Thresholding in high order transfer function estimation

A problem in prediction error system identification methods is estimation of pole locations. Typically, iterative numerical optimization methods are used. Reliable initial values are then necessary for good results. The parameterization is often done in the coefficients of transfer function polynomials or some canonical form. In this contribution we discuss a couple of issues related to the above problem. First, we study how all-pass systems can be used to generate suitable model structures. This analysis is based on the relation between balanced realizations of all-pass filters and orthonormal basis transfer functions. Next, we investigate the effects of a priori fixed pole locations, such as in Laguerre and Kautz models. One idea is to use very flexible high-order models. However, the corresponding estimation problem has to be regularized in order to reduce the variance errors due to noise. We will discuss how this can be done by using thresholding of the estimated coefficients