Robust Guaranteed Cost Steady-State Kalman Predictors for Systems with Uncertain Noise Variances and Missing Measurements

The system with uncertain noise variances and missing measurements can be converted into that only with uncertain noise variances, on this basis, two classes of guaranteed cost robust Kalman predictors are presented by the Lyapunov equation approach based on the minimax robust estimation principle and parameterization representation of uncertain noise variances. One class is to construct a maximal perturbation region of uncertain noise variances such that for all admissible perturbations in this region, the deviations of its actual accuracies with respect to the robust accuracy are guaranteed to remain within the prescribed range, and the maximal lower bound and minimal upper bound of accuracy deviations are given. The other class is to find minimal upper bound and maximal lower bound of accuracy deviations under given a perturbation region of uncertain noise variances. The proof of the guaranteed cost robustness is presented by the Lyapunov equation approach. A simulation example shows the correctness and effectiveness of the proposed results.