Covariance Matrix Of Observations Research Articles

Underlying Topography Estimation over Forest Using Maximum a Posteriori Inversion with Spaceborne Polarimetric SAR Interferometry

This paper presents a method for extracting the digital elevation model (DEM) of forested areas from polarimetric interferometric synthetic aperture radar (PolInSAR) data. The method models the ground phase as a Von Mises distribution, with a mean of the topographic phase computed from an external DEM. By combining the prior distribution of the ground phase with the complex Wishart distribution of the observation covariance matrix, we derive the maximum a posterior (MAP) inversion method based on the RVoG model and analyze its Cramer–Rao Lower Bound (CRLB). Furthermore, considering the characteristics of the objective function, this paper introduces a Four-Step Optimization (FSO) method based on gradient optimization, which solves the inefficiency problem caused by exhaustive search in solving ground phase using the MAP method. The method is validated using spaceborne L-band repeat-pass SAOCOM data from a test forest area. The test results for FSO indicate that it is approximately 5.6 times faster than traditional methods without compromising accuracy. Simultaneously, the experimental results demonstrate that the method effectively solves the problem of elevation jumps in DEM inversion when modeling the ground phase with the Gaussian distribution. ICESAT-2 data are used to evaluate the accuracy of the inverted DEM, revealing that our method improves the root mean square error (RMSE) by about 23.6% compared to the traditional methods.

Closet In-Path Vehicle Detection and Recognition Algorithm Based on Camera and Millimeter-Wave Radar Fusion

<div>The closet in-path vehicle (CIPV) is recognized relying on the detection results for road lane lines in most current ACC system, which may not work well in the poor conditions, for example, unclear road lane lines, low light level, bad weather, and so on. To solve this problem, the article proposes a sensor fusion-based CIPV recognition algorithm independent of road lane lines. First, a robust Kalman filter based on the global coordinate system is designed to fuse the millimeter-wave radar and camera targets. The fusion algorithm can dynamically adjust the covariance matrix of sensor observations to avoid the influence of anomalous observations on the fusion results. Stable detection of targets by the fusion algorithm is the basis of the CIPV recognition algorithm. Then, the CIPV recognition algorithm generates virtual lane lines using the motion parameters of self-vehicle or the driving trajectory of vehicle target and develops a mode switch strategy for virtual lane lines generation based on the driving state of target. This strategy can flexibly switch to the applicable virtual lane lines generation method in different scenarios. Finally, field tests are conducted in typical scenarios to verify the performance of the CIPV recognition algorithm. The results show that the algorithm is able to recognize CIPV stably and accurately without relying on road lane lines.</div>

A Spatial–Temporal Bayesian Deep Image Prior Model for Moderate Resolution Imaging Spectroradiometer Temporal Mixture Analysis

Time-series remote sensing images are important in agricultural monitoring and investigation. However, most time-series data with high temporal resolution have the problem of insufficient spatial resolution which cannot meet the requirement of precision agriculture. The unmixing technique can obtain the object abundances with richer spatial information from the coarse-resolution images. Although the unmixing technique is widely used in hyperspectral data, it is insufficiently researched for time-series data. Temporal unmixing extends spectral unmixing to the time domain from the spectral domain, and describes the temporal characteristics rather than the spectral characteristics of different ground objects. Deep learning (DL) techniques have achieved promising performance for the unmixing problem in recent years, but there are still few studies on temporal mixture analysis (TMA), especially in the application of crop phenological monitoring. This paper presents a novel spatial–temporal deep image prior method based on a Bayesian framework (ST-Bdip), which innovatively combines the knowledge-driven TMA model and the DL-driven model. The normalized difference vegetation index (NDVI) time series of moderate resolution imaging spectroradiometer (MODIS) data is used as the object for TMA, while the extracted seasonal crop signatures and the fractional coverages are perceived as the temporal endmembers (tEMs) and corresponding abundances. The proposed ST-Bdip method mainly includes the following contributions. First, a deep image prior model based on U-Net architecture is designed to efficiently learn the spatial context information, which enhances the representation of abundance modeling compared to the traditional non-negative least squares algorithm. Second, The TMA model is incorporated into the U-Net training process to exploit the knowledge in the forward temporal model effectively. Third, the temporal noise heterogeneity in time-series images is considered in the model optimization process. Specifically, the anisotropic covariance matrix of observations from different time dimensions is modeled as a multivariate Gaussian distribution and incorporated into the calculation of the loss function. Fourth, the "purified means" approach is used to further optimize crop tEMs and the corresponding abundances. Finally, the expectation–maximization (EM) algorithm is designed to solve the maximum a posterior (MAP) problem of the model in the Bayesian framework. Experimental results on three synthetic datasets with different noise levels and two real MODIS datasets demonstrate the superiority of the proposed approach in comparison with seven traditional and advanced unmixing algorithms.

