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AbstractIn this study, the boundaries of the chaotic region in the response of a shape memory alloy (SMA) microelectromechanical beam with a magnetostrictive layer under non-Gaussian parametric noise were determined using an analytical approach. By introducing several dimensionless parameters, the nonlinear governing equations for the random vibration of the system were derived. Subsequently, an enhanced version of Melnikov’s function was derived for the stochastic equations, leading to the calculation of analytical expressions to define the boundaries of the chaotic region. The resulting boundaries of the chaotic zone were plotted to illustrate the behavior of the cantilever exposed to noises with varying bandwidths and magnetic field intensities (MFIs). The primary objective of this research is to establish a comprehensive analytical framework for the assessment of dynamic instability in advanced microelectromechanical systems (MEMS). This framework will take into account the complexities associated with nonlinearity, inherent smart functionalities, and stochastic behaviors of the external loads. The results provide valuable insights into how different parameters influence system instability, serving as a foundation for the design of such systems. To validate the methodology and satisfy the necessary conditions for the Melnikov’s function, Poincaré mapping was employed to confirm the analytical results. A good correlation between these results was observed as presented in the results. [ABSTRACT FROM AUTHOR]

Summary: Kalman smoother is an effective algorithm to estimate the state of the dynamic systems with Gaussian noise. However, when the system is affected by non‐Gaussian noise, the traditional Kalman smoother may suffer severe performance degradation, since it is derived from the minimum mean square error criterion. By introducing the maximum correntropy criterion, which accounts for all higher order moments and has the ability to resist non‐Gaussian noise, this article studies the state estimation problem of the bilinear state‐space system with non‐Gaussian noises and parametric uncertainties. The bilinear system with parametric uncertainties is transformed into a linear time‐varying system, and a robust fixed‐point Kalman filter algorithm is derived based on the Cauchy kernel‐based correntropy criterion. To improve the state estimation accuracy, a Cauchy kernel‐based fixed‐point Kalman smoother (CK‐FPKS) algorithm is presented by introducing the backward smoothing. Simulation results show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Xi'an Jiaotong University is the property of Editorial Office of Journal of Xi'an Jiaotong University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Summary The noise that affects underwater acoustic communication (UWAC) is primarily characterised by its non‐stationary nature and is predominantly non‐Gaussian in distribution. The Minimum Mean Square Error (MMSE) criterion‐based receiver/equaliser is suboptimal for Underwater Acoustic Communication (UWAC). An underwater acoustic communication (UWAC) system that is resilient should have the capability to effectively manage a wide range of underwater noise patterns and complex multipath, non‐stationary channels with a high level of reliability. To address these challenges, we suggest the deployment of a robust receiver that autonomously handles the communication channel. This receiver would consist of two stages: the first stage would involve a prefilter based on the time‐reversal mirror (TRM), while the second stage would utilise a Recurrent Neural Network (RNN). Analysis of the proposed receiver in different scenarios unequivocally demonstrates its superiority over the conventional Decision Feedback Equalise (DFE) and Deep Neural Network (DNN) based receiver. [ABSTRACT FROM AUTHOR]

Based on the fast kurtogram, many previous studies have focused on frequency band selection (FBS) affected by interference due to impulsive noise and varying speed conditions. Recently, machine learning algorithms have been considered effective for bearing diagnosis. However, most of these methods are supervised learning and thus suffer from data imbalance in the practical applications. This study proposes a semi-supervised learning indicator called outlier rate diagram (ORgram) based on the signal changes before and after bearing damage. ORgram is suitable for impulsive noise and varying speed conditions. First, the healthy bearing data is segmented by rotational speed and modeled with one-class support vector machine (SVM) for each frequency band. As bearing defects sprout, the defect response will produce the highest outlier rate in the informative frequency band (IFB). After selecting the IFB, techniques such as envelope analysis and order tracking are used to identify damaged bearing components for an alarm to reduce the losses caused by unplanned downtime. [ABSTRACT FROM AUTHOR]

We establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. The SDGs have q players and are driven by a general-dimensional vector Lévy process. By establishing a vector-form Ito-Ventzell formula and a 4-tuple vector-field solution to the unified SPDE, we obtain a Pareto optimal Nash equilibrium policy process or a saddle point policy process to the SDG in a non-zero-sum or zero-sum sense. The unified SPDE is in both a general-dimensional vector form and forward–backward coupling manner. The partial differential operators in its drift, diffusion, and jump coefficients are in time-variable and position parameters over a domain. Since the unified SPDE is of general nonlinearity and a general high order, we extend our recent study from the existing Brownian motion (BM)-driven backward case to a general Lévy-driven forward–backward coupled case. In doing so, we construct a new topological space to support the proof of the existence and uniqueness of an adapted solution of the unified SPDE, which is in a 4-tuple strong sense. The construction of the topological space is through constructing a set of topological spaces associated with a set of exponents { γ 1 , γ 2 , ... } under a set of general localized conditions, which is significantly different from the construction of the single exponent case. Furthermore, due to the coupling from the forward SPDE and the involvement of the discontinuous Lévy jumps, our study is also significantly different from the BM-driven backward case. The coupling between forward and backward SPDEs essentially corresponds to the interaction between noise encoding and noise decoding in the current hot diffusion transformer model for generative AI. [ABSTRACT FROM AUTHOR]

