non-Gaussian Noise Research Articles

Stochastic Gradient Descent for Kernel-Based Maximum Correntropy Criterion

Maximum correntropy criterion (MCC) has been an important method in machine learning and signal processing communities since it was successfully applied in various non-Gaussian noise scenarios. In comparison with the classical least squares method (LS), which takes only the second-order moment of models into consideration and belongs to the convex optimization problem, MCC captures the high-order information of models that play crucial roles in robust learning, which is usually accompanied by solving the non-convexity optimization problems. As we know, the theoretical research on convex optimizations has made significant achievements, while theoretical understandings of non-convex optimization are still far from mature. Motivated by the popularity of the stochastic gradient descent (SGD) for solving nonconvex problems, this paper considers SGD applied to the kernel version of MCC, which has been shown to be robust to outliers and non-Gaussian data in nonlinear structure models. As the existing theoretical results for the SGD algorithm applied to the kernel MCC are not well established, we present the rigorous analysis for the convergence behaviors and provide explicit convergence rates under some standard conditions. Our work can fill the gap between optimization process and convergence during the iterations: the iterates need to converge to the global minimizer while the obtained estimator cannot ensure the global optimality in the learning process.

EIF-SlideWindow: Enhancing Simultaneous Localization and Mapping Efficiency and Accuracy with a Fixed-Size Dynamic Information Matrix

This paper introduces EIF-SlideWindow, a novel enhancement of the Extended Information Filter (EIF) algorithm for Simultaneous Localization and Mapping (SLAM). Traditional EIF-SLAM, while effective in many scenarios, struggles with inaccuracies in highly non-linear systems or environments characterized by significant non-Gaussian noise. Moreover, the computational complexity of EIF/EKF-SLAM scales with the size of the environment, often resulting in performance bottlenecks. Our proposed EIF-SlideWindow approach addresses these limitations by maintaining a fixed-size information matrix and vector, ensuring constant-time processing per robot step, regardless of trajectory length. This is achieved through a sliding window mechanism centered on the robot’s pose, where older landmarks are systematically replaced by newer ones. We assess the effectiveness of EIF-SlideWindow using simulated data and demonstrate that it outperforms standard EIF/EKF-SLAM in both accuracy and efficiency. Additionally, our implementation leverages PyTorch for matrix operations, enabling efficient execution on both CPU and GPU. Additionally, the code for this approach is made available for further exploration and development.

Gaussian–Student’s t Mixture Distribution-Based Robust Kalman Filter for Global Navigation Satellite System/Inertial Navigation System/Odometer Data Fusion

Multi-source heterogeneous information fusion based on the Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS)/odometer is an important technical means to solve the problem of navigation and positioning in complex environments. The measurement noise of the GNSS/INS/odometer integrated navigation system is complex and non-stationary; it approximates a Gaussian distribution in an open-sky environment, and it has heavy-tailed properties in the GNSS challenging environment. This work models the measurement noise and one-step prediction as the Gaussian and Student’s t mixture distribution to adjust to different scenarios. The mixture distribution is formulated as the hierarchical Gaussian form by introducing Bernoulli random variables, and the corresponding hierarchical Gaussian state-space model is constructed. Then, the mixing probability of Gaussian and Student’s t distributions could adjust adaptively according to the real-time kinematic solution state. Based on the novel distribution, a robust variational Bayesian Kalman filter is proposed. Finally, two vehicle test cases conducted in GNSS-friendly and challenging environments demonstrate that the proposed robust Kalman filter with the Gaussian–Student’s t mixture distribution can better model heavy-tailed non-Gaussian noise. In challenging environments, the proposed algorithm has position root mean square (RMS) errors of 0.80 m, 0.62 m, and 0.65 m in the north, east, and down directions, respectively. With the assistance of inertial sensors, the positioning gap caused by GNSS outages has been compensated. During seven periods of 60 s simulated GNSS data outages, the RMS position errors in the north, east, and down directions were 0.75 m, 0.30 m, and 0.20 m, respectively.

