L2 optimal reduced order filter design

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 steady-state filtering error variance associated with the reduced order filter is minimised. By an orthogonal parameterization, the above problem is formulated as minimising the filtering error variance over a set of orthogonal matrices. Both continuous and iterative algorithms are derived to compute an optimal reduced order filter. The algorithms are shown to possess nice properties, including the desirable convergence property. The proposed algorithms are simple and effective. A numerical example is presented to demonstrate: the effectiveness and the significant advantages of the proposed algorithms over the existing open-loop methods such as the well known balanced truncation methods