Robust Bias-Compensated LMS Algorithm: Design, Performance Analysis and Applications

This paper considers the problem of system parameter estimation using adaptive filter. Conventional adaptive algorithms will result in degraded performance in the presence of impulsive noise and biased estimation when the input signal is noisy. To address these issues, this paper proposes a robust bias-compensated least mean squares (R-BC-LMS) algorithm. It is derived by performing the maximum-a-posteriori estimation subject to a constraint on the squared norm of the weight vector difference, and then introducing an unbiasedness criterion to insert a bias compensation term in the update. Under common statistical assumptions, the mean and mean square behaviors of weight deviation are derived for the R-BC-LMS algorithm. In addition, we develop the estimator for the input and output noise variances. Simulations in channel estimation, vehicle handsfree echo cancellation, and direction-of-arrival estimation demonstrate that our method outperforms the competing algorithms.