Many current image denoising works focus on Gaussian noise removal. However, in many real-life applications, the noise in an image can follow non-Gaussian distributions, such as compressed speckle noise, salt-and-pepper impulse noise (SPIN), and random-valued impulse noise (RVIN). In such scenarios, image denoising models with mean squared error loss will fail to obtain the best noise estimation results. Thus, we propose a non-Gaussian denoising convolutional neural network (DTNet) with truncation loss, which can address compressed speckle noise, SPIN, and RVIN with the same denoising framework. The model is composed of Res2Net blocks with the ability to extract multiscale information. Experiments show that our proposed DTNet method can effectively remove compressed speckle noise and impulse noise, including SPIN and RVIN. In particular, DTNet can recover the original images from images with 90% SPIN or images with 70% RVIN. [ABSTRACT FROM AUTHOR]

Polynomial Decision Rules (DR) for the problems of discrete RZ (Return-to-Zero) signal distinction in asymmetric-excess non-Gaussian noise are proposed. A new approach is proposed, which is based on the use of a modified moment quality criterion of statistical hypothesis testing and the application of higher-order statistics to describe the characteristics of non-Gaussian noise. Simulation of the DR with different parameters of the signal and noise was carried out. It is shown that taking into account the coefficients of skewness and kurtosis of the non-Gaussian noise the efficiency of signal distinction increases with non-linear processing DR compared to known results, which are optimal for the Gaussian noise model. The conducted studies demonstrate a reduction in false decisions in the processing of RZ signals when considering the coefficients of skewness and kurtosis of non-Gaussian noise. Such an increase in efficiency can exceed twofold, depending on the noise parameters. It is shown that the efficiency of the proposed approach is much higher for small SNR (Signal-to-Noise Ratio) values, for example, less than 1. [ABSTRACT FROM AUTHOR]

This paper addresses a distributed nonlinear filtering issue based on maximum correntropy for dealing with randomly occurring hybrid cyber‐attacks in non‐Gaussian environment. The types of cyber‐attacks include denial of service attacks and deception attacks. First, a modified distributed unscented Kalman filter is proposed, using Cauchy kernel‐based maximum correntropy criterion instead of the traditional mean square error criterion, against cyber‐attacks and non‐Gaussian noise. Then based on fixed‐point iterative rules and information fusion strategy, the update equations of state estimates and covariance matrices of the proposed filter are obtained. Furthermore, the sufficient condition guaranteeing its convergence and computational complexity are also given. Finally, an illustrative example is presented to verify the effectiveness of the proposed filter under hybrid cyber‐attacks in non‐Gaussian environment. [ABSTRACT FROM AUTHOR]

Lattice Kalman filter (LKF) is a nonlinear Kalman filter that utilizes a deterministic sampling method with the advantages of optional sampling points and a flexible balance between computational burden and estimation accuracy. However, the fixed angle of sampling points in LKF can limit the optimality of the selected points. To this end, this paper proposes a novel maximum correntropy square-root rotating lattice Kalman filter (MCSRLKF) to improve the performance of LKF by adjusting the angle of sampling points. In MCSRLKF, a rotation matrix is first constructed to enhance the estimation accuracy of LKF and the optimal rotation angle of sampling points is selected to generate rotating lattice Kalman filter (RLKF). Then, the square-root RLKF (SRLKF) is proposed to enhance the stability and estimation accuracy of RLKF. Due to the utilization of the minimum mean square error criterion in SRLKF, there is a potential for significant performance degradation in non-Gaussian noises. Thus, to enhance the robustness against non-Gaussian noises, the maximum correntropy criterion is applied to SRLKF, generating MCSRLKF. Moreover, the Cramér-Rao lower bound (CRLB) serves as an indicator for assessing the performance of MCSRLKF. Finally, simulations on the nonlinear function model and reentry vehicle tracking model are used to demonstrate that MCSRLKF exhibits excellent filtering accuracy and robustness when dealing with non-Gaussian noises. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power is the property of Electric Power Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Summary: In wireless communication, impulsive noise often degrades channel quality, which poses challenges for equalizers. Although robust equalization methods offer some effectiveness, the occurrence of impulsive noise after training significantly impacts the symbol error rate (SER). To mitigate this issue, we propose a method that involves denoising the received signal using robust wavelet decomposition before equalization. This approach combines the discrete wavelet transform with median and morphological filters to reduce impulsive noise. A pre‐impulsive noise detection mechanism triggers denoising only when impulsive noise is detected. We evaluate the SER performance of the proposed technique using simulations of a 16‐QAM orthogonal frequency division multiplexing (OFDM) system with kernel interpolation‐based frequency domain equalization (FDE) in a Rayleigh fading channel with impulsive noise. Results show that our approach achieves SER levels comparable to conventional methods in Gaussian noise scenarios, demonstrating its effectiveness in challenging wireless communication environments. The simulation results demonstrate that the proposed technique in non‐Gaussian noise gives the SER on par with the FDE in a Gaussian noise environment. [ABSTRACT FROM AUTHOR]

