Bias-Compensated Normalized Least Mean Fourth Algorithm for Adaptive Filtering of Impulsive Measurement Noises and Noisy Inputs

In this paper, normalized least mean fourth (NLMF) algorithm which compensates the bias caused by noisy inputs and is robust to impulsive noises is proposed. A bias compensation vector is added to the NLMF algorithm to eliminate the bias and the modified Huber function is used to improve robustness to the impulsive noises. In the elimination process of the bias, the estimation method for the input noise variance is calculated by various methods and compared with each other. Simulations in a system identification context show that the proposed algorithm effectively removes the bias of the noisy inputs and performs correctly in the impulsive noise environment.