УЧЕТ СКОРРЕЛИРОВАННОСТИ ОШИБОК СПУТНИКОВЫХ ДАННЫХ НАБЛЮДЕНИЙ AMV В АНСАМБЛЕВОЙ СИСТЕМЕ УСВОЕНИЯ ДАННЫХ

The effect of considering correlated errors in AMV (Atmospheric Motion Vectors) satellite observations of wind in the local ensemble transform Kalman filter data assimilation system is studied. It is customary to use a diagonal covariance matrix of errors in observations taking part in assimilation. When assimilating satellite data with correlated errors, the data are thinned, and the values of diagonal elements of the error covariance matrix are often overestimated. This is accompanied by the loss of useful information about the correlation between the errors. The present study uses a different method: the elements of the error covariance matrix for AMV satellite observations are simulated using a second-order autoregressive function. It is shown that such approach reduces the root-mean-square error in initial data for a numerical weather prediction model, in particular on small scales, and improves the forecast quality. It is found that the application of the non-diagonal AMV observation error covariance matrix increases the accuracy of analysis and forecast fields.

Forecasting Financial and Macroeconomic Variables Using an Adaptive Parameter VAR-KF Model

The primary objective of this article is to present an adaptive parameter VAR-KF technique (APVAR-KF) to forecast stock market performance and macroeconomic factors. The method exploits a vector autoregressive model as a system identification technique, and the Kalman filter is served as a recursive state parameter estimation tool. A further development was designed by incorporating the GARCH model to quantify an automatic observation covariance matrix in the Kalman filter step. To verify the efficiency of our proposed method, we conducted an experimental simulation applied to the main stock exchange index, real effective exchange rate and consumer price index of Thailand and Indonesia from January 1997 to May 2021. The APVAR-KF method is generally shown to have a superior performance relative to the conventional VAR(1) model and the VAR-KF model with constant parameters.

Confirmatory Factor Analyses in Psychological Test Adaptation and Development

Confirmatory Factor Analyses in Psychological Test Adaptation and Development

Construction and characteristic of the media exhibitionism construct and the Media Exhibitionism Questionnaire

Abstract Introduction: Internet users often reveal online intimate details from their lives, such as pictures with naked parts of their bodies or posts about their emotional states. The first part of the article presents an attempt to create media exhibitionism construct based on psychopathological criteria from ICD-10. The second part of the article presents psychometric properties of the Media Exhibitionism Questionnaire. Material and methods: After extracting 49 items, based on the theoretical foundations of the media exhibitionism construct, the competent judges assessed the accuracy of individual items. This resulted in the selection of 20 statements. Then the revised questionnaire was sent to Facebook users asking them to fill it out and send it to other users of the portal. The exploratory factor analysis (EFA) was carried out by the method of main components with Varimax rotation on N=65 persons, and confirmatory factor analysis (CFA) was conducted on N=554 persons. Results: After EFA the questionnaire consisted of 14 items and 4 factors: physical exhibitionism, exhibitionism of narcissistic traits, emotional exhibitionism, exhibitionism of histrionic traits. The four-factor solution was adopted on the basis of theoretical assumptions. The chi2 value was significant (χ2=286.01; p<0.001), which indicated discrepancies between the observed covariance matrix and the one implied by the model. Other indicators have shown a satisfactory agreement between the data and the model. Conclusions: The questionnaire has satisfactory psychometric properties (α=0.846) and can be used to predict problem behaviours on social media, as well as in counselling regarding responsible development of self-image on the Internet.

