Variable forgetting factor least squares identification algorithm : a convergence analysis

Abstract

This paper studies the convergences of the least-squares identification algorithm with variable forgetting factor. The evolution of the parameter estimator with respect to initial conditions, actual parameter changes and stochastic perturbations is analysed. Bounds on the deterministic and stochastic parts of their estimator error are found and their relation to a persistent excitation condition is discussed. This relation explains the possibility of having “bursting” phenomena during the identification process. Special attention is paid to the consistency of these results with the classical ones obtained for the ordinary least-squares algorithm when the forgetting factor tends to unity.