L-2 OPTIMAL FILTER REDUCTION - A CLOSED-LOOP APPROACH

This paper is concerned with the problem of order reduction of a full- order Kalman filter for a stable linear signal model so that the stead y-state filtering error variance associated with the reduced order fil ter is minimized. By an orthogonal parameterization, the above problem is formulated to minimize the filtering error variance over a set of orthogonal matrices. Both continuous and iterative algorithms are deri ved to compute an optimal reduced-order filter. The algorithms are sho wn to possess nice properties, including the desirable convergence pro perty. The proposed algorithms are simple and effective. Numerical exa mples are presented to demonstrate the effectiveness and the significa nt advantages of the proposed algorithms over the existing open-loop m ethods such as the well-known balanced truncation method.