Smoothed least mean p-power error criterion for adaptive filtering

In this paper, we propose a novel error criterion for adaptive filtering, namely the smoothed least mean p-power (SLMP) error criterion, which aims to minimize the mean p-power of the error plus an independent and scaled smoothing variable. Some important properties of the SLMP criterion are presented. In particular, we show that if the smoothing variable is symmetric and zero-mean, and p is an even number, then the SLMP error criterion will become a weighted sum of the even-order moments of the error, and as the smoothing factor (i.e. the scale factor) is large enough, this new criterion will be approximately equivalent to the well-known mean square error (MSE) criterion. Based on the proposed error criterion, we develop a new adaptive filtering algorithm and its kernelized version, and derive a theoretical value of the steady-state excess mean square error (EMSE). Simulation results suggest that the new algorithms with proper choice of the smoothing factor may perform quite well.