Convergent algorithms for H2 optimal discrete filter reduction

This paper deals with an order reduction problem for a given full order filter associated with a stable discrete linear signal model. The reduced order filter is required to minimize the H-2-norm of the filtering error transfer function rather than that of the error between the full order filter and the reduced order filter. By an orthogonal parameterization, the above problem is formulated as minimising the filtering error variance over a set of orthogonal matrices. Two gradient based algorithms are derived to compute an optimal reduced order filter. The algorithms are very simple and more importantly, they possess nice properties, including the desirable convergence property. A numerical example is presented to demonstrate the effectiveness and significance of the proposed algorithms.