A minimax receding-horizon estimator for uncertain discrete-time linear systems

An approach to robust receding-horizon state estimation for discrete-time linear systems is presented. Estimates of the state variables can be obtained by minimizing a worst-case least squares cost function according to a sliding-window strategy. The resulting optimal robust filter can be approximated by a simpler and computationally efficient estimator. Stability properties are proved for both proposed filters. Specifically, the estimation errors of such filters converge exponentially to zero when the system is not affected by noise, and a bounding sequence can be given in the presence of bounded system and measurement disturbances. Simulation results are reported to show the effectiveness of the proposed approach.