A novel least Cauchy error algorithm and its kernel extension

Cauchy estimator has been successfully applied to the statistical learning owing to its unique distribution characteristics and robustness to outliers. In this paper, Cauchy loss function is utilized to update the weight of filter, generating a novel robust least Cauchy error (LCE) algorithm and its kernel extension (KLCE). The proposed filter algorithms are effective for the impulsive non-Gaussian noises (e.g.,α-stable noise), and can achieve a fine accuracy for filter. Simulations on the system identification and nonlinear channel equalization confirm that the proposed filters based on Cauchy cost function show strong robustness against large outliers.