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To date, most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or heavy-tailed) non-Gaussian noises, the maximum correntropy criterion (MCC) has recently been used to replace the MMSE criterion in developing several robust Kalman-type filters. To deal with more complicated non-Gaussian noises such as noises from multimodal distributions, in this article, we develop a new Kalman-type filter, called minimum error entropy KF (MEE-KF), by using the minimum error entropy (MEE) criterion instead of the MMSE or MCC. Similar to the MCC-based KFs, the proposed filter is also an online algorithm with the recursive process, in which the propagation equations are used to give prior estimates of the state and covariance matrix, and a fixed-point algorithm is used to update the posterior estimates. In addition, the MEE extended KF (MEE-EKF) is also developed for performance improvement in the nonlinear situations. The high accuracy and strong robustness of MEE-KF and MEE-EKF are confirmed by experimental results. [ABSTRACT FROM AUTHOR]

Recently, maximum correntropy criterion (MCC) has been widely and successfully used in robust signal processing and machine learning, in which the correntropy is maximized instead of minimizing the popular mean square error (MSE) to improve the robustness with respect to outliers or impulsive noises. A lot of efforts have been devoted to derive different adaptive algorithms under MCC, but to date, little insight has been gained as to how the MCC solution will be influenced by outliers. In this paper, we investigate this problem and our focus is mainly on the parameter estimation of a simple linear errors-in-variables (EIVs) model with scalar variables. Under some conditions, we derive an upper bound on the absolute value of the estimation error and show that the MCC solution can get very close to the true value of the unknown parameter even with arbitrarily large outliers in both the input and output variables. Illustrative examples are provided to verify and clarify the theory. [ABSTRACT FROM AUTHOR]

The unscented Kalman filter (UKF) provides a powerful tool for power system forecasting-aided state estimation (FASE). However, when the power systems are affected by the abnormal operating situations, i.e., the non-Gaussian communication noises, sudden loads or state changes, and instrument failures, the original UKF based on the minimum mean square error (MMSE) criterion may suffer from performance degradation. In contrast to the MMSE criterion, the minimum error entropy (MEE) exhibits the robustness with respect to complex non-Gaussian disturbances. In this article, we develop a new unscented Kalman-type filter based on the MEE criterion, termed MEE-UKF. To derive the MEE-UKF, a statistical linearization approach is adopted in the augmented model such that the state and measurement errors are combined in the MEE cost function simultaneously. Then, a fixed-point iteration algorithm is used to recursively update the posterior estimates and covariance matrix. Apart from the impulsive noises, the MEE-UKF can deal with complex multimodal distribution noises in both process and measurement. The high accuracy and strong robustness of MEE-UKF are confirmed by the simulation results on IEEE 14, 30, and 57 bus test systems under different non-Gaussian disturbances. [ABSTRACT FROM AUTHOR]

Common spatial pattern (CSP) is a classic method commonly used in multichannel electroencephalogram (EEG) signal processing, which aims to extract effective features for binary classification by solving spatial filters that maximize the ratio of filtered dispersion between two classes. The aim of this paper is to improve the performance of the conventional CSP method, which will be badly influenced by noises. The recently proposed quantized minimum error entropy (QMEE) criterion is applied to structure a new objective function instead of the ${L} _{2}$ -norm in the conventional CSP. Quantization is utilized to reduce the computational complexity. The new objective function is optimized by a gradient-based iterative algorithm. The desirable performance of the QMEE-based CSP method, namely CSP-QMEE, is demonstrated with a toy example and two real EEG datasets, including Dataset IIb of the brain–computer interfaces (BCIs) Competition IV (three channels) and Dataset IIIa of the BCI Competition III (60 channels). The new method can achieve satisfactory performance compared to existing methods on all datasets. The promising results in this paper suggest that the CSP-QMEE may become a powerful tool for BCIs. [ABSTRACT FROM AUTHOR]

Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non Gaussian signal processing and machine learning. In this paper, we propose a new similarity measure in kernel space, called the kernel risk-sensitive loss (KRSL), and provide some important properties. We apply the KRSL to adaptive filtering and investigate the robustness, and then develop the MKRSL algorithm and analyze the mean square convergence performance. Compared with correntropy, the KRSL can offer a more efficient performance surface, thereby enabling a gradient-based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers. Theoretical analysis results and superior performance of the new algorithm are confirmed by simulation. [ABSTRACT FROM PUBLISHER]

