This book focuses on theoretical aspects of the affine projection algorithm (APA) for adaptive
filtering. The APA is a natural generalization of the classical normalized least-mean-squares
(NLMS) algorithm. The book first explains how the APA evolved from the NLMS algorithm where an
affine projection view is emphasized. By looking at those adaptation algorithms from such a
geometrical point of view we can find many of the important properties of the APA e.g. the
improvement of the convergence rate over the NLMS algorithm especially for correlated input
signals. After the birth of the APA in the mid-1980s similar algorithms were put forward by
other researchers independently from different perspectives. This book shows that they are
variants of the APA forming a family of APAs. Then it surveys research on the convergence
behavior of the APA where statistical analyses play important roles. It also reviews
developments of techniques to reduce the computational complexity of the APA which are
important for real-time processing. It covers a recent study on the kernel APA which extends
the APA so that it is applicable to identification of not only linear systems but also
nonlinear systems. The last chapter gives an overview of current topics on variable parameter
APAs. The book is self-contained and is suitable for graduate students and researchers who are
interested in advanced theory of adaptive filtering.