Abstract We address the issue of detecting hidden periodicity when the signal exhibits periodic correlation, but is additionally affected by non-Gaussian noise with unknown characteristics. This scenario is common in various applications. The conventional approach for identifying periodically correlated (PC) behavior involves the frequency domain-based analysis. In our investigation, we also employ such an approach; however, we use a robust version of the discrete Fourier transform incorporating the Huber function-based M-estimation, unlike the classical algorithm. Building upon this approach, we propose robust coherent and incoherent statistics originally designed to identify hidden periodicity in pure PC models. The novelty of this paper lies in introducing robust coherent and incoherent statistics through the application of the robust discrete Fourier transform in classical algorithms and proposing a new technique for period estimation based on the proposed methodology. We explore two types of PC models and two types of additive noise, resulting in PC signals disturbed by non-Gaussian additive noise. Detecting hidden periodicity in such cases proves to be significantly more challenging than in classical scenarios. Through Monte Carlo simulations, we demonstrate the effectiveness of the proposed robust approaches and their superiority over classical. To further substantiate our findings, we analyze three datasets in which hidden periodicity had previously been confirmed in the literature. Among them, two datasets correspond to the condition monitoring area, being a main motivation of our research.

This paper discusses the identification problem of the nonlinear exponential autoregressive model in the non‐Gaussian noise environment. To suppress the negative influence caused by the non‐Gaussian noise on the accuracy of the identification, this paper employs a Cauchy kernel correntropy‐based criterion function to present a robust gradient algorithm for calculating the parameter estimates of the model. To solve the difficulty of selecting the step‐size in the gradient algorithm, this paper derives an optimal step‐size related to the bandwidth of the Cauchy kernel. Moreover, in order to improve the accuracy of the parameter estimations, a Cauchy kernel correntropy‐based robust multi‐innovation identification method is developed by utilizing the multi‐innovation identification theory. Two simulation examples exhibit that the proposed algorithms can effectively reduce the negative influence of the non‐Gaussian noise on parameter estimation in contrast with the conventional least mean squares algorithm. [ABSTRACT FROM AUTHOR]

Accurate parameters are crucial in modern energy systems to ensure the reliable operation of all components. Given the substantial volume of data in monitored systems, high-performance methods are necessary. This paper proposes a new Bayesian multi-output regressor for estimating the parameters of a three-phase transmission line. The presented approach achieves acceptable accuracy in parameter estimation using only one end of the line. The Bayesian regressor is developed using information derived from the data themselves, eliminating the need to explicitly model the system. This capability allows the method to estimate parameters while accommodating different noise models, even in the presence of systematic errors and non-Gaussian random noise. The methodology was validated on various systems, including a two-bus system, IEEE 14-bus, IEEE 39-bus, and IEEE 118-bus, under diverse conditions such as varying sample sizes, loads, and noise levels. These tests demonstrate the robustness of the proposed approach. [ABSTRACT FROM AUTHOR]

In order to reduce the use of wheel angular velocity sensors and improve the estimation accuracy and robustness of the tire–road friction coefficient (TRFC) in non-Gaussian noise environments, this paper proposes a sensorless control-based distributed drive electric vehicle TRFC estimation algorithm using a permanent magnet synchronous motor (PMSM). The algorithm replaces the wheel angular velocity signal with the rotor speed signal obtained from the sensorless control of the PMSM. Firstly, a seven-degree-of-freedom vehicle dynamics model and a mathematical model of the PMSM are established, and the maximum correntropy singular value decomposition generalized high-degree cubature Kalman filter algorithm (MCSVDGHCKF) is derived. Secondly, a sensorless control system of a PMSM based on the MCSVDGHCKF algorithm is established to estimate the rotor speed and position of the PMSM, and its effectiveness is verified. Finally, the feasibility of the algorithm for TRFC estimation in non-Gaussian noise is demonstrated through simulation experiments, the Root Mean Square Error (RMSE) of TRFC estimates for the right front wheel and the left rear wheel were reduced by at least 41.36% and 40.63%, respectively. The results show that the MCSVDGHCKF has a higher accuracy and stronger robustness compared to the maximum correntropy high-degree cubature Kalman filter (MCHCKF), singular value decomposition generalized high-degree cubature Kalman filter (SVDGHCKF), and high-degree cubature Kalman filter (HCKF). [ABSTRACT FROM AUTHOR]

