non-Gaussian Impulsive Noise Research Articles

Robustness enhancement in neural networks with alpha-stable training noise

With the increasing use of deep learning on data collected by non-perfect sensors and in non-perfect environments, the robustness of deep learning systems has become an important issue. A common approach for obtaining robustness to noise has been to train deep learning systems with data augmented with Gaussian noise. In this work, the common choice of Gaussian noise is challenged and the possibility of stronger robustness for non-Gaussian impulsive noise is explored, specifically alpha-stable noise. Justified by the Generalized Central Limit Theorem and evidenced by observations in various application areas, alpha-stable noise is widely present in nature. By comparing the testing accuracy of models trained with Gaussian noise and alpha-stable noise on data corrupted by different noise, it is found that training with alpha-stable noise is more effective than Gaussian noise, especially when the dataset is corrupted by impulsive noise, thus improving the robustness of the model. Moreover, in the testing on the common corruption benchmark dataset, training with alpha-stable noise also achieves promising results, improving the robustness of the model to other corruption types and demonstrating comparable performance with other state-of-the-art data augmentation methods. Consequently, a novel data augmentation method is proposed that replaces Gaussian noise, which is typically added to the training data, with alpha-stable noise.

Convex regularized recursive kernel risk-sensitive loss adaptive filtering algorithm and its performance analysis

In the context of channel estimation amid non-Gaussian impulse noise, traditional non-kernel-space methods face challenges of divergence, while many kernel-space methods fail to fully exploit the a priori information embedded in the channel. To address this, we introduce a robust sparse recursive adaptive filtering algorithm named convex regularized recursive kernel risk-sensitive loss (CR-RKRSL) in this paper. By combining the KRSL with a convex function constraint term, our proposed algorithm maximizes the utilization of channel a priori information. Furthermore, we delve into the theoretical aspects of the proposed algorithm, presenting expressions for the convergence and steady-state error. Through extensive simulation results, we demonstrate that CR-RKRSL outperforms the APSA, LHCAF, PRMCC, CR-RMC, RZAMCC algorithms. In comparison to existing algorithms, CR-RKRSL exhibits superior robustness and faster convergence, particularly in scenarios involving highly sparse systems.

Enhanced Underwater Single Vector-Acoustic DOA Estimation via Linear Matched Stochastic Resonance Preprocessing

Underwater acoustic vector sensors (UAVSs) are increasingly utilized for remote passive sonar detection, but the accuracy of direction-of-arrival (DOA) estimation remains a challenging problem, particularly under low signal-to-noise ratio (SNR) conditions and complex background noise. In this paper, a comprehensive theoretical analysis is conducted on UAVS signal preprocessing subjected to gain-phase uncertainties for average acoustic intensity measurement (AAIM) and complex acoustic intensity measurement (CAIM)-based vector DOA estimation, aiming to explain the theoretical restrictions of intensity-based vector acoustic preprocessing approaches. On this basis, a generalized vector acoustic preprocessing optimization model is established in which the principle can be described as “maximizing the denoising performance under the constraints of an equivalent amplitude-gain response and phase-bias response”. A novel vector acoustic preprocessing method named linear matched stochastic resonance (LMSR) is proposed within the framework of matched stochastic resonance theory, which can naturally guarantee the linear gain-phase restrictions, as well achieving effective denoising performance. Numerical analyses demonstrate the superior vector DOA estimation performance of our proposed LMSR-AAIM and LMSR-CAIM methods in comparison to classical intensity-based AAIM and CAIM methods, especially under low-SNR conditions and non-Gaussian impulsive noise circumstances. Experimental verification conducted in the South China Sea further verifies its the effectiveness for practical application. This work can lay a solid foundation to break through the challenges of underwater remote vector acoustic DOA estimation under low-SNR conditions and complex ocean ambient noise and can provide important guidance for future research work.

Matched Stochastic Resonance Enhanced Underwater Passive Sonar Detection under Non-Gaussian Impulsive Background Noise.

