Generalized Versoria Soft-Root-Sign-Based Adaptive Filter for System Identification Under Impulsive Noise

Robust adaptive filtering algorithms using correntropy, Versoria, logarithmic cost, generalized soft root sign (GSRS), and hyperbolic cosine functions (HCF) have been successfully employed for the system identification (SI) problem under non-Gaussian noise. However, the existing correntropy and GSRS-based algorithms suffer from high steady-state misalignment and are difficult to realize over a practical hardware due to the presence of exponential term in its weight update equation. To circumvent the above limitations, a novel generalized Versoria soft-root-sign (GVSRS) based adaptive algorithm is proposed in this paper, which replaces the exponential term in GSRS by a simple algebraic function. The proposed GVSRS algorithm provides infinitesimal weight update for large outliers, thereby resulting in improved robustness against heavy tailed impulsive/non-Gaussian noise. Furthermore, a family of robust sparsity-aware GVSRS algorithms are developed in this paper for sparse SI problem. Lastly, both the first and the second oder convergence analysis is performed for the proposed algorithm over non-stationary environments. Simulations confirm enhanced performance of the proposed algorithm over the existing benchmarks.