Input-state-parameter-noise identification and virtual sensing in dynamical systems: A Bayesian expectation-maximization (BEM) perspective

Structural identification and damage detection can be generalized as the simultaneous estimation of input forces, physical parameters, and dynamical states. Although Kalman-type filters are efficient tools to address this problem, the calibration of noise covariance matrices is cumbersome. For instance, calibration of input noise covariance matrix in augmented or dual Kalman filters is a critical task since a slight variation in its value can adversely affect estimations. The present study develops a Bayesian Expectation-Maximization (BEM) methodology for the uncertainty quantification and propagation in coupled input-state-parameter-noise identification problems. It also proposes the incorporation of input dummy observations for stabilizing low-frequency components of the latent states and mitigating potential drifts. In this respect, the covariance matrix of the dummy observations is also calibrated based on the measured data. Additionally, an explicit formulation is provided to study the theoretical observability of the Bayesian estimators, which helps characterize the minimum sensor requirements. Ultimately, the BEM is tested and verified through numerical and experimental examples, wherein sensor configurations, multiple input forces, and abrupt stiffness changes are investigated. It is confirmed that the BEM provides accurate estimations of states, input, and parameters while characterizing the degree of belief in these estimations based on the posterior uncertainties driven by applying a Bayesian perspective.

Mock catalogues of emission-line galaxies based on the local mass density in dark-matter only simulations

ABSTRACT The high-precision measurement of spatial clustering of emission-line galaxies (ELGs) is a primary objective for upcoming cosmological spectroscopic surveys. The source of strong emission of ELGs is nebular emission from surrounding ionized gas irradiated by massive short-lived stars in star-forming galaxies. As a result, ELGs are more likely to reside in newly formed haloes and this leads to a non-linear relation between ELG number density and matter density fields. In order to estimate the covariance matrix of cosmological observables, it is essential to produce many independent realizations to simulate ELG distributions for large survey volumes. To this end, we present a novel and fast scheme to populate ELGs in dark-matter only N-body simulations based on local density field. This method enables fast production of mock ELG catalogues suitable for verifying analysis methods and quantifying observational systematics in upcoming spectroscopic surveys and can populate ELGs in moderately high-density regions even though the halo structure cannot be resolved due to low resolution. The power spectrum of simulated ELGs is consistent with results of hydrodynamical simulations up to fairly small scales ($\lesssim 1 h \, \mathrm{Mpc}^{-1}$), and the simulated ELGs are more likely to be found in filamentary structures, which is consistent with results of semi-analytic and hydrodynamical simulations. Furthermore, we address the redshift-space power spectrum of simulated ELGs. The measured multipole moments of simulated ELGs clearly exhibit a weaker Finger-of-God effect than those of matter due to infalling motions towards halo centre, rather than random virial motions inside haloes.

A new multivariate CUSUM chart for monitoring of covariance matrix with individual observations under estimated parameter

AbstractMultivariate charts for process dispersion detect changes in the variance‐covariance matrix of a process. Most of the existing multivariate charts for monitoring the dispersion of individual observations were designed based on exponentially weighted moving average (EWMA) charting schemes. However, an alternative to the EWMA scheme is the cumulative sum (CUSUM) control chart, which has proven to be better in some cases. In the last decades, few studies have been conducted on methods based on multivariate CUSUM (MCUSUM) schemes to monitor the covariance matrix of individual observations. Consequently, we propose a new MCUSUM dispersion chart. Besides, most of the existing methods have been developed by assuming that the process parameters are known and that the process distribution is normal; these assumptions are not always true in practice. Hence, we compare the performance of the proposed chart and its counterparts based on the estimation effects under normal and non‐normal distributions. The results show that the proposed chart outperforms the other charts in terms of minor shifts in the process. Similarly, the proposed chart is the most robust to the normality assumption among the compared charts. The average value of the conditional average run length was used as the performance measure. Finally, the proposed method was also implemented with a simulated dataset to support the stated proposal findings.

