Robust time‐varying Kalman estimators for systems with packet dropouts and uncertain‐variance multiplicative and linearly correlated additive white noises

This paper is concerned with robust estimation problem for a class of time‐varying networked systems with 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 conservative upper bounds of uncertain noise variance, the robust time‐varying Kalman estimators (filter, predictor, and smoother) are presented. A unified approach of designing the robust Kalman estimators is presented 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 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. Finally, a simulation example applied to uninterruptible power system shows the correctness and effectiveness of the proposed results.