Dynamic Variance Error System Analysis Research Articles

Robust integrated sequential covariance intersection fusion Kalman filters and their convergence and stability for networked sensor systems with five uncertainties

AbstractFor networked sensor systems (NSSs) with hard and soft sensors including five uncertainties, two universal approaches of solving the robust fusion estimation problems are presented. It includes an integrated sequential covariance intersection (SCI) fusion minimax robust Kalman filtering approach with cross‐covariance information and a generalized Lyapunov equation approach with four pairs of Lyapunov equations. Applying them, the robust local and SCI fused time‐varying and steady‐state Kalman filters are presented in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. The equivalent batch SCI fusers are also presented. Their robustness and accuracy relations are proved, and the sensitivity of the SCI fuser with respect to the fused orders of sensors is analyzed. Applying the dynamic error system analysis method and the dynamic variance error system analysis method, a new convergence and absolute asymptotic stability theory of robust fusion Kalman filtering is presented. The classical Kalman filtering convergence and stability theory is developed. Compared with the original covariance intersection fuser, they significantly reduced the computational complexity and burden. Compared with the optimal and conservative SCI fusers, they significantly improved the robust accuracies. They are suitable to deal with asynchronous or random delayed data and are suitable for real‐time applications. A simulation applied to the two‐mass spring damper mechanical system shows their effectiveness.

Sequential Covariance Intersection Fusion Robust Time-Varying Kalman Filters with Uncertainties of Noise Variances for Advanced Manufacturing.

This paper addresses the robust Kalman filtering problem for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of noise variances, the robust local time-varying Kalman filters are presented. Further, the batch covariance intersection (BCI) fusion and a fast sequential covariance intersection (SCI) fusion robust time-varying Kalman filters are presented. They have the robustness that the actual filtering error variances or their traces are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. Their robustness is proved based on the proposed Lyapunov equations approach. The concepts of the robust and actual accuracies are presented, and the robust accuracy relations are proved. It is also proved that the robust accuracies of the BCI and SCI fusers are higher than that of each local Kalman filter, the robust accuracy of the BCI fuser is higher than that of the SCI fuser, and the actual accuracies of each robust Kalman filter are higher than its robust accuracy for all admissible uncertainties of noise variances. The corresponding steady-state robust local and fused Kalman filters are also presented for multisensor time-invariant systems, and the convergence in a realization between the local and fused time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and the correctness of the robust accuracy relations.

WMF self-tuning Kalman estimators for multisensor singular system

For the multisensor linear stochastic singular system with unknown noise variances, the weighted measurement fusion (WMF) self-tuning Kalman estimation problem is solved in this paper. The consistent estimates of these unknown noise variances are obtained based on the correlation method. Applying the WMF method and the singular value decomposition (SVD) method yields the WMF reduced-order subsystems. Based on these consistent estimates of unknown noise variances and the new non-singular systems, the WMF self-tuning Kalman estimators of the state components and white noise deconvolution estimators are presented. Then the WMF self-tuning Kalman estimators of the original state are presented, and their convergence has been proved by dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example of 3-sensors circuits systems verifies the effectiveness, the accuracy relationship and the convergence.

Robust Time-Varying Kalman State Estimators with Uncertain Noise Variances

This paper addresses the design of robust Kalman estimators (filter, predictor and smoother) for the time-varying system with uncertain noise variances. According to the unbiased linear minimum variance (ULMV) optimal estimation rule, the robust time-varying Kalman estimators are presented. Specially, two robust Kalman smoothing algorithms are presented by the augmented and non-augmented state approaches, respectively. They have the robustness in the sense that their actual estimation error variances are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. Their robustness is proved by the Lyapunov equation approach, and their robust accuracy relations are proved. The corresponding steady-state robust Kalman estimators are also presented for the time-invariant system, and the convergence in a realization between the time-varying and steady-state robust Kalman estimators is proved by the dynamic error system analysis (DESA) method and the dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.

