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.
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.
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…
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.
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.
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.
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.
Kalman Filtering with Inequality Constraints for Turbofan Engine Health Estimation
Simon, Dan; Simon, Donald L.
2003-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops two analytic methods of incorporating state variable inequality constraints in the Kalman filter. The first method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satisfied rather than exactly satisfied.) The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results. The use of the algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate health parameters. The turbofan engine model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.
Kalman Filter Constraint Tuning for Turbofan Engine Health Estimation
Simon, Dan; Simon, Donald L.
2005-01-01
Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter, which has been shown to generally improve the filter s estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy as the Kalman filter is theoretically optimal. This paper proposes a way to tune the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.
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.
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.
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...
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.
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.
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.
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.
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.
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.
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
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.
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
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.
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...
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.
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.
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...
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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...
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.
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.
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 ...
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.
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.
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)
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.
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.
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.
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.
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.
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.
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.
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.
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:…
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.
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.
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.
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.
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.
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.
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.
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...
Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering
Directory of Open Access Journals (Sweden)
Xiu Kan
2012-01-01
Full Text Available The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameter θ:dXt=(θα(t+β(tXtdt+σ(tdWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameter θ based on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.
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).
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.
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
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.
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
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.
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.
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.
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.
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.
Target Centroid Position Estimation of Phase-Path Volume Kalman Filtering
Directory of Open Access Journals (Sweden)
Fengjun Hu
2016-01-01
Full Text Available For the problem of easily losing track target when obstacles appear in intelligent robot target tracking, this paper proposes a target tracking algorithm integrating reduced dimension optimal Kalman filtering algorithm based on phase-path volume integral with Camshift algorithm. After analyzing the defects of Camshift algorithm, compare the performance with the SIFT algorithm and Mean Shift algorithm, and Kalman filtering algorithm is used for fusion optimization aiming at the defects. Then aiming at the increasing amount of calculation in integrated algorithm, reduce dimension with the phase-path volume integral instead of the Gaussian integral in Kalman algorithm and reduce the number of sampling points in the filtering process without influencing the operational precision of the original algorithm. Finally set the target centroid position from the Camshift algorithm iteration as the observation value of the improved Kalman filtering algorithm to fix predictive value; thus to make optimal estimation of target centroid position and keep the target tracking so that the robot can understand the environmental scene and react in time correctly according to the changes. The experiments show that the improved algorithm proposed in this paper shows good performance in target tracking with obstructions and reduces the computational complexity of the algorithm through the dimension reduction.
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.
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.
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
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...
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.
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...
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.
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.
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.
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.
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.
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...
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.
Canfield, Stephen
1999-01-01
This work will demonstrate the integration of sensor and system dynamic data and their appropriate models using an optimal filter to create a robust, adaptable, easily reconfigurable state (motion) estimation system. This state estimation system will clearly show the application of fundamental modeling and filtering techniques. These techniques are presented at a general, first principles level, that can easily be adapted to specific applications. An example of such an application is demonstrated through the development of an integrated GPS/INS navigation system. This system acquires both global position data and inertial body data, to provide optimal estimates of current position and attitude states. The optimal states are estimated using a Kalman filter. The state estimation system will include appropriate error models for the measurement hardware. The results of this work will lead to the development of a "black-box" state estimation system that supplies current motion information (position and attitude states) that can be used to carry out guidance and control strategies. This black-box state estimation system is developed independent of the vehicle dynamics and therefore is directly applicable to a variety of vehicles. Issues in system modeling and application of Kalman filtering techniques are investigated and presented. These issues include linearized models of equations of state, models of the measurement sensors, and appropriate application and parameter setting (tuning) of the Kalman filter. The general model and subsequent algorithm is developed in Matlab for numerical testing. The results of this system are demonstrated through application to data from the X-33 Michael's 9A8 mission and are presented in plots and simple animations.
Estimation of FBMC/OQAM fading channels using dual Kalman filters.
Aldababseh, Mahmoud; Jamoos, Ali
2014-01-01
We address the problem of estimating time-varying fading channels in filter bank multicarrier (FBMC/OQAM) wireless systems based on pilot symbols. The standard solution to this problem is the least square (LS) estimator or the minimum mean square error (MMSE) estimator with possible adaptive implementation using recursive least square (RLS) algorithm or least mean square (LMS) algorithm. However, these adaptive filters cannot well-exploit fading channel statistics. To take advantage of fading channel statistics, the time evolution of the fading channel is modeled by an autoregressive process and tracked by Kalman filter. Nevertheless, this requires the autoregressive parameters which are usually unknown. Thus, we propose to jointly estimate the FBMC/OQAM fading channels and their autoregressive parameters based on dual optimal Kalman filters. Once the fading channel coefficients at pilot symbol positions are estimated by the proposed method, the fading channel coefficients at data symbol positions are then estimated by using some interpolation methods such as linear, spline, or low-pass interpolation. The comparative simulation study we carried out with existing techniques confirms the effectiveness of the proposed method.
Estimation of FBMC/OQAM Fading Channels Using Dual Kalman Filters
Directory of Open Access Journals (Sweden)
Mahmoud Aldababseh
2014-01-01
Full Text Available We address the problem of estimating time-varying fading channels in filter bank multicarrier (FBMC/OQAM wireless systems based on pilot symbols. The standard solution to this problem is the least square (LS estimator or the minimum mean square error (MMSE estimator with possible adaptive implementation using recursive least square (RLS algorithm or least mean square (LMS algorithm. However, these adaptive filters cannot well-exploit fading channel statistics. To take advantage of fading channel statistics, the time evolution of the fading channel is modeled by an autoregressive process and tracked by Kalman filter. Nevertheless, this requires the autoregressive parameters which are usually unknown. Thus, we propose to jointly estimate the FBMC/OQAM fading channels and their autoregressive parameters based on dual optimal Kalman filters. Once the fading channel coefficients at pilot symbol positions are estimated by the proposed method, the fading channel coefficients at data symbol positions are then estimated by using some interpolation methods such as linear, spline, or low-pass interpolation. The comparative simulation study we carried out with existing techniques confirms the effectiveness of the proposed method.
Particle and Kalman filtering for state estimation and control of DC motors.
Rigatos, Gerasimos G
2009-01-01
State estimation is a major problem in industrial systems. To this end, Gaussian and nonparametric filters have been developed. In this paper the Kalman Filter, which assumes Gaussian measurement noise, is compared to the Particle Filter, which does not make any assumption on the measurement noise distribution. As a case study the estimation of the state vector of a DC motor is used. The reconstructed state vector is used in a feedback control loop to generate the control input of the DC motor. In simulation tests it was observed that for a large number of particles the Particle Filter could succeed in accurately estimating the motor's state vector, but at the same time it required higher computational effort.
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.
Bootstrapping Nonlinear Least Squares Estimates in the Kalman Filter Model.
1986-01-01
Bias Bootstrapa 3.933 x 103 0.651 x 103 -0.166 x 10-- b b Newton - Rapshon 1.380 x 10- 0.479 x 10- 10_c 0_ c , e -.., Emperical 3.605 x 10 -0.026 x 10...most cases, parameter estimation for the KF model has been accomplished by maximum likelihood techniques involving the use of scoring or Newton ...is well behaved, the Newton -Raphson and scoring procedures enjoy quadratic convergence in the neighborhood of the maximum and one has a ready-made
Delay Kalman Filter to Estimate the Attitude of a Mobile Object with Indoor Magnetic Field Gradients
Directory of Open Access Journals (Sweden)
Christophe Combettes
2016-05-01
Full Text Available More and more services are based on knowing the location of pedestrians equipped with connected objects (smartphones, smartwatches, etc.. One part of the location estimation process is attitude estimation. Many algorithms have been proposed but they principally target open space areas where the local magnetic field equals the Earth’s field. Unfortunately, this approach is impossible indoors, where the use of magnetometer arrays or magnetic field gradients has been proposed. However, current approaches omit the impact of past state estimates on the current orientation estimate, especially when a reference field is computed over a sliding window. A novel Delay Kalman filter is proposed in this paper to integrate this time correlation: the Delay MAGYQ. Experimental assessment, conducted in a motion lab with a handheld inertial and magnetic mobile unit, shows that the novel filter better estimates the Euler angles of the handheld device with an 11.7° mean error on the yaw angle as compared to 16.4° with a common Additive Extended Kalman filter.
Rhythmic Extended Kalman Filter for Gait Rehabilitation Motion Estimation and Segmentation.
Joukov, Vladimir; Bonnet, Vincent; Karg, Michelle; Venture, Gentiane; Kulic, Dana
2017-01-26
This work proposes a method to enable the use of non-intrusive, small, wearable, wireless sensors to estimate the pose of the lower body during gait and other periodic motions and to extract objective performance measures useful for physiotherapy. The Rhythmic Extended Kalman Filter (Rhythmic- EKF) algorithm is developed to estimate the pose, learn an individualized model of periodic movement over time, and use the learned model to improve pose estimation. The proposed approach learns a canonical dynamical system model of the movement during online observation, which is used to accurately model the acceleration during pose estimation. The canonical dynamical system models the motion as a periodic signal. The estimated phase and frequency of the motion also allow the proposed approach to segment the motion into repetitions and extract useful features such as gait symmetry, step length, and mean joint movement and variance. The algorithm is shown to outperform the extended Kalman filter in simulation, on healthy participant data, and stroke patient data. For the healthy participant marching dataset, the Rhythmic-EKF improves joint acceleration and velocity estimates over regular EKF by 40% and 37% respectively, estimates joint angles with 2.4° RMSE, and segments the motion into repetitions with 96% accuracy.
A simulation study of turbofan engine deterioration estimation using Kalman filtering techniques
Lambert, Heather H.
1991-01-01
Deterioration of engine components may cause off-normal engine operation. The result is an unecessary loss of performance, because the fixed schedules are designed to accommodate a wide range of engine health. These fixed control schedules may not be optimal for a deteriorated engine. This problem may be solved by including a measure of deterioration in determining the control variables. These engine deterioration parameters usually cannot be measured directly but can be estimated. A Kalman filter design is presented for estimating two performance parameters that account for engine deterioration: high and low pressure turbine delta efficiencies. The delta efficiency parameters model variations of the high and low pressure turbine efficiencies from nominal values. The filter has a design condition of Mach 0.90, 30,000 ft altitude, and 47 deg power level angle (PLA). It was evaluated using a nonlinear simulation of the F100 engine model derivative (EMD) engine, at the design Mach number and altitude over a PLA range of 43 to 55 deg. It was found that known high pressure turbine delta efficiencies of -2.5 percent and low pressure turbine delta efficiencies of -1.0 percent can be estimated with an accuracy of + or - 0.25 percent efficiency with a Kalman filter. If both the high and low pressure turbine are deteriorated, the delta efficiencies of -2.5 percent to both turbines can be estimated with the same accuracy.
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....
Kim, Kiyoung; Sohn, Hoon
2017-01-01
This paper presents a smoothing based Kalman filter to estimate dynamic displacement in real-time by fusing the velocity measured from a laser Doppler vibrometer (LDV) and the displacement from a light detection and ranging (LiDAR). LiDAR can measure displacement based on the time-of-flight information or the phase-shift of the laser beam reflected off form a target surface, but it typically has a high noise level and a low sampling rate. On the other hand, LDV primarily measures out-of-plane velocity of a moving target, and displacement is estimated by numerical integration of the measured velocity. Here, the displacement estimated by LDV suffers from integration error although LDV can achieve a lower noise level and a much higher sampling rate than LiDAR. The proposed data fusion technique estimates high-precision and high-sampling rate displacement by taking advantage of both LiDAR and LDV measurements and overcomes their limitations by adopting a real-time smoothing based Kalman filter. To verify the performance of the proposed dynamic displacement estimation technique, a series of lab-scale tests are conducted under various loading conditions.
A cascaded two-step Kalman filter for estimation of human body segment orientation using MEMS-IMU.
Zihajehzadeh, S; Loh, D; Lee, M; Hoskinson, R; Park, E J
2014-01-01
Orientation of human body segments is an important quantity in many biomechanical analyses. To get robust and drift-free 3-D orientation, raw data from miniature body worn MEMS-based inertial measurement units (IMU) should be blended in a Kalman filter. Aiming at less computational cost, this work presents a novel cascaded two-step Kalman filter orientation estimation algorithm. Tilt angles are estimated in the first step of the proposed cascaded Kalman filter. The estimated tilt angles are passed to the second step of the filter for yaw angle calculation. The orientation results are benchmarked against the ones from a highly accurate tactical grade IMU. Experimental results reveal that the proposed algorithm provides robust orientation estimation in both kinematically and magnetically disturbed conditions.
Sen, Subhamoy; Crinière, Antoine; Mevel, Laurent; Cerou, Frederic; Dumoulin, Jean
2017-04-01
Keywords: Parameter estimation; Kalman filter; Particle filter; Particle-Kalman filter; Correlated noise Although Kalman filter (KF) was originally proposed for system control i.e. steering a system as desired by monitoring the system states, its application for parameter estimation problems is widespread because of the excellent similarity between these two apparently different problem types in state space description. In standard Kalman filter, system dynamics is described through the dynamics of certain internal variable, termed as states, evolving over time as defined by an assumed process model, while a measurement model maps these states to measurements. In some parameter estimation problems, the system is replaced by a state space formulation of the dynamic model with parameters appended in the unobserved states and collectively observed through the response measurements. Filtering based parameter estimation problems are thus inherently nonlinear due to the required nonlinear mapping of parameters to the corresponding observations. Being a linear estimator, Kalman Filter (KF) cannot be employed for such nonlinear system estimation and alternative filtering algorithms (eg. Particle filter) are therefore generally used. However, being model based, these filters optimally estimate the parameters of a quasi-static model of the real dynamic system. Consequently, any time variation in the system dynamics may completely diverge the estimation yielding a false or infeasible solution. By decoupling the estimation of system states and parameters, and applying concurrent filtering strategy that attempts conditional estimation of states based on parameters and vice versa, time varying systems can be estimated. This article attempts to combine KF with Particle filter (PF) and apply them for estimation of states and system parameters respectively on a system with correlated noise in process and measurement. The idea is to nest a bank of linear KFs for state estimation
DEFF Research Database (Denmark)
Wang, Yunlong; Soltani, Mohsen; Hussain, Dil muhammed Akbar
2016-01-01
Satellite tracking is a challenging task for marine applications due to the disturbance from ocean waves. An Attitude Heading and Reference System (AHRS) for measuring ship attitude, based on Microelectromechanical Systems (MEMS) sensors, is a key part for satellite tracking. In this paper......, 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...
Galvan, Jose Ramon; Saxena, Abhinav; Goebel, Kai Frank
2012-01-01
This article discusses several aspects of uncertainty representation and management for model-based prognostics methodologies based on our experience with Kalman Filters when applied to prognostics for electronics components. In particular, it explores the implications of modeling remaining useful life prediction as a stochastic process, and how it relates to uncertainty representation, management and the role of prognostics in decision-making. A distinction between the interpretations of estimated remaining useful life probability density function is explained and a cautionary argument is provided against mixing interpretations for two while considering prognostics in making critical decisions.
A SAS/IML program using the Kalman filter for estimating state space models.
Gu, Fei; Yung, Yiu-Fai
2013-03-01
To help disseminate the knowledge and software implementation of a state space model (SSM), this article provides a SAS/IML (SAS Institute, 2010) program for estimating the parameters of general linear Gaussian SSMs using the Kalman filter algorithm. In order to use this program, the user should have SAS installed on a computer and have a valid license for SAS/IML. Since the code is completely open, it is expected that this program can be used not only by applied researchers, but also by quantitative methodologists who are interested in improving their methods and promoting SSM as a research instrument.
Sadaghzadeh N, Nargess; Poshtan, Javad; Wagner, Achim; Nordheimer, Eugen; Badreddin, Essameddin
2014-03-01
Based on a cascaded Kalman-Particle Filtering, gyroscope drift and robot attitude estimation method is proposed in this paper. Due to noisy and erroneous measurements of MEMS gyroscope, it is combined with Photogrammetry based vision navigation scenario. Quaternions kinematics and robot angular velocity dynamics with augmented drift dynamics of gyroscope are employed as system state space model. Nonlinear attitude kinematics, drift and robot angular movement dynamics each in 3 dimensions result in a nonlinear high dimensional system. To reduce the complexity, we propose a decomposition of system to cascaded subsystems and then design separate cascaded observers. This design leads to an easier tuning and more precise debugging from the perspective of programming and such a setting is well suited for a cooperative modular system with noticeably reduced computation time. Kalman Filtering (KF) is employed for the linear and Gaussian subsystem consisting of angular velocity and drift dynamics together with gyroscope measurement. The estimated angular velocity is utilized as input of the second Particle Filtering (PF) based observer in two scenarios of stochastic and deterministic inputs. Simulation results are provided to show the efficiency of the proposed method. Moreover, the experimental results based on data from a 3D MEMS IMU and a 3D camera system are used to demonstrate the efficiency of the method.
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.
Directory of Open Access Journals (Sweden)
P. A. Ermolaev
2014-03-01
Full Text Available Data processing in the interferometer systems requires high-resolution and high-speed algorithms. Recurrence algorithms based on parametric representation of signals execute consequent processing of signal samples. In some cases recurrence algorithms make it possible to increase speed and quality of data processing as compared with classic processing methods. Dependence of the measured interferometer signal on parameters of its model and stochastic nature of noise formation in the system is, in general, nonlinear. The usage of nonlinear stochastic filtering algorithms is expedient for such signals processing. Extended Kalman filter with linearization of state and output equations by the first vector parameters derivatives is an example of these algorithms. To decrease approximation error of this method the second order extended Kalman filtering is suggested with additionally usage of the second vector parameters derivatives of model equations. Examples of algorithm implementation with the different sets of estimated parameters are described. The proposed algorithm gives the possibility to increase the quality of data processing in interferometer systems in which signals are forming according to considered models. Obtained standard deviation of estimated amplitude envelope does not exceed 4% of the maximum. It is shown that signal-to-noise ratio of reconstructed signal is increased by 60%.
Simultaneous estimation of phase derivative and phase using parallel Kalman filter implementation
Kulkarni, Rishikesh; Rastogi, Pramod
2016-06-01
This paper proposes a technique for the simultaneous estimation of interference phase derivative and phase from a complex interferogram recorded in an optical interferometric setup. The complex interferogram is represented as a spatially varying autoregressive process in a given row or column at a time. The phase derivative is estimated from the poles of the transfer function representation of the autoregressive process. The poles are computed using the spatially varying autoregressive coefficients which are estimated by a computationally efficient Rauch-Tung-Striebel smoothing algorithm. The estimated phase derivative is used as a control input to a state space model designed for the phase estimation at each pixel. The unscented Kalman filter is utilized to deal with the nonlinear measurement process for the accurate estimation of the unwrapped phase. Numerical and experimental results substantiate the ability of the proposed method in handling noisy phase fringe patterns.
Recursive Starlight and Bias Estimation for High-Contrast Imaging with an Extended Kalman Filter
Riggs, A J Eldorado; Groff, Tyler D
2016-01-01
For imaging faint exoplanets and disks, a coronagraph-equipped observatory needs focal plane wavefront correction to recover high contrast. The most efficient correction methods iteratively estimate the stellar electric field and suppress it with active optics. The estimation requires several images from the science camera per iteration. To maximize the science yield, it is desirable both to have fast wavefront correction and to utilize all the correction images for science target detection. Exoplanets and disks are incoherent with their stars, so a nonlinear estimator is required to estimate both the incoherent intensity and the stellar electric field. Such techniques assume a high level of stability found only on space-based observatories and possibly ground-based telescopes with extreme adaptive optics. In this paper, we implement a nonlinear estimator, the iterated extended Kalman filter (IEKF), to enable fast wavefront correction and a recursive, nearly-optimal estimate of the incoherent light. In Prince...
