Bias-compensated robust set-membership NLMS algorithm against impulsive noises and noisy inputs

By minimising a new cost function that contains robust set-membership error bound, a bias-compensated robust set-membership normalised least mean square (NLMS) algorithm is proposed, which is characterised by its robustness against impulsive noises and noisy inputs. To estimate the input noise variance in impulsive noise environments, a new estimation method is proposed in which there is no need to know the input–output noise variance ratio in advance. Simulations in a system identification context demonstrate that the proposed algorithm achieves improved robustness and better performance than the existing algorithms.