Robust fusion steady‐state estimators for networked stochastic uncertain systems with packet dropouts and missing measurements

Abstract

In this article, the robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties. The uncertainties include state‐dependent and noise‐dependent multiplicative noises, missing measurements, packet dropouts, and uncertain noise variances, the phenomena of missing measurements and packet dropouts occur in a random way, and are described by two Bernoulli distributed random variables with known conditional probabilities. Using a model transformation approach, which consists of augmented approach, de‐randomization approach and fictitious noise approach, the original multisensor system under study is converted into a multi‐model multisensor system with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the optimal fusion algorithm weighted by matrices, the robust distributed weighted state fusion steady‐state Kalman estimators are derived for the considered system. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of non‐negative definite matrix, matrix representation approach of quadratic form, and Lyapunov equation approach, such that for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady‐state Kalman estimators are proved. An example with application to autoregressive moving average (ARMA) signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.

Robust weighted fusion Kalman estimators for systems with uncertain noise variances, multiplicative noises, missing measurements, packets dropouts and two‐step random measurement delays

“…The proposed results expand the research of robust Kalman estimation problem for system with mixed uncertainties in the literature, such as the uncertain noise variances are not considered in References 29,30, the only single networked-induced uncertainty is considered in References 31-33, the random measurement delay, 34 the packet dropouts, 35,36 and missing measurement 37 are not considered. The robust FCI fusion Kalman estimation problem is seldom considered.…”

“…Following Reference 16, the robust Kalman estimation problem for system with uncertain noise variance, multiplicative noise and single networked‐induced uncertainty are addressed in References 31–33, where packet dropouts 31,32 and one‐step measurements delay 33 are considered respectively. Further, the robust fusion Kalman estimation problem for system with two networked‐induced uncertainties are addressed in References 34–37, where missing measurements and packets dropouts, 34 random measurements delay and missing measurements, 35,36 random measurements delay and packets dropouts 37 are considered, respectively. However, robust weighted fusion estimation problem for system with uncertainties of noise variance, multiplicative noise and multiple networked‐inducements, including missing measurements, packets dropouts and two‐step measurement delays, has not been presented in existing literature.…”

Robust weighted fusion Kalman filters under linearly correlated noise and mixed uncertainties of noise variances, multiplicative noises, and multiple networked inducements

“…The robust filtering problem for networked systems with modeling uncertainty and networked-induced uncertainties has also received research interest [30][31][32][33][34][35][36][37][38][39]. For example, suppose that noise statistics are accurately known, an optimal weighted fusion filter weighted by matrix is proposed by an innovation approach for systems with multiplicative noises and correlated random delays in transmission in [30], and the optimal filtering problem is addressed for systems with multiplicative noises, packet dropouts, input delays, and measurement delays in [32].…”

“…On the other hand, the problem of RKFs is addressed for system with UBBA noise variance, multiplicative noise, and a single networked-induced uncertainty in [34,35], where packet dropouts [34] and missing measurements [35] are considered respectively. Further, the problem of weighted fusion RKFs for system with two kinds of networked-induced uncertainties is solved in [36,37], where random measurements delay and missing measurements [36] and missing measurements and packets dropouts [37] are considered.…”

“…However, to the best of the author's knowledge, weighted fusion RKFs problem for systems under linearly correlated noise and mixed uncertainties of UBBA noise variance, multiplicative noises, and multiple networked inducements including missing measurements, packets dropouts, and two-step random measurement delays has not been presented in existing literatures. The uncertain noise variances are not considered in [24][25][26][27][28][29][30][31][32][33], at most two kinds of networked-induced uncertainties are considered in [34][35][36][37], and two-step random measurement delays are still not considered. Furthermore, the fast CI fusion (FCI) method can reduce the computation burden significantly in the distributed networked system, but there is little relative research [38].…”