Enhanced Batch Adaptive Filter Based on Fractional-Order Generalized Cauchy Kernel Loss

Abstract

Adaptive filters utilizing the low-order moments hidden in robust loss functions have achieved desirable performance under Gaussian input and impulsive noises. However, when the input cannot be modeled by Gaussian process and is simultaneously contaminated by outliers, these filters may suffer from misalignment. To this end, applying fractional-order calculus in stochastic gradient descent method, this letter proposes a fractional-order generalized Cauchy kernel loss (FoGCKL) algorithm to model complex $\alpha$-stable process input. The mean square deviation (MSD) is calculated to evaluate the steady-state performance of FoGCKL. To further avoid steady-state jitters and improve filtering accuracy, an enhanced batch method is constructed in FoGCKL using optimized weighted term, generating another enhanced batch FoGCKL (EB-FoGCKL) algorithm. Simulations on system identification verify the correctness of theoretical analysis and demonstrate the superiorities of FoGCKL and EB-FoGCKL.