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On the Bias Distribution of Pseudo‐Linear Regression Algorithms for Recursive Identification

Year: 2026

Type: article

Abstract: ABSTRACT This paper presents a detailed analysis of the asymptotic bias distribution of recursive identification schemes based on Pseudo‐Linear Regression. As shown in a previous article, the criterion asymptotically minimized is the variance of a non‐measurable signal (called the equivalent prediction error) when the system to be identified is in the model set. We prove a similar but slightly weaker (however still relevant) result when the true system does not belong to the model set, provided that the resulting bias remains small: if the bias tends towards 0, the stationary condition of the variance of the equivalent prediction error becomes identical to that of the criterion minimized by PLR. It is also shown that the open‐loop output error algorithm obtained with Pseudo‐Linear Regression provides a limit model which has the same bias distribution as the one obtained by the Instrumental Variable algorithm with auxiliary model.

Source: International Journal of Adaptive Control and Signal Processing

DOI: 10.1002/acs.70155

Authors: Bernard Vau, Henri Bourlés

Institutions: Conservatoire National des Arts et Métiers, École Normale Supérieure, Laboratoire des systèmes et applications des technologies de l'information et de l'énergie, Laboratoire de Biologie et Pharmacologie Appliquée

Language: English

Topic: Control Systems and Identification

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W4416038293

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