  When the input signal is correlated input signals, and the input and output
signal is contaminated by Gaussian noise, the total least squares normalized
subband adaptive filter (TLS-NSAF) algorithm shows good performance. However,
when it is disturbed by impulse noise, the TLS-NSAF algorithm shows the rapidly
deteriorating convergence performance. To solve this problem, this paper
proposed the robust total minimum mean M-estimator normalized subband filter
(TLMM-NSAF) algorithm. In addition, this paper also conducts a detailed
theoretical performance analysis of the TLMM-NSAF algorithm and obtains the
stable step size range and theoretical steady-state mean squared deviation
(MSD) of the algorithm. To further improve the performance of the algorithm, we
also propose a new variable step size (VSS) method of the algorithm. Finally,
the robustness of our proposed algorithm and the consistency of theoretical and
simulated values are verified by computer simulations of system identification
and echo cancellation under different noise models.
