Abstract
The purpose of this paper is to generalize various adaptive algorithms and to give a unified analysis on their properties.
The performance of an adaptive system is generally dominated by the adaptive algorithm implemented in it. Therefore it is extremely important in designing such a system to well understand the properties of the various algorithms and to select the one meeting design specifications best. This paper is written from this point of view, taking the following organization. First, a general adaptive law is presented that includes not only the generalized adaptive law proposed by Landau et al. but also the recursive least squares algorithm in general form. Next, an ellegant analysis on the properties of the presented law is given. This analysis results in a unified one on the properties of a variety of algorithms. Finally, it is shown that an attractive algorithm, enabling us to control the rate of convergence, can be obtained from the presented general adaptive law.