Online Internal Temperature Estimation for Lithium-Ion Batteries Based on Kalman Filter
Directory of Open Access Journals (Sweden)
Jinlei Sun
2015-05-01
Full Text Available The battery internal temperature estimation is important for the thermal safety in applications, because the internal temperature is hard to measure directly. In this work, an online internal temperature estimation method based on a simplified thermal model using a Kalman filter is proposed. As an improvement, the influences of entropy change and overpotential on heat generation are analyzed quantitatively. The model parameters are identified through a current pulse test. The charge/discharge experiments under different current rates are carried out on the same battery to verify the estimation results. The internal and surface temperatures are measured with thermocouples for result validation and model construction. The accuracy of the estimated result is validated with a maximum estimation error of around 1 K.
Directory of Open Access Journals (Sweden)
O. Jakubov
2013-09-01
Full Text Available Common techniques for position-velocity-time estimation in satellite navigation, iterative least squares and the extended Kalman filter, involve matrix operations. The matrix inversion and inclusion of a matrix library pose requirements on a computational power and operating platform of the navigation processor. In this paper, we introduce a novel distributed algorithm suitable for implementation in simple parallel processing units each for a tracked satellite. Such a unit performs only scalar sum, subtraction, multiplication, and division. The algorithm can be efficiently implemented in hardware logic. Given the fast position-velocity-time estimator, frequent estimates can foster dynamic performance of a vector tracking receiver. The algorithm has been designed from a factor graph representing the extended Kalman filter by splitting vector nodes into scalar ones resulting in a cyclic graph with few iterations needed. Monte Carlo simulations have been conducted to investigate convergence and accuracy. Simulation case studies for a vector tracking architecture and experimental measurements with a real-time software receiver developed at CTU in Prague were conducted. The algorithm offers compromises in stability, accuracy, and complexity depending on the number of iterations. In scenarios with a large number of tracked satellites, it can outperform the traditional methods at low complexity.
DEFF Research Database (Denmark)
Mohd. Azam, Sazuan Nazrah
2017-01-01
In this paper, we used the modified quadruple tank system that represents a multi-input-multi-output (MIMO) system as an example to present the realization of a linear discrete-time state space model and to obtain the state estimation using Kalman filter in a methodical mannered. First, an existing...... dynamics of the system of stochastic differential equations is linearized to produce the deterministic-stochastic linear transfer function. Then the linear transfer function is discretized to produce a linear discrete-time state space model that has a deterministic and a stochastic component. The filtered...... part of the Kalman filter is used to estimates the current state, based on the model and the measurements. The static and dynamic Kalman filter is compared and all results is demonstrated through simulations....
Azam, Sazuan N. M.
2017-01-01
In this paper, we used the modified quadruple tank system that represents a multi-input-multi-output (MIMO) system as an example to present the realization of a linear discrete-time state space model and to obtain the state estimation using Kalman filter in a methodical mannered. First, an existing dynamics of the system of stochastic differential equations is linearized to produce the deterministic-stochastic linear transfer function. Then the linear transfer function is discretized to produce a linear discrete-time state space model that has a deterministic and a stochastic component. The filtered part of the Kalman filter is used to estimates the current state, based on the model and the measurements. The static and dynamic Kalman filter is compared and all results is demonstrated through simulations.
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.
Dynamic State Estimation and Parameter Calibration of DFIG based on Ensemble Kalman Filter
Energy Technology Data Exchange (ETDEWEB)
Fan, Rui; Huang, Zhenyu; Wang, Shaobu; Diao, Ruisheng; Meng, Da
2015-07-30
With the growing interest in the application of wind energy, doubly fed induction generator (DFIG) plays an essential role in the industry nowadays. To deal with the increasing stochastic variations introduced by intermittent wind resource and responsive loads, dynamic state estimation (DSE) are introduced in any power system associated with DFIGs. However, sometimes this dynamic analysis canould not work because the parameters of DFIGs are not accurate enough. To solve the problem, an ensemble Kalman filter (EnKF) method is proposed for the state estimation and parameter calibration tasks. In this paper, a DFIG is modeled and implemented with the EnKF method. Sensitivity analysis is demonstrated regarding the measurement noise, initial state errors and parameter errors. The results indicate this EnKF method has a robust performance on the state estimation and parameter calibration of DFIGs.
Ait-El-Fquih, Boujemaa; Hoteit, Ibrahim
2015-01-01
Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The Joint-EnKF directly updates the augmented state-parameter vector while the Dual-EnKF employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. In this paper, we reverse the order of the forecast-update steps following the one-step-ahead (OSA) smoothing formulation of the Bayesian filtering problem, based on which we propose a new dual EnKF scheme, the Dual-EnKF$_{\\rm OSA}$. Compared to the Dual-EnKF, this introduces a new update step to the state in a fully consistent Bayesian framework...
Luo, Xiaodong
2014-10-01
The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an observation-space-based strategy, called residual nudging, to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor and, if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In the present study, residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that, under suitable conditions, is able to achieve the objective of residual nudging for data assimilation problems with nonlinear observation operators. The 40-dimensional Lorenz-96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge with nonlinear observation operators, the proposed iterative filter remains stable and leads to reasonable estimation accuracy under various experimental settings.
Zhang, X L; Su, G F; Yuan, H Y; Chen, J G; Huang, Q Y
2014-09-15
Atmospheric dispersion models play an important role in nuclear power plant accident management. A reliable estimation of radioactive material distribution in short range (about 50 km) is in urgent need for population sheltering and evacuation planning. However, the meteorological data and the source term which greatly influence the accuracy of the atmospheric dispersion models are usually poorly known at the early phase of the emergency. In this study, a modified ensemble Kalman filter data assimilation method in conjunction with a Lagrangian puff-model is proposed to simultaneously improve the model prediction and reconstruct the source terms for short range atmospheric dispersion using the off-site environmental monitoring data. Four main uncertainty parameters are considered: source release rate, plume rise height, wind speed and wind direction. Twin experiments show that the method effectively improves the predicted concentration distribution, and the temporal profiles of source release rate and plume rise height are also successfully reconstructed. Moreover, the time lag in the response of ensemble Kalman filter is shortened. The method proposed here can be a useful tool not only in the nuclear power plant accident emergency management but also in other similar situation where hazardous material is released into the atmosphere.
DEFF Research Database (Denmark)
Drews, Martin; Lauritzen, Bent; Madsen, Henrik
2005-01-01
A Kalman filter method is discussed for on-line estimation of radioactive release and atmospheric dispersion from a time series of off-site radiation monitoring data. The method is based on a state space approach, where a stochastic system equation describes the dynamics of the plume model...... parameters, and the observables are linked to the state variables through a static measurement equation. The method is analysed for three simple state space models using experimental data obtained at a nuclear research reactor. Compared to direct measurements of the atmospheric dispersion, the Kalman filter...... estimates are found to agree well with the measured parameters, provided that the radiation measurements are spread out in the cross-wind direction. For less optimal detector placement it proves difficult to distinguish variations in the source term and plume height; yet the Kalman filter yields consistent...
DEFF Research Database (Denmark)
Wang, Yanbo; Tian, Yanjun; Wang, Xiongfei
2014-01-01
State monitoring and analysis of distribution systems has become an urgent issue, and state estimation serves as an important tool to deal with it. In this paper, a Kalman-Filter-based state estimation method for a multi-bus islanded microgrid is presented. First, an overall small signal model wi...
Adaptive UAV attitude estimation employing unscented Kalman Filter, FOAM and low-cost MEMS sensors.
de Marina, Héctor García; Espinosa, Felipe; Santos, Carlos
2012-01-01
Navigation employing low cost MicroElectroMechanical Systems (MEMS) sensors in Unmanned Aerial Vehicles (UAVs) is an uprising challenge. One important part of this navigation is the right estimation of the attitude angles. Most of the existent algorithms handle the sensor readings in a fixed way, leading to large errors in different mission stages like take-off aerobatic maneuvers. This paper presents an adaptive method to estimate these angles using off-the-shelf components. This paper introduces an Attitude Heading Reference System (AHRS) based on the Unscented Kalman Filter (UKF) using the Fast Optimal Attitude Matrix (FOAM) algorithm as the observation model. The performance of the method is assessed through simulations. Moreover, field experiments are presented using a real fixed-wing UAV. The proposed low cost solution, implemented in a microcontroller, shows a satisfactory real time performance.
Estimation of intra-operative brain shift based on constrained Kalman filter.
Shakarami, M; Suratgar, A A; Talebi, H A
2015-03-01
In this study, the problem of estimation of brain shift is addressed by which the accuracy of neuronavigation systems can be improved. To this end, the actual brain shift is considered as a Gaussian random vector with a known mean and an unknown covariance. Then, brain surface imaging is employed together with solutions of linear elastic model and the best estimation is found using constrained Kalman filter (CKF). Moreover, a recursive method (RCKF) is presented, the computational cost of which in the operating room is significantly lower than CKF, because it is not required to compute inverse of any large matrix. Finally, the theory is verified by the simulation results, which show the superiority of the proposed method as compared to one existing method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Robust SLAM using square-root cubature Kalman filter and Huber’ s GM-estimator
Institute of Scientific and Technical Information of China (English)
徐巍军
2016-01-01
Mobile robot systems performing simultaneous localization and mapping ( SLAM) are generally plagued by non-Gaussian noise.To improve both accuracy and robustness under non-Gaussian meas-urement noise, a robust SLAM algorithm is proposed.It is based on the square-root cubature Kal-man filter equipped with a Huber’ s generalized maximum likelihood estimator ( GM-estimator) .In particular, the square-root cubature rule is applied to propagate the robot state vector and covariance matrix in the time update, the measurement update and the new landmark initialization stages of the SLAM.Moreover, gain weight matrices with respect to the measurement residuals are calculated by utilizing Huber’ s technique in the measurement update step.The measurement outliers are sup-pressed by lower Kalman gains as merging into the system.The proposed algorithm can achieve bet-ter performance under the condition of non-Gaussian measurement noise in comparison with benchmark algorithms.The simulation results demonstrate the advantages of the proposed SLAM algorithm.
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
Ait-El-Fquih, Boujemaa; El Gharamti, Mohamad; Hoteit, Ibrahim
2016-08-01
Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The joint EnKF directly updates the augmented state-parameter vector, whereas the dual EnKF empirically employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. To develop a Bayesian consistent dual approach and improve the state-parameter estimates and their consistency, we propose in this paper a one-step-ahead (OSA) smoothing formulation of the state-parameter Bayesian filtering problem from which we derive a new dual-type EnKF, the dual EnKFOSA. Compared with the standard dual EnKF, it imposes a new update step to the state, which is shown to enhance the performance of the dual approach with almost no increase in the computational cost. Numerical experiments are conducted with a two-dimensional (2-D) synthetic groundwater aquifer model to investigate the performance and robustness of the proposed dual EnKFOSA, and to evaluate its results against those of the joint and dual EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, providing further reliable estimates of their uncertainties. Furthermore, it is found to be more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25 % more accurate state and parameter estimations than the joint and dual approaches.
Ait-El-Fquih, Boujemaa
2016-08-12
Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface ground-water models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model\\'s state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The joint EnKF directly updates the augmented state-parameter vector, whereas the dual EnKF empirically employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. To develop a Bayesian consistent dual approach and improve the state-parameter estimates and their consistency, we propose in this paper a one-step-ahead (OSA) smoothing formulation of the state-parameter Bayesian filtering problem from which we derive a new dual-type EnKF, the dual EnKF(OSA). Compared with the standard dual EnKF, it imposes a new update step to the state, which is shown to enhance the performance of the dual approach with almost no increase in the computational cost. Numerical experiments are conducted with a two-dimensional (2-D) synthetic groundwater aquifer model to investigate the performance and robustness of the proposed dual EnKFOSA, and to evaluate its results against those of the joint and dual EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, providing further reliable estimates of their uncertainties. Furthermore, it is found to be more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25% more accurate state and parameter estimations than the joint and dual approaches.
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....
Xie, XianMing; Li, YingHui
2014-06-20
This paper presents an enhanced phase unwrapping algorithm by combining an unscented Kalman filter, an enhanced local phase gradient estimator based on an amended matrix pencil model, and a path-following strategy. This technology is able to accurately unwrap seriously noisy wrapped phase images by applying the unscented Kalman filter to simultaneously perform noise suppression and phase unwrapping along the path from the high-quality region to the low-quality region of the wrapped phase images. Results obtained with synthetic data and real data validate the effectiveness of the proposed method and show improved performance of this new algorithm with respect to some of the most used algorithms.
DEFF Research Database (Denmark)
Drews, Martin; Lauritzen, Bent; Madsen, Henrik
2005-01-01
parameters, and the observables are linked to the state variables through a static measurement equation. The method is analysed for three simple state space models using experimental data obtained at a nuclear research reactor. Compared to direct measurements of the atmospheric dispersion, the Kalman filter...... estimates are found to agree well with the measured parameters, provided that the radiation measurements are spread out in the cross-wind direction. For less optimal detector placement it proves difficult to distinguish variations in the source term and plume height; yet the Kalman filter yields consistent...... scheme are outlined, to account for realistic accident scenarios....
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.
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
Tampere, C.M.J.; Immers, L.H.
2007-01-01
Abstract— This paper presents a traffic state estimation and prediction model based on the cell transmission model (CTM). The nonlinear CTM is transcribed in a closed analytical statespace form for use within a general extended Kalman filtering framework. The state-space CTM switches implicitly betw
Pauwels, V. R. N.; DeLannoy, G. J. M.; Hendricks Franssen, H.-J.; Vereecken, H.
2013-01-01
In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the discrete Kalman filter, and the state variables using the ensemble Kalman filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware ensemble Kalman filter. Furthermore, minimal code modification in existing data assimilation software is needed to implement the method. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.
Directory of Open Access Journals (Sweden)
V. R. N. Pauwels
2013-04-01
Full Text Available In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the Discrete Kalman Filter, and the state variables using the Ensemble Kalman Filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware Ensemble Kalman Filter. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.
National Aeronautics and Space Administration — Estimation of aerodynamic models for the control of damaged aircraft using an innovative differential vortex lattice method tightly coupled with an extended Kalman...
Briseño, Jessica; Herrera, Graciela S.
2010-05-01
Herrera (1998) proposed a method for the optimal design of groundwater quality monitoring networks that involves space and time in a combined form. The method was applied later by Herrera et al (2001) and by Herrera and Pinder (2005). To get the estimates of the contaminant concentration being analyzed, this method uses a space-time ensemble Kalman filter, based on a stochastic flow and transport model. When the method is applied, it is important that the characteristics of the stochastic model be congruent with field data, but, in general, it is laborious to manually achieve a good match between them. For this reason, the main objective of this work is to extend the space-time ensemble Kalman filter proposed by Herrera, to estimate the hydraulic conductivity, together with hydraulic head and contaminant concentration, and its application in a synthetic example. The method has three steps: 1) Given the mean and the semivariogram of the natural logarithm of hydraulic conductivity (ln K), random realizations of this parameter are obtained through two alternatives: Gaussian simulation (SGSim) and Latin Hypercube Sampling method (LHC). 2) The stochastic model is used to produce hydraulic head (h) and contaminant (C) realizations, for each one of the conductivity realizations. With these realization the mean of ln K, h and C are obtained, for h and C, the mean is calculated in space and time, and also the cross covariance matrix h-ln K-C in space and time. The covariance matrix is obtained averaging products of the ln K, h and C realizations on the estimation points and times, and the positions and times with data of the analyzed variables. The estimation points are the positions at which estimates of ln K, h or C are gathered. In an analogous way, the estimation times are those at which estimates of any of the three variables are gathered. 3) Finally the ln K, h and C estimate are obtained using the space-time ensemble Kalman filter. The realization mean for each one
Lorente-Plazas, Raquel; Hacker, Josua P.; Collins, Nancy; Lee, Jared A.
2017-04-01
The impact of assimilating surface observations has been shown in several publications, for improving weather prediction inside of the boundary layer as well as the flow aloft. However, the assimilation of surface observations is often far from optimal due to the presence of both model and observation biases. The sources of these biases can be diverse: an instrumental offset, errors associated to the comparison of point-based observations and grid-cell average, etc. To overcome this challenge, a method was developed using the ensemble Kalman filter. The approach consists on representing each observation bias as a parameter. These bias parameters are added to the forward operator and they extend the state vector. As opposed to the observation bias estimation approaches most common in operational systems (e.g. for satellite radiances), the state vector and parameters are simultaneously updated by applying the Kalman filter equations to the augmented state. The method to estimate and correct the observation bias is evaluated using observing system simulation experiments (OSSEs) with the Weather Research and Forecasting (WRF) model. OSSEs are constructed for the conventional observation network including radiosondes, aircraft observations, atmospheric motion vectors, and surface observations. Three different kinds of biases are added to 2-meter temperature for synthetic METARs. From the simplest to more sophisticated, imposed biases are: (1) a spatially invariant bias, (2) a spatially varying bias proportional to topographic height differences between the model and the observations, and (3) bias that is proportional to the temperature. The target region characterized by complex terrain is the western U.S. on a domain with 30-km grid spacing. Observations are assimilated every 3 hours using an 80-member ensemble during September 2012. Results demonstrate that the approach is able to estimate and correct the bias when it is spatially invariant (experiment 1). More
Sun, Xiaodian; Jin, Li; Xiong, Momiao
2008-01-01
It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.
Extended Kalman Filter with a Fuzzy Method for Accurate Battery Pack State of Charge Estimation
Directory of Open Access Journals (Sweden)
Saeed Sepasi
2015-06-01
Full Text Available As the world moves toward greenhouse gas reduction, there is increasingly active work around Li-ion chemistry-based batteries as an energy source for electric vehicles (EVs, hybrid electric vehicles (HEVs and smart grids. In these applications, the battery management system (BMS requires an accurate online estimation of the state of charge (SOC in a battery pack. This estimation is difficult, especially after substantial battery aging. In order to address this problem, this paper utilizes SOC estimation of Li-ion battery packs using a fuzzy-improved extended Kalman filter (fuzzy-IEKF for Li-ion cells, regardless of their age. The proposed approach introduces a fuzzy method with a new class and associated membership function that determines an approximate initial value applied to SOC estimation. Subsequently, the EKF method is used by considering the single unit model for the battery pack to estimate the SOC for following periods of battery use. This approach uses an adaptive model algorithm to update the model for each single cell in the battery pack. To verify the accuracy of the estimation method, tests are done on a LiFePO4 aged battery pack consisting of 120 cells connected in series with a nominal voltage of 432 V.
Menegaldo, Luciano L
2017-08-01
State-space control of myoelectric devices and real-time visualization of muscle forces in virtual rehabilitation require measuring or estimating muscle dynamic states: neuromuscular activation, tendon force and muscle length. This paper investigates whether regular (KF) and extended Kalman filters (eKF), derived directly from Hill-type muscle mechanics equations, can be used as real-time muscle state estimators for isometric contractions using raw electromyography signals (EMG) as the only available measurement. The estimators' amplitude error, computational cost, filtering lags and smoothness are compared with usual EMG-driven analysis, performed offline, by integrating the nonlinear Hill-type muscle model differential equations (offline simulations-OS). EMG activity of the three triceps surae components (soleus, gastrocnemius medialis and gastrocnemius lateralis), in three torque levels, was collected for ten subjects. The actualization interval (AI) between two updates of the KF and eKF was also varied. The results show that computational costs are significantly reduced (70x for KF and 17[Formula: see text] for eKF). The filtering lags presented sharp linear relationships with the AI (0-300 ms), depending on the state and activation level. Under maximum excitation, amplitude errors varied in the range 10-24% for activation, 5-8% for tendon force and 1.4-1.8% for muscle length, reducing linearly with the excitation level. Smoothness, measured by the ratio between the average standard variations of KF/eKF and OS estimations, was greatly reduced for activation but converged exponentially to 1 for the other states by increasing AI. Compared to regular KF, extended KF does not seem to improve estimation accuracy significantly. Depending on the particular application requirements, the most appropriate KF actualization interval can be selected.
