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In recent years, correntropy has been successfully applied to robust adaptive filtering to eliminate adverse effects of impulsive noises or outliers. Correntropy is generally defined as the expectation of a Gaussian kernel between two random variables. This definition is reasonable when the error between the two random variables is symmetrically distributed around zero. For the case of asymmetric error distribution, the symmetric Gaussian kernel is however inappropriate and cannot adapt to the error distribution well. To address this problem, in this brief we propose a new variant of correntropy, named asymmetric correntropy, which uses an asymmetric Gaussian model as the kernel function. In addition, a robust adaptive filtering algorithm based on asymmetric correntropy is developed and its steady-state convergence performance is analyzed. Simulations are provided to confirm the theoretical results and good performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In recent years, the sparse system identification (SSI) has received increasing attention, and various sparsity-aware adaptive algorithms based on the minimum mean square error (MMSE) criterion have been developed, which are optimal under the assumption of Gaussian distributions. However, the Gaussian assumption does not always hold in real-world environments. The maximum correntropy criterion (MCC) is used to replace the MMSE criterion to suppress the heavy-tailed non-Gaussian noises. For some more complex non-Gaussian noises such as those from multimodal distributions, the minimum error entropy (MEE) criterion can outperform MCC although it is computationally somewhat more expensive. To improve the performance of SSI in non-Gaussian noises, in this brief we develop a class of sparsity-aware MEE algorithms with the fixed point iteration (MEE-FP) by incorporating the zero-attracting ($\ell _{1}$ -norm), reweighted zero-attracting (reweighted $\ell _{1}$ -norm) and correntropy induced metric (CIM) penalty terms into the cost function. The corresponding algorithms are termed as ZA-MEE-FP, RZA-MEE-FP, and CIM-MEE-FP, which can achieve better performance than the original MEE-FP algorithm and the MCC based sparsity-aware algorithms. Simulation results confirm the excellent performance of the new algorithms. [ABSTRACT FROM AUTHOR]

Many real-world problems can be modeled as sparse matrix recovery from two-dimensional (2D) measurements, which is recognized as one of the most important topics in signal processing community. Benefited from the roaring success of compressed sensing, many classical iterative algorithms can be directly applied or reinvented for matrix recovery, though they are computationally expensive. To alleviate this, we propose a neural network named 2D learned proximal gradient algorithm (2D-LPGA), which aims to quickly reconstruct the target matrix. Theoretical analysis reveals that if the parameters of the network satisfy certain conditions, it can reconstruct the sparse signal with linear convergence rate. Moreover, numerical experiments demonstrate the superiority of the proposed method over other classical schemes. [ABSTRACT FROM AUTHOR]

This brief developed a novel sparsity constrained recursive adaptive filtering algorithm via the generalized correntropy criterion with variable center (GMCC-VC) for sparse system parameters estimation. In order to improve the performance of the adaptive filtering algorithm with GMCC under the non-Gaussian and non-zero mean noise environments, the GMCC is extended by adding a center which can be located at any position in the generalized Gaussian kernel function. Specifically, we proposed a novel adaptive online update method to optimize the kernel method and center. In addition, we mainly derived a recursive GMCC-VC algorithm based on the GMCC with the sparse constraint to exploit sparsity. Numerical simulation results are given to show that the proposed algorithm is efficient for sparse system parameter estimation problems in non-Gaussian and non-mean noise environments. [ABSTRACT FROM AUTHOR]

In this brief, a separable maximum correntropy criterion (SMCC) algorithm is developed by exploiting the typical separability property of tensors. Utilizing the separability property, a great number savings are obtained along with accelerated learning rate and improved estimate accuracy. In the proposed SMCC, a correntropy scheme is used to construct a adaptive algorithm to combat the impulsive noise and outliers in non-Gaussian environment. The complexity and convergence analysis of the SMCC are presented and discussed. Examples with two-way matrix and three-way tensor are carried out to verify the performance of the proposed SMCC algorithm under mixture Gaussian and Student’s t noises. [ABSTRACT FROM AUTHOR]

A blocked proportionate normalized maximum correntropy criterion (PNMCC) is presented to improve the estimation behavior of the traditional maximum correntropy criterion (MCC) algorithm for identifying the blocked sparse systems. The proposed blocked MCC is implemented by constructing a new cost function based on a hybrid-norm constraint (HNC) of the filter coefficient vector to adaptively utilize the cluster-sparse characteristic of unknown systems, denoting as hybrid-norm constrained PNMCC (HNC-PNMCC). The proposed HNC-PNMCC algorithm is achieved by using the basis pursuit. Various simulations are brought out to confirm the validity of the HNC-PNMCC. Simulation results indicate that the HNC-PNMCC is better than the PNMCC, MCC, and sparse MCC with respect to the estimation performance for the cluster-sparse system identification under the impulsive noises. [ABSTRACT FROM AUTHOR]

This brief focuses on the development of a linear Kalman filtering algorithm when the control input variable is corrupted by noises. The noisy input is considered in the derivation process of the Kalman filter, and an extra term is included in the covariance matrix of the one step error. A bias estimation is naturally generated by the input noise. To reduce the bias, a new cost function of the state estimation error with a regularization term is proposed to obtain the Kalman gain matrix. Simulation results in the context of discrete time state estimation demonstrate that the proposed algorithm can achieve excellent estimation performance in terms of the steady-state misalignment under noisy input environments. [ABSTRACT FROM AUTHOR]

Distributed estimation over networks draws much attraction in recent years. In many situations, due to imperfect information communication among nodes, the performance of traditional diffusion adaptive algorithms such as the diffusion least mean squares (DLMS) may degrade. To deal with this problem, several modified DLMS algorithms have been proposed. However, these DLMS based algorithms still suffer from biased estimation and are not robust against impulsive link noise. In this brief, we focus on improving the performance of diffusion adaptation with noisy links from two aspects: accuracy and robustness. A new algorithm called diffusion maximum total correntropy (DMTC) is proposed. The new algorithm is theoretically unbiased in Gaussian noise, and can efficiently handle the link noise in the presence of large outliers. The adaptive combination rule is applied to further improve the performance. The stability analysis of the proposed algorithm is given. Simulation results show that the DMTC algorithm can achieve good performance in both Gaussian and non-Gaussian noise environments. [ABSTRACT FROM AUTHOR]

This brief proposes a bias-compensated proportionate normalized least mean square (BCPNLMS) method for identifying sparse system when subjected to the noisy input. The proposed BCPNLMS algorithm, which combines the proportionate scheme and the unbiasedness criterion, is able to identify the system parameters with better steady-state accuracy and faster convergence speed than conventional NLMS, bias-compensated NLMS, and PNLMS algorithms. Robustness and high identification accuracy with noisy input can be achieved by introducing the bias-compensation term derived from the unbiasedness criterion. Simulation results on sparse system identification confirm the excellent performance of the proposed BCPNLMS in the presence of both input and output noises. [ABSTRACT FROM AUTHOR]

Kernel adaptive filtering is implemented by evaluating the inner product between the kernel function-based vector and the coefficient vector. In this brief, the coefficient vector is decomposed into the direction vector and the scale, which are updated using the steepest descent method and thus generate a novel online learning method, namely kernel online learning algorithm with scale adaptation (KOL-SA). In addition, the convergence of KOL-SA is proved and an upper bound of steady-state mean square error is therefore obtained. Simulation results confirm that the proposed KOL-SA achieves desirable filtering performance from the aspects of the filtering accuracy and stability. [ABSTRACT FROM AUTHOR]

One of the main problems facing beamforming in smart antenna system is the $ {\alpha }$ -stable noise. To address this problem, a novel algorithm, named the recursive continuous logarithmic mixed ${p}$ -norm (RCLMP) algorithm, which employs a logarithmic cost, is proposed in this brief. The proposed algorithm combines the logarithmic ${p}$ -norms ${1}{\leq } p \leq 2$ which does not need the parameter selection and prior knowledge of ${\alpha }$ -stable noise, and exhibits good robustness against ${\alpha }$ -stable noise. Moreover, we show some ${H}^{{\infty }}$ norm bounds for the proposed algorithm. Simulation results show that the RCLMP algorithm outperforms the existing algorithms in terms of interference rejection capability and estimation accuracy. [ABSTRACT FROM AUTHOR]

Minimum error entropy (MEE), as a robust adaption criterion, has received considerable attention due to its broad applicability, especially in the presence of non-Gaussian noises. In this brief, we propose a constrained adaptive filtering algorithm under MEE criterion, called CMEE, which is derived by incorporating a set of linear equality constrains into MEE to handle a constrained MEE optimization problem. In addition, convergence analysis of the proposed CMEE including the stability and steady-state mean square deviation is studied. Simulation results validate the theoretical conclusions, and confirm the effectiveness of the new algorithm in non-Gaussian noises. [ABSTRACT FROM AUTHOR]

Compared with the least-mean-square algorithm, the least mean $p$th power algorithm shows a better robustness performance against impulsive noises such as the $\alpha$-stable noises. However, it still exhibits slow convergence rate and high kernel misadjustment. To overcome this drawback, a novel recursive logarithmic least mean $p$th (RLLMP) algorithm is proposed for the Volterra system identification under $\alpha$-stable noise environments. Instead of minimizing the $p$th power, the new algorithm aims to minimize the $p$th logarithmic cost, which makes it more robust against impulsive interferences. Furthermore, to enhance tracking performance, an improved variable forgetting factor (IVFF) algorithm (IVFF-RLLMP) is proposed, which is based on the robust estimation of outliers. Simulation results are presented to demonstrate the improved performance of the RLLMP and IVFF-RLLMP. [ABSTRACT FROM AUTHOR]