Data-Based Filters for Non-Gaussian Dynamic Systems With Unknown Output Noise Covariance

This paper proposes linear and nonlinear filters for a non-Gaussian dynamic system with an unknown nominal covariance of the output noise.The challenge of designing a suitable filter in the presence of an unknown covariance matrix is addressed by focusing on the output data set of the system.Considering that data generated from a Gaussian distribution exhibit ellipsoidal scattering,we first propose the weighted sum of norms(SON)clustering method that prioritizes nearby points,reduces distant point influence,and lowers computational cost.Then,by introducing the weighted maximum likelihood,we propose a semi-definite program(SDP)to detect outliers and reduce their impacts on each cluster.Detecting these weights paves the way to obtain an appropriate covariance of the output noise.Next,two filtering approaches are presented:a cluster-based robust linear filter using the maximum a posterior(MAP)estimation and a clusterbased robust nonlinear filter assuming that output noise distribution stems from some Gaussian noise resources according to the ellipsoidal clusters.At last,simulation results demonstrate the effectiveness of our proposed filtering approaches.

CL2ES-KDBC:A Novel Covariance Embedded Selection Based on Kernel Distributed Bayes Classifier for Detection of Cyber-Attacks in IoT Systems

The Internet of Things(IoT)is a growing technology that allows the sharing of data with other devices across wireless networks.Specifically,IoT systems are vulnerable to cyberattacks due to its opennes The proposed work intends to implement a new security framework for detecting the most specific and harmful intrusions in IoT networks.In this framework,a Covariance Linear Learning Embedding Selection(CL2ES)methodology is used at first to extract the features highly associated with the IoT intrusions.Then,the Kernel Distributed Bayes Classifier(KDBC)is created to forecast attacks based on the probability distribution value precisely.In addition,a unique Mongolian Gazellas Optimization(MGO)algorithm is used to optimize the weight value for the learning of the classifier.The effectiveness of the proposed CL2ES-KDBC framework has been assessed using several IoT cyber-attack datasets,The obtained results are then compared with current classification methods regarding accuracy(97%),precision(96.5%),and other factors.Computational analysis of the CL2ES-KDBC system on IoT intrusion datasets is performed,which provides valuable insight into its performance,efficiency,and suitability for securing IoT networks.

Low-Complexity Reconstruction of Covariance Matrix in Hybrid Uniform Circular Array

Spatial covariance matrix(SCM) is essential in many multi-antenna systems such as massive multiple-input multiple-output(MIMO). For multi-antenna systems operating at millimeter-wave bands, hybrid analog-digital structure has been widely adopted to reduce the cost of radio frequency chains.In this situation, signals received at the antennas are unavailable to the digital receiver, and as a consequence, traditional sample average approach cannot be used for SCM reconstruction in hybrid multi-antenna systems. To address this issue, beam sweeping algorithm(BSA) which can reconstruct the SCM effectively for a hybrid uniform linear array, has been proposed in our previous works. However, direct extension of BSA to a hybrid uniform circular array(UCA)will result in a huge computational burden. To this end, a low-complexity approach is proposed in this paper. By exploiting the symmetry features of SCM for the UCA, the number of unknowns can be reduced significantly and thus the complexity of reconstruction can be saved accordingly. Furthermore, an insightful analysis is also presented in this paper, showing that the reduction of the number of unknowns can also improve the accuracy of the reconstructed SCM. Simulation results are also shown to demonstrate the proposed approach.

Optimal Estimation of High-Dimensional Covariance Matrices with Missing and Noisy Data

The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.

Empirical Likelihood Statistical Inference for Compound Poisson Vector Processes under Infinite Covariance Matrix

The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.

Evaluation of Multiplicative Weight of Covariance Matrix on Hybrid Data Assimilation Schemes

This research develops a comparative study between different multiplicative weights that are assigned to the covariance matrix that represents the background error in two hybrid assimilation schemes: 3DEnVAR and 4DEnVAR. These weights are distributed between the static and time-invariant matrix and the matrix generated from the perturbations of a previous ensemble. The assigned values are 25%, 50%, and 75%, always having as a reference the ensemble matrix. The experiments are applied to the short-range Prediction System (SisPI) that works operationally at the Institute of Meteorology. The impact of Tropical Storm Eta on November 7 and 8, 2020 was selected as a study case. The results suggest that by giving the main weight to the ensemble matrix more realistic solutions are achieved because it shows a better representation of the synoptic flow. On the other hand, it is observed that 3DEnVAR method is more sensitive to multiplicative weight change of the first guess. More realistic results are obtained with 50% and 75% relations with 4DEnVAR method, whereas with 3DEnVAR a weight of 75% for the ensemble matrix is required.

