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

In this paper, we present the convergence analysis of the recursive least M-estimate (RLM) adaptive filter algorithm, which was recently proposed for robust adaptive filtering in impulse noise environment. The mean and mean squares behaviors of the RLM algorithm, based on the modified Huber M-estimate function (MHF), in contaminated Gaussian (CG) noise model arc analyzed. Close-form expressions arc 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.