Robust weighted information fusion steady-state Kalman smoothers for multisensor system with uncertain noise variances

This paper considers the problem of designing the robust weighted fusion steady-state Kalman smoothers for multisensor system with uncertain noise variances. Applying the augmented state method, the problem of designing the robust Kalman smoothers can be converted into that of designing the equivalent robust Kalman filters. According to the minimax robust estimation principle and the unbiased linear minimum variance optimal estimation rule, based on the worst-case conservative system with conservative upper bounds of noise variances, the local and five weighted fusion robust steady-state Kalman smoothers are presented. For all admissible uncertainties of noise variances, the minimal upper bound of the actual smoothing error variances is given. A Lyapunov equation approach for the robustness analysis is presented, the concept of robust accuracy is presented, and the robust accuracy relations of the local and fused robust Kalman smoothers are proved. A simulation example verifies the robustness and robust accuracy relations.