A fast converging, low complexity adaptive filtering algorithm

This paper introduces a new adaptive filtering algorithm called fast affine projections (FAP). Its main attributes include RLS (recursive least squares) like convergence and tracking with NLMS (normalized least mean squares) like complexity. This mix of complexity and performance is similar to the recently introduced fast Newton transversal filter (FNTF) algorithm. While FAP shares some similar properties with FNTF it is derived from a different perspective, namely the generalization of the affine projection interpretation of NLMS. FAP relies on a sliding windowed fast RLS (FRLS) algorithm to generate forward and backward prediction vectors and expected prediction error energies. Since sliding windowed FRLS algorithms easily incorporate regularization of the implicit inverse of the covariance matrix, FAP is regularized as well.<>