The Unified Structure of Unbiased Minimum-Variance Reduced-Order Filters

A unified two-stage functional filter (UTSFF) is proposed, serving as a unified structure of unbiased minimum-variance reduced-order filters for linear time-varying discrete-time systems. The UTSFF includes two parts: one is for the main functional estimate, which defines the main computing structure of the filter, and the other is for the complementary functional estimate, which is added to the former in order to further enhance the filtering performance. The relationships between the UTSFF and existing reduced-order filters are explored. Through the UTSFF, a general procedure for applying a suitable unbiased minimum-variance reduced-order filter is given. Simulation examples are also given to illustrate the proposed results.