Fractional-order generalized complex correntropy algorithm for robust active noise control

In recent years, several adaptive filtering algorithms based on fractional-order calculation or correntropy criterion have been proposed. However, these algorithms suffer from rapid performance degradation when confronted with complex-valued non-Gaussian noise environments. To address this issue, this paper introduces the Filtered-X Fractional-Order Generalized Complex Correntropy (FxFOGCC) algorithm for complex domain Active Noise Control (ANC), utilizing the complex generalized Gaussian density (CGGD) function as the kernel function. Compared to existing adaptive ANC algorithms, the FxFOGCC algorithm demonstrates significantly improved robustness and effectiveness. Furthermore, to achieve a faster convergence rate and lower steady-state error, a Convex Combination scheme of the FxFOGCC (CFxFOGCC) algorithm is derived. The paper also presents stability analysis and computational complexity analysis for theoretical derivation. Finally, simulation results validate the superior performance of the proposed algorithms in scenarios involving complex-valued impulsive noise, a mixture of sinusoidal and impulsive noise, as well as real-world vehicle interior noise.