Robust Adaptive Filtering Based on Adaptive Projected Subgradient Method: Moreau Enhancement of Distance Function

This paper presents an outlier-robust adaptive filtering algorithm based on the adaptive projected subgradient method (APSM). The proposed algorithm is derived from a cost function involving the Moreau enhancement of the distance function to a hyperslab which permits a prespecified amount of estimation residuals. A data-dependent penalty is also exploited to preserve the overall convexity of the instantaneous cost with a minimal amount of estimation bias. Our instantaneous cost function involves a constant term to make the minimum of the cost be exactly zero so that the monotone approximation property of APSM holds with a fixed step size. Numerical examples show remarkable robustness of the proposed algorithm for both white and colored input signals.