Least total logistic distance metric algorithm and its variable step-size version

Abstract

Classical mean-square error (MSE)-based adaptive filtering algorithms are useful for noise-free inputs. However, if the input signal of the adaptive filter with such an adaptive filtering algorithm is corrupted by noise, it will suffer from serious degradation of steady-state performance. To address the problem, a new adaptive filtering algorithm is proposed in this work. This algorithm not only uses the total method to compensate the bias caused by noisy input but also minimizes the cost function based on logistic distance metric (LDM) to achieve robustness against impulsive noise. Compared with the existing algorithms, the proposed least total logistic distance metric (LTLDM) algorithm has less misalignment when the input signal is disturbed by noise and has good robustness to impulsive noise. This work also tackles the crucial trade-off between convergence rate and misalignment by developing a variable step-size for LTLDM. In addition, to give deep insight into the stochastic behavior of the proposed LTLDM, its mean-square deviation is analyzed at steady state. The advantage of LTLDM and the accuracy of theoretical expressions are verified by extensive simulations.