A New Parametrizing Technique for the Derivation of Unbiased Minimum-Variance Filters

In this paper, the problem of designing an unbiased minimum-variance filter for systems with unknown inputs which affect both the system model and the measurements is addressed. A new parametrizing technique for the derivation of unbiased minimum-variance filters is presented. The derived parametrized unbiased minimum-variance filter serves as a unified filter structure to derive existing unbiased minimum-variance filters, e.g., the optimal estimator filter and the well-known Kalman filter. Furthermore, the proposed parametrizing methodology also suggests a method to derive other unbiased minimum-variance filters. A numerical example is included in order to illustrate the proposed method.