Pseudo-linear regression identification based on generalized orthonormal transfer functions: Convergence conditions and bias distribution

TL;DR

This paper introduces a generalized orthonormal transfer function approach for pseudo-linear regression identification, relaxing convergence constraints and analyzing bias distribution, thereby improving the identification of complex discrete-time systems.

Contribution

It proposes a new predictor parameterization based on generalized orthonormal functions that removes pole constraints and modifies bias distribution in pseudo-linear regression algorithms.

Findings

Relaxed convergence conditions for recursive schemes.

Bias distribution analysis linked to basis pole placement.

Enhanced identification of fast and stiff systems.

Abstract

In this paper we generalize three identification recursive algorithms belonging to the pseudo-linear class, by introducing a predictor established on a generalized orthonormal function basis. Contrary to the existing identification schemes that use such functions, no constraint on the model poles is imposed. Not only this predictor parameterization offers the opportunity to relax the convergence conditions of the associated recursive schemes, but it entails a modification of the bias distribution linked to the basis poles. This result is specific to pseudo-linear regression properties, and cannot be transposed to most of prediction error method algorithms. A detailed bias distribution is provided, using the concept of equivalent prediction error, which reveals strong analogies between the three proposed schemes, corresponding to ARMAX, Output Error and a generalization of ARX models. That leads to introduce an indicator of the basis poles location effect on the bias distribution in the frequency domain. As shown by the simulations, the said basis poles play the role of tuning parameters, allowing to manage the model fit in the frequency domain, and allowing efficient identification of fast sampled or stiff discrete-time systems.