We address the issue of detecting hidden periodicity when the signal exhibits periodic correlation, but is additionally affected by non-Gaussian noise with unknown characteristics. This scenario is common in various applications. The conventional approach for identifying periodically correlated (PC) behavior involves the frequency domain-based analysis. In our investigation, we also employ such an approach; however, we use a robust version of the discrete Fourier transform incorporating the Huber function-based M-estimation, unlike the classical algorithm. Building upon this approach, we propose robust coherent and incoherent statistics originally designed to identify hidden periodicity in pure PC models. The novelty of this paper lies in introducing robust coherent and incoherent statistics through the application of the robust discrete Fourier transform in classical algorithms and proposing a new technique for period estimation based on the proposed methodology. We explore two types of PC models and two types of additive noise, resulting in PC signals disturbed by non-Gaussian additive noise. Detecting hidden periodicity in such cases proves to be significantly more challenging than in classical scenarios. Through Monte Carlo simulations, we demonstrate the effectiveness of the proposed robust approaches and their superiority over classical. To further substantiate our findings, we analyze three datasets in which hidden periodicity had previously been confirmed in the literature. Among them, two datasets correspond to the condition monitoring area, being a main motivation of our research. [ABSTRACT FROM AUTHOR]

The prerequisite for intelligent vehicles to achieve autonomous driving and active safety functions is acquiring accurate vehicle state parameters. Traditional Kalman filters often underperform in non-Gaussian noise environments due to their reliance on Gaussian assumptions. This paper presents the IMM-MCCKF filter, which integrates the interacting multiple model theory (IMM) and the maximum correntropy cubature Kalman filter method (MCCKF), for estimating the state parameters of intelligent vehicles. The IMM-MCCKF successfully suppresses non-Gaussian noise by optimizing a nonlinear cost function using the maximum correntropy criteria, allowing it to capture and analyze signal data outliers accurately. The filter designs various state and measurement noise submodels to adapt to the environment dynamically, thus reducing the impact of unknown noise statistical properties. Accurately measuring the velocity of a vehicle and the angle at which its center of mass drifts sideways is of utmost importance for its ability to maneuver, maintain stability, and ensure safety. These parameters are critical for implementing advanced control systems in intelligent vehicles. The study begins by constructing a nonlinear Dugoff tire model and a three-degrees-of-freedom (3DOF) vehicle model. Subsequently, utilizing low-cost vehicle sensor signals, joint simulations are conducted on the CarSim-Simulink platform to estimate vehicle state parameters. The results demonstrate that in terms of estimation accuracy and robustness in non-Gaussian noise scenarios, the proposed IMM-MCCKF filter consistently outperforms the MCCKF and CKF algorithms. [ABSTRACT FROM AUTHOR]

Summary: The cubature Kalman filter (CKF) based on the maximum correntropy criterion (MCC) has been widely used in the target tracking. However, numerical problems usually occur when there are outliers in the measurement noise. In order to solve the problems of state estimation under the non‐Gaussian measurement noise, a new combined cost function is defined based on the weighted least squares (WLS) method and MCC. In addition, a new method is also used to adaptively adjust the kernel size, then the improved maximum correntropy CKF (PMCCKF) and its corresponding improved maximum correntropy cubature information filter (PMCCIF) are proposed. Compared with the existing algorithms, the new method can not only obtain similar or even better estimation performance, but also avoid numerical problems. Moreover, when the kernel size is infinite, the performance of proposed algorithms will reduce to the standard CKF and corresponding cubature information filter (CIF) respectively, but the classical maximum correntropy CIF (MCCIF) will not, and even the performance is poor in this case. The advantages of the proposed algorithms are verified by four classical nonlinear models. [ABSTRACT FROM AUTHOR]

This paper introduces a novel constrained maximum complex correntropy criterion (CMCCC) for adaptive beamforming. The work addresses the reception of the desired signal in the presence of non-Gaussian noise sources by leveraging the CMCCC within the beamforming framework. It is essential to highlight that correntropy, a similarity function that can extract high-order statistical insights from data, has found application in various domains as a cost function, particularly excelling in non-Gaussian noise environments. One recent application involves its utilization in the realm of adaptive beamforming. However, due to the restriction of correntropy to real-valued data, straightforward application to beamforming scenarios involving complex-valued measurements was not feasible. This paper introduces an approach tailored to handle complex-valued data. We provide an analysis of the mean square convergence of the proposed algorithm and derive the stability condition for convergence. Our simulation results indicate the effectiveness and superiority of the proposed CMCCC method, which maintains robustness against impulsive outliers while achieving superior performance compared to conventional adaptive beamformers. [ABSTRACT FROM AUTHOR]