A Real-Time BLE/PDR Integrated System by Using an Improved Robust Filter for Indoor Position

Indoor position technologies have attracted the attention of many researchers. To provide a real-time indoor position system with high precision and stability is necessary under many circumstances. In a real-time position scenario, gross errors of the Bluetooth low energy (BLE) fingerprint method are more easily occurring and the heading angle of the pedestrian will drift without acceleration and magnetic field compensation. A real-time BLE/pedestrian dead-reckoning (PDR) integrated system by using an improved robust filter has been proposed. In the PDR method, the improved Mahony complementary filter based on the pedestrian motion states is adopted to estimate the heading angle reducing the drift error. Then, an improved robust filter is utilized to detect and restrain the gross error of the BLE fingerprint method. The robust filter detected the gross error at different granularity by constructing a robust vector changing the observation covariance matrix of the extended Kalman filter (EKF) adaptively when the application is running. Several experiments are conducted in the true position scenario. The mean position accuracy obtained by the proposed method in the experiment is 0.844 m and RMSE is 0.74 m. Compared with the classic EKF, these two values are increased by 38% and 18%, respectively. The results show that the improved filter can avoid the gross error in the BLE method and provide high precision and scalability in indoor position service.

Resolving power of MUSIC-like algorithms for circular or rectilinear correlated sources in CES data models

The concept of threshold array signal-to-noise ratio (ASNR) which is defined as the minimal SNR at which specific high-resolution algorithms are able to resolve two closely spaced far-field sources, allows to quantify and to compare sensors array performance in localizing remote targets. This paper generalizes and extends the expressions of the threshold ASNR given in the literature for the conventional and non-circular (NC) MUSIC direction-of-arrival (DOA) estimation algorithms in the context of uncorrelated stochastic circular or rectilinear Gaussian sources and circular complex Gaussian (C-CG) noise, in a more general stochastic framework. We assume that the sources are correlated with an arbitrary distribution, which is inherent in a context of multipath or smart jammers, and that the noise is circular complex elliptically symmetric (C-CES) distributed, which can model impulsive noise with heavy-tailed distributions. The C-CES and NC-CES distributed observations are also considered to quantify the gain in resolution provided when the sample covariance matrix (SCM) of the observations is replaced by M-estimates of this matrix. Asymptotic approaches and perturbation analysis have been performed to derive closed-form expressions of the mean null spectra of the two considered MUSIC algorithms for both observation models, which allow us to derive, for the first time, general unified explicit analytical expressions of the threshold ASNR along the Cox and the Sharman and Durrani criteria. These expressions allow us to quantify the impact of the non-Gaussianity of noise and observations, as well as of the phase and magnitude of the correlation on the resolution threshold, and to quantify the benefit provided when the SCM is replaced by M-estimates of this covariance matrix for CES observations. Finally, numerical illustrations are included to support our theoretical analysis.

A simplified processing algorithm for multi-baseline RTK positioning in urban environments

The real-time kinematic (RTK) positioning with the multi-baseline solution (MBS) can provide high accuracy and availability for emerging applications. When the multi-systems and multi-frequencies observations for multiple stations are adopted, a heavy computational burden can arise to degrade the performance of RTK positioning. In this paper, a simplified multi-baseline solution (SMBS) algorithm based on the equivalence principle is proposed to improve the computational efficiency. Firstly, the classical equivalent observation equations (COE) are introduced and the variance–covariance (VC) matrix for SD observations is presented. Then, the simplified equivalent observation equations (SOE) can be obtained throughthe formuladerivationof transformation matrix. Secondly, the sequential Kalman filter (SKF) with multiple groups is used instead of the classical Kalman filter (CKF) to improve filtering efficiency. Finally, the performance of the proposed algorithm is comprehensively evaluated and analyzed by the static and kinematic experiments. The results demonstrate that the SMBS algorithm adopting SOE and SKF strategies can significantly accelerate the processing procedure of RTK positioning and reduce the processing time for a single epoch. The SOE strategy has an average efficiency improvement by approximately 74.7% for static, and 60.6% for the kinematic experiment, and the improvement of the SKF strategy is 49.6% and 58.0%. Moreover, the SMBS algorithm can provide a higher positioning accuracy and availability than the single-baseline solution (SBS) model. Especially for multiple reference stations, the state parameters of the rover station can be compressed to enhance the geometric strength of the positioning model, which can provide a smaller PDOP and ADOP values and improve the performance of ambiguity resolution (AR).

