Time-varying coefficient tracking and noise suppression properties of a class of adaptive algorithms

A class of adaptive algorithms is defined on the basis of a local optimality principle trading time variance of the filter coefficients for power of the error signal. The LMS (least-mean-squares) and RLS (recursive-least-squares) algorithms are important members of this class. A unified analysis of the class with respect to time-varying coefficient tracking and noise suppression properties is given in terms of learning filters. The total coefficient error is shown to be the combined output of two first-order filters acting on the reference coefficients and the observation noise, respectively. This behavior is related to the underlying optimality principle and a way to improved learning filters for nonstationary environments is suggested