Guaranteed Cost Robust Kalman Estimators for Systems with Uncertain-Variance Multiplicative and Colored Measurements Noises

The guaranteed cost (GC) robust estimation problem for discrete-time systems with uncertain-variance multiplicative and colored measurements noises is considered. By applying the augmented state approach and fictitious measurement noise technology, the system under considered is converted into one only with uncertain noise variances. By parameterizing the perturbations of uncertain noise variances, two classes of GC robust Kalman estimators are presented based on the minimax robust estimation principle. The proposed GC robust estimators can concurrently give the minimal upper bound and maximal lower bound of accuracy deviations. A unified approach of designing the robust Kalman estimators is addressed based on the robust Kalman predictor. The GC robustness is proved by the Lyapunov equation method. A example applied to uninterruptible power system verifies the robustness of the proposed estimators.