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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]

To solve the conflicting requirement of fast convergence and low steady-state misalignment, a variable step-size shrinkage set-membership affine projection algorithm is proposed, which is efficient for the correlated input signal and noisy input environments. The new variable step size is derived by minimizing the square of noise-free a posteriori error, and the shrinkage method is employed to estimate the second-order statistics of the noise-free a priori error vector. Moreover, the stability analysis of the algorithm is conducted. Simulations demonstrate the effectiveness of the proposed algorithm for various noisy input environments. [ABSTRACT FROM AUTHOR]

In this paper, the Correntropy Induced Metric (CIM) as an alternative to the well-known mean square error (MSE) is employed in Chebyshev functional link artificial neural network (CFLANN) to deal with the noisy training data set and enhance the generalization performance. The MSE performs well under Gaussian noise but it is sensitive to large outliers. The CIM as a local similarity measure, however, can improve significantly the anti-noise ability of CFLANN. The convergence of the proposed algorithm, namely the CFLANN based on CIM (CFLANNCIM), has been analyzed. Simulation results on nonlinear channel identification show that CFLANNCIM can perform much better than the traditional CFLANN and multiple-layer perceptron (MLP) neural networks trained under MSE criterion. [ABSTRACT FROM AUTHOR]

A new diffusion sign subband adaptive filtering algorithm with an individual weighting factor (IWF-DSSAF) for each subband is proposed for distributed estimation in the impulsive noise environment. Since the inherent decorrelating property of subband adaptive filtering is fully used, the proposed algorithm obtains better performance in terms of convergence rate and tracking capability as compared with the diffusion sign subband adaptive filtering (DSSAF) algorithm. In addition, the stability analysis of the IWF-DSSAF algorithm is performed based on Price's theorem. After that, in order to obtain a faster convergence rate in sparse distributed system identification, the improved proportionate IWF-DSSAF algorithm is proposed, in which a gain distribution matrix is incorporated into the IWF-DSSAF algorithm. Finally, simulations are carried out in the distributed system identification context. The results of simulations demonstrate that the proposed algorithms achieve better convergence performance than their counterparts. [ABSTRACT FROM AUTHOR]

In acoustic echo cancellation (AEC), the sparseness of impulse responses can vary over time or/and context. For such scenario, the proportionate normalized subband adaptive filter (PNSAF) and μ -law (MPNSAF) algorithms suffer from performance deterioration. To this end, we propose their sparseness-measured versions by incorporating the estimated sparseness into the PNSAF and MPNSAF algorithms, respectively, which can adapt to the sparseness variation of impulse responses. In addition, based on the energy conservation argument, we provide a unified formula to predict the steady-state mean-square performance of any PNSAF algorithm, which is also supported by simulations. Simulation results in AEC have shown that the proposed algorithms not only exhibit faster convergence rate than their competitors in sparse, quasi-sparse and dispersive environments, but also are robust to the variation in the sparseness of impulse responses. [ABSTRACT FROM AUTHOR]

To improve the robustness of subband adaptive filter (SAF) against impulsive interferences, we propose two modified SAF algorithms with an individual scale function for each subband, which are derived by maximizing correntropy-based cost function and minimizing logarithm-based cost function, respectively, called MCC-SAF and LC-SAF. Whenever the impulsive interference happens, the subband scale functions can sharply drop the step size, which eliminate the influence of outliers on the tap-weight vector update. Therefore, the proposed algorithms are robust against impulsive interferences and exhibit the faster convergence rate and better tracking capability than the sign SAF (SSAF) algorithm. Besides, in impulse-free interference environments, the proposed algorithms achieve similar convergence performance as the normalized SAF (NSAF) algorithm. Simulation results have demonstrated the performance of our proposed algorithms. [ABSTRACT FROM AUTHOR]

