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This paper proposes a new adaptation algorithm named Least Mean Square Nonlinear Regressor Algorithm (LMS-NRA) that makes adaptive filters highly robust against impulse noise at the filter input for which a stochastic model is presented. The proposed algorithm uses a simple nonlinear function of the regressor. A Statistical analysis of the LMS-NRA is developed to calculate theoretical filter convergence. Through numerical experiments, we demonstrate that the proposed algorithm is effective in realizing a robust adaptive filter which is convergent as fast as with the LMS algorithm. Good agreement between simulated and theoretical filter convergence curves shows the validity and accuracy of the analysis.

This paper proposes an adaptation algorithm named Adaptive Step-Size q-Normalized Least Mean Modulus-Newton Algorithm (ASS-qNLMM-NewtonA) in which the normalizing factor is a generalized norm called “q-norm” of the filter input. Two types of impulse noise are considered: one is found in observation noise and another at filter input. Analysis of the ASS-qNLMM-NewtonA is developed to theoretically calculate filter convergence behavior. Through experiments we find that the steady-state excess mean square error takes the minimum value when q is infinity. We also demonstrate that the proposed algorithm is effective in improving the convergence speed, while preserving the robustness against both types of impulse noise. Good agreement between simulated and theoretical convergence curves shows the validity of the analysis.