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

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.