Specific features of potable water purification process

Under this consideration there is a process of potable water purification, where the chemical and physical characteristics (water turbidity and color, aluminum and chlorine content, etc) are monitored. To work with correlated characteristics it is necessary to apply to multivariate methods. The peculiarities of Hotelling charts plotting for individual observations are well known, but generalized variance charts plotting causes some problems connected with the assessment of covariance matrix for individual observations. Solving this problem one question arises: how often is it necessary to update the limit lines on the charts? We suggest applying to the test methods of the hypothesis on the equality of the mean.

Assimilating aerosol optical properties related to size and absorption from POLDER/PARASOL with an ensemble data assimilation system

Abstract. A data assimilation system for aerosol, based on an ensemble Kalman filter, has been developed for the ECHAM – Hamburg Aerosol Model (ECHAM-HAM) global aerosol model and applied to POLarization and Directionality of the Earth's Reflectances (POLDER)-derived observations of optical properties. The advantages of this assimilation system is that the ECHAM-HAM aerosol modal scheme carries both aerosol particle numbers and mass which are both used in the data assimilation system as state vectors, while POLDER retrievals in addition to aerosol optical depth (AOD) and the Ångström exponent (AE) also provide information related to aerosol absorption like aerosol absorption optical depth (AAOD) and single scattering albedo (SSA). The developed scheme can simultaneously assimilate combinations of multiple variables (e.g., AOD, AE, SSA) to optimally estimate mass mixing ratio and number mixing ratio of different aerosol species. We investigate the added value of assimilating AE, AAOD and SSA, in addition to the commonly used AOD, by conducting multiple experiments where different combinations of retrieved properties are assimilated. Results are evaluated with (independent) POLDER, Moderate Resolution Imaging Spectroradiometer (MODIS) Dark Target, MODIS Deep Blue and Aerosol Robotic Network (AERONET) observations. The experiment where POLDER AOD, AE and SSA are assimilated shows systematic improvement in mean error, mean absolute error and correlation for AOD, AE, AAOD and SSA compared to the experiment where only AOD is assimilated. The same experiment reduces the global ME against AERONET from 0.072 to 0.001 for AOD, from 0.273 to 0.009 for AE and from −0.012 to 0.002 for AAOD. Additionally, sensitivity experiments reveal the benefits of assimilating AE over AOD at a second wavelength or SSA over AAOD, possibly due to a simpler observation covariance matrix in the present data assimilation framework. We conclude that the currently available AE and SSA do positively impact data assimilation.

2D Laser SLAM With General Features Represented by Implicit Functions

The main contribution of this letter is the problem formulation and algorithm framework for 2D laser SLAM with general features represented by implicit functions. Since 2D laser data reflect the distances from the robot to the boundary of objects in the environment, it is natural to use the boundary of the general objects/features within the 2D environment to describe the features. Implicit functions can be used to represent almost arbitrary shapes from simple (e.g. circle, ellipse, line) to complex (e.g. a cross-section of a bunny model), thus it is worth studying implicit-expressed feature in 2D laser SLAM. In this letter, we clearly formulate the SLAM problem with implicit functions as features, with rigorously computed observation covariance matrix to be used in the SLAM objective function and propose a solution framework. Furthermore, we use ellipses and lines as examples to compare the proposed SLAM method with the traditional pre-fit method (represent the feature using its parameters and pre-fit the laser scan to get the fitted parameter as virtual observations). Simulation and experimental results show that our proposed method has a better performance compared with the pre-fit method and other methods, demonstrating the potential of this new SLAM formulation and method.

Using major depression polygenic risk scores to explore the depressive symptom continuum.

