Least Mean Square Nonlinear Regressor Algorithm

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.