Vector Estimation Research Articles

SBAS DInSAR and in situ monitoring of the Šumljak landslide (SW Slovenia) dynamics driven by rainfall and piezometric-level fluctuation

AbstractThis paper presents the first attempt at establishing the dynamics of the Šumljak debris slide by using a multidisciplinary approach, including long-term inclinometer and piezometer measurements and a time-series analysis of SAR images for displacement vector estimation. The Šumljak landslide is located in the Rebrnice area, SW Slovenia, where the regional highway Razdrto-Nova Gorica runs through and poses a threat to the highway viaduct’s stability. By combining both ascending and descending Sentinel-1 data, we have estimated 3D displacement vectors for the landslide, providing insights into the usability of the technique for this kind of slow-moving landslides. Furthermore, we have combined and compared the SBAS DInSAR results to the displacements measured by inclinometer to evaluate the rate of displacement of the landslide and the viaduct. The inclinometer measurement results show that the landslide has a single sliding plane between the flysch colluvium and the slope deposits and provide the proof of the enlargement of the sliding area above its main scarp. The displacement vectors are spatially heterogenous, suggesting that different sites have different velocities and slightly different directional vectors. These results partly comply with the InSAR results. We further discussed the estimated vectors of displacement and the possible mechanism of movements. By using the piezometric data, we studied the groundwater level fluctuation in relation to daily rainfall and its influence on the displacements. Our findings show a correlation between the movements and the wet/dry season, indicating that the landslide is driven by rainfall and consequently groundwater level fluctuation. In 2020, the groundwater level rise was smaller than in the years before due to less rainfall, resulting in lower velocity of the landslide (5.5 mm/year) than in 2019 (7 mm/year).

Further study on the RCB-like steering vector estimation method: closed-form solution derivation via accurate Lagrange multiplier calculation

Further study on the RCB-like steering vector estimation method: closed-form solution derivation via accurate Lagrange multiplier calculation

General Expression of Best Equivariant Estimators of Regression Coefficients in Seemingly Unrelated Regression Models

ABSTRACTSeemingly unrelated regression models have been commonly employed as regression models with multiple explanatory variables and multiple response variables having cross‐correlations. This paper discusses equivariant estimation of the regression coefficient vector and derives the best equivariant estimator under a generalized quadratic loss function. The result of this paper is shown to include the results of previous best equivariant estimators under specific loss functions as special cases.

An Automatic Solution for Registration Between Single-Image and Point Cloud in Manhattan World Using Line Primitives

2D-3D registration is increasingly being applied in various scientific and engineering scenarios. However, due to appearance differences and cross-modal discrepancies, it is demanding for image and point cloud registration methods to establish correspondences, making 2D-3D registration highly challenging. To handle these problems, we propose a novel and automatic solution for 2D-3D registration in Manhattan world based on line primitives, which we denote as VPPnL. Firstly, we derive the rotation matrix candidates by establishing the vanishing point coordinate system as the link of point cloud principal directions to camera coordinate system. Subsequently, the RANSAC algorithm, which accounts for the clustering of parallel lines, is employed in conjunction with the least-squares method for translation vectors estimation and optimization. Finally, a nonlinear least-squares graph optimization method is carried out to optimize the camera pose and realize the 2D-3D registration and point colorization. Experiments on synthetic data and real-world data illustrate that our proposed algorithm can address the problem of 2D-3D direct registration in the case of Manhattan scenes where images are limited and sparse.

