Robust normalized subband adaptive filter algorithm against impulsive noises and noisy inputs

This paper proposes a robust normalized subband adaptive filter (RNSAF) algorithm, which has robust performance for impulsive noise environments and noisy inputs. Although the M-estimate normalized subband adaptive filter (MNSAF) algorithm achieves robustness against impulsive noises, it generates biased estimates when the input is noisy. Based on the unbiasedness criterion, we propose a bias-compensation vector added in the RNSAF algorithm to compensate for the bias resulting from input noises. The statistical analysis reveals that the RNSAF algorithm can provide unbiased estimates. The stability analysis is also performed and the stability conditions are obtained. Moreover, by minimization of the mean-square deviation, a variable step size scheme is derived to achieve better performance. Simulation results in the context of system identification demonstrate that the proposed algorithm not only obtains robust performance in the impulsive noise environment but also achieves improved performance under noisy inputs.