An optimal error nonlinearity for robust adaptation against impulsive noise

The least-mean squares algorithm is non-robust against impulsive noise. Incorporating an error nonlinearity into the update equation is one useful way to mitigate the effects of impulsive noise. This work develops an adaptive structure that parametrically estimates the optimal error-nonlinearity jointly with the parameter of interest, thus obviating the need for a priori knowledge of the noise probability density function. The superior performance of the algorithm is established both analytically and experimentally.