Convergence Behaviors of the Fast LMM/Newton Algorithm with Gaussian Inputs and Contaminated Gaussian Noise

This paper studies the convergence behaviors of the fast least mean M-estimate/Newton adaptive filtering algorithm proposed in [4], which is based on the fast LMS/Newton principle and the minimization of an M-estimate function using robust statistics for robust filtering in impulsive noise. By using the Price's theorem and its extension for contaminated Gaussian (CG) noise case, the convergence behaviors of the fast LMM/Newton algorithm with Gaussian inputs and both Gaussian and CG noises are analyzed. Difference equations describing the mean and mean square behaviors of this algorithm and step size bound for ensuring stability are derived. These analytical results reveal the advantages of the fast LMM/Newton algorithm in combating impulsive noise, and they are in good agreement with computer simulation results.