Reconsideration of Adaptive Algorithm

Abstract

This exposition summarizes our papers on adaptive algorithms published over about twenty years. According to the results presented in them, adaptive algorithms can be classified by the type of approximation method used for the non-diagonal elements of the autocorrelation matrix. Among these methods, the arithmetic mean method has the lowest degree of approximation, followed by the coefficient reuse method, the normalized least mean square (NLMS) algorithm, and the individually normalized least mean square (INLMS) algorithm, with the sub-recursive least square (sub-RLS) algorithm having the highest degree of approximation. The adaptive algorithms are generally introduced in the order of the Wiener-Hopf solution, the least square (LS) method, the steepest descent method, the LMS algorithm, and the NLMS algorithm where the first two require the operation of the inverse matrix. In this exposition, we show that the reuse of the estimated coefficients makes this operation unnecessary. This coefficient reuse method can be assumed to be the source of steepest descent method type adaptive algorithms, from which various algorithms can be derived. Finally, we clarify the role of each element composing, the NLMS algorithm.