Kernel Adaptive Filtering Algorithm Based on Hyperbolic Tangent Mixed Error Function

This paper proposes an adaptive filtering algorithm based on the symmetry Kernel Hyperbolic Tangent Mixed Error Criterion (KHTMC), aimed at addressing the identification of nonlinear systems under non-Gaussian noise environments. The algorithm optimizes signal processing by constructing a mixed cost function that combines the symmetry logarithmic square error and the hyperbolic tangent function and integrates it with the kernel adaptive filtering method. Simulation results show that, compared to existing kernel adaptive filtering algorithms, the KHTMC algorithm exhibits significant advantages in terms of convergence speed and steady-state mean square error. It demonstrates strong robustness and tracking performance, especially when dealing with mixed non-Gaussian noise. Therefore, this algorithm shows great potential in signal processing applications under complex noise conditions, offering a more reliable and efficient solution.

Robust EKF based on the framework of dynamic data reconciliation for state estimation of chemical processes with gaussian/non-gaussian measurement noise

State estimation plays a critical role in modern industry. The extended Kalman filter (EKF) is effective for nonlinear chemical processes with Gaussian noise, but it struggles when gross errors are present. This paper addresses this limitation by reformulating the EKF within the dynamic data reconciliation (DDR) framework, resulting in a robust DDR-based EKF tailored for state estimation in chemical processes with non-Gaussian measurement noise. The combination of random and gross errors is modeled using a contaminated Gaussian distribution. Model predictions are incorporated as prior knowledge, and a fixed-point iterative strategy is employed to update the posterior probability. Additionally, a first-order linearization technique is applied for convergence analysis. The robustness and effectiveness of the DDR-based EKF are demonstrated through both a classic mathematical example and a styrene polymerization reaction. Simulation results show that the DDR-based EKF effectively mitigates gross errors, achieving reliable state estimation.

Sequential Mixed Cost-Based Multi-Sensor and Relative Dynamics Robust Fusion for Spacecraft Relative Navigation

The non-redescending convex functions degrade the filtering robustness, whereas the redescending non-convex functions improve filtering robustness, but they tend to converge towards local minima. This work investigates the properties of convex and non-convex cost functions from robustness and stability perspectives, respectively. To improve filtering robustness and stability to the high level of non-Gaussian noise, a sequential mixed convex and non-convex cost strategy is presented. To avoid the matrix singularity induced by applying the non-convex function, the M-estimation type Kalman filter is transformed into its information filtering form. Further, to address the problem of the estimation consistency in the iterated unscented Kalman filter, the iterated sigma point filtering framework is adopted using the statistical linear regression method. The simulation results show that, under different levels of heavy-tailed non-Gaussian noise, the mixed cost strategy can avoid the non-convex function-based filters falling into the local minimum, and further can improve the robustness of the convex function-based filter. Therefore, the mixed cost strategy provides a comprehensive improvement in the efficiency of the robust iterated filter.

A method for signal components identification in acoustic signal with non-Gaussian background noise using clustering of data in time-frequency domain

This paper presents a novel method for fault detection in vibration/acoustic signals contaminated with non-Gaussian noise, specifically addressing the challenge of random impulsive and wideband disturbances in industrial measurements. While damage detection in Gaussian noise environments is well understood, high-amplitude non-cyclic impulsive disturbances arising from random aspects of industrial processes, such as non-uniform operations and random impacts, pose significant analytical challenges.The proposed method analyzes the distribution densities of spectral vectors derived from spectrograms. It considers a simple additive model consisting of the signal of interest (SOI) and Gaussian and non-Gaussian noise. Using the density-based spatial clustering algorithm (DBSCAN), the method isolates distinct classes of spectral vectors from the spectrogram, effectively separating different signal behaviors and extracting fault-related information. The effectiveness of the proposed method was validated using an envelope spectrum-based indicator (ENVSI) and successfully demonstrated on real signals from an industrial machine with a faulty bearing.

