Tracking performance analysis of the forgetting factor RLS algorithm

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(√μ+γ/√μ), where μ=1-λ, λ is the forgetting factor, and γ 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 μ in a certain region