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

Abstract

Summary The robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, one‐step random delay, missing measurements, and uncertain noise variances, the phenomena of one‐step random delay and missing measurements 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, derandomization approach, and fictitious noise approach, the original multisensor system under study is converted into a multimodel 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. In addition, by using the proposed model transformation approach, the centralized fusion system is obtained, furthermore the robust centralized fusion steady‐state Kalman estimators are proposed. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of nonnegative 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 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 fusion steady‐state estimators for networked stochastic uncertain systems with packet dropouts and missing measurements

“…Lemma For all admissible uncertainties, we have that Proof Similar to the proof of lemma 9 in Reference 25, we can prove Lemma 8, which is omitted.…”

Robust CAWOF Kalman predictors for uncertain multi‐sensor generalized system

“…A linear minimal variance (the optimal) Kalman estimator for generalized system in the worst-case scenario is called the minimax robust Kalman estimator. [25][26][27] Considering a generalized system with multiplicative noises, the focus of this article is to design CAWOF Kalman predictors with robustness, including CAWOF Kalman predictors x(i) (𝜏 + 1|𝜏), i = 𝜑, 𝜀 under time-variant conditions, where i = 𝜑 represents a centralized fusion predictor as well as i = 𝜀 represents a weighted observation fusion predictor. For all possible uncertainty of noise variances, there is a minimum upper bound P (i) (𝜏 + 1|𝜏) for the practical prediction error variance P (i) (𝜏 + 1|𝜏), namely,…”

“…24 During the past two decades, the study concerning robust filtering theory for uncertain stochastic systems has reinvigorated researchers' interest. [25][26][27] The existing literature [25][26][27][28] mainly uses minimax robust Kalman filtering theory and extended virtual noise method to design robust estimation algorithm. Nevertheless, it must be mentioned that previous work has rarely been able to settle the problem of robust estimation for uncertain multi-sensor generalized systems.…”

Robust centralized and integrated covariance intersection fusion Kalman estimators for networked mixed‐uncertain systems

“…Similar to (29), the conservative and actual correlation matrices E[w ac (t)v T ac (t)] of w ac (t) and v ac (t) are given as…”

“…The extended Lyapunov equation approach is proposed in this article, which includes two Lyapunov equations (23) and (27). It is different from the existing Lyapunov equation approach with one single Lyapunov equation, [23][24][25][26][27][28][29]37 and is suitable to handle more complex mixed uncertain systems. Note that for the models (1)-(4) with Assumptions 1-4, if some r (t) are same as k (t), for example,…”