in flood forecasting
Husain, Tahir
Elementary precipitation and runoff estimation problems associated with hydrologic data collection networks are formulated in conjunction with the Kalman Filter Estimation Model. Examples involve the estimation of runoff using data from a single precipitation station and also from a number of precipitation stations. The formulations demonstrate the role of state-space, measurement, and estimation equations of the Kalman Filter Model in flood forecasting. To facilitate the formulation, the unit hydrograph concept and antecedent precipitation index is adopted in the estimation model. The methodology is then applied to estimate various flood events in the Carnation Creek of British Columbia.
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 that of the particle filter. We analyze the cross section of swap rates, which are mildly nonlinear in the states, and cap prices, which are highly nonlinear. When caps are used to filter the states, the unscented Kalman filter significantly outperforms its extended counterpart. The unscented Kalman filter also...
RAPID TRANSFER ALIGNMENT USING FEDERATED KALMAN FILTER
Institute of Scientific and Technical Information of China (English)
GUDong-qing; QINYong-yuan; PENGRong; LIXin
2005-01-01
The dimension number of the centralized Kalman filter (CKF) for the rapid transfer alignment (TA) is as high as 21 if the aircraft wing flexure motion is considered in the rapid TA. The 21-dimensional CKF brings the calculation burden on the computer and the difficulty to meet a high filtering updating rate desired by rapid TA. The federated Kalman filter (FKF) for the rapid TA is proposed to solve the dilemma. The structure and the algorithm of the FKF, which can perform parallel computation and has less calculation burden, are designed.The wing flexure motion is modeled, and then the 12-order velocity matching local filter and the 15-order attitud ematching local filter are devised. Simulation results show that the proposed EKE for the rapid TA almost has the same performance as the CKF. Thus the calculation burden of the proposed FKF for the rapid TA is markedly decreased.
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....
Reduced-order Kalman filtering with incomplete observability
Yonezawa, K.
1980-01-01
Kalman filtering is considered with reference to linear stochastic dynamic systems without complete observability. It is shown that the canonical decomposition theorem can be extended to the stochastic case and the matrix Riccati equation of the Kalman filter is order-reducible if some states are not observable. The inclusion of unobservable states in Kalman filtering makes the unobservable states 'asymptotically' observable in the filter if these unobservable states are dynamically connected to observable states and asymptotically stable. The reduced-order Kalman filter saves computation time when compared to the conventional Kalman filter.
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...
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, communica
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...
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.
Selection of noise parameters for Kalman filter
Institute of Scientific and Technical Information of China (English)
Ka-Veng Yuen; Ka-In Hoi; Kai-Meng Mok
2007-01-01
The Bayesian probabilistic approach is proposed to estimate the process noise and measurement noise parameters for a Kalman filter. With state vectors and covariance matrices estimated by the Kalman filter, the likehood of the measurements can be constructed as a function of the process noise and measurement noise parameters. By maximizing the likklihood function with respect to these noise parameters, the optimal values can be obtained. Furthermore, the Bayesian probabilistic approach allows the associated uncertainty to be quantified. Examples using a single-degree-of-freedom system and a ten-story building illustrate the proposed method. The effect on the performance of the Kalman filter due to the selection of the process noise and measurement noise parameters was demonstrated. The optimal values of the noise parameters were found to be close to the actual values in the sense that the actual parameters were in the region with significant probability density. Through these examples, the Bayesian approach was shown to have the capability to provide accurate estimates of the noise parameters of the Kalman filter, and hence for state estimation.
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
Steady-State Performance of Kalman Filter for DPLL
Institute of Scientific and Technical Information of China (English)
QIAN Yi; CUI Xiaowei; LU Mingquan; FENG Zhenming
2009-01-01
For certain system models, the structure of the Kalman filter is equivalent to a second-order vari-able gain digital phase-locked loop (DPLL). To apply the knowledge of DPLLs to the design of Kalman filters, this paper studies the steady-state performance of Kalman filters for these system models. The results show that the steady-state Kalman gain has the same form as the DPLL gain. An approximate simple form for the steady-state Kalman gain is used to derive an expression for the equivalent loop bandwidth of the Kalman filter as a function of the process and observation noise variances. These results can be used to analyze the steady-state performance of a Kalman filter with DPLL theory or to design a Kalman filter model with the same steady-state performance as a given DPLL.
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].
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.
Institute of Scientific and Technical Information of China (English)
Kailei Liu; Zhijia Li; Cheng Yao; Ji Chen; Ke Zhang; Muhammad Saifullah
2016-01-01
The Kalman filter (KF) updating method has been widely used as an efficient measure to assimilate real-time hydrological variables for reducing forecast uncertainty and providing improved forecasts. However, the accuracy of the KF relies much on the estimates of the state transition matrix and is limited due to the errors inherit from parameters and variables of the flood forecasting models. A new real-time updating approach (named KN2K) is produced by coupling the k-nearest neighbor (KNN) procedure with the KF for flood forecasting models. The nonparametric KNN algorithm, which can be utilized to predict the response of a system on the basis of the k most representative predictors, is still efficient when the descriptions for input-output mapping are insufficient. In this study, the KNN procedure is used to provide more accurate estimates of the state transition matrix to extend the applicability of the KF. The updating performance of KN2K is investigated in the middle reach of the Huai River based on a one-dimensional hydraulic model with the lead times ranging from 2 to 12 h. The forecasts from the KN2K are compared with the observations, the original forecasts and the KF-updated forecasts. The results indicate that the KN2K method, with the Nash-Sutcliffe efficiency larger than 0.85 in the 12-h-ahead forecasts, has a significant advantage in accuracy and robustness compared to the KF method. It is demonstrated that improved updating results can be obtained through the use of KNN procedure. The tests show that the KN2K method can be used as an effective tool for real-time flood forecasting.
Adaptive Federal Kalman Filtering for SINS/GPS Integrated System
Institute of Scientific and Technical Information of China (English)
杨勇; 缪玲娟
2003-01-01
A new adaptive federal Kalman filter for a strapdown integrated navigation system/global positioning system (SINS/GPS) is given. The developed federal Kalman filter is based on the trace operation of parameters estimation's error covariance matrix and the spectral radius of update measurement noise variance-covariance matrix for the proper choice of the filter weight and hence the filter gain factors. Theoretical analysis and results from simulation in which the SINS/GPS was compared to conventional Kalman filter are presented. Results show that the algorithm of this adaptive federal Kalman filter is simpler than that of the conventional one. Furthermore, it outperforms the conventional Kalman filter when the system is undertaken measurement malfunctions because of its possession of adaptive ability. This filter can be used in the vehicle integrated navigation system.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.
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.
An introduction to Kalman filtering with Matlab examples
Kovvali, Narayan; Spanias, Andreas
2013-01-01
The Kalman filter is the Bayesian optimum solution to the problem of sequentially estimating the states of a dynamical system in which the state evolution and measurement processes are both linear and Gaussian. Given the ubiquity of such systems, the Kalman filter finds use in a variety of applications, e.g., target tracking, guidance and navigation, and communications systems. The purpose of this book is to present a brief introduction to Kalman filtering. The theoretical framework of the Kalman filter is first presented, followed by examples showing its use in practical applications. Extensi
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.
A new iterative speech enhancement scheme based on Kalman filtering
DEFF Research Database (Denmark)
Li, Chunjian; Andersen, Søren Vang
2005-01-01
Subtraction filter is introduced as an initialization procedure. Iterations are then made sequential inter-frame, exploiting the fact that the AR model changes slowly between neighboring frames. The proposed algorithm is computationally more efficient than a baseline EM algorithm due to its fast convergence...... 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...
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......./current characteristic. These harmonics are not to be allowed to grow beyond a certain limit to avoid any grave consequence to the customer’s main supply. Filters can be implemented at the power source or utility location to eliminate these harmonics. In this paper we detect the instance at which these harmonics occur...
Ensemble-based Kalman Filters in Strongly Nonlinear Dynamics
Institute of Scientific and Technical Information of China (English)
Zhaoxia PU; Joshua HACKER
2009-01-01
This study examines the effectiveness of ensemble Kalman filters in data assimilation with the strongly nonlinear dynamics of the Lorenz-63 model, and in particular their use in predicting the regime transition that occurs when the model jumps from one basin of attraction to the other. Four configurations of the ensemble-based Kalman filtering data assimilation techniques, including the ensemble Kalman filter, ensemble adjustment Kalman filter, ensemble square root filter and ensemble transform Kalman filter, are evaluated with their ability in predicting the regime transition (also called phase transition) and also are compared in terms of their sensitivity to both observational and sampling errors. The sensitivity of each ensemble-based filter to the size of the ensemble is also examined.
Suboptimal distributed Kalman filtering fusion with feedback
Institute of Scientific and Technical Information of China (English)
Zhao Minhua; Zhu Zhuanmin; Shi Meng; Peng Qinke; Huang Yongxuan
2005-01-01
In order to improve the accuracy of fusion algorithm, feedback is introduced into Kalman filtering fusion. Fusion center broadcasts its latest estimated states to the local sensors, which can improve the performance of local tracking error through reducing the covariance of each local error, and only needs calculating the trace of error variance matrices without calculating the inverse of error variance matrices. Simulation results show that it can reduce the computational complexity and the covariance of error, and it is convenient for engineering applications.
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.
SIMULASI FILTER KALMAN UNTUK ESTIMASI SUDUT DENGAN MENGGUNAKAN SENSOR GYROSCOPE
Directory of Open Access Journals (Sweden)
Wahyudi Wahyudi
2012-02-01
Full Text Available The Kalman filter is a recursive solution to the process linear filtering problem that can remove the noisefrom signal and then the information can useful. The process that use Kalman filter must be approximatedas two equations of linear system, state equation and output equation. Computation of Kalman filter isminimizes the mean of the square error. This paper explore the basic consepts of the Kalman filteralgorithm and simulate its to filter data of gyroscope to get a rotation. The measurement noise covariancedetermines how much information from the sample is used. If measurement noise covariance is high showthat the measurement isn’t very accurate. The process noise covariance contributes to the overalluncertainty of the estimate as it is added to the error covariance matrix in each time step. If the errorcovariance matrix is small the Kalman filter incorporates a lot less of the measurement into estimate ofrotation.
Liquid Level Estimation in Dynamic Condition using Kalman Filter
Directory of Open Access Journals (Sweden)
Sagar Kapale
2016-08-01
Full Text Available The aim of this paper is to estimate true liquid level of tank from noisy measurements due to dynamic conditions using kalman filter algorithm. We proposed kalman filter based approach to reduce noise in liquid level measurement system due to effect like sloshing. The function of kalman filter is to reduce error in liquid level measurement that produced from sensor resulting from effect like sloshing in dynamic environment. A prototype model was constructed and placed in dynamic condition, level data was acquired using ultrasonic sensor to verify the effectiveness of kalman filter. The tabulated data are shown for comparison of accuracy and error analysis between both measurements with Kalman filter and statistical averaging filter. After several test with different liquid levels and analysis of the recorded data, the technique shows the usefulness in liquid level measurement application in dynamic condition.
VLBI TRF determination via Kalman filtering
Soja, Benedikt; Karbon, Maria; Nilsson, Tobias; Glaser, Susanne; Balidakis, Kyriakos; Heinkelmann, Robert; Schuh, Harald
2015-04-01
The determination of station positions is one of the primary tasks for space geodetic techniques. Station coordinate offsets are usually determined with respect to a linear coordinate model after removing elastic displacements caused by mass redistributions within the Earth's system. In operational VLBI analysis, the coordinate offsets are estimated in a least-squares adjustment as a constant over the duration of a 24-hour VLBI experiment. Terrestrial reference frames (TRF) are usually derived by adjusting the normal equations that contain the 24-hour constant offsets in order to estimate a linear model, possibly including breaks, for the station positions. We have created a VLBI TRF solution without the assumption of negligible subdaily motion and of linear behavior on longer time scales by applying a Kalman filter. As a preparation for the upcoming VLBI Global Observing System (VGOS), which aims for continuous observations that are available in real-time, a Kalman filter has been implemented into the VLBI software VieVS@GFZ. In addition to the real-time capability, the filter offers the possibility of stochastically modeling the parameters of interest. For station coordinates, changes in a subdaily time frame occur, for instance, from un- or mismodeled geophysical effects. The models for tidal and non-tidal ocean, atmosphere, and hydrology loading are known to have deficiencies and inconsistencies which propagate into the estimated station coordinates. The stochastic model of the Kalman filter can be adapted to take these subdaily effects into account. Comparing the resulting station coordinate time series with daily values from a least squares fit, we have investigated to what extent and in which regions the loading models currently have deficiencies. Due to the high correlation between station height and tropospheric delays, it is possible that errors in one group of parameters are partly absorbed by the other group. To detect problems with correlations and to
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; Krutelyov, Slava; Lantz, Steven; Lefebvre, Matthieu; McDermott, Kevin; Riley, Daniel; Tadel, Matevž; Wittich, Peter; Würthwein, Frank; Yagil, Avi
2016-11-01
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 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.
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.
Data assimilation in the early phase: Kalman filtering RIMPUFF
DEFF Research Database (Denmark)
Astrup, P.; Turcanu, C.; Puch, R.O.;
2004-01-01
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...... variables, the applied Kalman filter is the so-called Extended Kalman filter. In more ways the implementation is non standard: 1) the number of state vectorvariables varies with time, and 2) the state vector variables are prediction updated with 1-minute time steps but only Kalman filtered every 10 minutes......, and this based on time averaged measurements. Given reasonable conditions, i.e. a spatially densedistribution of gamma monitors and a realistic wind field, the developed ADUM module is found to be able to enhance the prediction of the gamma dose field. Based on some of the Kalman filtering parameters, another...
On sequential observation processing in localized ensemble Kalman filters
Nerger, Lars
2014-01-01
The different variants of current ensemble square-root Kalman filters assimilate either all observations at once or perform a sequence in which batches of observations or each single observation is assimilated. The sequential observation processing is used in filter algorithms like the ensemble adjustment Kalman filter (EAKF) and the ensemble square-root filter (EnSRF) and can result in computationally efficient algorithms because matrix inversions in the observation space are reduced to the ...
A novel extended Kalman filter for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
DONG Zhe; YOU Zheng
2006-01-01
Estimation of the state variables of nonlinear systems is one of the fundamental and significant problems in control and signal processing. A new extended Kalman filtering approach for a class of nonlinear discrete-time systems in engineering is presented in this paper. In contrast to the celebrated extended Kalman filter (EKF), there is no linearization operation in the design procedure of the filter, and the parameters of the filter are obtained through minimizing a proper upper bound of the mean-square estimation error. Simulation results show that this filter can provide higher estimation precision than that provided by the EKF.
Statistical Process Control of a Kalman Filter Model
Gamse, Sonja; Nobakht-Ersi, Fereydoun; Sharifi, Mohammad A.
2014-01-01
For the evaluation of measurement data, different functional and stochastic models can be used. In the case of time series, a Kalman filtering (KF) algorithm can be implemented. In this case, a very well-known stochastic model, which includes statistical tests in the domain of measurements and in the system state domain, is used. Because the output results depend strongly on input model parameters and the normal distribution of residuals is not always fulfilled, it is very important to perform all possible tests on output results. In this contribution, we give a detailed description of the evaluation of the Kalman filter model. We describe indicators of inner confidence, such as controllability and observability, the determinant of state transition matrix and observing the properties of the a posteriori system state covariance matrix and the properties of the Kalman gain matrix. The statistical tests include the convergence of standard deviations of the system state components and normal distribution beside standard tests. Especially, computing controllability and observability matrices and controlling the normal distribution of residuals are not the standard procedures in the implementation of KF. Practical implementation is done on geodetic kinematic observations. PMID:25264959
Statistical Process Control of a Kalman Filter Model
Directory of Open Access Journals (Sweden)
Sonja Gamse
2014-09-01
Full Text Available For the evaluation of measurement data, different functional and stochastic models can be used. In the case of time series, a Kalman filtering (KF algorithm can be implemented. In this case, a very well-known stochastic model, which includes statistical tests in the domain of measurements and in the system state domain, is used. Because the output results depend strongly on input model parameters and the normal distribution of residuals is not always fulfilled, it is very important to perform all possible tests on output results. In this contribution, we give a detailed description of the evaluation of the Kalman filter model. We describe indicators of inner confidence, such as controllability and observability, the determinant of state transition matrix and observing the properties of the a posteriori system state covariance matrix and the properties of the Kalman gain matrix. The statistical tests include the convergence of standard deviations of the system state components and normal distribution beside standard tests. Especially, computing controllability and observability matrices and controlling the normal distribution of residuals are not the standard procedures in the implementation of KF. Practical implementation is done on geodetic kinematic observations.
Statistical process control of a Kalman filter model.
Gamse, Sonja; Nobakht-Ersi, Fereydoun; Sharifi, Mohammad A
2014-09-26
For the evaluation of measurement data, different functional and stochastic models can be used. In the case of time series, a Kalman filtering (KF) algorithm can be implemented. In this case, a very well-known stochastic model, which includes statistical tests in the domain of measurements and in the system state domain, is used. Because the output results depend strongly on input model parameters and the normal distribution of residuals is not always fulfilled, it is very important to perform all possible tests on output results. In this contribution, we give a detailed description of the evaluation of the Kalman filter model. We describe indicators of inner confidence, such as controllability and observability, the determinant of state transition matrix and observing the properties of the a posteriori system state covariance matrix and the properties of the Kalman gain matrix. The statistical tests include the convergence of standard deviations of the system state components and normal distribution beside standard tests. Especially, computing controllability and observability matrices and controlling the normal distribution of residuals are not the standard procedures in the implementation of KF. Practical implementation is done on geodetic kinematic observations.
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.
Skew redundant MEMS IMU calibration using a Kalman filter
Jafari, M.; Sahebjameyan, M.; Moshiri, B.; Najafabadi, T. A.
2015-10-01
In this paper, a novel calibration procedure for skew redundant inertial measurement units (SRIMUs) based on micro-electro mechanical systems (MEMS) is proposed. A general model of the SRIMU measurements is derived which contains the effects of bias, scale factor error and misalignments. For more accuracy, the effect of lever arms of the accelerometers to the center of the table are modeled and compensated in the calibration procedure. Two separate Kalman filters (KFs) are proposed to perform the estimation of error parameters for gyroscopes and accelerometers. The predictive error minimization (PEM) stochastic modeling method is used to simultaneously model the effect of bias instability and random walk noise on the calibration Kalman filters to diminish the biased estimations. The proposed procedure is simulated numerically and has expected experimental results. The calibration maneuvers are applied using a two-axis angle turntable in a way that the persistency of excitation (PE) condition for parameter estimation is met. For this purpose, a trapezoidal calibration profile is utilized to excite different deterministic error parameters of the accelerometers and a pulse profile is used for the gyroscopes. Furthermore, to evaluate the performance of the proposed KF calibration method, a conventional least squares (LS) calibration procedure is derived for the SRIMUs and the simulation and experimental results compare the functionality of the two proposed methods with each other.
Kelly, D. A.; Fermelia, A.; Lee, G. K. F.
1990-01-01
An adaptive Kalman filter design that utilizes recursive maximum likelihood parameter identification is discussed. At the center of this design is the Kalman filter itself, which has the responsibility for attitude determination. At the same time, the identification algorithm is continually identifying the system parameters. The approach is applicable to nonlinear, as well as linear systems. This adaptive Kalman filter design has much potential for real time implementation, especially considering the fast clock speeds, cache memory and internal RAM available today. The recursive maximum likelihood algorithm is discussed in detail, with special attention directed towards its unique matrix formulation. The procedure for using the algorithm is described along with comments on how this algorithm interacts with the Kalman filter.
FUZZY OPTIMIZATION USING EXTENDED KALMAN FILTER
Directory of Open Access Journals (Sweden)
M.DIVYA
2013-01-01
Full Text Available Fuzzy Logic is based on the idea that in fuzzy sets each element in the set can assume a value from 0 to 1, not only 0 or 1, as in crisp set theory. The degree of membership function is defined as the gradation in the extent to which an element is belonging to the relevant sets. Optimizing the membership functions of a fuzzy system can be viewed as a system identification problem for nonlinear dynamic system. In this paper two input and one output fuzzy controller is designed for the dynamic process of aircraft. The addition of an EKF in the feedback loop improved the system response by blocking possible effects of measurement error based on Predictor-Corrector algorithm. An Extended Kalman Filter approach to optimize the membership functions of the inputs and outputs of the fuzzy controller. The performance of the fuzzy system before and after the optimization are compared, as well as the membership functions.
Kalman Filter Tracking on Parallel Architectures
Cerati, Giuseppe; Lantz, Steven; McDermott, Kevin; Riley, Dan; Tadel, Matevž; Wittich, Peter; Würthwein, Frank; Yagil, Avi
2015-01-01
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. Significant experience has...
Kalman Filter Tracking on Parallel Architectures
Cerati, Giuseppe; Krutelyov, Slava; Lantz, Steven; Lefebvre, Matthieu; McDermott, Kevin; Riley, Daniel; Tadel, Matevz; Wittich, Peter; Wuerthwein, Frank; Yagil, Avi
2016-01-01
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 such as GPGPU, ARM and Intel MIC. 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. 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 the Kalman Filter. Significant experience has been accumulated with these techniques on real tracking detector sy...
Vehicle Tracking Using Kalman Filter and Features
Directory of Open Access Journals (Sweden)
Amir Salarpour
2011-09-01
Full Text Available Vehicle tracking has a wide variety of applications. The image resolution of the video available from most traffic camera system is low. In many cases for tracking multi object, distinguishing them from another isn’t easy because of their similarity. In this paper we describe a method, for tracking multiple objects, where the objects are vehicles. The number of vehicles is unknown and varies. We detect all moving objects, and for tracking of vehicle we use the kalman filter and color feature and distance of it from one frame to the next. So the method can distinguish and tracking all vehicles individually. The proposed algorithm can be applied to multiple moving objects.
Kalman filtering approach to blind equalization
Kutlu, Mehmet
1993-12-01
Digital communication systems suffer from the channel distortion problem which introduces errors due to intersymbol interference. The solution to this problem is provided by equalizers which use a training sequence to adapt to the channel. However in many cases in which a training sequence is unfeasible, the channel must be adapted blindly. Most of the blind equalization algorithms known so far have problems of convergence to local minima. Our intention is to offer an alternative approach by using extended Kalman filtering and hidden Markov models. They seem to yield more efficient algorithms which take the statistics of the transmitted sequence into consideration. The theoretical development of these new algorithms is discussed in this thesis. Also these algorithms have been simulated under different conditions. The results of simulations and comparisons with existing systems are provided. The models for simulations are presented as MATLAB codes.
Optimized object tracking technique using Kalman filter
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Liana Ellen Taylor
2016-07-01
Full Text Available This paper focused on the design of an optimized object tracking technique which would minimize the processing time required in the object detection process while maintaining accuracy in detecting the desired moving object in a cluttered scene. A Kalman filter based cropped image is used for the image detection process as the processing time is significantly less to detect the object when a search window is used that is smaller than the entire video frame. This technique was tested with various sizes of the window in the cropping process. MATLAB® was used to design and test the proposed method. This paper found that using a cropped image with 2.16 multiplied by the largest dimension of the object resulted in significantly faster processing time while still providing a high success rate of detection and a detected center of the object that was reasonably close to the actual center.
Star-sensor-based predictive Kalman filter for satelliteattitude estimation
Institute of Scientific and Technical Information of China (English)
林玉荣; 邓正隆
2002-01-01
A real-time attitude estimation algorithm, namely the predictive Kalman filter, is presented. This algorithm can accurately estimate the three-axis attitude of a satellite using only star sensor measurements. The implementation of the filter includes two steps: first, predicting the torque modeling error, and then estimating the attitude. Simulation results indicate that the predictive Kalman filter provides robust performance in the presence of both significant errors in the assumed model and in the initial conditions.
Longitudinal Factor Score Estimation Using the Kalman Filter.
Oud, Johan H.; And Others
1990-01-01
How longitudinal factor score estimation--the estimation of the evolution of factor scores for individual examinees over time--can profit from the Kalman filter technique is described. The Kalman estimates change more cautiously over time, have lower estimation error variances, and reproduce the LISREL program latent state correlations more…
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.
Subspace System Identification of the Kalman Filter
Directory of Open Access Journals (Sweden)
David Di Ruscio
2003-07-01
Full Text Available Some proofs concerning a subspace identification algorithm are presented. It is proved that the Kalman filter gain and the noise innovations process can be identified directly from known input and output data without explicitly solving the Riccati equation. Furthermore, it is in general and for colored inputs, proved that the subspace identification of the states only is possible if the deterministic part of the system is known or identified beforehand. However, if the inputs are white, then, it is proved that the states can be identified directly. Some alternative projection matrices which can be used to compute the extended observability matrix directly from the data are presented. Furthermore, an efficient method for computing the deterministic part of the system is presented. The closed loop subspace identification problem is also addressed and it is shown that this problem is solved and unbiased estimates are obtained by simply including a filter in the feedback. Furthermore, an algorithm for consistent closed loop subspace estimation is presented. This algorithm is using the controller parameters in order to overcome the bias problem.
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.
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.
Concrete ensemble Kalman filters with rigorous catastrophic filter divergence.
Kelly, David; Majda, Andrew J; Tong, Xin T
2015-08-25
The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter. The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature.
Concrete ensemble Kalman filters with rigorous catastrophic filter divergence
Kelly, David; Majda, Andrew J.; Tong, Xin T.
2015-01-01
The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter. The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature. PMID:26261335
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.
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.
On the evaluation of uncertainties for state estimation with the Kalman filter
Eichstädt, S.; Makarava, N.; Elster, C.
2016-12-01
The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous areas. It provides sequentially calculated estimates of the system states along with a corresponding covariance matrix. For nonlinear systems, the extended Kalman filter is often used. This is derived from the Kalman filter by linearization around the current estimate. A key issue in metrology is the evaluation of the uncertainty associated with the Kalman filter state estimates. The ‘Guide to the Expression of Uncertainty in Measurement’ (GUM) and its supplements serve as the de facto standard for uncertainty evaluation in metrology. We explore the relationship between the covariance matrix produced by the Kalman filter and a GUM-compliant uncertainty analysis. In addition, the results of a Bayesian analysis are considered. For the case of linear systems with known system matrices, we show that all three approaches are compatible. When the system matrices are not precisely known, however, or when the system is nonlinear, this equivalence breaks down and different results can then be reached. For precisely known nonlinear systems, though, the result of the extended Kalman filter still corresponds to the linearized uncertainty propagation of the GUM. The extended Kalman filter can suffer from linearization and convergence errors. These disadvantages can be avoided to some extent by applying Monte Carlo procedures, and we propose such a method which is GUM-compliant and can also be applied online during the estimation. We illustrate all procedures in terms of a 2D dynamic system and compare the results with those obtained by particle filtering, which has been proposed for the approximate calculation of a Bayesian solution. Finally, we give some recommendations based on our findings.
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.
Application of Kalman Filtering Techniques for Microseismic Event Detection
Baziw, E.; Weir-Jones, I.
- Microseismic monitoring systems are generally installed in areas of induced seismicity caused by human activity. Induced seismicity results from changes in the state of stress which may occur as a result of excavation within the rock mass in mining (i.e., rockbursts), and changes in hydrostatic pressures and rock temperatures (e.g., during fluid injection or extraction) in oil exploitation, dam construction or fluid disposal. Microseismic monitoring systems determine event locations and important source parameters such as attenuation, seismic moment, source radius, static stress drop, peak particle velocity and seismic energy. An essential part of the operation of a microseismic monitoring system is the reliable detection of microseismic events. In the absence of reliable, automated picking techniques, operators rely upon manual picking. This is time-consuming, costly and, in the presence of background noise, very prone to error. The techniques described in this paper not only permit the reliable identification of events in cluttered signal environments they have also enabled the authors to develop reliable automated event picking procedures. This opens the way to use microseismic monitoring as a cost-effective production/operations procedure. It has been the experience of the authors that in certain noisy environments, the seismic monitoring system may trigger on and subsequently acquire substantial quantities of erroneous data, due to the high energy content of the ambient noise. Digital filtering techniques need to be applied on the microseismic data so that the ambient noise is removed and event detection simplified. The monitoring of seismic acoustic emissions is a continuous, real-time process and it is desirable to implement digital filters which can also be designed in the time domain and in real-time such as the Kalman Filter. This paper presents a real-time Kalman Filter which removes the statistically describable background noise from the recorded
An Adaptive Kalman Filter Excisor for Suppressing Narrowband Interference
1993-11-01
interferences in- connues. Le filtre de Kalman doit alors "apprendre" ý ajuster un de ses param~tres pour effectuer le meilleur traitement. L’erreur est...4"L l B"• -- -- - - -.- ,_, . An~. A)7cQ 0 -QGOP II liii 111111 IIa( Naional 06fenso I ’ I Deence nitonals I "It AN ADAPTIVE KALMAN FILTER EXCISOR...Ottawa 0 A o~ oO Best Available COpy 4INational Defense Defence nationals AN ADAPTIVE KALMAN FILTER EXCISOR FOR SUPPRESSING NARROWBAND INTERFERENCE by
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 stability of power system. State estimation with EKF and UKF methods can be used for monitoring and estimating the dynamic state variables of multi-machine power systems, which are generator rotor speed and rotor angle. This paper uses Powerfactory to solve power flow analysis of simulations, then a non......-linear state estimator is developed in MatLab to solve states by applying the unscented Kalman filter (UKF) and Extended Kalman Filter (EKF) algorithm. Finally, a DSE model is built for a 14 bus power system network to evaluate the proposed algorithm for the networks.This article will focus on comparing...
