Robust adaptive filters using student-t distribution

An important application of adaptive filters is in system identification. Robustness of the adaptive filters to impulsive noise has been studied. In this paper, we propose an alternative way to developing robust adaptive filters. Our approach is based on formulating the problem as a maximum penalized likelihood (MPL) problem. We use student-t distribution to model the noise and a quadratic penalty function to play a regularization role. The minorization-maximization principle is used to solve the optimization problem. Based on the solution, we propose two LMS-type of algorithms called MPL-LMS and robust MPL-LMS. The robustness of the latter algorithm is demonstrated both theoretically and experimentally.