El Gharamti, Mohamad
2014-02-01
The accuracy of groundwater flow and transport model predictions highly depends on our knowledge of subsurface physical parameters. Assimilation of contaminant concentration data from shallow dug wells could help improving model behavior, eventually resulting in better forecasts. In this paper, we propose a joint state-parameter estimation scheme which efficiently integrates a low-rank extended Kalman filtering technique, namely the Singular Evolutive Extended Kalman (SEEK) filter, with the prominent complex-step method (CSM). The SEEK filter avoids the prohibitive computational burden of the Extended Kalman filter by updating the forecast along the directions of error growth only, called filter correction directions. CSM is used within the SEEK filter to efficiently compute model derivatives with respect to the state and parameters along the filter correction directions. CSM is derived using complex Taylor expansion and is second order accurate. It is proven to guarantee accurate gradient computations with zero numerical round-off errors, but requires complexifying the numerical code. We perform twin-experiments to test the performance of the CSM-based SEEK for estimating the state and parameters of a subsurface contaminant transport model. We compare the efficiency and the accuracy of the proposed scheme with two standard finite difference-based SEEK filters as well as with the ensemble Kalman filter (EnKF). Assimilation results suggest that the use of the CSM in the context of the SEEK filter may provide up to 80% more accurate solutions when compared to standard finite difference schemes and is competitive with the EnKF, even providing more accurate results in certain situations. We analyze the results based on two different observation strategies. We also discuss the complexification of the numerical code and show that this could be efficiently implemented in the context of subsurface flow models. © 2013 Elsevier B.V.
Directory of Open Access Journals (Sweden)
Baker Syed
2011-01-01
Full Text Available Abstract In systems biology, experimentally measured parameters are not always available, necessitating the use of computationally based parameter estimation. In order to rely on estimated parameters, it is critical to first determine which parameters can be estimated for a given model and measurement set. This is done with parameter identifiability analysis. A kinetic model of the sucrose accumulation in the sugar cane culm tissue developed by Rohwer et al. was taken as a test case model. What differentiates this approach is the integration of an orthogonal-based local identifiability method into the unscented Kalman filter (UKF, rather than using the more common observability-based method which has inherent limitations. It also introduces a variable step size based on the system uncertainty of the UKF during the sensitivity calculation. This method identified 10 out of 12 parameters as identifiable. These ten parameters were estimated using the UKF, which was run 97 times. Throughout the repetitions the UKF proved to be more consistent than the estimation algorithms used for comparison.
Baker, Syed Murtuza; Poskar, C Hart; Junker, Björn H
2011-10-11
In systems biology, experimentally measured parameters are not always available, necessitating the use of computationally based parameter estimation. In order to rely on estimated parameters, it is critical to first determine which parameters can be estimated for a given model and measurement set. This is done with parameter identifiability analysis. A kinetic model of the sucrose accumulation in the sugar cane culm tissue developed by Rohwer et al. was taken as a test case model. What differentiates this approach is the integration of an orthogonal-based local identifiability method into the unscented Kalman filter (UKF), rather than using the more common observability-based method which has inherent limitations. It also introduces a variable step size based on the system uncertainty of the UKF during the sensitivity calculation. This method identified 10 out of 12 parameters as identifiable. These ten parameters were estimated using the UKF, which was run 97 times. Throughout the repetitions the UKF proved to be more consistent than the estimation algorithms used for comparison.
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...
Directory of Open Access Journals (Sweden)
Leandro Vargas-Meléndez
2016-08-01
Full Text Available This article presents a novel estimator based on sensor fusion, which combines the Neural Network (NN with a Kalman filter in order to estimate the vehicle roll angle. The NN estimates a “pseudo-roll angle” through variables that are easily measured from Inertial Measurement Unit (IMU sensors. An IMU is a device that is commonly used for vehicle motion detection, and its cost has decreased during recent years. The pseudo-roll angle is introduced in the Kalman filter in order to filter noise and minimize the variance of the norm and maximum errors’ estimation. The NN has been trained for J-turn maneuvers, double lane change maneuvers and lane change maneuvers at different speeds and road friction coefficients. The proposed method takes into account the vehicle non-linearities, thus yielding good roll angle estimation. Finally, the proposed estimator has been compared with one that uses the suspension deflections to obtain the pseudo-roll angle. Experimental results show the effectiveness of the proposed NN and Kalman filter-based estimator.
Vargas-Meléndez, Leandro; Boada, Beatriz L; Boada, María Jesús L; Gauchía, Antonio; Díaz, Vicente
2016-08-31
This article presents a novel estimator based on sensor fusion, which combines the Neural Network (NN) with a Kalman filter in order to estimate the vehicle roll angle. The NN estimates a "pseudo-roll angle" through variables that are easily measured from Inertial Measurement Unit (IMU) sensors. An IMU is a device that is commonly used for vehicle motion detection, and its cost has decreased during recent years. The pseudo-roll angle is introduced in the Kalman filter in order to filter noise and minimize the variance of the norm and maximum errors' estimation. The NN has been trained for J-turn maneuvers, double lane change maneuvers and lane change maneuvers at different speeds and road friction coefficients. The proposed method takes into account the vehicle non-linearities, thus yielding good roll angle estimation. Finally, the proposed estimator has been compared with one that uses the suspension deflections to obtain the pseudo-roll angle. Experimental results show the effectiveness of the proposed NN and Kalman filter-based estimator.
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.
Dai, Haifeng; Zhu, Letao; Zhu, Jiangong; Wei, Xuezhe; Sun, Zechang
2015-10-01
The accurate monitoring of battery cell temperature is indispensible to the design of battery thermal management system. To obtain the internal temperature of a battery cell online, an adaptive temperature estimation method based on Kalman filtering and an equivalent time-variant electrical network thermal (EENT) model is proposed. The EENT model uses electrical components to simulate the battery thermodynamics, and the model parameters are obtained with a least square algorithm. With a discrete state-space description of the EENT model, a Kalman filtering (KF) based internal temperature estimator is developed. Moreover, considering the possible time-varying external heat exchange coefficient, a joint Kalman filtering (JKF) based estimator is designed to simultaneously estimate the internal temperature and the external thermal resistance. Several experiments using the hard-cased LiFePO4 cells with embedded temperature sensors have been conducted to validate the proposed method. Validation results show that, the EENT model expresses the battery thermodynamics well, the KF based temperature estimator tracks the real central temperature accurately even with a poor initialization, and the JKF based estimator can simultaneously estimate both central temperature and external thermal resistance precisely. The maximum estimation errors of the KF- and JKF-based estimators are less than 1.8 °C and 1 °C respectively.
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.
Meng, S.; Xie, X.
2014-12-01
Hydrological model performance is usually not as acceptable as expected due to limited measurements and imperfect parameterization which is attributable to the uncertainties from model parameters and model structures. In applications, a general assumption is hold that model parameters are constant in a stationary condition during the simulation period, and the parameters are generally prescribed though calibration with observed data. In reality, but the model parameters related to the physical or conceptual characteristics of a catchment will travel in nonstationary conditions in response to climate transition and land use alteration. The travels or changes of parameters are especially evident for long-term hydrological simulations. Therefore, the assumption of using constant parameters under nonstationary condition is inappropriate, and it will deliver errors from the parameters to the outputs during the simulation and prediction. Even though a few of studies have acknowledged the parameter travel or change, little attention has been paid on the estimation of changing parameters. In this study, we employ an ensemble Kalman filter (EnKF) based method to trace parameter changes in real time. Through synthetic experiments, the capability of the EnKF-based is demonstrated by assimilating runoff observations into a rainfall-runoff model, i.e., the Xinanjing Model. In addition to the stationary condition, three typical nonstationary conditions are considered, i.e., the leap, linear and Ω-shaped transitions. To examine the robustness of the method, different errors from rainfall input, modelling and observations are investigated. The shuffled complex evolution (SCE-UA) algorithm is applied under the same conditions to make a comparison. The results show that the EnKF-based method is capable of capturing the general pattern of the parameter travels even for high levels of uncertainties. It provides better estimates than the SCE-UA method does by taking advantages of real
Zhang, Hongjuan; Hendricks-Franssen, Harrie-Jan; Han, Xujun; Vrugt, Jasper A.; Vereecken, Harry
2016-04-01
Land surface models (LSMs) resolve the water and energy balance with different parameters and state variables. Many of the parameters of these models cannot be measured directly in the field, and require calibration against flux and soil moisture data. Two LSMs are used in our work: Variable Infiltration Capacity Hydrologic Model (VIC) and the Community Land Model (CLM). Temporal variations in soil moisture content at 5, 20 and 50 cm depth in the Rollesbroich experimental watershed in Germany are simulated in both LSMs. Data assimilation (DA) provides a good way to jointly estimate soil moisture content and soil properties of the resolved soil domain. Four DA methods combined with the two LSMs are used in our work: the Ensemble Kalman Filter (EnKF) using state augmentation or dual estimation, the Residual Resampling Particle Filter (RRPF) and Markov chain Monte Carlo Particle Filter (MCMCPF). These four DA methods are tuned and calibrated for a five month period, and subsequently evaluated for another five month period. Performances of the two LSMs and the four DA methods are compared. Our results show that all DA methods improve the estimation of soil moisture content of the VIC and CLM models, especially if the soil hydraulic properties (VIC), the maximum baseflow velocity (VIC) and/or soil texture (CLM) are jointly estimated with soil moisture content. The augmentation and dual estimation methods performed slightly better than RRPF and MCMCPF in the evaluation period. The differences in simulated soil moisture content between CLM and VIC were larger than variations among the DA methods. The CLM performed better than the VIC model. The strong underestimation of soil moisture content in the third layer of the VIC model is likely related to an inadequate parameterization of groundwater drainage.
Pose and Motion Estimation Using Dual Quaternion-Based Extended Kalman Filtering
Energy Technology Data Exchange (ETDEWEB)
Goddard, J.S.; Abidi, M.A.
1998-06-01
A solution to the remote three-dimensional (3-D) measurement problem is presented for a dynamic system given a sequence of two-dimensional (2-D) intensity images of a moving object. The 3-D transformation is modeled as a nonlinear stochastic system with the state estimate providing the six-degree-of-freedom motion and position values as well as structure. The stochastic model uses the iterated extended Kalman filter (IEKF) as a nonlinear estimator and a screw representation of the 3-D transformation based on dual quaternions. Dual quaternions, whose elements are dual numbers, provide a means to represent both rotation and translation in a unified notation. Linear object features, represented as dual vectors, are transformed using the dual quaternion transformation and are then projected to linear features in the image plane. The method has been implemented and tested with both simulated and actual experimental data. Simulation results are provided, along with comparisons to a point-based IEKF method using rotation and translation, to show the relative advantages of this method. Experimental results from testing using a camera mounted on the end effector of a robot arm are also given.
Mazzà, Claudia; Donati, Marco; McCamley, John; Picerno, Pietro; Cappozzo, Aurelio
2012-01-01
The aim of this study was the fine tuning of a Kalman filter with the intent to provide optimal estimates of lower trunk orientation in the frontal and sagittal planes during treadmill walking at different speeds using measured linear acceleration and angular velocity components represented in a local system of reference. Data were simultaneously collected using both an inertial measurement unit (IMU) and a stereophotogrammetric system from three healthy subjects walking on a treadmill at natural, slow and fast speeds. These data were used to estimate the parameters of the Kalman filter that minimized the difference between the trunk orientations provided by the filter and those obtained through stereophotogrammetry. The optimized parameters were then used to process the data collected from a further 15 healthy subjects of both genders and different anthropometry performing the same walking tasks with the aim of determining the robustness of the filter set up. The filter proved to be very robust. The root mean square values of the differences between the angles estimated through the IMU and through stereophotogrammetry were lower than 1.0° and the correlation coefficients between the corresponding curves were greater than 0.91. The proposed filter design can be used to reliably estimate trunk lateral and frontal bending during walking from inertial sensor data. Further studies are needed to determine the filter parameters that are most suitable for other motor tasks.
An extended Kalman-filter for regional scale inverse emission estimation
Directory of Open Access Journals (Sweden)
D. Brunner
2012-04-01
Full Text Available A Kalman-filter based inverse emission estimation method for long-lived trace gases is presented for use in conjunction with a Lagrangian particle dispersion model like FLEXPART. The sequential nature of the approach allows tracing slow seasonal and interannual changes rather than estimating a single period-mean emission field. Other important features include the estimation of a slowly varying concentration background at each measurement station, the possibility to constrain the solution to non-negative emissions, the quantification of uncertainties, the consideration of temporal correlations in the residuals, and the applicability to potentially large inversion problems. The method is first demonstrated for a set of synthetic observations created from a prescribed emission field with different levels of (correlated noise, which closely mimics true observations. It is then applied to real observations of the three halocarbons HFC-125, HFC-152a and HCFC-141b at the remote research stations Jungfraujoch and Mace Head for the quantification of emissions in Western European countries from 2006 to 2010. Estimated HFC-125 emissions are mostly consistent with national totals reported to UNFCCC in the framework of the Kyoto Protocol and show a generally increasing trend over the considered period. Results for HFC-152a are much more variable with estimated emissions being both higher and lower than reported emissions in different countries. The highest emissions of the order of 700–800 Mg yr^{−1} are estimated for Italy, which so far does not report HFC-152a emissions. Emissions of HCFC-141b show a continuing strong decrease as expected due to its controls in developed countries under the Montreal Protocol. Emissions from France, however, were still rather large, in the range of 700–1000 Mg yr^{−1} in the years 2006 and 2007 but strongly declined thereafter.
An extended Kalman-filter for regional scale inverse emission estimation
Directory of Open Access Journals (Sweden)
D. Brunner
2011-10-01
Full Text Available A Kalman-filter based inverse emission estimation method for long-lived trace gases is presented for use in conjunction with a Lagrangian particle dispersion model like FLEXPART. The sequential nature of the approach allows tracing slow seasonal and interannual changes rather than estimating a single period-mean emission field. Other important features include the estimation of a slowly varying concentration background at each measurement station, the possibility to constrain the solution to non-negative emissions, the quantification of uncertainties, the consideration of temporal correlations in the residuals, and the applicability to potentially large inversion problems. The method is first demonstrated for a set of synthetic observations created from a prescribed emission field with different levels of (correlated noise, which closely mimics true observations. It is then applied to real observations of the three halocarbons HFC-125, HFC-152a and HCFC-141b at the remote research stations Jungfraujoch and Mace Head for the quantification of emissions in Western European countries from 2006 to 2010. Estimated HFC-125 emissions are mostly consistent with national totals reported to the Kyoto protocol and show a generally increasing trend over the considered period. Results for HFC-152a are much more variable with estimated emissions being both higher and lower in different countries. The highest emissions of the order of 1000 Mg yr^{−1} are estimated for Italy which so far does not report HFC-152a emissions. Emissions of HCFC-141b show a continuing strong decrease as expected due to its ban under the Montreal Protocol. Emissions from France, however, were still rather large (near 1000 Mg yr^{−1} in the years 2006 and 2007 but strongly declined thereafter.
An extended Kalman-filter for regional scale inverse emission estimation
Brunner, D.; Henne, S.; Keller, C. A.; Reimann, S.; Vollmer, M. K.; O'Doherty, S.; Maione, M.
2012-04-01
A Kalman-filter based inverse emission estimation method for long-lived trace gases is presented for use in conjunction with a Lagrangian particle dispersion model like FLEXPART. The sequential nature of the approach allows tracing slow seasonal and interannual changes rather than estimating a single period-mean emission field. Other important features include the estimation of a slowly varying concentration background at each measurement station, the possibility to constrain the solution to non-negative emissions, the quantification of uncertainties, the consideration of temporal correlations in the residuals, and the applicability to potentially large inversion problems. The method is first demonstrated for a set of synthetic observations created from a prescribed emission field with different levels of (correlated) noise, which closely mimics true observations. It is then applied to real observations of the three halocarbons HFC-125, HFC-152a and HCFC-141b at the remote research stations Jungfraujoch and Mace Head for the quantification of emissions in Western European countries from 2006 to 2010. Estimated HFC-125 emissions are mostly consistent with national totals reported to UNFCCC in the framework of the Kyoto Protocol and show a generally increasing trend over the considered period. Results for HFC-152a are much more variable with estimated emissions being both higher and lower than reported emissions in different countries. The highest emissions of the order of 700-800 Mg yr-1 are estimated for Italy, which so far does not report HFC-152a emissions. Emissions of HCFC-141b show a continuing strong decrease as expected due to its controls in developed countries under the Montreal Protocol. Emissions from France, however, were still rather large, in the range of 700-1000 Mg yr-1 in the years 2006 and 2007 but strongly declined thereafter.
Energy Technology Data Exchange (ETDEWEB)
Harlim, John, E-mail: jharlim@psu.edu [Department of Mathematics and Department of Meteorology, the Pennsylvania State University, University Park, PA 16802, Unites States (United States); Mahdi, Adam, E-mail: amahdi@ncsu.edu [Department of Mathematics, North Carolina State University, Raleigh, NC 27695 (United States); Majda, Andrew J., E-mail: jonjon@cims.nyu.edu [Department of Mathematics and Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (United States)
2014-01-15
A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.
Bersvendsen, Jorn; Orderud, Fredrik; Massey, Richard John; Fosså, Kristian; Gerard, Olivier; Urheim, Stig; Samset, Eigil
2016-01-01
As the right ventricle's (RV) role in cardiovascular diseases is being more widely recognized, interest in RV imaging, function and quantification is growing. However, there are currently few RV quantification methods for 3D echocardiography presented in the literature or commercially available. In this paper we propose an automated RV segmentation method for 3D echocardiographic images. We represent the RV geometry by a Doo-Sabin subdivision surface with deformation modes derived from a training set of manual segmentations. The segmentation is then represented as a state estimation problem and solved with an extended Kalman filter by combining the RV geometry with a motion model and edge detection. Validation was performed by comparing surface-surface distances, volumes and ejection fractions in 17 patients with aortic insufficiency between the proposed method, magnetic resonance imaging (MRI), and a manual echocardiographic reference. The algorithm was efficient with a mean computation time of 2.0 s. The mean absolute distances between the proposed and manual segmentations were 3.6 ± 0.7 mm. Good agreements of end diastolic volume, end systolic volume and ejection fraction with respect to MRI ( -26±24 mL , -16±26 mL and 0 ± 10%, respectively) and a manual echocardiographic reference (7 ± 30 mL, 13 ± 17 mL and -5±7% , respectively) were observed.
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...
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
Podladchikova, T.; Shprits, Y.; Kellerman, A. C.
2015-12-01
The Kalman filter technique combines the strengths of new physical models of the Earth's radiation belts with long-term spacecraft observations of electron fluxes and therefore provide an extremely useful method for the analysis of the state and evolution of the electron radiation belts. However, to get the reliable data assimilation output, the Kalman filter application is confronted with a set of fundamental problems. E.g., satellite measurements are usually limited to a single location in space, which confines the reconstruction of the global evolution of the radiation environment. The uncertainties arise from the imperfect description of the process dynamics and the presence of observation errors, which may cause the failure of data assimilation solution. The development of adaptive Kalman filter that combines the Van Allen Probes data and 3-D VERB code, its accurate customizations in the reconstruction of model describing the phase space density (PSD) evolution, extension of the possibilities to use measurement information, and the model adjustment by developing the identification techniques of model and measurement errors allowed us to reveal hidden and implicit regularities of the PSD dynamics and obtain quantitative and qualitative estimates of radial, energy and pitch angle diffusion characteristics from satellite observations. In this study we propose an approach to estimate radial, energy and pitch angle diffusion rates, as well as the direction of their propagation.
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.
