Noise Matrix Research Articles

VMD and self-attention mechanism-based Bi-LSTM model for fault detection of optical fiber composite submarine cables

As the main electrical equipment of offshore power grids, optical fiber composite submarine cables undertake the task of power transmission and data communication. In order to ensure the proper functioning of the submarine cable, it is necessary to analyze the working state of it and identify the fault event. This paper proposes a fault detection method for submarine cables, that is, the VMD and self-attention-based Bi-LSTM model. First, we use ANSYS software to generate the vibration waveforms of three main fault events of optical fiber composite submarine cables. Then, by generating the detection matrix of background noise and the vibration waveforms, it can realize the orientation and detection of fault events in single submarine cable. In addition, the vibration signal can be decomposed into IMF components using variational mode decomposition (VMD) for feature extraction. Moreover, the IMF components are input to the self-attention layer for feature fusion and Bi-LSTM module for further feature extraction. Finally, the result of the fault detection is output through the classification layer. According to the comparative experiment and the ablation experiment, the proposed model has proved to outperform the other benchmark models and is robust and stable under the condition of different signal-to-noise ratios.

Distribution-free model for community detection

AbstractCommunity detection for unweighted networks has been widely studied in network analysis, but the case of weighted networks remains a challenge. This paper proposes a general distribution-free model (DFM) for weighted networks in which nodes are partitioned into different communities. DFM can be seen as a generalization of the famous stochastic block models from unweighted networks to weighted networks. DFM does not require prior knowledge of a specific distribution for elements of the adjacency matrix but only the expected value. In particular, signed networks with latent community structures can be modeled by DFM. We build a theoretical guarantee to show that a simple spectral clustering algorithm stably yields consistent community detection under DFM. We also propose a four-step data generation process to generate adjacency matrices with missing edges by combining DFM, noise matrix, and a model for unweighted networks. Using experiments with simulated and real datasets, we show that some benchmark algorithms can successfully recover community membership for weighted networks generated by the proposed data generation process.

Adaptive denoising of photoacoustic signal and image based on modified Kalman filter.

As a burgeoning medical imaging method based on hybrid fusion of light and ultrasound, photoacoustic imaging (PAI) has demonstrated high potential in various biomedical applications, especially in revealing the functional and molecular information to improve diagnostic accuracy. However, stemming from weak amplitude and unavoidable random noise, caused by limited laser power and severe attenuation in deep tissue imaging, PA signals are usually of low signal-to-noise ratio, and reconstructed PA images are of low quality. Despite that conventional Kalman filter (KF) can remove Gaussian noise in time domain, it lacks adaptability in real-time estimation due to its fixed model. Moreover, KF-based denoising algorithm has not been applied in PAI before. In this paper, we propose an adaptive modified KF (MKF) targeted at PAI denoising by tuning system noise matrix Q and measurement noise matrix R in the conventional KF model. Additionally, in order to compensate the signal skewing caused by MKF, we cascade the backward part of Rauch-Tung-Striebel smoother, which utilizes the newly determined Q. Finally, as a supplement, we add a commonly used differential filter to remove in-band reflection artifacts. Experimental results using phantom and ex vivo colorectal tissue are provided to prove validity of the algorithm.

Noise Prior Knowledge Informed Bayesian Inference Network for Hyperspectral Super-Resolution.

