Robust optimal filtering algorithm for multiple sensors with different failure rates

In this paper, we present a robust recursive filtering algorithm for discrete time-varying systems with sensor failures and uncertain parameters in their state space models. The exiting results are generalized to the case where each sensor may fail at any sample time independently of the others. For robust performance, stochastic parameter uncertainties are included in the system matrix. The design filter has a one-step predictor-corrector structure and minimizes an upper bound of the mean square estimation error at each step based on linear matrix inequalities. Stochastic perturbations are allowed in the estimator gain to guarantee resilient operation. A numerical example is provided to demonstrate the validity of the proposed design approach.