Yao, Yu; Cheng, Kai; Zhou, Zhi-Jie; Zhang, Bang-Cheng; Dong, Chao; Zheng, Sen
2015-11-01
A tracked vehicle has been widely used in exploring unknown environments and military fields. In current methods for suiting soil conditions, soil parameters need to be given and the traction performance cannot always be satisfied on soft soil. To solve the problem, it is essential to estimate track-soil parameters in real-time. Therefore, a detailed mathematical model is proposed for the first time. Furthermore, a novel algorithm which is composed of Kalman filter (KF) and improved strong tracking filter (STF) is developed for online track-soil estimation and named as KF-ISTF. By this method, the KF is used to estimate slip parameters, and the ISTF is used to estimate motion states. Then the key soil parameters can be estimated by using a suitable soil model. The experimental results show that equipped with the estimation algorithm, the proposed model can be used to estimate the track-soil parameters, and make the traction performance satisfied with soil conditions.
Belkhatir, Zehor
2015-11-23
This paper discusses the estimation of distributed Cerebral Blood Flow (CBF) using spatiotemporal traveling wave model. We consider a damped wave partial differential equation that describes a physiological relationship between the blood mass density and the CBF. The spatiotemporal model is reduced to a finite dimensional system using a cubic b-spline continuous Galerkin method. A Kalman Filter with Unknown Inputs without Direct Feedthrough (KF-UI-WDF) is applied on the obtained reduced differential model to estimate the source term which is the CBF scaled by a factor. Numerical results showing the performances of the adopted estimator are provided.
Estimating Value at Risk with the Generalized Kalman Filter%基于Generalized Kalman Filter的VaR估计
Institute of Scientific and Technical Information of China (English)
赵利锋; 张崇岐
2009-01-01
在应用Kalman Filter方法估计时变风险β系数的基础上,引入Generalized Kalman Filter方法来估计时变卢系数,再通过Sharp对角线模型计算投资组合的VaR,并运用Backtesting检验判断两方法估计VaR的精确度.
Silva, Felipe O; Hemerly, Elder M; Leite Filho, Waldemar C
2017-02-23
This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the full SINS error model, the unobservable modes of the system are determined, and the SSAC error states (except the velocity errors) are proven to be individually unobservable. The estimability of the system is determined through the examination of the major diagonal terms of the covariance matrix and their eigenvalues/eigenvectors. Filter order reduction based on observability analysis is shown to be inadequate, and several misconceptions regarding SSAC observability and estimability deficiencies are removed. As the main contributions of this paper, we demonstrate that, except for the position errors, all error states can be minimally estimated in the SSAC problem and, hence, should not be removed from the filter. Corroborating the conclusions of the first part of this study, a 12-state Kalman filter is found to be the optimal error state selection for SSAC purposes. Results from simulated and experimental tests support the outlined conclusions.
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...
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.
COVARIANCE CORRECTION FOR ESTIMATING GROUNDWATER LEVEL USING DETERMINISTIC ENSEMBLE KALMAN FILTER
Directory of Open Access Journals (Sweden)
J. Behmanesh
2015-01-01
Full Text Available The main problem in developing a groundwater model is to determine model parameters, particularly hydrogeologic coefficients, in a precise way. In this research, Deterministic Ensemble Kalman Filter (DEnKF is described as a modern sequential method for data assimilation and a localization scheme within the framework of DEnKF is applied. Najafabad aquifer (in Iran with area of 1150 km2, is modeled in the time window of Oct. 2000 to Sept. 2007 to obtain water table level data when its values of hydrogeologic coefficients calibrated and verified. DEnKF assimilated 45 observations of true run into the model with 2, 5, and 10 times of calibrated values of hydraulic conductivity and specific yield. This filter has been run both with and without use of localization. Results show easily-implemented localized DEnKF is favorably robust in groundwater flow modeling.
Estimation of Launch and Impact Points of a Flight Trajectory using U-D Kalman Filter/Smoother
Directory of Open Access Journals (Sweden)
V.P.S. Naidu
2006-10-01
Full Text Available The launch and impact points of a flight trajectory are estimated using U-D Kalman filterand Rauch-Tung-Striebel (R-T-S smoother. Algorithms are implemented in PC MATLAB andvalidated using simulated data. The filter performance is evaluated in terms of state error,innovation sequence, and autocorrelation of residuals along with their theoretical bounds. TheR-T-S smoother was found to generate accurate state estimates, which led to better launch pointestimation. Launch and impact point prediction from real data of a guided target in ballistic modeis also evaluated.
Directory of Open Access Journals (Sweden)
T. Viskari
2012-07-01
Full Text Available Extended Kalman Filter (EKF is used to estimate particle size distributions from observations. The focus here is on the practical application of EKF to simultaneously merge information from different types of experimental instruments. Every 10 min, the prior state estimate is updated with size-segregating measurements from Differential Mobility Particle Sizer (DMPS and Aerodynamic Particle Sizer (APS as well as integrating measurements from a nephelometer. Error covariances are approximate in our EKF implementation. The observation operator assumes a constant particle density and refractive index. The state estimates are compared to particle size distributions that are a composite of DMPS and APS measurements. The impact of each instrument on the size distribution estimate is studied. Kalman Filtering of DMPS and APS yielded a temporally consistent state estimate. This state estimate is continuous over the overlapping size range of DMPS and APS. Inclusion of the integrating measurements further reduces the effect of measurement noise. Even with the present approximations, EKF is shown to be a very promising method to estimate particle size distribution with observations from different types of instruments.
Institute of Scientific and Technical Information of China (English)
LI JunWei; LIN BoLiang; SUN ZhiHui; GENG XueFei
2009-01-01
On the basis of measurable time series of mainline and ramp flows from traffic counts and the assumption of travel time distributions, this research presents a dynamic system model and its on-line estimation algorithm for recursive estimation of Ume-varying origin-destination (OD) matrices in expressway corridors. The proposed model employs a macro-traffic flow model to estimate travel times of OD flows and uses parameters of the traffic model as state variables, which are added to the constrained function of the system. To improve the model efficiency, we revise the travel time distribution based on the feature of normal distribution. The research employs a newly developed filtering technique, called unscented Kalman filter. The proposed model is evaluated with simulation experiments.Numerical analyses with respect to the sensitivity of the selection of initial parameters on the estimation results indicate that the proposed model is sufficiently reasonable and stable for real-world applications.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
On the basis of measurable time series of mainline and ramp flows from traffic counts and the assumption of travel time distributions, this research presents a dynamic system model and its on-line estimation algorithm for recursive estimation of time-varying origin-destination (OD) matrices in expressway corridors. The proposed model employs a macro-traffic flow model to estimate travel times of OD flows and uses parameters of the traffic model as state variables, which are added to the constrained function of the system. To improve the model efficiency, we revise the travel time distribution based on the feature of normal distribution. The research employs a newly developed filtering technique, called unscented Kalman filter. The proposed model is evaluated with simulation experiments. Numerical analyses with respect to the sensitivity of the selection of initial parameters on the estimation results indicate that the proposed model is sufficiently reasonable and stable for real-world appli-cations.
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
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.
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
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.
El Gharamti, Mohamad
2015-11-26
The ensemble Kalman filter (EnKF) recursively integrates field data into simulation models to obtain a better characterization of the model’s state and parameters. These are generally estimated following a state-parameters joint augmentation strategy. In this study, we introduce a new smoothing-based joint EnKF scheme, in which we introduce a one-step-ahead smoothing of the state before updating the parameters. Numerical experiments are performed with a two-dimensional synthetic subsurface contaminant transport model. The improved performance of the proposed joint EnKF scheme compared to the standard joint EnKF compensates for the modest increase in the computational cost.
Cheng, Xuemin; Hao, Qun; Xie, Mengdi
2016-04-07
Video stabilization is an important technology for removing undesired motion in videos. This paper presents a comprehensive motion estimation method for electronic image stabilization techniques, integrating the speeded up robust features (SURF) algorithm, modified random sample consensus (RANSAC), and the Kalman filter, and also taking camera scaling and conventional camera translation and rotation into full consideration. Using SURF in sub-pixel space, feature points were located and then matched. The false matched points were removed by modified RANSAC. Global motion was estimated by using the feature points and modified cascading parameters, which reduced the accumulated errors in a series of frames and improved the peak signal to noise ratio (PSNR) by 8.2 dB. A specific Kalman filter model was established by considering the movement and scaling of scenes. Finally, video stabilization was achieved with filtered motion parameters using the modified adjacent frame compensation. The experimental results proved that the target images were stabilized even when the vibrating amplitudes of the video become increasingly large.
Battery State-of-Charge and Parameter Estimation Algorithm Based on Kalman Filter
DEFF Research Database (Denmark)
Dragicevic, Tomislav; Sucic, Stjepan; Guerrero, Josep M.
2013-01-01
Electrochemical battery is the most widely used energy storage technology, finding its application in various devices ranging from low power consumer electronics to utility back-up power. All types of batteries show highly non-linear behaviour in terms of dependence of internal parameters...... on operating conditions, momentary replenishment and a number of past charge/discharge cycles. A good indicator for the quality of overall customer service in any battery based application is the availability and reliability of these informations, as they point out important runtime variables...... such as the actual state of charge (SOC) and state of health (SOH). Therefore, a modern battery management systems (BMSs) should incorporate functions that accommodate real time tracking of these nonlinearities. For that purpose, Kalman filter based algorithms emerged as a convenient solution due to their ability...
Directory of Open Access Journals (Sweden)
Hongjie Wu
2013-01-01
Full Text Available State of charge (SOC is a critical factor to guarantee that a battery system is operating in a safe and reliable manner. Many uncertainties and noises, such as fluctuating current, sensor measurement accuracy and bias, temperature effects, calibration errors or even sensor failure, etc. pose a challenge to the accurate estimation of SOC in real applications. This paper adds two contributions to the existing literature. First, the auto regressive exogenous (ARX model is proposed here to simulate the battery nonlinear dynamics. Due to its discrete form and ease of implemention, this straightforward approach could be more suitable for real applications. Second, its order selection principle and parameter identification method is illustrated in detail in this paper. The hybrid pulse power characterization (HPPC cycles are implemented on the 60AH LiFePO4 battery module for the model identification and validation. Based on the proposed ARX model, SOC estimation is pursued using the extended Kalman filter. Evaluation of the adaptability of the battery models and robustness of the SOC estimation algorithm are also verified. The results indicate that the SOC estimation method using the Kalman filter based on the ARX model shows great performance. It increases the model output voltage accuracy, thereby having the potential to be used in real applications, such as EVs and HEVs.
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 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.
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.
Simpson, Elizabeth C.
1989-01-01
Motion estimation is a field of great interest because of its many applications in areas such as robotics and image coding. The optic flow method is one such scheme which, although fairly accurate, is prone to error in the presence of noise. This thesis describes the use of the reduced order model Kalman filter (ROMKF) in reducing errors in displacement estimation due to degradation of the sequence. The implementation of filtering and motion estimation algorithms on the SUN workstation is also discussed. Results from preliminary testing were used to determine the degrees of freedom available for the ROMKF in the SUN software. The tests indicated that increasing the state to the left leads to slight improvement over the minimum state case. Therefore, the software uses the minimum model, with the option of adding states to the left only. The ROMKF was then used in conjunction with a hierarchical pel recursive motion estimation algorithm. Applying the ROMKF to the degraded displacements themselves generally yielded slight improvements in cases with noise degradation and noise plus blur. Filtering the images of the degraded sequence prior to motion estimation was less effective in these cases. Both methods performed badly in the case of blur alone, resulting in increased displacement errors. This is thought to be due in part to filter artifacts. Some improvements were obtained by varying the filter parameters when filtering the displacements directly. This result suggests that further study in varying filter parameters may lead to better results. The results of this thesis indicate that the ROMKF can play a part in reducing motion estimation errors from degraded sequences. However, more work needs to be done before the use of the ROMKF can be a practical solution.
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).
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.
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...
Directory of Open Access Journals (Sweden)
Yasser Diab
2017-07-01
Full Text Available A real-time determination of battery parameters is challenging because batteries are non-linear, time-varying systems. The transient behaviour of lithium-ion batteries is modelled by a Thevenin-equivalent circuit with two time constants characterising activation and concentration polarization. An experimental approach is proposed for directly determining battery parameters as a function of physical quantities. The model’s parameters are a function of the state of charge and of the discharge rate. These can be expressed by regression equations in the model to derive a continuous-discrete extended Kalman estimator of the state of charge and of other parameters. This technique is based on numerical integration of the ordinary differential equations to predict the state of the stochastic dynamic system and the corresponding error covariance matrix. Then a standard correction step of the extended Kalman filter (EKF is applied to increase the accuracy of estimated parameters. Simulations resulting from this proposed estimator model were compared with experimental results under a variety of operating scenarios—analysis of the results demonstrate the accuracy of the estimator for correctly identifying battery parameters.
Phan, Anh Tuan; Ho, Duc Du; Hermann, Gilles; Wira, Patrice
2015-12-01
For power quality issues like reducing harmonic pollution, reactive power and load unbalance, the estimation of the fundamental frequency of a power lines in a fast and precise way is essential. This paper introduces a new state-space model to be used with an extended Kalman filter (EKF) for estimating the frequency of distorted power system signals in real-time. The proposed model takes into account all the characteristics of a general three-phase power system and mainly the unbalance. Therefore, the symmetrical components of the power system, i.e., their amplitude and phase angle values, can also be deduced at each iteration from the proposed state-space model. The effectiveness of the method has been evaluated. Results and comparisons of online frequency estimation and symmetrical components identification show the efficiency of the proposed method for disturbed and time-varying signals.
Directory of Open Access Journals (Sweden)
Bao Han
2015-01-01
Full Text Available The obstacle motion state estimation is an essential task in intelligent vehicle. The ASCL group has developed such a system that uses a radar and GPS/INS. When running on the road, the acceleration of the vehicle is always changing, so it is hard for constant velocity (CV model and constant acceleration (CA model to describe the motion state of the vehicle. This paper introduced Current Statistical (CS model from military field, which uses the modified Rayleigh distribution to describe acceleration. The adaptive Kalman filter based on CS model was used to estimate the motion state of the target. We conducted simulation experiments and real vehicle tests, and the results showed that the estimation of position, velocity, and acceleration can be precise.
Yu, Qiuli
2001-12-01
Aircraft flight test data are processed by optimal estimation programs to estimate the aircraft state trajectory (3 DOF) and to identify the unknown parameters, including constant biases and scale factor of the measurement instrumentation system. The methods applied in processing aircraft flight test data are the iterative extended Kalman filter/smoother and fixed-point smoother (IEKFSFPS) method and the two-step estimator (TSE) method. The models of an aircraft flight dynamic system and measurement instrumentation system are established. The principles of IEKFSFPS and TSE methods are derived and summarized, and their algorithms are programmed with MATLAB codes. Several numerical experiments of flight data processing and parameter identification are carried out by using IEKFSFPS and TSE algorithm programs. Comparison and discussion of the simulation results with the two methods are made. The TSE+IEKFSFPS combination method is presented and proven to be effective and practical. Figures and tables of the results are presented.
Bonnet, V; Dumas, R; Cappozzo, A; Joukov, V; Daune, G; Kulić, D; Fraisse, P; Andary, S; Venture, G
2016-12-29
This paper presents a method for real-time estimation of the kinematics and kinetics of a human body performing a sagittal symmetric motor task, which would minimize the impact of the stereophotogrammetric soft tissue artefacts (STA). The method is based on a bi-dimensional mechanical model of the locomotor apparatus the state variables of which (joint angles, velocities and accelerations, and the segments lengths and inertial parameters) are estimated by a constrained extended Kalman filter (CEKF) that fuses input information made of both stereophotogrammetric and dynamometric measurement data. Filter gains are made to saturate in order to obtain plausible state variables and the measurement covariance matrix of the filter accounts for the expected STA maximal amplitudes. We hypothesised that the ensemble of constraints and input redundant information would allow the method to attenuate the STA propagation to the end results. The method was evaluated in ten human subjects performing a squat exercise. The CEKF estimated and measured skin marker trajectories exhibited a RMS difference lower than 4mm, thus in the range of STAs. The RMS differences between the measured ground reaction force and moment and those estimated using the proposed method (9N and 10Nm) were much lower than obtained using a classical inverse dynamics approach (22N and 30Nm). From the latter results it may be inferred that the presented method allows for a significant improvement of the accuracy with which kinematic variables and relevant time derivatives, model parameters and, therefore, intersegmental moments are estimated.
Directory of Open Access Journals (Sweden)
Xin Li
2016-06-01
Full Text Available The problem of heading drift error using only low cost Micro-Electro-Mechanical (MEMS Inertial-Measurement-Unit (IMU has not been well solved. In this paper, a heading estimation method with real-time compensation based on Kalman filter has been proposed, abbreviated as KHD. For the KHD method, a unified heading error model is established for various predictable errors in magnetic compass for pedestrian navigation, and an effective method for solving the model parameters is proposed in the indoor environment with regular structure. In addition, error model parameters are solved by Kalman filtering algorithm with building geometry information in order to achieve real-time heading compensation. The experimental results show that the KHD method can not only effectively correct the original heading information, but also effectively inhibit the accumulation effect of positioning errors. The performance observed in a field experiment performed on the fourth floor of the School of Environmental Science and Spatial Informatics (SESSI building on the China University of Mining and Technology (CUMT campus confirms that apply KHD method to PDR(Pedestrian Dead Reckoning algorithm can reliably achieve meter-level positioning using a low cost MEMS IMU only.
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.
Galante, Joseph M.; Van Eepoel, John; D'Souza, Chris; Patrick, Bryan
2016-01-01
The Raven ISS Hosted Payload will feature several pose measurement sensors on a pan/tilt gimbal which will be used to autonomously track resupply vehicles as they approach and depart the International Space Station. This paper discusses the derivation of a Relative Navigation Filter (RNF) to fuse measurements from the different pose measurement sensors to produce relative position and attitude estimates. The RNF relies on relative translation and orientation kinematics and careful pose sensor modeling to eliminate dependence on orbital position information and associated orbital dynamics models. The filter state is augmented with sensor biases to provide a mechanism for the filter to estimate and mitigate the offset between the measurements from different pose sensors
Bauser, H. H.; Jaumann, S.; Roth, K.
2015-12-01
The Ensemble Kalman Filter (EnKF) is a widely used data assimilation method in soil hydrology to estimate states and parameters, incorporating uncertainties in measurements and all model components.Of these components not only states and parameters, but also the representation of small scale heterogeneities of different soil layers suffers from large uncertainties. This is particularly severe when measuring soil water content, which reflects the soil's local texture and is typically discontinuous across heterogeneity boundaries. To address this challenge we enhance the EnKF to simultaneously also estimate a Miller scaling field for each soil layer.The enhanced EnKF is tested with a one-dimensional water content data set based on time domain reflectometry (TDR) measurements and leads to an improved consistency of model and measurements.
Energy Technology Data Exchange (ETDEWEB)
Kang, Chang Hyun; Bae, Ji Hwan; Kang, Bong Soo [Hannam University, Daejeon (Korea, Republic of)
2015-04-15
This paper presents the design concept of an intrinsic continuum robot for safe man-machine interface and characteristic behaviors of its end-effector based on real experiments. Since pneumatic artificial muscles having similar antagonistic actuation to human muscles are used for main backbones of the proposed robot as well as in the role of the actuating devices, variable stiffness of robotic joints can be available in the actual environment. In order to solve the inherent shortcoming of an intrinsic continuum robot due to bending motion of the backbone materials, a Kalman filter scheme based on a triaxial accelerometer and a triaxial gyroscope was proposed to conduct an attitude estimation of the end-effector of the robot. The experimental results verified that the proposed method was effective in estimating the attitude of the end-effector of the intrinsic continuum robot.
