Continuous Mixed $p$-Norm Adaptive Algorithm for System Identification

We propose a new adaptive filtering algorithm in system identification applications which is based on a continuous mixed p-norm. It enjoys the advantages of various error norms since it combines p-norms for 1 ≤ p ≤ 2. The mixture is controlled by a continuous probability density-like function of p which is assumed to be uniform in our derivations in this letter. Two versions of the suggested algorithm are developed. The robustness of the proposed algorithms against impulsive noise are demonstrated in a system identification simulation.