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]

Abstract: As an alternative adaptation criterion, the minimum error entropy (MEE) criterion has been receiving increasing attention due to its successful use in, especially, nonlinear and non-Gaussian signal processing. In this paper, we study the application of error entropy minimization to kernel adaptive filtering, a new and promising technique that implements the conventional linear adaptive filters in reproducing kernel Hilbert space (RKHS) and obtains the nonlinear adaptive filters in original input space. The kernel minimum error entropy (KMEE) algorithm is derived, which is essentially a generalized stochastic information gradient (SIG) algorithm in RKHS. The computational complexity of KMEE is just similar to the kernel affine projection algorithm (KAPA). We also utilize the quantization approach to constrain the network size growth, and develop the quantized KMEE (QKMEE) algorithm. Further, we analyze the mean square convergence of KMEE. The energy conservation relation is derived and a sufficient condition that ensures the mean square convergence is obtained. The performance of the new algorithm is demonstrated in nonlinear system identification and short-term chaotic time series prediction. [Copyright &y& Elsevier]

This paper presents a parameterized version of the stochastic information gradient (SIG) algorithm, in which the error distribution is modeled by generalized Gaussian density (GGD), with location, shape, and dispersion parameters. Compared with the kernel-based SIG (SIG-Kernel) algorithm, the GGD-based SIG (SIG-GGD) algorithm does not involve kernel width selection. If the error is zero-mean, the SIG-GGD algorithm will become the least mean p-power (LMP) algorithm with adaptive order and variable step-size. Due to its well matched density estimation and automatic switching capability, the proposed algorithm is favorably in line with existing algorithms. [ABSTRACT FROM AUTHOR]

Abstract: The maximum mutual information (MaxMI) criterion is used as the adaptation cost for the adaptive filtering. This criterion is robust to measure distortions, and has strong connection with traditional mean-square error (MSE) criterion. Under Gaussian assumption, the closed-form solution of the finite impulse response (FIR) filter is obtained. Further, based on the kernel density estimation, the stochastic mutual information gradient (SMIG) algorithm is derived. Simulation results emphasize the robustness of this new algorithm. [Copyright &y& Elsevier]

Recently, the Kalman filter algorithm based on the minimum error entropy criterion has been presented to outperform the conventional Kalman filter in the case of impulsive noise. In practice, it may be unstable in numerical calculation. This paper proposes a robust algorithm to solve the problem of instability in numerical calculation. The convergence and stability of the algorithm are verified by the performance analysis and simulations. In the mean square behavior analysis, we propose a method to estimate the steady-state errors. Simulations show that the experimental steady-state errors of the algorithms agreed with the theoretical values. [ABSTRACT FROM AUTHOR]

The normalized subband adaptive filtering algorithm provides fast convergence rate for colored input signals as compared to the normalized least mean square algorithm, but it suffers from a poor convergence issue in the α -stable noise. In light of this, the normalized subband p-norm (NSPN) algorithm, which is based on the least mean p-power error (MPE) criterion, is proposed in this study. This technique is not only robust against impulsive noise samples, but it also maintains a fast convergence rate when colored input signals are used. In addition to this, we develop both the steady-state and the transient models of the NSPN algorithm and provide some insights. Then, in order to solve the problem of making a choice regarding the order p in the NSPN algorithm, we design an autonomous system and come up with the NSPN algorithm with a variable p-norm (VP-NSPN). In addition, we offer the TFC-based VP-NSPN algorithm with a fast convergence rate and low steady-state misadjustment simultaneously by making use of the tap-weights feedback-based convex combination (TFC) scheme. In conclusion, simulation results on system identification and acoustic echo cancellation are undertaken in order to validate the superiority of the proposed algorithms and validate the usefulness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In order to reduce the steady-state misalignment of real-coefficient proportionate affine projection sign algorithm (RP-APSA) for sparse impulse responses, a memory RP-APSA is proposed in this paper by exploiting the historical values of proportionate factors, called MP-APSA. Further, to improve the robustness of MP-APSA and the recently proposed memory-improved RP-APSA (MIP-APSA) for impulse responses with mutative sparseness, two sparseness-controlled algorithms (SC-MP-APSA and SC-MIP-APSA) are developed by estimating the sparseness of the impulse response at each iteration. Simulation results in the context of acoustic echo cancellation show that the proposed algorithms retain good robustness against impulsive interferences. More importantly, the proposed sparseness-controlled algorithms can not only obtain low steady-state misalignment in both the sparse and dispersive situations, but also adapt to the variations in the sparseness of the impulse response. [ABSTRACT FROM AUTHOR]

