Robust time-varying Kalman smoothers with uncertain noise variances

This paper addresses the design of robust Kalman smoothers for the time-varying system with uncertain noise variances. According to the minimax robust estimation principle, and the unbiased linear minimum variance (ULMV) optimal estimation rule, based on the worst-case conservative system with the conservative upper bounds of noise variances, two robust Kalman state smoothing algorithms are presented by the augmented and non-augmented state approaches, respectively. Their robustness is proved by the Lyapunov equation approach, and their robust accuracy relations are proved. A simulation example is given to verify the robustness and the correctness of the robust accuracy relations.