Continuous gravitational-wave (CW) signals are long-lasting quasi-monochromatic gravitational-wave signals expected to be emitted by rapidly rotating non-axisymmetric neutron stars. Depending on the rotational frequency and sky location of the source, certain CW signals may behave in a similar manner to narrow-band artifacts present in ground-based interferometric detectors. Part of the detector characterization tasks in the current generation of interferometric detectors (Advanced LIGO, Advanced Virgo, and KAGRA) aim at understanding the origin of these narrow artifacts, commonly known as "spectral lines". It is expected that similar tasks will continue after the arrival of next-generation detectors (e.g., Einstein Telescope and Cosmic Explorer). Typically, a fraction of the observed lines in a given detector can be associated to one or more instrumental causes; others, however, have an unknown origin. In this work, we assess the similarity of CW signals to spectral lines in order to understand whether a CW signal may be mistaken for a noise artifact. Albeit astrophysically unlikely, our results do not rule out the possibility of a CW signal being visible in the detector's power spectrum. [ABSTRACT FROM AUTHOR]

The Gaussian noise distribution is typically used in dynamic state estimation (DSE) but it is not always true in practice because of abnormal system inputs, impulsive noise and measurement outliers. In this paper, a new robust DSE approach based on a new robust Lp norm based estimator and the cubature Kalman filter (CKF) is developed for power systems with non-Gaussian noise statistics. The Lp norm based estimator is derived from the Lp norm formula and the quadratic formula in order to alleviate the impacts from bad data and outliers. The proposed Lp-CKF DSE approach exhibits good accuracy because a new estimation error covariance is obtained by using the influence function. The robustness of the proposed Lp-CKF DSE approach is verified by performing simulations on a generator in the IEEE 39-bus system.

The Gaussian sum extended Kalman filter (GSEKF), as a nonlinear non-Gaussian filter, disregards the impact of colored noise components in non-Gaussian noise engendered by external interference, which may compromise the estimation accuracy in global navigation satellite system/strapdown inertial navigation system (GNSS/SINS) tightly coupled positioning and attitude determination systems. To address this problem, an improved Gaussian sum extended Kalman filter with colored noise (colored-GSEKF) is proposed to refine the random model by approximating non-Gaussian noise using Gaussian mixture models and whitening the colored noise components within the non-Gaussian colored noise through state and measurement augmentation. This improved algorithm further enhances the accuracy and stability of the filtering estimation in non-Gaussian colored noise environments. Simulations and experimental results indicate that the proposed colored-GSEKF exhibits superior accuracy in modeling a random model in non-Gaussian colored noise environments. By applying this filter to GNSS/SINS tightly coupled positioning and attitude determination systems utilized on unmanned aerial vehicles influenced by non-Gaussian colored noise, the estimation accuracy and stability can be improved.

We establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. The SDGs have q players and are driven by a general-dimensional vector Lévy process. By establishing a vector-form Ito-Ventzell formula and a 4-tuple vector-field solution to the unified SPDE, we obtain a Pareto optimal Nash equilibrium policy process or a saddle point policy process to the SDG in a non-zero-sum or zero-sum sense. The unified SPDE is in both a general-dimensional vector form and forward–backward coupling manner. The partial differential operators in its drift, diffusion, and jump coefficients are in time-variable and position parameters over a domain. Since the unified SPDE is of general nonlinearity and a general high order, we extend our recent study from the existing Brownian motion (BM)-driven backward case to a general Lévy-driven forward–backward coupled case. In doing so, we construct a new topological space to support the proof of the existence and uniqueness of an adapted solution of the unified SPDE, which is in a 4-tuple strong sense. The construction of the topological space is through constructing a set of topological spaces associated with a set of exponents {γ1,γ2,…} under a set of general localized conditions, which is significantly different from the construction of the single exponent case. Furthermore, due to the coupling from the forward SPDE and the involvement of the discontinuous Lévy jumps, our study is also significantly different from the BM-driven backward case. The coupling between forward and backward SPDEs essentially corresponds to the interaction between noise encoding and noise decoding in the current hot diffusion transformer model for generative AI.

In this paper, we focus on the investigations on the stochastic stability and the stochastic resonance (SR) phenomena for a FitzHugh-Nagumo system with time delay induced by a multiplicative non-Gaussian colored noise and an additive Gaussian colored noise. By use of the fast descent method, the unified colored noise approximation and the two-state theory for the SR, the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) caused by different noise terms and time delay are explored. The investigation results indicate that the two noise intensities, time delay and the departure parameter from the Gaussian noise can all reduce the probability density around the two stable states and destroy the stability of the neural system; while the two noise correlation times τ and τ 0 can both improve the probability density around both stable states and reinforce the biological stability of the neural system. As regards the SNR, it is found that the two noise intensities and the departure coefficient can all weaken the SR effect, while time delay α and the correlation time τ of the multiplicative noise will always magnify the SR phenomenon. It is worth to mention that the correlation time τ 0 of the additive noise can stimulate the SR effect, but not alter the maximum of the SNR. [ABSTRACT FROM AUTHOR]

