Robust Normalized Subband Adaptive Filter Algorithm Based on Logarithmic and Total Least Squares for Correlated Input Signals and Impulsive Noise

The total least squares normalized subband adaptive filter (TLS-NSAF) algorithm proposed in recent years has shown excellent performance in processing the errors-in-variables (EIV) model of correlated input signals. However, when the system is Interferenced by the impulsive noise, the convergence of TLS-NSAF algorithm will be seriously deteriorated. To address this problem, this letter improves the TLS-NSAF algorithm by using the logarithmic function, and proposes a robust NSAF algorithm based on logarithmic and total least squares method (RNSAF-LTLS). The algorithm performs well in an environment where input signal is a correlated input signal and output signal contains impulsive noise. In addition, there are few studies in the existing literature that apply the TLS method to subbands, and there are few performance analyses associated with it. To address this problem, this letter analyzes the local stability, derives the step size that guarantees the stability of the RNSAF-LTLS algorithm, and calculates the steady-state mean squared deviation (S-MSD). Finally, the RNSAF-LTLS algorithm is verified in system identification (SI) and acoustic echo cancellation (AEC) applications. The simulation results prove the superiority of the proposed algorithm and the correctness of the theoretical analysis.