Remote passive sonar detection with low-frequency band spectral lines has attracted much attention, while complex low-frequency non-Gaussian impulsive noisy environments would strongly affect the detection performance. This is a challenging problem in weak signal detection, especially for the high false alarm rate caused by heavy-tailed impulsive noise. In this paper, a novel matched stochastic resonance (MSR)-based weak signal detection model is established, and two MSR-based detectors named MSR-PED and MSR-PSNR are proposed based on a theoretical analysis of the MSR output response. Comprehensive detection performance analyses in both Gasussian and non-Gaussian impulsive noise conditions are presented, which revealed the superior performance of our proposed detector under non-Gasussian impulsive noise. Numerical analysis and application verification have revealed the superior detection performance with the proposed MSR-PSNR detector compared with energy-based detection methods, which can break through the high false alarm rate problem caused by heavy-tailed impulsive noise. For a typical non-Gasussian impulsive noise assumption with α=1.5, the proposed MSR-PED and MSR-PSNR can achieve approximately 16 dB and 22 dB improvements, respectively, in the detection performance compared to the classical PED method. For stronger, non-Gaussian impulsive noise conditions corresponding to α=1, the improvement in detection performance can be more significant. Our proposed MSR-PSNR methods can overcome the challenging problem of a high false alarm rate caused by heavy-tailed impulsive noise. This work can lay a solid foundation for breaking through the challenges of underwater passive sonar detection under non-Gaussian impulsive background noise, and can provide important guidance for future research work.

Constrained squared sine derived adaptive algorithm: Performance and analysis

A constrained squared sine derived adaptive (CSSDA) algorithm is proposed in this paper, which provides better steady-state behavior than existing algorithms in impulsive noise environments. The devised CSSDA works by constructing a squared sine function as the constrained cost function in solving the constrained adaptive filtering problem. Theoretical analysis of the CSSDA is presented and compared with the simulations. The simulation results show that the theoretical analysis agrees well with the simulations, helping to verify the effectiveness and correctness of the analysis. Also, the performance of the CSSDA is superior to the recent popular constraint adaptive algorithms for system identifications in a variety of environments with non-Gaussian impulsive noises.

Steady-state mean-square performance analysis of the block-sparse maximum Versoria criterion

The maximum Versoria criterion algorithm (MVC) exhibits lower steady-state misalignment and less complexity as compared to the maximum correntropy criterion (MCC) algorithm in the scenario of non-Gaussian impulsive noises. However, few scholars have discussed improving the MVC algorithm in sparse channels. This paper presents a block-sparse MVC (BS-MVC) algorithm by introducing the regularization norm, which has desirable performance in block-sparse channels and has excellent robustness to non-Gaussian conditions with impulsive noises. The steady-state excess mean-square error (EMSE) is discussed in Gaussian and non-Gaussian noise conditions. The effectiveness of BS-MVC and the theoretical expression is validated using multiple simulations. The BS-MVC achieves a lower steady-state mean-square deviation (MSD) and maintains a fast convergence rate compared with MCC and MVC algorithms.

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.

Blind separation of noisy piecewise-stationary mixtures via probability measure transform

In this paper, we consider the problem of blind source separation (BSS) under non-Gaussian impulsive noise. We consider the case of overdetermined instantaneous-linear-mixtures of piecewise-stationary signals. These are corrupted by additive stationary noise. Under this framework, we propose a two-stage separation method, called measure-transformed BSS (MT-BSS), that applies a transform to the probability distribution associated with each data segment. The generating function of the transform at hand is a non-negative function, called MT-function, that weights the data points. We show that proper choice of the involved MT-functions can lead to enhanced separation performance. The performance advantage of MT-BSS over alternative BSS techniques is illustrated in simulation examples. In these studies, we consider synthetic data and real audio signals.