MEEF criterion-based spline adaptive filtering algorithm and its application

This paper presents an innovative the minimum error entropy with fiducial points (MEEF)-based spline adaptive filtering (S-AF) algorithm, called SAF-MEEF algorithm, which outperforms the conventional SAF algorithms that use the mean square error (MSE) criterion in reducing non-Gaussian interference. To overcome the limitation of the fixed step-size, a variable step-size strategy is also developed, resulting in the SAF-VMEEF algorithm, which improves the convergence speed and steady-state error performance. Furthermore, the computational complexity and convergence analysis of the SAF-MEEF are discussed. Nonlinear system identification simulations test the performance of the presented algorithms. Furthermore, this article accomplishes the application of nonlinear active noise control (ANC). Their effectiveness and robustness against non-Gaussian noise are demonstrated in different experimental scenarios, including α-stable noise, real-world functional magnetic resonance imaging (fMRI) noise, and real-life server room (SR) noise.

Sparse Bayesian correntropy learning for robust muscle activity reconstruction from noisy brain recordings

Sparse Bayesian learning has promoted many effective frameworks of brain activity decoding for the brain–computer interface, including the direct reconstruction of muscle activity using brain recordings. However, existing sparse Bayesian learning algorithms mainly use Gaussian distribution as error assumption in the reconstruction task, which is not necessarily the truth in the real-world application. On the other hand, brain recording is known to be highly noisy and contains many non-Gaussian noises, which could lead to large performance degradation for sparse Bayesian learning algorithms. The goal of this paper is to propose a novel robust implementation of sparse Bayesian learning so that robustness and sparseness can be realized simultaneously. Motivated by the exceptional robustness of maximum correntropy criterion (MCC), we proposed integrating MCC to the sparse Bayesian learning regime. To be specific, we derived the explicit error assumption inherent in the MCC, and then leveraged it for the likelihood function. Meanwhile, we utilized the automatic relevance determination technique as the sparse prior distribution. To fully evaluate the proposed method, a synthetic example and a real-world muscle activity reconstruction task with two different brain modalities were leveraged. Experimental results showed, our proposed sparse Bayesian correntropy learning framework significantly improves the robustness for the noisy regression tasks. Our proposed algorithm could realize higher correlation coefficients and lower root mean squared errors for the real-world muscle activity reconstruction scenario. Sparse Bayesian correntropy learning provides a powerful approach for brain activity decoding which will promote the development of brain–computer interface technology.

The INS/GPS integrated navigation based on autonomous underwater vehicle using modified extended Kalman filter

Ensuring highhtab accuracy and robustness remains a paramount concern in the realm of underwater positioning and navigation research. This paper proposes a filtering algorithm grounded in Inertial Measurement Unit/Global Positioning System (INS/GPS) integrated navigation to effectively address the challenges posed by non-Gaussian noise, stemming from outliers and measurement inaccuracies. Currently, most filtering algorithms are developed based on the criteria of minimum mean square error (MMSE) or maximum entropy criteria (MCC). To address the challenge of handling complex non-Gaussian noises, this paper uses the Minimum Error Entropy Criterion (MEE) and Extended Kalman Filter (EKF) with Kernel Risk-Sensitive Loss (KRSL) instead of MMSE or MCC to develop an online filtering algorithm with a recursive process, and adjusts the kernel size of MEE within a reasonable range by constructing an adaptive factor to deal with outliers generated during measurement and excessive convergence caused by the inapplicability of the kernel size. Through extensive target tracking simulations and surface Autonomous Underwater Vehicle (AUV) localization experiments, results demonstrate the efficacy of the proposed algorithm. Notably, the algorithm optimizes kernel sizes for different types of noises, ensuring robust state estimation and rapid convergence without compromising filtering accuracy.