Sensor management of LEO constellation based on covariance control

This paper studies the multi-sensor management problem for low earth orbit(LEO) infrared warning constellation used to track a midcourse missile. A covariance control approach, which selects sensor combinations or subset based on the difference between the desired covariance matrix and the actual covariance of each target, is used for sensor management, including some matrix metrics to measure the differentia between two covariance matrices. Besides, to meet the requirements of the space based warning system, the original covariance control approach is improved. Simulation results demonstrate that the covariance control approach is able to provide a better tracking performance by providing a well-designed desired covariance and balance tracking performance goals with system demands.

ON THE OPTIMAL BACKGROUND ERROR COVARIANCES: DIFFERENT SCALE ERRORS' CONTRIBUTION

The large-scale and small-scale errors could affect background error covariances for a regional numerical model with the specified grid resolution.Based on the different background error covariances influenced by different scale errors,this study tries to construct a so-called"optimal background error covariances"to consider the interactions among different scale errors.For this purpose,a linear combination of the forecast differences influenced by information of errors at different scales is used to construct the new forecast differences for estimating optimal background error covariances.By adjusting the relative weight of the forecast differences influenced by information of smaller-scale errors,the relative influence of different scale errors on optimal background error covariances can be changed.For a heavy rainfall case,the corresponding optimal background error covariances can be estimated through choosing proper weighting factor for forecast differences influenced by information of smaller-scale errors.The data assimilation and forecast with these optimal covariances show that,the corresponding analyses and forecasts can lead to superior quality,compared with those using covariances that just introduce influences of larger-or smallerscale errors.Due to the interactions among different scale errors included in optimal background error covariances,relevant analysis increments can properly describe weather systems(processes)at different scales,such as dynamic lifting,thermodynamic instability and advection of moisture at large scale,high-level and low-level jet at synoptic scale,and convective systems at mesoscale and small scale,as well as their interactions.As a result,the corresponding forecasts can be improved.

ASSESSMENT OF LOCAL INFLUENCE IN A GROWTH CURVE MODEL WITH RAO'S SIMPLE COVARIANCE STRUCTURE

The present paper deals with the problem of assessing the local influence in a growth curve model with Rao’s simple covariance structure. Based on the likelihood displacement,the curvature measure is employed to evaluate the effects of some minor perturbations on the statistical inference, thus leading to the large curvature direction, which is the most critical diagnostic statistic in the context of the local influence analysis. As an application, the common covariance-weighted perturbation scheme is thoroughly considered.

Fast and accurate covariance matrix reconstruction for adaptive beamforming using Gauss-Legendre quadrature

Most of the reconstruction-based robust adaptive beamforming(RAB)algorithms require the covariance matrix reconstruction(CMR)by high-complexity integral computation.A Gauss-Legendre quadrature(GLQ)method with the highest algebraic precision in the interpolation-type quadrature is proposed to reduce the complexity.The interference angular sector in RAB is regarded as the GLQ integral range,and the zeros of the threeorder Legendre orthogonal polynomial is selected as the GLQ nodes.Consequently,the CMR can be efficiently obtained by simple summation with respect to the three GLQ nodes without integral.The new method has significantly reduced the complexity as compared to most state-of-the-art reconstruction-based RAB techniques,and it is able to provide the similar performance close to the optimal.These advantages are verified by numerical simulations.

Underdetermined DOA estimation via multiple time-delay covariance matrices and deep residual network

Higher-order statistics based approaches and signal sparseness based approaches have emerged in recent decades to resolve the underdetermined direction-of-arrival(DOA)estimation problem.These model-based methods face great challenges in practical applications due to high computational complexity and dependence on ideal assumptions.This paper presents an effective DOA estimation approach based on a deep residual network(DRN)for the underdetermined case.We first extract an input feature from a new matrix calculated by stacking several covariance matrices corresponding to different time delays.We then provide the input feature to the trained DRN to construct the super resolution spectrum.The DRN learns the mapping relationship between the input feature and the spatial spectrum by training.The proposed approach is superior to existing model-based estimation methods in terms of calculation efficiency,independence of source sparseness and adaptive capacity to non-ideal conditions(e.g.,low signal to noise ratio,short bit sequence).Simulations demonstrate the validity and strong performance of the proposed algorithm on both overdetermined and underdetermined cases.

