On the bias distribution of pseudo-linear regression algorithms for recursive identification

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, in a sense that is specified in the paper. 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.