Robust weighted state fusion Kalman estimators for networked systems with mixed uncertainties

This paper is concerned with robust weighted state fusion estimation problem for a class of time-varying multisensor networked systems with mixed uncertainties including 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 the conservative upper bounds of uncertain noise variances, four weighted state fusion robust Kalman estimators (filter, predictor and smoother) are presented in a unified form that the robust filter and smoother are designed 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 local and fused 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 by the dynamic error system analysis (DESA) method. Finally, a simulation example applied to uninterruptible power system (UPS) shows the correctness and effectiveness of the proposed results.