non-Gaussian Noise Research Articles

Robust locally linear embedding and its application in analogue circuit fault diagnosis

During long-term operation of analogue circuits, fault diagnosis is important for preventing the occurrence of hazards. However, noise often accompanies sampled signals and makes the task of fault diagnosis more difficult. Therefore, developing a robust feature extraction technique is an indispensable part of fault diagnosis. The locally linear embedding (LLE) algorithm has recently emerged as a promising technique for dimensional reduction and feature extraction because it preserves linear neighborhoods, and it is quite effective when there is a locally linear dependent structure embedded in fault data. However, LLE is sensitive to noise. Therefore, the maximum correntropy criterion is adopted to resist non-Gaussian noise by seeking the optimal weight coefficient, and a half-quadratic optimization procedure is introduced to address the objective function. Moreover, softmax regression is applied to locate faults. Finally, two typical analogue circuit systems are used to demonstrate the robustness of the modified algorithm to non-Gaussian noise. The experimental results show that the robust LLE algorithm can outperform LLE in the extraction of fault features when there is non-Gaussian noise in the fault signals, and the proposed fault diagnosis method has a better effect in locating faults compared with other feature extraction methods.

Graph Diffusion Kernel Maximum Correntropy Criterion Over Sensor Network and Its Performance Analysis

In recent years, graph signal processing has attracted much attention due to its ability to model irregular and interactive data generated by wireless sensor networks (WSNs). However, there is no practical method to deal with the problem of modeling nonlinear systems in non-Gaussian noise environments. Given that the maximum correntropy criterion (MCC) exhibits robustness to impulsive and non-Gaussian noise, this paper introduces it into the graph kernel adaptive filtering algorithm and develops a graph diffusion kernel MCC (GDKMCC) algorithm. To suppress the problem of the infinite growth of the filter coefficient vector of the proposed algorithm, a pre-trained dictionary (PD) method is used in this paper. In addition, the mean-square transient behavior and the convergence condition of the GDKMCC-PD algorithm are also provided under some assumptions. Finally, the simulation results verify the superiority of the proposed algorithm in modeling nonlinear systems under non-Gaussian noise environments and the correctness of the theoretical model.

Time Series of Space Observations: Analysis of Local Meteorological and Solar Series

A range of issues related to the results of the analysis of some meteorological and solar series of satellite observations in the Kara-Dag area (Crimea) is considered. A qualitative and quantitative picture of changes in the total insolation falling on the Earth’s surface, air temperature at a height of 2 m, and the Earth’s surface temperature in Kara-Dag over the past 38 years is presented. A numerical model has been constructed that makes it possible to predict the most powerful fluctuation with a period of 1 year in the analyzed data. The following methods were used in the work: the method of wavelet analysis, statistical methods for extracting Gaussian and non-Gaussian noise, an iterative method for constructing and estimating the accuracy of model approximations. Coherent variations in the analyzed and some global geodynamic and solar time series were established using two-channel autoregressive analysis. A qualitative characteristic of the process of changing the main variations in the analyzed time series was obtained using the analysis of phase trajectories on the Poincaré plane.

Maximum Correntropy-Based Extended Particle Filter for Nonlinear System

To solve the particle degradation and sample impoverishment, a maximum correntropy-based extended particle filter method is proposed by optimizing the important density function. In the proposed method, the importance sampling is guided by the measurement information, the entropy criterion and high-order moments information of the signal are fully utilized, and the non-Gaussian heavy-tailed distribution noise and the noise with outliers are effectively suppressed. The simulation results demonstrate the effectiveness and feasibility of the filtering method.

A Graph-Space Optimal Transport Approach Based on Kaniadakis κ-Gaussian Distribution for Inverse Problems Related to Wave Propagation.

Data-centric inverse problems are a process of inferring physical attributes from indirect measurements. Full-waveform inversion (FWI) is a non-linear inverse problem that attempts to obtain a quantitative physical model by comparing the wave equation solution with observed data, optimizing an objective function. However, the FWI is strenuously dependent on a robust objective function, especially for dealing with cycle-skipping issues and non-Gaussian noises in the dataset. In this work, we present an objective function based on the Kaniadakis κ-Gaussian distribution and the optimal transport (OT) theory to mitigate non-Gaussian noise effects and phase ambiguity concerns that cause cycle skipping. We construct the κ-objective function using the probabilistic maximum likelihood procedure and include it within a well-posed version of the original OT formulation, known as the Kantorovich-Rubinstein metric. We represent the data in the graph space to satisfy the probability axioms required by the Kantorovich-Rubinstein framework. We call our proposal the κ-Graph-Space Optimal Transport FWI (κ-GSOT-FWI). The results suggest that the κ-GSOT-FWI is an effective procedure to circumvent the effects of non-Gaussian noise and cycle-skipping problems. They also show that the Kaniadakis κ-statistics significantly improve the FWI objective function convergence, resulting in higher-resolution models than classical techniques, especially when κ=0.6.

Joint Detection and Reconstruction of Weak Spectral Lines under Non-Gaussian Impulsive Noise with Deep Learning

Non-Gaussian impulsive noise in marine environments strongly influences the detection of weak spectral lines. However, existing detection algorithms based on the Gaussian noise model are futile under non-Gaussian impulsive noise. Therefore, a deep-learning method called AINP+LR-DRNet is proposed for joint detection and the reconstruction of weak spectral lines. First, non-Gaussian impulsive noise suppression was performed by an impulsive noise preprocessor (AINP). Second, a special detection and reconstruction network (DRNet) was proposed. An end-to-end training application learns to detect and reconstruct weak spectral lines by adding into an adaptive weighted loss function based on dual classification. Finally, a spectral line-detection algorithm based on DRNet (LR-DRNet) was proposed to improve the detection performance. The simulation indicated that the proposed AINP+LR-DRNet can detect and reconstruct weak spectral line features under non-Gaussian impulsive noise, even for a mixed signal-to-noise ratio as low as −26 dB. The performance of the proposed method was validated using experimental data. The proposed AINP+LR-DRNet detects and reconstructs spectral lines under strong background noise and interference with better reliability than other algorithms.

Robust automatic modulation classification under noise mismatch

Automatic modulation classification plays a critical role in the intelligent reception of unknown wireless signals. In practice, the dynamic wireless environment brings a great challenge, and the actual test model is inconsistent with the training model. Therefore, aiming at the problem of noise mismatch, this paper proposes a new modulation classification method based on KD-GoogLeNet and Squeeze-Excitation (KD-GSENet). Using the k-dimensional tree, the complex wireless signals are converted into color images rather than normal constellations, which can enhance the classification features. Considering the attention block has the inherent advantage of assigning more weights to important features, this paper further uses it to improve the GoogLeNet. Finally, extensive experiments are presented including Gaussian noise, non-Gaussian noise, and the scenarios of noise mismatch. Numerical results verify the superior classification performance of the proposed KD-GSENet under different scenarios.

Analysis on the inherent noise tolerance of feedforward network and one noise-resilient structure

In the past few decades, feedforward neural networks have gained much attraction in their hardware implementations. However, when we realize a neural network in analog circuits, the circuit-based model is sensitive to hardware nonidealities. The nonidealities, such as random offset voltage drifts and thermal noise, may lead to variation in hidden neurons and further affect neural behaviors. This paper considers that time-varying noise exists at the input of hidden neurons, with zero-mean Gaussian distribution. First, we derive lower and upper bounds on the mean square error loss to estimate the inherent noise tolerance of a noise-free trained feedforward network. Then, the lower bound is extended for any non-Gaussian noise cases based on the Gaussian mixture model concept. The upper bound is generalized for any non-zero-mean noise case. As the noise could degrade the neural performance, a new network architecture is designed to suppress the noise effect. This noise-resilient design does not require any training process. We also discuss its limitation and give a closed-form expression to describe the noise tolerance when the limitation is exceeded.

State of charge estimation for Li-ion batteries based on iterative Kalman filter with adaptive maximum correntropy criterion

Nonlinear filter methods are commonly employed for model-driven based battery state of charge (SOC) estimation because of their ability to suppress Gaussian noise. Due to the uncertainty of complicated operational conditions, the minimum mean square error (MMSE) criterion based Kalman filter (KF) methods may not guarantee sufficient SOC estimation accuracy in the presence of non-Gaussian noise. To enhance the anti-interference performance of the KFs based SOC estimation method, a novel methodology that combines the adaptive kernel width based maximum correntropy criterion (AMCC) with the Levenberg-Marguardt (L-M) principle based adaptive iterative extended KF (AIEKF) is proposed. Firstly, the MMSE criterion of the EKF is replaced by the MCC criterion and an adaptive kernel width strategy is designed to weaken the effect of anomalous data. Then, the AMCC-corrected covariance matrix and state are updated using an L-M optimized multi-step iterative filter during the measurement update phase. Finally, the combination of AMCC and AIEKF is devised to execute SOC estimation. Several sets of data from different temperatures and operational conditions are used to verify the validity of the proposed AMCC-AIEKF method. Compared with the adaptive EKF (AEKF) and the adaptive iterative EKF (AIEKF) method, the AMCC-AIEKF method has the advantage in terms of SOC estimation accuracy and robustness under different operational conditions with noiseless, Gaussian noise and non-Gaussian noise.

A diffusion strategy for robust distributed estimation based on streaming graph signals

The problem of robust distributed estimation over dynamic and streaming graph signals is investigated in this paper. Existing works related to distributed estimation over dynamic and streaming graph signals are mainly derived from the Mean-Square-Error criterion, and they are vulnerable to non-Gaussian noise. Therefore, a new kind of diffusion Mixture correntropy (d-MC) algorithm is developed to deal with the disadvantage in this paper. Incorporating the diffusion strategy and a novel cost function, the proposed algorithm could accurately estimate the graph filter parameter with the dynamic and streaming graph signals, and achieve desirable performance under both Gaussian and impulsive noise environment. Besides, the theoretical analysis results of mean and mean-square stability are derived. Simulations on various case studies indicate the desirable performance of proposed d-MC algorithm by comparing it to other benchmarks.

Resource-efficient digital characterization and control of classical non-Gaussian noise

We show the usefulness of frame-based characterization and control [PRX Quantum 2, 030315 (2021)] for non-Markovian open quantum systems subject to classical non-Gaussian dephasing. By focusing on the paradigmatic case of random telegraph noise and working in a digital window frame, we demonstrate how to achieve higher-order control-adapted spectral estimation for the noise-optimized dynamical decoupling design. We find that, depending on the operating parameter regime, control that is optimized based on non-Gaussian noise spectroscopy can substantially outperform standard Walsh decoupling sequences as well as sequences that are optimized based solely on Gaussian noise spectroscopy. This approach is also intrinsically more resource-efficient than frequency-domain comb-based methods.

Using long-term condition monitoring data with non-Gaussian noise for online diagnostics

The number of timely diagnoses based on condition monitoring data is increasing with the growing usage of monitoring systems. In most of the methods used in these systems, a pre-established fault detection threshold is needed, while there are no specific limit values or thresholds in many cases, especially when the machine is unique. Also, in most actual applications, due to the kind of process and harsh environment, the noise inherent in the observed process exhibits non-Gaussian characteristics, making it a challenging task for diagnostics based on condition monitoring (CM) data. Therefore, this paper introduced a robust methodology based on the switching maximum correntropy Kalman filter (SMCKF) to address the mentioned problems (threshold and online diagnostics in the presence of non-Gaussian noise by using CM data). This approach uses multiple dynamic system models to explain different degradation stages, utilizing robust Bayesian estimation. As this approach is based on dynamic behavior, a threshold for diagnostics is no longer needed. Ultimately, the proposed approach is applied to the online diagnosis of simulated and actual data sets. The results of both simulated and real data sets prove the method’s efficacy.

Cyclogram: an effective method for selecting frequency bands for fault diagnosis of rolling element bearings

Frequency band selection for repetitive transient extraction using the kurtogram and its variants plays a vital role in fault diagnosis of rolling element bearings. However, cyclostationarity, one of the most typical symptoms of faulty bearings, is always neglected in these methods, leading to failure of the extraction of the weak fault features. To address this shortcoming, a novel method for selecting frequency bands, called Cyclogram, is here proposed based on kurtosis and cyclostationarity. In the proposed method, a signal is decomposed into several signals in different frequency bands by a wavelet packet transform, and squared envelopes (SEs) are calculated for these decomposed signals. Then, a robust indicator of SEs for evaluating repetitive transients is constructed based on cyclic spectral coherence and kurtosis, which helps to select useful frequency bands. Afterwards, the envelope spectrum of these selected frequency bands are averaged rather than only selecting one frequency band to enhance fault features. Compared with traditional fault-diagnosis methods for rolling element bearings, the proposed method is able to identify faults from signals corrupted seriously with Gaussian and non-Gaussian noise. The effectiveness of Cyclogram is validated based on simulation and three real-world vibration signals from faulty bearings.

Beyond Gaussian Noise: A Generalized Approach to Likelihood Analysis with Non-Gaussian Noise

Likelihood analysis is typically limited to normally distributed noise due to the difficulty of determining the probability density function of complex, high-dimensional, non-Gaussian, and anisotropic noise. This is a major limitation for precision measurements in many domains of science, including astrophysics, for example, for the analysis of the cosmic microwave background, gravitational waves, gravitational lensing, and exoplanets. This work presents Score-based LIkelihood Characterization, a framework that resolves this issue by building a data-driven noise model using a set of noise realizations from observations. We show that the approach produces unbiased and precise likelihoods even in the presence of highly non-Gaussian correlated and spatially varying noise. We use diffusion generative models to estimate the gradient of the probability density of noise with respect to data elements. In combination with the Jacobian of the physical model of the signal, we use Langevin sampling to produce independent samples from the unbiased likelihood. We demonstrate the effectiveness of the method using real data from the Hubble Space Telescope and James Webb Space Telescope.

