  This paper proposed a bias-compensated normalized maximum correntropy
criterion (BCNMCC) algorithm charactered by its low steady-state misalignment
for system identification with noisy input in an impulsive output noise
environment. The normalized maximum correntropy criterion (NMCC) is derived
from a correntropy based cost function, which is rather robust with respect to
impulsive noises. To deal with the noisy input, we introduce a bias-compensated
vector (BCV) to the NMCC algorithm, and then an unbiasedness criterion and some
reasonable assumptions are used to compute the BCV. Taking advantage of the
BCV, the bias caused by the input noise can be effectively suppressed. System
identification simulation results demonstrate that the proposed BCNMCC
algorithm can outperform other related algorithms with noisy input especially
in an impulsive output noise environment.
