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 et al. (2003) 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