Recently, robust adaptive filtering approaches relied on the Maximum Versoria Criterion (MVC) have gained the attention of researchers and have been widely studied. In this brief, with the energy conservation approach, transient and steady-state mean-square deviation (MSD) analysis of the standard constrained MVC (CMVC) are derived under both Gaussian and non-Gaussian noise distributions. For a Gaussian noise condition, an accurate solution is obtained, while for non-Gaussian noise conditions, we used approximate Taylor's expansion to derive the transient and steady-state MSD. Finally, we evaluated the theoretical analysis with some numerical simulations of system identification in different Gaussian and non-Gaussian noise scenarios to validate the finding.

In recent years, algorithms based on the Maximum Versoria Criterion (MVC) and a relative logarithmic cost function have gained the attention of researchers because they improve the filtering accuracy and robustness towards non-Gaussian/impulsive noises. To further enhance the steady-state convergence behavior of these aforementioned algorithms in impulsive noise scenarios, we introduce a generalized, robust logarithmic family (GRLF) framework that underlies the relative logarithmic cost function and MVC, and the corresponding GRLF-based adaptive filters called least mean square based-GRLF (GRLF-LMS) and least absolute difference based-GRLF (GRLF-LAD) algorithms are designed. With an approximate solution using Taylors expansion, the steady-state behavior of the GRLF-LMS and GRLF-LAD methods is presented. Then, algorithms are used in practical simulation studies in system identification to compare the performance of GRLF-LMS and GRLF-LAD filtering in Gaussian and non-Gaussian impulsive environments in terms of accuracy and robustness to that of their competitors.

In adaptive filtering for direction-of-arrival (DOA) estimation, traditional bias-compensated models often suffer from significant performance degradation in the presence of impulsive noise affecting both input and output signals. This paper addresses this challenge by introducing new algorithms for robust DOA estimation tailored for environments contaminated by impulsive noise. We initially employ the error-in-variable (EIV) model to derive a generalized framework for robust adaptive DOA estimation algorithms. Our methodology incorporates the Maximum Versoria (MV) criterion as a cost function, facilitating the development of the robust Gradient Total MV (GTMV) algorithm. To further enhance performance, we introduce a variable step-size mechanism within the GTMV framework (VSS-GTMV), which dynamically adjusts the step size based on the signal-to-noise ratio (SNR) to optimize the trade-off between convergence speed and steady-state error. The convergence properties of the GTMV algorithm are analytically examined, and its effectiveness is substantiated through extensive numerical simulations in impulsive noise environments. Comparative results demonstrate the superiority of our proposed methods over existing competitive approaches in terms of accuracy and robustness.

This paper addresses the issue of direction finding of a cyclostationary signal under impulsive noise environments modeled byα-stable distribution. Sinceα-stable distribution does not have finite second-order statistics, the conventional cyclic correlation-based signal-selective direction finding algorithms do not work effectively. To resolve this problem, we define two robust cyclic correlation functions which are derived from robust statistics property of the correntropy and the nonlinear transformation, respectively. The MUSIC algorithm with the robust cyclic correlation matrix of the received signals of arrays is then used to estimate the direction of cyclostationary signal in the presence of impulsive noise. The computer simulation results demonstrate that the two proposed robust cyclic correlation-based algorithms outperform the conventional cyclic correlation and the fractional lower order cyclic correlation based methods.