Multisensor-Based Maneuvering Target Tracking Algorithm under Non-Gaussian Measurement Noise

The UAVs have become a huge threat in the battlefield. The excellent maneuverability makes them competent for the actual combat operations such as investigation and strike. Therefore, accurate tracking of UAVs is critical. Centralized radar/IR fusion system has been widely concerned to track the UAVs because of the complementary characteristics between these two sensors. The appearance of non-Gaussian measurement noise produces a negative impact on tracking accuracy. This paper proposes a novel IMM-CMCSCKF algorithm which can improve the tracking accuracy of radar/IR fusion system for maneuvering target under non-Gaussian measurement noise. The heterogeneous measurements from radar and IR are firstly fused. Then, CMCSCKF algorithm is presented based on MCC to deal with non-Gaussian measurement noise. To improve maneuvering target tracking accuracy, CMCSCKF is embed into IMM algorithm. Numerical simulation verifies the effectiveness of the proposed IMM-CMCSCKF.

An Agent-Based Distributed State Estimation Approach for Interconnected Power Systems

Phasor measurement units (PMUs) are becoming more popular in power systems and most of the distributed state estimation methods are based on the Gaussian measurement noise assumption. However, the PMU measurement noise has been demonstrated to be non-Gaussian. This article presents a distributed multiarea state estimation approach based on the quadratic and exponential functions for power systems to deal with the non-Gaussian measurement noise efficiently. The matrix splitting technique is utilized to implement a robust estimator in a fully distributed scheme. Based on the local measurements and the limited information exchanged between neighboring areas, each local area only estimates its local states and the computation time needed is further reduced. The effective and robust performance of the proposed distributed multiarea state estimation approach is demonstrated using the IEEE 30-, 118-, and 300-bus systems.

PMSM Combination Modeling for Multiparameter Estimation Using Bayesian Learning With Inverter Distortion Cancellation and Temperature Compensation

Permanent magnet synchronous machine (PMSM) drives with better efficiency are highly demanded, and accurate flux linkage and inductance models or maps are critical to achieve such drives. However, precise modeling and estimation of these parameters should employ redundant data and are affected by magnetic saturation and inverter distortion. This paper firstly derives a flux linkage combination model from machine model for flux linkage and inductance estimation, in which inverter distortion is cancelled and thus inverter influence is minimized for performance improvement. To consider magnetic saturation, radial basis functions are employed to model the nonlinear flux linkages with a small number of relevance vectors, which can effectively depict the nonlinear variation. Bayesian learning approach is then explored to estimate the sparse coefficients of the flux linkage model in the context of radial basis functions, which can deal with non-Gaussian noise to improve the estimation accuracy and guarantee flux linkage model with better computation efficiency and less memory occupation. Moreover, temperature effect is considered to ensure the model accuracy under temperature rise. The proposed approach is validated with experiments and comparisons on a laboratory PMSM drive.

Variable Step Size Methods of the Hybrid Affine Projection Adaptive Filtering Algorithm under Symmetrical Non-Gaussian Noise

The idea of variable step-size was introduced into the Hybrid Affine Projection Algorithm (H-APA) and we propose two variable step size algorithms based on H-APA, which are called the Variable Step-Size Hybrid Affine Projection Algorithm (VSS-H-APA) and the Modified Variable Step-Size Hybrid Affine Projection Algorithm (MVSS-H-APA). These are two variable-step algorithms aim to further improve the robust performance and convergence speed of H-APA under non-Gaussian noise. This allows for faster convergence while maintaining stability. The MVSS-H-APA goes further than VSS-H-APA to estimate the noise in order to achieve better convergence performance. The proposed algorithm performs better than the existing algorithms in system identification under symmetric non-Gaussian noise.

Adaptive robust maximum correntropy cubature Kalman filter for spacecraft attitude estimation

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.

Noise Level Free Regularization of General Linear Inverse Problems under Unconstrained White Noise

In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian) noise is controlled via introducing an auxiliary discretization dimension and choosing it in an adaptive fashion. We first show convergence for completely arbitrary compact forward operator and ground solution. Then the uncertainty of reaching the optimal convergence rate is quantified in a specific Bayesian-like environment. We conclude with numerical experiments.