An output signal based combination of three LMS adaptive filters

This paper investigates a combination of three LMS adaptive algorithms. The structure consists of filters that simultaneously adapt on the same input and desired signals but have different step sizes. The outputs of the individual filters are then adaptively combined together to form a common output signal. This combination is an interesting new way of achieving a fast initial convergence and a small steady state error of an adaptive filter at the same time. We compute the combination parameters from the output signals of the individual filters. In this paper we show that the straightforward posing of the minimization problems we need to solve for the combination parameters results in a need to solve a singular system of linear equations. We therefore suggest to include a regularization term to our optimization problem. We also provide an analysis of the resulting algorithm. The theoretical results are verified by simulations.