Well-known deep learning (DL) is widely used in fusion based hyperspectral image super-resolution (HS-SR). However, DL-based HS-SR models have been designed mostly using off-the-shelf components from current deep learning toolkits, which lead to two inherent challenges: i) they have largely ignored the prior information contained in the observed images, which may cause the output of the network to deviate from the general prior configuration; ii) they are not specifically designed for HS-SR, making it hard to intuitively understand its implementation mechanism and therefore uninterpretable. In this paper, we propose a noise prior knowledge informed Bayesian inference network for HS-SR. Instead of designing a "black-box" deep model, our proposed network, termed as BayeSR, reasonably embeds the Bayesian inference with the Gaussian noise prior assumption to the deep neural network. In particular, we first construct a Bayesian inference model with the Gaussian noise prior assumption that can be solved iteratively by the proximal gradient algorithm, and then convert each operator involved in the iterative algorithm into a specific form of network connection to construct an unfolding network. In the process of network unfolding, based on the characteristics of the noise matrix, we ingeniously convert the diagonal noise matrix operation which represents the noise variance of each band into the channel attention. As a result, the proposed BayeSR explicitly encodes the prior knowledge possessed by the observed images and considers the intrinsic generation mechanism of HS-SR through the whole network flow. Qualitative and quantitative experimental results demonstrate the superiority of the proposed BayeSR against some state-of-the-art methods.

Gaussian Mechanism Design for Prescribed Privacy Sets in Data Releasing Systems

The data transmitted by cyber-physical systems can be intercepted and exploited by malicious individuals to infer privacy-sensitive information regarding the physical system. This motivates us to study the problem of preserving privacy in data releasing of linear dynamical system using stochastic perturbation. In this study, the privacy sensitive quantity is the initial state value of the system where for protecting its privacy, we directly design the covariance matrix of a Gaussian output noise to achieve a prescribed uncertainty set in the form of hyper-ellipsoids. This is done by correlated noise and through a convex optimization problem by considering the utility of released signals. Compared to other available methods, our proposed technique for designing the Gaussian output noise provides enhanced flexibility for system designers. As a case study, the results are applied to a heating ventilation and air conditioning system.

Adaptive Kalman filter based on integer ambiguity validation in moving base RTK

In high-precision dynamic positioning, it is necessary to ensure the positioning accuracy and reliability of the navigation system, especially for safety–critical applications, such as intelligent vehicle navigation. In the face of a complex observation environment, when the global navigation satellite system (GNSS) uses carrier phase observations for high-precision relative positioning, ambiguity resolution will be affected, and it is difficult to estimate all ambiguities. In addition, when the GNSS signal quality and measurement noise level are difficult to predict in an environment with many occlusions, the received satellite observations are prone to very large errors, resulting in apparent deviations in the positioning solution. However, traditional positioning algorithms assume that the measurement noise is constant, which is unrealistic. This will cause incorrect ambiguity resolution, lead to meter-level positioning errors, reduce the reliability of the system, and increase the integrity risk of the system. We proposed an innovative adaptive Kalman filter based on integer ambiguity validation (IAVAKF) to improve the efficiency of ambiguity resolution (AR) and positioning accuracy. The partial ambiguity resolution (PAR) method is applied to solve the integer ambiguities. Then, the accuracy of the fixed ambiguity is verified by the ambiguity success rate. Taking the ambiguity success rate as a dynamic adjustment factor, the measurement noise matrix and variance–covariance matrix of the state estimation is adaptively adjusted at each time interval in the Kalman filter to provide a smoothing effect for filtering. The optimal Kalman filter gain matrix is obtained to improve positioning accuracy and reliability. As a result, the static and dynamic vehicle experiments show that the positioning accuracy of the proposed IAVAKF is improved by 26% compared with the KF. Through the IAVAKF, a more realistic PL can be obtained and applied to evaluate the integrity of the navigation system in the position domain. It can reduce the false alarm rate by 2.45% and 1.85% in the horizontal and vertical directions, respectively.