$\ell _{0}$-Norm Minimization Based Robust Matrix Completion Approach for MIMO Radar Target Localization

In this paper, we propose a robust matrix completion approach based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula> -norm minimization for target localization in sub-Nyquist sampled multiple-input multiple-output (MIMO) radar. Owing to the low-rank property of the noise-free MIMO radar transmit matrix, our approach is able to recover the missing data and resist impulsive noise from the receive matrix. We adopt proximal block coordinate descent and adaptive penalty parameter adjustment by complex Laplacian kernel and normalized median absolute deviation. We analyze the resultant algorithm convergence and computational complexity, and demonstrate through simulations that it outperforms existing methods in terms of pseudospectrum, mean square error, and target detection probability in non-Gaussian impulsive noise, even for the full sampling schemes. While in the presence of Gaussian noise, our approach performs comparably with other sub-Nyquist methods.

Super-resolution time delay estimation using exponential kernel correlation in impulsive noise and multipath environments

The time delay estimation (TDE) is an important and fundamental part in wireless communication signal processing, which has been widely used in localization, intelligent navigation, and radio monitoring. However, it remains a challenging task to support such TDE mechanisms with super-resolution in impulsive noise and multipath environments. Aiming at improving the TDE performance in both impulsive noise and multipath environments, in this paper, a novel super-resolution TDE method is proposed by using the defined exponential kernel correlation (EKC) function. In the proposed TDE method, EKC function is defined to suppress the non-Gaussian impulsive noise. Specifically, the theoretical analysis is also given to prove its boundedness and its effectiveness in non-Gaussian impulsive noise suppression. Further, a novel super-resolution TDE method is proposed by combining EKC function and multiple signal classification (MUSIC) method, which can significantly improve the estimation performance in terms of resolution and accuracy with both non-Gaussian impulsive noise and multipath environments. Finally, simulation experiments demonstrate that the proposed super-resolution TDE method maintains good performance even with a low characteristic exponent and low generalized signal-to-noise ratio (GSNR).

Adaptive sign algorithm for graph signal processing

Efficient and robust online processing techniques for irregularly structured data are crucial in the current era of data abundance. In this paper, we propose a graph/network version of the classical adaptive Sign algorithm for online graph signal estimation under impulsive noise. The recently introduced graph adaptive least mean squares algorithm is unstable under non-Gaussian impulsive noise and has high computational complexity. The Graph-Sign algorithm proposed in this work is based on the minimum dispersion criterion and therefore impulsive noise does not hinder its estimation quality. Unlike the recently proposed graph adaptive least mean pth power algorithm, our Graph-Sign algorithm can operate without prior knowledge of the noise distribution. The proposed Graph-Sign algorithm has a faster run time because of its low computational complexity compared to the existing adaptive graph signal processing algorithms. Experimenting on steady-state and time-varying graph signals estimation utilizing spectral properties of bandlimitedness and sampling, the Graph-Sign algorithm demonstrates fast, stable, and robust graph signal estimation performance under impulsive noise modeled by alpha stable, Cauchy, Student’s t, or Laplace distributions.

Kalman Filtering in Non-Gaussian Model Errors: A New Perspective [Tips &amp; Tricks

It is well known that the optimality of the Kalman filter relies on the Gaussian distribution of process and observation model errors, which in many situations is well justified <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> – <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> <xref ref-type="bibr" rid="ref3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[3]</xref> . However, this optimality is useless in applications where the distribution assumptions of the model errors do not hold in practice. Even minor deviations from the assumed (or nominal) distribution may cause the Kalman filter’s performance to drastically degrade or completely break down. In particular, when dealing with perceptually important signals, such as speech, image, medical, campaign, and ocean engineering, measurements have confirmed the presence of non-Gaussian impulsive (heavy-tailed) and Laplace noises <xref ref-type="bibr" rid="ref4" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[4]</xref> . Therefore, the classical Kalman filter, which is derived under the nominal Gaussian probability model, is biased and even fails in such situations.

