Tracking performance analysis of the forgetting factor RLS algorithm
Lei Guo, Lennart Ljung, P. Priouret · 2005
The authors present a theoretical analysis for the performance of the standard forgetting factor recursive least squares (RLS) algorithm used in the tracking of time-varying linear regression models. Under some explicit excitation conditions on the regressors, it is shown that the parameter tracking error is on the order O( square root mu + gamma / square root mu ), where mu =1- lambda , lambda is the forgetting factor, and gamma is the quantity reflecting the speed of parameter variation. Furthermore, for a large class of weakly dependent regressors, simple approximations for the covariance matrix of this error are derived. These approximations are not asymptotic in nature: they hold over all time intervals and for all mu in a certain region.>