Robust weighted fusion time-varying Kalman smoothers for multisensor system with uncertain noise variances

This paper addresses the design of robust weighted fusion time-varying Kalman smoothers for multisensor time-varying system with uncertain noise variances by the augmented state approach. According to the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) optimal estimation rule, the six robust weighted fusion time-varying Kalman smoothers are presented based on the worst-case conservative system with the conservative upper bounds of noise variances. The actual smoothing error variances of each fuser are guaranteed to have a minimal upper bound for all admissible uncertainties. Their robustness is proved by the Lyapunov equation approach. Their robust accuracy relations are analyzed and proved. Specially, the corresponding steady-state robust Kalman smoothers are also presented for multisensor time-invariant system, and the convergence in a realization between the time-varying and steady-state robust Kalman smoothers is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and robust accuracy relations.