Set-membership NLMS algorithm based on bias-compensated and regression noise variance estimation for noisy inputs

The bias-compensated set-membership normalised LMS (BCSMNLMS) algorithm is proposed based on the concept of set-membership filtering, which incorporates the bias-compensation technique to mitigate the negative effect of noisy inputs. Moreover, an efficient regression noise variance estimation method is developed by taking the iterative-shrinkage method. Simulations in the context of system identification demonstrate that the misalignment of the proposed BCSM-NLMS algorithm is low for noisy inputs.