Performance analysis of the forgetting factor RLS algorithm

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Abstract
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.

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