Major depression (MD) is often characterised as a categorical disorder; however, observational studies comparing sub-threshold and clinical depression suggest MD is continuous. Many of these studies do not explore the full continuum and are yet to consider genetics as a risk factor. This study sought to understand if polygenic risk for MD could provide insight into the continuous nature of depression. Factor analysis on symptom-level data from the UK Biobank (N = 148 957) was used to derive continuous depression phenotypes which were tested for association with polygenic risk scores (PRS) for a categorical definition of MD (N = 119 692). Confirmatory factor analysis showed a five-factor hierarchical model, incorporating 15 of the original 18 items taken from the PHQ-9, GAD-7 and subjective well-being questionnaires, produced good fit to the observed covariance matrix (CFI = 0.992, TLI = 0.99, RMSEA = 0.038, SRMR = 0.031). MD PRS associated with each factor score (standardised β range: 0.057-0.064) and the association remained when the sample was stratified into case- and control-only subsets. The case-only subset had an increased association compared to controls for all factors, shown via a significant interaction between lifetime MD diagnosis and MD PRS (p value range: 2.23 × 10-3-3.94 × 10-7). An association between MD PRS and a continuous phenotype of depressive symptoms in case- and control-only subsets provides support against a purely categorical phenotype; indicating further insights into MD can be obtained when this within-group variation is considered. The stronger association within cases suggests this variation may be of particular importance.

Characterization of the Observational Covariance Matrix of Hyper-Spectral Infrared Satellite Sensors Directly from Measured Earth Views

The observational covariance matrix, whose diagonal square root is currently named radiometric noise, is one of the most important elements to characterize a given instrument. It determines the precision of measurements and their possible spectral inter-correlation. The characterization of this matrix is currently performed with blackbody targets of known temperature and is, therefore, an output of the calibration unit of the instrument system. We developed a methodology that can estimate the observational covariance matrix directly from calibrated Earth-scene observations. The technique can complement the usual analysis based on onboard blackbody calibration and is, therefore, a useful back up to check the overall quality of the calibration unit. The methodology was exemplified by application to three satellite Fourier transform spectrometers: IASI (Infrared Atmospheric Sounder Interferometer), CrIS (Cross-Track Infrared Sounder), and HIRAS (Hyperspectral Infrared Atmospheric Sounder). It was shown that these three instruments are working as expected based on the pre-flight and in-flight characterization of the radiometric noise. However, for all instruments, the analysis of the covariance matrix reveals extra correlation among channels, especially in the short wave spectral regions.

A novel model-based state of charge estimation for lithium-ion battery using adaptive robust iterative cubature Kalman filter

Accurate and robust state of charge (SOC) estimation is the key evaluation index for battery management system (BMS) in electric vehicles (EVs). To improve the SOC estimation precision and reliability, a novel model-based estimation approach has been proposed. Firstly, the dynamic property of lithium-ion battery (LIB) is approximated by the auto-regressive and moving average (ARMA) model which compensates the measurement errors of terminal voltage and discharge current. Secondly, a variant of the Kalman filter (KF), namely improved cubature Kalman filter (CKF) based on the combination of singular value decomposition (SVD) and Gauss–Newton iterative technology is employed to develop a reliable estimator for SOC. Furthermore, an adaptive robust strategy is used to improve anti-interference performance by accounting for bidirectional adjustment of observation covariance and gain matrix. Finally, the Dynamic Stress Test (DST) and Federal Urban Driving Schedule (FUDS) are loaded on LIB to test the validity of the improved approach. The experiment results demonstrate the effectiveness of the combination of ARMA model and filtering method in terms of SOC estimation. Besides, simulated measurement noise is added to the test data to prove the robustness of the proposed method.

Score Predictor Factor Analysis: Reproducing Observed Covariances by Means of Factor Score Predictors.

The non-diagonal elements of the observed covariances are more exactly reproduced by the factor loadings than by the model implied by the corresponding factor score predictors. This is a limitation to the validity of factor score predictors. It is therefore investigated whether it is possible to estimate factor loadings for which the model implied by the factor score predictors optimally reproduces the non-diagonal elements of the observed covariance matrix. Accordingly, loading estimates are proposed for which the model implied by the factor score predictors allows for a least-squares approximation of the non-diagonal elements of the observed covariance matrix. This estimation method is termed score predictor factor analysis and algebraically compared with Minres factor analysis as well as principal component analysis. A population-based and a sample-based simulation study was performed in order to compare score predictor factor analysis, Minres factor analysis, and principal component analysis. It turns out that the non-diagonal elements of the observed covariance matrix can more exactly be reproduced from the factor score predictors computed from score predictor factor analysis than from the factor score predictors computed from Minres factor analysis and from principal components.