Robust Widely Nonlinear Quaternion Volterra Adaptive Filter Based on Recursive General Barron Algorithm and its Performance Analysis

Recent developments in signal processing have led to the introduction of a novel set of algorithms known as the quaternion-valued second-order Volterra (QSOV) least mean square family, alongside an advanced algorithm termed the widely nonlinear QSOV recursive least square (WNL-QSOV-RLS). These innovative methods are adept at handling signals in 3D and 4D dimensions. Nonetheless, their effectiveness is often challenged in real-world conditions where the error sensor is subjected to impulsive or non-Gaussian noise. Under these circumstances, algorithms relying on the MSE criterion tend to underperform or even diverge. In response to these limitations, this brief introduces the General Barron cost function (GBF), leading to the creation of a novel adaptive filter - the widely nonlinear quaternion-valued second-order Volterra adaptive filter based on recursive GBF (WNL-QSOV-RGBF) algorithm. This brief includes an extensive steady-state analysis of the WNL-QSOV-RGBF algorithm. Furthermore, the efficacy of this newly proposed algorithm, along with its family, is rigorously evaluated through simulation-based system identification and wind prediction tests. These tests unequivocally demonstrate the superior performance of the WNL-QSOV-RGBF algorithm in environments plagued by impulsive noise, compared to existing methods. Complementary to the theoretical analysis, this brief also presents a corroborative simulation study to validate the performance metrics.