Kernel Filtered-x LMS Algorithm for Active Noise Control System with Nonlinear Primary Path

In active noise control (ANC) systems, the primary path may exhibit nonlinear impulse responses. Conventional linear ANC controllers based on a filtered-x least mean square (FxLMS) algorithm exhibit performance degradation when compensating for nonlinear distortions of the primary path. Several nonlinear active noise control algorithms, including Volterra filtered-x least mean square (VFxLMS) and filtered-s least mean square (FsLMS), have been utilized to overcome this nonlinear effect. However, the performance still needs to be improved when the reference noise is mixed with multiple narrowband signals and additional Gaussian white noise. Over the last several years, kernel adaptive filters have exhibited powerful capabilities in multiple signal processing domains. When kernel adaptive filters are introduced into the ANC system, a great challenge is to compensate for the inherent delay caused by the secondary path. Due to the implicit mapping of the kernel method, it is difficult to filter the reference signal in the high-dimensional feature space. In this paper, an approximate method is proposed in which the filtered reference signal is mapped to the high-dimensional feature space. In addition, a kernel filtered-x least mean square (KFxLMS) algorithm is developed for an ANC system with a nonlinear primary path. Simulation experiments demonstrate that the performance of the proposed KFxLMS algorithm is better than that of the FxLMS, VFxLMS, and FsLMS algorithms.