Graph-based clustering commonly provides promising clustering effectiveness as it can preserve samples' local geometric information. Inspired by it, multi-view graph clustering was developed to integrate complementary information among graphs of diverse views and it has received intensive attention recently. Nevertheless, on the one hand, most existing methods require extra k-means after obtaining embedding representations to generate a discrete cluster indicator, which reduces effectiveness due to the two-stage mismatch. On the other hand, numerous complex noises in real-world multi-view data challenge the robustness of existing clustering methods. In this paper, we established a discrete correntropy-based multi-view anchor-graph clustering (DCMAC) model that not only emphasizes the aforementioned issues but also makes use of anchor graphs to improve the efficiency of the graph construction stage. To optimize this non-convex model, we propose a fast half-quadratic-based coordinate descent strategy to acquire the discrete cluster indicator directly without extra k-means. Furthermore, we extend the DCMAC model to a single-view form and provide optimization strategies for it. Extensive experiments illustrate that the proposed method is effective and robust compared to those advanced baselines. • A new discrete correntropy-based multi-view anchor-graph clustering (DCMAC) model is proposed. • A novel half-quadratic-based coordinate descent algorithm is proposed to solve the DCMAC model. • To handle single-view clustering instances, DCMAC is extended to a single-view form named DCAC. • Numerous experiments demonstrate the outstanding effectiveness and robustness of DCMAC. [ABSTRACT FROM AUTHOR]

Partial discharge (PD) detection plays a vital role in on-line condition monitoring of electrical apparatus in the power systems. However, the noise of PD measurements significantly degrades the performance of detection algorithms. In this paper, we focus on developing an adaptive filtering technique for the PD denoising problem. Heretofore, there are just a few literature reviews addressing the PD denoising based on such a method. The proposed recursive continuous S-shaped (RCSS) algorithm integrates the advantages of recursive strategy and continuous S-shaped function into adaptive noise cancellation (ANC) system, yielding enhanced filtering performance. The proposed algorithm can tackle PD noises in both Gaussian and impulsive scenarios, which is easy to implement in practical applications. The convergence behavior is also analyzed. Extensive simulation and experimental results confirm that the proposed algorithm can address polluted PD pulses, even in excessively noisy conditions, resulting in smaller mean square error (MSE) as compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

An adaptive estimation algorithm based on the Lorentzian norm is proposed for echo cancellation in vehicle hands-free communication systems and video teleconferencing systems, namely the affine-projection Lorentzian (APL) algorithm. By minimizing the Lorentzian norm of the a posteriori error vector with a suitable constraint on the weight vector and providing a dynamic Lorentzian-norm-controlling parameter, the proposed APL algorithm achieves robustness against impulsive disturbances and speeds up convergence for colored input signals. The computational complexity of the APL algorithm is analyzed and a fast recursive filtering method is employed to reduce its complexity. The stability analysis, based on energy-conservation arguments, shows that the APL algorithm converges. Furthermore, its tracking behavior is also investigated and a step size optimizing the tracking performance is derived. Simulation results agree well with the theoretical analysis. Simulation results for channel estimation and in-car echo cancellation scenarios demonstrate that the APL algorithm achieves better performance compared to the maximum-correntropy-criterion, affine-projection-generalized-maximum-correntropy, affine-projection-sign, affine-projection-like M-estimate, and Lorentzian adaptive filtering algorithms in various impulsive interference environments. [ABSTRACT FROM AUTHOR]