Self‐tuning full‐order WMF Kalman filter for multisensor descriptor systems

For the multisensor descriptor systems with correlated measurement noises and unknown noise variances, a self-tuning full-order weighted measurement fusion (WMF) Kalman filter is presented. First, based on the controlled autoregressive moving average innovation model of the multisensor descriptor systems, the consistent estimates of the unknown noise variances are obtained applying correlation function method. A compressed measurement equation for the multisensor descriptor systems is obtained by the WMF method, and an optimal full-order WMF descriptor Kalman filter is given. Based on the optimal full-order WMF Kalman filter and the estimates of noise variances, a self-tuning full-order WMF Kalman filter with the self-tuning descriptor Riccati equation is presented. By the dynamic variance error system analysis method, it is proven that the solution of the self-tuning descriptor Riccati equation converges to the solution of the optimal descriptor Riccati equation. Then, the convergence of the presented self-tuning full-order WMF Kalman filter is proven. A simulation example of a six-sensor descriptor system verifies the effectiveness and convergence of the presented algorithms.

Robust weighted fusion time-varying Kalman smoothers for multisensor system with uncertain noise variances

This paper addresses the design of robust weighted fusion time-varying Kalman smoothers for multisensor time-varying system with uncertain noise variances by the augmented state approach. According to the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) optimal estimation rule, the six robust weighted fusion time-varying Kalman smoothers are presented based on the worst-case conservative system with the conservative upper bounds of noise variances. The actual smoothing error variances of each fuser are guaranteed to have a minimal upper bound for all admissible uncertainties. Their robustness is proved by the Lyapunov equation approach. Their robust accuracy relations are analyzed and proved. Specially, the corresponding steady-state robust Kalman smoothers are also presented for multisensor time-invariant system, and the convergence in a realization between the time-varying and steady-state robust Kalman smoothers is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.

Robust Centralized Fusion Kalman Filters with Uncertain Noise Variances

This paper studies the problem of the designing the robust local and centralized fusion Kalman filters for multisensor system with uncertain noise variances. Using the minimax robust estimation principle, the centralized fusion robust time-varying Kalman filters are presented based on the worst-case conservative system with the conservative upper bound of noise variances. A Lyapunov approach is proposed for the robustness analysis and their robust accuracy relations are proved. It is proved that the robust accuracy of robust centralized fuser is higher than those of robust local Kalman filters. Specially, the corresponding steady-state robust local and centralized fusion Kalman filters are also proposed and the convergence in a realization between time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A Monte-Carlo simulation example shows the robustness and accuracy relations. DOI : http://dx.doi.org/10.11591/telkomnika.v12i6.5490 Full Text: PDF

Robust weighted fusion Kalman predictors with uncertain noise variances

In this paper, the problem of designing weighted fusion robust time-varying Kalman predictors is considered for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) rule, based on the worst-case conservative system with the conservative upper bounds of noise variances, the local and five weighted fused robust time-varying Kalman predictors are designed, which include a robust weighted measurement fuser, three robust weighted state fusers, and a robust covariance intersection (CI) fuser. Their actual prediction error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties of noise variances. Their robustness is proved based on the proposed Lyapunov equation approach. The concept of the robust accuracy is presented, and the robust accuracy relations are proved. The corresponding steady-state robust local and fused Kalman predictors are also presented, and the convergence in a realization between the time-varying and steady-state robust Kalman predictors is proved by the dynamic error system analysis (DESA) method and the dynamic variance error system analysis (DVESA) method. Simulation results show the effectiveness and correctness of the proposed results.

