Fractional-Order Maximum Versoria Criterion Algorithms for α-Stable Environment

Recent advances in adaptive filtering have highlighted the effectiveness of the robust algorithms employing error nonlinearity cost functions such as the maximum versoria criterion (MVC), which utilizes stochastic gradient descent (SGD). Traditional SGD-based methods struggle with signals exhibiting sharp spikes and outliers, typical in many modern applications and cannot be adequately modeled by Gaussian processes. To address this issue, we model both the input and noise signals using $\alpha $ -stable distribution. We enhance the MVC method through a fractional-order SGD (FoSGD) approach, resulting in a new method called the fractional-order maximum versoria criterion (FoMVC) algorithm. Then, we rigorously analyze the algorithm’s mean stability and demonstrate its superior performance over existing methods through Monte Carlo simulations in diverse non-Gaussian environments.