Improved variable forgetting factor proportionate RLS algorithm with sparse penalty and fast implementation using DCD iterations

The proportionate recursive least squares (PRLS) algorithm has shown faster convergence and better performance than both proportionate updating (PU) mechanism based least mean squares (LMS) algorithms and RLS algorithms with a sparse regularization term. In this paper, we propose a variable forgetting factor (VFF) PRLS algorithm with a sparse penalty, e.g., l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -norm, for sparse identification. To reduce the computation complexity of the proposed algorithm, a fast implementation method based on dichotomous coordinate descent (DCD) algorithm is also derived. Simulation results indicate superior performance of the proposed algorithm.