Mitigating the Scintillation Effect on GNSS Signals Using MP and ROTI

Ionospheric scintillation is one of the main error sources of Global Navigation Satellite System (GNSS) positioning. The presence of scintillation may result in cycle slips, measurement errors or even losses of lock on satellites, eventually leading to complete failure of positioning. Typically, scintillation parameters S4 and σϕ are used to characterize amplitude and phase scintillation, respectively. However, the scintillation parameters can only be generated from data with a frequency of at least 1 Hz. Rate of change of total electron content index (ROTI) is often used as a proxy for scintillation parameters, which can be obtained from 1/30 Hz data. However, previous research has shown the inefficiency of ROTI to represent scintillation. Therefore, the multipath parameter (MP) has been proposed as another proxy for scintillation parameters, which can also be obtained from 1/30 Hz data. In this paper, both MP and ROTI (standard parameters) were used to mitigate scintillation effects on precise point positioning (PPP). To evaluate the effectiveness of MP and ROTI in mitigating scintillation effects, S4 and σϕ were also used for comparison and validation. Three strategies are proposed: (1) remove all observations from the satellite that is most affected by scintillation; (2) remove the scintillation-affected observations; (3) weight the measurement noise matrix in the Kalman Filter (KF) process. The results show that the observation removal and weighting strategies are considerably more effective than the satellite removal strategy. The results also show that the improvement of PPP outputs reaches 93.1% and the performance of standard parameters is comparable to that of scintillation parameters in the observation removal and weighting strategies.

Exponential Graph Regularized Non-Negative Low-Rank Factorization for Robust Latent Representation

Non-negative matrix factorization (NMF) is a fundamental theory that has received much attention and is widely used in image engineering, pattern recognition and other fields. However, the classical NMF has limitations such as only focusing on local information, sensitivity to noise and small sample size (SSS) problems. Therefore, how to develop the NMF to improve the performance and robustness of the algorithm is a worthy challenge. Based on the bottlenecks above, we propose an exponential graph regularization non-negative low-rank factorization algorithm (EGNLRF) combining sparseness, low rank and matrix exponential. Firstly, based on the assumption that the data is corroded, we decompose a given raw data item with a data error fitting noise matrix, applying a low-rank constraint to the denoising data. Then, we perform a non-negative factorization on the resulting low-rank matrix, from which we derive the low-dimensional representation of the original matrix. Finally, we use the low-dimensional representation for graph embedding to maintain the geometry between samples. The graph embedding terms are matrix exponentiated to cope with SSS problems and nearest neighbor sensitivity. The above three steps will be incorporated into a joint framework to validate and optimize each other; therefore, we can learn latent data representations that are undisturbed by noise and preserve the local structure of known samples. We conducted simulation experiments on different datasets and verified the effectiveness of the algorithm by comparing the proposed with the lasting ones related to NMF, low rank and graph embedding.

GPR ringing suppression using lateral outliers' swap filter

Recent advances in automatic target recognition in ground penetrating radar (GPR) data dictates the need for an effective ringing noise removal tool that does not degrade features of interest. While there are many techniques to attenuate this persistent type of noise, each technique has its own limitations and drawbacks. In the current study, a new method is introduced to efficiently attenuate ringing noise while maintaining the integrity of hyperbolic features of interest. The new method uses a laterally sliding filter that detects potential outliers and replaces them with interpolated values from neighboring samples. This filter imposes minimal or no changes to majority of ringing noise and manipulates only those in the proximity of hyperbolic features. This approach guarantees that subtracting the estimated ringing noise matrix from the original data leaves a smooth and clear GPR section in which hyperbolic features are significantly preserved. Tests conducted on both synthetic and real field data show that the new method produces clearer and more accurate results than other ringing noise removal methods. Moreover, the flexibility of the user-defined parameters, such as operator length, operator step, and outlier detection limits, makes the new method applicable to the wide range of GPR data available today.

