Dynamic 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.

Robust Weighted Fusion Kalman Estimators for Networked Multisensor Mixed Uncertain Systems With Random One-Step Sensor Delays, Uncertain-Variance Multiplicative, and Additive White Noises

For networked multisensor systems with mixed uncertainties, including random one-step sensor delays, multiplicative noises and uncertain noise variances, a new augmented state approach with the fictitious noises is presented, by which the original system model is transformed into one without sensor delays and only with white noises. An extended Lyapunov equation approach with two Lyapunov equations is presented, which is applied to prove the robustness of the estimators. According to the minimax robust estimation principle, based on the worst-case system with conservative upper bounds of uncertain noise variances, the four weighted fusion robust time-varying and steady-state Kalman estimators (predictor, filter and smoother) are presented in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their robustness and accuracy relations are proved, and their convergence in a realization is proved by the dynamic error system analysis (DESA) method. Specially, the presented modified robust covariance intersection (CI) fuser has higher robust accuracy than the original one. A simulation example applied to the uninterruptible power system (UPS) shows the effectiveness of the proposed approaches and results.

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.

Robust weighted state fusion Kalman estimators for networked systems with mixed uncertainties

This paper is concerned with robust weighted state fusion estimation problem for a class of time-varying multisensor networked systems with mixed uncertainties including uncertain-variance multiplicative and linearly correlated additive white noises, and packet dropouts. By augmented state method and fictitious noise technique, the original system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, four weighted state fusion robust Kalman estimators (filter, predictor and smoother) are presented in a unified form that the robust filter and smoother are designed based on the robust Kalman predictor. Their robustness is proved by the Lyapunov equation approach in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their accuracy relations are proved. The corresponding robust local and fused steady-state Kalman estimators are also presented, 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. Finally, a simulation example applied to uninterruptible power system (UPS) shows the correctness and effectiveness of the proposed results.

Robust Kalman estimators for systems with mixed uncertainties

SummaryThis paper addresses the problem of designing robust Kalman estimators for uncertain systems with mixed uncertainties including the same uncertain‐variance multiplicative noise in state and measurement matrices, missing measurements, and uncertain‐variance linearly correlated measurement and process white noise. By introducing fictitious noise to compensate for multiplicative noise, the system under consideration is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, on the basis of the worst‐case system with known conservative upper bounds of uncertain variances, the minimax robust time‐varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved by using a Lyapunov equation approach, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The corresponding robust steady‐state Kalman estimators are also presented, and 3 modes of convergence in a realization among the time‐varying and steady‐state robust Kalman estimators for the time‐varying and time‐invariant systems are presented and proved by the dynamic error system analysis method. A simulation example with application to autoregressive signal processing is also given to show the effectiveness and correctness of the proposed results.

Robust Kalman estimators for systems with multiplicative and uncertain-variance linearly correlated additive white noises

For linear discrete-time stochastic systems with mixed uncertainties including multiplicative and uncertain-variance linearly correlated additive white noises, this paper addresses the problem of designing robust Kalman estimators. By the fictitious noise-based Lyapunov equation approach, the system under consideration is converted into one with only uncertain noise variances. Based on the worst-case system with conservative upper bounds of actual noise variances, the minimax robust time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The corresponding robust steady-state Kalman estimators are also presented. An innovation test rule and a search technique of selecting the less-conservative upper bounds of actual noise variances are presented, by which the two classes of guaranteed robust accuracy Kalman estimators are presented. One class is robust Kalman estimators with improved robust accuracy, the other class is ones with the prescribed robust accuracy index. Three modes of convergence in a realization among the time-varying and steady-state robust Kalman estimators for the time-varying and time-invariant systems are presented and proved by the dynamic error system analysis (DESA) method. Two simulation examples applied to autoregressive (AR) signal processing and uninterruptible power system (UPS) show the effectiveness of the proposed results.

Robust Centralized and Weighted Measurement Fusion Kalman Predictors with Multiplicative Noises, Uncertain Noise Variances, and Missing Measurements

For multisensor uncertain systems with mixed uncertainties, including multiplicative noises in state and process noise transition matrices, uncertain-variance multiplicative and additive white noises, and missing measurements, this paper addresses the problem of designing robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman predictors. By introducing fictitious noises, the system under study is converted into a system with only uncertain noise variances. According to the minimax robust estimation principle, which is based on the worst-case system with conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman predictors are presented in a unified framework. Using the Lyapunov equation, the robustness of these predictors is proven in the sense that the actual prediction error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using an information filter, they are proven to have the same robust and actual accuracies. The complexity analysis shows that when the number of sensors is larger, the WMF algorithm more significantly reduces the computational burden than the CF algorithm. The corresponding robust fused steady-state Kalman predictors are also presented. The three modes of convergence in a realization among the time-varying and steady-state robust fused Kalman predictors are proposed and proven using the dynamic error system analysis method. Two simulation examples, autoregressive moving average signal processing and an uninterruptible power system, demonstrate the effectiveness of the proposed methods.