Robust weighted fusion Kalman filters for multisensor time-varying systems with uncertain noise variances

This paper addresses the design of robust weighted fusion Kalman filters for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) optimal estimation rule, the five robust weighted fusion time-varying Kalman filters are presented based on the worst-case conservative systems with the conservative upper bounds of noise variances. The actual filtering error variances or their traces of each fuser are guaranteed to have a minimal upper bound for all the admissible uncertainties of noise variances. A Lyapunov equation approach is presented to prove the robustness of the robust Kalman filters. The concept of robust accuracy is presented and the robust accuracy relations among the local and fused robust Kalman filters are proved. Specially, the corresponding steady-state robust local and fused Kalman filters are also presented for multisensor time-invariant systems, and the convergence in a realization of the local and fused time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.

Self‐tuning weighted fusion Kalman filter for ARMA signal with colored measurement noise and its convergence analysis

SUMMARYFor the multisensor single‐channel autoregressive moving average (ARMA) signal with colored measurement noise, when the partial model parameters and the noise variance are unknown, a self‐tuning fusion Kalman filter weighted by scalar is presented based on the ARMA innovation model by the modern time series analysis method. With the application of the recursive instrumental variable algorithm and the Gevers–Wouters iterative algorithm with dead band, the information fusion estimators for the unknown model parameters and noise variance are obtained, and their consistence is proved by the existence and continuity theorem of implicit function. Then, substituting them into the optimal weighted fusion Kalman filter, one can obtain the corresponding self‐tuning weighted fusion Kalman filter. Further, with the application of the dynamic variance error system analysis method, the convergence of the self‐tuning Lyapunov equations for filtering error cross‐covariances is proved. With the application of the dynamic error system analysis method, it is rigorously proved that the self‐tuning weighted fusion Kalman filter converges to the optimal weighted fusion Kalman filter in a realization; that is, it has asymptotic optimality. A simulation example shows its effectiveness.Copyright © 2012 John Wiley & Sons, Ltd.

Self-tuning weighted measurement fusion Kalman filtering algorithm

For the multisensor linear discrete system with correlated noises and same measurement matrix, the self-tuning weighted measurement fusion Kalman filtering algorithm is presented when the model parameters and noise variances are all unknown. It can handle the self-tuning fused Kalman filtering, smoothing, and prediction problem and the input white noise deconvolution estimation problem. By the dynamic variance error system analysis (DVESA) method, it is proved that the solution of the self-tuning Riccati equation converges to the solution of the steady-state Riccati equation. Based on the convergence of the self-tuning Riccati equation, the convergence of the proposed self-tuning weighted measurement fusion Kalman estimator is proved. So it has asymptotic global optimality. Applying to the multi-channel autoregressive moving average (ARMA) signal with sensor bias, the corresponding self-tuning weighted measurement fusion Kalman estimator of the signal is also presented, where the estimates of unknown model parameters and noise variances are obtained by the multi-dimension recursive extended least squares (RELS) algorithm, the correlation method and the Gevers–Wouters algorithm with a dead band. One simulation example shows the effectiveness.

Self-Tuning Fusion Wiener Filter and Its Convergence

For the multisensor system with unknown model parameters and noise variances, based on the system identification method, the online information fusion estimators of model parameters and noise variances can be obtained. Substituting them into the optimal fused Wiener filter weighted by scalars for components, a self-tuning information fusion Wiener filter weighted by scalars for components is presented. By the dynamic error system analysis (DESA) method and the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the proposed self-tuning Wiener fuser converges to the optimal fusion Wiener fuser in a realization, so that it has asymptotic optimality. A simulation example applied to signal processing shows its effectiveness.

Convergence of self-tuning Riccati equation with correlated noises

For the linear discrete time-invariant stochastic system with correlated noises, and with unknown model parameters and noise statistics, substituting the online consistent estimators of the model parameters and noise statistics into the optimal time-varying Riccati equation, a self-tuning Riccati equation is presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self-tuning Riccati equation converges to the optimal time-varying Riccati equation. Based on this, by the dynamic error system analysis (DESA) method, it is proved that the corresponding self-tuning Kalman filter converges to the optimal time-varying Kalman filter in a realization, so that it has asymptotic optimality. As an application to adaptive signal processing, a self-tuning Kalman signal filter with the self-tuning Riccati equation is presented. A simulation example shows the effectiveness.

