Optimal robust filtering for uncertain discrete-time systems

This paper deals with the robust filtering problem for uncertain, lnear, dicrete-time systems, and considers the finite horizon time-varying case and the infinite horizon time-invariant case. An upper bound on the variance of the estimation error is found for all admissible parameter uncertainties. The necessary and sufficient conditions of existence, and state-space formulas for an optimal robust filter are obtained in the sense of error variance upper bound It is also demonstrated, via an example, that the proposed filter performs far better than the standard Kalman filter or robust Kalman filter in [4] when the parameter uncertainty exists.