Optimal Filtering for Systems with Unknown Inputs Via Unbiased Minimum-Variance Estimation

This paper considers the optimal unbiased minimum-variance estimation for systems with unknown inputs that affect both the system model and the measurements. By making use of the well-known matrix equation solution theory, the optimal unbiased minimum-variance filter, which appears to have the most general form, is proposed. Specific forms of this new filter are also presented to illustrate their relationships with the existing literature results. A numerical example is included in order to illustrate the proposed results