A Generalized Robust Logarithmic Family-Based Adaptive Filtering Algorithms

Abstract

In recent years, algorithms based on the Maximum Versoria Criterion (MVC) and a relative logarithmic cost function have gained the attention of researchers because they improve the filtering accuracy and robustness towards non-Gaussian/impulsive noises. To further enhance the steady-state convergence behavior of these aforementioned algorithms in impulsive noise scenarios, we introduce a generalized, robust logarithmic family (GRLF) framework that underlies the relative logarithmic cost function and MVC, and the corresponding GRLF-based adaptive filters called least mean square based-GRLF (GRLF-LMS) and least absolute difference based-GRLF (GRLF-LAD) algorithms are designed. With an approximate solution using Taylors expansion, the steady-state behavior of the GRLF-LMS and GRLF-LAD methods is presented. Then, algorithms are used in practical simulation studies in system identification to compare the performance of GRLF-LMS and GRLF-LAD filtering in Gaussian and non-Gaussian impulsive environments in terms of accuracy and robustness to that of their competitors.