Optimal minimum-variance filtering for systems with unknown inputs

In this paper, the optimal minimum-variance filtering for systems with unknown inputs which affect both the system model and the measurements is addressed. A filtering performance degradation problem encountered in the optimal estimator filter proposed by Darouach, Zasadzinski, and Boutayeb [5] has been explored. The main problem encountered in the filter lies in the fact that the sufficient condition which guarantees the unbiasedness of the filter may exhibit restricted applications. A new optimal minimum-variance filter which compromises between the unbiasedness and the minimum-variance estimation has been proposed to remedy the problem. A numerical example is included in order to illustrate the proposed method.