This article develops a subband Hammerstein spline adaptive filtering (SHSAF) algorithm with the exponential hyperbolic cosine (EHC) cost to acquire robustness against non-Gaussian noises, which is called the SHSAF-EHC algorithm. The delayless multiband-structured subband strategy is employed to enhance the convergence property in the Hammerstein-type nonlinear filtering structure. In addition, the statistical performance analysis of SHSAF-EHC is rigorously derived in the mean and mean-square senses. Numerical experiments under non-Gaussian noise scenarios corroborate the accuracy of theoretical findings and validate the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

One of the main disadvantages of the traditional mean square error (MSE)-based constructive networks is their poor performance in the presence of non-Gaussian noises. In this paper, we propose a new incremental constructive network based on the correntropy objective function (correntropy-based constructive neural network (C2N2)), which is robust to non-Gaussian noises. In the proposed learning method, input and output side optimizations are separated. It is proved theoretically that the new hidden node, which is obtained from the input side optimization problem, is not orthogonal to the residual error function. Regarding this fact, it is proved that the correntropy of the residual error converges to its optimum value. During the training process, the weighted linear least square problem is iteratively applied to update the parameters of the newly added node. Experiments on both synthetic and benchmark datasets demonstrate the robustness of the proposed method in comparison with the MSE-based constructive network, the radial basis function (RBF) network. Moreover, the proposed method outperforms other robust learning methods including the cascade correntropy network (CCOEN), Multi-Layer Perceptron based on the Minimum Error Entropy objective function (MLPMEE), Multi-Layer Perceptron based on the correntropy objective function (MLPMCC) and the Robust Least Square Support Vector Machine (RLS-SVM). [ABSTRACT FROM AUTHOR]

In hidden Markov chain (HMC) models, widely used for target tracking, the process noise and measurement noise are in general assumed to be independent and Gaussian for mathematical simplicity. However, the independence and Gaussian assumptions do not always hold in practice. For instance, in a typical radar tracking application, the measurement noise is correlated over time as the sampling frequency of a radar is generally much higher than the bandwidth of the measurement noise. In addition, target maneuvers and measurement outliers imply that the process noise and measurement noise are non-Gaussian. To solve this problem, we resort to triplet Markov chain (TMC) models to describe stochastic systems with correlated noise and derive a new filter under the maximum correntropy criterion to deal with non-Gaussian noise. By stacking the state vector, measurement vector, and auxiliary vector into a triplet state vector, the TMC model can capture the complete dynamics of stochastic systems, which may be subjected to potential parameter uncertainty, non-stationarity, or error sources. Correntropy is used to measure the similarity of two random variables; unlike the commonly used minimum mean square error criterion, which uses only second-order statistics, correntropy uses second-order and higher-order information, and is more suitable for systems in the presence of non-Gaussian noise, particularly some heavy-tailed noise disturbances. Furthermore, to reduce the influence of round-off errors, a square-root implementation of the new filter is provided using QR decomposition. Instead of the full covariance matrices, corresponding Cholesky factors are recursively calculated in the square-root filtering algorithm. This is more numerically stable for ill-conditioned problems compared to the conventional filter. Finally, the effectiveness of the proposed algorithms is illustrated via three numerical examples. [ABSTRACT FROM AUTHOR]

Recent advances in data science are opening up new research fields and broadening the range of applications of stochastic dynamical systems. Considering the complexities in real-world systems (e.g., noisy data sets and high dimensionality) and challenges in mathematical foundation of machine learning, this review presents two perspectives in the interaction between stochastic dynamical systems and data science. On the one hand, deep learning helps to improve first principle-based methods for stochastic dynamical systems. AI for science, combining machine learning methods with available scientific understanding, is becoming a valuable approach to study stochastic dynamical systems with the help of observation data. On the other hand, a challenge is the theoretical explanations for deep learning. It is crucial to build explainable deep learning structures with the help of stochastic dynamical systems theory in order to demonstrate how and why deep learning works. In this review, we seek better understanding of the mathematical foundation of the state-of-the-art techniques in data science, with the help of stochastic dynamical systems, and we further apply machine learning tools for studying stochastic dynamical systems. This is achieved through stochastic analysis, algorithm development, and computational implementation. Topics involved with this review include Stochastic Analysis, Dynamical Systems, Inverse Problems, Data Assimilation, Numerical Analysis, Optimization, Nonparametric Statistics, Uncertainty Quantification, Deep Learning, and Deep Reinforcement Learning. Moreover, we emphasize available analytical tools for non-Gaussian fluctuations in scientific and engineering modeling. [ABSTRACT FROM AUTHOR]

Using nonlinear stochastic dynamics, the impact of non-Gaussian noise is investigated for vibration to electric energy conversion schemes. For the purpose of utilizing noise in energy harvesting, which offers helpful tips for the development of micropower generators of practical importance, we consider that noise can either be additive or multiplicative in nature. We found that when the property of the noise deviates from the Gaussian characteristics, maximum power generation due to autonomous stochastic resonances disappears. Furthermore, in terms of power generation, non-Gaussian noise outperforms the Gaussian noise.

Purposes In navigation and positioning system, the multipath estimation algorithms based on Kalman filter framework can effectively improve the positioning accuracy. When the initial value of the process noise and observation noise covariance of such algorithms is improperly selected, a large error or even divergence of the estimation results may occur. In addition, because the algorithm is based on the minimum mean squared error criterion, it is susceptible to non-Gaussian noise, especially under heavy-tailed non-Gaussian noise, which has the problem of significant degradation of estimation accuracy. Methods In order to maintain good multipath estimation results under both Gaussian noise and non-Gaussian noise and improve positioning accuracy, an adaptive maximum correntropy unscented Kalman Filter (AMCUKF) multipath estimation algorithm is proposed in this paper. The AMCUKF algorithm introduces the maximum correntropy as an optimization criterion in the process of observation update to solve the problem of estimation accuracy degradation under non-Gaussian noise. In the process of noise covariance update, the residual sequence of the observed quantity is used to recursively update the noise covariance to solve the improper initial value selection of the process noise and the observed noise covariance. Findings Simulation experiments are carried out under Gaussian noise and non-Gaussian noise, and by comparing with two estimation algorithms based on Kalman filter framework, it is shown that AMCUKF multipath algorithm can not only maintain better multipath estimation results under Gaussian noise, but also maintain higher multipath estimation accuracy under non-Gaussian noise, effectively suppressing the interference of non-Gaussian noise.

Accurate parameters are crucial in modern energy systems to ensure the reliable operation of all components. Given the substantial volume of data in monitored systems, high-performance methods are necessary. This paper proposes a new Bayesian multi-output regressor for estimating the parameters of a three-phase transmission line. The presented approach achieves acceptable accuracy in parameter estimation using only one end of the line. The Bayesian regressor is developed using information derived from the data themselves, eliminating the need to explicitly model the system. This capability allows the method to estimate parameters while accommodating different noise models, even in the presence of systematic errors and non-Gaussian random noise. The methodology was validated on various systems, including a two-bus system, IEEE 14-bus, IEEE 39-bus, and IEEE 118-bus, under diverse conditions such as varying sample sizes, loads, and noise levels. These tests demonstrate the robustness of the proposed approach.

In order to reduce the use of wheel angular velocity sensors and improve the estimation accuracy and robustness of the tire–road friction coefficient (TRFC) in non-Gaussian noise environments, this paper proposes a sensorless control-based distributed drive electric vehicle TRFC estimation algorithm using a permanent magnet synchronous motor (PMSM). The algorithm replaces the wheel angular velocity signal with the rotor speed signal obtained from the sensorless control of the PMSM. Firstly, a seven-degree-of-freedom vehicle dynamics model and a mathematical model of the PMSM are established, and the maximum correntropy singular value decomposition generalized high-degree cubature Kalman filter algorithm (MCSVDGHCKF) is derived. Secondly, a sensorless control system of a PMSM based on the MCSVDGHCKF algorithm is established to estimate the rotor speed and position of the PMSM, and its effectiveness is verified. Finally, the feasibility of the algorithm for TRFC estimation in non-Gaussian noise is demonstrated through simulation experiments, the Root Mean Square Error (RMSE) of TRFC estimates for the right front wheel and the left rear wheel were reduced by at least 41.36% and 40.63%, respectively. The results show that the MCSVDGHCKF has a higher accuracy and stronger robustness compared to the maximum correntropy high-degree cubature Kalman filter (MCHCKF), singular value decomposition generalized high-degree cubature Kalman filter (SVDGHCKF), and high-degree cubature Kalman filter (HCKF).

Unmanned Aerial Vehicle (UAV) communication is a promising technology that provides swift and flexible on-demand wireless connectivity for devices without infrastructure support. With recent developments in UAVs, spectrum and energy efficient green UAV communication has become crucial. To deal with this issue, Spectrum Sharing Policy (SSP) is introduced to support green UAV communication. Spectrum sensing in SSP must be carefully formulated to control interference to the primary users and ground communications. In this paper, we propose spectrum sensing for opportunistic spectrum access in green UAV communication to improve the spectrum utilization efficiency. Different from most existing works, we focus on the problem of spectrum sensing of randomly arriving primary signals in the presence of non-Gaussian noise/interference. We propose a novel and improved p-norm-based spectrum sensing scheme to improve the spectrum utilization efficiency in green UAV communication. Firstly, we construct the p-norm decision statistic based on the assumption that the random arrivals of signals follow a Poisson process. Then, we analyze and derive the approximate analytical expressions of the false-alarm and detection probabilities by utilizing the central limit theorem. Simulation results illustrate the validity and superiority of the proposed scheme when the primary signals are corrupted by additive non-Gaussian noise and arrive randomly during spectrum sensing in the green UAV communication.

