System identification using generalized orthonormal basis

Abstract

A linear time-invariant model can be described either by a parametric model or by a nonparametric model. Nonparametric models, for which a priori information is not necessary, are basically the response of the dynamical system such as impulse response model and frequency models. Parametric models, such as transfer function models, can be easily described by a small number. In this paper, we will expand and generalize the orthogonal functions as basis functions for dynamical system representations. To this end, use is made of balanced realizations as inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion.