Robust generalized hyperbolic secant algorithm for nonlinear active noise control

Abstract

In nonlinear active noise control (ANC) system where the primary noise obeys non-Gaussian distribution, the traditional filter-s least mean square (FsLMS) algorithm is hardly satisfactory. In order to surmount this deficiency, a novel generalized hyperbolic secant function with lp norm (FsGHSFP) algorithm is proposed for nonlinear ANC system, which designs a robust optimization criterion utilizing the generalized hyperbolic secant distribution function. The FsGHSFP algorithm has robust noise attenuation capability for non-Gaussian noise, but suffers from the problem of tuning the parameter. To address this problem, an improved FsGHSFP (IFsGHSFP) algorithm is developed by taking advantage of the fact that continuous mixed norm does not need to adjust norm parameter. Moreover, in order to strike a balance between convergence and misalignment, thereby further enhancing the robustness of the ANC system, a convex combination algorithm of IFsGHSFP is suggested. The robustness mechanism of the proposed algorithms is analyzed, as well as stability conditions and computational complexity. It is verified by simulations that the proposed algorithms accelerate the convergence speed and improve the noise attenuation performance. In addition, the experimental results further validate the effectiveness of the proposed algorithms.