Xiong, Binyu; Zhao, Jiyun; Wei, Zhongbao; Skyllas-Kazacos, Maria
2014-09-01
State of charge (SOC) estimation is a key issue for battery management since an accurate estimation method can ensure safe operation and prevent the over-charge/discharge of a battery. Traditionally, open circuit voltage (OCV) method is utilized to estimate the stack SOC and one open flow cell is needed in each battery stack [1,2]. In this paper, an alternative method, extended Kalman filter (EKF) method, is proposed for SOC estimation for VRBs. By measuring the stack terminal voltages and applied currents, SOC can be predicted with a state estimator instead of an additional open circuit flow cell. To implement EKF estimator, an electrical model is required for battery analysis. A thermal-dependent electrical circuit model is proposed to describe the charge/discharge characteristics of the VRB. Two scenarios are tested for the robustness of the EKF. For the lab testing scenarios, the filtered stack voltage tracks the experimental data despite the model errors. For the online operation, the simulated temperature rise is observed and the maximum SOC error is within 5.5%. It is concluded that EKF method is capable of accurately predicting SOC using stack terminal voltages and applied currents in the absence of an open flow cell for OCV measurement.
Gharamti, M. E.
2015-05-11
The ensemble Kalman filter (EnKF) is a popular method for state-parameters estimation of subsurface flow and transport models based on field measurements. The common filtering procedure is to directly update the state and parameters as one single vector, which is known as the Joint-EnKF. In this study, we follow the one-step-ahead smoothing formulation of the filtering problem, to derive a new joint-based EnKF which involves a smoothing step of the state between two successive analysis steps. The new state-parameters estimation scheme is derived in a consistent Bayesian filtering framework and results in separate update steps for the state and the parameters. This new algorithm bears strong resemblance with the Dual-EnKF, but unlike the latter which first propagates the state with the model then updates it with the new observation, the proposed scheme starts by an update step, followed by a model integration step. We exploit this new formulation of the joint filtering problem and propose an efficient model-integration-free iterative procedure on the update step of the parameters only for further improved performances. Numerical experiments are conducted with a two-dimensional synthetic subsurface transport model simulating the migration of a contaminant plume in a heterogenous aquifer domain. Contaminant concentration data are assimilated to estimate both the contaminant state and the hydraulic conductivity field. Assimilation runs are performed under imperfect modeling conditions and various observational scenarios. Simulation results suggest that the proposed scheme efficiently recovers both the contaminant state and the aquifer conductivity, providing more accurate estimates than the standard Joint and Dual EnKFs in all tested scenarios. Iterating on the update step of the new scheme further enhances the proposed filter’s behavior. In term of computational cost, the new Joint-EnKF is almost equivalent to that of the Dual-EnKF, but requires twice more model
National Aeronautics and Space Administration — This article discusses several aspects of uncertainty represen- tation and management for model-based prognostics method- ologies based on our experience with Kalman...
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.
Feng, Kaiqiang; Li, Jie; Zhang, Xiaoming; Shen, Chong; Bi, Yu; Zheng, Tao; Liu, Jun
2017-09-19
In order to reduce the computational complexity, and improve the pitch/roll estimation accuracy of the low-cost attitude heading reference system (AHRS) under conditions of magnetic-distortion, a novel linear Kalman filter, suitable for nonlinear attitude estimation, is proposed in this paper. The new algorithm is the combination of two-step geometrically-intuitive correction (TGIC) and the Kalman filter. In the proposed algorithm, the sequential two-step geometrically-intuitive correction scheme is used to make the current estimation of pitch/roll immune to magnetic distortion. Meanwhile, the TGIC produces a computed quaternion input for the Kalman filter, which avoids the linearization error of measurement equations and reduces the computational complexity. Several experiments have been carried out to validate the performance of the filter design. The results demonstrate that the mean time consumption and the root mean square error (RMSE) of pitch/roll estimation under magnetic disturbances are reduced by 45.9% and 33.8%, respectively, when compared with a standard filter. In addition, the proposed filter is applicable for attitude estimation under various dynamic conditions.
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, ...
Crestani, E.; Camporese, M.; Salandin, P.
2011-12-01
Hydraulic properties of natural aquifers, such as porosity, hydraulic conductivity, and storativity, exhibit an erratic spatial variability at different scales that is difficult to recognize without expensive in situ sampling campaigns, laboratory analyses, and, when available, spatially distributed pumping tests. Nevertheless, the importance of the heterogeneous structure of natural formations on solute transport is well recognized, being the non-Fickian evolution of contaminant plumes and the relevant dispersive phenomena controlled by the variability of the hydraulic conductivity K at the local scale. Tracer test analyses have been widely adopted to identify the complex distribution of in situ hydraulic properties. In particular, the use of geophysical methods like the borehole Electrical Resistivity Tomography (ERT) have been in rapid increase, due to their potential to accurately describe the spatio-temporal evolution of the injected solute. Under the assumptions that the solute spreads as a passive tracer and with high values of the Peclet number, the plume evolution is controlled by the porosity and the spatial distribution of hydraulic conductivity. Combining the Lagrangian formulation of transport and the ensemble Kalman filter (EnKF) data assimilation technique, the purpose of this study is to infer the spatial distribution of K at the local scale from a sequence of time-lapse concentration imaging. The capabilities of the proposed approach are investigated simulating various assimilation experiments via synthetic tracer tests in a three-dimensional finite domain reproducing a heterogeneous aquifer. In a first scenario, all the available concentration measurements are assimilated and the entire hydraulic conductivity field is updated, while in the remaining scenarios the K values are updated only in a limited number of nodes by assimilating the concentrations in these same nodes, the hydraulic conductivity in the rest of the domain being the result of a
Dong, Guangzhong; Wei, Jingwen; Chen, Zonghai
2016-10-01
To evaluate the continuous and instantaneous load capability of a battery, this paper describes a joint estimator for state-of-charge (SOC) and state-of-function (SOF) of lithium-ion batteries (LIB) based on Kalman filter (KF). The SOC is a widely used index for remain useful capacity left in a battery. The SOF represents the peak power capability of the battery. It can be determined by real-time SOC estimation and terminal voltage prediction, which can be derived from impedance parameters. However, the open-circuit-voltage (OCV) of LiFePO4 is highly nonlinear with SOC, which leads to the difficulties in SOC estimation. To solve these problems, this paper proposed an onboard SOC estimation method. Firstly, a simplified linearized equivalent-circuit-model is developed to simulate the dynamic characteristics of a battery, where the OCV is regarded as a linearized function of SOC. Then, the system states are estimated based on the KF. Besides, the factors that influence peak power capability are analyzed according to statistical data. Finally, the performance of the proposed methodology is demonstrated by experiments conducted on a LiFePO4 LIBs under different operating currents and temperatures. Experimental results indicate that the proposed approach is suitable for battery onboard SOC and SOF estimation.
Directory of Open Access Journals (Sweden)
Ines Baccouche
2017-05-01
Full Text Available Accurate modeling of the nonlinear relationship between the open circuit voltage (OCV and the state of charge (SOC is required for adaptive SOC estimation during the lithium-ion (Li-ion battery operation. Online SOC estimation should meet several constraints, such as the computational cost, the number of parameters, as well as the accuracy of the model. In this paper, these challenges are considered by proposing an improved simplified and accurate OCV model of a nickel manganese cobalt (NMC Li-ion battery, based on an empirical analytical characterization approach. In fact, composed of double exponential and simple quadratic functions containing only five parameters, the proposed model accurately follows the experimental curve with a minor fitting error of 1 mV. The model is also valid at a wide temperature range and takes into account the voltage hysteresis of the OCV. Using this model in SOC estimation by the extended Kalman filter (EKF contributes to minimizing the execution time and to reducing the SOC estimation error to only 3% compared to other existing models where the estimation error is about 5%. Experiments are also performed to prove that the proposed OCV model incorporated in the EKF estimator exhibits good reliability and precision under various loading profiles and temperatures.
Directory of Open Access Journals (Sweden)
Xuebing Yuan
2015-05-01
Full Text Available Inertial navigation based on micro-electromechanical system (MEMS inertial measurement units (IMUs has attracted numerous researchers due to its high reliability and independence. The heading estimation, as one of the most important parts of inertial navigation, has been a research focus in this field. Heading estimation using magnetometers is perturbed by magnetic disturbances, such as indoor concrete structures and electronic equipment. The MEMS gyroscope is also used for heading estimation. However, the accuracy of gyroscope is unreliable with time. In this paper, a wearable multi-sensor system has been designed to obtain the high-accuracy indoor heading estimation, according to a quaternion-based unscented Kalman filter (UKF algorithm. The proposed multi-sensor system including one three-axis accelerometer, three single-axis gyroscopes, one three-axis magnetometer and one microprocessor minimizes the size and cost. The wearable multi-sensor system was fixed on waist of pedestrian and the quadrotor unmanned aerial vehicle (UAV for heading estimation experiments in our college building. The results show that the mean heading estimation errors are less 10° and 5° to multi-sensor system fixed on waist of pedestrian and the quadrotor UAV, respectively, compared to the reference path.
Indian Academy of Sciences (India)
N Shantha Kumar; T Jann
2004-04-01
Due to costs, size and mass, commercially available inertial navigation systems are not suitable for small, autonomous ﬂying vehicles like ALEX and other UAVs. In contrast, by using modern MEMS (or of similar class) sensors, hardware costs, size and mass can be reduced substantially. However, low-cost sensors often suffer from inaccuracy and are inﬂuenced greatly by temperature variation. In this work, such inaccuracies and dependence on temperature variations have been studied, modelled and compensated in order to reach an adequate quality of measurements for the estimation of attitudes. This has been done applying a Kalman Filter-based sensor fusion algorithm that combines sensor models, error parameters and estimation scheme. Attitude estimation from low-cost sensors is ﬁrst realized in a Matlab/Simulink platform and then implemented on hardware by programming the micro controller and validated. The accuracies of the estimated roll and pitch attitudes are well within the stipulated accuracy level of ±5° for the ALEX. However, the estimation of heading, which is mainly derived from the magnetometer readings, seems to be inﬂuenced greatly by the variation in local magnetic ﬁeld.
Institute of Scientific and Technical Information of China (English)
LAI Rui-xun; FANG Hong-wei; HE Guo-jian; YU Xin; YANG Ming; WANG Ming
2013-01-01
In this paper,both state variables and parameters of one-dimensional open channel model are estimated using a framework of the Ensemble Kalman Filter (EnKF).Compared with observation,the predicted accuracy of water level and discharge are improved while the parameters of the model are identified simultaneously.With the principles of the EnKF,a state-space description of the Saint-Venant equation is constructed by perturbing the measurements with Gaussian error distribution.At the same time,the roughness,one of the key parameters in one-dimensional open channel,is also considered as a state variable to identify its value dynamically.The updated state variables and the parameters are then used as the initial values of the next time step to continue the assimilation process.The usefulness and the capability of the dual EnKF are demonstrated in the lower Yellow River during the water-sediment regulation in 2009.In the optimization process,the errors between the prediction and the observation are analyzed,and the rationale of inverse roughness is discussed.It is believed that (1) the flexible approach of the dual EnKF can improve the accuracy of predicting water level and discharge,(2) it provides a probabilistic way to identify the model error which is feasible to implement but hard to handle in other filter systems,and (3) it is practicable for river engineering and management.
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.
Ferrari, Alberto; Ginis, Pieter; Hardegger, Michael; Casamassima, Filippo; Rocchi, Laura; Chiari, Lorenzo
2016-07-01
Gait impairments are among the most disabling symptoms in several musculoskeletal and neurological conditions, severely limiting personal autonomy. Wearable gait sensors have been attracting attention as diagnostic tool for gait and are emerging as promising tool for tutoring and guiding gait execution. If their popularity is continuously growing, still there is room for improvement, especially towards more accurate solutions for spatio-temporal gait parameters estimation. We present an implementation of a zero-velocity-update gait analysis system based on a Kalman filter and off-the-shelf shoe-worn inertial sensors. The algorithms for gait events and step length estimation were specifically designed to comply with pathological gait patterns. More so, an Android app was deployed to support fully wearable and stand-alone real-time gait analysis. Twelve healthy subjects were enrolled to preliminarily tune the algorithms; afterwards sixteen persons with Parkinson's disease were enrolled for a validation study. Over the 1314 strides collected on patients at three different speeds, the total root mean square difference on step length estimation between this system and a gold standard was 2.9%. This shows that the proposed method allows for an accurate gait analysis and paves the way to a new generation of mobile devices usable anywhere for monitoring and intervention.
Energy Technology Data Exchange (ETDEWEB)
Ray, Jaideep; Lee, Jina; Lefantzi, Sophia; Yadav, Vineet; Michalak, Anna M.; van Bloemen Waanders, Bart Gustaaf; McKenna, Sean Andrew
2013-09-01
The estimation of fossil-fuel CO2 emissions (ffCO2) from limited ground-based and satellite measurements of CO2 concentrations will form a key component of the monitoring of treaties aimed at the abatement of greenhouse gas emissions. The limited nature of the measured data leads to a severely-underdetermined estimation problem. If the estimation is performed at fine spatial resolutions, it can also be computationally expensive. In order to enable such estimations, advances are needed in the spatial representation of ffCO2 emissions, scalable inversion algorithms and the identification of observables to measure. To that end, we investigate parsimonious spatial parameterizations of ffCO2 emissions which can be used in atmospheric inversions. We devise and test three random field models, based on wavelets, Gaussian kernels and covariance structures derived from easily-observed proxies of human activity. In doing so, we constructed a novel inversion algorithm, based on compressive sensing and sparse reconstruction, to perform the estimation. We also address scalable ensemble Kalman filters as an inversion mechanism and quantify the impact of Gaussian assumptions inherent in them. We find that the assumption does not impact the estimates of mean ffCO2 source strengths appreciably, but a comparison with Markov chain Monte Carlo estimates show significant differences in the variance of the source strengths. Finally, we study if the very different spatial natures of biogenic and ffCO2 emissions can be used to estimate them, in a disaggregated fashion, solely from CO2 concentration measurements, without extra information from products of incomplete combustion e.g., CO. We find that this is possible during the winter months, though the errors can be as large as 50%.
Energy Technology Data Exchange (ETDEWEB)
Barut, Murat, E-mail: muratbarut27@yahoo.co [Nigde University, Department of Electrical and Electronics Engineering, 51245 Nigde (Turkey)
2010-10-15
This study offers a novel extended Kalman filter (EKF) based estimation technique for the solution of the on-line estimation problem related to uncertainties in the stator and rotor resistances inherent to the speed-sensorless high efficiency control of induction motors (IMs) in the wide speed range as well as extending the limited number of states and parameter estimations possible with a conventional single EKF algorithm. For this aim, the introduced estimation technique in this work utilizes a single EKF algorithm with the consecutive execution of two inputs derived from the two individual extended IM models based on the stator resistance and rotor resistance estimation, differently from the other approaches in past studies, which require two separate EKF algorithms operating in a switching or braided manner; thus, it has superiority over the previous EKF schemes in this regard. The proposed EKF based estimation technique performing the on-line estimations of the stator currents, the rotor flux, the rotor angular velocity, and the load torque involving the viscous friction term together with the rotor and stator resistance is also used in the combination with the speed-sensorless direct vector control of IM and tested with simulations under the challenging 12 scenarios generated instantaneously via step and/or linear variations of the velocity reference, the load torque, the stator resistance, and the rotor resistance in the range of high and zero speed, assuming that the measured stator phase currents and voltages are available. Even under those variations, the performance of the speed-sensorless direct vector control system established on the novel EKF based estimation technique is observed to be quite good.
Hoffmann, Stefan A; Wohltat, Christian; Müller, Kristian M; Arndt, Katja M
2017-01-01
For various experimental applications, microbial cultures at defined, constant densities are highly advantageous over simple batch cultures. Due to high costs, however, devices for continuous culture at freely defined densities still experience limited use. We have developed a small-scale turbidostat for research purposes, which is manufactured from inexpensive components and 3D printed parts. A high degree of spatial system integration and a graphical user interface provide user-friendly operability. The used optical density feedback control allows for constant continuous culture at a wide range of densities and offers to vary culture volume and dilution rates without additional parametrization. Further, a recursive algorithm for on-line growth rate estimation has been implemented. The employed Kalman filtering approach based on a very general state model retains the flexibility of the used control type and can be easily adapted to other bioreactor designs. Within several minutes it can converge to robust, accurate growth rate estimates. This is particularly useful for directed evolution experiments or studies on metabolic challenges, as it allows direct monitoring of the population fitness.
Liu, Di; Mishra, Ashok K.; Yu, Zhongbo
2016-07-01
This paper examines the combination of support vector machines (SVM) and the dual ensemble Kalman filter (EnKF) technique to estimate root zone soil moisture at different soil layers up to 100 cm depth. Multiple experiments are conducted in a data rich environment to construct and validate the SVM model and to explore the effectiveness and robustness of the EnKF technique. It was observed that the performance of SVM relies more on the initial length of training set than other factors (e.g., cost function, regularization parameter, and kernel parameters). The dual EnKF technique proved to be efficient to improve SVM with observed data either at each time step or at a flexible time steps. The EnKF technique can reach its maximum efficiency when the updating ensemble size approaches a certain threshold. It was observed that the SVM model performance for the multi-layer soil moisture estimation can be influenced by the rainfall magnitude (e.g., dry and wet spells).
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.
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.
Directory of Open Access Journals (Sweden)
T. O. Ting
2014-01-01
Full Text Available In this work, a state-space battery model is derived mathematically to estimate the state-of-charge (SoC of a battery system. Subsequently, Kalman filter (KF is applied to predict the dynamical behavior of the battery model. Results show an accurate prediction as the accumulated error, in terms of root-mean-square (RMS, is a very small value. From this work, it is found that different sets of Q and R values (KF’s parameters can be applied for better performance and hence lower RMS error. This is the motivation for the application of a metaheuristic algorithm. Hence, the result is further improved by applying a genetic algorithm (GA to tune Q and R parameters of the KF. In an online application, a GA can be applied to obtain the optimal parameters of the KF before its application to a real plant (system. This simply means that the instantaneous response of the KF is not affected by the time consuming GA as this approach is applied only once to obtain the optimal parameters. The relevant workable MATLAB source codes are given in the appendix to ease future work and analysis in this area.
Ting, T O; Man, Ka Lok; Lim, Eng Gee; Leach, Mark
2014-01-01
In this work, a state-space battery model is derived mathematically to estimate the state-of-charge (SoC) of a battery system. Subsequently, Kalman filter (KF) is applied to predict the dynamical behavior of the battery model. Results show an accurate prediction as the accumulated error, in terms of root-mean-square (RMS), is a very small value. From this work, it is found that different sets of Q and R values (KF's parameters) can be applied for better performance and hence lower RMS error. This is the motivation for the application of a metaheuristic algorithm. Hence, the result is further improved by applying a genetic algorithm (GA) to tune Q and R parameters of the KF. In an online application, a GA can be applied to obtain the optimal parameters of the KF before its application to a real plant (system). This simply means that the instantaneous response of the KF is not affected by the time consuming GA as this approach is applied only once to obtain the optimal parameters. The relevant workable MATLAB source codes are given in the appendix to ease future work and analysis in this area.
Alatise, Mary B; Hancke, Gerhard P
2017-09-21
Using a single sensor to determine the pose estimation of a device cannot give accurate results. This paper presents a fusion of an inertial sensor of six degrees of freedom (6-DoF) which comprises the 3-axis of an accelerometer and the 3-axis of a gyroscope, and a vision to determine a low-cost and accurate position for an autonomous mobile robot. For vision, a monocular vision-based object detection algorithm speeded-up robust feature (SURF) and random sample consensus (RANSAC) algorithms were integrated and used to recognize a sample object in several images taken. As against the conventional method that depend on point-tracking, RANSAC uses an iterative method to estimate the parameters of a mathematical model from a set of captured data which contains outliers. With SURF and RANSAC, improved accuracy is certain; this is because of their ability to find interest points (features) under different viewing conditions using a Hessain matrix. This approach is proposed because of its simple implementation, low cost, and improved accuracy. With an extended Kalman filter (EKF), data from inertial sensors and a camera were fused to estimate the position and orientation of the mobile robot. All these sensors were mounted on the mobile robot to obtain an accurate localization. An indoor experiment was carried out to validate and evaluate the performance. Experimental results show that the proposed method is fast in computation, reliable and robust, and can be considered for practical applications. The performance of the experiments was verified by the ground truth data and root mean square errors (RMSEs).