Kinematic landslide monitoring with Kalman filtering
Directory of Open Access Journals (Sweden)
M. Acar
2008-03-01
Full Text Available Landslides are serious geologic disasters that threat human life and property in every country. In addition, landslides are one of the most important natural phenomena, which directly or indirectly affect countries' economy. Turkey is also the country that is under the threat of landslides. Landslides frequently occur in all of the Black Sea region as well as in many parts of Marmara, East Anatolia, and Mediterranean regions. Since these landslides resulted in destruction, they are ranked as the second important natural phenomenon that comes after earthquake in Turkey. In recent years several landslides happened after heavy rains and the resulting floods. This makes the landslide monitoring and mitigation techniques an important study subject for the related professional disciplines in Turkey. The investigations on surface deformations are conducted to define the boundaries of the landslide, size, level of activity and direction(s of the movement, and to determine individual moving blocks of the main slide.
This study focuses on the use of a kinematic deformation analysis based on Kalman Filtering at a landslide area near Istanbul. Kinematic deformation analysis has been applied in a landslide area, which is located to the north of Istanbul city. Positional data were collected using GPS technique. As part of the study, conventional static deformation analysis methodology has also been applied on the same data. The results and comparisons are discussed in this paper.
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.
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
Directory of Open Access Journals (Sweden)
S. Roh
2015-05-01
Full Text Available 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, Xiaodong; 10.3402/tellusa.v64i0.17130
2012-01-01
Covariance inflation and localization 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/o...
Multivariate localization methods for ensemble Kalman filtering
Roh, S.; Jun, M.; Szunyogh, I.; Genton, M. G.
2015-12-01
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.
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.
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
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.
Switching Kalman filter for failure prognostic
Lim, Chi Keong Reuben; Mba, David
2015-02-01
The use of condition monitoring (CM) data to predict remaining useful life have been growing with increasing use of health and usage monitoring systems on aircraft. There are many data-driven methodologies available for the prediction and popular ones include artificial intelligence and statistical based approach. The drawback of such approaches is that they require a lot of failure data for training which can be scarce in practice. In lieu of this, methods using state-space and regression-based models that extract information from the data history itself have been explored. However, such methods have their own limitations as they utilize a single time-invariant model which does not represent changing degradation path well. This causes most degradation modeling studies to focus only on segments of their CM data that behaves close to the assumed model. In this paper, a state-space based method; the Switching Kalman Filter (SKF), is adopted for model estimation and life prediction. The SKF approach however, uses multiple models from which the most probable model is inferred from the CM data using Bayesian estimation before it is applied for prediction. At the same time, the inference of the degradation model itself can provide maintainers with more information for their planning. This SKF approach is demonstrated with a case study on gearbox bearings that were found defective from the Republic of Singapore Air Force AH64D helicopter. The use of in-service CM data allows the approach to be applied in a practical scenario and results showed that the developed SKF approach is a promising tool to support maintenance decision-making.
Strong tracking adaptive Kalman filters for underwater vehicle dead reckoning
Institute of Scientific and Technical Information of China (English)
XIAO Kun; FANG Shao-ji; PANG Yong-jie
2007-01-01
To improve underwater vehicle dead reckoning, a developed strong tracking adaptive kalman filter is proposed. The filter is improved with an additional adaptive factor and an estimator of measurement noise covariance. Since the magnitude of fading factor is changed adaptively, the tracking ability of the filter is still enhanced in low velocity condition of underwater vehicles. The results of simulation tests prove the presented filter effective.
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...
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...
Bridging the ensemble Kalman filter and particle filters: the adaptive Gaussian mixture filter
Stordal, Andreas Størksen; Karlsen, Hans A.; Nævdal, Geir; Hans J. Skaug; Vallès, Brice
2010-01-01
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 (EnKF) 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 a Gauss...
Tracking whole hand kinematics using extended Kalman filter.
Fu, Qiushi; Santello, Marco
2010-01-01
This paper describes the general procedure, model construction, and experimental results of tracking whole hand kinematics using extended Kalman filter (EKF) based on data recorded from active surface markers. We used a hand model with 29 degrees of freedom that consists of hand global posture, wrist, and digits. The marker protocol had 4 markers on the distal forearm and 20 markers on the dorsal surface of the joints of the digits. To reduce computational load, we divided the state space into four sub-spaces, each of which were estimated with an EKF in a specific order. We tested our framework and found reasonably accurate results (2-4 mm tip position error) when sampling tip to tip pinch at 120 Hz.
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.
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 observed signal strengths and gives interpolated values at specific timestamps. Information from the first filter is transferred to the second filter which estimates the positions. Methods for estimating the parameters of the filters are given and these provide a straightforward calibration of the system...
Recursive three-dimensional model reconstruction based on Kalman filtering.
Yu, Ying Kin; Wong, Kin Hong; Chang, Michael Ming Yuen
2005-06-01
A recursive two-step method to recover structure and motion from image sequences based on Kalman filtering is described in this paper. The algorithm consists of two major steps. The first step is an extended Kalman filter (EKF) for the estimation of the object's pose. The second step is a set of EKFs, one for each model point, for the refinement of the positions of the model features in the three-dimensional (3-D) space. These two steps alternate from frame to frame. The initial model converges to the final structure as the image sequence is scanned sequentially. The performance of the algorithm is demonstrated with both synthetic data and real-world objects. Analytical and empirical comparisons are made among our approach, the interleaved bundle adjustment method, and the Kalman filtering-based recursive algorithm by Azarbayejani and Pentland. Our approach outperformed the other two algorithms in terms of computation speed without loss in the quality of model reconstruction.
Nonlinear dynamical system identification using unscented Kalman filter
Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan
2016-11-01
Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.
Kalman Filter Based Tracking in an Video Surveillance System
Directory of Open Access Journals (Sweden)
SULIMAN, C.
2010-05-01
Full Text Available In this paper we have developed a Matlab/Simulink based model for monitoring a contact in a video surveillance sequence. For the segmentation process and corect identification of a contact in a surveillance video, we have used the Horn-Schunk optical flow algorithm. The position and the behavior of the correctly detected contact were monitored with the help of the traditional Kalman filter. After that we have compared the results obtained from the optical flow method with the ones obtained from the Kalman filter, and we show the correct functionality of the Kalman filter based tracking. The tests were performed using video data taken with the help of a fix camera. The tested algorithm has shown promising results.
Improved Kalman Filter-Based Speech Enhancement with Perceptual Post-Filtering
Institute of Scientific and Technical Information of China (English)
WEIJianqiang; DULimin; YANZhaoli; ZENGHui
2004-01-01
In this paper, a Kalman filter-based speech enhancement algorithm with some improvements of previous work is presented. A new technique based on spectral subtraction is used for separation speech and noise characteristics from noisy speech and for the computation of speech and noise Autoregressive (AR) parameters. In order to obtain a Kalman filter output with high audible quality, a perceptual post-filter is placed at the output of the Kalman filter to smooth the enhanced speech spectra.Extensive experiments indicate that this newly proposed method works well.
Methodology for adapting the parameters of a fuzzy system using the extended Kalman filter
2011-01-01
When we try to analyze and to control a system whose model was obtained only based on input/output data, accuracy is essential in the model. On the other hand, to make the procedure practical, the modeling stage must be computationally efficient. In this regard, this paper presents the application of extended Kalman filter for the parametric adaptation of a fuzzy model.
The path prediction of cyclones with Kalman filters
Taskin, Dogan
1990-01-01
Approved for public release; distribution unlimited. The Kalman filter is used to provide estimates of the position and velocity of a storm based upon observation of the storm's longitude and latitude. Nonstationary noise is shown to degrade the performance of the filter and cause tracking divergence. Time varying values for the noise covariance matricies R and Q, and the addition of an external forcing function to the filter, effectively compensated for this tracking error. Results for th...
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.
Adaptive robust Kalman filtering for precise point positioning
Guo, Fei; Zhang, Xiaohong
2014-10-01
The optimality of precise point postioning (PPP) solution using a Kalman filter is closely connected to the quality of the a priori information about the process noise and the updated mesurement noise, which are sometimes difficult to obtain. Also, the estimation enviroment in the case of dynamic or kinematic applications is not always fixed but is subject to change. To overcome these problems, an adaptive robust Kalman filtering algorithm, the main feature of which introduces an equivalent covariance matrix to resist the unexpected outliers and an adaptive factor to balance the contribution of observational information and predicted information from the system dynamic model, is applied for PPP processing. The basic models of PPP including the observation model, dynamic model and stochastic model are provided first. Then an adaptive robust Kalmam filter is developed for PPP. Compared with the conventional robust estimator, only the observation with largest standardized residual will be operated by the IGG III function in each iteration to avoid reducing the contribution of the normal observations or even filter divergence. Finally, tests carried out in both static and kinematic modes have confirmed that the adaptive robust Kalman filter outperforms the classic Kalman filter by turning either the equivalent variance matrix or the adaptive factor or both of them. This becomes evident when analyzing the positioning errors in flight tests at the turns due to the target maneuvering and unknown process/measurement noises.
Institute of Scientific and Technical Information of China (English)
XIA Yuanqing; HAN Jingqing
2005-01-01
This paper concerns robust Kalman filtering for systems under norm bounded uncertainties in all the system matrices and error covariance constraints. Sufficient conditions are given for the existence of such filters in terms of Riccati equations. The solutions to the conditions can be used to design the filters. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed design procedure.
A THEORETICAL STUDY ON SIMPLIFIED KALMAN FILTER IN DATA ASSIMILATION
Institute of Scientific and Technical Information of China (English)
Ma Zhai-pu; Huang Da-ji; Zhang Ben-zhao
2003-01-01
In this paper, we put forward a new method to reduce the calculation amount of the gain matrix of Kalman filter in data assimilation. We rewrite the vector describing the total state variables with two vectors whose dimensions are small and thus obtain the main parts and the trivial parts of the state variables. On the basis of the rewrittten formula, we not only develop a reduced Kalman filter scheme, but also obtain the transition equations about truncation errors, with which the validity of the main parts acting for the total state variables can be evaluated quantitatively. The error transition equations thus offer an indirect testimony to the rationality of the main parts.
Filtering Meteoroid Flights Using Multiple Unscented Kalman Filters
Sansom, E. K.; Bland, P. A.; Rutten, M. G.; Paxman, J.; Towner, M. C.
2016-11-01
Estimator algorithms are immensely versatile and powerful tools that can be applied to any problem where a dynamic system can be modeled by a set of equations and where observations are available. A well designed estimator enables system states to be optimally predicted and errors to be rigorously quantified. Unscented Kalman filters (UKFs) and interactive multiple models can be found in methods from satellite tracking to self-driving cars. The luminous trajectory of the Bunburra Rockhole fireball was observed by the Desert Fireball Network in mid-2007. The recorded data set is used in this paper to examine the application of these two techniques as a viable approach to characterizing fireball dynamics. The nonlinear, single-body system of equations, used to model meteoroid entry through the atmosphere, is challenged by gross fragmentation events that may occur. The incorporation of the UKF within an interactive multiple model smoother provides a likely solution for when fragmentation events may occur as well as providing a statistical analysis of the state uncertainties. In addition to these benefits, another advantage of this approach is its automatability for use within an image processing pipeline to facilitate large fireball data analyses and meteorite recoveries.
Scheme of adaptive polarization filtering based on Kalman model
Institute of Scientific and Technical Information of China (English)
Song Lizhong; Qi Haiming; Qiao Xiaolin; Meng Xiande
2006-01-01
A new kind of adaptive polarization filtering algorithm in order to suppress the angle cheating interference for the active guidance radar is presented. The polarization characteristic of the interference is dynamically tracked by using Kalman estimator under variable environments with time. The polarization filter parameters are designed according to the polarization characteristic of the interference, and the polarization filtering is finished in the target cell. The system scheme of adaptive polarization filter is studied and the tracking performance of polarization filter and improvement of angle measurement precision are simulated. The research results demonstrate this technology can effectively suppress the angle cheating interference in guidance radar and is feasible in engineering.
Kalman Filter for Generalized 2-D Roesser Models
Institute of Scientific and Technical Information of China (English)
SHENG Mei; ZOU Yun
2007-01-01
The design problem of the state filter for the generalized stochastic 2-D Roesser models, which appears when both the state and measurement are simultaneously subjected to the interference from white noise, is discussed. The wellknown Kalman filter design is extended to the generalized 2-D Roesser models. Based on the method of "scanning line by line", the filtering problem of generalized 2-D Roesser models with mode-energy reconstruction is solved. The formula of the optimal filtering, which minimizes the variance of the estimation error of the state vectors, is derived. The validity of the designed filter is verified by the calculation steps and the examples are introduced.
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.
Dual extended Kalman filtering in recurrent neural networks(1).
Leung, Chi-Sing; Chan, Lai-Wan
2003-03-01
In the classical deterministic Elman model, the estimation of parameters must be very accurate. Otherwise, the system performance is very poor. To improve the system performance, we can use a Kalman filtering algorithm to guide the operation of a trained recurrent neural network (RNN). In this case, during training, we need to estimate the state of hidden layer, as well as the weights of the RNN. This paper discusses how to use the dual extended Kalman filtering (DEKF) for this dual estimation and how to use our proposing DEKF for removing some unimportant weights from a trained RNN. In our approach, one Kalman algorithm is used for estimating the state of the hidden layer, and one recursive least square (RLS) algorithm is used for estimating the weights. After training, we use the error covariance matrix of the RLS algorithm to remove unimportant weights. Simulation showed that our approach is an effective joint-learning-pruning method for RNNs under the online operation.
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.
Kalman filtering and Standard Quantum Limits for broadband measurement
Mabuchi, H
1998-01-01
I utilize the Caves-Milburn model for continuous position measurements to formulate a broadband version of the Standard Quantum Limit (SQL) for monitoring the position of a free mass, and illustrate the use of Kalman filtering to recover the SQL for estimating a weak classical force that acts on a quantum-mechanical test particle under continuous observation.
Performance enhancement for GPS positioning using constrained Kalman filtering
Guo, Fei; Zhang, Xiaohong; Wang, Fuhong
2015-08-01
Over the past decades Kalman filtering (KF) algorithms have been extensively investigated and applied in the area of kinematic positioning. In the application of KF in kinematic precise point positioning (PPP), it is often the case where some known functional or theoretical relations exist among the unknown state parameters, which can be and should be made use of to enhance the performance of kinematic PPP, especially in an urban and forest environment. The central task of this paper is to effectively blend the commonly used GNSS data and internal/external additional constrained information to generate an optimal PPP solution. This paper first investigates the basic algorithm of constrained Kalman filtering. Then two types of PPP model with speed constraints and trajectory constraints, respectively, are proposed. Further validation tests based on a variety of situations show that the positioning performances (positioning accuracy, reliability and continuity) from the constrained Kalman filter are significantly superior to those from the conventional Kalman filter, particularly under extremely poor observation conditions.
Forecasting with the Standardized Self-Perturbed Kalman Filter
DEFF Research Database (Denmark)
Grassi, Stefano; Nonejad, Nima; Santucci de Magistris, Paolo
compared to other on-line, classical and Bayesian methods. The standardized self-perturbed Kalman filter is adopted to forecast the equity premium on the S&P500 index under several model specifications, and to investigate to what extent and how realized variance can be exploited to predict excess returns....
Kalman filter techniques for accelerated Cartesian dynamic cardiac imaging.
Feng, Xue; Salerno, Michael; Kramer, Christopher M; Meyer, Craig H
2013-05-01
In dynamic MRI, spatial and temporal parallel imaging can be exploited to reduce scan time. Real-time reconstruction enables immediate visualization during the scan. Commonly used view-sharing techniques suffer from limited temporal resolution, and many of the more advanced reconstruction methods are either retrospective, time-consuming, or both. A Kalman filter model capable of real-time reconstruction can be used to increase the spatial and temporal resolution in dynamic MRI reconstruction. The original study describing the use of the Kalman filter in dynamic MRI was limited to non-Cartesian trajectories because of a limitation intrinsic to the dynamic model used in that study. Here the limitation is overcome, and the model is applied to the more commonly used Cartesian trajectory with fast reconstruction. Furthermore, a combination of the Kalman filter model with Cartesian parallel imaging is presented to further increase the spatial and temporal resolution and signal-to-noise ratio. Simulations and experiments were conducted to demonstrate that the Kalman filter model can increase the temporal resolution of the image series compared with view-sharing techniques and decrease the spatial aliasing compared with TGRAPPA. The method requires relatively little computation, and thus is suitable for real-time reconstruction.
Reducing Support Vector Machine Classification Error by Implementing Kalman Filter
Directory of Open Access Journals (Sweden)
Muhsin Hassan
2013-08-01
Full Text Available The aim of this is to demonstrate the capability of Kalman Filter to reduce Support Vector Machine classification errors in classifying pipeline corrosion depth. In pipeline defect classification, it is important to increase the accuracy of the SVM classification so that one can avoid misclassification which can lead to greater problems in monitoring pipeline defect and prediction of pipeline leakage. In this paper, it is found that noisy data can greatly affect the performance of SVM. Hence, Kalman Filter + SVM hybrid technique has been proposed as a solution to reduce SVM classification errors. The datasets has been added with Additive White Gaussian Noise in several stages to study the effect of noise on SVM classification accuracy. Three techniques have been studied in this experiment, namely SVM, hybrid of Discrete Wavelet Transform + SVM and hybrid of Kalman Filter + SVM. Experiment results have been compared to find the most promising techniques among them. MATLAB simulations show Kalman Filter and Support Vector Machine combination in a single system produced higher accuracy compared to the other two techniques.
Nonlinear Kalman filtering in the presence of additive noise
Kraszewski, Tomasz; Czopik, Grzegorz
2017-04-01
Each modern navigation or localization system designed for ground, water or air objects should provide information on the estimated parameters continuously and as accurately as possible. The implementation of such a process requires the application to operate on non-linear transformations. The defined expectations necessitate the use of nonlinear filtering elements with particular emphasis on the extended Kalman filter. The article presents the simulation research elements of this filter type in the aspect of the possibility of its practical implementation. In the initial phase of the study the conclusion was based on nonlinear one-dimensional model. The possibility of improving the precision of the output through the use of unscented Kalman filters was also analyzed.
Autonomous orbit determination via Kalman filtering of gravity gradients
Sun; Chen,De; Macabiau, Christophe; Han
2016-01-01
International audience; Spaceborne gravity gradients are proposed in this paper to provide autonomous orbit determination capabilities for near Earth satellites. The gravity gradients contain useful position information which can be extracted by matching the observations with a precise gravity model. The extended Kalman filter is investigated as the principal estimator. The stochastic model of orbital motion, the measurement equation and the model configuration are discussed for the filter de...
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
Ensemble Kalman filtering in presence of inequality constraints
van Leeuwen, P. J.
2009-04-01
Kalman filtering is presence of constraints is an active area of research. Based on the Gaussian assumption for the probability-density functions, it looks hard to bring in extra constraints in the formalism. On the other hand, in geophysical systems we often encounter constraints related to e.g. the underlying physics or chemistry, which are violated by the Gaussian assumption. For instance, concentrations are always non-negative, model layers have non-negative thickness, and sea-ice concentration is between 0 and 1. Several methods to bring inequality constraints into the Kalman-filter formalism have been proposed. One of them is probability density function (pdf) truncation, in which the Gaussian mass from the non-allowed part of the variables is just equally distributed over the pdf where the variables are alolwed, as proposed by Shimada et al. 1998. However, a problem with this method is that the probability that e.g. the sea-ice concentration is zero, is zero! The new method proposed here does not have this drawback. It assumes that the probability-density function is a truncated Gaussian, but the truncated mass is not distributed equally over all allowed values of the variables, but put into a delta distribution at the truncation point. This delta distribution can easily be handled with in Bayes theorem, leading to posterior probability density functions that are also truncated Gaussians with delta distributions at the truncation location. In this way a much better representation of the system is obtained, while still keeping most of the benefits of the Kalman-filter formalism. In the full Kalman filter the formalism is prohibitively expensive in large-scale systems, but efficient implementation is possible in ensemble variants of the kalman filter. Applications to low-dimensional systems and large-scale systems will be discussed.
Development of Real-Time Error Ellipses as an Indicator of Kalman Filter Performance.
1984-03-01
S q often than 3 to 5 seconds. However, before the HP-86 can e considered feasible for real-time Kalman filtr procssinz, more investigaz ion i: needi...Subtitle) S. TYPE OF REPORT & PERIOD COVERED Development of Real-Time Error Master’s Thesis; Ellipses as an Indicator of Kalman March 1984 Filter...SUPP.LEETARY NOTES 19. KEY WORDS (Cmntine on reveo ole, It ndeeaey md Identil by block number) Error Ellipsoids; Kalman Filter; Extended Kalman Filter
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.
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.
Research on Kalman-filter based multisensor data fusion
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Multisensor data fusion has played a significant role in diverse areas ranging from local robot guidance to global military theatre defense etc.Various multisensor data fusion methods have been extensively investigated by researchers,of which Klaman filtering is one of the most important.Kalman filtering is the best-known recursive least mean-square algorithm to optimally estimate the unknown.states of a dynamic system,which has found widespread application in many areas.The scope of the work is restricted to investigate the various data fusion and track fusion techniques based on the Kalman Filter methods.then a new method of state fusion is proposed.Finally the simulation results demonstrate the effectiveness of the introduced method.
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.
An aperiodic phenomenon of the unscented Kalman filter in filtering noisy chaotic signals
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A non-periodic oscillatory behavior of the unscented Kalman filter (UKF) when used to filter noisy contaminated chaotic signals is reported. We show both theoretically and experimentally that the gain of the UKF may not converge or diverge but oscillate aperiodically. More precisely, when a nonlinear system is periodic, the Kalman gain and error covariance of the UKF converge to zero. However, when the system being considered is chaotic, the Kalman gain either converges to a fixed point with a magnitude larger than zero or oscillates aperiodically.
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.
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.
A Hierarchical Bayes Ensemble Kalman Filter
Tsyrulnikov, Michael; Rakitko, Alexander
2017-01-01
A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance matrices. The latter are treated as random matrices and updated in a hierarchical Bayes scheme along with the state. The (hyper)prior distribution of the covariance matrices is assumed to be inverse Wishart. The new Hierarchical Bayes Ensemble Filter (HBEF) assimilates ensemble members as generalized observations and allows ordinary observations to influence the covariances. The actual probability distribution of the ensemble members is allowed to be different from the true one. An approximation that leads to a practicable analysis algorithm is proposed. The new filter is studied in numerical experiments with a doubly stochastic one-variable model of "truth". The model permits the assessment of the variance of the truth and the true filtering error variance at each time instance. The HBEF is shown to outperform the EnKF and the HEnKF by Myrseth and Omre (2010) in a wide range of filtering regimes in terms of performance of its primary and secondary filters.
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...
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.
Streamflow Data Assimilation in SWAT Model Using Extended Kalman Filter
Sun, L.; Nistor, I.; Seidou, O.
2014-12-01
Although Extended Kalman Filter (EKF) is regarded as the de facto method for the application of Kalman Filter in non-linear system, it's application to complex distributed hydrological models faces a lot of challenges. Ensemble Kalman Filter (EnKF) is often preferred because it avoids the calculation of the linearization Jacobian Matrix and the propagation of estimation error covariance. EnKF is however difficult to apply to large models because of the huge computation demand needed for parallel propagation of ensemble members. This paper deals with the application of EKF in stream flow prediction using the SWAT model in the watershed of Senegal River, West Africa. In the Jacobian Matrix calculation, SWAT is regarded as a black box model and the derivatives are calculated in the form of differential equations. The state vector is the combination of runoff, soil, shallow aquifer and deep aquifer water contents. As an initial attempt, only stream flow observations are assimilated. Despite the fact that EKF is a sub-optimal filter, the coupling of EKF significantly improves the estimation of daily streamflow. The results of SWAT+EKF are also compared to those of a simpler quasi linear streamflow prediction model where both state and parameters are updated with the EKF.
Multiple Fading Factors Kalman Filter for SINS Static Alignment Application
Institute of Scientific and Technical Information of China (English)
GAO Weixi; MIAO Lingjuan; NI Maolin
2011-01-01
To solve the problem that the standard Kalman filter cannot give the optimal solution when the system model and stochastic information are unknown accurately,single fading factor Kalman filter is suitable for simple systems.But for complex systems with multi-variable,it may not be sufficient to use single fading factor as a multiplier for the covariance matrices.In this paper,a new multiple fading factors Kalman filtering algorithm is presented.By calculating the unbiased estimate of the innovation sequence covariance using fenestration,the fading factor matrix is obtained.Adjusting the covariance matrix of prediction error Pk|k-1 using fading factor matrix,the algorithm provides different rates of fading for different filter channels.The proposed algorithm is applied to strapdown inertial navigation system(SINS) initial alignment,and simulation and experimental results demonstrate that,the alignment accuracy can be upgraded dramatically when the actual system noise characteristics are different from the pre-set values.The new algorithm is less sensitive to uncertainty noise and has better estimation effect of the parameters.Therefore,it is of significant value in practical applications.
Acoustic cardiac signals analysis: a Kalman filter-based approach.
Salleh, Sheik Hussain; Hussain, Hadrina Sheik; Swee, Tan Tian; Ting, Chee-Ming; Noor, Alias Mohd; Pipatsart, Surasak; Ali, Jalil; Yupapin, Preecha P
2012-01-01
Auscultation of the heart is accompanied by both electrical activity and sound. Heart auscultation provides clues to diagnose many cardiac abnormalities. Unfortunately, detection of relevant symptoms and diagnosis based on heart sound through a stethoscope is difficult. The reason GPs find this difficult is that the heart sounds are of short duration and separated from one another by less than 30 ms. In addition, the cost of false positives constitutes wasted time and emotional anxiety for both patient and GP. Many heart diseases cause changes in heart sound, waveform, and additional murmurs before other signs and symptoms appear. Heart-sound auscultation is the primary test conducted by GPs. These sounds are generated primarily by turbulent flow of blood in the heart. Analysis of heart sounds requires a quiet environment with minimum ambient noise. In order to address such issues, the technique of denoising and estimating the biomedical heart signal is proposed in this investigation. Normally, the performance of the filter naturally depends on prior information related to the statistical properties of the signal and the background noise. This paper proposes Kalman filtering for denoising statistical heart sound. The cycles of heart sounds are certain to follow first-order Gauss-Markov process. These cycles are observed with additional noise for the given measurement. The model is formulated into state-space form to enable use of a Kalman filter to estimate the clean cycles of heart sounds. The estimates obtained by Kalman filtering are optimal in mean squared sense.
An Unbiased Unscented Transform Based Kalman Filter for 3D Radar
Institute of Scientific and Technical Information of China (English)
WANGGuohong; XIUJianjuan; HEYou
2004-01-01
As a derivative-free alternative to the Extended Kalman filter (EKF) in the framework of state estimation, the Unscented Kalman filter (UKF) has potential applications in nonlinear filtering. By noting the fact that the unscented transform is generally biased when converting the radar measurements from spherical coordinates into Cartesian coordinates, a new filtering algorithm for 3D radar, called Unbiased unscented Kalman filter (UUKF), is proposed. The new algorithm is validated by Monte Carlo simulation runs. Simulation results show that the UUKF is more effective than the UKF, EKF and the Converted measurement Kalman filter (CMKF).
Erna Apriliani; Dieky Adzkiya; Arief Baihaqi
2011-01-01
Kalman filter is an algorithm to estimate the state variable of dynamical stochastic system. The square root ensemble Kalman filter is an modification of Kalman filter. The square root ensemble Kalman filter is proposed to keep the computational stability and reduce the computational time. In this paper we study the efficiency of the reduced rank ensemble Kalman filter. We apply this algorithm to the non isothermal continue stirred tank reactor problem. We decompose the covariance of the ense...
Robust tracking with spatio-velocity snakes: Kalman filtering approach
Energy Technology Data Exchange (ETDEWEB)
Peterfreund, N.
1998-12-31
Using results from robust Kalman filtering, we present a new Kalman filter-based snake model for tracking of nonrigid objects in combined spatio-velocity space. The proposed model is the stochastic version of the velocity snake, an active contour model for combined tracking of position and velocity of nonrigid boundaries. The proposed model uses image gradient and optical flow measurements along the contour as system measurements. An optical-flow based measurement error is used to detect and reject image measurements which correspond to image clutter or to other objects. The method was applied to object tracking of both rigid and nonrigid objects, resulting in good tracking results and robustness to image clutter, occlusions and numerical noise. 19 refs., 3 figs.
Robust tracking with spatio-velocity snakes: Kalman filtering approach
Energy Technology Data Exchange (ETDEWEB)
Peterfreund, N.
1997-06-01
Using results from robust Kalman filtering, the author presents a new Kalman filter-based snake model for tracking of nonrigid objects in combined spatio-velocity space. The proposed model is the stochastic version of the velocity snake, an active contour model for combined tracking of position and velocity of nonrigid boundaries. The proposed model uses image gradient and optical flow measurements along the contour as system measurements. An optical-flow based measurement error is used to detect and reject image measurements which correspond to image clutter or to other objects. The method was applied to object tracking of both rigid and nonrigid objects, resulting in good tracking results and robustness to image clutter, occlusions and numerical noise.
