A class of robust nonlinear quaternion volterra adaptive filter based on recursive Tukey’s Biweight M-estimate and its performance analysis

This paper introduces a novel class of nonlinear adaptive filters based on Tukey’s Biweight M-Estimate (TBM). Specifically, we present a robust quaternion-valued second-order Volterra adaptive filtering algorithm that utilizes a recursive TBM (QSOV-RTBM). This study includes a comprehensive analysis of the proposed algorithms. Additionally, the effectiveness of this newly introduced algorithm, along with its counterparts, is meticulously assessed via system identification. In environments characterized by impulsive noise, these evaluations illustrate the better performance of the QSOV-RTBM algorithms, surpassing the efficacy of existing methods. In addition to the analysis insights, this paper includes a comprehensive simulation study to corroborate the performance analysis.