Joint detection and localization of False Data Injection Attacks in smart grids: An enhanced state estimation approach

The transition to smart grids introduces significant cybersecurity vulnerabilities, particularly with the rise of False Data Injection Attacks (FDIAs). These attacks allow malicious actors to manipulate sensor data, alter the internal state of the grid, and bypass traditional Bad Data Detection (BDD) systems. FDIAs pose a serious threat to grid security, potentially leading to incorrect state estimation and destabilization of the power system, which could result in system outages and economic losses. To address this challenge, this paper proposes a novel detection and localization method. First, false data and measurement errors are modeled as non-Gaussian noise. Recognizing the limitations of the traditional Extended Kalman Filter (EKF) under non-Gaussian conditions, the Maximum Correntropy Criterion (MCC) is integrated into the EKF to improve the robustness of state estimation. Additionally, the Maximum Correntropy Criterion Extended Kalman Filter (MCCEKF) is combined with Weighted Least Squares (WLS), and cosine similarity is introduced to quantify the differences between these two estimators for FDIA detection. A partition approach is then used to construct a logical localization matrix, with cosine similarity detection applied in each section to generate a detection matrix. By performing a logical AND operation on these matrices, the attacked bus is identified. Simulations on IEEE-14-bus and IEEE-30-bus systems validate the proposed approach, demonstrating its effectiveness in reliably detecting and localizing FDIAs in smart grids.

FastSLAM-MO-PSO: A Robust Method for Simultaneous Localization and Mapping in Mobile Robots Navigating Unknown Environments

In the realm of mobile robotics, the capability to navigate and map uncharted territories is paramount, and Simultaneous Localization and Mapping (SLAM) stands as a cornerstone technology enabling this capability. While traditional SLAM methods like Extended Kalman Filter (EKF) and FastSLAM have made strides, they often struggle with the complexities of non-linear dynamics and non-Gaussian noise, particularly in dynamic settings. Moreover, these methods can be computationally intensive, limiting their applicability in real-world scenarios. This paper introduces an innovative enhancement to the FastSLAM framework by integrating Multi-Objective Particle Swarm Optimization (MO-PSO), aiming to bolster the robustness and accuracy of SLAM in mobile robots. We outline the theoretical underpinnings of FastSLAM and underscore its significance in robotic autonomy for mapping and exploration. Our approach innovates by crafting a specialized fitness function within the MO-PSO paradigm, which is instrumental in optimizing the particle distribution and addressing the challenges inherent in traditional particle filtering methods. This strategic fusion of MO-PSO with FastSLAM not only circumvents the pitfalls of particle degeneration, but also enhances the overall robustness and precision of the SLAM process across a spectrum of operational environments. Our empirical evaluation involves testing the proposed method on three distinct simulation benchmarks, comparing its performance against four other algorithms. The results indicate that our MO-PSO-enhanced FastSLAM method outperforms the traditional particle filtering approach by significantly reducing particle degeneration and ensuring more reliable and precise SLAM performance in challenging environments. This research demonstrates that the integration of MO-PSO with FastSLAM is a promising direction for improving SLAM in mobile robots, providing a robust solution for accurate mapping and localization even in complex and unknown settings.

Event-Driven Maximum Correntropy Filter Based on Cauchy Kernel for Spatial Orientation Using Gyros/Star Sensor Integration.