Self-tuning measurement fusion Kalman predictors and their convergence analysis

For multisensor systems with unknown parameters and noise variances, three self-tuning measurement fusion Kalman predictors based on the information matrix equation are presented by substituting the online estimators of unknown parameters and noise variances into the optimal measurement fusion steady-state Kalman predictors. By the dynamic variance error system analysis method, the convergence of the self-tuning information matrix equation is proved. Further, it is proved by the dynamic error system analysis method that the proposed self-tuning measurement fusion Kalman predictors converge to the optimal measurement fusion steady-state Kalman predictors in a realisation, so they have asymptotical global optimality. Compared with the centralised measurement fusion Kalman predictors based on the Riccati equation, they can significantly reduce the computational burden. A simulation example applied to signal processing shows their effectiveness.

Optimal and self‐tuning weighted measurement fusion Kalman filters and their asymptotic global optimality

AbstractFor the multisensor linear discrete time‐invariant stochastic systems with unknown noise variances, using the correlation method, the information fusion noise variance estimators with consistency are given by taking the average of the local noise variance estimators. Substituting them into two optimal weighted measurement fusion steady‐state Kalman filters, two new self‐tuning weighted measurement fusion Kalman filters with a self‐tuning Riccati equation are presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self‐tuning Riccati equation converges to the steady‐state optimal Riccati equation. Further, by the dynamic error system analysis (DESA) method, it is proved that the steady‐state optimal and self‐tuning Kalman fusers converge to the global optimal centralized Kalman fuser, so that they have the asymptotic global optimality. Compared with the centralized Kalman fuser, they can significantly reduce the computational burden. A simulation example for the target tracking systems shows their effectiveness. Copyright © 2010 John Wiley & Sons, Ltd.

Self-Tuning Decoupled Fusion Kalman Predictor and Its Convergence Analysis

For the multisensor systems with unknown noise variances, by the correlation method, the information fusion noise variance estimators are presented by taking the average of the local noise variance estimators under the least squares fusion rule. They have the average accuracy and have consistency. A self-tuning Riccati equation with the fused noise variance estimators is presented, and then a self-tuning decoupled fusion Kalman predictor is presented based on the optimal fusion rule weighted by scalars for state component predictors. In order to prove their convergence, the dynamic variance error system analysis (DVESA) method is presented, which transforms the convergence problem of the self-tuning Riccati equation into a stability problem of a dynamic variance error system described by the Lyapunov equation. A stability decision criterion of the Lyapunov equation is presented. By the DVESA method, the convergence of the self-tuning Riccati equation is proved, and then it is proved that the self-tuning decoupled fusion Kalman predictor converges to the optimal decoupled fusion Kalman predictor in a realization, so it has asymptotic optimality. A simulation example for a tracking system with 3-sensor shows the effectiveness, and verifies the convergence.

Convergence analysis of self-tuning Riccati equation for systems with correlation noises

For linear discrete time-invariant stochastic system with correlated noises, and with unknown state transition matrix and unknown noise statistics, substituting the online consistent estimators of the state transition matrix and noise statistics into steady-state optimal Riccati equation, a new self-tuning Riccati equation is presented. A dynamic variance error system analysis (DVESA) method is presented, which transforms the convergence problem of self-tuning Riccati equation into the stability problem of a time-varying Lyapunov equation. Two decision criterions of the stability for the Lyapunov equation are presented. Using the DVESA method and Kalman filtering stability theory, it proves that with probability 1, the solution of self-tuning Riccati equation converges to the solution of the steady-state optimal Riccati equation or time-varying optimal Riccati equation. The proposed method can be applied to design a new selftuning information fusion Kalman filter and will provide the theoretical basis for solving the convergence problem of self-tuning filters. A numerical simulation example shows the effectiveness of the proposed method.