A Multiresolution Ensemble Kalman Filter using Wavelet Decomposition
Hickmann, Kyle S
2015-01-01
We present a method of using classical wavelet based multiresolution analysis to separate scales in model and observations during data assimilation with the ensemble Kalman filter. In many applications, the underlying physics of a phenomena involve the interaction of features at multiple scales. Blending of observational and model error across scales can result in large forecast inaccuracies since large errors at one scale are interpreted as inexact data at all scales. Our method uses a transformation of the observation operator in order to separate the information from different scales of the observations. This naturally induces a transformation of the observation covariance and we put forward several algorithms to efficiently compute the transformed covariance. Another advantage of our multiresolution ensemble Kalman filter is that scales can be weighted independently to adjust each scale's effect on the forecast. To demonstrate feasibility we present applications to a one dimensional Kuramoto-Sivashinsky (...
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.
Multiplicative Quaternion Extended Kalman Filtering for Nonspinning Guided Projectiles
2013-07-01
micro- electromechanical system ( MEMS ) gyroscopes have been able to measure the spin-rates of fin- stabilized projectiles such as mortars, which...model, the statistics of the gyroscope and accelerometer noise are measureable, and can be easily incorporated into an extended Kalman filtering...tradeoff between affordability, durability, and performance. Automotive-grade MEMS components have been used in the harsh gun-launch environment for
Unscented Kalman Filter for Autonomous Warship Attitude Determination
Institute of Scientific and Technical Information of China (English)
FU Jian-guo; WANG Xiao-tong; JIN Lian-gan; MA Ye
2005-01-01
To address a problem of autonomous attitude determination algorithm using gravitational field and geomagnetic field observation, a new recursive optimization autonomous attitude estimation algorithm is proposed. The algorithm is based on unscented Kalman filter(UKF), and can synchronously provide the attitude rate information. The simulated results show that the measurement precision of the method could be increased by 2 times compared to that of the common methods.
Robust Optical User Motion Tracking Using a Kalman Filter
Dorfmüller-Ulhaas, Klaus
2007-01-01
Optical tracking has a great future in applications of virtual and augmented reality. It will assist to enhance the acceptance of virtual reality user interfaces, since optical tracking allows wireless interaction and precise tracking. Existing commercial motion capture systems are neither working reliably in real-time. Additionally, only few optical trackers can smooth and predict motion and include a motion estimator supplying similar results to the presented approach. A Kalman filter formu...
Adaptive high-gain extended kalman filter and applications
Boizot, Nicolas Richard
2010-01-01
The work concerns the ``observability problem” --- the reconstruction of a dynamic process's full state from a partially measured state--- for nonlinear dynamic systems. The Extended Kalman Filter (EKF) is a widely-used observer for such nonlinear systems. However it suffers from a lack of theoretical justifications and displays poor performance when the estimated state is far from the real state, e.g. due to large perturbations, a poor initial state estimate, etc… We propose a solution to...
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.
Improvements of Analog Neural Networks Based on Kalman Filter
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Z. Raida
2002-04-01
Full Text Available In the paper, original improvements of recurrent analog neuralnetworks, which are based on Kalman filter, are presented. Theseimprovements eliminate some disadvantages of the classical Kalmanneural network and enable a real time processing of quickly changingsignals, which appear in adaptive antennas and similar applications.This goal is reached using such circuit elements, which increase theconvergence rate of the network and decrease the dependence ofconvergence rate on the ratio of eigenvalues of the correlation matrixof input signals.
Kalman Filter Based Tracking in an Video Surveillance System
SULIMAN, C.; CRUCERU, C.; Moldoveanu, F.
2010-01-01
In this paper we have developed a Matlab/Simulink based model for monitoring a contact in a video surveillance sequence. For the segmentation process and corect identification of a contact in a surveillance video, we have used the Horn-Schunk optical flow algorithm. The position and the behavior of the correctly detected contact were monitored with the help of the traditional Kalman filter. After that we have compared the results obtained from the optical flow method with the ones obtaine...
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
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...
Three-dimensional motion tracking by Kalman filtering
Gao, Jean; Kosaka, Akio; Kak, Avinash C.
2000-10-01
In this paper, a 3D semantic object motion tracking method based on Kalman filtering is proposed. First, we use a specially designed Color Image Segmentation Editor (CISE) to devise shapes that more accurately describe the object to be tracked. CISE is an integration of edge and region detection, which is based on edge-linking, split-and-merge and the energy minimization for active contour detection. An ROI is further segmented into single motion blobs by considering the constancy of the motion parameters in each blob. Over short time intervals, each blob can be tracked separately and, over longer times, the blobs can be allowed to fragment and coalesce into new blobs as motion evolves. The tracking of each blob is based on a Kalman filter derived from linearization of a constraint equation satisfied by the pinhole model of a camera. The Kalman filter allows the tracker to project the uncertainties associated with a blob center (or with the coordinates of any other features) into the next frame. This projected uncertainty region can then be searched rot eh pixels belonging to the blob. Future work includes investigation of the effects of illumination changes and simultaneous tracking of multiple targets.
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.
Autonomous Orbit Determination via Kalman Filtering of Gravity Gradients
Sun, Xiucong; Macabiau, Christophe; Han, Chao
2016-01-01
Spaceborne gravity gradients are proposed in this paper to provide autonomous orbit determination capabilities for near Earth satellites. The gravity gradients contain useful position information which can be extracted by matching the observations with a precise gravity model. The extended Kalman filter is investigated as the principal estimator. The stochastic model of orbital motion, the measurement equation and the model configuration are discussed for the filter design. An augmented state filter is also developed to deal with unknown significant measurement biases. Simulations are conducted to analyze the effects of initial errors, data-sampling periods, orbital heights, attitude and gradiometer noise levels, and measurement biases. Results show that the filter performs well with additive white noise observation errors. Degraded observability for the along-track position is found for the augmented state filter. Real flight data from the GOCE satellite are used to test the algorithm. Radial and cross-track...
An adaptive Kalman filter for ECG signal enhancement.
Vullings, Rik; de Vries, Bert; Bergmans, Jan W M
2011-04-01
The ongoing trend of ECG monitoring techniques to become more ambulatory and less obtrusive generally comes at the expense of decreased signal quality. To enhance this quality, consecutive ECG complexes can be averaged triggered on the heartbeat, exploiting the quasi-periodicity of the ECG. However, this averaging constitutes a tradeoff between improvement of the SNR and loss of clinically relevant physiological signal dynamics. Using a bayesian framework, in this paper, a sequential averaging filter is developed that, in essence, adaptively varies the number of complexes included in the averaging based on the characteristics of the ECG signal. The filter has the form of an adaptive Kalman filter. The adaptive estimation of the process and measurement noise covariances is performed by maximizing the bayesian evidence function of the sequential ECG estimation and by exploiting the spatial correlation between several simultaneously recorded ECG signals, respectively. The noise covariance estimates thus obtained render the filter capable of ascribing more weight to newly arriving data when these data contain morphological variability, and of reducing this weight in cases of no morphological variability. The filter is evaluated by applying it to a variety of ECG signals. To gauge the relevance of the adaptive noise-covariance estimation, the performance of the filter is compared to that of a Kalman filter with fixed, (a posteriori) optimized noise covariance. This comparison demonstrates that, without using a priori knowledge on signal characteristics, the filter with adaptive noise estimation performs similar to the filter with optimized fixed noise covariance, favoring the adaptive filter in cases where no a priori information is available or where signal characteristics are expected to fluctuate.
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.
Kalman filtering for time-delayed linear systems
Institute of Scientific and Technical Information of China (English)
LU Xiao; WANG Wei
2006-01-01
This paper is to study the linear minimum variance estimation for discrete- time systems. A simple approach to the problem is presented by developing re-organized innovation analysis for the systems with instantaneous and double time-delayed measurements. It is shown that the derived estimator involves solving three different standard Kalman filtering with the same dimension as the original system. The obtained results form the basis for solving some complicated problems such as H∞ fixed-lag smoothing, preview control, H∞ filtering and control with time delays.
2014-09-01
attitude estimate. 1. INTRODUCTION The utility of using brightness ( radiometric flux intensity) measurements to determine a space object (SO)’s...a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE SEP...2014 2. REPORT TYPE 3. DATES COVERED 00-00-2014 to 00-00-2014 4. TITLE AND SUBTITLE Comparison of Unscented Kalman Filter and Unscented Schmidt
Object Tracking System Using Approximate Median Filter, Kalman Filter and Dynamic Template Matching
Directory of Open Access Journals (Sweden)
G. Mallikarjuna Rao
2014-04-01
Full Text Available In this work, we dealt with the tracking of single object in a sequence of frames either from a live camera or a previously saved video. A moving object is detected frame-by-frame with high accuracy and efficiency using Median approximation technique. As soon as the object has been detected, the same is tracked by kalman filter estimation technique along with a more accurate Template Matching algorithm. The templates are dynamically generated for this purpose. This guarantees any change in object pose which does not be hindered from tracking procedure. The system is capable of handling entry and exit of an object. Such a tracking scheme is cost effective and it can be used as an automated video conferencing system and also has application as a surveillance tool. Several trials of the tracking show that the approach is correct and extremely fast, and it's a more robust performance throughout the experiments.
Software Would Largely Automate Design of Kalman Filter
Chuang, Jason C. H.; Negast, William J.
2005-01-01
Embedded Navigation Filter Automatic Designer (ENFAD) is a computer program being developed to automate the most difficult tasks in designing embedded software to implement a Kalman filter in a navigation system. The most difficult tasks are selection of error states of the filter and tuning of filter parameters, which are timeconsuming trial-and-error tasks that require expertise and rarely yield optimum results. An optimum selection of error states and filter parameters depends on navigation-sensor and vehicle characteristics, and on filter processing time. ENFAD would include a simulation module that would incorporate all possible error states with respect to a given set of vehicle and sensor characteristics. The first of two iterative optimization loops would vary the selection of error states until the best filter performance was achieved in Monte Carlo simulations. For a fixed selection of error states, the second loop would vary the filter parameter values until an optimal performance value was obtained. Design constraints would be satisfied in the optimization loops. Users would supply vehicle and sensor test data that would be used to refine digital models in ENFAD. Filter processing time and filter accuracy would be computed by ENFAD.
VLBI real-time analysis by Kalman Filtering
Karbon, Maria; Soja, Benedikt; Nilson, Tobias; Heinkelmann, Robert; Liu, Li; Lu, Ciuxian; Xu, Minghui; Raposo-Pulido, Virginia; Mora-Diaz, Julian; Schuh, Harald
2014-05-01
Geodetic Very Long Baseline Interferometry (VLBI) is one of the primary space geodetic techniques. It provides the full set of Earth Orientation Parameter (EOP) and is unique for observing long term Universal Time (UT1) and precession/nutation. Currently the VLBI products are delivered with a delay of about two weeks from the moment of the observation. However, the need for near-real time estimates of the parameters is increasing, e.g. for satellite based navigation and positioning or for enabling precise tracking of interplanetary spacecraft. The goal is thus to reduce the time span between observation and the final result to less than one day. This can be archived by replacing the classical least squares method with an adaptive Kalman filter. We have developed a Kalman filter for VLBI data analysis. This method has the advantage that it is simultaneously possible to estimate stationary parameters, e.g. station positions, and to model the highly variable stochastic behavior of non-stationary parameters like clocks or atmospheric parameters. The filter is able to perform without any human interaction, making it a completely autonomous tool. In this work we describe the filter and discuss its application for EOP determination and prediction. We discuss the implementation of the stochastic models to statistically account for unpredictable changes in EOP. Furthermore, additional data like results from other techniques can be included to improve the performance. For example, atmospheric angular momentum calculated from numerical weather models can be introduced to supplement the short-term prediction of UT1 and polar motion. This Kalman filter will be extended and embedded in the newly developed Vienna VLBI Software (VieVS) as a completely autonomous tool enabling the VLBI analysis in near real-time and providing all the parameters of interest with the highest possible accuracy.
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...
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.
Stochastic Optimal Estimation with Fuzzy Random Variables and Fuzzy Kalman Filtering
Institute of Scientific and Technical Information of China (English)
FENG Yu-hu
2005-01-01
By constructing a mean-square performance index in the case of fuzzy random variable, the optimal estimation theorem for unknown fuzzy state using the fuzzy observation data are given. The state and output of linear discrete-time dynamic fuzzy system with Gaussian noise are Gaussian fuzzy random variable sequences. An approach to fuzzy Kalman filtering is discussed. Fuzzy Kalman filtering contains two parts: a real-valued non-random recurrence equation and the standard Kalman filtering.
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.
KALMAN FILTERING CORRECTION IN REAL-TIME FORECASTING WITH HYDRODYNAMIC MODEL
Institute of Scientific and Technical Information of China (English)
WU Xiao-ling; WANG Chuan-hai; CHEN Xi; XIANG Xiao-hua; ZHOU Quan
2008-01-01
Accurate and reliable flood forecast is crucial for efficient real-time river management, including flood control, flood warning, reservoir operation and river regulation. In order to improve the estimate of the initial state of the forecasting system and to reduce the errors in the forecast period a data assimilation procedure was often need. The Kalman filter was proven to be an efficient method to adjust real-time flood series and improve the initial conditions before the forecast. A new model integrating the hydraulic model with the Kalman filter for real-time correction of flood forecast was developed and applied in the Three Gorges interzone of the Yangtze River. The method was calibrated and verified against the observed flood stage and discharge during Three Gorges Dam construction periods (2004). The results demonstrate that the new model incorporates an accurate and fast updating technique can improve the reliability of the flood forecast.
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.
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.
Wellbore Surveying While Drilling Based on Kalman Filtering
Directory of Open Access Journals (Sweden)
Mahmoud ElGizawy
2010-01-01
by designing a reliable real-time low cost MWD surveying system based on MEMS inertial sensors miniaturized inside the RSS housing installed directly behind the drill bit. A continuous borehole surveying module based on MEMS inertial sensors integrated with other drilling measurements was developed using Kalman filtering.
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.
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
Moaveni, Bijan; Khosravi Roqaye Abad, Mahdi; Nasiri, Sayyad
2015-10-01
In this paper, vehicle longitudinal velocity during the braking process is estimated by measuring the wheels speed. Here, a new algorithm based on the unknown input Kalman filter is developed to estimate the vehicle longitudinal velocity with a minimum mean square error and without using the value of braking torque in the estimation procedure. The stability and convergence of the filter are analysed and proved. Effectiveness of the method is shown by designing a real experiment and comparing the estimation result with actual longitudinal velocity computing from a three-axis accelerometer output.
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.
Non-linear Kalman filters for calibration in radio interferometry
Tasse, Cyril
2014-01-01
We present a new calibration scheme based on a non-linear version of Kalman filter that aims at estimating the physical terms appearing in the Radio Interferometry Measurement Equation (RIME). We enrich the filter's structure with a tunable data representation model, together with an augmented measurement model for regularization. We show using simulations that it can properly estimate the physical effects appearing in the RIME. We found that this approach is particularly useful in the most extreme cases such as when ionospheric and clock effects are simultaneously present. Combined with the ability to provide prior knowledge on the expected structure of the physical instrumental effects (expected physical state and dynamics), we obtain a fairly cheap algorithm that we believe to be robust, especially in low signal-to-noise regime. Potentially the use of filters and other similar methods can represent an improvement for calibration in radio interferometry, under the condition that the effects corrupting visib...
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.
Arcasoy, C. C.
1992-11-01
The problem of multi-output, infinite-time, linear time-invariant optimal Kalman-Bucy filter both in continuous and discrete-time cases in frequency domain is addressed. A simple new algorithm is given for the analytical solution to the steady-state gain of the optimum filter based on a transfer function approach. The algorithm is based on spectral factorization of observed spectral density matrix of the filter which generates directly the return-difference matrix of the optimal filter. The method is more direct than by algebraic Riccati equation solution and can easily be implemented on digital computer. The design procedure is illustrated by examples and closed-form solution of ECV and ECA radar tracking filters are considered as an application of the method.
Kalman filter based algorithms for PANDA rate at FAIR
Energy Technology Data Exchange (ETDEWEB)
Prencipe, Elisabetta; Ritman, James [IKP, Forschungszentrum Juelich (Germany); Rauch, Johannes [E18, Technische Universitaet Muenchen (Germany); Collaboration: PANDA-Collaboration
2015-07-01
PANDA at the future FAIR facility in Darmstadt is an experiment with a cooled antiproton beam in a range between 1.5 and 15 GeV/c, allowing a wide physics program in nuclear and particle physics. High average reaction rates up to 2.10{sup 7} interactions/s are expected. PANDA is the only experiment worldwide, which combines a solenoid field and a dipole field in an experiment with a fixed target topology. The tracking system must be able to reconstruct high momenta in the laboratory frame. The tracking system of PANDA involves the presence of a high performance silicon vertex detector, a GEM detector, a Straw-Tubes central tracker, a forward tracking system, and a luminosity monitor. The first three of those, are inserted in a solenoid homogeneous magnetic field (B=2 T), the latter two are inside a dipole magnetic field (B=2 Tm), The offline tracking algorithm is developed within the PandaRoot framework, which is a part of the FAIRRoot project. The algorithm is based on a tool containing the Kalman Filter equations and a deterministic annealing filter (GENFIT). The Kalman-Filter-based routines can perform extrapolations of track parameters and covariance matrices. In GENFIT2, the Runge-Kutta track representation is available. First results of an implementation of GENFIT2 in PandaRoot are presented. Resolutions and efficiencies for different beam momenta and different track hypotheses are shown.
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.
Consensus+Innovations Distributed Kalman Filter With Optimized Gains
Das, Subhro; Moura, Jose M. F.
2017-01-01
In this paper, we address the distributed filtering and prediction of time-varying random fields represented by linear time-invariant (LTI) dynamical systems. The field is observed by a sparsely connected network of agents/sensors collaborating among themselves. We develop a Kalman filter type consensus+innovations distributed linear estimator of the dynamic field termed as Consensus+Innovations Kalman Filter. We analyze the convergence properties of this distributed estimator. We prove that the mean-squared error of the estimator asymptotically converges if the degree of instability of the field dynamics is within a pre-specified threshold defined as tracking capacity of the estimator. The tracking capacity is a function of the local observation models and the agent communication network. We design the optimal consensus and innovation gain matrices yielding distributed estimates with minimized mean-squared error. Through numerical evaluations, we show that, the distributed estimator with optimal gains converges faster and with approximately 3dB better mean-squared error performance than previous distributed estimators.
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...
An Extended Kalman Filter with a Computed Mean Square Error Bound
Hexner, Gyorgy; Weiss, Haim
2014-01-01
The paper proposes a new recursive filter for non-linear systems that inherently computes a valid bound on the mean square estimation error. The proposed filter, bound based extended Kalman, (BEKF) is in the form of an extended Kalman filter. The main difference of the proposed filter from the conventional extended Kalman filter is in the use of a computed mean square error bound matrix, to calculate the filter gain, and to serve as bound on the actual mean square error. The paper shows that ...
Application of Kalman Filter on modelling interest rates
Directory of Open Access Journals (Sweden)
Long H. Vo
2014-03-01
Full Text Available This study aims to test the feasibility of using a data set of 90-day bank bill forward rates from the Australian market to predict spot interest rates. To achieve this goal I utilized the application of Kalman Filter in a state space model with time-varying state variable. It is documented that in the case of short-term interest rates,the state space model yields robust predictive power. In addition, this predictive power of implied forward rate is heavily impacted by the existence of a time-varying risk premium in the term structure.
4-D-Var or ensemble Kalman filter?
Kalnay, Eugenia; LI, HONG; Miyoshi, Takemasa; Yang, Shu-Chih; Ballabrera-Poy, Joaquim
2007-01-01
We consider the relative advantages of two advanced data assimilation systems, 4-D-Var and ensemble Kalman filter (EnKF), currently in use or under consideration for operational implementation. With the Lorenz model, we explore the impact of tuning assimilation parameters such as the assimilation window length and background error covariance in 4-D-Var, variance inflation in EnKF, and the effect of model errors and reduced observation coverage. For short assimilation windows EnKF gives more a...
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.).
Optimal subband Kalman filter for normal and oesophageal speech enhancement.
Ishaq, Rizwan; García Zapirain, Begoña
2014-01-01
This paper presents the single channel speech enhancement system using subband Kalman filtering by estimating optimal Autoregressive (AR) coefficients and variance for speech and noise, using Weighted Linear Prediction (WLP) and Noise Weighting Function (NWF). The system is applied for normal and Oesophageal speech signals. The method is evaluated by Perceptual Evaluation of Speech Quality (PESQ) score and Signal to Noise Ratio (SNR) improvement for normal speech and Harmonic to Noise Ratio (HNR) for Oesophageal Speech (OES). Compared with previous systems, the normal speech indicates 30% increase in PESQ score, 4 dB SNR improvement and OES shows 3 dB HNR improvement.
Telescope Multi-Field Wavefront Control with a Kalman Filter
Lou, John Z.; Redding, David; Sigrist, Norbert; Basinger, Scott
2008-01-01
An effective multi-field wavefront control (WFC) approach is demonstrated for an actuated, segmented space telescope using wavefront measurements at the exit pupil, and the optical and computational implications of this approach are discussed. The integration of a Kalman Filter as an optical state estimator into the wavefront control process to further improve the robustness of the optical alignment of the telescope will also be discussed. Through a comparison of WFC performances between on-orbit and ground-test optical system configurations, the connection (and a possible disconnection) between WFC and optical system alignment under these circumstances are analyzed. Our MACOS-based computer simulation results will be presented and discussed.
Application of Unscented Kalman Filter in Satellite Orbit Simulation
Institute of Scientific and Technical Information of China (English)
ZHAO Dongming; CAI Zhiwu
2006-01-01
A new estimate method is proposed, which takes advantage of the unscented transform method, thus the true mean and covariance are approximated more accurately. The new method can be applied to non-linear systems without the linearization process necessary for the EKF, and it does not demand a Gaussian distribution of noise and what's more, its ease of implementation and more accurate estimation features enables it to demonstrate its good performance in the experiment of satellite orbit simulation. Numerical experiments show that the application of the unscented Kalman filter is more effective than the EKF.
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.
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.
Wang, Xudong; Syrmos, Vassilis L.
2004-07-01
In this paper, an adaptive reconfigurable control system based on extended Kalman filter approach and eigenstructure assignments is proposed. System identification is carried out using an extended Kalman filter (EKF) approach. An eigenstructure assignment (EA) technique is applied for reconfigurable feedback control law design to recover the system dynamic performance. The reconfigurable feedforward controllers are designed to achieve the steady-state tracking using input weighting approach. The proposed scheme can identify not only actuator and sensor variations, but also changes in the system structures using the extended Kalman filtering method. The overall design is robust with respect to uncertainties in the state-space matrices of the reconfigured system. To illustrate the effectiveness of the proposed reconfigurable control system design technique, an aircraft longitudinal vertical takeoff and landing (VTOL) control system is used to demonstrate the reconfiguration procedure.
Rigatos, Gerasimos
2016-07-01
The Derivative-free nonlinear Kalman Filter is used for developing a communication system that is based on a chaotic modulator such as the Duffing system. In the transmitter's side, the source of information undergoes modulation (encryption) in which a chaotic signal generated by the Duffing system is the carrier. The modulated signal is transmitted through a communication channel and at the receiver's side demodulation takes place, after exploiting the estimation provided about the state vector of the chaotic oscillator by the Derivative-free nonlinear Kalman Filter. Evaluation tests confirm that the proposed filtering method has improved performance over the Extended Kalman Filter and reduces significantly the rate of transmission errors. Moreover, it is shown that the proposed Derivative-free nonlinear Kalman Filter can work within a dual Kalman Filtering scheme, for performing simultaneously transmitter-receiver synchronisation and estimation of unknown coefficients of the communication channel.
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. T...
A Tensor Network Kalman filter with an application in recursive MIMO Volterra system identification
Batselier, Kim; Chen, Zhongming; Wong, Ngai
2016-01-01
This article introduces a Tensor Network Kalman filter, which can estimate state vectors that are exponentially large without ever having to explicitly construct them. The Tensor Network Kalman filter also easily accommodates the case where several different state vectors need to be estimated simultaneously. The key lies in rewriting the standard Kalman equations as tensor equations and then implementing them using Tensor Networks, which effectively transforms the exponential storage cost and...
Hierarchical Bayes Ensemble Kalman Filter for geophysical data assimilation
Tsyrulnikov, Michael; Rakitko, Alexander
2016-04-01
In the Ensemble Kalman Filter (EnKF), the forecast error covariance matrix B is estimated from a sample (ensemble), which inevitably implies a degree of uncertainty. This uncertainty is especially large in high dimensions, where the affordable ensemble size is orders of magnitude less than the dimensionality of the system. Common remedies include ad-hoc devices like variance inflation and covariance localization. The goal of this study is to optimize the account for the inherent uncertainty of the B matrix in EnKF. Following the idea by Myrseth and Omre (2010), we explicitly admit that the B matrix is unknown and random and estimate it along with the state (x) in an optimal hierarchical Bayes analysis scheme. We separate forecast errors into predictability errors (i.e. forecast errors due to uncertainties in the initial data) and model errors (forecast errors due to imperfections in the forecast model) and include the two respective components P and Q of the B matrix into the extended control vector (x,P,Q). Similarly, we break the traditional forecast ensemble into the predictability-error related ensemble and model-error related ensemble. The reason for the separation of model errors from predictability errors is the fundamental difference between the two sources of error. Model error are external (i.e. do not depend on the filter's performance) whereas predictability errors are internal to a filter (i.e. are determined by the filter's behavior). At the analysis step, we specify Inverse Wishart based priors for the random matrices P and Q and conditionally Gaussian prior for the state x. Then, we update the prior distribution of (x,P,Q) using both observation and ensemble data, so that ensemble members are used as generalized observations and ordinary observations are allowed to influence the covariances. We show that for linear dynamics and linear observation operators, conditional Gaussianity of the state is preserved in the course of filtering. At the forecast
Reconstruction of spacecraft rotational motion using a Kalman filter
Pankratov, V. A.; Sazonov, V. V.
2016-05-01
Quasi-static microaccelerations of four satellites of the Foton series (nos. 11, 12, M-2, M-3) were monitored as follows. First, according to measurements of onboard sensors obtained in a certain time interval, spacecraft rotational motion was reconstructed in this interval. Then, along the found motion, microacceleration at a given onboard point was calculated according to the known formula as a function of time. The motion was reconstructed by the least squares method using the solutions to the equations of satellite rotational motion. The time intervals in which these equations make reconstruction possible were from one to five orbital revolutions. This length is increased with the modulus of the satellite angular velocity. To get an idea on microaccelerations and satellite motion during an entire flight, the motion was reconstructed in several tens of such intervals. This paper proposes a method for motion reconstruction suitable for an interval of arbitrary length. The method is based on the Kalman filter. We preliminary describe a new version of the method for reconstructing uncontrolled satellite rotational motion from magnetic measurements using the least squares method, which is essentially used to construct the Kalman filter. The results of comparison of both methods are presented using the data obtained on a flight of the Foton M-3.
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.
Attitude Estimation Using Kalman Filtering: External Acceleration Compensation Considerations
Directory of Open Access Journals (Sweden)
Romy Budhi Widodo
2016-01-01
Full Text Available Attitude estimation is often inaccurate during highly dynamic motion due to the external acceleration. This paper proposes extended Kalman filter-based attitude estimation using a new algorithm to overcome the external acceleration. This algorithm is based on an external acceleration compensation model to be used as a modifying parameter in adjusting the measurement noise covariance matrix of the extended Kalman filter. The experiment was conducted to verify the estimation accuracy, that is, one-axis and multiple axes sensor movement. Five approaches were used to test the estimation of the attitude: (1 the KF-based model without compensating for external acceleration, (2 the proposed KF-based model which employs the external acceleration compensation model, (3 the two-step KF using weighted-based switching approach, (4 the KF-based model which uses the threshold-based approach, and (5 the KF-based model which uses the threshold-based approach combined with a softened part approach. The proposed algorithm showed high effectiveness during the one-axis test. When the testing conditions employed multiple axes, the estimation accuracy increased using the proposed approach and exhibited external acceleration rejection at the right timing. The proposed algorithm has fewer parameters that need to be set at the expense of the sharpness of signal edge transition.
3D hand tracking using Kalman filter in depth space
Park, Sangheon; Yu, Sunjin; Kim, Joongrock; Kim, Sungjin; Lee, Sangyoun
2012-12-01
Hand gestures are an important type of natural language used in many research areas such as human-computer interaction and computer vision. Hand gestures recognition requires the prior determination of the hand position through detection and tracking. One of the most efficient strategies for hand tracking is to use 2D visual information such as color and shape. However, visual-sensor-based hand tracking methods are very sensitive when tracking is performed under variable light conditions. Also, as hand movements are made in 3D space, the recognition performance of hand gestures using 2D information is inherently limited. In this article, we propose a novel real-time 3D hand tracking method in depth space using a 3D depth sensor and employing Kalman filter. We detect hand candidates using motion clusters and predefined wave motion, and track hand locations using Kalman filter. To verify the effectiveness of the proposed method, we compare the performance of the proposed method with the visual-based method. Experimental results show that the performance of the proposed method out performs visual-based method.
Multimodal Degradation Prognostics Based on Switching Kalman Filter Ensemble.