A new outlier rejection approach for non-Lambertian photometric stereo

Photometric stereo (PS) has garnered increasing attention due to its adeptness in restoring local fine textures. However, non-Lambertian reflections present in almost all real-world objects limit the effectiveness of the Lambertian model for surface normal vector estimation. Although BRDF-based and deep learning-based methods have become mainstream, recent research shows that comparable accuracy can also be achieved through simple filtering of observed intensity values. Nevertheless, these methods only consider the relative bias of pixel values and require manual specification of the number of pixels to be culled and the number of iterations. To address these issues, this paper proposes corresponding improvement methods. Firstly, a weighted inter-relationship function (IRF) fused with Huber loss is introduced to robustly and effectively evaluate the abnormal degree of pixel value. Secondly, based on the IRF curve and histogram statistical analysis, the number of excluded pixels is adaptively calculated. Thirdly, linear equations are then constructed based on the photometric equations, and the maximum between-class variance method is employed to achieve a high degree of sparsity, enabling fast and effective normal vector estimation. Finally, to verify the effectiveness of the proposed algorithm for non-Lambertian PS vision, quantitative verification tests on the synthetic dataset and the open-source datasets “DiLiGenT” and “DiLiGenT-PI” in real-world scenarios, and qualitative assessment experiments on real metal roughness samples are conducted. The experimental results demonstrate that, compared with the position threshold and IRF methods, our algorithms not only significantly enhance the accuracy of normal vector solutions but also markedly improve the operational efficiency of the algorithm, laying a solid foundation for practical online applications. These results fully validate the correctness and effectiveness of the proposed algorithm and provide a reference for the further development of outlier removal algorithms.

Joint Modeling of Longitudinal and Survival Data

In medical studies, time-to-event outcomes such as time to death or relapse of a disease are routinely recorded along with longitudinal data that are observed intermittently during the follow-up period. For various reasons, marginal approaches to model the event time, corresponding to separate approaches for survival data/longitudinal data, tend to induce bias and lose efficiency. Instead, a joint modeling approach that brings the two types of data together can reduce or eliminate the bias and yield a more efficient estimation procedure. A well-established avenue for joint modeling is the joint likelihood approach that often produces semiparametric efficient estimators for the finite-dimensional parameter vectors in both models. Through a transformation survival model with an unspecified baseline hazard function, this review introduces joint modeling that accommodates both baseline covariates and time-varying covariates. The focus is on the major challenges faced by joint modeling and how they can be overcome. A review of available software implementations and a brief discussion of future directions of the field are also included.

A Small Sigma Asymptomatic Approach Generalized Quasi Minimax and Mock Minimax Estimators in Linear Regression Model

In this paper concern with priority two generalized classes of estimators utilizing both types of information apriori and sample, for the estimation of coefficient vector in classical linear regression model in the presence of ellipsoidal Constraints on the parameter vector when the variance of the distribution are unknown. A vectors mean square matrices and weighted quadratic risk are found employing small sigma asymptotic. Some better estimators in the sense of having lesser risk than those of the estimators.

An ADCP Attitude Dynamic Errors Correction Method Based on Angular Velocity Tensor and Radius Vector Estimation

An acoustic Doppler current profiler (ADCP) installed on a platform produces rotational tangential velocity as a result of variations in the platform’s attitude, with both the tangential velocity and radial orientation varying between each pulse’s transmission and reception by the transducer. These factors introduce errors into the measurements of vessel velocity and flow velocity. In this study, we address the errors induced by dynamic factors related to variations in attitude and propose an ADCP attitude dynamic error correction method based on angular velocity tensor and radius vector estimation. This method utilizes a low-sampling-rate inclinometer and compass data and estimates the angular velocity tensor based on a physical model of vessel motion combined with nonlinear least-squares estimation. The angular velocity tensor is then used to estimate the transducers’ radius vectors. Finally, the radius vectors are employed to correct the instantaneous tangential velocity within the measured velocities of the vessel and flow. To verify the effectiveness of the proposed method, field tests were conducted in a water pool. The results demonstrate that the proposed method surpasses the attitude static correction approach. In comparison with the ASC method, the average relative error in vessel velocity during free-swaying movement decreased by 20.94%, while the relative standard deviation of the error was reduced by 17.38%.

