Juan Carlos Gómez
PhD. Thesis
Department of Electrical and Computer Engineering
The University of Newcastle
Callaghan, NSW 2308
Australia

Title: Analysis of Dynamic System Identification using Rational Orthonormal Bases
Abstract
This thesis illustrates the use of a particular class of rational orthonormal bases for the purposes of analyzing the performance of least-squares dynamic system estimates that involve model structures which are linear in the parameters. The genesis of this work comes from seminal results on approximating variance error of estimated frequency responses, and work on the use of restricted classes of orthonormal bases (Laguerre and two-parameter Kautz for example) as a model structure parameterization option. A key original perspective of this thesis is that by generalizing the bases involved to the case of arbitrary pole locations, these bases can be viewed as more than an implementational option, but also as an analysis tool of great utility, since it can be applied regardless of whether the bases are used for model structure parameterization or not. This utility is illustrated by deriving approximations of estimate variability that are extensions of pre-existing ones, in that for scenarios where poles are not all fixed at the origin, they can provide improved accuracy. The key tools in this analysis involve the development of new results of generalized Fourier series convergence and generalization of the asymptotic properties of Toeplitz matrices. Initially these results are derived for time invariant and single-input, single-output scenarios, but subsequently extensions to multiple-input, multiple-output and time varying situations are also provided.
Degree Awarded: August, 1998.
Supervisor: Dr. Brett Ninness
Here you can find the PDF file of the Thesis.

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