The traditional image quality assessments, such as the mean squared error (MSE), the signal-to-noise ratio (SNR), and the Peak signal-to-noise ratio (PSNR), are all based on the absolute error of images. Structural similarity (SSIM) index is another important image quality assessment which has been shown to be more effective in the human vision system (HVS). Although there are many essential differences between MSE and SSIM, some important associations exist between them. In this paper, the associations between MSE and SSIM as cost functions in linear decomposition are investigated. Based on the associations, a bit-allocation algorithm for sparse coding is proposed by considering both the reconstructed image quality and the reconstructed image contrast. In the proposed algorithm, the space occupied by a linear coefficient of a basis in sparse coding is reduced to only 9 to 10 bits, in which 1 bit is used to save the sign of linear coefficient, 3 bits are used to save the number of powers of 10 in scientific notation, and only 5 to 6 bits are used to save the significance digits. The experimental results show that the proposed bit-allocation algorithm for sparse coding can maintain both the image quality and the image contrast well. [ABSTRACT FROM AUTHOR]

• A variant of the quantized minimum error entropy (QMEE) algorithm is proposed. • The mean square convergence performance analysis for QMEE algorithm is given. • The theoretical values of the steady-state EMSE for QMEE algorithm are validated by simulations. • QMEE algorithm is applied in electroencephalo (EEG) de-noising task. Adaptive filtering algorithms have been widely used in many areas, among which the minimum error entropy (MEE) algorithm is a superior choice, due to its excellent performance in the non-Gaussian noise situations. However, the computational complexity of the MEE algorithm is expensive, which leads to the computational bottlenecks, especially for large-scale datasets. In order to address the problem, we propose an adaptive filtering algorithm based on the quantized minimum error entropy (QMEE) criterion with an online quantization method, named QMEE algorithm. Moreover, we analyze the transient behavior characteristic and derive an approximate analytical expression for the steady-state excess mean square error (EMSE) based on the Taylor expansion. The extensive simulation results in linear modeling and electroencephalogram (EEG) denoising task demonstrate that the proposed method can outperform other robust adaptive filtering algorithms. [ABSTRACT FROM AUTHOR]

• Correntropy is introduced to the registration problem as a distance metric. • A closed-form solution is given out at each iterative step of the algorithm. • Pointwise correspondences are used to make sure the efficiency. • It's a general framework for m-D point set registration. The iterative closest point (ICP) algorithm is fast and accurate for rigid point set registration, but it works badly when handling noisy data or point clouds with outliers. This paper instead proposes a novel method based on the ICP algorithm to deal with this problem. Firstly, correntropy is introduced into the rigid registration problem which could handle noises and outliers well, and then a new energy function based on maximum correntropy criterion is proposed. After that, a new ICP algorithm based on correntropy is proposed, which performs well in dealing with rigid registration with noises and outliers. This new algorithm converges monotonically from any given parameters, which is similar to the ICP algorithm. Experimental results demonstrate its accuracy and robustness compared with the traditional ICP algorithm. [ABSTRACT FROM AUTHOR]

Summary: Two novel adaptive filtering algorithms based on the mixed square/fourth error criterion are proposed for solving sparse system identification problems. Motivated by the fact that the proportionate update scheme can enhance the tracking ability of the system, we develop a proportionate least mean square/fourth (PLMS/F) algorithm in this paper. Combining the proportionate update scheme and the LMS/F algorithm, the proposed PLMS/F algorithm shows superiority for non‐Gaussian noise environments. Moreover, to further improve the performance of the PLMS/F algorithm in the noisy input cases, a bias‐compensated PLMS/F algorithm is developed by incorporating an unbiased criterion to compensate the bias caused by input noises. Simulation results in the context of the sparse system identification framework demonstrate that the proposed PLMS/F and bias‐compensated PLMS/F algorithms can achieve excellent identification performance in terms of steady‐state misalignment and convergence speed under noisy input and non‐Gaussian output noise environments. [ABSTRACT FROM AUTHOR]

In this brief, a robust and sparse recursive adaptive filtering algorithm, called convex regularized recursive maximum correntropy (CR-RMC), is derived by adding a general convex regularization penalty term to the maximum correntropy criterion (MCC). An approximate expression for automatically selecting the regularization parameter is also introduced. Simulation results show that the CR-RMC can significantly outperform the original recursive maximum correntropy (RMC) algorithm especially when the underlying system is very sparse. Compared with the convex regularized recursive least squares (CR-RLS) algorithm, the new algorithm also shows strong robustness against impulsive noise. The CR-RMC also performs much better than other LMS-type sparse adaptive filtering algorithms based on MCC. [ABSTRACT FROM AUTHOR]