Lim, Pin; Goh, Chi Keong; Tan, Kay Chen; Dutta, Partha
2017-01-01
For accurate prognostics, users have to determine the current health of the system and predict future degradation pattern of the system. An increasingly popular approach toward tackling prognostic problems involves the use of switching models to represent various degradation phases, which the system undergoes. Such approaches have the advantage of determining the exact degradation phase of the system and being able to handle nonlinear degradation models through piecewise linear approximation. However, limitations of such existing methods include, limited applicability due to the discretization of predicted remaining useful life, insufficient robustness due to the use of single models and others. This paper circumvents these limitations by proposing a hybrid of ensemble methods with switching methods. The proposed method first implements a switching Kalman filter (SKF) to classify between various linear degradation phases, then predict the future propagation of fault dimension using appropriate Kalman filters for each phase. This proposed method achieves both continuous and discrete prediction values representing the remaining life and degradation phase of the system, respectively. The proposed framework is shown via a case study on benchmark simulated aeroengine data sets. The evaluation of the proposed framework shows that the proposed method achieves better accuracy and robustness against noise compared with other methods reported in the literature. The results also indicate the effectiveness of the SKF in detecting the switching point between various degradation modes.
Tractography from HARDI using an intrinsic unscented Kalman filter.
Cheng, Guang; Salehian, Hesamoddin; Forder, John R; Vemuri, Baba C
2015-01-01
A novel adaptation of the unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multitensor estimation and fiber tractography from diffusion MRI. This technique has the advantage over other tractography methods in terms of computational efficiency, due to the fact that the UKF simultaneously estimates the diffusion tensors and propagates the most consistent direction to track along. This UKF and its variants reported later in literature however are not intrinsic to the space of diffusion tensors. Lack of this key property can possibly lead to inaccuracies in the multitensor estimation as well as in the tractography. In this paper, we propose a novel intrinsic unscented Kalman filter (IUKF) in the space of diffusion tensors which are symmetric positive definite matrices, that can be used for simultaneous recursive estimation of multitensors and propagation of directional information for use in fiber tractography from diffusion weighted MR data. In addition to being more accurate, IUKF retains all the advantages of UKF mentioned above. We demonstrate the accuracy and effectiveness of the proposed method via experiments publicly available phantom data from the fiber cup-challenge (MICCAI 2009) and diffusion weighted MR scans acquired from human brains and rat spinal cords.
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.
Secure Tracking in Sensor Networks using Adaptive Extended Kalman Filter
Fard, Ali P
2012-01-01
Location information of sensor nodes has become an essential part of many applications in Wireless Sensor Networks (WSN). The importance of location estimation and object tracking has made them the target of many security attacks. Various methods have tried to provide location information with high accuracy, while lots of them have neglected the fact that WSNs may be deployed in hostile environments. In this paper, we address the problem of securely tracking a Mobile Node (MN) which has been noticed very little previously. A novel secure tracking algorithm is proposed based on Extended Kalman Filter (EKF) that is capable of tracking a Mobile Node (MN) with high resolution in the presence of compromised or colluding malicious beacon nodes. It filters out and identifies the malicious beacon data in the process of tracking. The proposed method considerably outperforms the previously proposed secure algorithms in terms of either detection rate or MSE. The experimental data based on different settings for the netw...
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.
CSIR Research Space (South Africa)
Salmon, BP
2012-07-01
Full Text Available In this paper, the internal operations of an Extended Kalman Filter is investigated to see if any useful information can be derived to detect land cover change in a MODIS time series. The Extended Kalman Filter expands its internal covariance if a...
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.
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.
Unscented Kalman filtering in the additive noise case
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The unscented Kalman filter(UKF) has four implementations in the additive noise case,according to whether the state is augmented with noise vectors and whether a new set of sigma points is redrawn from the predicted state(which is so-called resampling) for the observation prediction.This paper concerns the differences of performances for those implementations,such as accuracy,adaptability,computational complexity,etc.The conditionally equivalent relationships between the augmented and non-augmented unscented transforms(UTs) are proved for several sampling strategies that are commonly used.Then,we find that the augmented and non-augmented UKFs have the same filter results with the additive measurement noise,but only have the same state predictions with the additive process noise.Resampling is not believed to be necessary in some researches.However,we find out that resampling can be helpful for an adaptive Kalman gain.This will improve the convergence and accuracy of the filter when the large scale state modeling bias or unknown maneuvers occur.Finally,some universal designing principles for a practical UKF are given as follows:1) for the additive observation noise case,it’s better to use the non-augmented UKF;2) for the additive process noise case,when the small state modeling bias or maneuvers are involved,the non-resampling algorithms with state whether augmented or not are candidates for filters;3) the resampling and non-augmented algorithm is the only choice while the large state modeling bias or maneuvers are latent.
Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter
Miller, Bard A.; Howard, Samuel A.
2008-01-01
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter
Miller, Brad A.; Howard, Samuel A.
2008-01-01
An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.
Alternatives to an extended Kalman Filter for target image tracking
Leuthauser, P. R.
1981-12-01
Four alternative filters are compared to an extended Kalman filter (EKF) algorithm for tracking a distributed (elliptical) source target in a closed loop tracking problem, using outputs from a forward looking (FLIR) sensor as measurements. These were (1) an EKF with (second order) bias correction term, (2) a constant gain EKF, (3) a constant gain EKF with bias correction term, and (4) a statistically linearized filter. Estimates are made of both actual target motion and of apparent motion due to atmospheric jitter. These alternative designs are considered specifically to address some of the significant biases exhibited by an EKF due to initial acquisition difficulties, unmodelled maneuvering by the target, low signal-to-noise ratio, and real world conditions varying significantly from those assumed in the filter design (robustness). Filter performance was determined with a Monte Carlo study under both ideal and non ideal conditions for tracking targets on a constant velocity cross range path, and during constant acceleration turns of 5G, 10G, and 20G.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Representing earthquake ground motion as time varying ARMA model, the instantaneous spectrum can only be determined by the time varying coefficients of the corresponding ARMA model. In this paper, unscented Kalman filter is applied to estimate the time varying coefficients. The comparison between the estimation results of unscented Kalman filter and Kalman filter methods shows that unscented Kalman filter can more precisely represent the distribution of the spectral peaks in time-frequency plane than Kalman filter, and its time and frequency resolution is finer which ensures its better ability to track the local properties of earthquake ground motions and to identify the systems with nonlinearity or abruptness. Moreover, the estimation results of ARMA models with different orders indicate that the theoretical frequency resolving power ofARMA model which was usually ignored in former studies has great effect on the estimation precision of instantaneous spectrum and it should be taken as one of the key factors in order selection of ARMA model.
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.
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...... is to be encouraged in this perspective. However, the predicted uncertainty of the assimilation results are sensitive to the parameters and hence must be applied with care. The sensitivity study further demonstrates the effectiveness of the steady Kalman filter in the given system as well as the great impact...
Estimating ice-affected streamflow by extended Kalman filtering
Holtschlag, D.J.; Grewal, M.S.
1998-01-01
An extended Kalman filter was developed to automate the real-time estimation of ice-affected streamflow on the basis of routine measurements of stream stage and air temperature and on the relation between stage and streamflow during open-water (ice-free) conditions. The filter accommodates three dynamic modes of ice effects: sudden formation/ablation, stable ice conditions, and eventual elimination. The utility of the filter was evaluated by applying it to historical data from two long-term streamflow-gauging stations, St. John River at Dickey, Maine and Platte River at North Bend, Nebr. Results indicate that the filter was stable and that parameters converged for both stations, producing streamflow estimates that are highly correlated with published values. For the Maine station, logarithms of estimated streamflows are within 8% of the logarithms of published values 87.2% of the time during periods of ice effects and within 15% 96.6% of the time. Similarly, for the Nebraska station, logarithms of estimated streamflows are within 8% of the logarithms of published values 90.7% of the time and within 15% 97.7% of the time. In addition, the correlation between temporal updates and published streamflows on days of direct measurements at the Maine station was 0.777 and 0.998 for ice-affected and open-water periods, respectively; for the Nebraska station, corresponding correlations were 0.864 and 0.997.
Using Kalman filters to reduce noise from RFID location system.
Abreu, Pedro Henriques; Xavier, José; Silva, Daniel Castro; Reis, Luís Paulo; Petry, Marcelo
2014-01-01
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).
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.
Constrained Kalman Filtering Via Density Function Truncation for Turbofan Engine Health Estimation
Simon, Dan; Simon, Donald L.
2006-01-01
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 an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the PDF (probability density function) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. The turbofan engine model contains 3 state variables, 11 measurements, and 10 component health parameters. It is also shown that the truncated Kalman filter may be a more accurate way of incorporating inequality constraints than other constrained filters (e.g., the projection approach to constrained filtering).
Interaction of Lyapunov vectors in the formulation of the nonlinear extension of the Kalman filter.
Palatella, Luigi; Trevisan, Anna
2015-04-01
When applied to strongly nonlinear chaotic dynamics the extended Kalman filter (EKF) is prone to divergence due to the difficulty of correctly forecasting the forecast error probability density function. In operational forecasting applications ensemble Kalman filters circumvent this problem with empirical procedures such as covariance inflation. This paper presents an extension of the EKF that includes nonlinear terms in the evolution of the forecast error estimate. This is achieved starting from a particular square-root implementation of the EKF with assimilation confined in the unstable subspace (EKF-AUS), that is, the span of the Lyapunov vectors with non-negative exponents. When the error evolution is nonlinear, the space where it is confined is no more restricted to the unstable and neutral subspace causing filter divergence. The algorithm presented here, denominated EKF-AUS-NL, includes the nonlinear terms in the error dynamics: These result from the nonlinear interaction among the leading Lyapunov vectors and account for all directions where the error growth may take place. Numerical results show that with the nonlinear terms included, filter divergence can be avoided. We test the algorithm on the Lorenz96 model, showing very promising results.
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.
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.
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.
Constraining the Ensemble Kalman Filter for improved streamflow forecasting
Maxwell, Deborah; Jackson, Bethanna; McGregor, James
2016-04-01
Data assimilation techniques such as the Kalman Filter and its variants are often applied to hydrological models with minimal state volume/capacity constraints. Flux constraints are rarely, if ever, applied. Consequently, model states can be adjusted beyond physically reasonable limits, compromising the integrity of model output. In this presentation, we investigate the effect of constraining the Ensemble Kalman Filter (EnKF) on forecast performance. An EnKF implementation with no constraints is compared to model output with no assimilation, followed by a 'typical' hydrological implementation (in which mass constraints are enforced to ensure non-negativity and capacity thresholds of model states are not exceeded), and then a more tightly constrained implementation where flux as well as mass constraints are imposed to limit the rate of water movement within a state. A three year period (2008-2010) with no significant data gaps and representative of the range of flows observed over the fuller 1976-2010 record was selected for analysis. Over this period, the standard implementation of the EnKF (no constraints) contained eight hydrological events where (multiple) physically inconsistent state adjustments were made. All were selected for analysis. Overall, neither the unconstrained nor the "typically" mass-constrained forecasts were significantly better than the non-filtered forecasts; in fact several were significantly degraded. Flux constraints (in conjunction with mass constraints) significantly improved the forecast performance of six events relative to all other implementations, while the remaining two events showed no significant difference in performance. We conclude that placing flux as well as mass constraints on the data assimilation framework encourages physically consistent state updating and results in more accurate and reliable forward predictions of streamflow for robust decision-making. We also experiment with the observation error, and find that this
Comparison of robust H∞ filter and Kalman filter for initial alignment of inertial navigation system
Institute of Scientific and Technical Information of China (English)
HAO Yan-ling; CHEN Ming-hui; LI Liang-jun; XU Bo
2008-01-01
There are many filtering methods that can be used for the initial alignment of an integrated inertial navigation system.This paper discussed the use of GPS,but focused on two kinds of filters for the initial alignment of an integrated strapdown inertial navigation system (SINS).One method is based on the Kalman filter (KF),and the other is based on the robust filter.Simulation results showed that the filter provides a quick transient response and a little more accurate estimate than KF,given substantial process noise or unknown noise statistics.So the robust filter is an effective and useful method for initial alignment of SINS.This research should make the use of SINS more popular,and is also a step for further research.
Kalman Filtering with Intermittent Observations: Weak Convergence and Moderate Deviations
Kar, Soummya
2009-01-01
The paper considers the problem of Kalman filtering with intermittent observations, where the observation packet arrival process is modeled as a Bernoulli process. We start by extending the results of \\cite{Riccati-weakconv} to show that the sequence of random conditional error covariance matrices converges in distribution to a unique invariant distribution $\\mathbb{\\mu}^{\\bar{\\gamma}}$, as long as the packet arrival probability $\\bar{\\gamma}>0$. We completely characterize the sequence ${\\mathbb{\\mu}^{\\bar{\\gamma}}}$ of invariant distributions as $\\bar{\\gamma}\\uparrow 1$, by showing that the sequence ${\\mathbb{\\mu}^{\\bar{\\gamma}}}$ satisfies a moderate deviations principle (MDP) with a good rate function $I$, which is explicitly characterized. We then study the sequence of invariant distributions ${\\mathbb{\\mu}^{\\bar{\\gamma}}}$ as $\\bar{\\gamma}\\uparrow 1$. We show that, as $\\bar{\\gamma}\\uparrow 1$, ...
Wet Refractivity Tomography with an hnproved Kalman-Filter Method
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
An improved retrieval method, which uses the solution with a Gaussian constraint as the initial state variables for the Kalman Filtering (KF) method, was developed to retrieve the wet refractivity profiles from slant wet delays (SWD) extracted by the double-differenced (DD) GPS method. The accuracy of the GPS-derived SWDs is also tested in this study against the measurements of a water vapor radiometer (WVR) and a weather model. It is concluded that the GPS-derived SWDs have similar accuracy to those measured with WVR and are much higher in quality than those derived from the weather model used. The developed method is used to retrieve the 3D wet refractivity distribution in the Hong Kong region. The retrieved profiles agree well with the radiosonde observations, with a difference of about 4 mm km-1 in the low levels. The accurate profiles obtained with this method are applicable in a number of meteorological applications.
Model Calibration of Exciter and PSS Using Extended Kalman Filter
Energy Technology Data Exchange (ETDEWEB)
Kalsi, Karanjit; Du, Pengwei; Huang, Zhenyu
2012-07-26
Power system modeling and controls continue to become more complex with the advent of smart grid technologies and large-scale deployment of renewable energy resources. As demonstrated in recent studies, inaccurate system models could lead to large-scale blackouts, thereby motivating the need for model calibration. Current methods of model calibration rely on manual tuning based on engineering experience, are time consuming and could yield inaccurate parameter estimates. In this paper, the Extended Kalman Filter (EKF) is used as a tool to calibrate exciter and Power System Stabilizer (PSS) models of a particular type of machine in the Western Electricity Coordinating Council (WECC). The EKF-based parameter estimation is a recursive prediction-correction process which uses the mismatch between simulation and measurement to adjust the model parameters at every time step. Numerical simulations using actual field test data demonstrate the effectiveness of the proposed approach in calibrating the parameters.
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...... May 2004-March 2005 for 7 times approximately at monthly intervals from dairy cows (n=80) stationed at the Chamau research farm of Eidgenössische Technische Hochschule (ETH), Switzerland. Benefits of KF were demonstrated using random walk models via simulations. Breeding values were predicted over...... for variance components were found (with standard errors) 0.03 (0.006) for animal genetic variance 0.04 (0.007) for permanent environmental variance and 0.21 (0.02) for error variance. Since KF gives online estimation of breeding values and does not need to store or invert matrices, this methodology could...
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.
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.
Damping strapdown inertial navigation system based on a Kalman filter
Zhao, Lin; Li, Jiushun; Cheng, Jianhua; Hao, Yong
2016-11-01
A damping strapdown inertial navigation system (DSINS) can effectively suppress oscillation errors of strapdown inertial navigation systems (SINSs) and improve the navigation accuracy of SINSs. Aiming at overcoming the disadvantages of traditional damping methods, a DSINS, based on a Kalman filter (KF), is proposed in this paper. Using the measurement data of accelerometers and calculated navigation parameters during the navigation process, the expression of the observation equation is derived. The calculation process of the observation in both the internal damping state and the external damping state is presented. Finally, system oscillation errors are compensated by a KF. Simulation and test results show that, compared with traditional damping methods, the proposed method can reduce system overshoot errors and shorten the convergence time of oscillation errors effectively.
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.
Directory of Open Access Journals (Sweden)
Malinowski Marcin
2015-02-01
Full Text Available In navigation practice, there are various navigational architecture and integration strategies of measuring instruments that affect the choice of the Kalman filtering algorithm. The analysis of different methods of Kalman filtration and associated smoothers applied in object tracing was made on the grounds of simulation tests of algorithms designed and presented in this paper. EKF (Extended Kalman Filter filter based on approximation with (jacobians partial derivations and derivative-free filters like UKF (Unscented Kalman Filter and CDKF (Central Difference Kalman Filter were implemented in comparison. For each method of filtration, appropriate smoothers EKS (Extended Kalman Smoother, UKS (Unscented Kalman Smoother and CDKS (Central Difference Kalman Smoother were presented as well. Algorithms performance is discussed on the theoretical base and simulation results of two cases are presented.
Estimation of noise parameters in dynamical system identification with Kalman filters.
Kwasniok, Frank
2012-09-01
A method is proposed for determining dynamical and observational noise parameters in state and parameter identification from time series using Kalman filters. The noise covariances are estimated in a secondary optimization by maximizing the predictive likelihood of the data. The approach is based on internal consistency; for the correct noise parameters, the uncertainty projected by the Kalman filter matches the actual predictive uncertainty. The method is able to disentangle dynamical and observational noise. The algorithm is demonstrated for the linear, extended, and unscented Kalman filters using an Ornstein-Uhlenbeck process, the noise-driven Lorenz system, and van der Pol oscillator as well as a paleoclimatic ice-core record as examples. The approach is also applicable to the ensemble Kalman filter and can be readily extended to non-Gaussian estimation frameworks such as Gaussian-sum filters and particle filters.
Attitude Determination for MAVs Using a Kalman Filter
Institute of Scientific and Technical Information of China (English)
LIU Cheng; ZHOU Zhaoying; FU Xu
2008-01-01
This paper presents a Kalman filter to effectively and economically determine the Euler angles for micro aerial vehicles(MAVs),whose size and payload are severely limited.The filter uses data from a series of micro-electro mechanical system sensors to determine the selected 3 vanables of the direction cosine matrix and the bias of the rata gyro sensors as state elements in a dynamic model,with the gravitational acceleration to build a measurement model.For high speed maneuvers,rigid motion equations are used to correct the measurements of the gravitational acceleration.The filter is designed to automatically tune its gain based on the dynamic system state.Simulations indicate that the Euler angles can be determined with standard deviations less than 3.The algorithm was successfully implemented in a miniature attitude measurement system suitable for MAVs.Aerobatic flights show that the attitude determination algorithm works effectively.The attitude determination algorithm is effective and economical,and can also be applied to bionic rebofishs and land vehicles,whose size and payload are also greatly limited.
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
Kalman-median Compound Filter for Gaussian and Impulse Noise Reduction on Digital Images
山森, 一人; 山田, 義治; 相川, 勝
2013-01-01
This paper proposes an image restoration method from degraded images which include additive gaussian noise and impulse noise. This method tries to achieve image restoration by using combination of canonical state space model kalman filter and median filter. Kalman filter estimates internal state of a dynamic system based on system model. The canonical state space models are described by two equations; state equation that expresses a transition process of the region including the focusing pixe...
Institute of Scientific and Technical Information of China (English)
Changyun Liu; Penglang Shui; Gang Wei; Song Li
2014-01-01
To improve the low tracking precision caused by lagged filter gain or imprecise state noise when the target highly maneu-vers, a modified unscented Kalman filter algorithm based on the improved filter gain and adaptive scale factor of state noise is pre-sented. In every filter process, the estimated scale factor is used to update the state noise covariance Qk, and the improved filter gain is obtained in the filter process of unscented Kalman filter (UKF) via predicted variance Pk|k-1, which is similar to the standard Kalman filter. Simulation results show that the proposed algorithm provides better accuracy and ability to adapt to the highly maneu-vering target compared with the standard UKF.
Zero Gyro Kalman Filtering in the Presence of a Reaction Wheel Failure
Hur-Diaz, Sun; Wirzburger, John; Smith, Dan; Myslinski, Mike
2007-01-01
Typical implementation of Kalman filters for spacecraft attitude estimation involves the use of gyros for three-axis rate measurements. When there are less than three axes of information available, the accuracy of the Kalman filter depends highly on the accuracy of the dynamics model. This is particularly significant during the transient period when a reaction wheel with a high momentum fails, is taken off-line, and spins down. This paper looks at how a reaction wheel failure can affect the zero-gyro Kalman filter performance for the Hubble Space Telescope and what steps are taken to minimize its impact.
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...... 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...
Hypersonic entry vehicle state estimation using nonlinearity-based adaptive cubature Kalman filters
Sun, Tao; Xin, Ming
2017-05-01
Guidance, navigation, and control of a hypersonic vehicle landing on the Mars rely on precise state feedback information, which is obtained from state estimation. The high uncertainty and nonlinearity of the entry dynamics make the estimation a very challenging problem. In this paper, a new adaptive cubature Kalman filter is proposed for state trajectory estimation of a hypersonic entry vehicle. This new adaptive estimation strategy is based on the measure of nonlinearity of the stochastic system. According to the severity of nonlinearity along the trajectory, the high degree cubature rule or the conventional third degree cubature rule is adaptively used in the cubature Kalman filter. This strategy has the benefit of attaining higher estimation accuracy only when necessary without causing excessive computation load. The simulation results demonstrate that the proposed adaptive filter exhibits better performance than the conventional third-degree cubature Kalman filter while maintaining the same performance as the uniform high degree cubature Kalman filter but with lower computation complexity.
Global Systems for Mobile Position Tracking Using Kalman and Lainiotis Filters
Directory of Open Access Journals (Sweden)
Nicholas Assimakis
2014-01-01
Full Text Available We present two time invariant models for Global Systems for Mobile (GSM position tracking, which describe the movement in x-axis and y-axis simultaneously or separately. We present the time invariant filters as well as the steady state filters: the classical Kalman filter and Lainiotis Filter and the Join Kalman Lainiotis Filter, which consists of the parallel usage of the two classical filters. Various implementations are proposed and compared with respect to their behavior and to their computational burden: all time invariant and steady state filters have the same behavior using both proposed models but have different computational burden. Finally, we propose a Finite Impulse Response (FIR implementation of the Steady State Kalman, and Lainiotis filters, which does not require previous estimations but requires a well-defined set of previous measurements.
IAE-adaptive Kalman filter for INS/GPS integrated navigation system
Institute of Scientific and Technical Information of China (English)
Bian Hongwei; Jin Zhihua; Tian Weifeng
2006-01-01
A marine INS/GPS adaptive navigation system is presented in this paper. GPS with two antenna providing vessel's altitude is selected as the auxiliary system fusing with INS to improve the performance of the hybrid system. The Kalman filter is the most frequently used algorithm in the integrated navigation system, which is capable of estimating INS errors online based on the measured errors between INS and GPS. The standard Kalman filter (SKF) assumes that the statistics of the noise on each sensor are given. As long as the noise distributions do not change, the Kalman filter will give the optimal estimation. However GPS receiver will be disturbed easily and thus temporally changing measurement noise will join into the outputs of GPS, which will lead to performance degradation of the Kalman filter. Many researchers introduce fuzzy logic control method into innovation-based adaptive estimation adaptive Kalman filtering (IAE-AKF) algorithm, and accordingly propose various adaptive Kalman filters. However how to design the fuzzy logic controller is a very complicated problem still without a convincing solution. A novel IAE-AKF is proposed herein, which is based on the maximum likelihood criterion for the proper computation of the filter innovation covariance and hence of the filter gain. The approach is direct and simple without having to establish fuzzy inference rules. After having deduced the proposed IAE-AKF algorithm theoretically in detail, the approach is tested by the simulation based on the system error model of the developed INS/GPS integrated marine navigation system. Simulation results show that the adaptive Kalman filter outperforms the SKF with higher accuracy, robustness and less computation. It is demonstrated that this proposed approach is a valid solution for the unknown changing measurement noise exited in the Kalman filter.
Directory of Open Access Journals (Sweden)
Wei Zhu
2016-06-01
Full Text Available 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.
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).
Adaptive Kalman Filter of Transfer Alignment with Un-modeled Wing Flexure of Aircraft
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The alignment accuracy of the strap-down inertial navigation system (SINS) of airborne weapon is greatly degraded by the dynamic wing flexure of the aircraft. An adaptive Kalman filter uses innovation sequences based on the maximum likelihood estimated criterion to adapt the system noise covariance matrix and the measurement noise covariance matrix on line, which is used to estimate the misalignment if the model of wing flexure of the aircraft is unknown. From a number of simulations, it is shown that the accuracy of the adaptive Kalman filter is better than the conventional Kalman filter, and the erroneous misalignment models of the wing flexure of aircraft will cause bad estimation results of Kalman filter using attitude match method.
A new approach to UTC calculation by means of the Kalman filter
Parisi, Federica; Panfilo, Gianna
2016-10-01
In this paper a new approach to Coordinated Universal Time (UTC) calculation is presented by means of the Kalman filter. An ensemble of atomic clocks participating in UTC is selected for analyzing and testing the potentiality of this new method.
National Research Council Canada - National Science Library
Saad, George; Azizi, Fouad
... the sweep efficiency inside the reservoir. Controlling the flood front dynamics is achieved by coupling an ensemble Kalman filter scheme with a two-phase immiscible flow reservoir simulator and thus relying on a set of observational data...
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.
INFLUENCE OF STOCHASTIC NOISE STATISTICS ON KALMAN FILTER PERFORMANCE BASED ON VIDEO TARGET TRACKING
Institute of Scientific and Technical Information of China (English)
Chen Ken; Napolitano; Zhang Yun; Li Dong
2010-01-01
The system stochastic noises involved in Kalman filtering are preconditioned on being ideally white and Gaussian distributed. In this research,efforts are exerted on exploring the influence of the noise statistics on Kalman filtering from the perspective of video target tracking quality. The correlation of tracking precision to both the process and measurement noise covariance is investigated; the signal-to-noise power density ratio is defined; the contribution of predicted states and measured outputs to Kalman filter behavior is discussed; the tracking precision relative sensitivity is derived and applied in this study case. The findings are expected to pave the way for future study on how the actual noise statistics deviating from the assumed ones impacts on the Kalman filter optimality and degradation in the application of video tracking.
Wang, Rui; Li, Yanxiao; Sun, Hui; Chen, Zengqiang
2017-07-11
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.
Borodachev, S. M.
2016-06-01
The simple derivation of recursive least squares (RLS) method equations is given as special case of Kalman filter estimation of a constant system state under changing observation conditions. A numerical example illustrates application of RLS to multicollinearity problem.
Directory of Open Access Journals (Sweden)
Qiguang Zhu
2014-05-01
Full Text Available To resolve the difficulty in establishing accurate priori noise model for the extended Kalman filtering algorithm, propose the fractional-order Darwinian particle swarm optimization (PSO algorithm has been proposed and introduced into the fuzzy adaptive extended Kalman filtering algorithm. The natural selection method has been adopted to improve the standard particle swarm optimization algorithm, which enhanced the diversity of particles and avoided the premature. In addition, the fractional calculus has been used to improve the evolution speed of particles. The PSO algorithm after improved has been applied to train fuzzy adaptive extended Kalman filter and achieve the simultaneous localization and mapping. The simulation results have shown that compared with the geese particle swarm optimization training of fuzzy adaptive extended Kalman filter localization and mapping algorithm, has been greatly improved in terms of localization and mapping.
On-Orbit Multi-Field Wavefront Control with a Kalman Filter
Lou, John; Sigrist, Norbert; Basinger, Scott; Redding, David
2008-01-01
A document describes a multi-field wavefront control (WFC) procedure for the James Webb Space Telescope (JWST) on-orbit optical telescope element (OTE) fine-phasing using wavefront measurements at the NIRCam pupil. The control is applied to JWST primary mirror (PM) segments and secondary mirror (SM) simultaneously with a carefully selected ordering. Through computer simulations, the multi-field WFC procedure shows that it can reduce the initial system wavefront error (WFE), as caused by random initial system misalignments within the JWST fine-phasing error budget, from a few dozen micrometers to below 50 nm across the entire NIRCam Field of View, and the WFC procedure is also computationally stable as the Monte-Carlo simulations indicate. With the incorporation of a Kalman Filter (KF) as an optical state estimator into the WFC process, the robustness of the JWST OTE alignment process can be further improved. In the presence of some large optical misalignments, the Kalman state estimator can provide a reasonable estimate of the optical state, especially for those degrees of freedom that have a significant impact on the system WFE. The state estimate allows for a few corrections to the optical state to push the system towards its nominal state, and the result is that a large part of the WFE can be eliminated in this step. When the multi-field WFC procedure is applied after Kalman state estimate and correction, the stability of fine-phasing control is much more certain. Kalman Filter has been successfully applied to diverse applications as a robust and optimal state estimator. In the context of space-based optical system alignment based on wavefront measurements, a KF state estimator can combine all available wavefront measurements, past and present, as well as measurement and actuation error statistics to generate a Maximum-Likelihood optimal state estimator. The strength and flexibility of the KF algorithm make it attractive for use in real-time optical system
A novel Kalman filter based video image processing scheme for two-photon fluorescence microscopy
Sun, Wenqing; Huang, Xia; Li, Chunqiang; Xiao, Chuan; Qian, Wei
2016-03-01
Two-photon fluorescence microscopy (TPFM) is a perfect optical imaging equipment to monitor the interaction between fast moving viruses and hosts. However, due to strong unavoidable background noises from the culture, videos obtained by this technique are too noisy to elaborate this fast infection process without video image processing. In this study, we developed a novel scheme to eliminate background noises, recover background bacteria images and improve video qualities. In our scheme, we modified and implemented the following methods for both host and virus videos: correlation method, round identification method, tree-structured nonlinear filters, Kalman filters, and cell tracking method. After these procedures, most of noises were eliminated and host images were recovered with their moving directions and speed highlighted in the videos. From the analysis of the processed videos, 93% bacteria and 98% viruses were correctly detected in each frame on average.