Kernel Least Logarithmic Absolute Difference Algorithm

Kernel adaptive filtering (KAF) algorithms derived from the second moment of error criterion perform very well in nonlinear system identification under assumption of the Gaussian observation noise; however, they inevitably suffer from severe performance degradation in the presence of non-Gaussian impulsive noise and interference. To resolve this dilemma, we propose a novel robust kernel least logarithmic absolute difference (KLLAD) algorithm based on logarithmic error cost function in reproducing kernel Hilbert spaces, taking into account of the non-Gaussian impulsive noise. The KLLAD algorithm shows considerable improvement over the existing KAF algorithms without restraining impulsive interference in terms of robustness and convergence speed. Moreover, the convergence condition of KLLAD algorithm with Gaussian kernel and fixed dictionary is presented in the mean sense. The superior performance of KLLAD algorithm is confirmed by the simulation results.

Spectrum sensing for cognitive radio based on Kendall's tau in the presence of non-Gaussian impulsive noise

Traditional spectrum sensing techniques optimized against Gaussian noise may suffer from severe performance deterioration when non-Gaussian noise is present. To overcome such drawback, this paper proposes a novel Kendall's tau (KT) based detector for detecting the primary signal in additive non-Gaussian noise characterized by contaminated Gaussian model (CGM). The proposed detector, which exploits the ordinary information rather than the cardinal information from the observed raw data, is both computationally efficient and robust against large-valued outliers. The analytic expressions concerning the expectation and variance of KT are firstly established under this specific CGM, which emulates a frequently encountered scenario in practice. Performance analyses are further conducted in terms of false alarm probability, detection probability and receiver operating characteristic (ROC) curve. Comparative results with the traditional energy detection (ED) and three other state-of-the-art detectors demonstrate the superiority of KT, including: 1) robustness against impulsive noise compared to ED, 2) accurate control of the false alarm probability without any prior information about the noise distribution, and 3) better detection performance over three popular detectors with either Gaussian or non-Gaussian background noise.

A novel targeted method of informative frequency band selection based on lagged information for diagnosis of gearbox single and compound faults

Detection of compound faults in rotating machinery remained a challenge in the field of fault diagnosis since the presence of multiple faults at the same time acts as an interference in the isolation of a specific fault signature. One of the widely used methods in rotating machinery fault diagnosis is envelope analysis. The envelope spectrum of a properly band-pass filtered signal could be informative about the presence of a fault. The main challenge in envelope analysis is the selection of appropriate criteria to choose the most informative frequency band. A novel targeted informative frequency band selection method have been proposed in this work, which will be referred as Lagged Information Spectrum (LIS). Lagged information inspired by the fractional lower order autocorrelation and its logarithm-based derivation results in a close relation to the concept of negentropy. The proposed method can reduce the effect of both Gaussian and non-Gaussian noise in the signal, and in the same time, separate the signatures of compound faults. The performance of the proposed method has been evaluated under both simulated and experimental gearbox vibration signals and compared to a wide range of other previously established methods of informative frequency band selection. The results of simulated signal verify that the proposed method is more robust than other methods in the presence of Gaussian noise for noise to signal ratios up to 3 dB while its efficiency under moderate non-Gaussian impulsive noise is acceptable (up to 11 dB noise to signal ratio). One experimental case study of single chipping fault and two experimental case studies of compound wear/crack and chipping/spalling faults have been accomplished to show the performance of the proposed method in separation of fault signatures. The proposed method outperforms other methods in isolation of fault characteristic frequencies and generating higher quality spectra based on Fault Feature Coefficient (FFC) criterion, especially, in two compound fault case studies.

Spatial-Temporal Minimum Error Random Interaction Networks for Distributed Estimation

In this letter, we study the problem of adaptive parameter estimation for distributed wireless sensor networks (WSNs), where the non-Gaussian impulsive noises in the communication links are considered. In such cases, if the traditional distributed collaborative strategy is still adopted, the estimation performance of the network will decline significantly. Aiming at this problem, we propose a new spatial-temporal minimum error random interaction strategy for the distributed estimation in the presence of impulsive link noises. Furthermore, the maximum correlation entropy criterion and the stochastic gradient descent method are used to update the combination factor so that the network has dynamic and real-time adaptability to the link noises. The proposed algorithm is also compared with the classic DLMS algorithm and a state-of-the-art algorithm designed for the impulsive link noises. Simulation results show that the proposed algorithm can not only reduce the network traffic effectively, but also be robust to the non-Gaussian link impulsive noises while maintaining its advantage over the non-cooperative algorithm and achieving the optimal estimation performance.

