Weibull M-transform least mean square algorithm

This paper proposes a new robust learning strategy, which is based on a Weibull M-transform function. The suitability of the Weibull M-transform function as a robust norm has been investigated for different shape and scale parameters, and a Weibull M-transform least mean square (WMLMS) algorithm has been developed. Further, the bound of learning rate has been derived for the proposed algorithm. The proposed WMLMS algorithm has been evaluated for the problem of system identification and simulation studies carried out demonstrate its robustness. In addition, a filtered-x WMLMS (Fx-WMLMS) algorithm has been developed for robust room equalization and has been shown to offer stable room equalization even in the presence of strong disturbances picked up by the microphone.