Hyperbolic Secant Function Algorithms for Nonlinear Active Noise Control models of Kernel Mapping Types

In the case of nonlinear characteristics of noise signals and control systems, the control effect of linear active noise control(ANC) algorithms will be degraded. The kernel adaptive filters (KAFs) can better solve the nonlinear problem by mapping the filtered reference signal to the high dimensional reproductive kernel Hilbert feature space (RKHFS). However, the operations of kernel function require incremental costs with mass input data. To solve this problems, the random Fourier filters (RFFs) achieves nonlinear approximation by mapping the filtered reference signal to the random Fourier feature space (RFFS). This article briefly reviews these two models, and proposes the K-FxHSF and RFF-FxHSF algorithms for impulsive noise environment. Simulation experiments show that the proposed algorithm can achieve ideal performance in the case of nonlinear noise paths.