A new Recommender system based on target tracking: a Kalman Filter approach
Nowakowski, Samuel; Boyer, Anne
2010-01-01
In this paper, we propose a new approach for recommender systems based on target tracking by Kalman filtering. We assume that users and their seen resources are vectors in the multidimensional space of the categories of the resources. Knowing this space, we propose an algorithm based on a Kalman filter to track users and to predict the best prediction of their future position in the recommendation space.
Target tracking in the recommender space: Toward a new recommender system based on Kalman filtering
Nowakowski, Samuel; Boyer, Anne
2010-01-01
In this paper, we propose a new approach for recommender systems based on target tracking by Kalman filtering. We assume that users and their seen resources are vectors in the multidimensional space of the categories of the resources. Knowing this space, we propose an algorithm based on a Kalman filter to track users and to predict the best prediction of their future position in the recommendation space.
Institute of Scientific and Technical Information of China (English)
L(U) Wei-cai; XU Shao-quan
2004-01-01
Using similar single-difference methodology(SSDM) to solve the deformation values of the monitoring points, there is unstability of the deformation information series, at sometimes.In order to overcome this shortcoming, Kalman filtering algorithm for this series is established,and its correctness and validity are verified with the test data obtained on the movable platform in plane. The results show that Kalman filtering can improve the correctness, reliability and stability of the deformation information series.
Kalman filtering techniques for reducing variance of digital speckle displacement measurement noise
Institute of Scientific and Technical Information of China (English)
Donghui Li; Li Guo
2006-01-01
@@ Target dynamics are assumed to be known in measuring digital speckle displacement. Use is made of a simple measurement equation, where measurement noise represents the effect of disturbances introduced in measurement process. From these assumptions, Kalman filter can be designed to reduce variance of measurement noise. An optical and analysis system was set up, by which object motion with constant displacement and constant velocity is experimented with to verify validity of Kalman filtering techniques for reduction of measurement noise variance.
Institute of Scientific and Technical Information of China (English)
Li Shu; Zhuo Jiashou; Ren Qingwen
2000-01-01
In this paper, an optimal criterion is presented for adaptive Kalman filter in a control sys tem with unknown variances of stochastic vibration by constructing a function of noise variances and minimizing the function. We solve the model and measure variances by using DFP optimal method to guarantee the results of Kalman filter to be optimized. Finally, the control of vibration can be implemented by LQG method.
2011-01-01
Modeling phase is fundamental both in the analysis process of a dynamic system and the design of a control system. If this phase is in-line is even more critical and the only information of the system comes from input/output data. Some adaptation algorithms for fuzzy system based on extended Kalman filter are presented in this paper, which allows obtaining accurate models without renounce the computational efficiency that characterizes the Kalman filter, and allows ...
Hybrid Kalman Filter: A New Approach for Aircraft Engine In-Flight Diagnostics
Kobayashi, Takahisa; Simon, Donald L.
2006-01-01
In this paper, a uniquely structured Kalman filter is developed for its application to in-flight diagnostics of aircraft gas turbine engines. The Kalman filter is a hybrid of a nonlinear on-board engine model (OBEM) and piecewise linear models. The utilization of the nonlinear OBEM allows the reference health baseline of the in-flight diagnostic system to be updated to the degraded health condition of the engines through a relatively simple process. Through this health baseline update, the effectiveness of the in-flight diagnostic algorithm can be maintained as the health of the engine degrades over time. Another significant aspect of the hybrid Kalman filter methodology is its capability to take advantage of conventional linear and nonlinear Kalman filter approaches. Based on the hybrid Kalman filter, an in-flight fault detection system is developed, and its diagnostic capability is evaluated in a simulation environment. Through the evaluation, the suitability of the hybrid Kalman filter technique for aircraft engine in-flight diagnostics is demonstrated.
Discrete Kalman Filter based Sensor Fusion for Robust Accessibility Interfaces
Ghersi, I.; Mariño, M.; Miralles, M. T.
2016-04-01
Human-machine interfaces have evolved, benefiting from the growing access to devices with superior, embedded signal-processing capabilities, as well as through new sensors that allow the estimation of movements and gestures, resulting in increasingly intuitive interfaces. In this context, sensor fusion for the estimation of the spatial orientation of body segments allows to achieve more robust solutions, overcoming specific disadvantages derived from the use of isolated sensors, such as the sensitivity of magnetic-field sensors to external influences, when used in uncontrolled environments. In this work, a method for the combination of image-processing data and angular-velocity registers from a 3D MEMS gyroscope, through a Discrete-time Kalman Filter, is proposed and deployed as an alternate user interface for mobile devices, in which an on-screen pointer is controlled with head movements. Results concerning general performance of the method are presented, as well as a comparative analysis, under a dedicated test application, with results from a previous version of this system, in which the relative-orientation information was acquired directly from MEMS sensors (3D magnetometer-accelerometer). These results show an improved response for this new version of the pointer, both in terms of precision and response time, while keeping many of the benefits that were highlighted for its predecessor, giving place to a complementary method for signal acquisition that can be used as an alternative-input device, as well as for accessibility solutions.
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.
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.
Adaptive error covariances estimation methods for ensemble Kalman filters
Energy Technology Data Exchange (ETDEWEB)
Zhen, Yicun, E-mail: zhen@math.psu.edu [Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 (United States); Harlim, John, E-mail: jharlim@psu.edu [Department of Mathematics and Department of Meteorology, The Pennsylvania State University, University Park, PA 16802 (United States)
2015-08-01
This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of Belanger's recursive method, to avoid an expensive computational cost in inverting error covariance matrices of product of innovation processes of different lags when the number of observations becomes large. When we use only product of innovation processes up to one-lag, the computational cost is indeed comparable to a recently proposed method by Berry–Sauer's. However, our method is more flexible since it allows for using information from product of innovation processes of more than one-lag. Extensive numerical comparisons between the proposed method and both the original Belanger's and Berry–Sauer's schemes are shown in various examples, ranging from low-dimensional linear and nonlinear systems of SDEs and 40-dimensional stochastically forced Lorenz-96 model. Our numerical results suggest that the proposed scheme is as accurate as the original Belanger's scheme on low-dimensional problems and has a wider range of more accurate estimates compared to Berry–Sauer's method on L-96 example.
Face Tracking in Video by Using Kalman Filter
Directory of Open Access Journals (Sweden)
Saranya M
2014-06-01
Full Text Available Face Tracking has been one of the most studied topics in computer vision literature. Facial feature extraction has some problems which must be researched. Small variations of face size and orientation can affect the result of face tracking. Since the input image is captured from a surveillance camera, certain conditions have to be considered - like different levels of brightness, shadows and clearness - which are challenges for detection and tracking purpose. Most facial feature extraction methods are sensitive to various non-ideal such as variation in illumination, noise, orientation, time-consumption and color space used. So there is a need for a good feature extraction method that will enhance the quality and performance of face recognition system. First, segmentation of foreground and background object is the one by using histogram equalization. By this method we are able to segment face based on skin color. After segmenting, Kalman filter is used to track the faces under several conditions. This feature is helpful for the development of a real-time visual tracking control system.
Paris law parameter identification based on the Extended Kalman Filter
Directory of Open Access Journals (Sweden)
Melgar M.
2016-01-01
Full Text Available Aircraft structures are commonly subjected to repeated loading cycles leading to fatigue damage. Fatigue data can be extrapolated by fatigue models which are adopted to describe the fatigue damage behaviour. Such models depend on their parameters for accurate prediction of the fatigue life. Therefore, several methods have been developed for estimating the model parameters for both linear and nonlinear systems. It is useful for a broad class of parameter identification problems when the dynamic model is not known. In this paper, the Paris law is used as fatigue-crack-length growth model on a metallic component under loading cycles. The Extended Kalman Filter (EKF is proposed as estimation method. Simulated crack length data is used to validate the estimation method. Based on experimental data obtained from fatigue experiment, the crack length and model parameters are estimated. Accurate model parameters allow a more realistic prediction of the fatigue life, consequently, the remaining useful life (RUL of component can be accurately computed. In this sense, maintenance performance could be improved.
Evolutionary Dynamic Multiobjective Optimization Via Kalman Filter Prediction.
Muruganantham, Arrchana; Tan, Kay Chen; Vadakkepat, Prahlad
2016-12-01
Evolutionary algorithms are effective in solving static multiobjective optimization problems resulting in the emergence of a number of state-of-the-art multiobjective evolutionary algorithms (MOEAs). Nevertheless, the interest in applying them to solve dynamic multiobjective optimization problems has only been tepid. Benchmark problems, appropriate performance metrics, as well as efficient algorithms are required to further the research in this field. One or more objectives may change with time in dynamic optimization problems. The optimization algorithm must be able to track the moving optima efficiently. A prediction model can learn the patterns from past experience and predict future changes. In this paper, a new dynamic MOEA using Kalman filter (KF) predictions in decision space is proposed to solve the aforementioned problems. The predictions help to guide the search toward the changed optima, thereby accelerating convergence. A scoring scheme is devised to hybridize the KF prediction with a random reinitialization method. Experimental results and performance comparisons with other state-of-the-art algorithms demonstrate that the proposed algorithm is capable of significantly improving the dynamic optimization performance.
Vehicle State Information Estimation with the Unscented Kalman Filter
Directory of Open Access Journals (Sweden)
Hongbin Ren
2014-01-01
Full Text Available The vehicle state information plays an important role in the vehicle active safety systems; this paper proposed a new concept to estimate the instantaneous vehicle speed, yaw rate, tire forces, and tire kinemics information in real time. The estimator is based on the 3DoF vehicle model combined with the piecewise linear tire model. The estimator is realized using the unscented Kalman filter (UKF, since it is based on the unscented transfer technique and considers high order terms during the measurement and update stage. The numerical simulations are carried out to further investigate the performance of the estimator under high friction and low friction road conditions in the MATLAB/Simulink combined with the Carsim environment. The simulation results are compared with the numerical results from Carsim software, which indicate that UKF can estimate the vehicle state information accurately and in real time; the proposed estimation will provide the necessary and reliable state information to the vehicle controller in the future.
Automated septum thickness measurement--a Kalman filter approach.
Snare, Sten Roar; Mjølstad, Ole Christian; Orderud, Fredrik; Dalen, Håvard; Torp, Hans
2012-11-01
Interventricular septum thickness in end-diastole (IVSd) is one of the key parameters in cardiology. This paper presents a fast algorithm, suitable for pocket-sized ultrasound devices, for measurement of IVSd using 2D B-mode parasternal long axis images. The algorithm is based on a deformable model of the septum and the mitral valve. The model shape is estimated using an extended Kalman filter. A feasibility study using 32 unselected recordings is presented. The recordings originate from a database consisting of subjects from a normal healthy population. Five patients with suspected hypertrophy were included in the study. Reference B-mode measurements were made by two cardiologists. A paired t-test revealed a non-significant mean difference, compared to the B-mode reference, of (mean±SD) 0.14±1.36 mm (p=0.532). Pearson's correlation coefficient was 0.79 (p<0.001). The results are comparable to the variability between the two cardiologists, which was found to be 1.29±1.23 mm (p<0.001). The results indicate that the method has potential as a tool for rapid assessment of IVSd. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.
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 reduced order model based on Kalman filtering for sequential data assimilation of turbulent flows
Meldi, M.; Poux, A.
2017-10-01
A Kalman filter based sequential estimator is presented in this work. The estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows. This technique provides an augmented flow state integrating available observation in the CFD model, naturally preserving a zero-divergence condition for the velocity field. Because of the prohibitive costs associated with a complete Kalman Filter application, two model reduction strategies have been proposed and assessed. These strategies dramatically reduce the increase in computational costs of the model, which can be quantified in an augmentation of 10%- 15% with respect to the classical numerical simulation. In addition, an extended analysis of the behavior of the numerical model covariance Q has been performed. Optimized values are strongly linked to the truncation error of the discretization procedure. The estimator has been applied to the analysis of a number of test cases exhibiting increasing complexity, including turbulent flow configurations. The results show that the augmented flow successfully improves the prediction of the physical quantities investigated, even when the observation is provided in a limited region of the physical domain. In addition, the present work suggests that these Data Assimilation techniques, which are at an embryonic stage of development in CFD, may have the potential to be pushed even further using the augmented prediction as a powerful tool for the optimization of the free parameters in the numerical simulation.
Kalman filter based fault diagnosis of networked control system with white noise
Institute of Scientific and Technical Information of China (English)
Yanwei WANG; Ying ZHENG
2005-01-01
The networked control system NCS is regarded as a sampled control system with output time-variant delay.White noise is considered in the model construction of NCS.By using the Kalman filter theory to compute the filter parameters,a Kalman filter is constructed for this NCS.By comparing the output of the filter and the practical system,a residual is generated to diagnose the sensor faults and the actuator faults.Finally,an example is given to show the feasibility of the approach.
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.
Highway traffic estimation of improved precision using the derivative-free nonlinear Kalman Filter
Rigatos, Gerasimos; Siano, Pierluigi; Zervos, Nikolaos; Melkikh, Alexey
2015-12-01
The paper proves that the PDE dynamic model of the highway traffic is a differentially flat one and by applying spatial discretization its shows that the model's transformation into an equivalent linear canonical state-space form is possible. For the latter representation of the traffic's dynamics, state estimation is performed with the use of the Derivative-free nonlinear Kalman Filter. The proposed filter consists of the Kalman Filter recursion applied on the transformed state-space model of the highway traffic. Moreover, it makes use of an inverse transformation, based again on differential flatness theory which enables to obtain estimates of the state variables of the initial nonlinear PDE model. By avoiding approximate linearizations and the truncation of nonlinear terms from the PDE model of the traffic's dynamics the proposed filtering methods outperforms, in terms of accuracy, other nonlinear estimators such as the Extended Kalman Filter. The article's theoretical findings are confirmed through simulation experiments.
Ensemble Kalman filters for dynamical systems with unresolved turbulence
Energy Technology Data Exchange (ETDEWEB)
Grooms, Ian, E-mail: grooms@cims.nyu.edu [Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Lee, Yoonsang [Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Majda, Andrew J. [Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Center for Prototype Climate Modelling, NYU Abu Dhabi, Abu Dhabi (United Arab Emirates)
2014-09-15
Ensemble Kalman filters are developed for turbulent dynamical systems where the forecast model does not resolve all the active scales of motion. Coarse-resolution models are intended to predict the large-scale part of the true dynamics, but observations invariably include contributions from both the resolved large scales and the unresolved small scales. The error due to the contribution of unresolved scales to the observations, called ‘representation’ or ‘representativeness’ error, is often included as part of the observation error, in addition to the raw measurement error, when estimating the large-scale part of the system. It is here shown how stochastic superparameterization (a multiscale method for subgridscale parameterization) can be used to provide estimates of the statistics of the unresolved scales. In addition, a new framework is developed wherein small-scale statistics can be used to estimate both the resolved and unresolved components of the solution. The one-dimensional test problem from dispersive wave turbulence used here is computationally tractable yet is particularly difficult for filtering because of the non-Gaussian extreme event statistics and substantial small scale turbulence: a shallow energy spectrum proportional to k{sup −5/6} (where k is the wavenumber) results in two-thirds of the climatological variance being carried by the unresolved small scales. Because the unresolved scales contain so much energy, filters that ignore the representation error fail utterly to provide meaningful estimates of the system state. Inclusion of a time-independent climatological estimate of the representation error in a standard framework leads to inaccurate estimates of the large-scale part of the signal; accurate estimates of the large scales are only achieved by using stochastic superparameterization to provide evolving, large-scale dependent predictions of the small-scale statistics. Again, because the unresolved scales contain so much energy
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.
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
Analysis of dynamic deformation processes with adaptive KALMAN-filtering
Eichhorn, Andreas
2007-05-01
In this paper the approach of a full system analysis is shown quantifying a dynamic structural ("white-box"-) model for the calculation of thermal deformations of bar-shaped machine elements. The task was motivated from mechanical engineering searching new methods for the precise prediction and computational compensation of thermal influences in the heating and cooling phases of machine tools (i.e. robot arms, etc.). The quantification of thermal deformations under variable dynamic loads requires the modelling of the non-stationary spatial temperature distribution inside the object. Based upon FOURIERS law of heat flow the high-grade non-linear temperature gradient is represented by a system of partial differential equations within the framework of a dynamic Finite Element topology. It is shown that adaptive KALMAN-filtering is suitable to quantify relevant disturbance influences and to identify thermal parameters (i.e. thermal diffusivity) with a deviation of only 0,2%. As result an identified (and verified) parametric model for the realistic prediction respectively simulation of dynamic temperature processes is presented. Classifying the thermal bend as the main deformation quantity of bar-shaped machine tools, the temperature model is extended to a temperature deformation model. In lab tests thermal load steps are applied to an aluminum column. Independent control measurements show that the identified model can be used to predict the columns bend with a mean deviation (r.m.s.) smaller than 10 mgon. These results show that the deformation model is a precise predictor and suitable for realistic simulations of thermal deformations. Experiments with modified heat sources will be necessary to verify the model in further frequency spectra of dynamic thermal loads.
Identification of hydrological model parameter variation using ensemble Kalman filter
Deng, Chao; Liu, Pan; Guo, Shenglian; Li, Zejun; Wang, Dingbao
2016-12-01
Hydrological model parameters play an important role in the ability of model prediction. In a stationary context, parameters of hydrological models are treated as constants; however, model parameters may vary with time under climate change and anthropogenic activities. The technique of ensemble Kalman filter (EnKF) is proposed to identify the temporal variation of parameters for a two-parameter monthly water balance model (TWBM) by assimilating the runoff observations. Through a synthetic experiment, the proposed method is evaluated with time-invariant (i.e., constant) parameters and different types of parameter variations, including trend, abrupt change and periodicity. Various levels of observation uncertainty are designed to examine the performance of the EnKF. The results show that the EnKF can successfully capture the temporal variations of the model parameters. The application to the Wudinghe basin shows that the water storage capacity (SC) of the TWBM model has an apparent increasing trend during the period from 1958 to 2000. The identified temporal variation of SC is explained by land use and land cover changes due to soil and water conservation measures. In contrast, the application to the Tongtianhe basin shows that the estimated SC has no significant variation during the simulation period of 1982-2013, corresponding to the relatively stationary catchment properties. The evapotranspiration parameter (C) has temporal variations while no obvious change patterns exist. The proposed method provides an effective tool for quantifying the temporal variations of the model parameters, thereby improving the accuracy and reliability of model simulations and forecasts.
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
Self-tuning decoupled fusion Kalman filter based on the Riccati equation
Institute of Scientific and Technical Information of China (English)
Xiaojun SUN; Peng ZHANG; Zili DENG
2008-01-01
An online noise variance estimator for multi-sensor systems with unknown noise variances is proposed by using the correlation method. Based on the Riccati equa-tion and optimal fusion rule "weighted by scalars for state components, a self-tuning component decoupled informa-tion fusion Kalman filter is presented. It is proved that the filter converges to the optimal fusion Kalman filter in a realization by dynamic error system analysis method, so that it has asymptotic optimality. Its effectiveness is demon-strated by simulation for a tracking system with 3 sensors.
Modified Extended Kalman Filtering for Tracking with Insufficient and Intermittent Observations
Directory of Open Access Journals (Sweden)
Pengpeng Chen
2015-01-01
Full Text Available This paper is concerned with the Kalman filtering problem for tracking a single target on the fixed-topology wireless sensor networks (WSNs. Both the insufficient anchor coverage and the packet dropouts have been taken into consideration in the filter design. The resulting tracking system is modeled as a multichannel nonlinear system with multiplicative noise. Noting that the channels may be correlated with each other, we use a general matrix to express the multiplicative noise. Then, a modified extended Kalman filtering algorithm is presented based on the obtained model to achieve high tracking accuracy. In particular, we evaluate the effect of various parameters on the tracking performance through simulation studies.
Dynamic Optimization of Feedforward Automatic Gauge Control Based on Extended Kalman Filter
Institute of Scientific and Technical Information of China (English)
YANG Bin-hu; YANG Wei-dong; CHEN Lian-gui; QU Lei
2008-01-01
Automatic gauge control is an essentially nonlinear process varying with time delay, and stochastically varying input and process noise always influence the target gauge control accuracy. To improve the control capability of feedforward automatic gauge control, Kalman filter was employed to filter the noise signal transferred from one stand to another. The linearized matrix that the Kalman filter algorithm needed was concluded; thus, the feedforward automatic gauge control architecture was dynamically optimized. The theoretical analyses and simulation show that the proposed algorithm is reasonable and effective.
Penggunaan Extended Kalman Filter Sebagai Estimator Sikap pada Sistem Kendali Servo Visual Robot
Directory of Open Access Journals (Sweden)
Noor Cholis Basjaruddin
2012-03-01
Full Text Available Extended Kalman Filter (EKF is the non-linear version of Kalman filter and the said filter is usually used in nonlinear state estimation. In this study EKF is applied to process the image features of a single camera mounted on the end effector of a robot. Data generated by the EKF then is to be processed to obtain the motion parameters. Simulation of visual servo control system was built with the aim to examine the use of the EKF as a pose estimator. The simulation results using Matlab show that the EKF is able to well estimate the robot pose.
Penggunaan Extended Kalman Filter Sebagai Estimator Sikap pada Sistem Kendali Servo Visual Robot
Noor Cholis Basjaruddin
2012-01-01
Extended Kalman Filter (EKF) is the non-linear version of Kalman filter and the said filter is usually used in nonlinear state estimation. In this study EKF is applied to process the image features of a single camera mounted on the end effector of a robot. Data generated by the EKF then is to be processed to obtain the motion parameters. Simulation of visual servo control system was built with the aim to examine the use of the EKF as a pose estimator. The simulation results using Matlab show ...
Control of underactuated robotic systems with the use of the derivative-free nonlinear Kalman filter
Rigatos, Gerasimos G.; Siano, Pierluigi
2013-10-01
The Derivative-free nonlinear Kalman Filter is used for developing a robust controller which can be applied to underactuated MIMO robotic systems. Using differential flatness theory it is shown that the model of a closed-chain 2-DOF robotic manipulator can be transformed to linear canonical form. For the linearized equivalent of the robotic system it is shown that a state feedback controller can be designed. Since certain elements of the state vector of the linearized system can not be measured directly, it is proposed to estimate them with the use of a novel filtering method, the so-called Derivative-free nonlinear Kalman Filter. Moreover, by redesigning the Kalman Filter as a disturbance observer, it is is shown that one can estimate simultaneously external disturbances terms that affect the robotic model or disturbance terms which are associated with parametric uncertainty.
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.
State-Of-Charge Estimation of Li-Ion Battery Using Extended Kalman Filter
Directory of Open Access Journals (Sweden)
Feng Jin
2013-07-01
Full Text Available The Li-ion battery is studied base on its equivalent circuit PNGV model. The model parameters are identified by HPPC test. The discrete state space equation is established according to the model. The basic theory of extended Kalman filter algorithm is studied and then the filtering algorithm is set up under the noisy environments. Finally, a kind of electric car is used for testing under the UDDS driving condition. The difference between the simulation value using extended Kalman filter under the noisy environment and the theoretical value is compared. The result indicated that the extended Kalman filter keeps an excellent precision in state of charge estimation of Li-ion battery and performs well when disturbance happens.
High Resolution Order Tracking at Extreme Slew Rates Using Kalman Tracking Filters
Directory of Open Access Journals (Sweden)
Håvard Vold
1995-01-01
Full Text Available The analysis of the periodic components in noise and vibration signals measured on rotating equipment such as car power trains, must be done more and more under rapid changes of an axle, or reference RPM. Normal tracking filters (analog or digital implementations have limited resolution in such situations; wavelet methods, even when applied after resampling the data to be proportional to an axle RPM, must compromise between time and frequency resolution. The authors propose the application of nonstationary Kalman filters for the tracking of periodic components in such noise and vibration signals. These filters are designed to accurately track signals with a known structure among noise and signal components of different, “unknown,” structure. The tracking characteristics of these filters, i.e., the predicted signal amplitude versus time values versus exact signal amplitude versus time values, can be tailored to accurate tracking of harmonics buried in other signal components and noise, even at high rates of change of the reference RPM. A key to the successful construction is the precise knowledge of the structure of the signal to be tracked. For signals that vary with an axle RPM, an accurate estimate of the instantaneous RPM is essential, and procedures to this end will also be presented.
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...
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...
Efficient decoding with steady-state Kalman filter in neural interface systems.
Malik, Wasim Q; Truccolo, Wilson; Brown, Emery N; Hochberg, Leigh R
2011-02-01
The Kalman filter is commonly used in neural interface systems to decode neural activity and estimate the desired movement kinematics. We analyze a low-complexity Kalman filter implementation in which the filter gain is approximated by its steady-state form, computed offline before real-time decoding commences. We evaluate its performance using human motor cortical spike train data obtained from an intracortical recording array as part of an ongoing pilot clinical trial. We demonstrate that the standard Kalman filter gain converges to within 95% of the steady-state filter gain in 1.5±0.5 s (mean ±s.d.). The difference in the intended movement velocity decoded by the two filters vanishes within 5 s, with a correlation coefficient of 0.99 between the two decoded velocities over the session length. We also find that the steady-state Kalman filter reduces the computational load (algorithm execution time) for decoding the firing rates of 25±3 single units by a factor of 7.0±0.9. We expect that the gain in computational efficiency will be much higher in systems with larger neural ensembles. The steady-state filter can thus provide substantial runtime efficiency at little cost in terms of estimation accuracy. This far more efficient neural decoding approach will facilitate the practical implementation of future large-dimensional, multisignal neural interface systems.
Estimation of Sonobuoy Position Relative to an Aircraft Using Extended Kalman Filters
1979-09-01
SECURITY CLASS. (a# this swot ) Naval Postgraduate School Ucasfe Monterey, California 93940 UnDcl assi F AIeNDONRDG SCHEDULE 1B. DISTRIBUTION...22 C. TEE SIX-STATE SYSTEM-----------------23 I). TEE TWO-STATE SYSTEM- ---------------- IV. ANAYLSIS ---------------------------- Z A. THE...simplifing techniques used in Kalman filters include precomputed gains. Although forfeiting the optimal Kalman gains, this has the advantage of reducing
Design and Simulation of the Integrated Navigation System based on Extended Kalman Filter
Directory of Open Access Journals (Sweden)
Zhou Weidong
2017-04-01
Full Text Available The integrated navigation system is used to estimate the position, velocity, and attitude of a vehicle with the output of inertial sensors. This paper concentrates on the problem of the INS/GPS integrated navigation system design and simulation. The structure of the INS/GPS integrated navigation system is made up of four parts: 1 GPS receiver, 2 Inertial Navigation System, 3 Extended Kalman filter, and 4 Integrated navigation scheme. Afterwards, we illustrate how to simulate the integrated navigation system with the extended Kalman filter by measuring position, velocity and attitude. Particularly, the extended Kalman filter can estimate states of the nonlinear system in the noisy environment. In extended Kalman filter, the estimation of the state vector and the error covariance matrix are computed by steps: 1 time update and 2 measurement update. Finally, the simulation process is implemented by Matlab, and simulation results prove that the error rate of statement measuring is lower when applying the extended Kalman filter in the INS/GPS integrated navigation system.
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.
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.
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 Filter Realization for Orientation and Position Estimation on Dedicated Processor
Directory of Open Access Journals (Sweden)
Romaniuk Sławomir
2014-08-01
Full Text Available This paper presents Kalman filter design which has been programmed and evaluated in dedicated STM32 platform. The main aim of the work performed was to achieve proper estimation of attitude and position signals which could be further used in unmanned aeri-al vehicle autopilots. Inertial measurement unit and GPS receiver have been used as measurement devices in order to achieve needed raw sensor data. Results of Kalman filter estimation were recorded for signals measurements and compared with raw data. Position actualization frequency was increased from 1 Hz which is characteristic to GPS receivers, to values close to 50 Hz. Furthermore it is shown how Kalman filter deals with GPS accuracy decreases and magnetometer measurement noise.
Cuff-less blood pressure measurement using pulse arrival time and a Kalman filter
Zhang, Qiang; Chen, Xianxiang; Fang, Zhen; Xue, Yongjiao; Zhan, Qingyuan; Yang, Ting; Xia, Shanhong
2017-02-01
The present study designs an algorithm to increase the accuracy of continuous blood pressure (BP) estimation. Pulse arrival time (PAT) has been widely used for continuous BP estimation. However, because of motion artifact and physiological activities, PAT-based methods are often troubled with low BP estimation accuracy. This paper used a signal quality modified Kalman filter to track blood pressure changes. A Kalman filter guarantees that BP estimation value is optimal in the sense of minimizing the mean square error. We propose a joint signal quality indice to adjust the measurement noise covariance, pushing the Kalman filter to weigh more heavily on measurements from cleaner data. Twenty 2 h physiological data segments selected from the MIMIC II database were used to evaluate the performance. Compared with straightforward use of the PAT-based linear regression model, the proposed model achieved higher measurement accuracy. Due to low computation complexity, the proposed algorithm can be easily transplanted into wearable sensor devices.