Gyros/star sensor integration provides a potential method to obtain high-accuracy spatial orientation for turntable structures. However, it is subjected to the problem of accuracy loss when the measurement noises become non-Gaussian due to the complex spatial environment. This paper presents an event-driven maximum correntropy filter based on Cauchy kernel to handle the above problem. In this method, a direct installation mode of gyros/star sensor integration is established and the associated mathematical model is derived to improve the turntable's control stability. Based on this, a Cauchy kernel-based maximum correntropy filter is developed to curb the influence of non-Gaussian measurement noise for enhancing the gyros/star sensor integration's robustness. Subsequently, an event-driven mechanism is constructed based on the filter's innovation information for further reducing the unnecessary computational cost to optimize the real-time performance. The effectiveness of the proposed method has been validated by simulations of the gyros/star sensor integration for spatial orientation. This shows that the proposed filtering methodology not only has strong robustness to deal with the influence of non-Gaussian measurement noise but can also achieve superior real-time spatial applications with a small computational cost, leading to enhanced performance for the turntable's spatial orientation using gyros/star sensor integration.

Distributed minimum error entropy with fiducial points Kalman filter for state tracking

With the growing size of the system, this distributed Kalman filter (DKF) is widely used in multi-sensor networks. However, it is difficult for DKF to accurately estimate state values in non-Gaussian noise environments. In this paper, a regression equation is first constructed to contain all sensor node information. Then, by bringing the minimum error entropy with fiducial points (MEEF) standard into the process of information fusion, a robust algorithm named centralized MEEF KF (CMEEF-KF) is presented, which is robust to non-Gaussian noise and unusual data. Furthermore, to overcome the communication burden of CMEEF-KF in sensor networks, the distributed MEEF-KF (DMEEF-KF) is developed, which construct a framework of consensus average method for node information fusion. Specifically, each sensor only exchanges the key information with its neighborhoods. In addition, in order to make the algorithm able to cope with the nonlinear state estimation problem, the distributed MEEF extended Kalman filter is also proposed. Eventually, the effectiveness of the suggested algorithms is demonstrated by land vehicle navigation and power system tracking state estimation using a 10-node sensor network.

Experience-based noise model of infrared detectors for system dimensioning and simulation

We show that infrared detectors frequently exhibit non-Gaussian spatial noise, which makes it difficult to compare their performance. The power-law-like behavior we show can be very detrimental to certain detection missions, hence the need to characterize this noise. We demonstrate that a simple mixture of Gaussian and Student processes corresponds to the observed example, and that the parameter determination procedure described here reaches its theoretical limit.

Cross-attention mechanism-based spectrum sensing in generalized Gaussian noise

Spectrum sensing (SS) technology is essential for cognitive radio (CR) networks to effectively identify and utilize idle spectrum resources. Due to the influence of noise characteristics in the channel, providing accurate sensing results is challenging. In order to improve the performance of SS under non-Gaussian noise and overcome the limitations of existing methods that are mostly based on a single feature, we propose a novel time-frequency cross fusion network (TFCFN). Specifically, we utilize gated recurrent units (GRU) to capture long-term dependencies in the time domain on the original signals, meanwhile, we perform a fast Fourier transform (FFT) on the original signals to obtain the frequency domain information, and subsequently use convolutional neural networks (CNN) to extract the local spatial features in the frequency domain. Ultimately, these time-domain and frequency-domain features are dynamically fused through a cross-attention mechanism to construct more comprehensive and robust features for signal classification. We use generalized Gaussian distribution (GGD) as the noise model and reconstruct the RadioML2016.10a dataset to explore the performance under various noise conditions. The experimental results show that compared with the baseline methods, TFCFN exhibits better detection ability and maintains lower complexity in both Gaussian and non-Gaussian noise environments. Notably, when the shape parameter of GGD is set to 0.5 and the signal-to-noise ratio (SNR) of the received signal is -16dB, it can maintain the probability of false alarm (Pf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_f$$\\end{document}) of 10% while still ensuring the probability of detection (Pd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_d$$\\end{document}) of over 90%.