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.
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...
Baker Syed; Poskar C; Junker Björn
2011-01-01
Abstract In systems biology, experimentally measured parameters are not always available, necessitating the use of computationally based parameter estimation. In order to rely on estimated parameters, it is critical to first determine which parameters can be estimated for a given model and measurement set. This is done with parameter identifiability analysis. A kinetic model of the sucrose accumulation in the sugar cane culm tissue developed by Rohwer et al. was taken as a test case model. Wh...
Directory of Open Access Journals (Sweden)
Lin Zhang
2016-10-01
Full Text Available To measure the pushing distance of a hydraulic-powered roof support, and reduce the cost from a non-reusable displacement sensor embedded in pushing a hydraulic cylinder, an inertial sensor is used to measure the pushing distance, and a Kalman filter is applied to process the inertial data. To obtain better estimation performance, an improved fruit fly optimization algorithm (IFOA is proposed to tune the parameters of the Kalman filter, processing noise covariance Q and observation noise covariance R. The key procedures of the proposed method, including state-space model, fitness function, and Kalman filter implementation, are presented. Finally, an artificial signal is utilized to verify the feasibility of the proposed method, and the tuning results of other algorithms, particle swarm optimization (PSO, genetic algorithm (GA, basic FOA, and 3D-FOA are compared. The proposed method is also applied in the pushing distance estimation scenario. The simulation and application results prove the effectiveness and superiority of the proposed method.
Barber, Jared; Tanase, Roxana; Yotov, Ivan
2016-06-01
Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion.
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...
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.
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
National Aeronautics and Space Administration — The problem of estimating the aerodynamic models for flight control of damaged aircraft using an innovative differential vortex lattice method tightly coupled with...
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...
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The paper investigates the ability to retrieve the true soil moisture profile by assimilating near-surface soil moisture into a soil moisture model with an ensemble Kalman filter (EnKF) assimilation scheme,including the effect of ensemble size, update interval and nonlinearities in the profile retrieval, the required time for full retrieval of the soil moisture profiles, and the possible influence of the depth of the soil moisture observation. These questions are addressed by a desktop study using synthetic data. The "true"soil moisture profiles are generated from the soil moisture model under the boundary condition of 0.5 cm d-1 evaporation. To test the assimilation schemes, the model is initialized with a poor initial guess of the soil moisture profile, and different ensemble sizes are tested showing that an ensemble of 40 members is enough to represent the covariance of the model forecasts. Also compared are the results with those from the direct insertion assimilation scheme, showing that the EnKF is superior to the direct insertion assimilation scheme, for hourly observations, with retrieval of the soil moisture profile being achieved in 16 h as compared to 12 days or more. For daily observations, the true soil moisture profile is achieved in about 15 days with the EnKF, but it is impossible to approximate the true moisture within 18 days by using direct insertion. It is also found that observation depth does not have a significant effect on profile retrieval time for the EnKF. The nonlinearities have some negative influence on the optimal estimates of soil moisture profile but not very seriously.
Adaptive UAV Attitude Estimation Employing Unscented Kalman Filter, FOAM and Low-Cost MEMS Sensors
Garcia de Marina Peinado, Hector; Espinosa, Felipe; Santos, Carlos
2012-01-01
Navigation employing low cost MicroElectroMechanical Systems (MEMS) sensors in Unmanned Aerial Vehicles (UAVs) is an uprising challenge. One important part of this navigation is the right estimation of the attitude angles. Most of the existent algorithms handle the sensor readings in a fixed way, le
Adaptive UAV Attitude Estimation Employing Unscented Kalman Filter, FOAM and Low-Cost MEMS Sensors
Garcia de Marina Peinado, Hector; Espinosa, Felipe; Santos, Carlos
2012-01-01
Navigation employing low cost MicroElectroMechanical Systems (MEMS) sensors in Unmanned Aerial Vehicles (UAVs) is an uprising challenge. One important part of this navigation is the right estimation of the attitude angles. Most of the existent algorithms handle the sensor readings in a fixed way, le
2012-09-01
different decisions as com- pared to an unmanned aerial vehicle (UAV) mission reconfig- uration based on prognostics indication on power train fail- ures...Degradation Modeling Training Trajectories Test Trajectory Parameter Estimation State-space Representation Prognostics Dynamic System Realization Health...and ASME. Kai Goebel received the degree of Diplom-Ingenieur from the Technische University Munchen, Germany in 1990. He received the M.S. and Ph.D
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.
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).
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.
Deutschmann, Julie; Bar-Itzhack, Itzhack
1997-01-01
Traditionally satellite attitude and trajectory have been estimated with completely separate systems, using different measurement data. The estimation of both trajectory and attitude for low earth orbit satellites has been successfully demonstrated in ground software using magnetometer and gyroscope data. Since the earth's magnetic field is a function of time and position, and since time is known quite precisely, the differences between the computed and measured magnetic field components, as measured by the magnetometers throughout the entire spacecraft orbit, are a function of both the spacecraft trajectory and attitude errors. Therefore, these errors can be used to estimate both trajectory and attitude. This work further tests the single augmented Extended Kalman Filter (EKF) which simultaneously and autonomously estimates spacecraft trajectory and attitude with data from the Rossi X-Ray Timing Explorer (RXTE) magnetometer and gyro-measured body rates. In addition, gyro biases are added to the state and the filter's ability to estimate them is presented.
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.
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
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.
Botto, Anna; Camporese, Matteo
2017-04-01
Hydrological models allow scientists to predict the response of water systems under varying forcing conditions. In particular, many physically-based integrated models were recently developed in order to understand the fundamental hydrological processes occurring at the catchment scale. However, the use of this class of hydrological models is still relatively limited, as their prediction skills heavily depend on reliable parameter estimation, an operation that is never trivial, being normally affected by large uncertainty and requiring huge computational effort. The objective of this work is to test the potential of data assimilation to be used as an inverse modeling procedure for the broad class of integrated hydrological models. To pursue this goal, a Bayesian data assimilation (DA) algorithm based on a Monte Carlo approach, namely the ensemble Kalman filter (EnKF), is combined with the CATchment HYdrology (CATHY) model. In this approach, input variables (atmospheric forcing, soil parameters, initial conditions) are statistically perturbed providing an ensemble of realizations aimed at taking into account the uncertainty involved in the process. Each realization is propagated forward by the CATHY hydrological model within a parallel R framework, developed to reduce the computational effort. When measurements are available, the EnKF is used to update both the system state and soil parameters. In particular, four different assimilation scenarios are applied to test the capability of the modeling framework: first only pressure head or water content are assimilated, then, the combination of both, and finally both pressure head and water content together with the subsurface outflow. To demonstrate the effectiveness of the approach in a real-world scenario, an artificial hillslope was designed and built to provide real measurements for the DA analyses. The experimental facility, located in the Department of Civil, Environmental and Architectural Engineering of the
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.
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.
A modified iterative ensemble Kalman filter data assimilation method
Xu, Baoxiong; Bai, Yulong; Wang, Yizhao; Li, Zhe; Ma, Boyang
2017-08-01
High nonlinearity is a typical characteristic associated with data assimilation systems. Additionally, iterative ensemble based methods have attracted a large amount of research attention, which has been focused on dealing with nonlinearity problems. To solve the local convergence problem of the iterative ensemble Kalman filter, a modified iterative ensemble Kalman filter algorithm was put forward, which was based on a global convergence strategy from the perspective of a Gauss-Newton iteration. Through self-adaption, the step factor was adjusted to enable every iteration to approach expected values during the process of the data assimilation. A sensitivity experiment was carried out in a low dimensional Lorenz-63 chaotic system, as well as a Lorenz-96 model. The new method was tested via ensemble size, observation variance, and inflation factor changes, along with other aspects. Meanwhile, comparative research was conducted with both a traditional ensemble Kalman filter and an iterative ensemble Kalman filter. The results showed that the modified iterative ensemble Kalman filter algorithm was a data assimilation method that was able to effectively estimate a strongly nonlinear system state.
Ensemble Kalman filtering 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.
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...
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.
Celaya, Jose R.; Saxen, Abhinav; Goebel, Kai
2012-01-01
This article discusses several aspects of uncertainty representation and management for model-based prognostics methodologies based on our experience with Kalman Filters when applied to prognostics for electronics components. In particular, it explores the implications of modeling remaining useful life prediction as a stochastic process and how it relates to uncertainty representation, management, and the role of prognostics in decision-making. A distinction between the interpretations of estimated remaining useful life probability density function and the true remaining useful life probability density function is explained and a cautionary argument is provided against mixing interpretations for the two while considering prognostics in making critical decisions.
Directory of Open Access Journals (Sweden)
H. Zhang
2017-09-01
Full Text Available Land surface models (LSMs use a large cohort of parameters and state variables to simulate the water and energy balance at the soil–atmosphere interface. Many of these model parameters cannot be measured directly in the field, and require calibration against measured fluxes of carbon dioxide, sensible and/or latent heat, and/or observations of the thermal and/or moisture state of the soil. Here, we evaluate the usefulness and applicability of four different data assimilation methods for joint parameter and state estimation of the Variable Infiltration Capacity Model (VIC-3L and the Community Land Model (CLM using a 5-month calibration (assimilation period (March–July 2012 of areal-averaged SPADE soil moisture measurements at 5, 20, and 50 cm depths in the Rollesbroich experimental test site in the Eifel mountain range in western Germany. We used the EnKF with state augmentation or dual estimation, respectively, and the residual resampling PF with a simple, statistically deficient, or more sophisticated, MCMC-based parameter resampling method. The performance of the calibrated LSM models was investigated using SPADE water content measurements of a 5-month evaluation period (August–December 2012. As expected, all DA methods enhance the ability of the VIC and CLM models to describe spatiotemporal patterns of moisture storage within the vadose zone of the Rollesbroich site, particularly if the maximum baseflow velocity (VIC or fractions of sand, clay, and organic matter of each layer (CLM are estimated jointly with the model states of each soil layer. The differences between the soil moisture simulations of VIC-3L and CLM are much larger than the discrepancies among the four data assimilation methods. The EnKF with state augmentation or dual estimation yields the best performance of VIC-3L and CLM during the calibration and evaluation period, yet results are in close agreement with the PF using MCMC resampling. Overall, CLM demonstrated the
Directory of Open Access Journals (Sweden)
Oh Hyunmin
2015-01-01
Full Text Available Tracking system is essential for Image Guided Surgery(IGS. The Optical Tracking Sensor(OTS has been widely used as tracking system for IGS due to its high accuracy and easy usage. However, OTS has a limit that tracking fails when occlusion of marker occurs. In this paper, sensor fusion with OTS and Inertial Measurement Unit(IMU is proposed to solve this problem. The proposed algorithm improves the accuracy of tracking system by eliminating scattering error of the sensor and supplements the disadvantages of OTS and IMU through sensor fusion based on Kalman filter. Also, coordinate axis calibration method that improves the accuracy is introduced. The performed experiment verifies the effectualness of the proposed algorithm.
2014-12-27
work presents a non-intrusive methodology named Multi-Model Ensemble Kalman Filter that allows assimilating the local drifter data into such a set of...purpose it is then assumed the bulk of the model state corrections resulting from local and remote observations are being performed through routine... local state : xı ¼ Z xi¼1;...;n xipðxi¼1;...;nÞdxi¼1;...;n ¼ Z xj–i pðxj–i n xiÞdxj–i Z xi xipðxiÞdxi ¼ wimi ð2Þ In here p(xi = 1, . . . ,n) is the joint
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.
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.
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.
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 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.
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.
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.
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.
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...
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...
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.
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...
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.
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.
Sun, Yong; Ma, Zilin; Tang, Gongyou; Chen, Zheng; Zhang, Nong
2016-07-01
Since the main power source of hybrid electric vehicle(HEV) is supplied by the power battery, the predicted performance of power battery, especially the state-of-charge(SOC) estimation has attracted great attention in the area of HEV. However, the value of SOC estimation could not be greatly precise so that the running performance of HEV is greatly affected. A variable structure extended kalman filter(VSEKF)-based estimation method, which could be used to analyze the SOC of lithium-ion battery in the fixed driving condition, is presented. First, the general lower-order battery equivalent circuit model(GLM), which includes column accumulation model, open circuit voltage model and the SOC output model, is established, and the off-line and online model parameters are calculated with hybrid pulse power characteristics(HPPC) test data. Next, a VSEKF estimation method of SOC, which integrates the ampere-hour(Ah) integration method and the extended Kalman filter(EKF) method, is executed with different adaptive weighting coefficients, which are determined according to the different values of open-circuit voltage obtained in the corresponding charging or discharging processes. According to the experimental analysis, the faster convergence speed and more accurate simulating results could be obtained using the VSEKF method in the running performance of HEV. The error rate of SOC estimation with the VSEKF method is focused in the range of 5% to 10% comparing with the range of 20% to 30% using the EKF method and the Ah integration method. In Summary, the accuracy of the SOC estimation in the lithium-ion battery cell and the pack of lithium-ion battery system, which is obtained utilizing the VSEKF method has been significantly improved comparing with the Ah integration method and the EKF method. The VSEKF method utilizing in the SOC estimation in the lithium-ion pack of HEV can be widely used in practical driving conditions.
Institute of Scientific and Technical Information of China (English)
SUN Yong; MA Zilin; TANG Gongyou; CHEN Zheng; ZHANG Nong
2016-01-01
Since the main power source of hybrid electric vehicle(HEV) is supplied by the power battery, the predicted performance of power battery, especially the state-of-charge(SOC) estimation has attracted great attention in the area of HEV. However, the value of SOC estimation could not be greatly precise so that the running performance of HEV is greatly affected. A variable structure extended kalman filter(VSEKF)-based estimation method, which could be used to analyze the SOC of lithium-ion battery in the fixed driving condition, is presented. First, the general lower-order battery equivalent circuit model(GLM), which includes column accumulation model, open circuit voltage model and the SOC output model, is established, and the off-line and online model parameters are calculated with hybrid pulse power characteristics(HPPC) test data. Next, a VSEKF estimation method of SOC, which integrates the ampere-hour(Ah) integration method and the extended Kalman filter(EKF) method, is executed with different adaptive weighting coefficients, which are determined according to the different values of open-circuit voltage obtained in the corresponding charging or discharging processes. According to the experimental analysis, the faster convergence speed and more accurate simulating results could be obtained using the VSEKF method in the running performance of HEV. The error rate of SOC estimation with the VSEKF method is focused in the range of 5%to 10%comparing with the range of 20%to 30%using the EKF method and the Ah integration method. In Summary, the accuracy of the SOC estimation in the lithium-ion battery cell and the pack of lithium-ion battery system, which is obtained utilizing the VSEKF method has been significantly improved comparing with the Ah integration method and the EKF method. The VSEKF method utilizing in the SOC estimation in the lithium-ion pack of HEV can be widely used in practical driving conditions.
Novelli, Antonio
2016-08-01
Leaf Area Index (LAI) is essential in ecosystem and agronomic studies, since it measures energy and gas exchanges between vegetation and atmosphere. In the last decades, LAI values have widely been estimated from passive remotely sensed data. Common approaches are based on semi-empirical/statistic techniques or on radiative transfer model inversion. Although the scientific community has been providing several LAI retrieval methods, the estimated results are often affected by noise and measurement uncertainties. The sequential data assimilation theory provides a theoretical framework to combine an imperfect model with incomplete observation data. In this document a data fusion Kalman filter algorithm is proposed in order to estimate the time evolution of LAI by combining MODIS LAI data and PROBA-V surface reflectance data. The reflectance data were linked to LAI by using the Reduced Simple Ratio index. The main working hypotheses were lacking input data necessary for climatic models and canopy reflectance models.
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 ...
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.
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.
Coelho, Emanuel F.; Hogan, P.; Jacobs, G.; Thoppil, P.; Huntley, H. S.; Haus, B. K.; Lipphardt, B. L.; Kirwan, A. D.; Ryan, E. H.; Olascoaga, J.; Beron-Vera, F.; Poje, A. C.; Griffa, A.; Özgökmen, T. M.; Mariano, A. J.; Novelli, G.; Haza, A. C.; Bogucki, D.; Chen, S. S.; Curcic, M.; Iskandarani, M.; Judt, F.; Laxague, N.; Reniers, A. J. H. M.; Valle-Levinson, A.; Wei, M.
2015-03-01
In the summer and fall of 2012, during the GLAD experiment in the Gulf of Mexico, the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE) used several ocean models to assist the deployment of more than 300 surface drifters. The Navy Coastal Ocean Model (NCOM) at 1 km and 3 km resolutions, the US Navy operational NCOM at 3 km resolution (AMSEAS), and two versions of the Hybrid Coordinates Ocean Model (HYCOM) set at 4 km were running daily and delivering 72-h range forecasts. They all assimilated remote sensing and local profile data but they were not assimilating the drifter's observations. This work presents a non-intrusive methodology named Multi-Model Ensemble Kalman Filter that allows assimilating the local drifter data into such a set of models, to produce improved ocean currents forecasts. The filter is to be used when several modeling systems or ensembles are available and/or observations are not entirely handled by the operational data assimilation process. It allows using generic in situ measurements over short time windows to improve the predictability of local ocean dynamics and associated high-resolution parameters of interest for which a forward model exists (e.g. oil spill plumes). Results can be used for operational applications or to derive enhanced background fields for other data assimilation systems, thus providing an expedite method to non-intrusively assimilate local observations of variables with complex operators. Results for the GLAD experiment show the method can improve water velocity predictions along the observed drifter trajectories, hence enhancing the skills of the models to predict individual trajectories.
Directory of Open Access Journals (Sweden)
Zhongwei Deng
2016-06-01
Full Text Available In the field of state of charge (SOC estimation, the Kalman filter has been widely used for many years, although its performance strongly depends on the accuracy of the battery model as well as the noise covariance. The Kalman gain determines the confidence coefficient of the battery model by adjusting the weight of open circuit voltage (OCV correction, and has a strong correlation with the measurement noise covariance (R. In this paper, the online identification method is applied to acquire the real model parameters under different operation conditions. A criterion based on the OCV error is proposed to evaluate the reliability of online parameters. Besides, the equivalent circuit model produces an intrinsic model error which is dependent on the load current, and the property that a high battery current or a large current change induces a large model error can be observed. Based on the above prior knowledge, a fuzzy model is established to compensate the model error through updating R. Combining the positive strategy (i.e., online identification and negative strategy (i.e., fuzzy model, a more reliable and robust SOC estimation algorithm is proposed. The experiment results verify the proposed reliability criterion and SOC estimation method under various conditions for LiFePO4 batteries.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Stetzel, KD; Aldrich, LL; Trimboli, MS; Plett, GL
2015-03-15
This paper addresses the problem of estimating the present value of electrochemical internal variables in a lithium-ion cell in real time, using readily available measurements of cell voltage, current, and temperature. The variables that can be estimated include any desired set of reaction flux and solid and electrolyte potentials and concentrations at any set of one-dimensional spatial locations, in addition to more standard quantities such as state of charge. The method uses an extended Kalman filter along with a one-dimensional physics-based reduced-order model of cell dynamics. Simulations show excellent and robust predictions having dependable error bounds for most internal variables. (C) 2014 Elsevier B.V. All rights reserved.
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...
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...
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.
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.
