This paper proposes two gradient-based adaptive algorithms, called the least mean M-estimate and the transform domain least mean M-estimate (TLMM) algorithms, for robust adaptive filtering in impulse noise. A robust M-estimator is used as the objective function to suppress the adverse effects of impulse noise on the filter weights. They have a computational complexity of order O(N) and can he viewed, respectively, as the generalization of the least mean square and the transform-domain least mean square algorithms. A robust method for estimating the required thresholds in the Al-estimator is also given. Simulation results show that the TLMM algorithm, in particular, is more robust and effective than other commonly used algorithms in suppressing the adverse effects of the impulses.
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