Sparse adaptive filtering algorithms are utilized to exploit system sparsity as well as to mitigate interferences in many applications such as channel estimation and system identification. In order to improve the robustness of the sparse adaptive filtering, a novel adaptive filter is developed in this work by incorporating a correntropy-induced metric (CIM) constraint into the least logarithmic absolute difference (LLAD) algorithm. The CIM as an $$l_{0}$$ -norm approximation exerts a zero attraction, and hence, the LLAD algorithm performs well with robustness against impulsive noises. Numerical simulation results show that the proposed algorithm may achieve much better performance than other robust and sparse adaptive filtering algorithms such as the least mean p-power algorithm with $$l_{1}$$ -norm or reweighted $$l_{1}$$ -norm constraints. [ABSTRACT FROM AUTHOR]

Proposed is a new subband adaptive filter (SAF) algorithm by minimizing Huber’s cost function that is robust to impulsive noises. Generally, this algorithm works in the mode of the normalized SAF (NSAF) algorithm, while it behaves like the sign SAF (SSAF) algorithm only when the impulsive noises appear. To further improve the robustness of this algorithm against impulsive noises, the subband cutoff parameters are updated in a recursive way. Moreover, the proposed algorithm can be interpreted as a variable step size NSAF algorithm, thus it exhibits faster convergence rate and lower steady-state error than the NSAF. Simulation results, using different colored input signals in both impulsive and free-impulsive noise environments, show that the proposed algorithm works better than some existing algorithms. [ABSTRACT FROM AUTHOR]

Abstract: To improve performance of nonlinear adaptive filter based on radius basis function (RBF) networks, a generalized combination scheme is proposed for nonlinear dynamic system identification in this paper. The nonlinear filter proposed is constructed by the convex combination of multiple RBF networks (MCRBF). Its adaptive algorithm with different step sizes is derived by the gradient descent rule, and can overcome the contradiction between convergence speed and precision of the stochastic gradient (SG) algorithm for RBF networks, which is imposed by the selection of a fixed value for the adaption step. Computer simulations demonstrate that the performance of the nonlinear filter proposed is superior to the RBF for nonlinear dynamic system identification in terms of convergence speed, steady state error and tracking capability. [Copyright &y& Elsevier]

To reduce the computational complexity of the bilinear recurrent neural network (BLRNN), a novel low-complexity nonlinear adaptive filter with a pipelined bilinear recurrent neural network (PBLRNN) is presented in this paper. The PBLRNN, inheriting the modular architectures of the pipelined RNN proposed by Haykin and Li, comprises a number of BLRNN modules that are cascaded in a chained form. Each module is implemented by a small-scale BLRNN with internal dynamics. Since those modules of the PBLRNN can be performed simultaneously in a pipelined parallelism fashion, it would result in a significant improvement of computational efficiency. Moreover, due to nesting module, the performance of the PBLRNN can be further improved. To suit for the modular architectures, a modified adaptive amplitude real-time recurrent learning algorithm is derived on the gradient descent approach. Extensive simulations are carried out to evaluate the performance of the PBLRNN on nonlinear system identification, nonlinear channel equalization, and chaotic time series prediction. Experimental results show that the PBLRNN provides considerably better performance compared to the single BLRNN and RNN models. [ABSTRACT FROM AUTHOR]

Abstract: In actual nonlinear active noise control (NANC) systems, there often exist nonlinear distortions in such cases: the primary path may be nonlinear, the reference noise may exhibit nonlinear distortion, and the secondary path may have nonminimum-phase. To solve the problems of nonlinear distortions, two novel feedback adaptive filters based on the functional link neural network (FLNN) for NANC systems with low computational complexity are proposed in this paper, which are a feedback functional link neural network (FFLNN) and a reduced feedback functional link neural network (RFFLNN), respectively. To train the proposed nonlinear filters for NANC systems, a reduced complexity filtered-s least mean square (FSLMS) algorithm using filter bank approach is developed. The analysis of computational complexity shows that the RFFLNN adaptive filter involves less computation as compared to FFLNN and FLNN adaptive filters. Moreover, it is demonstrated through computer simulations for nonlinear noise processes that the RFFLNN adaptive filter outperforms FLNN and FFLNN in term of convergence speed and steady-state error. Furthermore, it is more effective in reducing nonlinear effects in NANC systems than other filters. [Copyright &y& Elsevier]