Wei, Jingwen; Dong, Guangzhong; Chen, Zonghai
2017-10-01
With the rapid development of battery-powered electric vehicles, the lithium-ion battery plays a critical role in the reliability of vehicle system. In order to provide timely management and protection for battery systems, it is necessary to develop a reliable battery model and accurate battery parameters estimation to describe battery dynamic behaviors. Therefore, this paper focuses on an on-board adaptive model for state-of-charge (SOC) estimation of lithium-ion batteries. Firstly, a first-order equivalent circuit battery model is employed to describe battery dynamic characteristics. Then, the recursive least square algorithm and the off-line identification method are used to provide good initial values of model parameters to ensure filter stability and reduce the convergence time. Thirdly, an extended-Kalman-filter (EKF) is applied to on-line estimate battery SOC and model parameters. Considering that the EKF is essentially a first-order Taylor approximation of battery model, which contains inevitable model errors, thus, a proportional integral-based error adjustment technique is employed to improve the performance of EKF method and correct model parameters. Finally, the experimental results on lithium-ion batteries indicate that the proposed EKF with proportional integral-based error adjustment method can provide robust and accurate battery model and on-line parameter estimation.
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.
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...
DEFF Research Database (Denmark)
Vedel-Larsen, Esben; Fuglø, Jacob; Channir, Fouad;
2010-01-01
, are variable and depend on cognitive function. This study compares the performance of a simplified Kalman filter with Sliding Window Averaging in tracking dynamical changes in single trial P300. The comparison is performed on simulated P300 data with added background noise consisting of both simulated and real...... background EEG in various input signal to noise ratios. While both methods can be applied to track dynamical changes, the simplified Kalman filter has an advantage over the Sliding Window Averaging, most notable in a better noise suppression when both are optimized for faster changing latency and amplitude...
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.
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.
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.
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...
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.
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 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.
White Noise Estimation Theory Based on Kalman Filtering%基于Kalman滤波的白噪声估计理论
Institute of Scientific and Technical Information of China (English)
邓自立; 许燕
2003-01-01
应用Kalman滤波方法,首次提出了一种统一的和通用的白噪声估计理论.它可统一处理线性离散时变和定常随机系统的输入白噪声和观测白噪声的滤波、平滑和预报问题.提出了最优和稳态白噪声估值器,且提出了白噪声新息滤波器和Wiener滤波器.它们可应用于石油勘探地震数据处理,且为解决状态和信号估计问题提供一种新工具.两个仿真例子说明了其有效性.%By using the Kalman filtering method, a unified and general white noise estimation theory is presented for the first time. It can handle the filtering, smoothing and prediction problems in a unified framework for both the input white noise and measurement white noise in linear discrete time-varying and time-invariant stochastic systems. The optimal and steady-state white noise estimators are presented, and white noise innovation filters and Wiener filters are also presented. They can be applied to seismic data processing in oil exploration, and provide a new tool to solve the state and signal estimation problems. Two simulation examples show their effectiveness.
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
Lateral states using Kalman-Bucy filter estimation of vehicle%基于Kalman—Bucy滤波的车辆横向运动状态估计
Institute of Scientific and Technical Information of China (English)
赵津; 王婷
2011-01-01
研究了车辆横向运动中的状态估计问题。在两自由度车辆横向动力学模型的基础上，考虑了车辆纵向速度对车辆横向运动状态的影响，设计了基于Kalman-Bucy滤波的车辆状态观测器。仿真实验结果显示，该滤波器能够有效的过滤系统的过程噪声和观测噪声，并能够准确地估计出车辆横向运动速度与横摆角速度的实际值。%This paper concentrates on the estimation of vehicle lateral states. Based on the two-degree- freedom vehicle model, considering the impacts of vehicle longitudinal velocity on vehicle lateral states, we propose a vehicle lateral state observer based on the KaJman-Bucy filter. The proposed observer has been verified by simulation experiments, The results have showed that the proposed method can effectively filter the process noise and measurement noise, and provide accurate estimation of the vehicle lateral velocity and yaw rate.
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...
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
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.
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...
DEFF Research Database (Denmark)
Vedel-Larsen, Esben; Fuglø, Jacob; Channir, Fouad
2010-01-01
, are variable and depend on cognitive function. This study compares the performance of a simplified Kalman filter with Sliding Window Averaging in tracking dynamical changes in single trial P300. The comparison is performed on simulated P300 data with added background noise consisting of both simulated and real...
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.
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.
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.
Shi, Yuning; Davis, Kenneth J.; Zhang, Fuqing; Duffy, Christopher J.; Yu, Xuan
2015-09-01
The capability of an ensemble Kalman filter (EnKF) to simultaneously estimate multiple parameters in a physically-based land surface hydrologic model using multivariate field observations is tested at a small watershed (0.08 km2). Multivariate, high temporal resolution, in situ measurements of discharge, water table depth, soil moisture, and sensible and latent heat fluxes encompassing five months of 2009 are assimilated. It is found that, for five out of the six parameters, the EnKF estimated parameter values from different test cases converge strongly, and the estimates after convergence are close to the manually calibrated parameter values. The EnKF estimated parameters and manually calibrated parameters yield similar model performance, but the EnKF sequential method significantly decreases the time and labor required for calibration. The results demonstrate that, given a limited number of multi-state, site-specific observations, an automated sequential calibration method (EnKF) can be used to optimize physically-based land surface hydrologic models.
Directory of Open Access Journals (Sweden)
Xiangwei Guo
2016-02-01
Full Text Available An estimation of the power battery state of charge (SOC is related to the energy management, the battery cycle life and the use cost of electric vehicles. When a lithium-ion power battery is used in an electric vehicle, the SOC displays a very strong time-dependent nonlinearity under the influence of random factors, such as the working conditions and the environment. Hence, research on estimating the SOC of a power battery for an electric vehicle is of great theoretical significance and application value. In this paper, according to the dynamic response of the power battery terminal voltage during a discharging process, the second-order RC circuit is first used as the equivalent model of the power battery. Subsequently, on the basis of this model, the least squares method (LS with a forgetting factor and the adaptive unscented Kalman filter (AUKF algorithm are used jointly in the estimation of the power battery SOC. Simulation experiments show that the joint estimation algorithm proposed in this paper has higher precision and convergence of the initial value error than a single AUKF algorithm.
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.
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...
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.
Directory of Open Access Journals (Sweden)
R. Zhuravlev
2011-10-01
Full Text Available In this work we propose an approach to solving a source estimation problem based on representation of carbon dioxide surface emissions as a linear combination of a finite number of pre-computed empirical orthogonal functions (EOFs. We used National Institute for Environmental Studies (NIES transport model for computing response functions and Kalman filter for estimating carbon dioxide emissions. Our approach produces results similar to these of other models participating in the TransCom3 experiment.
Using the EOFs we can estimate surface fluxes at higher spatial resolution, while keeping the dimensionality of the problem comparable with that in the regions approach. This also allows us to avoid potentially artificial sharp gradients in the fluxes in between pre-defined regions. EOF results generally match observations more closely given the same error structure as the traditional method.
Additionally, the proposed approach does not require additional effort of defining independent self-contained emission regions.
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.
Directory of Open Access Journals (Sweden)
Ariel Omar Cepero Díaz
2015-04-01
Full Text Available La determinación de la posición angular instantánea del rotor es parte integral del control en los accionamientos de Motores de Reluctancia Conmutada. La medición directa de esta variable adiciona complejidad y costo al sistema y no siempre brinda buenos resultados, lo que ha motivado el desarrollo y prueba de algoritmos de estimación de la posición angular del rotor. En este trabajo se presenta el empleo de un Filtro Desaromatizado de Kalman para estimar la velocidad y la posición angular del rotor del motor MFR 132.5, basado en un modelo de caja gris de dicho motor que también es presentado en este trabajo. Los resultados demuestran que este estimador ofrece estimaciones satisfactorias del estado del motor, lo mismo durante el arranque que durante el funcionamiento regular, aún bajo la presencia de perturbaciones en el torque de la carga y errores en la estimación inicial de la posición angular del rotor. The measure of the instant angular position of the rotor is integral part of the control of Switching Reluctance Motors drivers. The direct measurement of this variable adds complexity and cost to the system and it doesn’t give good results sometimes. That has motivated the development and test of algorithms for estimating the rotor angular position of the motor. In this work is presented the use of an Unscented Kalman Filter for estimating the speed and rotor angular position of the motor MFR 132.5, based on a grey box model of the motor which is also presented in this work. The results show that this kind of estimator gives good estimations of the state of the motor, as well during the starting as during the regular operation, even under the presence of perturbations of the load torque and errors in the initial estimation of the angular position.
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.
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
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.
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...
Institute of Scientific and Technical Information of China (English)
李德东; 王振臣; 郭小星
2011-01-01
混合动力汽车(HEV)电池管理系统工作于恶劣工况环境中,采用常规卡尔曼滤波算法估计电池荷电状态(SOC)时,量测噪声统计特性随实际工况条件剧烈变化,会导致估测不准,甚至滤波发散.采用基于模糊自适应卡尔曼滤波的氢镍动力电池SOC估算算法,通过监视理论残差与实际残差的比值,对量测噪声协方差阵进行递推在线修正,使其逐渐逼近真实噪声水平,从而使滤波器执行最优估计,提高估算精度.仿真结果表明,这种算法对随机的量测噪声具有较强的抑制能力.%Hybrid electric vehicle (HEV) battery management system works in bad condition environment, when using the conventional Kalman filtering algorithms estimating SOC(state of charge) of batteries, the acute changes of the statistical properties of measurement noise will lead to inaccurate estimates, even divergent filtering. The estimation algorithm for SOC of Ni-MH batteries based on the fuzzy adaptive Kalman filter was used in this paper. By monitoring the filter residual and actual residual, this algorithm modified recursively the measurement noise covariance of Kalman filtering online using the fuzzy inference system (FIS) to make the covariance close to real measurement covariance gradually. Accordingly, the accuracy of the estimate system was improved. Matlab simulation and experiments were carried out. The comparison indicates that the fuzzy adaptive Kalman filtering performs well when disturbance happens.
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 ...
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.
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.
Application of Kalman Filtering in Yule-Walker Spectral Estimation%Kalman滤波在Yule-Walker谱估计中的应用
Institute of Scientific and Technical Information of China (English)
侯杰虎
2011-01-01
在现代谱估计中,由于Yule-Walker沃克谱估计算法中平稳随机序列的长度n在某些情况下偏小,使计算出的ARMA随机过程的功率谱密度不能精确逼近真实值,所以我们在用自相关法估计AR模型参数时加入了kalman滤波器。将估计的AR模型系数及高斯白噪声作为滤波器的输入及部分参数,对最终估计的功率谱进行修正。实验结果表明,在Yule-Walker谱估计中加入kalman滤波,其计算精度及结果稳定性都有了一定的提高,可以作为解决相关问题的方法之一。%In modern spectral estimation,because in some cases the steady random sequence which in Yule-Walker spectrum estimated is short,and the power spectral density of the ARMA random process is hard to approaches the real density,so kalman filtering was introd
Vargas-Melendez, Leandro; Boada, Beatriz L; Boada, Maria Jesus L; Gauchia, Antonio; Diaz, Vicente
2017-04-29
Vehicles with a high center of gravity (COG), such as light trucks and heavy vehicles, are prone to rollover. This kind of accident causes nearly 33 % of all deaths from passenger vehicle crashes. Nowadays, these vehicles are incorporating roll stability control (RSC) systems to improve their safety. Most of the RSC systems require the vehicle roll angle as a known input variable to predict the lateral load transfer. The vehicle roll angle can be directly measured by a dual antenna global positioning system (GPS), but it is expensive. For this reason, it is important to estimate the vehicle roll angle from sensors installed onboard in current vehicles. On the other hand, the knowledge of the vehicle's parameters values is essential to obtain an accurate vehicle response. Some of vehicle parameters cannot be easily obtained and they can vary over time. In this paper, an algorithm for the simultaneous on-line estimation of vehicle's roll angle and parameters is proposed. This algorithm uses a probability density function (PDF)-based truncation method in combination with a dual Kalman filter (DKF), to guarantee that both vehicle's states and parameters are within bounds that have a physical meaning, using the information obtained from sensors mounted on vehicles. Experimental results show the effectiveness of the proposed algorithm.
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.
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.
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.).
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.
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.
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...
Xiao, D.; Shi, Y.; Li, L.
2015-12-01
Parameter estimation is generally required for land surface models (LSMs) and hydrologic models to reproduce observed water and energy fluxes in different watersheds. Using soil moisture observations for parameter estimation in addition to discharge and land surface temperature observations can improve the prediction of land surface and subsurface processes. Due to their representativity, point measurements cannot capture the watershed-scale soil moisture conditions and may lead to notable bias in watershed soil moisture predictions if used for model calibration. The intermediate-scale cosmic-ray soil moisture observing system (COSMOS) provides average soil water content measurement over a footprint of 0.34 m2 and depths up to 50 cm, and may provide better calibration data for low-order watersheds. In this study, we will test using COSMOS observations for Flux-PIHM parameter and state estimation via the ensemble Kalman filter (EnKF). Flux-PIHM is a physically-based land surface hydrologic model that couples the Penn State Integrated Hydrologic Model (PIHM) with the Noah land surface model. Synthetic data experiments will be performed at the Shale Hills watershed (area: 0.08 km2, smaller than COSMOS footprint) and the Garner Run watershed (1.34 km2, larger than COSMOS footprint) in the Shale Hills Susquehanna Critical Zone Observatory in central Pennsylvania. COSMOS observations will be assimilated into Flux-PIHM using the EnKF, in addition to discharge and land surface temperature (LST) observations. The accuracy of EnKF estimated parameters and water and energy flux predictions will be evaluated. In addition, the results will be compared with assimilating point soil moisture measurement (in addition to discharge and LST), to assess the effects of using different scales of soil moisture observations for parameter estimation. The results at Shale Hills and Garner Run will be compared to test whether performance of COSMOS data assimilation is affected by the size of
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
Directory of Open Access Journals (Sweden)
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.
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).
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.
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.
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 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.
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.
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
Directory of Open Access Journals (Sweden)
S. Dance
2009-04-01
Full Text Available We have developed an ensemble Kalman Filter (EnKF to estimate 8-day regional surface fluxes of CO2 from space-borne CO2 dry-air mole fraction observations (XCO2 and evaluate the approach using a series of synthetic experiments, in preparation for data from the NASA Orbiting Carbon Observatory (OCO. The 32-day duty cycle of OCO alternates every 16 days between nadir and glint measurements of backscattered solar radiation at short-wave infrared wavelengths. The EnKF uses an ensemble of states to represent the error covariances to estimate 8-day CO2 surface fluxes over 144 geographical regions. We use a 12×8-day lag window, recognising that XCO2 measurements include surface flux information from prior time windows. The observation operator that relates surface CO2 fluxes to atmospheric distributions of XCO2 includes: a the GEOS-Chem transport model that relates surface fluxes to global 3-D distributions of CO2 concentrations, which are sampled at the time and location of OCO measurements that are cloud-free and have aerosol optical depths 2 profiles to XCO2, accounting for differences between nadir and glint measurements, and the associated scene-dependent observation errors. We show that OCO XCO2 measurements significantly reduce the uncertainties of surface CO2 flux estimates. Glint measurements are generally better at constraining ocean CO2 flux estimates. Nadir XCO2 measurements over the terrestrial tropics are sparse throughout the year because of either clouds or smoke. Glint measurements provide the most effective constraint for estimating tropical terrestrial CO2 fluxes by accurately sampling fresh continental outflow over neighbouring oceans. We also present results from sensitivity experiments that investigate how flux estimates change with 1 bias and unbiased errors, 2 alternative duty cycles, 3 measurement density and correlations, 4 the spatial resolution of estimated flux estimates, and 5 reducing the length of the lag window and the
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.
2009-06-01
p. 452) Pfe = [S0 + H rWH]-1 = E[eer] (3.60) Assuming that E[e] — 0, where the estimation error vector e = x° - x°, and E denotes the expected...the a posteriori estimate Pfe (tfc). These a posteriori estimates are then propagated to tfe+1 to become the a priori xfc(tfe+1) and Pfe (tfe+1) for...1 (3.80) The error covariance for the smoothed estimates is given by the recursive equation (37 p. 250): pfe = pfe + sfe( pfe +i - pfe +i)sfe (3.81
Real-time upper-body human pose estimation from depth data using Kalman filter for simulator
Lee, D.; Chi, S.; Park, C.; Yoon, H.; Kim, J.; Park, C. H.
2014-08-01
Recently, many studies show that an indoor horse riding exercise has a positive effect on promoting health and diet. However, if a rider has an incorrect posture, it will be the cause of back pain. In spite of this problem, there is only few research on analyzing rider's posture. Therefore, the purpose of this study is to estimate a rider pose from a depth image using the Asus's Xtion sensor in real time. In the experiments, we show the performance of our pose estimation algorithm in order to comparing the results between our joint estimation algorithm and ground truth data.
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 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.
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
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.
The scale mismatch between remotely sensed observations and crop growth models simulated state variables decreases the reliability of crop yield estimates. To overcome this problem, we used a two-step data assimilation phases: first we generated a complete leaf area index (LAI) time series by combin...
Leeuwenburgh, O.
2008-01-01
The assimilation of high-quality in situ data into ocean models is known to lead to imbalanced analyses and spurious circulations when the model dynamics or the forcing contain systematic errors. Use of a bias estimation and correction scheme has been shown to significantly improve the balance of
Leeuwenburgh, O.
2008-01-01
The assimilation of high-quality in situ data into ocean models is known to lead to imbalanced analyses and spurious circulations when the model dynamics or the forcing contain systematic errors. Use of a bias estimation and correction scheme has been shown to significantly improve the balance of th
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.
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.
Ferrari, Alberto; Ginis, Pieter; Hardegger, Michael; Casamassima, Filippo; Rocchi, Laura; Chiari, Lorenzo
2016-01-01
Gait impairments are among the most disabling symptoms in several musculoskeletal and neurological conditions, severely limiting personal autonomy. Wearable gait sensors have been attracting attention as diagnostic tool for gait and are emerging as promising tool for tutoring and guiding gait execution. If their popularity is continuously growing, still there is room for improvement, especially towards more accurate solutions for spatio-temporal gait parameters estimation. We present an imple...
De Groote, F; De Laet, T; Jonkers, I; De Schutter, J
2008-12-05
We developed a Kalman smoothing algorithm to improve estimates of joint kinematics from measured marker trajectories during motion analysis. Kalman smoothing estimates are based on complete marker trajectories. This is an improvement over other techniques, such as the global optimisation method (GOM), Kalman filtering, and local marker estimation (LME), where the estimate at each time instant is only based on part of the marker trajectories. We applied GOM, Kalman filtering, LME, and Kalman smoothing to marker trajectories from both simulated and experimental gait motion, to estimate the joint kinematics of a ten segment biomechanical model, with 21 degrees of freedom. Three simulated marker trajectories were studied: without errors, with instrumental errors, and with soft tissue artefacts (STA). Two modelling errors were studied: increased thigh length and hip centre dislocation. We calculated estimation errors from the known joint kinematics in the simulation study. Compared with other techniques, Kalman smoothing reduced the estimation errors for the joint positions, by more than 50% for the simulated marker trajectories without errors and with instrumental errors. Compared with GOM, Kalman smoothing reduced the estimation errors for the joint moments by more than 35%. Compared with Kalman filtering and LME, Kalman smoothing reduced the estimation errors for the joint accelerations by at least 50%. Our simulation results show that the use of Kalman smoothing substantially improves the estimates of joint kinematics and kinetics compared with previously proposed techniques (GOM, Kalman filtering, and LME) for both simulated, with and without modelling errors, and experimentally measured gait motion.
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...
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.
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.
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
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.
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.
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.
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.