Robust weighted fusion Kalman estimators for systems with multiplicative noises, missing measurements and uncertain-variance linearly correlated white noises

For linear discrete time-varying and time-invariant multisensor uncertain systems with multiplicative noises, missing measurements and uncertain-variance linearly correlated white noises, by introducing the fictitious noises to compensate the stochastic uncertainties, the system under consideration can be converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with conservative upper bounds of uncertain noise variances, the four robust weighted state fusion time-varying and steady-state Kalman estimators (predictor, filter, smoother) are presented respectively. They include the three fusers weighted respectively by matrices, scalar and diagonal matrices and a new modified covariance intersection (CI) fuser. They are designed in a unified framework, such that the filters and smoothers are designed based on the predictors. By the Lyapunov equation approach, their robustness is proved in the sense that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. The convergence in a realization between the robust fused time-varying and steady-state Kalman estimators for the time-varying and time-invariant systems are proved by the dynamic error system analysis (DESA) method. Their accuracy relations are also proved. A simulation example applied to uninterruptible power system (UPS) shows the effectiveness of the proposed results.

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 centralized and weighted measurement fusion Kalman estimators for multisensor systems with multiplicative and uncertain-covariance linearly correlated white noises

This paper addresses the design of robust centralized and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated measurement and process white noises. The uncertainties of the systems include the same multiplicative noises in state and measurement matrices, and the uncertain noise variances. By introducing the fictitious noises to compensate the multiplicative noises, the system under consideration is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of the noise variances, the robust centralized and two WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved by using Lyapunov equation approach, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities are analyzed and compared. Compared with the centralized fusion algorithm, the two WMF algorithms can significantly reduce the computational burden when the number of sensors is larger. The corresponding robust local and fused steady-state Kalman estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused Kalman estimators is proved by the dynamic error system analysis (DESA) method. A simulation example with application to signal processing to show the effectiveness and correctness of the proposed results.

Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises

This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include multiplicative noises, missing measurements, and uncertain noise variances. By introducing the fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities of their algorithms are analyzed and compared. Compared with CF algorithm, the WMF algorithm can significantly reduce the computational burden when the number of sensors is larger. A robust weighted least squares (WLS) measurement fusion filter is also presented only based on the measurement equation, and it is proved that the robust accuracy of the robust CF or WMF Kalman filter is higher than that of robust WLS filter. The corresponding robust fused steady-state estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused estimators is proved by the dynamic error system analysis (DESA) method. A simulation example shows the effectiveness and correctness of the proposed results.

Self‐tuning fusion Kalman filter weighted by scalars and its convergence analysis for multi‐channel autoregressive moving average signals

SummaryFor the multi‐sensor multi‐channel autoregressive (AR) moving average signals with white measurement noises and an AR‐colored measurement noise, a multi‐stage information fusion identification method is presented when model parameters and noise variances are partially unknown. The local estimators of model parameters and noise variances are obtained by the multidimensional recursive instrumental variable algorithm and correlation method, and the fused estimators are obtained by taking the average of the local estimators. They have the strong consistency. Substituting them into the optimal information fusion Kalman filter weighted by scalars, a self‐tuning fusion Kalman filter for multi‐channel AR moving average signals is presented. Applying the dynamic error system analysis method, it is proved that the proposed self‐tuning fusion Kalman filter converges to the optimal fusion Kalman filter in a realization, so that it has asymptotic optimality. A simulation example for a target tracking system with three sensors shows its effectiveness. Copyright © 2014 John Wiley & Sons, Ltd.

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 Measurement Fusion Kalman Predictors with Uncertain Noise Variances

For the multisensor system with uncertain noise variances, using the minimax robust estimation principle, the local and weighted measurement fusion robust time-varying Kalman predictors are presented based on the worst-case conservative system with the conservative upper bound of noise variances. The actual prediction error variances are guaranteed to have a minimal upper bound for all admissible uncertainties 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 weighted measurement robust fuser is higher than that of each local robust Kalman predictor. Specially, the corresponding steady-state robust local and weighted measurement fusion Kalman predictors are also proposed and the convergence in a realization between time-varying and steady-state Kalman predictors is proved by the dynamic error system analysis (DESA) method. A Monte-Carlo simulation example shows the effectiveness of the robustness and accuracy relations. DOI : http://dx.doi.org/10.11591/telkomnika.v12i6.5453 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.

Hierarchical fusion robust Kalman filter for clustering sensor network time‐varying systems with uncertain noise variances

SUMMARYFor the clustering time‐varying sensor network systems with uncertain noise variances, according to the minimax robust estimation principle, based on the worst‐case conservative system with conservative upper bounds of noise variances, applying the optimal Kalman filtering, the two‐level hierarchical fusion time‐varying robust Kalman filter is presented, where the first‐level fusers consist of the local decentralized robust fusers for the clusters, and the second‐level fuser is a global decentralized robust fuser for the cluster heads. It can reduce the communication load and save energy resources of sensors. Its robustness is proved by the proposed Lyapunov equation method. The concept of robust accuracy is presented, and the robust accuracy relations of the local, decentralized, and centralized fused robust Kalman filters are proved. Specially, the corresponding steady‐state robust local and fused Kalman filters are also presented, and the convergence in a realization between the time‐varying and steady‐state robust Kalman filters is proved by the dynamic error system analysis method. A simulation example shows correctness and effectiveness. Copyright © 2013 John Wiley & Sons, Ltd.