Geometric Covariance Modeling for Surface Variation of Compliant Parts Based on Hybrid Polynomial Approximation and Spectrum Analysis

Part variation characterization is essential to analyze the variation propagation in flexible assemblies. Aiming at two governing types of surface variation,warping and waviness,a comprehensive approach of geometric covariance modeling based on hybrid polynomial approximation and spectrum analysis is proposed,which can formulate the level and the correlation of surface variations accurately. Firstly,the form error data of compliant part is acquired by CMM. Thereafter,a Fourier-Legendre polynomial decomposition is conducted and the error data are approximated by a Legendre polynomial series. The weighting coefficient of each component is decided by least square method for extracting the warping from the surface variation. Consequently,a geometrical covariance expression for warping deformation is established. Secondly,a Fourier-sinusoidal decomposition is utilized to approximate the waviness from the residual error data. The spectrum is analyzed is to identify the frequency and the amplitude of error data. Thus,a geometrical covariance expression for the waviness is deduced. Thirdly,a comprehensive geometric covariance model for surface variation is developed by the combination the Legendre polynomials with the sinusoidal polynomials. Finally,a group of L-shape sheet metals is measured along a specific contour,and the covariance of the profile errors is modeled by the proposed method. Thereafter,the result is compared with the covariance from two other methods and the real data. The result shows that the proposed covariance model can match the real surface error effectively and represents a tighter approximation error compared with the referred methods.

Uncertainty Principle for the Quaternion Linear Canonical Transform in Terms of Covariance

An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.

USING COVARIANCE INTERSECTION FOR CHANGE DETECTION IN REMOTE SENSING IMAGES

In this paper,an unsupervised change detection technique for remote sensing images acquired on the same geographical area but at different time instances is proposed by conducting Covariance Intersection(CI) to perform unsupervised fusion of the final fuzzy partition matrices from the Fuzzy C-Means(FCM) clustering for the feature space by applying compressed sampling to the given remote sensing images.The proposed approach exploits a CI-based data fusion of the membership function matrices,which are obtained by taking the Fuzzy C-Means(FCM) clustering of the frequency-domain feature vectors and spatial-domain feature vectors,aimed at enhancing the unsupervised change detection performance.Compressed sampling is performed to realize the image local feature sampling,which is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery.The experimental results demonstrate that the proposed algorithm has a good change detection results and also performs quite well on denoising purpose.

Using position specific scoring matrix and auto covariance to predict protein subnuclear localization

The knowledge of subnuclear localization in eukaryotic cells is indispensable for under-standing the biological function of nucleus, genome regulation and drug discovery. In this study, a new feature representation was pro-posed by combining position specific scoring matrix (PSSM) and auto covariance (AC). The AC variables describe the neighboring effect between two amino acids, so that they incorpo-rate the sequence-order information;PSSM de-scribes the information of biological evolution of proteins. Based on this new descriptor, a support vector machine (SVM) classifier was built to predict subnuclear localization. To evaluate the power of our predictor, the benchmark dataset that contains 714 proteins localized in nine subnuclear compartments was utilized. The total jackknife cross validation ac-curacy of our method is 76.5%, that is higher than those of the Nuc-PLoc (67.4%), the OET- KNN (55.6%), AAC based SVM (48.9%) and ProtLoc (36.6%). The prediction software used in this article and the details of the SVM parameters are freely available at http://chemlab.scu.edu.cn/ predict_SubNL/index.htm and the dataset used in our study is from Shen and Chou’s work by downloading at http://chou.med.harvard.edu/ bioinf/Nuc-PLoc/Data.htm.

Joint Variable Selection of Mean-Covariance Model for Longitudinal Data

In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. Simulation studies are undertaken to assess the finite sample performance of the proposed variable selection procedure.

