Some remarks on the bias distribution analysis of discrete-time identification algorithms based on pseudo-linear regressions

TL;DR

This paper corrects and extends the bias distribution analysis of pseudo-linear regression (PLR) identification algorithms in the frequency domain, showing that PLR outperforms prediction error methods at high frequencies.

Contribution

It provides the first correct frequency domain bias analysis for PLR algorithms in open- and closed-loop conditions, clarifying their performance relative to PEM.

Findings

PLR algorithms have better high-frequency bias performance than PEM.

The paper offers a corrected bias distribution expression for PLR methods.

PLR is not just an approximation of PEM but can outperform it at high frequencies.

Abstract

In 1998, A. Karimi and I.D. Landau published in the journal "Systems and Control letters" an article entitled "Comparison of the closed-loop identification methods in terms of bias distribution". One of its main purposes was to provide a bias distribution analysis in the frequency domain of closed-loop output error identification algorithms that had been recently developed. The expressions provided in that paper are only valid for prediction error identification methods (PEM), not for pseudo-linear regression (PLR) ones, for which we give the correct frequency domain bias analysis, both in open- and closed-loop. Although PLR was initially (and is still) considered as an approximation of PEM, we show that it gives better results at high frequencies.