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

Abstract

AbstractIn 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.