Institute of Scientific and Technical Information of China (English)
林旭; 罗志才
2015-01-01
采用Kalman滤波方法进行钟差参数计算和预报时，需确定Kalman滤波噪声协方差矩阵。针对这一问题，提出了一种新的卫星钟差Kalman滤波噪声协方差估计方法，通过建立新息的相关函数序列与未知的噪声参数间的线性函数模型，采用最小二乘法进行噪声参数估计。采用精密钟差数据进行钟差参数估计和预报分析，结果表明，该方法具有较好的收敛性，并与顾及随机噪声模型的开窗分类因子自适应抗差估计方法进行对比分析，验证了新方法的正确性和有效性。%The satellite clock plays a key role in the global navigation satellite system (GNSS). The accuracy of GNSS and its applications depend on the quality of the satellite clock. Therefore, precisely estimating and predicting the satellite clock is an important issue in the fields of GNSS and its application. As an optimal estimation algorithm, Kalman filter has been used to estimate and predict the satellite clock. However, in a conventional Kalman filter algorithm, the noise covariance matrices of satellite clock need to be predetermined, which restricts its further applications since the noise covariance matrices, especially the process noise covariance matrix, are usually unknown in the real cases. With inappropriate noise covariance matrices, the state estimation of conventional Kalman filter is suboptimal. To cope with this problem, a new noise covariance matrix estimation method of Kalman filter is proposed, and then we apply it to the problem of satellite clock estimation and prediction. Considering the fact that the process noise covariance matrix depends on the unknown noise parameters, the problem of estimating process noise covariance matrix can be solved by estimating the unknown noise parameters. First, the correlation between the Kalman innovations is used to establish a linear relationship with the unknown noise parameters. Then the unknown parameters can be
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.
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.
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.
结合卡尔曼滤波的城市路段速度估计%Urban link speed estimation with Kalman filter
Institute of Scientific and Technical Information of China (English)
曾伟良; 何兆成; 沙志仁; 佘锡伟
2013-01-01
本文以城市出租车为浮动车数据采集源,介绍了基于GPS数据的实时路段速度估计的基本方法.针对目标路段GPS数据样本量不足的情况,考虑邻近区域的路段速度、上周同日速度、前一时刻速度等与目标路段当前时刻速度等密切相关的变量,建立多元线性回归方程,利用卡尔曼滤波融合预测值和测量值,从而提高路段行驶速度的估计精度.选择广州市东风路作为测试实例,融合值比测量值误差降低9％,绝对相对误差变动系数减少4％,表明结合卡尔曼滤波技术的城市路段速度估计精度和稳定性均得到提高.%Regarded taxi as the source of probe vehicle data, a basic approach of urban real-time link speed estimation based on GPS data was introduced. Aimed at the condition of insufficient samples of GPS data, a multi-linear regression model was established by considering several variables such as the speeds of neighboring links, the speed of the objective link last week, and the previous speed of the objective link and so on, which closely relate to the real-time speed of the objective link. In order to improve the estimation precision, Kalman filter was adopted to merge the measured value and the predicted value. A case study of Dongfeng road in Guangzhou city was selected to test the proposed method and the experimental result indicated that the mean absolute percent error reduced 9% and the coefficient of absolute percent error alteration reduced 4%.
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.
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.
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.
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.
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...
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.
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...
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.
Identification Filtering with fuzzy estimations
Directory of Open Access Journals (Sweden)
J.J Medel J
2012-10-01
Full Text Available A digital identification filter interacts with an output reference model signal known as a black-box output system. The identification technique commonly needs the transition and gain matrixes. Both estimation cases are based on mean square criterion obtaining of the minimum output error as the best estimation filtering. The evolution system represents adaptive properties that the identification mechanism includes considering the fuzzy logic strategies affecting in probability sense the evolution identification filter. The fuzzy estimation filter allows in two forms describing the transition and the gain matrixes applying actions that affect the identification structure. Basically, the adaptive criterion conforming the inference mechanisms set, the Knowledge and Rule bases, selecting the optimal coefficients in distribution form. This paper describes the fuzzy strategies applied to the Kalman filter transition function, and gain matrixes. The simulation results were developed using Matlab©.
Rochoux, M. C.; Emery, C.; Ricci, S.; Cuenot, B.; Trouve, A.
2015-08-01
This paper is the second part in a series of two articles, which aims at presenting a data-driven modeling strategy for forecasting wildfire spread scenarios based on the assimilation of the observed fire front location and on the sequential correction of model parameters or model state. This model relies on an estimation of the local rate of fire spread (ROS) as a function of environmental conditions based on Rothermel's semi-empirical formulation, in order to propagate the fire front with an Eulerian front-tracking simulator. In Part I, a data assimilation (DA) system based on an ensemble Kalman filter (EnKF) was implemented to provide a spatially uniform correction of biomass fuel and wind parameters and thereby, produce an improved forecast of the wildfire behavior (addressing uncertainties in the input parameters of the ROS model only). In Part II, the objective of the EnKF algorithm is to sequentially update the two-dimensional coordinates of the markers along the discretized fire front, in order to provide a spatially distributed correction of the fire front location and thereby, a more reliable initial condition for further model time-integration (addressing all sources of uncertainties in the ROS model). The resulting prototype data-driven wildfire spread simulator is first evaluated in a series of verification tests using synthetically generated observations; tests include representative cases with spatially varying biomass properties and temporally varying wind conditions. In order to properly account for uncertainties during the EnKF update step and to accurately represent error correlations along the fireline, it is shown that members of the EnKF ensemble must be generated through variations in estimates of the fire's initial location as well as through variations in the parameters of the ROS model. The performance of the prototype simulator based on state estimation (SE) or parameter estimation (PE) is then evaluated by comparison with data taken from
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.
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...
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.
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.
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.
Institute of Scientific and Technical Information of China (English)
朱岩; 付巍
2014-01-01
In order to resolve the problem of attitude estimation for four rotor unmanned aircraft ,unscented kalman filter (UKF) attitude estimation algorithm was proposed .Firstly ,Euler method was employed to de-scribe the aircraft attitude solution model ,and based on the solution model ,the aircraft system state equation and observation equation were established .Secondly ,UKF was used to obtain the attitude angles .The theory analysis and simulation results show that ,compared with the spacecraft attitude angle information obtained by extended Kalman filter algorithm ,although calculation time of UKF is slightly longer than that of extended kalman filter (EKF) ,the calculation accuracy and convergence rate of UKF is significantly higher than that of EK F .%针对四旋翼无人飞行器姿态测量问题，提了一种基于无迹卡尔曼滤波的飞行器姿态估计算法。采用欧拉角法描述了飞行器的姿态解算模型，并在此基础上建立了飞行器的系统状态方程和观测方程；采用无迹卡尔曼滤波算法实现飞行器姿态角的解算。理论分析和仿真表明：与采用扩展卡尔曼滤波算法获得的飞行器姿态角信息相比较，虽然无迹卡尔曼滤波算法的计算时间稍有增加，但无迹卡尔曼滤波算法的计算精度和收敛速度比扩展卡尔曼滤波算法有显著的提高。
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.
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.
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.
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....
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.
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...
基于Kalman过滤器的实时拖拉机位置确定系统%Real-Time Tractor Position Estimation System Using a Kalman Filter
Institute of Scientific and Technical Information of China (English)
郭林松; 何勇; 张勤; 韩树丰
2002-01-01
该文提出了一个实时拖拉机位置确定系统,该系统由一个六轴惯性测量单元(IMU)和一个Garmin全球定位系统(GPS)组成.在系统中,设计了一个Kalman过滤器来综合两个传感器的信号,以滤去GPS信号中的噪音,融合冗余信息,最后得到一个有较高更新速度的输出信号.此外该系统还能够补偿IMU的偏移误差.通过使用该系统,低价的GPS可以替代高价的GPS,并且保持良好的精确性.试验和融合结果表明该系统确定的拖拉机位置误差比单一使用GPS的系统的误差要大大减小:当拖拉机速度约为1.34 m/s时,该系统东向轴的平均偏差为0.48 m,而GPS的平均偏差为1.28 m;北向轴的偏差从1.48 m降为0.32 m.系统的更新频率则从原有GPS的1Hz增加到9Hz.%A real-time tractor position estimation system, which consists of a six-axis inertial measurement unit (IMU) and a Garmin global positioning system (GPS) was developed. A Kalman filter was designed to integrate the signals from both sensors so that the noise in GPS signal was smoothed out, the redundant information fused and a high update rate of output signals obtained. The drift error of IMU was also compensated. By using this system, a low cost GPS can be used to replace expensive one with a high accuracy. Test and fusion results showed that the positioning error of the tractor estimated using this system was greatly reduced from a GPS-only system. At a tractor speed of about 1.34 m/s, the mean bias in easting axis of the system was 0.48 m, comparing to the GPS mean bias of 1.28 m, and the mean bias in northing axis was reduced from 1.48 m to 0.32 m. The update frequency of the GPS system was increased from 1 to 9 Hz.
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
Institute of Scientific and Technical Information of China (English)
冯尚明; 杨波
2009-01-01
A speed estimation method of linear induction motor(LIM) using a novel extended kalman filter(EKF) was presented in this paper. The modification for dynamic end effect of LIM was designed to achieve exact estimation results when LIM ran at high speed. A new approach of optimizing the performance of the extended kalman filter using simulated annealing genetic algorithm (SAGA) was compared with the use of a genetic algorithm(GA). The optimization techniques are verified effective by simulation on a field-oriented controller under various operating conditions including motor parame-ter sensitivity and load disturbance.%采用一种新颖的扩展卡尔曼滤波器(EKF)实现了对直线感应电动机的速度检测,并考虑边端效应的影响进行了修正.采用模拟退火遗传算法(SAGA)对EKF性能进行优化,并与遗传算法(GA)优化的EKF进行了比较,表明SAGA具有更强的寻优能力.包括电机参数变化、负载扰动等情况下的仿真结果证明了该方案的有效性.
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.
Institute of Scientific and Technical Information of China (English)
苏卫强; 张如花; 王超
2013-01-01
A feedforward timing estimation algorithm of MSK short-term burst signal base on Kalman filtering is intro-duced, which was proposed by M. Moreli and U. Mengali. An improvement algorithm of timing estimation based on Kalman filter-ing is presented to solve the problem that the estimation capacity of the algorithm has degraded for dealing with MSK short-term burst signal. The optimal filter parameter is acquired by Monte Carlo tests, all of which turns out to be better accuracy. The al-gorithm was simulated with Matlab. The result proved the feasibility and effectiveness of the method proposed in the paper. In the actual engineering application, the algorithm was realized and the timing information of MSK short-term burst signal was re-covered by Intel IPP signal-processing function library.%给出了一种利用卡尔曼滤波的短时突发MSK前向定时估计算法.首先介绍了M.Moreli及U.Mengali的MSK前向定时估计算法,并针对算法在处理短时突发MSK定时估计性能下降的问题,提出了一种基于卡尔曼滤波的定时估计的改进方法,并利用Monte Carlo实验选取最优滤波参数,提高了定时估计的精度.最后,对算法进行了Madab仿真,证明了该方法的可行性及有效性,并在实际的工程应用中,利用Intel IPP信号处理函数库编程实现该算法,恢复了突发MSK调制信号的定时信息.
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.
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...
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
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.
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....
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.
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.
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.
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].
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.
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
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.
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
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.
Institute of Scientific and Technical Information of China (English)
张传斌; 田蔚风; 金志华
2005-01-01
In a land vehicle navigation system, generally the Extended Kalman Filter (EKF) is as a state estimation method to improve the accuracy of navigation. However, as defects of the EKF in nonlinear estimation, there exists estimated error, which affects the accuracy of the navigation system, when it is adopted in nonlinear estimation of a navigation system. In order to yield the higher accuracy of navigation, a novel method-Unscented Kalman Filter (UKF) was employed in state estimation for a land vehicle navigation system. For a land vehicle DR/GPS navigation system, the EKF and UKF are compared through simulation. Simulation results show that the UKF is superior to the EKF in state estimation for a land vehicle navigation system.%在车载导航系统中,通常采用EKF作为状态估计方法提高导航的精度.由于EKF进行非线性估计存在一些缺陷,因此将其用于导航系统的非线性估计时,存在估计误差,从而影响导航系统的精度.为了获得更高的导航精度,将一种新的滤波方法-UKF方法用于车载导航系统的状态估计中.对一个车载DR/GPS组合系统,将EKF和UKF方法分别进行了滤波仿真.仿真结果表明:在车载导航状态估计中,UKF方法优于EKF方法.
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
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.
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.
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.
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).
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.
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.
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.
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...
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.
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.
Institute of Scientific and Technical Information of China (English)
李雪松; 李颖晖; 李霞; 王志科
2011-01-01
针对一般多输入多输出不确定系统,提出一种基于鲁棒时变卡尔曼滤波的估计算法.该方法将时变卡尔曼滤波与自适应神经网络相结合,利用自适应神经网络克服外界非线性不确定因素,采用两个误差信号对其进行训练以提高估计精度,并对估计误差有界性进行证明.将该方法用于无人机视觉编队视线信息的状态估计,仿真结果表明该算法能够很好地估计不确定机动长机的加速度,实现了僚机对长机的有效跟踪.%A robust time-varying Kalman filter for a class of multi-input multi-output uncetain system is proposed. This method combines a time-varying Kalman filter with an adaptive neural network. It can overcome nonlinear uncertainty with the adaptive neural network trained by two error signals. The method can improve approaching precision, and the boundedness of the estimation error is proven by the Lyapunov theory. The proposed method is used to design state estimation of leader in the unmanned aerial vehicle(UAV) formation flight. Simulation results show that the method can estimate acceleration of leader flying with uncertain maneuvers. The follower can effectively track the leader. Thus effectiveness of the method is validated.
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 (...
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
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
Directory of Open Access Journals (Sweden)
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...
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...
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.
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.
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.
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.
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.
Real-Time Diagnosis of Faults Using a Bank of Kalman Filters
Kobayashi, Takahisa; Simon, Donald L.
2006-01-01
or actuator fault occurs, large estimation errors are generated by all filters except the one using the correct hypothesis. By monitoring the residual output of each filter, the specific fault that has occurred can be detected and isolated on the basis of the decision rules. A set of parameters that indicate the performance of the engine components is estimated by the "correct" Kalman filter for use in detecting component faults. To reduce the loss of diagnostic accuracy and sensitivity in the face of aging, the FDI system accepts information from a steady-state-condition-monitoring system. This information is used to update the Kalman filters and a data bank of trim values representative of the current aging condition.
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.
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...
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...
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
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.
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.
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.
Institute of Scientific and Technical Information of China (English)
QI Wen-Juan; ZHANG Peng; DENG Zi-Li
2014-01-01
This paper deals with the problem of designing robust sequential covariance intersection (SCI) fusion Kalman filter for the clustering multi-agent sensor network system with measurement delays and uncertain noise variances. The sensor network is partitioned into clusters by the nearest neighbor rule. Using the minimax robust estimation principle, based on the worst-case conservative sensor network system with conservative upper bounds of noise variances, and applying the unbiased linear minimum variance (ULMV) optimal estimation rule, we present the two-layer SCI fusion robust steady-state Kalman filter which can reduce communication and computation burdens and save energy sources, and guarantee that the actual filtering error variances have a less-conservative upper-bound. A Lyapunov equation method for robustness analysis is proposed, 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 of the local and fused robust Kalman filters are proved. It is proved that the robust accuracy of the global SCI fuser is higher than those of the local SCI fusers and the robust accuracies of all SCI fusers are higher than that of each local robust Kalman filter. A simulation example for a tracking system verifies the robustness and robust accuracy relations.
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.
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.
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.
Study on Vehicle Speed Estimation based on Central Difference Kalman Filter%基于中心差分卡尔曼滤波的车速估计研究
Institute of Scientific and Technical Information of China (English)
解瑞春; 卫绍元; 李刚
2015-01-01
针对车辆行驶过程中车速估计问题，论文基于中心差分卡尔曼滤波理论设计了车速的估计算法。建立了非线性三自由度车辆估算模型，根据纵向加速度、侧向加速度和方向盘转角低成本传感器信号的信息融合，实现对车速的准确估计，应用CarSim与Matlab/Simulink联合仿真实验对算法进行验证。结果表明：估计算法能够准确估计车辆行驶过程中的纵向车速、侧向车速和质心侧偏角。%For the vehicle speed estimated problem in the process of vehicle driving.the algorithm was Proposed to estimate the vehicle speed based on Central Difference Kalman Filter. The Nonlinear 3-DOF vehicle estimated model was build. Through the information fusion between the Longitudinal Acceleration, Lateral Acceleration and steering wheel angle. The algorithm is verified by CarSim and Matlab/Simulink Co-Simulation. The results show that the estimation algorithm can accurately estimate the Longitudinal speed, Lateral speed and vehicle slip angle.
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.
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.
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.
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.
基于卡尔曼滤波的多径估计延迟锁定环算法%A Multipath Estimating Delay Lock Loop Based on Kalman Filter
Institute of Scientific and Technical Information of China (English)
胡辉; 张雪丽; 方玲; 杨德进; 欧敏辉
2015-01-01
The multipath estimating delay lock loop needs massive correlators,and it is difficult to guarantee the multipath mitigation performance in the case of low SNR.Aiming at the problems,a multipath estimating delay lock loop based on Kalman filter (K-MEDLL)was presented in this paper.The algorithm utilized Kalman Filter to filter the correlators output so as to suppress the noise;then,estimatied the parameters of multipath signal by utilizing MEDLL to separate the direct signal from the received signal.Simulation results showed that the code error of K-MEDLL was 0.1 6 chips less than MEDLL when using 41 correlators,and 0.08 chips less than MEDLL in the case of 201 correlators.Meanwhile,when the SNR was-30dB,the code error varied significant-ly,the maximum code error of MEDLL was up to 0.48 chips,whereas the code error of K-MEDLL did not vary obviously,the maximum code error was up to 0.08 chips.%针对多径估计延迟锁定环(MEDLL-Multipath Estimating Delay Lock Loop)算法所需相关器数量大,并在低信噪比时难以保证多径抑制效果的问题,提出了基于卡尔曼滤波(KF)的多径估计延迟锁定环算法。该算法首先用 KF 对相关器输出进行噪声抑制,然后用 MEDLL 来估计多径信号的幅度、相位和码延迟等参数,通过消除多径信号来得到直达信号。仿真结果表明：当采用41路相关器时,K-MEDLL 算法比 MEDLL 算法的伪码误差减小了0.16 chip,这比采用了201路相关器的 MEDLL 算法的伪码误差还少0.08 chip；当信噪比为-30 dB 时,MEDLL 算法的多径误差包络变化剧烈,最大误差为0.48 chip,K-MEDLL 的多径包络误差比较平缓,最大误差为0.08 chip。
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.
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.
Power grid integration using Kalman filtering
Djerf, Magnus
2012-01-01
Renewable power sources with a relatively uneven or constant DC power production require synchronization methods to work with the current utility power grid. The solution to this synchronization problem has been solved with semiconductor based converters and advanced switching algorithms. To enable switching algorithms that work well with the grids amplitude, phase-shift and frequency, the current waveform has to be measured and estimated. There are many sources of noise that will add dist...
When long memory meets the Kalman filter
DEFF Research Database (Denmark)
Grassi, Stefano; Santucci de Magistris, Paolo
2014-01-01
shifts. Missing values and several alternative sources of misspecification are also considered. It emerges that the state space methodology provides a valuable alternative for the estimation of the long memory models, under different data generating processes, which are common in financial and economic......The finite sample properties of the state space methods applied to long memory time series are analyzed through Monte Carlo simulations. The state space setup allows to introduce a novel modeling approach in the long memory framework, which directly tackles measurement errors and random level...
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
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.
Rapid Transfer Alignment of MEMS SINS Based on Adaptive Incremental Kalman Filter
Directory of Open Access Journals (Sweden)
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.
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.
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 .