On the bias distribution of pseudo-linear regression algorithms in 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 paper, the criterion asymptotically minimized is the variance of an unmeasurable signal (called the equivalent prediction error) when the system to be identified is in the model set. We prove that this is still approximately true if the true system is not in the model set provided that the bias (which necessarily occurs) remains small.