A Hybrid Extended Kalman Filter as an Observer for a Pot-Electro-Magnetic Actuator
Schmidt, Simon; Mercorelli, Paolo
2017-01-01
This paper deals with an application in which a hybrid extended Kalman Filter (HEKF) is used to estimate state variables in a U-shaped electro-magnetic actuator to be used in mechanical systems. In this context a hybrid Kalman Filter is the one which switches between different models. The paper proposes a hybrid model for an extended Kalman Filter to be used as an observer to estimate the state and to control the force of the actuator. Applications include position, velocity and force control in automotive, engine and manufacturing systems. This work is focused on the estimation of state variables of the actuator. Simulated results show the effectiveness of the proposed approach.
On the Kalman Filter error covariance collapse into the unstable subspace
Trevisan, A.; Palatella, L.
2011-03-01
When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N+ + N0 where N+ and N0 are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with non-negative Lyapunov exponents. Theoretical arguments and numerical verification are provided to show that the asymptotic state and covariance estimates of the full EKF and of its reduced form, with assimilation in the unstable and neutral subspace (EKF-AUS) are the same. The consequences of these findings on applications of Kalman type Filters to chaotic models are discussed.
On the equivalence of Kalman filtering and least-squares estimation
Mysen, E.
2016-07-01
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.
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.
Convergence study in extended Kalman filter-based training of recurrent neural networks.
Wang, Xiaoyu; Huang, Yong
2011-04-01
Recurrent neural network (RNN) has emerged as a promising tool in modeling nonlinear dynamical systems, but the training convergence is still of concern. This paper aims to develop an effective extended Kalman filter-based RNN training approach with a controllable training convergence. The training convergence problem during extended Kalman filter-based RNN training has been proposed and studied by adapting two artificial training noise parameters: the covariance of measurement noise (R) and the covariance of process noise (Q) of Kalman filter. The R and Q adaption laws have been developed using the Lyapunov method and the maximum likelihood method, respectively. The effectiveness of the proposed adaption laws has been tested using a nonlinear dynamical benchmark system and further applied in cutting tool wear modeling. The results show that the R adaption law can effectively avoid the divergence problem and ensure the training convergence, whereas the Q adaption law helps improve the training convergence speed.
Gauterin, Eckhard; Kammerer, Philipp; Kühn, Martin; Schulte, Horst
2016-05-01
Advanced model-based control of wind turbines requires knowledge of the states and the wind speed. This paper benchmarks a nonlinear Takagi-Sugeno observer for wind speed estimation with enhanced Kalman Filter techniques: The performance and robustness towards model-structure uncertainties of the Takagi-Sugeno observer, a Linear, Extended and Unscented Kalman Filter are assessed. Hence the Takagi-Sugeno observer and enhanced Kalman Filter techniques are compared based on reduced-order models of a reference wind turbine with different modelling details. The objective is the systematic comparison with different design assumptions and requirements and the numerical evaluation of the reconstruction quality of the wind speed. Exemplified by a feedforward loop employing the reconstructed wind speed, the benefit of wind speed estimation within wind turbine control is illustrated.
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.
Fuzzy adaptive Kalman filter for indoor mobile target positioning with INS/WSN integrated method
Institute of Scientific and Technical Information of China (English)
杨海; 李威; 罗成名
2015-01-01
Pure inertial navigation system (INS) has divergent localization errors after a long time. In order to compensate the disadvantage, wireless sensor network (WSN) associated with the INS was applied to estimate the mobile target positioning. Taking traditional Kalman filter (KF) as the framework, the system equation of KF was established by the INS and the observation equation of position errors was built by the WSN. Meanwhile, the observation equation of velocity errors was established by the velocity difference between the INS and WSN, then the covariance matrix of Kalman filter measurement noise was adjusted with fuzzy inference system (FIS), and the fuzzy adaptive Kalman filter (FAKF) based on the INS/WSN was proposed. The simulation results show that the FAKF method has better accuracy and robustness than KF and EKF methods and shows good adaptive capacity with time-varying system noise. Finally, experimental results further prove that FAKF has the fast convergence error, in comparison with KF and EKF methods.
Event-triggered Kalman-consensus filter for two-target tracking sensor networks.
Su, Housheng; Li, Zhenghao; Ye, Yanyan
2017-06-24
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.
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.
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....... A sensitivity analysis of key parameters in the schemes is undertaken for a setup in an idealised bay. The sensitivity of the resulting root mean square error (RMSE) is shown to be low to moderate. Hence the schemes are robust within an acceptable range and their application even with misspecified parameters...... is to be encouraged in this perspective. However, the predicted uncertainty of the assimilation results are sensitive to the parameters and hence must be applied with care. The sensitivity study further demonstrates the effectiveness of the steady Kalman filter in the given system as well as the great impact...
OPTIMASI LEARNING RADIAL BASIS FUNCTION NEURAL NETWORK DENGAN EXTENDED KALMAN FILTER
Directory of Open Access Journals (Sweden)
Oni Soesanto
2015-09-01
Full Text Available Dalam paper ini dibahas mengenai optimasi Radial Basis Function Neural Network (RBFNN dengan Extended Kalman Filter. Proses learning RBF dengan Extended Kalman Filter menggunakan parameter bobot pada hidden center RBF yaitu noise proses pada perhitungan bobot hidden center dan noise pengukuran pada data output. Extended Kalman Filter pada jaringan syaraf RBF berfungsi mengoptimalkan bobot pada hidden center dengan meminimalkan error pada output RBF dengan parameter proses pada unit center RBF dan parameter bobot output pada output layer. Bobot output optimal diperoleh pada saat error output pada training RBF telah konvergen, selanjutnya digunakan untuk proses testing. Algoritma Extended Kalman Filter dan Radial Basis Fuction (EKF-RBF memungkinkan proses learning memungkinkan center dan variansi pada hidden layer tidak perlu dihitung sebelum bobot output optimum ditemukan. Hasil simulasi menunjukkan bahwa pada training, performansi klasifikasi algoritma EKF-RBF mampu mengenali rata-rata 92.42% dan untuk prediksi didapatkan MAE sebesar 5,3846 dan RMSE sebesar 16,2398 dengan CPU time 24,4146 detik dengan iterasi rata-rata 68,8 iterasi, testing in sample rata-rata MAE sebesar 4,3388, rata-rata RMSE sebesar 13,2230 dan rata-rata CPU time sebesar 0,1123 detik sedangkan pada testing out sample didapatkan rata-rata MAE sebesar 4,1065, RMSE sebesar 11,0126 dan CPU time sebesar 0,0265 detik. Kata kunci : Extended Kalman Filter, Extended Kalman Filter â€“ Radial Basis Function (EKF-RBF, Optimasi Jaringan Syaraf RBF
Adaptive system noise covariance for performance enhancement of Kalman filter-based algorithms
Lee, Vika; Chan, Keith C. C.; Leung, Henry
1996-06-01
Several designs of Kalman filters and the interacting multiple models algorithm were used in real tracking tasks involving high dynamic targets. The data were obtained through the joint effort of the defense departments of Canada and the US. Their performance, measured in terms of positional deviation and the number of track losses, are rather unsatisfactory even though they perform particularly well when using simulated data. To identify the reasons behind, we compared and analyzed the differences between the model assumptions behind the design of these Kalman filters and the model required for accurate tracking of these targets. In this paper, we discussed our findings. Moreover, based on the characteristics of real tracking data, we present an alternative methodology for measuring the effectiveness of various Kalman filter based trackers in stressful environmental. It can also be used to explain the well known characteristics of Kalman filter. A lower bound for the deviation, obtained from this equation, shows that deviation could be too large to manage if noise bandwidth is as high as the real data instead of a pre-assumed magnitude. Instead of having to redesign many existing Kalman filters to suit for stressful environment, we developed a design-independent module that can be added to different types of Kalman filters based trackers to enhance their performance in the tracking high dynamic targets. The module is called adaptive systems noise covariance estimation. It is not only safe (i.e. almost no negative effect) but it can sometimes even double the performance of trackers in stressful environment.
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.
Speed Estimation of Induction Motor Using Model Reference Adaptive System with Kalman Filter
Directory of Open Access Journals (Sweden)
Pavel Brandstetter
2013-01-01
Full Text Available The paper deals with a speed estimation of the induction motor using observer with Model Reference Adaptive System and Kalman Filter. For simulation, Hardware in Loop Simulation method is used. The first part of the paper includes the mathematical description of the observer for the speed estimation of the induction motor. The second part describes Kalman filter. The third part describes Hardware in Loop Simulation method and its realization using multifunction card MF 624. In the last section of the paper, simulation results are shown for different changes of the induction motor speed which confirm high dynamic properties of the induction motor drive with sensorless control.
Institute of Scientific and Technical Information of China (English)
Xiaogu ZHENG
2009-01-01
An adaptive estimation of forecast error covariance matrices is proposed for Kalman filtering data assimilation. A forecast error covariance matrix is initially estimated using an ensemble of perturbation forecasts. This initially estimated matrix is then adjusted with scale parameters that are adaptively estimated by minimizing -2log-likelihood of observed-minus-forecast residuals. The proposed approach could be applied to Kalman filtering data assimilation with imperfect models when the model error statistics are not known. A simple nonlinear model (Burgers' equation model) is used to demonstrate the efficacy of the proposed approach.
DEFF Research Database (Denmark)
Pierobon, Leonardo; Schlanbusch, Rune; Kandepu, Rambabu
2014-01-01
for this project. Considering the plant dynamics, it is of paramount importance to monitor the peak temperatures within the once-through boiler serving the bottoming unit to prevent the decomposition of the working fluid. This paper accordingly aims at applying the unscented Kalman filter to estimate...... the temperature distribution inside the primary heat exchanger by engaging a detailed and distributed model of the system and available measurements. Simulation results prove the robustness of the unscented Kalman filter with respect to process noise, measurement disturbances and initial conditions....
Souza, André L. G.; Ishihara, João Y.; Ferreira, Henrique C.; Borges, Renato A.; Borges, Geovany A.
2016-12-01
The present work proposes a new approach for an antenna pointing system for satellite tracking. Such a system uses the received signal to estimate the beam pointing deviation and then adjusts the antenna pointing. The present work has two contributions. First, the estimation is performed by a Kalman filter based conical scan technique. This technique uses the Kalman filter avoiding the batch estimator and applies a mathematical manipulation avoiding the linearization approximations. Secondly, a control technique based on the model predictive control together with an explicit state feedback solution are obtained in order to reduce the computational burden. Numerical examples illustrate the results.
Pérez-Ortiz, Juan Antonio; Gers, Felix A; Eck, Douglas; Schmidhuber, Jürgen
2003-03-01
The long short-term memory (LSTM) network trained by gradient descent solves difficult problems which traditional recurrent neural networks in general cannot. We have recently observed that the decoupled extended Kalman filter training algorithm allows for even better performance, reducing significantly the number of training steps when compared to the original gradient descent training algorithm. In this paper we present a set of experiments which are unsolvable by classical recurrent networks but which are solved elegantly and robustly and quickly by LSTM combined with Kalman filters.
Extended Kalman Filter Based Neural Networks Controller For Hot Strip Rolling mill
Moussaoui, A. K.; Abbassi, H. A.; Bouazza, S.
2008-06-01
The present paper deals with the application of an Extended Kalman filter based adaptive Neural-Network control scheme to improve the performance of a hot strip rolling mill. The suggested Neural Network model was implemented using Bayesian Evidence based training algorithm. The control input was estimated iteratively by an on-line extended Kalman filter updating scheme basing on the inversion of the learned neural networks model. The performance of the controller is evaluated using an accurate model estimated from real rolling mill input/output data, and the usefulness of the suggested method is proved.
Application of Extended Kalman Filter to Tactical Ballistic Missile Re-entry Problem
Bhowmik, Subrata
2007-01-01
The objective is to investigate the advantages and performance of Extended Kalman Filter for the estimation of non-linear system where linearization takes place about a trajectory that was continually updated with the state estimates resulting from the measurement. Here tactile ballistic missile Re-entry problem is taken as a nonlinear system model and Extended Kalman Filter technique is used to estimate the positions and velocities at the X and Y direction at different values of ballistic coefficients. The result shows that the method gives better estimation with the increase of ballistic coefficient.
A NEW METHOD OF CHANNEL FRICTION INVERSION BASED ON KALMAN FILTER WITH UNKNOWN PARAMETER VECTOR
Institute of Scientific and Technical Information of China (English)
CHENG Wei-ping; MAO Gen-hai; LIU Guo-hua
2005-01-01
Channel friction is an important parameter in hydraulic analysis.A channel friction parameter inversion method based on Kalman Filter with unknown parameter vector is proposed.Numerical simulations indicate that when the number of monitoring stations exceeds a critical value, the solution is hardly affected.In addition, Kalman Filter with unknown parameter vector is effective only at unsteady state.For the nonlinear equations, computations of sensitivity matrices are time-costly.Two simplified measures can reduce computing time, but not influence the results.One is to reduce sensitivity matrix analysis time, the other is to substitute for sensitivity matrix.
Directory of Open Access Journals (Sweden)
Erna Apriliani
2011-01-01
Full Text Available Kalman filter is an algorithm to estimate the state variable of dynamical stochastic system. The square root ensemble Kalman filter is an modification of Kalman filter. The square root ensemble Kalman filter is proposed to keep the computational stability and reduce the computational time. In this paper we study the efficiency of the reduced rank ensemble Kalman filter. We apply this algorithm to the non isothermal continue stirred tank reactor problem. We decompose the covariance of the ensemble estimation by using the singular value decomposition (the SVD, and then we reduced the rank of the diagonal matrix of those singular values. We make a simulation by using Matlab program. We took some the number of ensemble such as 100, 200 and 500. We compared the computational time and the accuracy between the square root ensemble Kalman filter and the ensemble Kalman filter. The reduced rank ensemble Kalman filter can’t be applied in this problem because the dimension of state variable is too less.
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.
Energy Technology Data Exchange (ETDEWEB)
Sebastien Massart [CERFACS / URA 1875, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, (France)
2005-07-01
Imperviousness of French nuclear power plants containments has to secure radioactive products confinement during incident or accident. Temporal evolution of containments is obtained through the numerical model Code Aster that purpose is to detect if some fissure could appear and as a consequence, imperviousness lost. In parallel, sensors are placed all around the containments to follow real time deformations. In this paper, Kalman filter analysis of an extensometer data is used to optimize eight parameters of the numerical model Code Aster. This method allows us to improve the concrete delayed behaviors modelization and supplies uncertainties to the forecast of the containment evolution. (author)
Meng, Yang; Gao, Shesheng; Zhong, Yongmin; Hu, Gaoge; Subic, Aleksandar
2016-03-01
The use of the direct filtering approach for INS/GNSS integrated navigation introduces nonlinearity into the system state equation. As the unscented Kalman filter (UKF) is a promising method for nonlinear problems, an obvious solution is to incorporate the UKF concept in the direct filtering approach to address the nonlinearity involved in INS/GNSS integrated navigation. However, the performance of the standard UKF is dependent on the accurate statistical characterizations of system noise. If the noise distributions of inertial instruments and GNSS receivers are not appropriately described, the standard UKF will produce deteriorated or even divergent navigation solutions. This paper presents an adaptive UKF with noise statistic estimator to overcome the limitation of the standard UKF. According to the covariance matching technique, the innovation and residual sequences are used to determine the covariance matrices of the process and measurement noises. The proposed algorithm can estimate and adjust the system noise statistics online, and thus enhance the adaptive capability of the standard UKF. Simulation and experimental results demonstrate that the performance of the proposed algorithm is significantly superior to that of the standard UKF and adaptive-robust UKF under the condition without accurate knowledge on system noise, leading to improved navigation precision.
Directory of Open Access Journals (Sweden)
Jenita Subash
2011-12-01
Full Text Available Users of geospatial data in government, military, industry, research, and other sectors have need foraccurate display of roads and other terrain information in areas where there are ongoing operations orlocations of interest. Hence, road extraction that is significantly more automated than the employment ofcostly and scarce human resources has become a challenging technical issue for the geospatialcommunity. An automatic road extraction based on Extended Kalman Filtering (EKF and variablestructured multiple model particle filter (VS-MMPF from satellite images is addressed. EKF traces themedian axis of a single road segment while VS-MMPF traces all road branches initializing at theintersection. In case of Local Linearization Particle filter (LLPF, a large number of particles are usedand therefore high computational expense is usually required in order to attain certain accuracy androbustness. The basic idea is to reduce the whole sampling space of the multiple model system to the modesubspace by marginalization over the target subspace and choose better importance function for modestate sampling. The core of the system is based on profile matching. During the estimation, new referenceprofiles were generated and stored in the road template memory for future correlation analysis, thuscovering the space of road profiles. .
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.
Directory of Open Access Journals (Sweden)
Giovanni Capellari
2015-12-01
Full Text Available Health monitoring of lightweight structures, like thin flexible plates, is of interest in several engineering fields. In this paper, a recursive Bayesian procedure is proposed to monitor the health of such structures through data collected by a network of optimally placed inertial sensors. As a main drawback of standard monitoring procedures is linked to the computational costs, two remedies are jointly considered: first, an order-reduction of the numerical model used to track the structural dynamics, enforced with proper orthogonal decomposition; and, second, an improved particle filter, which features an extended Kalman updating of each evolving particle before the resampling stage. The former remedy can reduce the number of effective degrees-of-freedom of the structural model to a few only (depending on the excitation, whereas the latter one allows to track the evolution of damage and to locate it thanks to an intricate formulation. To assess the effectiveness of the proposed procedure, the case of a plate subject to bending is investigated; it is shown that, when the procedure is appropriately fed by measurements, damage is efficiently and accurately estimated.
Capellari, Giovanni; Azam, Saeed Eftekhar; Mariani, Stefano
2015-12-22
Health monitoring of lightweight structures, like thin flexible plates, is of interest in several engineering fields. In this paper, a recursive Bayesian procedure is proposed to monitor the health of such structures through data collected by a network of optimally placed inertial sensors. As a main drawback of standard monitoring procedures is linked to the computational costs, two remedies are jointly considered: first, an order-reduction of the numerical model used to track the structural dynamics, enforced with proper orthogonal decomposition; and, second, an improved particle filter, which features an extended Kalman updating of each evolving particle before the resampling stage. The former remedy can reduce the number of effective degrees-of-freedom of the structural model to a few only (depending on the excitation), whereas the latter one allows to track the evolution of damage and to locate it thanks to an intricate formulation. To assess the effectiveness of the proposed procedure, the case of a plate subject to bending is investigated; it is shown that, when the procedure is appropriately fed by measurements, damage is efficiently and accurately estimated.
Aguirre, Luis Antonio; Teixeira, Bruno Otávio S.; Tôrres, Leonardo Antônio B.
2005-08-01
This paper addresses the problem of state estimation for nonlinear systems by means of the unscented Kalman filter (UKF). Compared to the traditional extended Kalman filter, the UKF does not require the local linearization of the system equations used in the propagation stage. Important results using the UKF have been reported recently but in every case the system equations used by the filter were considered known. Not only that, such models are usually considered to be differential equations, which requires that numerical integration be performed during the propagation phase of the filter. In this paper the dynamical equations of the system are taken to be difference equations—thus avoiding numerical integration—and are built from data without prior knowledge. The identified models are subsequently implemented in the filter in order to accomplish state estimation. The paper discusses the impact of not knowing the exact equations and using data-driven models in the context of state and joint state-and-parameter estimation. The procedure is illustrated by means of examples that use simulated and measured data.
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.
Two-level Robust Measurement Fusion Kalman Filter for Clustering Sensor Networks
Institute of Scientific and Technical Information of China (English)
ZHANG Peng; QI Wen-Juan; DENG Zi-Li
2014-01-01
This paper investigates the distributed fusion Kalman filtering over clustering sensor networks. The sensor network is partitioned as clusters by the nearest neighbor rule and each cluster consists of sensing nodes and cluster-head. Using the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of noise variances, two-level robust measurement fusion Kalman filter is presented for the clustering sensor network systems with uncertain noise variances. It can significantly reduce the communication load and save energy when the number of sensors is very large. A Lyapunov equation approach for the robustness analysis is presented, by which the robustness of the local and fused Kalman filters is proved. The concept of the robust accuracy is presented, and the robust accuracy relations among the local and fused robust Kalman filters are proved. It is proved that the robust accuracy of the two-level weighted measurement fuser is equal to that of the global centralized robust fuser and is higher than those of each local robust filter and each local weighted measurement fuser. A simulation example shows the correctness and effectiveness of the proposed results.
The Unscented Kalman Filter estimates the plasma insulin from glucose measurement.
Eberle, Claudia; Ament, Christoph
2011-01-01
Understanding the simultaneous interaction within the glucose and insulin homeostasis in real-time is very important for clinical treatment as well as for research issues. Until now only plasma glucose concentrations can be measured in real-time. To support a secure, effective and rapid treatment e.g. of diabetes a real-time estimation of plasma insulin would be of great value. A novel approach using an Unscented Kalman Filter that provides an estimate of the current plasma insulin concentration is presented, which operates on the measurement of the plasma glucose and Bergman's Minimal Model of the glucose insulin homeostasis. We can prove that process observability is obtained in this case. Hence, a successful estimator design is possible. Since the process is nonlinear we have to consider estimates that are not normally distributed. The symmetric Unscented Kalman Filter (UKF) will perform best compared to other estimator approaches as the Extended Kalman Filter (EKF), the simplex Unscented Kalman Filter (UKF), and the Particle Filter (PF). The symmetric UKF algorithm is applied to the plasma insulin estimation. It shows better results compared to the direct (open loop) estimation that uses a model of the insulin subsystem.
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.
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.
Acoustic tomography of the atmosphere using iterated unscented Kalman filter
Kolouri, Soheil
Tomography approaches are of great interests because of their non-intrusive nature and their ability to generate a significantly larger amount of data in comparison to the in-situ measurement method. Acoustic tomography is an approach which reconstructs the unknown parameters that affect the propagation of acoustic rays in a field of interest by studying the temporal characteristics of the propagation. Acoustic tomography has been used in several different disciplines such as biomedical imaging, oceanographic studies and atmospheric studies. The focus of this thesis is to study acoustic tomography of the atmosphere in order to reconstruct the temperature and wind velocity fields in the atmospheric surface layer using the travel-times collected from several pairs of transmitter and receiver sensors distributed in the field. Our work consists of three main parts. The first part of this thesis is dedicated to reviewing the existing methods for acoustic tomography of the atmosphere, namely statistical inversion (SI), time dependent statistical inversion (TDSI), simultaneous iterative reconstruction technique (SIRT), and sparse recovery framework. The properties of these methods are then explained extensively and their shortcomings are also mentioned. In the second part of this thesis, a new acoustic tomography method based on Unscented Kalman Filter (UKF) is introduced in order to address some of the shortcomings of the existing methods. Using the UKF, the problem is cast as a state estimation problem in which the temperature and wind velocity fields are the desired states to be reconstructed. The field is discretized into several grids in which the temperature and wind velocity fields are assumed to be constant. Different models, namely random walk, first order 3-D autoregressive (AR) model, and 1-D temporal AR model are used to capture the state evolution in time-space. Given the time of arrival (TOA) equation for acoustic propagation as the observation equation, the
Identification of observer/Kalman filter Markov parameters: Theory and experiments
Juang, Jer-Nan; Phan, Minh; Horta, Lucas G.; Longman, Richard W.
1991-01-01
An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed. The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design. The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes. The relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and gives bounds on the proper choice of observer order. It is shown that if one uses data containing noise, and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. Results are demonstrated in numerical studies and in experiments on an ten-bay truss structure.
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.
Nonlinear Kalman Filtering in Affine Term Structure Models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris;
When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi…ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze...... 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...... in fi…xed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using coupon bonds and the estimation of quadratic term structure models....
Directory of Open Access Journals (Sweden)
Yi-Ming Chen
2017-01-01
Full Text Available Noninvasive medical procedures are usually preferable to their invasive counterparts in the medical community. Anemia examining through the palpebral conjunctiva is a convenient noninvasive procedure. The procedure can be automated to reduce the medical cost. We propose an anemia examining approach by using a Kalman filter (KF and a regression method. The traditional KF is often used in time-dependent applications. Here, we modified the traditional KF for the time-independent data in medical applications. We simply compute the mean value of the red component of the palpebral conjunctiva image as our recognition feature and use a penalty regression algorithm to find a nonlinear curve that best fits the data of feature values and the corresponding levels of hemoglobin (Hb concentration. To evaluate the proposed approach and several relevant approaches, we propose a risk evaluation scheme, where the entire Hb spectrum is divided into high-risk, low-risk, and doubtful intervals for anemia. The doubtful interval contains the Hb threshold, say 11 g/dL, separating anemia and nonanemia. A suspect sample is the sample falling in the doubtful interval. For the anemia screening purpose, we would like to have as less suspect samples as possible. The experimental results show that the modified KF reduces the number of suspect samples significantly for all the approaches considered here.
Implementation of a Parallel Kalman Filter for Stratospheric Chemical Tracer Assimilation
Chang, Lang-Ping; Lyster, Peter M.; Menard, R.; Cohn, S. E.
1998-01-01
A Kalman filter for the assimilation of long-lived atmospheric chemical constituents has been developed for two-dimensional transport models on isentropic surfaces over the globe. An important attribute of the Kalman filter is that it calculates error covariances of the constituent fields using the tracer dynamics. Consequently, the current Kalman-filter assimilation is a five-dimensional problem (coordinates of two points and time), and it can only be handled on computers with large memory and high floating point speed. In this paper, an implementation of the Kalman filter for distributed-memory, message-passing parallel computers is discussed. Two approaches were studied: an operator decomposition and a covariance decomposition. The latter was found to be more scalable than the former, and it possesses the property that the dynamical model does not need to be parallelized, which is of considerable practical advantage. This code is currently used to assimilate constituent data retrieved by limb sounders on the Upper Atmosphere Research Satellite. Tests of the code examined the variance transport and observability properties. Aspects of the parallel implementation, some timing results, and a brief discussion of the physical results will be presented.
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...
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...
Target Centroid Position Estimation of Phase-Path Volume Kalman Filtering
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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.
Alternate approach for terrain-aided navigation using parallel extended Kalman filters
Energy Technology Data Exchange (ETDEWEB)
Sheives, T.C.; Andreas, R.D.
1979-12-01
A new approach for applying SITAN (Sandia Inertial Terrain Aided Navigation) to applications involving large initial position errors is described and analyzed. The approach uses parallel Kalman filters in combination with a selection algorithm to estimate the errors in the reference navigation system. Monte Carlo simulation and covariance analysis results are presented which demonstrate the feasibility and practicality of the approach.
Impact and point prediction using a neural extended Kalman filter with multiple sensors
Stubberud, Stephen C.; Kramer, Kathleen A.
2007-04-01
The neural extended Kalman filter is an adaptive estimation technique that has been shown to learn on-line the maneuver model of the trajectory of a target. This improved motion model can be used to better predict the location of a target at given point in time, especially when the target, such as a mortar shell, has limited maneuvering capabilities. In this paper, the neural extended Kalman filter is used to predict, with multiple-sensor-systems provided measurement reports, impact point and impact time of a ballistic-like projectile when the drag on the shell was not accurately modeled in the motion model. In previous work, the neural extended Kalman filter was shown to work well with a single sensor with a uniform sample rate. Multiple sensors can incorporate two major differences into the problem. The first difference is that of the multiple aspect angles and uncertainty that are used in the model adaptation. The second difference is that of a non-uniform update rate of the measurements to the tracking system. While most tracking systems can easily handle this difference, the adaptation of the neural network training parameters can be deleteriously affected by these variations. The first of these two differences, potential concerns to the neural extended Kalman filter's implementation, is investigated in this effort. In this effort, performance of this adaptive and predictive scheme with multiple sensors in a three dimensional space is shown to provide a quality impact estimate.
A convergence result for the unscented Kalman-Bucy filter using contraction theory
DEFF Research Database (Denmark)
Maree, J. P.; Imsland, L.; Jouffroy, J.
2013-01-01
This paper applies contraction theory to establish necessary conditions for contraction, hence, exponential convergence of the unscented Kalman-Bucy Filter. It follows that regions of contraction can subsequently be defined, given such necessary conditions. Both state and measurement models are I...
Application of the Kalman Filter to Estimate the State of an Aerobraking Maneuver
Directory of Open Access Journals (Sweden)
Willer Gomes dos Santos
2013-01-01
Full Text Available This paper presents a study about the application of a Kalman filter to estimate the position and velocity of a spacecraft in an aerobraking maneuver around the Earth. The cis-lunar aerobraking of the Hiten spacecraft as well as an aerobraking in a LEO orbit are simulated in this paper. The simulator developed considers a reference trajectory and a trajectory perturbed by external disturbances combined with nonidealities of sensors and actuators. It is able to operate in closed loop controlling the trajectory at each instant of time using a PID controller and propulsive jets. A Kalman filter utilizes the sensor data to estimate the state of the spacecraft. The estimation algorithms and propagation equations used in this process are presented. The U.S. Standard Atmosphere is adopted as the atmospheric model. The main results are compared with the case where the Kalman filter is not used. Therefore, it was possible to perform an analysis of the Kalman filter importance applied to an aerobraking maneuver.
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
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 model
Inexpensive CubeSat attitude estimation using COTS components and Unscented Kalman Filtering
DEFF Research Database (Denmark)
Larsen, Jesper Abildgaard; Vinther, Kasper
2011-01-01
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...
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).
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.
Kalman filtering naturally accounts for visually guided and predictive smooth pursuit dynamics.