Robust and stochastic sparse subspace clustering

Sparse subspace clustering (SSC) has been widely employed in machine learning and pattern recognition, but it still faces scalability challenges when dealing with large-scale datasets. Recently, stochastic SSC (SSSC) has emerged as an effective solution by leveraging the dropout technique. However, SSSC cannot robustly handle noise, especially non-Gaussian noise, leading to unsatisfactory clustering performance. To address the above issues, we propose a novel robust and stochastic method called stochastic sparse subspace clustering with the Huber function (S3CH). The key idea is to introduce the Huber surrogate to measure the loss of the stochastic self-expression framework, thus S3CH inherits the advantage of the stochastic framework for large-scale problems while mitigating sensitivity to non-Gaussian noise. In algorithms, an efficient proximal alternating minimization (PAM)-based optimization scheme is developed. In theory, the convergence of the generated sequence is rigorously proved. Extensive numerical experiments on synthetic and six real datasets validate the advantages of the proposed method in clustering accuracy, noise robustness, parameter sensitivity, post-hoc analysis, and model stability.

Comparing Kurtosis-adjusted weighted levels with other metrics to assess the risk of hearing loss from non-Gaussian noise exposures

Several studies have shown that impulsive noise can cause more damage to hearing than steady-state noise of equal energy. As a result, a large body of research has been devoted to evaluating the hazards of impulsive noise. However, work environments often have varying noise patterns, including Gaussian background noise combined with high-level transient noises contributing to the worker's daily dose. Thus, an energy-based noise metric underestimates the risk of hearing loss unless incorporating a temporal structure correction term. Kurtosis has been reported as an effective adjunct to energy for predicting hearing hazards from non-Gaussian noise exposures. In this work, recordings of real impulsive noise were conducted using a portable measuring system at a very high sampling frequency and using high-pressure microphones. Controlled synthetic non-Gaussian noise was generated using these impulsive signals and steady-state background noise. After exploring the detailed temporal structure of the noise, the daily exposure time has been determined using different metrics, including kurtosis-adjusted weighted levels, weighted peak levels, and auditory risk units. The examples presented here aim to demonstrate how kurtosis can help develop more accurate methods to prevent noise-induced hearing loss.

Low-complexity recursive constrained maximum Versoria criterion adaptive filtering algorithm

Linearly-constrained adaptive filtering algorithms have emerged as promising candidates for system estimation. The existing methods such as the constrained least mean square algorithm rely on mean square error based learning, which delivers suboptimal performance under non-Gaussian noise environments. Therefore, the recursive constrained maximum Versoria criterion (RCMVC) algorithm has been derived and is robust against impulsive distortions. Nonetheless, RCMVC suffers from a notable computational overhead stemming from matrix inversion operations. To circumvent this issue, utilizing the weighting method and the dichotomous coordinate descent (DCD) iteration method, this paper derives a low-complexity version of the RCMVC algorithm called DCD-RCMVC, which alleviates the requirement of matrix inversion and enhances the estimation accuracy and robustness against non-Gaussian interference. Furthermore, we also present a comprehensive theoretical analysis of the DCD-RCMVC algorithm, encompassing discussions on its equivalence, convergence properties, and computational complexity. Simulations performed for system identification problems indicate that the DCD-RCMVC algorithm outperforms the existing state-of-art approaches.

Influence of Imperfections on the Operational Correctness of DNN-kWTA Model.

The dual neural network (DNN)-based k -winner-take-all (WTA) model is able to identify the k largest numbers from its m input numbers. When there are imperfections, such as non-ideal step function and Gaussian input noise, in the realization, the model may not output the correct result. This brief analyzes the influence of the imperfections on the operational correctness of the model. Due to the imperfections, it is not efficient to use the original DNN- k WTA dynamics for analyzing the influence. In this regard, this brief first derives an equivalent model to describe the dynamics of the model under the imperfections. From the equivalent model, we derive a sufficient condition for which the model outputs the correct result. Thus, we apply the sufficient condition to design an efficiently estimation method for the probability of the model outputting the correct result. Furthermore, for the inputs with uniform distribution, a closed form expression for the probability value is derived. Finally, we extend our analysis for handling non-Gaussian input noise. Simulation results are provided to validate our theoretical results.