Robust Guaranteed Cost Steady-State Kalman Predictors for Systems with Multiplicative Noises, Colored Measurements Noises and Uncertain Noise Variances

This paper is concerned with the guaranteed robust prediction problem for discrete-time systems with multiplicative noises, colored measurements noises and uncertain noise variances. By applying the augmented state approach, combining with a fictitious measurement noise technique, the system under considered is converted into a system only with uncertain noise variances. By parameterizing the perturbations of uncertain noise variances, two classes of guaranteed cost robust Kalman predictors are presented based on the minimax robust estimation principle. The proposed guaranteed cost robust predictors can concurrently give the minimal upper bound and maximal lower bound of accuracy deviations. The guaranteed cost robustness is proved by the Lyapunov equation method. A numerical example verifies the robustness of the proposed estimators.