Robust fusion time‐varying Kalman estimators for multisensor networked systems with mixed uncertainties

Abstract

Summary This paper addresses the problem of designing robust fusion time‐varying Kalman estimators for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, missing measurements, packet dropouts, and uncertain‐variance linearly correlated measurement and process white noises. By the augmented approach, the original system is converted into a stochastic parameter system with uncertain noise variances. Furthermore, applying the fictitious noise approach, the original system is converted into one with constant parameters and 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 five robust fusion time‐varying Kalman estimators (predictor, filter, and smoother) are presented by using a unified design approach that the robust filter and smoother are designed based on the robust Kalman predictor, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, and scalar weights, a modified robust covariance intersection fusion estimator, and robust centralized fusion estimator. Their robustness is proved by using a combination method, which consists of Lyapunov equation approach, augmented noise approach, and decomposition approach of nonnegative definite matrix, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the robust local and fused time‐varying Kalman estimators are proved. A simulation example is shown with application to the continuous stirred tank reactor system to show the effectiveness and correctness of the proposed results.

Robust fusion steady‐state filtering for multisensor networked systems with one‐step random delay, missing measurements, and uncertain‐variance multiplicative and additive white noises

“…For multisensor systems with multiplicative noises, uncertain noise variances, and correlated measurement and process noises, applying the minimax robust estimation principle and fictitious noise technique, the robust local and information fusion Kalman estimators have been proposed in some works . More concretely, for multisensor systems with same multiplicative noises in state and measurement matrices, and uncertain‐variance linearly correlated additive white noises, the weighted state fusion robust Kalman estimators are presented .…”

“…However, the missing measurements and packet dropouts are not considered in the work of Liu et al For multisensor systems with multiplicative noises in state matrix, missing measurements, and uncertain‐variance linearly correlated additive white noises, the robust centralized and weighted measurement fusion Kalman estimators are presented . However, the packet dropouts and multiplicative noises in measurement matrix are not considered in the work of Liu et al For the multisensor networked systems with mixed uncertainties including multiplicative noises in state matrix, missing measurements, packet dropouts, and uncertain noise variances, the weighted state fusion and centralized fusion robust time‐varying Kalman estimators are presented in the work of Liu et al, the limitation of the aforementioned work is that only the robust time‐varying Kalman estimators are proposed, whereas the robust steady‐state filtering problems are not studied, and the multiplicative noises in measurement matrix are not considered. For the multisensor networked systems with multiplicative noises in state and measurement matrix, packet dropouts, and uncertain noise variances, the weighted state fusion robust Kalman estimators are proposed in the work of Yang et al However, the missing measurements are not considered in the aforementioned work .…”

Distributed fusion cubature Kalman filters for nonlinear systems

“…Distributed fusion algorithms have a good performance in accuracy, computational cost, robustness, and flexibility because of the parallel processing structures . They are usually preferable in wireless sensor networks, as they allow each sensor node to process locally measurements and they are much more efficient in communication compared to the centralized fusion algorithm that must transmit all measurements .…”

Weighted fusion robust steady‐state estimators for multisensor networked systems with one‐step random delay and inconsecutive packet dropouts

“…For multisensor systems with multiplicative noises, uncertain noise variances, and correlated measurement and process noises, applying the minimax robust estimation principle and fictitious noise technique, the robust local and information fusion Kalman estimators have been proposed in other works . More concretely, for linear discrete‐time systems with same multiplicative noises in the state and measurement matrices, as well as the process and measurement noise transition matrices, and with the uncertain‐variance linearly correlated white noises, the robust time‐varying and steady‐state Kalman estimators were presented in the work of Liu et al However, it is limited to the single‐sensor systems.…”

“…For multisensor systems with same multiplicative noises in state and measurement matrices, and with uncertain‐variance linearly correlated additive white noises, the weighted state fusion robust Kalman estimators were presented in the work of Liu et al However, the noise‐dependent multiplicative noises were not considered in the work of Liu et al, and the packet dropouts were not considered in the works of the aforementioned authors . For the multisensor networked systems with mixed uncertainties including multiplicative noises in state matrix, missing measurements, packet dropouts, and uncertain noise variances, the weighted state fusion and centralized fusion robust time‐varying Kalman estimators were presented in the work of Liu et al; the limitation of the work of the aforementioned authors is that the robust steady‐state filtering problems are not studied, and the multiplicative noises in measurement matrices and noise transition matrices are not considered. For the multisensor networked systems with multiplicative noises in state and measurement matrix, packet dropouts, and uncertain noise variances, the weighted state fusion robust Kalman estimators were proposed in the work of Yang et al However, the noise‐dependent multiplicative noises were not considered in the work of the aforementioned authors .…”