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<p>The filtered-x least mean square (Fx-LMS) algorithm has been widely applied in active noise control (ANC) systems. However, in an environment with impulsive noise, this algorithm encounters instability issues, which affect its performance. To deal with this drawback, we propose a novel algorithm called the filtered-error maximum correntropy criterion with adaptive kernel width (Fe-MCC-AKW) to the ANC system. Furthermore, the proposed algorithm can significantly reduce the computational burden because it avoids the computational cost of filtering the reference signal through the secondary path. The challenge of this solution lies in the fact that the weight update equation (at time <i>n</i> ) includes the delayed signal components which may contain impulsive noise at time <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n-m_k\)</EquationSource> </InlineEquation> (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(m_k\)</EquationSource> </InlineEquation> is the memory length of the secondary path), which causes the algorithm to become unstable. To address this problem, the Gaussian kernel width is adaptively adjusted based on an estimated window of residual noise to obtain time-varying step sizes. This solution not only stabilizes the algorithm but also improves its performance. In addition, we have implemented the proposed Fe-MCC-AKW algorithm on a generalized function links artificial neural networks (GFLANN)-based nonlinear controller to enhance its computational efficiency. The study has provided discussions on the convergence conditions and complexity of the proposed algorithm. Simulation results have shown that the ANC system based on the proposed Fe-MCC-AKW algorithm outperforms the ANC systems based on recently developed algorithms for the problem of impulsive noise and nonlinearity.</p>

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Filtered-Error Maximum Correntropy Criterion Algorithm with Adaptive Kernel Width for Nonlinear Active Control of Impulsive Noise

  • 期刊论文

  • 发表日期：

    2025年8月7日

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  • Dinh Cong Le

摘要

The filtered-x least mean square (Fx-LMS) algorithm has been widely applied in active noise control (ANC) systems. However, in an environment with impulsive noise, this algorithm encounters instability issues, which affect its performance. To deal with this drawback, we propose a novel algorithm called the filtered-error maximum correntropy criterion with adaptive kernel width (Fe-MCC-AKW) to the ANC system. Furthermore, the proposed algorithm can significantly reduce the computational burden because it avoids the computational cost of filtering the reference signal through the secondary path. The challenge of this solution lies in the fact that the weight update equation (at time n ) includes the delayed signal components which may contain impulsive noise at time \(n-m_k\) ( \(m_k\) is the memory length of the secondary path), which causes the algorithm to become unstable. To address this problem, the Gaussian kernel width is adaptively adjusted based on an estimated window of residual noise to obtain time-varying step sizes. This solution not only stabilizes the algorithm but also improves its performance. In addition, we have implemented the proposed Fe-MCC-AKW algorithm on a generalized function links artificial neural networks (GFLANN)-based nonlinear controller to enhance its computational efficiency. The study has provided discussions on the convergence conditions and complexity of the proposed algorithm. Simulation results have shown that the ANC system based on the proposed Fe-MCC-AKW algorithm outperforms the ANC systems based on recently developed algorithms for the problem of impulsive noise and nonlinearity.