Orban de Xivry, Jean-Jacques; Coppe, Sébastien; Blohm, Gunnar; Lefèvre, Philippe
2013-10-30
The brain makes use of noisy sensory inputs to produce eye, head, or arm motion. In most instances, the brain combines this sensory information with predictions about future events. Here, we propose that Kalman filtering can account for the dynamics of both visually guided and predictive motor behaviors within one simple unifying mechanism. Our model relies on two Kalman filters: (1) one processing visual information about retinal input; and (2) one maintaining a dynamic internal memory of target motion. The outputs of both Kalman filters are then combined in a statistically optimal manner, i.e., weighted with respect to their reliability. The model was tested on data from several smooth pursuit experiments and reproduced all major characteristics of visually guided and predictive smooth pursuit. This contrasts with the common belief that anticipatory pursuit, pursuit maintenance during target blanking, and zero-lag pursuit of sinusoidally moving targets all result from different control systems. This is the first instance of a model integrating all aspects of pursuit dynamics within one coherent and simple model and without switching between different parallel mechanisms. Our model suggests that the brain circuitry generating a pursuit command might be simpler than previously believed and only implement the functional equivalents of two Kalman filters whose outputs are optimally combined. It provides a general framework of how the brain can combine continuous sensory information with a dynamic internal memory and transform it into motor commands.
Combination of Kalman Filtering Algorithm%一种组合式的Kalman滤波算法
Institute of Scientific and Technical Information of China (English)
余翔; 冯璐; 漆晶
2013-01-01
Because the noise impact and process signals in Kalman filtering can't be directly observed,a kind of combination of Kalman filtering algorithm is proposed.Firstly,the observation data is adaptively weighted fused.Secondly,the fusion results as a priori estimated value of the second step Kalman filtering is filtered.The adaptive algorithm combined with the Kalman algorithm improves the accuracy and precision.Finally,simulations confirme the effectiveness of the algorithm.%针对Kalman滤波算法在估计过程中存在噪声影响和过程信号无法直接观测等问题,提出一种组合式的Kalman滤波算法.首先对观测的数据进行自适应加权融合,然后将融合的结果作为第二级Kalman滤波的先验估计值,进行Kalman滤波.通过自适应算法与Kalman算法的组合算法进行数据融合,可以提高融合的准确度和精度.最后通过仿真证实算法的有效性.
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.
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 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.
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...
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.
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...
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...
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 ...
Recent advances in hydrologic data assimilation have demonstrated the value of remotely sensed surface soil moisture in improving forecasts of key hydrologic variables such as root-zone soil moisture and surface runoff. In hydrologic data assimilation, the ensemble Kalman filter (EnKF) provides a ro...
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...
Institute of Scientific and Technical Information of China (English)
王铁成; 李伟力; 孙建伟
2003-01-01
A mathematical model has been built up for compound cage rotor induction machine with the rotor re-sistance and leakage inductance in the model identified through Kalman filtering method. Using the identifiedparameters, simulation studies are performed, and simulation results are compared with testing results.
Kalman filter based data fusion for neutral axis tracking in wind turbine towers
DEFF Research Database (Denmark)
Soman, Rohan; Malinowski, Pawel; Ostachowicz, Wieslaw;
2015-01-01
downtime, hence increasing the availability of the system. The present work is based on the use of neutral axis (NA) for SHM of the structure. The NA is tracked by data fusion of measured yaw angle and strain through the use of Extended Kalman Filter (EKF). The EKF allows accurate tracking even...
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 ...
Real-time tracking for virtual environments using scaat kalman filtering and unsynchronised cameras
DEFF Research Database (Denmark)
Rasmussen, Niels Tjørnly; Störring, Morritz; Moeslund, Thomas B.;
2006-01-01
to achieve high update rates and to cope with the unsynchronised data a single-constraint-at-a-time (SCAAT) Extended Kalman Filtering approach is used that recursively integrates measurements as soon as they are available one-at-a-time. Tests show that this approach is more robust to occlusions and provides...
General formulation of process noise matrix for track fitting with Kalman filter
Bhattacharya, Kolahal; Mondal, Naba K
2015-01-01
In the context of track fitting problems by a Kalman filter, the general functional forms of the elements of the random noise matrix are derived for tracking through thick layers of materials and magnetic fields. This work generalizes the form of the random noise matrix obtained by Mankel[1].
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
Tracking and convergence of multi-channel kalman filters for active noise control
Berkhoff, A.; Ophem, S. van
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
Tracking and convergence of multi-channel Kalman filters for active noise control
Berkhoff, A.P.; Ophem, S. van
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
Data Assimilation for Wildland Fires: Ensemble Kalman filters in coupled atmosphere-surface models
Mandel, Jan; Beezley, Jonathan D.; Coen, Janice L.; Kim, Minjeong
2007-01-01
Two wildland fire models are described, one based on reaction-diffusion-convection partial differential equations, and one based on semi-empirical fire spread by the level let method. The level set method model is coupled with the Weather Research and Forecasting (WRF) atmospheric model. The regularized and the morphing ensemble Kalman filter are used for data assimilation.
Data Assimilation for Wildland Fires: Ensemble Kalman filters in coupled atmosphere-surface models
Mandel, Jan; Coen, Janice L; Kim, Minjeong
2007-01-01
Two wildland fire models are described, one based on reaction-diffusion-convection partial differential equations, and one based on empirical fire spread by the level let method. The level set method model is coupled with the Weather Research and Forecasting (WRF) atmospheric model. The regularized and the morphing ensemble Kalman filter are used for data assimilation.
Software alignment of the BESⅢ main drift chamber using the Kalman Filter method
Institute of Scientific and Technical Information of China (English)
WANG Ji-Ke; MAO Ze-Pu; BIAN Jian-Ming; CAO Guo-Fu; CAO Xue-Xiang; CHEN Shen-Jian; DENG Zi-Yan; FU Cheng-Dong; GAO Yuan-Ning; HE Kang-Lin; HE Miao; HUA Chun-Fei; HUANG Bin; HUANG Xing-Tao; JI Xiao-Bin; LI Fei; LI Hai-Bo; LI Wei-Dong; LIANG Yu-Tie; LIU Chun-Xiu; LIU Huai-Min; LIU Suo; LIU Ying-Jie; MA Qiu-Mei; MA Xiang; MAO Ya-Jun; MO Xiao-Hu; PAN Ming-Hua; PANG Cai-Ying; PING Rong-Gang; QIN Ya-Hong; QIU Jin-Fa; SUN Sheng-Sen; SUN Yong-Zhao; WANG Liang-Liang; WEN Shuo-Pin; WU Ling-Hui; XIE Yu-Guang; XU Min; YAN Liang; YOU Zheng-Yun; YUAN Chang-Zheng; YUAN Ye; ZHANG Bing-Yun; ZHANG Chang-Chun; ZHANG Jian-Yong; ZHANG Xue-Yao; ZHANG Yao; ZHENG Yang-Heng; ZHU Ke-Jun; ZHU Yong-Sheng; ZHU Zhi-Li; ZOU Jia-Heng
2009-01-01
Software alignment is quite important for a tracking detector to reach its ultimate position accuracy and momentum resolution. We developed a new alignment algorithm for the BESⅢ Main Drift Chamber using the Kalman Filter method. Two different types of data which are helix tracks and straight tracks are used to test this algorithm, and the results show that the design and implementation is successful.
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.
A Kalman Filter for SINS Self-Alignment Based on Vector Observation.
Xu, Xiang; Xu, Xiaosu; Zhang, Tao; Li, Yao; Tong, Jinwu
2017-01-29
In this paper, a self-alignment method for strapdown inertial navigation systems based on the q-method is studied. In addition, an improved method based on integrating gravitational apparent motion to form apparent velocity is designed, which can reduce the random noises of the observation vectors. For further analysis, a novel self-alignment method using a Kalman filter based on adaptive filter technology is proposed, which transforms the self-alignment procedure into an attitude estimation using the observation vectors. In the proposed method, a linear psuedo-measurement equation is adopted by employing the transfer method between the quaternion and the observation vectors. Analysis and simulation indicate that the accuracy of the self-alignment is improved. Meanwhile, to improve the convergence rate of the proposed method, a new method based on parameter recognition and a reconstruction algorithm for apparent gravitation is devised, which can reduce the influence of the random noises of the observation vectors. Simulations and turntable tests are carried out, and the results indicate that the proposed method can acquire sound alignment results with lower standard variances, and can obtain higher alignment accuracy and a faster convergence rate.
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 filter is implemented, as it is primarily made necessary by modelling errors. In this paper, two different methods for modelling the process noise are described and evaluated; a traditional one based on Gaussian noise models and a new one based on propagating modelling uncertainties. We discuss which...... method to use and how to tune the filter to achieve the lowest estimation error....
Noise Removing of Audio Speech Signals by Means of Kalman Filter
Directory of Open Access Journals (Sweden)
Soleyman Shirzadi
2016-06-01
Full Text Available Nowadays, multimedia (audio and video processing is among the most important subjects discussed in engineering sciences. To apply digital filters, especially adapting filters, in the above process, are of crucial importance. Theory of adapting filters such as that of Wiener or Kalman, have been fully discussed within the continuous field, the same as in discrete-time one; in spite of this, due to the presence of computers and digital processors, the adaptable filters defiantly have more efficiency in continuous field rather than discrete-time filed. One digital filter along with an adaptable algorithm is usually applied in adaptable filters so that the filter factor can be determined by means of adaptable algorithm. In the present article the Kalman filter-which counts as one of the best filters- has been surveyed whose appropriate factors is being calculated to design a efficient filter. First of all a sample signal is randomly selected which can be the same as an Autoregressive signal. Then a merely random Gaussian noise is applied on Autoregressive signal; and consequently the noisy signal is analyzed. As soon as we analyze the noise removed. The aforesaid operation has been assimilated through the Matlab software. The results have been demonstrated as well.
Real-Time Diagnosis of Faults Using a Bank of Kalman Filters
Kobayashi, Takahisa; Simon, Donald L.
2006-01-01
A new robust method of automated real-time diagnosis of faults in an aircraft engine or a similar complex system involves the use of a bank of Kalman filters. In order to be highly reliable, a diagnostic system must be designed to account for the numerous failure conditions that an aircraft engine may encounter in operation. The method achieves this objective though the utilization of multiple Kalman filters, each of which is uniquely designed based on a specific failure hypothesis. A fault-detection-and-isolation (FDI) system, developed based on this method, is able to isolate faults in sensors and actuators while detecting component faults (abrupt degradation in engine component performance). By affording a capability for real-time identification of minor faults before they grow into major ones, the method promises to enhance safety and reduce operating costs. The robustness of this method is further enhanced by incorporating information regarding the aging condition of an engine. In general, real-time fault diagnostic methods use the nominal performance of a "healthy" new engine as a reference condition in the diagnostic process. Such an approach does not account for gradual changes in performance associated with aging of an otherwise healthy engine. By incorporating information on gradual, aging-related changes, the new method makes it possible to retain at least some of the sensitivity and accuracy needed to detect incipient faults while preventing false alarms that could result from erroneous interpretation of symptoms of aging as symptoms of failures. The figure schematically depicts an FDI system according to the new method. The FDI system is integrated with an engine, from which it accepts two sets of input signals: sensor readings and actuator commands. Two main parts of the FDI system are a bank of Kalman filters and a subsystem that implements FDI decision rules. Each Kalman filter is designed to detect a specific sensor or actuator fault. When a sensor
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.
Robust double gain unscented Kalman filter for small satellite attitude estimation
Cao, Lu; Yang, Weiwei; Li, Hengnian; Zhang, Zhidong; Shi, Jianjun
2017-08-01
Limited by the low precision of small satellite sensors, the estimation theories with high performance remains the most popular research topic for the attitude estimation. The Kalman filter (KF) and its extensions have been widely applied in the satellite attitude estimation and achieved plenty of achievements. However, most of the existing methods just take use of the current time-step's priori measurement residuals to complete the measurement update and state estimation, which always ignores the extraction and utilization of the previous time-step's posteriori measurement residuals. In addition, the uncertainty model errors always exist in the attitude dynamic system, which also put forward the higher performance requirements for the classical KF in attitude estimation problem. Therefore, the novel robust double gain unscented Kalman filter (RDG-UKF) is presented in this paper to satisfy the above requirements for the small satellite attitude estimation with the low precision sensors. It is assumed that the system state estimation errors can be exhibited in the measurement residual; therefore, the new method is to derive the second Kalman gain Kk2 for making full use of the previous time-step's measurement residual to improve the utilization efficiency of the measurement data. Moreover, the sequence orthogonal principle and unscented transform (UT) strategy are introduced to robust and enhance the performance of the novel Kalman Filter in order to reduce the influence of existing uncertainty model errors. Numerical simulations show that the proposed RDG-UKF is more effective and robustness in dealing with the model errors and low precision sensors for the attitude estimation of small satellite by comparing with the classical unscented Kalman Filter (UKF).
Bds/gps Integrated Positioning Method Research Based on Nonlinear Kalman Filtering
Ma, Y.; Yuan, W.; Sun, H.
2017-09-01
In order to realize fast and accurate BDS/GPS integrated positioning, it is necessary to overcome the adverse effects of signal attenuation, multipath effect and echo interference to ensure the result of continuous and accurate navigation and positioning. In this paper, pseudo-range positioning is used as the mathematical model. In the stage of data preprocessing, using precise and smooth carrier phase measurement value to promote the rough pseudo-range measurement value without ambiguity. At last, the Extended Kalman Filter(EKF), the Unscented Kalman Filter(UKF) and the Particle Filter(PF) algorithm are applied in the integrated positioning method for higher positioning accuracy. The experimental results show that the positioning accuracy of PF is the highest, and UKF is better than EKF.
Accounting for model error due to unresolved scales within ensemble Kalman filtering
Mitchell, Lewis
2014-01-01
We propose a method to account for model error due to unresolved scales in the context of the ensemble transform Kalman filter (ETKF). The approach extends to this class of algorithms the deterministic model error formulation recently explored for variational schemes and extended Kalman filter. The model error statistic required in the analysis update is estimated using historical reanalysis increments and a suitable model error evolution law. Two different versions of the method are described; a time-constant model error treatment where the same model error statistical description is time-invariant, and a time-varying treatment where the assumed model error statistics is randomly sampled at each analysis step. We compare both methods with the standard method of dealing with model error through inflation and localization, and illustrate our results with numerical simulations on a low order nonlinear system exhibiting chaotic dynamics. The results show that the filter skill is significantly improved through th...
Soken, Halil Ersin; Hajiyev, Chingiz
2010-07-01
In the normal operation conditions of a pico satellite, a conventional Unscented Kalman Filter (UKF) gives sufficiently good estimation results. However, if the measurements are not reliable because of any kind of malfunction in the estimation system, UKF gives inaccurate results and diverges by time. This study introduces Robust Unscented Kalman Filter (RUKF) algorithms with the filter gain correction for the case of measurement malfunctions. By the use of defined variables named as measurement noise scale factor, the faulty measurements are taken into consideration with a small weight, and the estimations are corrected without affecting the characteristics of the accurate ones. Two different RUKF algorithms, one with single scale factor and one with multiple scale factors, are proposed and applied for the attitude estimation process of a pico satellite. The results of these algorithms are compared for different types of measurement faults in different estimation scenarios and recommendations about their applications are given.
Kalman filter of the force signal of identifying weld seam in remote teaching
Institute of Scientific and Technical Information of China (English)
Liu Lijun; Zhu Ronghua; Zhang Guangjun; Gao Hongming; Wu Lin
2008-01-01
For reasons of the vibration of robot, the rough surface of weld seam and electromagnetic disturbance of welding machine, the force signals of identifying weld seam become unstable. The position error of remote teaching point is too big to meet teaching requirements in remote welding. The force signals of identifying weld seam can be filtered by Kalman. The force signals of identifying weld seam of next teaching point is accurately predicted according to predicting algorithms, such as the equation of the state, the equation of the observation, the gain matrix of the filter and the covariance matrix of predicting state. The experimental results show that the precision of identifying weld seam is improved by Kalman filter.
A cognition-based method to ease the computational load for an extended Kalman filter.
Li, Yanpeng; Li, Xiang; Deng, Bin; Wang, Hongqiang; Qin, Yuliang
2014-12-03
The extended Kalman filter (EKF) is the nonlinear model of a Kalman filter (KF). It is a useful parameter estimation method when the observation model and/or the state transition model is not a linear function. However, the computational requirements in EKF are a difficulty for the system. With the help of cognition-based designation and the Taylor expansion method, a novel algorithm is proposed to ease the computational load for EKF in azimuth predicting and localizing under a nonlinear observation model. When there are nonlinear functions and inverse calculations for matrices, this method makes use of the major components (according to current performance and the performance requirements) in the Taylor expansion. As a result, the computational load is greatly lowered and the performance is ensured. Simulation results show that the proposed measure will deliver filtering output with a similar precision compared to the regular EKF. At the same time, the computational load is substantially lowered.
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...... using past and present estimates of the Kalman filter and calculating an optimal gain for this extrapolated measurement...... there is at hand, the designer has to make trade offs between optimality and computational burden of the filter. In this paper various methods in the literature along with a new method proposed by the authors will be presented and compared. The new method is based on “extrapolating” the measurement to present time...
Multi-sensor Data Processing and Fusing Based on Kalman Filtering
Directory of Open Access Journals (Sweden)
Bian Guangrong
2013-01-01
Full Text Available The background of this paper is the warehouse target localization and tracking system which is composed of a number of wireless sensor nodes. Firstly this paper established a model of warehouse target localization and tracking system, then a model of multi-sensor data preprocessing and data fusion was established, and self-adaptive linear recursive method was used to eliminate outliers of the original measured data. Then least squares fitting filter was used to do filtering and denoising for the measured data. In the end, the data which were measured by multi-sensor can be fused by Kalman Filtering algorithm. Data simulation analysis shows that the use of kalman filtering algorithm for the fusion of the data measured by multi-sensor is to obtain more accurate warehouse target location data, so as to increase the positioning and tracking accuracy of the warehouse target localization and tracking system. Key Words:Wireless Sensor Network,Data Fusion,Kalman Filtering
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.
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.
Rahimi, Afshin; Kumar, Krishna Dev; Alighanbari, Hekmat
2017-05-01
Reaction wheels, as one of the most commonly used actuators in satellite attitude control systems, are prone to malfunction which could lead to catastrophic failures. Such malfunctions can be detected and addressed in time if proper analytical redundancy algorithms such as parameter estimation and control reconfiguration are employed. Major challenges in parameter estimation include speed and accuracy of the employed algorithm. This paper presents a new approach for improving parameter estimation with adaptive unscented Kalman filter. The enhancement in tracking speed of unscented Kalman filter is achieved by systematically adapting the covariance matrix to the faulty estimates using innovation and residual sequences combined with an adaptive fault annunciation scheme. The proposed approach provides the filter with the advantage of tracking sudden changes in the system non-measurable parameters accurately. Results showed successful detection of reaction wheel malfunctions without requiring a priori knowledge about system performance in the presence of abrupt, transient, intermittent, and incipient faults. Furthermore, the proposed approach resulted in superior filter performance with less mean squared errors for residuals compared to generic and adaptive unscented Kalman filters, and thus, it can be a promising method for the development of fail-safe satellites.
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.
Institute of Scientific and Technical Information of China (English)
常国宾; 柳明
2015-01-01
In inertial navigation system (INS) and global positioning system (GPS) integrated system, GPS antennas are usually not located at the same location as the inertial measurement unit (IMU) of the INS, so the lever arm effect exists, which makes the observation equation highly nonlinear. The INS/GPS integration with constant lever arm effect is studied. The position relation of IMU and GPS’s antenna is represented in the earth centered earth fixed frame, while the velocity relation of these two systems is represented in local horizontal frame. Due to the small integration time interval of INS, i.e. 0.1 s in this work, the nonlinearity in the INS error equation is trivial, so the linear INS error model is constructed and addressed by Kalman filter’s prediction step. On the other hand, the high nonlinearity in the observation equation due to lever arm effect is addressed by unscented Kalman filter’s update step to attain higher accuracy and better applicability. Simulation is designed and the performance of the hybrid filter is validated.
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.
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...
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.
An Unscented Kalman-Particle Hybrid Filter for Space Object Tracking
Raihan A. V, Dilshad; Chakravorty, Suman
2017-04-01
Optimal and consistent estimation of the state of space objects is pivotal to surveillance and tracking applications. However, probabilistic estimation of space objects is made difficult by the non-Gaussianity and nonlinearity associated with orbital mechanics. In this paper, we present an unscented Kalman-particle hybrid filtering framework for recursive Bayesian estimation of space objects. The hybrid filtering scheme is designed to provide accurate and consistent estimates when measurements are sparse without incurring a large computational cost. It employs an unscented Kalman filter (UKF) for estimation when measurements are available. When the target is outside the field of view (FOV) of the sensor, it updates the state probability density function (PDF) via a sequential Monte Carlo method. The hybrid filter addresses the problem of particle depletion through a suitably designed filter transition scheme. To assess the performance of the hybrid filtering approach, we consider two test cases of space objects that are assumed to undergo full three dimensional orbital motion under the effects of J 2 and atmospheric drag perturbations. It is demonstrated that the hybrid filters can furnish fast, accurate and consistent estimates outperforming standard UKF and particle filter (PF) implementations.
Reduction of power line interference in electrocardiographic signals by dual Kalman filtering
Directory of Open Access Journals (Sweden)
Luis David Avendaño Valencia
2010-04-01
Full Text Available This paper presents a filter for reducing powerline interference in electrocardiographic signals (ECG, based on dual parameter and state estimation using with a Kalman filter. Two models were used to represent power-line interference and ECG signal. Both models were combined to simulate the ECG signal whose state was estimated for separating the ECG signal from the interference. The proposed algorithm was fine-tuned and compared using a set of tests relying on the QT arrhythmia database. Tuning tests were done for tracking clean ECG; these results were used for setting the algorithm’s parameters for later filtering tests. Exhaustive filtering tests were carried out on artificially corrupted database registers for given signal to noise ratios; performance curves were thus obtained, leading to comparing the proposed algorithm with other filtering methods. The proposed algorithm was compared to an recursive infinite impulse response filter (IIR and a Kalman filter based on a simpler model. A filtering algorithm was thus obtained which is robust for changes in interference amplitude and keeps these properties for different types of ECG morphologies.
Extracting a common pulse like signal from Time Serie using a non linear Kalman Filter
Gazeaux, J.; Batista, D.; Ammann, C.; Naveau, P.; Jégat, C.; Gao, C.
2009-04-01
To understand the nature and cause of natural climate variability, it is important to attribute past climate variations to particular forcing factors. In this work, our main focus is to introduce an automatic assimilation procedure to estimate the magnitude of strong but short-lived perturbations, such as large explosive volcanic eruptions, using climate/proxies time series. The extraction and decomposition procedure is run on real multivariate time series of sulfate from ice cores drilled at different sites in Greenland. The sulfate ejected by volcanoes is transported through the stratosphere towards the poles and deposited via sedimentation near the pole. Sulfate in Greenland is then a marker of huge volcanic eruptions which occur all over the world. Such pulse-like processes are highly non linear, as much in time as for their intensity. If they are not detected, such pulse-like signals of extreme and rare events can perturb an objective calculation of the trend. This work is then as much an estimation procedure for such signals, as a first step to estimate a posteriori trend in the time series. Our extraction algorithm handles multivariate time series with a common but unknown forcing. This statistical procedure is based on a multivariate multi-state space model and a non linear Kalman Filter. The non linearity is solved using the calculation of a twice conditional expectation and variance. It can provide an accurate estimate of the timing and duration of individual pulse-like events from a set of different series covering the same temporal space. It not only allows for a more objective estimation of its associated peak amplitude and the subsequent time evolution of the signal, but at the same time it provides a measure of confidence through the posterior probability for each pulse-like event. The flexibility, robustness and limitations of our approach are discussed by applying our method to simulated time series and to the Monte-Carlo method to test the
Beretta, Elisa; De Momi, Elena; Camomilla, Valentina; Cereatti, Andrea; Cappozzo, Aurelio; Ferrigno, Giancarlo
2014-09-01
In computer-assisted knee surgery, the accuracy of the localization of the femur centre of rotation relative to the hip-bone (hip joint centre) is affected by the unavoidable and untracked pelvic movements because only the femoral pose is acquired during passive pivoting manoeuvres. We present a dual unscented Kalman filter algorithm that allows the estimation of the hip joint centre also using as input the position of a pelvic reference point that can be acquired with a skin marker placed on the hip, without increasing the invasiveness of the surgical procedure. A comparative assessment of the algorithm was carried out using data provided by in vitro experiments mimicking in vivo surgical conditions. Soft tissue artefacts were simulated and superimposed onto the position of a pelvic landmark. Femoral pivoting made of a sequence of star-like quasi-planar movements followed by a circumduction was performed. The dual unscented Kalman filter method proved to be less sensitive to pelvic displacements, which were shown to be larger during the manoeuvres in which the femur was more adducted. Comparable accuracy between all the analysed methods resulted for hip joint centre displacements smaller than 1 mm (error: 2.2 ± [0.2; 0.3] mm, median ± [inter-quartile range 25%; inter-quartile range 75%]) and between 1 and 6 mm (error: 4.8 ± [0.5; 0.8] mm) during planar movements. When the hip joint centre displacement exceeded 6 mm, the dual unscented Kalman filter proved to be more accurate than the other methods by 30% during multi-planar movements (error: 5.2 ± [1.2; 1] mm).
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.
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
Directory of Open Access Journals (Sweden)
Vaibhav Awale
2015-11-01
Full Text Available Most submarines carry more than one set of inertial navigation system (INS for redundancy and reliability. Apart from INS systems, the submarine carries other sensors that provide different navigation information. A major challenge is to combine these sensors and INS estimates in an optimal and robust manner for navigation. This issue has been addressed by Farrell1. The same approach is used in this paper to combine different sensor measurements along with INS system. However, since more than one INS system is available onboard, it would be better to use multiple INS systems at the same time to obtain a better estimate of states and to provide autonomy in the event of failure of one INS system. This would require us to combine the estimates obtained from local filters (one set of INS system integrated with external sensors, in some optimal way to provide a global estimate. Individual sensor and IMU measurements cannot be accessed in this scenario. Also, autonomous operation requires no sharing of information among local filters. Hence a decentralised Kalman filter approach is considered for combining the estimates of local filters to give a global estimate. This estimate would not be optimal, however. A better optimal estimate can be obtained by accessing individual measurements and augmenting the state vector in Kalman filter, but in that case, corruption of one INS system will lead to failure of the whole filter. Hence to ensure satisfactory performance of the filter even in the event of failure of some INS system, a decentralised Kalman filtering approach is considered.
On serial observation processing in localized ensemble Kalman filters
Nerger, Lars
2015-01-01
Ensemble square root filters can either assimilate all observations that are available at a given time at once, or assimilate the observations in batches or one at a time. For large-scale models, the filters are typically applied with a localized analysis step. This study demonstrates that the interaction of serial observation processing and localization can destabilize the analysis process and examines under which conditions the instability becomes significant. The instabil...
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
Xiong, Jieqing; Huang, Zhitong; Zhuang, Kaiyu; Ji, Yuefeng
2016-08-01
We propose a novel handover scheme for indoor microcellular visible light communication (VLC) network. With such a scheme, the room, which is fully coverage by light, is divided into several microcells according to the layout of light-emitting diodes (LEDs). However, the directionality of light arises new challenges in keeping the connectivity between the mobile devices and light source under the mobile circumstances. The simplest solution is that all LEDs broadcast data of every user simultaneously, but it wastes too much bandwidth resource, especially when the amount of users increases. To solve this key problem, we utilize the optical positioning assisting handover procedure in this paper. In the positioning stage, the network manager obtains the location information of user device via downlink and uplink signal strength information, which is white light and infrared, respectively. After that, a Kalman filter is utilized for improving the tracking performance of a mobile device. Then, the network manager decides how to initiate the handover process by the previous information. Results show that the proposed scheme can achieve low-cost, seamless data communication, and a high probability of successful handover.
New approach to safeguards accounting. [Kalman filter method for detecting continual small losses
Energy Technology Data Exchange (ETDEWEB)
Pike, D.H.; Morrison, G.W.
1977-03-01
In recent years there has been widespread concern over the problem of nuclear safeguards. Due to the proliferation of nuclear reactors throughout the world, the concern about the loss or diversion of nuclear materials at various points in the fuel cycle has greatly increased. To minimize the possibility of material loss, the nuclear industry relies on physical protection systems and materials accountability procedures at licensed facilities. Present techniques of material accountability rely on double-entry accounting systems. For various reasons, only noisy observations of on-hand inventory are available. Hence one is forced to use statistical techniques in an attempt to detect the existence of missing material. Current practice is to use control charts as the basis for detecting significant material losses. Control charts may aid in detecting large material losses but are insensitive to small quantities of material loss, even if these small losses occur repeatedly over a long period of time. The purpose of this research is to show the feasibility of using linear state estimation theory in nuclear material accountability. The Kalman Filter is used as the state estimation technique. The state vector which consists of on-hand inventory and material losses is estimated recursively.
An Optimal Orthogonal Decomposition Method for Kalman Filter-Based Turbofan Engine Thrust Estimation
Litt, Jonathan S.
