Performance of RLS identification algorithms with forgetting factor : A Φ-mixing approach

In this paper, systems with unknown time-varying parameters and subject to stochastic disturbances are considered. The problem of tracking the parameters is tackled by resorting to a class of adaptive recursive least squares algorithms, equipped with variable forgetting factor. The basic assumption in the analysis is that the observation vector, the noise and the parameter drift are stochastic processes satisfying a {mixing condition. Furthermore, it is assumed that the observation vector satisses an excitation condition imposed on its minimum power. It is shown that the algorithm provides estimates with bounded error whenever the so-called \co-variance matrix" of the algorithm keeps bounded. Moreover, the size of such a matrix can be controlled by a suitable choice of the feasible range for the forgetting factor.