Abstract The problem of designing a robustified Kalman filtering technique, insensitive to spiky observations, or outliers, contaminating the Gaussian observations has been presented in the paper. Firstly, a class of M-robustified dynamic stochastic approximation algorithms is derived by minimizing at each stage a specific time-varying M-robust performance index, that is, general for a family of algorithms to be considered. The gain matrix of a particular algorithm is calculated at each stage by minimizing an additional criterion of the approximate minimum variance type, with the aid of the statistical linearization method. By combining the proposed M-robust estimator with the one-stage optimal prediction, in the minimum mean-square error sense, a new statistically linearized M-robustified Kalman filtering technique has been derived. Two simple practical versions of the proposed M-robustified state estimator are derived by approximating the mean-square optimal statistical linearization coefficient with the fixed and the time-varying factors. The feasibility of the approaches has been analysed by the simulations, using a manoeuvring target radar tracking example, and the real data, related to an object video tracking using short-wave infrared camera.

For power system state estimation, the measurement noise is usually assumed to follow the Gaussian distribution, and the widely used estimator is the weighted least squares (WLS). However, the Gaussian distribution assumption is not always true, and the performance of WLS becomes bad when the measurement noise is non-Gaussian. In this paper, a new distributed state estimation (SE) method is proposed for multi-area power systems. The proposed distributed method is based on the generalized loss function so that it can reduce the influence of non-Gaussian noise and bad data. Further, thanks to the matrix-splitting technology, the proposed distributed method can be implemented in a distributed way so that the computation time in each local area can be reduced. The simulation results carried out in the IEEE 30-bus and 118-bus systems verify the robustness and effectiveness of the proposed distributed SE method. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive robust maximum correntropy cubature Kalman filter (AMCCKF) for spacecraft attitude estimation is proposed. The main aim is to enable the algorithm to resist the influence of noise non-Gaussian and insufficient statistical information on process noise in the system. Based on the maximum correntropy criterion in this study, the robust filtering algorithm is derived by establishing the regression model. In addition, the Cauchy kernel function is used to replace the Gaussian kernel function in the cost function to prevent a singular matrix from appearing in algorithm operation. Furthermore, the process noise is corrected by an adaptive fading factor. The quaternion normalization problem is solved by constructing a minimum constraint cost function using additive quaternion property. The simulation results show that the proposed AMCCKF algorithm has better estimation accuracy and robustness under the conditions of non-Gaussian noise and insufficient statistical information of process noise. [ABSTRACT FROM AUTHOR]

This study considers a robust quadratic covariance‐constrained filtering problem for discrete time‐varying linear and non‐linear dynamic systems with non‐Gaussian noises. Non‐Gaussian noises are presumed to be unknown, bounded, and limited in a specified ellipsoidal set. In this approach, first, a general standard linear form of the filter is introduced for state estimation in linear dynamic systems. The filter gain is obtained by minimizing the upper bound of the estimation error's covariance matrix. The Lyapunov theory demonstrates the stability of this filter. Second, we extend the proposed filtering approach to non‐linear dynamic systems that are considered as a combination of linear and non‐linear terms. The Lipschitz‐like condition is assumed for the non‐linear part. A new filter structure is proposed in this case and the filter gain is obtained by the same idea to minimize the upper bound of the error's covariance matrix. Finally, four numerical examples are presented to signify the effectiveness and performance of the proposed filters for linear and non‐linear systems. [ABSTRACT FROM AUTHOR]

The prerequisite for intelligent vehicles to achieve autonomous driving and active safety functions is acquiring accurate vehicle state parameters. Traditional Kalman filters often underperform in non-Gaussian noise environments due to their reliance on Gaussian assumptions. This paper presents the IMM-MCCKF filter, which integrates the interacting multiple model theory (IMM) and the maximum correntropy cubature Kalman filter method (MCCKF), for estimating the state parameters of intelligent vehicles. The IMM-MCCKF successfully suppresses non-Gaussian noise by optimizing a nonlinear cost function using the maximum correntropy criteria, allowing it to capture and analyze signal data outliers accurately. The filter designs various state and measurement noise submodels to adapt to the environment dynamically, thus reducing the impact of unknown noise statistical properties. Accurately measuring the velocity of a vehicle and the angle at which its center of mass drifts sideways is of utmost importance for its ability to maneuver, maintain stability, and ensure safety. These parameters are critical for implementing advanced control systems in intelligent vehicles. The study begins by constructing a nonlinear Dugoff tire model and a three-degrees-of-freedom (3DOF) vehicle model. Subsequently, utilizing low-cost vehicle sensor signals, joint simulations are conducted on the CarSim-Simulink platform to estimate vehicle state parameters. The results demonstrate that in terms of estimation accuracy and robustness in non-Gaussian noise scenarios, the proposed IMM-MCCKF filter consistently outperforms the MCCKF and CKF algorithms.