Gaussian Mixture Distribution Based Random Fourier Quasi Newton Algorithm for Nonlinear Active Noise Control

This paper proposes a novel algorithm, called the Gaussian mixture distribution random Fourier L-BFGS (GMRFLBFGS), to enhance the performance of kernel adaptive filters (KAFs) in the scenario of nonlinear active noise control. The proposed algorithm leverages random Fourier feature (RFF) approach based on a Gaussian mixture distribution to perform nonlinear mapping, which can effectively capture complex nonlinear relation within data while avoiding the structural growth issues commonly associated with standard KAFs. Furthermore, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method within the quasi-Newton framework is adopted to optimize the filtering model, which further improves the convergence speed and filtering accuracy of KAFs. To further enhance the robustness of KAFs against outliers, the proposed algorithm incorporates a general similarity measure termed correntropy to construct the cost function. Simulation results are reported to demonstrate the desired filtering capabilities of the GMRFLBFGS algorithm.