Generalized Modified Blake–Zisserman Robust Sparse Adaptive Filters

In the past years, the generalized maximum correntropy criterion (GMCC) has been widely used in adaptive filters to provide robust behavior under non-Gaussian/impulsive noise environments. However, GMCC-based adaptive filters are affected by high steady-state misalignment. In order to enhance the robustness under non-Gaussian noise environments and reduce steady-state misalignment, a generalized modified Blake–Zisserman (GMBZ) robust loss function is introduced in this correspondence. Furthermore, a GMBZ adaptive filter (GMBZ-AF) has been developed that provides improved convergence performance over other existing algorithms. The proposed learning scheme has a computational complexity very similar to that of the GMCC-based adaptive filtering method. In order to further exploit the sparse nature of the system for identifying sparse systems and simultaneously provide robust convergence, two new robust sparse adaptive filters: 1) zero attracting GMBZ-AF (ZA-GMBZ-AF) and 2) reweighted ZA-GMBZ-AF (RZA-GMBZ-AF) have also been proposed. To further enhance the filter convergence performance, a new robust and sparsity-aware loss function called generalized modified dual Blake–Zisserman (GMDBZ) is also introduced in this correspondence and the corresponding GMDBZ adaptive filter (GMDBZ-AF) has been developed.