Background Error Covariance Statistics of Hydrometeor Control Variables Based on Gaussian Transform

Use of data assimilation to initialize hydrometeors plays a vital role in numerical weather prediction(NWP).To directly analyze hydrometeors in data assimilation systems from cloud-sensitive observations,hydrometeor control variables are necessary.Common data assimilation systems theoretically require that the probability density functions(PDFs)of analysis,background,and observation errors should satisfy the Gaussian unbiased assumptions.In this study,a Gaussian transform method is proposed to transform hydrometeors to more Gaussian variables,which is modified from the Softmax function and renamed as Quasi-Softmax transform.The Quasi-Softmax transform method then is compared to the original hydrometeor mixing ratios and their logarithmic transform and Softmax transform.The spatial distribution,the non-Gaussian nature of the background errors,and the characteristics of the background errors of hydrometeors in each method are studied.Compared to the logarithmic and Softmax transform,the Quasi-Softmax method keeps the vertical distribution of the original hydrometeor mixing ratios to the greatest extent.The results of the D′Agostino test show that the hydrometeors transformed by the Quasi-Softmax method are more Gaussian when compared to the other methods.The Gaussian transform has been added to the control variable transform to estimate the background error covariances.Results show that the characteristics of the hydrometeor background errors are reasonable for the Quasi-Softmax method.The transformed hydrometeors using the Quasi-Softmax transform meet the Gaussian unbiased assumptions of the data assimilation system,and are promising control variables for data assimilation systems.

AN IMPROVED SAR-GMTI METHOD BASED ON EIGEN-DECOMPOSITION OF THE SAMPLE COVARIANCE MATRIX

An improved two-channel Synthetic Aperture Radar Ground Moving Target Indication (SAR-GMTI) method based on eigen-decomposition of the covariance matrix is investigated. Based on the joint Probability Density Function (PDF) of the Along-Track Interferometric (ATI) phase and the similarity between the two SAR complex images, a novel ellipse detector is presented and is applied to the indication of ground moving targets. We derive its statistics and analyze the performance of detection process in detail. Compared with the approach using the ATI phase, the ellipse detector has a better performance of detection in homogenous clutter. Numerical experiments on simulated data are presented to validate the improved performance of the ellipse detector with respect to the ATI phase approach. Finally, the detection capability of the proposed method is demonstrated by measured SAR data.

Tuning of Prior Covariance in Generalized Least Squares

Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of prior information. These assignments often are very subjective, especially when correlations among data or among prior information are believed to occur. However, in cases in which the general form of these matrices can be anticipated up to a set of poorly-known parameters, the data and prior information may be used to better-determine (or “tune”) the parameters in a manner that is faithful to the underlying Bayesian foundation of GLS. We identify an objective function, the minimization of which leads to the best-estimate of the parameters and provide explicit and computationally-efficient formula for calculating the derivatives needed to implement the minimization with a gradient descent method. Furthermore, the problem is organized so that the minimization need be performed only over the space of covariance parameters, and not over the combined space of model and covariance parameters. We show that the use of trade-off curves to select the relative weight given to observations and prior information is not a form of tuning, because it does not, in general maximize the posterior probability of the model parameters, and can lead to a different weighting than the procedure described here. We also provide several examples that demonstrate the viability, and discuss both the advantages and limitations of the method.

Eddy covariance measurements of turbulent fluxes in the surf zone

Turbulent eddies play a critical role in oceanic flows. Direct measurements of turbulent eddy fluxes beneath the sea surface were taken to study the direction of flux-carrying eddies as a means of supplementing our understanding of vertical fluxes exchange processes and their relationship to tides. The observations were made at 32 Hz at a water depth of ~1.5 m near the coast of Sanya, China, using an eddy covariance system, which mainly consists of an acoustic doppler velocimeter(ADV) and a fast temperature sensor. The cospectra-fit method-an established semi-empirical model of boundary layer turbulence to the measured turbulent cospectra at frequencies below those of surface gravity waves-was used in the presence of surface gravity waves to quantify the turbulent eddy fluxes(including turbulent heat flux and Reynolds stress). As much as 87% of the total turbulent stress and 88% of the total turbulent heat flux were determined as being at band frequencies below those of surface gravity waves. Both the turbulent heat flux and Reynolds stress showed a daily successive variation;the former peaked during the low tide period and the later peaked during the ebb tide period.Estimation of roll-off wavenumbers, k0, and roll-off wavelengths, λ0(where λ0=2π/k0), which were estimated as the horizontal length scales of the dominant flux-carrying turbulent eddies, indicated that the λ0 of the turbulent heat flux was approximately double that of the Reynolds stress. Wavelet analysis showed that both the turbulent heat flux and the Reynolds stress have a close relationship to the semi-diurnal and diurnal tides, and therefore indicate the energy that is transported from tides to turbulence.