Frequency domain maximum correntropy criterion spline adaptive filtering

A filtering algorithm based on frequency domain spline type, frequency domain spline adaptive filters (FDSAF), effectively reducing the computational complexity of the filter. However, the FDSAF algorithm is unable to suppress non-Gaussian impulsive noises. To suppression non-Gaussian impulsive noises along with having comparable operation time, a maximum correntropy criterion (MCC) based frequency domain spline adaptive filter called frequency domain maximum correntropy criterion spline adaptive filter (FDSAF-MCC) is developed in this paper. Further, the bound on learning rate for convergence of the proposed algorithm is also studied. And through experimental simulations verify the effectiveness of the proposed algorithm in suppressing non-Gaussian impulsive noises. Compared with the existing frequency domain spline adaptive filter, the proposed algorithm has better performance.

Recursive Constrained Adaptive Algorithm Under q-Rényi Kernel Function

In this brief, we proposed a recursive constrained maximum $q$ - $\text{R}\acute {\text e}$ nyi kernel (RCMqR) adaptive filtering algorithm, which is derived via introducing a $q$ - $\text{R}\acute {\text e}$ nyi kernel function into constrained adaptive algorithm and using $q$ - $\text{R}\acute {\text e}$ nyi kernel function to construct a new cost function and providing its recursive form to create a linear constrained filter. The created RCMqR algorithm can achieve superior performance compared with other conventional algorithms under non-Gaussian noises environment. Theoretical transient mean-square deviation (MSD) of the RCMqR algorithm is presented when the system background noises are Gaussian-noise and non-Gaussian noise, and a sufficient condition has been achieved to make sure RCMqR algorithm converge. Various computer simulations are performed in system identification for the purpose of comparison. The simulation results verified that the theoretical analysis match well with the simulations and the proposed algorithm has better robustness than other algorithms under non-Gaussian impulsive noise.

Constrained least lncosh adaptive filtering algorithm

We propose a constrained least lncosh (CLL) adaptive filtering algorithm, which, as we show, provides better performance than other algorithms in impulsive noise environment. The proposed CLL algorithm is derived via incorporating a lncosh function in a constrained optimization problem under non-Gaussian noise environment. The lncosh cost function is a natural logarithm of a hyperbolic cosine function, and it can be considered as a combination of mean-square error and mean-absolute-error criteria. The theoretical analysis of convergence and steady-state mean-squared-deviation of the CLL algorithm in identification scenarios is presented. The theoretical analysis agrees well with simulation results and these results verify that the CLL algorithm possesses superior performance and higher robustness than other CAF algorithms under various non-Gaussian impulsive noises.

An enhanced normalized step-size algorithm based on adjustable nonlinear transformation function for active control of impulsive noise

Impulsive noise is widely distributed in various scenarios and becomes an important challenge for the practical applications of active noise control (ANC) system. The conventional ANC algorithms based on the transformation function have a fixed compression level for error signal, leading to slow convergence and weak noise reduction under certain circumstances. To overcome this defect, this paper proposes an enhanced filtered-x arctangent error Least Mean Square (EFxatanLMS) algorithm by designing an adjustable nonlinear transformation function of error signal with arctangent form. Specifically, a compression factor is introduced in the transformation function to govern the compression shape of the function so as to realize ideal effect on impulsive noise with different intensities. For the purpose of further optimizing the capability of the proposed algorithm, an improved normalized step-size EFxatanLMS (NSS-EFxatanLMS) algorithm is proposed. It adopts a novel time-varying normalized function to adjust the step-size coefficient to the appropriate value adaptively. Numerical simulations verify the effectiveness of the proposed algorithms for Gaussian noise and non-Gaussian impulsive noise.