Deterministic convergence analysis of RLS estimators with different forgetting factors

Three forgetting factors recursive-least-squares (RLS) algorithms, as well as the classical error-forgetting one, are considered. The basic assumptions are that the data-generation mechanism is deterministic, the unknown parameter vector is constant, and the observation vector is persistently exciting. It is possible to prove the convergence of the estimates supplied by the various algorithms to the true parameter vector. This conclusion does not mean that the algorithm possess tracking capabilities when the unknown parameter vector is time-varying. In this case, the exponential convergence in the case of constant unknown parameters is much more important