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Highlights • The filtered-x least mean square/fourth (FXLMS/F) algorithm for active noise control. • A convex combination of the FXLMS/F algorithm (C-FXLMS/F) for active noise control. • The stability condition of the proposed algorithm is analyzed, and computational complexity is provided. • Computer simulations demonstrate good convergence speed and noise reduction performance for active noise control. Abstract The filtered-x least mean square (FXLMS) algorithm is widely used for active noise control (ANC) systems. However, due to the fixed step-size of FXLMS algorithm being used, the FXLMS algorithm results in a compromise between noise reduction performance and convergence speed. Therefore, this paper proposes the filtered-x least mean square/fourth (FXLMS/F) algorithm for ANC systems, which can be viewed as a variable step-size FXLMS (VSS-FXLMS) algorithm. In order to further improve the algorithm performance, the convex combination of the FXLMS/F (C-FXLMS/F) algorithm for ANC systems is presented. Moreover, the computational complexity of the proposed algorithms is analyzed, and a stability condition for the proposed algorithms is provided. Simulation results show that the proposed FXLMS/F and C-FXLMS/F algorithms can achieve better convergence performance as compared to the FXLMS and FXLMF algorithms under various noise input conditions, and the C-FXLMS/F algorithm outperforms the FXLMS/F algorithm. [ABSTRACT FROM AUTHOR]

The standard adaptive filtering algorithm with a single error norm exhibits slow convergence rate and poor noise reduction performance under specific environments. To overcome this drawback, a filtered-x generalized mixed norm (FXGMN) algorithm for active noise control (ANC) system is proposed. The FXGMN algorithm is developed by using a convex mixture of l p and l q norms as the cost function that it can be viewed as a generalized version of the most existing adaptive filtering algorithms, and it will reduce to a specific algorithm by choosing certain parameters. Especially, it can be used to solve the ANC under Gaussian and non-Gaussian noise environments (including impulsive noise with symmetric α -stable ( S α S ) distribution). To further enhance the algorithm performance, namely convergence speed and noise reduction performance, a convex combination of the FXGMN algorithm (C-FXGMN) is presented. Moreover, the computational complexity of the proposed algorithms is analyzed, and a stability condition for the proposed algorithms is provided. Simulation results show that the proposed FXGMN and C-FXGMN algorithms can achieve better convergence speed and higher noise reduction as compared to other existing algorithms under various noise input conditions, and the C-FXGMN algorithm outperforms the FXGMN. [ABSTRACT FROM AUTHOR]

• A novel generalized hyperbolic secant function with l p -norm algorithm is proposed for nonlinear ANC system. • An improved FsGHSFP (IFsGHSFP) algorithm is developed to address the problem of tuning the parameter. • A convex combination algorithm of IFsGHSFP is suggested to strike a balance between convergence and misalignment. 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 l p 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. [ABSTRACT FROM AUTHOR]