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Abstract We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l 1 -norm penalty function on the filter coefficients. This l 1 -norm penalty exploits the sparsity of a system in the coefficients update formulation, thus improving the performance when identifying sparse systems. Compared with prior work, the proposed algorithms have lower computational complexity with comparable performance. We study and devise statistical models for these sparsity-aware NSAF algorithms in the mean square sense involving their transient and steady-state behaviors. This study relies on the vectorization argument and the paraunitary assumption imposed on the analysis filter banks, and thus does not restrict the input signal to being Gaussian or having another distribution. In addition, we propose to adjust adaptively the intensity parameter of the sparsity attraction term. Finally, simulation results in sparse system identification demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract A bias-compensated constrained least mean square (BC-CLMS) adaptive filter algorithm for noisy input is proposed. To derive the proposed algorithm, we present a novel cost function whose gradient vector is unbiased. Thereby, the proposed algorithm can mitigate the effect of input noise and obtain an unbiased estimation. Then, the detail performance analysis of the proposed algorithm is also provided. Finally, simulations are carried out to illustrate the advantage of the proposed algorithm. In addition, the correctness of performance analysis is also verified by simulations. [ABSTRACT FROM AUTHOR]

Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adapt then combine MCC and combine then adapt MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distributed estimation are in general based on the mean square error (MSE) criterion, which is desirable when the measurement noise is Gaussian. In non-Gaussian situations, especially for the impulsive-noise case, MCC based methods may achieve much better performance than the MSE methods as they take into account higher order statistics of error distribution. The proposed methods can also outperform the robust diffusion least mean p-power (DLMP) and diffusion minimum error entropy (DMEE) algorithms. The mean and mean square convergence analysis of the new algorithms are also carried out. [ABSTRACT FROM AUTHOR]