Robust guaranteed cost steady-state Kalman estimators with uncertain noise variances

This paper is concerned with guaranteed cost robust steady-state Kalman estimation problem for system with uncertain noise variances. Two classes of guaranteed cost robust steady-state Kalman estimators (predictor, filter and smoother) are presented by the Lyapunov equation approach, based on the minimax robust estimation principle and parameterization representation of uncertain noise variance perturbations. The maximal lower bound and minimal upper bound of actual accuracy deviations are given. A unified approach of designing the robust Kalman estimators is presented based on the robust Kalman predictor. A simulation example shows the correctness and effectiveness of the proposed results.