Implementation issues of unbiased minimum-variance state estimation for systems with unknown inputs

In this paper, a filtering performance degradation problem of the globally optimal unbiased minimum-variance filter (GOUMVF) for systems with unknown inputs has been explored. The main problem encountered in the GOUMVF lies in the fact that its gain matrix is in some degeneration forms, which are defined as those that are not fully connected to the process noise and the measurement noise covariances; in such cases, the filter may not preserve the minimum-variance property. To remedy this problem, a parameterized augmented system reformation approach has been proposed, and the parameterized augmented RTSKF (PARTSKF) is proposed to give a tradeoff between the unbiasedness and the minimum variance in a practical unknown input filtering. An illustrative example is given to show the usefulness of the proposed results.