Combination of Recursive Least $p$ -Norm Algorithms for Robust Adaptive Filtering in Alpha-Stable Noise

A method for adaptively minimizing the lp norm relying on the convex combination of two recursive least p -norm (RLpN) filters is presented. The approach is of interest when the noise is not Gaussian, for instance in the presence of impulsive or alpha-stable (α-S) distributed noise. In these cases, the RLpN algorithm, aiming at recursively minimizing the lp norm, offers a more stable and robust solution than adaptive filtering schemes based on the minimization of the squared error. However, since the RLpN solution cannot be obtained in closed form for p ≠ 2, it is necessary to introduce some approximations that critically affect the filter behavior. The main observed drawback is a poor convergence rate in nonstationary scenarios, especially in the presence of abrupt changes in the model. In this correspondence, we show how this problem can be overcome by relying on convex combinations of two RLpN filters with long and short memories. The proposed methods are empirically shown to outperform state-of-the-art methods for this problem, requiring just slightly higher computation than its close competitors.