2007-01-01
A new linear point design technique is presented for the determination of tuning parameters that enable the optimal estimation of unmeasured engine outputs, such as thrust. The engine's performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters related to each major engine component. Accurate thrust reconstruction depends on knowledge of these health parameters, but there are usually too few sensors to be able to estimate their values. In this new technique, a set of tuning parameters is determined that accounts for degradation by representing the overall effect of the larger set of health parameters as closely as possible in a least squares sense. The technique takes advantage of the properties of the singular value decomposition of a matrix to generate a tuning parameter vector of low enough dimension that it can be estimated by a Kalman filter. A concise design procedure to generate a tuning vector that specifically takes into account the variables of interest is presented. An example demonstrates the tuning parameters ability to facilitate matching of both measured and unmeasured engine outputs, as well as state variables. Additional properties of the formulation are shown to lend themselves well to diagnostics.
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
Institute of Scientific and Technical Information of China (English)
FENG Bo; MA Hong-Bin; FU Meng-Yin; WANG Shun-Ting
2013-01-01
Kalman filtering techniques have been widely used in many applications,however,standard Kalman filters for linear Gaussian systems usually cannot work well or even diverge in the presence of large model uncertainty.In practical applications,it is expensive to have large number of high-cost experiments or even impossible to obtain an exact system model.Motivated by our previous pioneering work on finite-model adaptive control,a framework of finite-model Kalman filtering is introduced in this paper.This framework presumes that large model uncertainty may be restricted by a finite set of known models which can be very different from each other.Moreover,the number of known models in the set can be flexibly chosen so that the uncertain model may always be approximated by one of the known models,in other words,the large model uncertainty is "covered" by the "convex hull" of the known models.Within the presented framework according to the idea of adaptive switching via the minimizing vector distance principle,a simple finite-model Kalman filter,MVDP-FMKF,is mathematically formulated and illustrated by extensive simulations.An experiment of MEMS gyroscope drift has verified the effectiveness of the proposed algorithm,indicating that the mechanism of finite-model Kalman filter is useful and efficient in practical applications of Kalman filters,especially in inertial navigation systems.
Rapid Transfer Alignment of MEMS SINS Based on Adaptive Incremental Kalman Filter
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Hairong Chu
2017-01-01
Full Text Available 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.
Comparison of Kalman filter and optimal smoother estimates of spacecraft attitude
Sedlak, J.
1994-01-01
Given a valid system model and adequate observability, a Kalman filter will converge toward the true system state with error statistics given by the estimated error covariance matrix. The errors generally do not continue to decrease. Rather, a balance is reached between the gain of information from new measurements and the loss of information during propagation. The errors can be further reduced, however, by a second pass through the data with an optimal smoother. This algorithm obtains the optimally weighted average of forward and backward propagating Kalman filters. It roughly halves the error covariance by including future as well as past measurements in each estimate. This paper investigates whether such benefits actually accrue in the application of an optimal smoother to spacecraft attitude determination. Tests are performed both with actual spacecraft data from the Extreme Ultraviolet Explorer (EUVE) and with simulated data for which the true state vector and noise statistics are exactly known.
Model Predictive Control Based on Kalman Filter for Constrained Hammerstein-Wiener Systems
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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.
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...... computational cost of estimating bias in measurements is worthwhile. The simulations where performed in a simulation environment for the CubeSat AAUSAT3, where robustness has been an important factor during tuning of the attitude estimators. The results indicate that it is possible to achieve acceptable Cube...
Xin, Tiantian; Zhao, Hongying; Liu, Sijie; Wang, Lu
2015-03-01
Videos from a small Unmanned Aerial Vehicle (UAV) are always unstable because of the wobble of the vehicle and the impact of surroundings, especially when the motion has a large drifting. Electronic image stabilization aims at removing the unwanted wobble and obtaining the stable video. Then estimation of intended motion, which represents the tendency of global motion, becomes the key to image stabilization. It is usually impossible for general methods of intended motion estimation to obtain stable intended motion remaining as much information of video images and getting a path as much close to the real flying path at the same time. This paper proposed a fuzzy Kalman filtering method to estimate the intended motion to solve these problems. Comparing with traditional methods, the fuzzy Kalman filtering method can achieve better effect to estimate the intended motion.
Interharmonics analysis of power signals with fundamental frequency deviation using Kalman filtering
Energy Technology Data Exchange (ETDEWEB)
Koese, Neslihan; Salor, Oezguel; Leblebicioglu, Kemal [TUBITAK UZAY, Power Electronics Group, TR 06531 Ankara (Turkey); METU, Electrical and Electronics Eng. Dept., TR 06531 Ankara (Turkey)
2010-09-15
In this paper a spectral decomposition-based method for interharmonic computation is proposed for power systems where the fundamental frequency fluctuates significantly. In the proposed method, the frequency domain components of the voltage waveform are obtained by Kalman filtering. Both the system fundamental frequency and the correct spectrum of the voltage waveform, and hence the exact interharmonics are obtained. The proposed method is tested with both simulated and field data obtained from different electric arc furnace (EAF) plants, where the system frequency deviates continuously due to the fluctuating load demands. Since the interharmonic frequencies are obtained by using Kalman filtering, no leakage effect of the DFT-based methods is involved in case of frequency deviations, which is an important advantage of the proposed method. (author)
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.
Using Kalman Filter to Guarantee QoS Robustness of Web Server
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The exponential growth of the Internet coupled with the increasing popularity of dynamically generated content on the World Wide Web, has created the need for more and faster Web servers capable of serving the over 100 million Internet users. To converge the control method has emerged as a promising technique to solve the Web QoS problem. In this paper, a model of adaptive session is presented and a session flow self-regulating algorism based on Kalman Filter are proposed towards Web Server. And a Web QoS self-regulating scheme is advanced. To attain the goal of on-line system identification, the optimized estimation of QoS parameters is fulfilled by utilizing Kalman Filter in full domain. The simulation results shows that the proposed scheme can guarantee the QoS with both robustness and stability .
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.
Characterizing Curvilinear Features Using the Localized Normal-Score Ensemble Kalman Filter
Directory of Open Access Journals (Sweden)
Haiyan Zhou
2012-01-01
Full Text Available The localized normal-score ensemble Kalman filter is shown to work for the characterization of non-multi-Gaussian distributed hydraulic conductivities by assimilating state observation data. The influence of type of flow regime, number of observation piezometers, and the prior model structure are evaluated in a synthetic aquifer. Steady-state observation data are not sufficient to identify the conductivity channels. Transient-state data are necessary for a good characterization of the hydraulic conductivity curvilinear patterns. Such characterization is very good with a dense network of observation data, and it deteriorates as the number of observation piezometers decreases. It is also remarkable that, even when the prior model structure is wrong, the localized normal-score ensemble Kalman filter can produce acceptable results for a sufficiently dense observation network.
River Flow Lane Detection and Kalman Filtering-Based B-Spline Lane Tracking
Directory of Open Access Journals (Sweden)
King Hann Lim
2012-01-01
Full Text Available A novel lane detection technique using adaptive line segment and river flow method is proposed in this paper to estimate driving lane edges. A Kalman filtering-based B-spline tracking model is also presented to quickly predict lane boundaries in consecutive frames. Firstly, sky region and road shadows are removed by applying a regional dividing method and road region analysis, respectively. Next, the change of lane orientation is monitored in order to define an adaptive line segment separating the region into near and far fields. In the near field, a 1D Hough transform is used to approximate a pair of lane boundaries. Subsequently, river flow method is applied to obtain lane curvature in the far field. Once the lane boundaries are detected, a B-spline mathematical model is updated using a Kalman filter to continuously track the road edges. Simulation results show that the proposed lane detection and tracking method has good performance with low complexity.
Noise adaptive fading Kalman filter for free-space laser communication beacon tracking.
Li, Lixing; Huang, Yongmei; Wang, Qiang; Yang, Fasheng
2016-10-20
We proposed a prediction algorithm for laser communication pointing, acquisition, and tracking (PAT) subsystems in order to further improve PAT accuracy and reduce the effect of processing delay. In terms of this prediction algorithm, a fading Kalman filter is employed, with the observation noise obtained by the gray value distribution of the laser images. Moreover, to better fit the dynamics of a laser target, the two-stage dynamic model has been chosen as the state transition model for Kalman filtering. In addition, the two-stage dynamic model has been modified by accommodating its form to a change of time lag, thereby compensating the effect of time delay. A series of horizontal path (17 km) experiments under different atmospheric conditions were conducted in the fields. According to the experimental results, the algorithm we proposed could effectively reduce the tracking error and improve pointing accuracy.
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.
Unscented Kalman Filter-Trained Neural Networks for Slip Model Prediction.
Li, Zhencai; Wang, Yang; Liu, Zhen
2016-01-01
The purpose of this work is to investigate the accurate trajectory tracking control of a wheeled mobile robot (WMR) based on the slip model prediction. Generally, a nonholonomic WMR may increase the slippage risk, when traveling on outdoor unstructured terrain (such as longitudinal and lateral slippage of wheels). In order to control a WMR stably and accurately under the effect of slippage, an unscented Kalman filter and neural networks (NNs) are applied to estimate the slip model in real time. This method exploits the model approximating capabilities of nonlinear state-space NN, and the unscented Kalman filter is used to train NN's weights online. The slip parameters can be estimated and used to predict the time series of deviation velocity, which can be used to compensate control inputs of a WMR. The results of numerical simulation show that the desired trajectory tracking control can be performed by predicting the nonlinear slip model.
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.
Frequency-scanning interferometry for dynamic absolute distance measurement using Kalman filter.
Tao, Long; Liu, Zhigang; Zhang, Weibo; Zhou, Yangli
2014-12-15
We propose a frequency-scanning interferometry using the Kalman filtering technique for dynamic absolute distance measurement. Frequency-scanning interferometry only uses a single tunable laser driven by a triangle waveform signal for forward and backward optical frequency scanning. The absolute distance and moving speed of a target can be estimated by the present input measurement of frequency-scanning interferometry and the previously calculated state based on the Kalman filter algorithm. This method not only compensates for movement errors in conventional frequency-scanning interferometry, but also achieves high-precision and low-complexity dynamic measurements. Experimental results of dynamic measurements under static state, vibration and one-dimensional movement are presented.
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.
Directory of Open Access Journals (Sweden)
P. Kalyana Sundaram
2016-11-01
Full Text Available The paper presents a novel method for the assessment of the power quality disturbances in the distribution system using the Kalman filter and fuzzy expert system. In this method the various classes of disturbance signals are developed through the Matlab Simulink on the test system model. The characteristic features of the disturbance signals are extracted based on the Kalman filter technique. The obtained features such as amplitude and slope are given as the two inputs to the fuzzy expert system. It applied some rules on these inputs to assess the various PQ disturbances. Fuzzy classifier has been carried out and tested for various power quality disturbances. The results clearly demonstrate that the proposed method in the distribution system has the ability to detect and classify PQ events.
Takahashi, Kazuhiko; Naemura, Masahide
2005-12-01
This paper proposes a human body posture estimation method based on analysis of human silhouette and Kalman filter. The proposed method is based on both the heuristically extraction method of estimating the significant points of human body and the contour analysis of the human silhouette. The 2D coordinates of the human body's significant points, such as top of the head, and tips of feet, are located by applying the heuristically extraction method to the human silhouette, those of tips of hands are obtained by using the result of the contour analysis, and the joints of elbows and knees are estimated by introducing some heuristic rules to the contour image of the human silhouette. The estimated results are optimized and tracked by using Kalman filter. The proposed estimation method is implemented on a personal computer and runs in real-time. Experimental results show both the feasibility and the effectiveness of the proposed method for estimating human body postures.
Zhang, Hao; Niu, Yanxiong; Lu, Jiazhen; Zhang, He
2016-11-20
Angular velocity information is a requisite for a spacecraft guidance, navigation, and control system. In this paper, an approach for angular velocity estimation based merely on star vector measurement with an improved current statistical model Kalman filter is proposed. High-precision angular velocity estimation can be achieved under dynamic conditions. The amount of calculation is also reduced compared to a Kalman filter. Different trajectories are simulated to test this approach, and experiments with real starry sky observation are implemented for further confirmation. The estimation accuracy is proved to be better than 10-4 rad/s under various conditions. Both the simulation and the experiment demonstrate that the described approach is effective and shows an excellent performance under both static and dynamic conditions.
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.
A Comparative Analysis of Kalman Filters Using a Hypervelocity Missile Simulation.
1981-12-01
qoa.1.ity TIT " 5 1oth expehns[V, ,,! bulky. Y i 3.1.3 Obst , rv;dmility. For .n ;roposed model, ohservability was a .jkey IS,,. IO b, cuapl,.etily...Patterson AFB, 1980. 15. Wors]ey, William I., Comparison of Three Extended Kalman Filters for Air-to-Air Tracking. M.S. thesis. right-Patterson Air Force
Characterizing Curvilinear Features Using the Localized Normal-Score Ensemble Kalman Filter
Haiyan Zhou; Liangping Li; J. Jaime Gómez-Hernández
2012-01-01
The localized normal-score ensemble Kalman filter is shown to work for the characterization of non-multi-Gaussian distributed hydraulic conductivities by assimilating state observation data. The influence of type of flow regime, number of observation piezometers, and the prior model structure are evaluated in a synthetic aquifer. Steady-state observation data are not sufficient to identify the conductivity channels. Transient-state data are necessary for a good characterization of the hydraul...
Application of Kalman filter in detecting pre-earthquake ionospheric TEC anomaly
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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.
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).
Emulation of an ensemble Kalman filter algorithm on a flood wave propagation model
Barthélémy, S.; Ricci, S.; Pannekoucke, O.; Thual, O.; Malaterre, P.O.
2013-01-01
This study describes the emulation of an Ensemble Kalman Filter (EnKF) algorithm on a 1-D flood wave propagation model. This model is forced at the upstream boundary with a random variable with gaussian statistics and a correlation function in time with gaussian shape. This allows for, in the case without assimilation, the analytical study of the covariance functions of the propagated signal anomaly. This study is validated numerically wit...
Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering
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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.
DAKHLALLAH, Jamil; Imine, Hocine; Sellami, Yamine; BELLOT, D
2007-01-01
Safety driving is due to the prevention of risks situation, one of the important risk is the rollover of a heavy vehicle. Preventing this accident requires the knowledge of the rollover coefficient which depends on the vehicle dynamic state and other vehicle parameters. Thus, we estimate the vehicle dynamic state using the Extended and Unscented Kalman Filter and the Sliding Mode Observer. Thereafter, we calculate the probability to have a rollover risk using the previous result and Monte-Car...
Derivative free Kalman filtering used for orchard navigation
DEFF Research Database (Denmark)
Hansen, Søren; Bayramoglu, Enis; Andersen, Jens Christian
2010-01-01
representing the surrounding fruit trees. The line features are created on basis of 2D laser scanner data by a least square algorithm. The Matlab (R) toolbox Kalmtool is used for easy switching between different filter implementations without the need for changing the base structure of the system....
Multi-channel Kalman filters for active noise control
Ophem, S. van; Berkhoff, A.P.
2013-01-01
By formulating the feed-forward broadband active noise control problem as a state estimation problem it is possible 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
Multi-channel Kalman filters for active noise control
van Ophem, S.; Berkhoff, Arthur P.
By formulating the feed-forward broadband active noise control problem as a state estimation problem it is possible 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
Quaternion-Based Kalman Filter for AHRS Using an Adaptive-Step Gradient Descent Algorithm
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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.
Shen, Zheqi; Tang, Youmin
2016-04-01
The ensemble Kalman particle filter (EnKPF) is a combination of two Bayesian-based algorithms, namely, the ensemble Kalman filter (EnKF) and the sequential importance resampling particle filter(SIR-PF). It was recently introduced to address non-Gaussian features in data assimilation for highly nonlinear systems, by providing a continuous interpolation between the EnKF and SIR-PF analysis schemes. In this paper, we first extend the EnKPF algorithm by modifying the formula for the computation of the covariancematrix, making it suitable for nonlinear measurement functions (we will call this extended algorithm nEnKPF). Further, a general form of the Kalman gain is introduced to the EnKPF to improve the performance of the nEnKPF when the measurement function is highly nonlinear (this improved algorithm is called mEnKPF). The Lorenz '63 model and Lorenz '96 model are used to test the two modified EnKPF algorithms. The experiments show that the mEnKPF and nEnKPF, given an affordable ensemble size, can perform better than the EnKF for the nonlinear systems with nonlinear observations. These results suggest a promising opportunity to develop a non-Gaussian scheme for realistic numerical models.
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.
Incremental Activation Detection for Real-Time fMRI Series Using Robust Kalman Filter
Directory of Open Access Journals (Sweden)
Liang Li
2014-01-01
Full Text Available Real-time functional magnetic resonance imaging (rt-fMRI is a technique that enables us to observe human brain activations in real time. However, some unexpected noises that emerged in fMRI data collecting, such as acute swallowing, head moving and human manipulations, will cause much confusion and unrobustness for the activation analysis. In this paper, a new activation detection method for rt-fMRI data is proposed based on robust Kalman filter. The idea is to add a variation to the extended kalman filter to handle the additional sparse measurement noise and a sparse noise term to the measurement update step. Hence, the robust Kalman filter is designed to improve the robustness for the outliers and can be computed separately for each voxel. The algorithm can compute activation maps on each scan within a repetition time, which meets the requirement for real-time analysis. Experimental results show that this new algorithm can bring out high performance in robustness and in real-time activation detection.
A Discontinuous Extended Kalman Filter for non-smooth dynamic problems
Chatzis, M. N.; Chatzi, E. N.; Triantafyllou, S. P.
2017-08-01
Problems that result into locally non-differentiable and hence non-smooth state-space equations are often encountered in engineering. Examples include problems involving material laws pertaining to plasticity, impact and highly non-linear phenomena. Estimating the parameters of such systems poses a challenge, particularly since the majority of system identification algorithms are formulated on the basis of smooth systems under the assumption of observability, identifiability and time invariance. For a smooth system, an observable state remains observable throughout the system evolution with the exception of few selected realizations of the state vector. However, for a non-smooth system the observable set of states and parameters may vary during the evolution of the system throughout a dynamic analysis. This may cause standard identification (ID) methods, such as the Extended Kalman Filter, to temporarily diverge and ultimately fail in accurately identifying the parameters of the system. In this work, the influence of observability of non-smooth systems to the performance of the Extended and Unscented Kalman Filters is discussed and a novel algorithm particularly suited for this purpose, termed the Discontinuous Extended Kalman Filter (DEKF), is proposed.
Penalized Ensemble Kalman Filters for High Dimensional Non-linear Systems
Hou, Elizabeth; Hero, Alfred O
2016-01-01
The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a non-linear system. It does so by using an empirical approximation to the well-known Kalman filter. Unfortunately, its performance suffers when the ensemble size is smaller than the state space, as is often the case for computationally burdensome models. This scenario means that the empirical estimate of the state covariance is not full rank and possibly quite noisy. To solve this problem in this high dimensional regime, a computationally fast and easy to implement algorithm called the penalized ensemble Kalman filter (PEnKF) is proposed. Under certain conditions, it can be proved that the PEnKF does not require more ensemble members than state dimensions in order to have good performance. Further, the proposed approach does not require special knowledge of the system such as is used by localization methods. These theoretical results are supported with superior...
On the Kalman Filter error covariance collapse into the unstable subspace
Directory of Open Access Journals (Sweden)
A. Trevisan
2011-03-01
Full Text Available When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N^{+} + N^{0} where N^{+} and N^{0} are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with non-negative Lyapunov exponents. Theoretical arguments and numerical verification are provided to show that the asymptotic state and covariance estimates of the full EKF and of its reduced form, with assimilation in the unstable and neutral subspace (EKF-AUS are the same. The consequences of these findings on applications of Kalman type Filters to chaotic models are discussed.
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.
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.
Accounting for spatial correlations of the observation errors with Ensemble Kalman filters
Cosme, Emmanuel; Jean-Michel, Brankart; Clément, Ubelmann; Jacques, Verron; Pierre, Brasseur
2013-04-01
The standard Kalman filter observational update requires the inversion of the innovation error covariance matrix, what is often impractical. Most implementations of the Ensemble Kalman filter circumvent this difficulty assuming the diagonality of the observation error covariance matrix, what makes the analysis calculation numerically tractable. However, when observation errors are actually correlated spatially, such hypothesis leads to an inappropriate use of observations. Experiments show that the analysis state error variances yielded by the Ensemble Kalman filter can be severely underestimated. In this presentation, we describe a parameterization of the observation error covariance matrix which preserves its diagonal shape, but represents a simple first order autoregressive correlation structure of the observation errors. This parameterization is based upon an augmentation of the observation vector with gradients of observations. Numerical applications to ocean altimetry show the detrimental effects of specifying a diagonal matrix when observations errors are correlated, and how the new parameterization not only removes the detrimental effects of correlations, but also makes use of these correlations to improve the data assimilation products.
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.
Bourgeois, Brian S.; Elmore, Paul A.; Avera, William E.; Zambo, Samantha J.
2016-07-01
This paper examines and contrasts two estimation methods, Kalman filtering and linear smoothing, for creating interpolated data products from bathymetry measurements. Using targeted examples, we demonstrate previously obscured behavior showing the dependence of linear smoothers on the spatial arrangement of the measurements, yielding markedly different estimation results than the Kalman filter. For bathymetry data, we have modified the variance estimates from both the Kalman filter and linear smoothers to obtain comparable estimators for dense data. These comparable estimators produce uncertainty estimates that have statistically insignificant differences via hypothesis testing. Achieving comparable estimation is accomplished by applying the "propagated uncertainty" concept and a numerical realization of Tobler's principle to the measurement data prior to the computation of the estimate. We show new mathematical derivations for these modifications. In addition, we show test results with (a) synthetic data and (b) gridded bathymetry in the area of the Scripps and La Jolla Canyons. Our tenfold cross-validation for case (b) shows that the modified equations create comparable uncertainty for both gridding algorithms with null hypothesis acceptance rates of greater than 99.95% of the data points. In contrast, bilinear interpolation has 10 times the amount of rejection. We then discuss how the uncertainty estimators are, in principle, applicable to interpolate geophysical data other than bathymetry.
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.
Soja, Benedikt; Nilsson, Tobias; Balidakis, Kyriakos; Glaser, Susanne; Heinkelmann, Robert; Schuh, Harald
2016-12-01
Terrestrial reference frames (TRF), such as the ITRF2008, are primary products of geodesy. In this paper, we present TRF solutions based on Kalman filtering of very long baseline interferometry (VLBI) data, for which we estimate steady station coordinates over more than 30 years that are updated for every single VLBI session. By applying different levels of process noise, non-linear signals, such as seasonal and seismic effects, are taken into account. The corresponding stochastic model is derived site-dependent from geophysical loading deformation time series and is adapted during periods of post-seismic deformations. Our results demonstrate that the choice of stochastic process has a much smaller impact on the coordinate time series and velocities than the overall noise level. If process noise is applied, tests with and without additionally estimating seasonal signals indicate no difference between the resulting coordinate time series for periods when observational data are available. In a comparison with epoch reference frames, the Kalman filter solutions provide better short-term stability. Furthermore, we find out that the Kalman filter solutions are of similar quality when compared to a consistent least-squares solution, however, with the enhanced attribute of being easier to update as, for instance, in a post-earthquake period.
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
Chen, Xiyuan; Wang, Xiying; Xu, Yuan
2014-12-09
This paper deals with the problem of state estimation for the vector-tracking loop of a software-defined Global Positioning System (GPS) receiver. For a nonlinear system that has the model error and white Gaussian noise, a noise statistics estimator is used to estimate the model error, and based on this, a modified iterated extended Kalman filter (IEKF) named adaptive iterated Kalman filter (AIEKF) is proposed. A vector-tracking GPS receiver utilizing AIEKF is implemented to evaluate the performance of the proposed method. Through road tests, it is shown that the proposed method has an obvious accuracy advantage over the IEKF and Adaptive Extended Kalman filter (AEKF) in position determination. The results show that the proposed method is effective to reduce the root-mean-square error (RMSE) of position (including longitude, latitude and altitude). Comparing with EKF, the position RMSE values of AIEKF are reduced by about 45.1%, 40.9% and 54.6% in the east, north and up directions, respectively. Comparing with IEKF, the position RMSE values of AIEKF are reduced by about 25.7%, 19.3% and 35.7% in the east, north and up directions, respectively. Compared with AEKF, the position RMSE values of AIEKF are reduced by about 21.6%, 15.5% and 30.7% in the east, north and up directions, respectively.
Incremental activation detection for real-time fMRI series using robust Kalman filter.
Li, Liang; Yan, Bin; Tong, Li; Wang, Linyuan; Li, Jianxin
2014-01-01
Real-time functional magnetic resonance imaging (rt-fMRI) is a technique that enables us to observe human brain activations in real time. However, some unexpected noises that emerged in fMRI data collecting, such as acute swallowing, head moving and human manipulations, will cause much confusion and unrobustness for the activation analysis. In this paper, a new activation detection method for rt-fMRI data is proposed based on robust Kalman filter. The idea is to add a variation to the extended kalman filter to handle the additional sparse measurement noise and a sparse noise term to the measurement update step. Hence, the robust Kalman filter is designed to improve the robustness for the outliers and can be computed separately for each voxel. The algorithm can compute activation maps on each scan within a repetition time, which meets the requirement for real-time analysis. Experimental results show that this new algorithm can bring out high performance in robustness and in real-time activation detection.
Rajabioun, Mehdi; Nasrabadi, Ali Motie; Shamsollahi, Mohammad Bagher
2017-08-29
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.
Soja, Benedikt; Nilsson, Tobias; Balidakis, Kyriakos; Glaser, Susanne; Heinkelmann, Robert; Schuh, Harald
2016-06-01
Terrestrial reference frames (TRF), such as the ITRF2008, are primary products of geodesy. In this paper, we present TRF solutions based on Kalman filtering of very long baseline interferometry (VLBI) data, for which we estimate steady station coordinates over more than 30 years that are updated for every single VLBI session. By applying different levels of process noise, non-linear signals, such as seasonal and seismic effects, are taken into account. The corresponding stochastic model is derived site-dependent from geophysical loading deformation time series and is adapted during periods of post-seismic deformations. Our results demonstrate that the choice of stochastic process has a much smaller impact on the coordinate time series and velocities than the overall noise level. If process noise is applied, tests with and without additionally estimating seasonal signals indicate no difference between the resulting coordinate time series for periods when observational data are available. In a comparison with epoch reference frames, the Kalman filter solutions provide better short-term stability. Furthermore, we find out that the Kalman filter solutions are of similar quality when compared to a consistent least-squares solution, however, with the enhanced attribute of being easier to update as, for instance, in a post-earthquake period.
Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics
Rodriguez, G.
1986-01-01
The inverse and forward dynamics problems for multi-link serial manipulators are solved by using recursive techniques from linear filtering and smoothing theory. The pivotal step is to cast the system dynamics and kinematics as a two-point boundary-value problem. Solution of this problem leads to filtering and smoothing techniques identical to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The solutions prescribe an inward filtering recursion to compute a sequence of constraint moments and forces followed by an outward recursion to determine a corresponding sequence of angular and linear accelerations. In addition to providing techniques to compute joint accelerations from applied joint moments (and vice versa), the report provides an approach to evaluate recursively the composite multi-link system inertia matrix and its inverse. The report lays the foundation for the potential use of filtering and smoothing techniques in robot inverse and forward dynamics and in robot control design.
Two-step measurement update for extended Kalman filtering
Institute of Scientific and Technical Information of China (English)
Zhang Yong'an; Zhou Di; Duan Guangren
2005-01-01
The nonlinear filtering for a class of discrete-time stochastic dynamic systems whose measurement equations contain linear (or universal linearizable) components and nonlinear components which are mutually statistical independent is investigated. A two-step measurement update is proposed for the filtering of the systems. The first-step update is a linear (or universal linearization) measurement correction which introduces an intermediate estimate, while the second-step nonlinear linearization update produces the final posterior estimate based on the first-step estimate.Since the first measurement correction is a linear or universal linearization update, it provides an accurate linearization reference point for the second nonlinear measurement update. Two simulation examples show superiority of the new estimation method.
Directory of Open Access Journals (Sweden)
G. Wu
2014-04-01
Full Text Available The Ensemble Transform Kalman Filter (ETKF assimilation scheme has recently seen rapid development and wide application. As a specific implementation of the Ensemble Kalman Filter (EnKF, the ETKF is computationally more efficient than the conventional EnKF. However, the current implementation of the ETKF still has some limitations when the observation operator is strongly nonlinear. One problem is that the nonlinear operator and its tangent-linear operator are iteratively calculated in the minimization of a nonlinear objective function similar to 4DVAR, which may be computationally expensive. Another problem is that it uses the tangent-linear approximation of the observation operator to estimate the multiplicative inflation factor of the forecast errors, which may not be sufficiently accurate. This study seeks a way to avoid these problems. First, we apply the second-order Taylor approximation of the nonlinear observation operator to avoid iteratively calculating the operator and its tangent-linear operator. The related computational cost is also discussed. Second, we propose a scheme to estimate the inflation factor when the observation operator is strongly nonlinear. Experimentation with the Lorenz-96 model shows that using the second-order Taylor approximation of the nonlinear observation operator leads to a reduction of the analysis error compared with the traditional linear approximation. Similarly, the proposed inflation scheme leads to a reduction of the analysis error compared with the procedure using the traditional inflation scheme.
On robust kalman filtering with using wavelet analysis
Lobach, V. I.
2013-01-01
One presents a nonlinear filtering algorithm that propagates the entire condi- tional probability density functions. These functions are recursively computed in efficient manner using the discrete wavelet transform. With the multiresolution analysis we can speed up the computation by ignoring the high-frequency details of the probability density function up to a certain level. The level of the wavelet decomposition can be determined at each time step adaptively.
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.