Performance analysis of the forgetting factor RLS algorithm

An analysis is given of the performance of the standard forgetting factor recursive least squares (RLS) algorithm when used for tracking time-varying linear regression models. Three basic results are obtained: (1) the ‘P-matrix’ in the algorithm remains bounded if and only if the (time-varying) covariance matrix of the regressors is uniformly non-singular; (2) if so, the parameter tracking error covariance matrix is of the order O(μ + γ²/μ), where μ = 1 - λ, λ is the forgetting factor and γ is a quantity reflecting the speed of the parameter variations; (3) this covariance matrix can be arbitrarily well approximated (for small enough μ) by an expression that is easy to compute.