Asymptotically Optimal RLS Adaptive Identification Algorithms

Abstract

A major, and yet unresolved, problem has been the choice of the gain adjusting parameter in some parameter estimation algorithms. This paper presents an adaptive setting method of the forgetting factor for estimating time-varying parameters when the Recursive Least Squares (RLS) algorithm is used. The method is to choose the forgetting factor λ so as to minimize the performance index defined by E {e2t (λ)} where et (λ) is the prediction error based on some λ. This is concretely done by solving the minimization problem of a certain object function with respect to λ. It is shown that this object function is unimodal with respect to λ and thus the minimization can be attained by using the stochastic Newton method. As a result, the proposed method becomes asymptotically optimal. The resultant algorithm can be executed by linking the minimization routine with RLS.Numerical examples indicate acceptable performance.