Robust Kalman Filtering for Discrete-Time Uncertain Stochastic Systems

Development of a robust Kalman filter for uncertain stochastic systems under persistent excitation and unknown measurement model is presented. The given discrete-time stochastic formulation does not require the knowledge of any bounds on parametric uncertainties and excitations. When there are no system uncertainties, the performance of the proposed robust estimator is similar to that of the traditional Kalman filter and the proposed approach asymptotically recovers the desired optimal performance in the presence of uncertainties and/or persistent excitation.