Steady-State Tracking Analysis of Adaptive Filter With Maximum Correntropy Criterion

Abstract

This letter studies the tracking performance of a stochastic gradient-based adaptive algorithm, namely the maximum correntropy criterion algorithm, where a random walk is used to model the non-stationarity. In our analysis, we use the energy conservation argument to derive expressions for the steady-state excess mean square error (EMSE). We consider two different cases for measurement of noise distribution including the Gaussian noise and general non-Gaussian noise. For the Gaussian case, we derive a fixed-point equation that can be solved numerically to find steady-state EMSE value. For the general non-Gaussian case, we derive an approximate closed-form expression for EMSE. For both cases, unlike the stationary environment, the EMSE curves are not increasing functions of step size parameter. We use this observation to find the optimum step size learning parameter for general non-Gaussian case. The validity of the theoretical results are justified via simulation results.