An improved feature extraction method using low-rank representation for motor imagery classification

Motor imagery (MI) classification using electroencephalography (EEG) signal analysis is gaining significant interest for movement intent recognition, where feature extraction is critical for recognition accuracy. Traditional feature extraction methods ignore the spatial and neighborhood structure information of feature signals. In this paper, we assume that an EEG sample can be partitioned into a clean task-related EEG matrix and a noise matrix at first, because of the low-rank structure on underlying data representation disclosed by Low-Rank Representation (LRR). Then, Bilinear Two-Dimensional Discriminant Locality Preserving Projection (B2DDLPP) and LRR are combined to form a new feature extraction method known as Bilinear Low-Rank 2D Discriminant Locality Preserving Projection (BLRDLPP). It keeps the global structure information while preserving the local neighborhood relation. During experimentation, the proposed algorithm achieved classification accuracies of 73.26 % and 82.27 % on the four-class MI of the BCI Competition IV-2a dataset and III-3a dataset, respectively. The results demonstrate that the proposed method can effectively improve the acquisition of discriminant features.

Intelligent Reflecting Surface Assisted Secure Transmission in UAV-MIMO Communication Systems.

This paper studies the intelligent reflecting surface (IRS) assisted secure transmission in unmanned aerial vehicle (UAV) communication systems, where the UAV base station, the legitimate receiver, and the malicious eavesdropper in the system are all equipped with multiple antennas. By deploying an IRS on the facade of a building, the UAV base station can be assisted to realize the secure transmission in this multiple-input multiple-output (MIMO) system. In order to maximize the secrecy rate (SR), the transmit precoding (TPC) matrix, artificial noise (AN) matrix, IRS phase shift matrix, and UAV position are jointly optimized subject to the constraints of transmit power limit, unit modulus of IRS phase shift, and maximum moving distance of UAV. Since the problem is non-convex, an alternating optimization (AO) algorithm is proposed to solve it. Specifically, the TPC matrix and AN covariance matrix are derived by the Lagrange dual method. The alternating direction method of multipliers (ADMM), majorization-minimization (MM), and Riemannian manifold gradient (RCG) algorithms are presented, respectively, to solve the IRS phase shift matrix, and then the performance of the three algorithms is compared. Based on the proportional integral (PI) control theory, a secrecy rate gradient (SRG) algorithm is proposed to iteratively search for the UAV position by following the direction of the secrecy rate gradient. The theoretic analysis and simulation results show that our proposed AO algorithm has a good convergence performance and can increase the SR by 40.5% compared with the method without IRS assistance.

P-step Kalman-like unbiased FIR algorithm for detecting anomalies of atomic clocks

An extended measurement model anomaly detection algorithm for atomic clocks is proposed based on the p-step Kalman-like iterative Unbiased finite impulse response (UFIR) algorithm. The novel of the proposed algorithm is that it breaks the disadvantage of initializing the noise matrix in the traditional Kalman filter improved algorithms. By accumulating the prediction residuals generated by the process of p-step Kalman-like iterative, the detection statistics are constructed to realize the weaker phase and frequency jump detection of atomic clocks. Simulation results show the effectiveness of the proposed algorithm, and Monte-Carlo (M-C) experiment is used to verify the theoretical calculation of detection probability. We also analyze the measured data of a cesium atomic clock in our timekeeping laboratory, and the results show that the new method is more sensitive to weak frequency jump than the improved algorithm based on the Kalman filter.

Online Voltage Event Detection Using Synchrophasor Data With Structured Sparsity-Inducing Norms

This paper develops an accurate and computationally efficient data-driven framework to detect voltage events from PMU data streams. It develops an innovative Proximal Bilateral Random Projection (PBRP) algorithm to quickly decompose the PMU data matrix into a low-rank matrix, a row-sparse event-pattern matrix and a noise matrix. The row-sparse pattern matrix significantly distinguishes events from normal behavior. These matrices are then fed into a clustering algorithm to separate voltage events from normal operating conditions. Large-scale numerical study results on real-world PMU data show that the proposed algorithm is computationally more efficient and achieves higher F scores than state-of-the-art benchmarks.

