Robust Subband Adaptive Filtering Algorithm Based on Fair Estimator

This paper tackles the challenge of identifying sparse systems in environments with impulsive noise and proposes the FNSAF algorithm, which combines the Fair estimator with normalized subband adaptive filter (NSAF) algorithm and exhibits high robustness to impulsive noise. To enhance the flexibility of the FNSAF algorithm and enable it to adaptively balance the trade-off between rapid convergence as well as low steady-state MSD, we propose the adaptive threshold FNSAF algorithm (AF-NSAF). In this algorithm, the threshold parameter of the Fair function is updated in real time, allowing for better handling of complex noise environments. Additionally, based on energy conservation argument, stability conditions for both AF-NSAF and NSAF algorithms are provided, along with the computational complexity for the algorithms used in the experiments. Ultimately, computer simulations in impulsive noise scenarios validate the effectiveness of our algorithms for sparse system identification.