Convergence analysis of the recursive least M-estimate adaptive filtering algorithm for impulse noise suppression

We present the convergence analysis of the recursive least M-estimate (RLM) adaptive filter algorithm, which was recently proposed for robust adaptive filtering in the impulse noise environment. The mean and mean squares behaviors of the RLM algorithm, based on the modified Huber M-estimate function (MHF), in the contaminated Gaussian (CG) noise model are analyzed. Close-form expressions are derived. The simulation and theoretical results agree very well with each other and suggest that the RLM algorithm is more robust than the RLS algorithm under the CG noise model.