Multiple targets tracking by using improved labeled multi-target multi-Bernoulli filter with FDA-MIMO radar

In the traditional multi-target multi-Bernoulli (MeMBer) filter, only the radar signal after constant false alarm rate (CFAR) is considered. In addition, it is also necessary to assume that the detection probability of the target and the covariance matrix of the measurement noise are known. In fact, the detection probability of the target and the covariance matrix of the noise are difficult to determine. Therefore, this paper proposes an improved labeled multi-target multi-Bernoulli (IL-MeMBer) filter that can avoid considering the detection probability of the target and the covariance matrix of the measurement noise. Firstly, the multi-target superposition measurement model of FDA-MIMO is given in the presence of false targets. Secondly, the target likelihood function under the superposition measurement model is derived by analyzing the characteristics of the traditional point measurement likelihood function and the Music spatial spectrum. Thirdly, considering the unknown and time-varying number of targets, the original echo signals without detection probability before (CFAR) processing, and no target tracks output by the traditional MeMBer filter, we put forward an analytical solution of the IL-MeMBer filter. Finally, a fusion strategy based on Euclidean distance is proposed to solve the problem that the same target can be estimated to have multiple tracks in the IL-MeMBer filter. In addition, the sequential Monte Carlo (SMC) implementation of the IL-MeMBer filter is provided. Numerical experiences verify the effectiveness and superiority of the proposed methods.

On-line harmonic signal denoising from the measurement with non-stationary and non-Gaussian noise

Harmonic denoising is one of the important preprocessing steps before extracting harmonic signal characteristics. Several signal processing techniques have been developed and applied for denoising the harmonics, which assume that the noise follows a Gaussian distribution and is stationary. However, the noise is often not so simple as a Gaussian distribution, and it could be non-Gaussian and non-stationary in most practical scenarios. A novel online denoising method for the harmonic signal with non-stationary complex noises based on the Bayesian Maximum a Posteriori (MAP) framework is proposed in this paper. The measured signal is divided equally into several frames. Then these frames are transformed into the time-frequency domain by the Short-Time Fourier transform (STFT) and are assumed to be the sum of a low-rank matrix and a noise matrix. The online model of the low-rank matrix and the noise matrix is then constructed between the frames. The online Gaussian mixture model (GMM) and low-rank matrix factorization are performed on the measurement matrix in the complex number domain to reconstruct the harmonic signal. The performance of the proposed method is validated in the simulations. The non-Gaussian and non-stationary noise can be removed more effectively, and the proposed algorithm can improve the frequency estimation accuracy.

Robust muscle force prediction using NMFSEMD denoising and FOS identification.

In this paper, an aliasing noise restraint technique and a system identification-based surface electromyography (sEMG)-force prediction model are proposed to realize a type of robust sEMG and muscle force prediction. For signal denoising, a novel non-negative matrix factorization screening empirical mode decomposition (NMFSEMD) and a fast orthogonal search (FOS)-based muscle force prediction model are developed. First, the NMFSEMD model is used to screen the empirical mode decomposition (EMD) results into the noisy intrinsic mode functions (IMF). Then, the noise matrix is computed using IMF translation and superposition, and the matrix is used as the input of NMF to obtain the denoised IMF. Furthermore, the reconstruction outcome of the NMFSEMD method can be used to estimate the denoised sEMG. Finally, a new sEMG muscle force prediction model, which considers a kind of candidate function in derivative form, is constructed, and a data-training-based linear weighted model is obtained. Extensive experimental results validate the suggested method’s correction: after the NMFSEMD denoising of raw sEMG signal, the signal-noise ratio (SNR) can be improved by about 15.0 dB, and the energy percentage (EP) can be greater than 90.0%. Comparing with the muscle force prediction models using the traditional pretreatment and LSSVM, and the NMFSEMD plus LSSVM-based method, the mean square error (MSE) of our approach can be reduced by at least 1.2%.

