An orthogonal adaptive IIR realization for efficient MSOE optimization

Orthogonal basis functions are a powerful tool for efficient system representation. Except for the lattice realization, that is based on the nice properties of Szego orthonormal polynomials, no other adaptive IIR filter realization using orthonormal characteristics seems to be extensively studied in the literature. However, many orthogonal realizations for adaptive FIR filters, that are particularly suitable for rational modeling, have been proposed in past years. In this paper, we present some theoretical results related to the properties of a generalized orthonormal realization when used for mean square output error minimization in a system identification application. One result is related to the low computational complexity of the updating gradient algorithm when some properties of the orthonormal realization are used. An additional result establishes conditions for the stationary points of the proposed updating algorithm