Robust weighted fusion Kalman filters for multisensor time-varying systems with uncertain noise variances

This paper addresses the design of robust weighted fusion Kalman filters for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) optimal estimation rule, the five robust weighted fusion time-varying Kalman filters are presented based on the worst-case conservative systems with the conservative upper bounds of noise variances. The actual filtering error variances or their traces of each fuser are guaranteed to have a minimal upper bound for all the admissible uncertainties of noise variances. A Lyapunov equation approach is presented to prove the robustness of the robust Kalman filters. The concept of robust accuracy is presented and the robust accuracy relations among the local and fused robust Kalman filters are proved. Specially, the corresponding steady-state robust local and fused Kalman filters are also presented for multisensor time-invariant systems, and the convergence in a realization of the local and fused time-varying and steady-state Kalman filters 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.

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