Identification of linear systems with multiplicative noise from multiple trajectory data

The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system matrices and the covariance matrix of the multiplicative noise. The algorithm does not need prior knowledge of the noise or stability of the system, but requires only independent inputs with pre-designed first and second moments and relatively small trajectory length. The study of identifiability of the noise covariance matrix shows that there exists an equivalent class of matrices that generate the same second-moment dynamic of system states. It is demonstrated how to obtain the equivalent class based on estimates of the noise covariance. Asymptotic consistency of the algorithm is verified under sufficiently exciting inputs and system controllability conditions. Non-asymptotic performance of the algorithm is also analyzed under the assumption that the system is bounded. The analysis provides high-probability bounds vanishing as the number of trajectories grows to infinity. The results are illustrated by numerical simulations.

Entrywise Estimation of Singular Vectors of Low-Rank Matrices With Heteroskedasticity and Dependence

We propose an estimator for the singular vectors of high-dimensional low-rank matrices corrupted by additive subgaussian noise, where the noise matrix is allowed to have dependence within rows and heteroskedasticity between them. We prove finite-sample $\ell_{2,\infty}$ bounds and a Berry-Esseen theorem for the individual entries of the estimator, and we apply these results to high-dimensional mixture models. Our Berry-Esseen theorem clearly shows the geometric relationship between the signal matrix, the covariance structure of the noise, and the distribution of the errors in the singular vector estimation task. These results are illustrated in numerical simulations. Unlike previous results of this type, which rely on assumptions of gaussianity or independence between the entries of the additive noise, handling the dependence between entries in the proofs of these results requires careful leave-one-out analysis and conditioning arguments. Our results depend only on the signal-to-noise ratio, the sample size, and the spectral properties of the signal matrix.

Edge statistics of large dimensional deformed rectangular matrices

We consider the edge statistics of large dimensional deformed rectangular matrices of the form Yt=Y+tX, where Y is a p×n deterministic signal matrix whose rank is comparable to n, X is a p×n random noise matrix with i.i.d. entries of mean zero and variance n−1, and t>0 gives the noise level. This model is referred to as the interference-plus-noise matrix in the study of massive multiple-input multiple-output (MIMO) system, which belongs to the category of the so-called signal-plus-noise model. For the case t=1, the spectral statistics of this model have been studied to a certain extent in the literature (Dozier and Silverstein, 2007[17,18]; Vallet et al., 2012). In this paper, we study the singular value and singular vector statistics of Yt around the right-most edge of the spectrum in the harder regime n−1/3≪t≪1. This regime is harder than the t=1 case, because on the one hand, the edge behavior of the empirical spectral distribution (ESD) of YY⊤ has a strong effect on the edge statistics of YtYt⊤ for a “small” t≪1, while on the other hand, the edge eigenvalue behavior of YtYt⊤ is not merely a perturbation of that of YY⊤ for a “large” t≫n−1/3. Under certain regularity assumptions on Y, we prove the Tracy–Widom law for the edge eigenvalues, the eigenvalue rigidity, and eigenvector delocalization for the matrices YtYt⊤ and Yt⊤Yt. These results can be used to estimate and infer the massive MIMO system. To prove the main results, we analyze the edge behavior of the asymptotic ESD of YtYt⊤ and establish optimal local laws on its resolvent. These results are of independent interest, and can be used as important inputs for many other problems regarding the spectral statistics of Yt.

Superresolution Performance of Different Spatial Smoothing Methods for Short Uniform Linear Array

Radar withuniform linear antenna array is commonly used to measure the angle of the target. The superresolution ability is of significant importance in applications where the array size is limited and the targets are crowded. In this letter, we test the superresolution performance of a six-element array by field data using two trihedral corner reflectors set on the ground. The spatial smoothing methods with different subaperture sizes are compared, and a new spatial smoothing method using interlaced subaperture is proposed. The interlaced subaperture has larger effective aperture size and independent noise matrix, which leads to better superresolution performance. Its computational complexity is smaller than the successive subaperture due to the smaller size of the data matrix. Results show that two reflectors with angular separation of about half the Fourier limit can be resolved with high probability when the peak signal-to-noise ratio is about 35 dB.