A robustification method of the adaptive filtering algorithms in impulsive noise environments based on the likelihood ratio test

In this paper, we propose a new approach for robustification of the adaptive filtering algorithms such as: LMS, RLS, APA (affine projection algorithm) and Kalman filtering, in impulsive environments. It is based on a LRT hypothesis test for impulses localization in the received signal. The LRT controls the two modes of the adaptive filter, the updating and the freezing modes. The approach proposed in this paper is seen to be robustly identify the unknown system. It presents the best performance behavior in terms of the convergence speed and the steady state error, when, compared to the classical approaches based on, a nonlinear function (M-estimator of Huber), or the median filter, such as the MNLMS, the NRLS and the median LMS algorithms.