  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.
