Robust Total Least Mean M-Estimate normalized subband filter Adaptive Algorithm for impulse noises and noisy inputs

TL;DR

This paper introduces a robust adaptive filtering algorithm that maintains high performance in the presence of impulse noise, improving upon existing methods by incorporating a minimum mean M-estimator and a variable step size.

Contribution

The paper proposes the TLMM-NSAF algorithm with theoretical analysis and a new variable step size method, enhancing robustness against impulse noise in adaptive filtering.

Findings

The TLMM-NSAF algorithm outperforms traditional TLS-NSAF under impulse noise.

Theoretical analysis provides stable step size range and steady-state MSD.

Simulations confirm improved robustness and accuracy in system identification and echo cancellation.

Abstract

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.