To overcome the performance degradation of adaptive filtering algorithms in the presence of impulsive noise, a novel normalized sign algorithm (NSA) based on a convex combination strategy, called NSA-NSA, is proposed in this paper. The proposed algorithm is capable of solving the conflicting requirement of fast convergence rate and low steady-state error for an individual NSA filter. To further improve the robustness to impulsive noises, a mixing parameter updating formula based on a sign cost function is derived. Moreover, a tracking weight transfer scheme of coefficients from a fast NSA filter to a slow NSA filter is proposed to speed up the convergence rate. The convergence behavior and performance of the new algorithm are verified by theoretical analysis and simulation studies. [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]

Ø The KRSL based adaptive filtering algorithm with sinusoidal signal is derived; Ø A recursive MKRSL based harmonic estimation method is developed; Ø A RMKRSL with adaptive gain factor is proposed to enhance the tracking ability. The development of effective harmonics estimation method plays a crucial role for safe operation of power system. Recently several existing parametric estimation approaches, however, are mainly developed and discussed under the assumption of Gaussian noise which is always unsuitable in real power systems. This work is mainly concerned with the robust parametric estimation methods. The kernel risk sensitive loss (KRSL) shows an advantage in that its performance surface is flat around the optimal solution while sharp far away from the optimal solution and it may exhibit outstanding performance in terms of faster convergence rate and higher estimation accuracy under non-Gaussian noise cases. Therefore, a minimum KRSL (MKRSL) algorithm with sinusoidal signal is designed, and we further develop a novel recursive MKRSL (RMKRSL) algorithm for harmonics estimation in non-Gaussian noise cases. In addition, an adaptive gain factor is introduced into the gain matrix of RMKRSL algorithm to enhance its tracking capability. Some simulations by using the signal generated from the given models and IEEE-1159-PQE databases are conducted to illustrate the performance of the proposed methods under different conditions. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) can be deployed as base stations (BSs) for emergency communications of user equipments (UEs) in 5G/6G networks. In multi-UAV communication networks, UAVs' load balancing and UEs' data rate fairness are two challenging problems and can be optimized by UAV deployment strategies. In this work, we found that these two problems are related by the same performance metric, which makes it possible to optimize the two problems simultaneously. To solve this joint optimization problem, we propose a UAV diffusion deployment algorithm based on the virtual force field method. Firstly, according to the unique performance metric, we define two new virtual forces, which are the UAV-UAV force and UE-UAV force defined by FU and FV, respectively. FV is the main contributor to load balancing and UEs' data rate fairness, and FU contributes to fine tuning the UEs' data rate fairness performance. Secondly, we propose a diffusion control stratedy to the update UAV-UAV force, which optimizes FV in a distributed manner. In this diffusion strategy, each UAV optimizes the local parameter by exchanging information with neighbor UAVs, which achieve global load balancing in a distributed manner. Thirdly, we adopt the successive convex optimization method to update FU, which is a non-convex problem. The resultant force of FV and FU is used to control the UAVs' motion. Simulation results show that the proposed algorithm outperforms the baseline algorithm on UAVs' load balancing and UEs' data rate fairness. [ABSTRACT FROM AUTHOR]

• A novel diffusion adaptation framework and two simple yet efficient sparsity adaptive diffusion algorithms are proposed for CS reconstruction. • Novel analyses on convergence conditions and improvement of the step size upper bound are proposed. • Experimental results confirm the theoretical analysis, and show that the proposed diffusion algorithms can achieve desirable reconstruction accuracy as well as much faster convergence speed compared with stand-alone l 0 -LMS algorithm. Compressive sensing (CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from a few measurement data has been intensively studied. In this paper, we propose a novel diffusion adaptation framework for CS reconstruction, where the reconstruction is performed in a distributed network. The data of the measurement matrix are partitioned into small parts and are stored in each node, which assigns the storage load in a decentralized manner. Information diffusion provides the reconstruction ability of each node. Then, a simple and efficient sparsity adaptive diffusion algorithm has been proposed to collaboratively recover the sparse signal over the network. The convergence of the proposed algorithm is analyzed. To further increase the convergence speed, a novel mini-batch based diffusion algorithm is also proposed. Simulation results show that the proposed framework and algorithms can achieve good reconstruction accuracy as well as a much faster convergence speed compared with stand-alone l 0 -LMS algorithm for CS. [ABSTRACT FROM AUTHOR]