Modified TRIAD Method for Solving the Problem of a Moving Object Orientation

Currently, it is relevant to create moving objects orientation systems based on the integration of various types of primary information sensors. One way to solve the orientation problem is to use the TRIAD (Tri-Axial Orientation Determination) method which allows determining the matrix of direction cosines between two coordinates. The traditional TRIAD force method is based on the use of two reference vectors – of gravitational and geomagnetic fields, measured by accelerometers and magnetometers, respectively. The disadvantage of this method is – appearance of additional deviations during the accelerated movement of the object and influence of primary information sensors’ random errors. Modified TRIAD method which is based on measurements of three triads of sensors: magnetometers, accelerometers and gyroscopes was proposed in the article. Estimates of acceleration vectors of gravitational and geomagnetic fields were calculated taking into account gyroscope measurements. Then these estimates were combined with the accelerometers’ and magnetometers’ data. The complex gravitational and geomagnetic fields’ accelerations were used to form the direction cosine matrix by the TRIAD method. The suggested modified method can be used to implement free-form moving objects’ orientation systems, since it is 6–8 times more accurate compared to the classic TRIAD method. Attenuation of random sensor errors and disturbances due to object acceleration can be adjusted by use of weigh factors.

Full Stokes-vector Inversion of the Solar Mg ii h and k Lines

The polarization of the Mg ii h and k resonance lines is the result of the joint action of scattering processes and the magnetic field–induced Hanle, Zeeman, and magneto-optical effects, thus holding significant potential for the diagnostic of the magnetic field in the solar chromosphere. The Chromospheric LAyer Spectro-Polarimeter sounding-rocket experiment, carried out in 2019, successfully measured at each position along the 196″ spectrograph slit the wavelength variation of the four Stokes parameters in the spectral region of this doublet around 280 nm, both in an active-region plage and in a quiet region close to the limb. We consider some of these CLASP2 Stokes profiles and apply to them the recently developed HanleRT Tenerife Inversion Code, which assumes a one-dimensional model atmosphere for each spatial pixel under consideration (i.e., it neglects the effects of horizontal radiative transfer). We find that the nonmagnetic causes of symmetry breaking, due to the horizontal inhomogeneities and the gradients of the horizontal components of the macroscopic velocity in the solar atmosphere, have a significant impact on the linear polarization profiles. By introducing such nonmagnetic causes of symmetry breaking as parameters in our inversion code, we can successfully fit the Stokes profiles and provide an estimation of the magnetic field vector. For example, in the quiet region pixels, where no circular polarization signal is detected, we find that the magnetic field strength in the upper chromosphere varies between 1 and 20 G.

Arch dam point cloud segmentation based on deep feature learning and normal vector data optimization

Separating the dam body, spillway, and other structures from the point cloud in the dam area is an important step in dam deformation monitoring. Manual segmentation is time consuming and inaccurate. This study proposes a point cloud segmentation neural network model based on normal vector optimization suitable for dam environment: (1) This model utilizes the voxel uniform sampling method of equal length cubes to solve the problem of uneven point cloud density caused by wide range and long-distance measurement during point cloud measurement in dam areas. (2) Designed block input and combined output modules in the model, achieving efficient input of large volume point cloud and eliminating the impact of interpolation points offset during seq2seq model decoding process. (3) In response to the diverse characteristics of point cloud normal vectors presented by vegetation, rock mass, and complex dam structures in the dam area, this paper proposes an adaptive radius plane fitting vector estimation method based on eigenvalue method to improve the accuracy of segmentation. The experiment on the prototype arch dam shows that the proposed normal estimation method improves the classification accuracy of PointNet + + from 96.26 to 98.27%. Compared with the other three normal estimation methods (2-jets, Hough CNN, iterative PCA), the overall accuracy is improved by 0.82%, 1.22%, and 0.22%, and the joint average intersection is improved by 0.0293, 0.0325, and 0.0104. The prototype arch dam experiment shows that our proposed method has a segmentation accuracy of 98.27%. Compared with 2-jets, Hough CNN, and iterative PCA, the overall accuracy has been improved by 0.82%, 1.22%, and 0.22%. This study provides a high-precision segmentation scheme for applications such as deformation detection of dam components based on point clouds.

Relative position estimation using modulated magnetic field for close proximity formation flight

This paper presents a method to estimate relative position vectors between spacecraft equipped with magnetic coils and magnetic field sensors for close proximity operation. Filters can segregate a magnetic field with a particular frequency if spacecraft drive their coils with this specific frequency. The proposed method utilizes the amplitude of the magnetic field with a particular frequency to estimate relative position vectors. The method consists of an initial position estimator and a sequential position estimator, which is an unscented Kalman filter. The initial position estimator provides a coarse estimate for the relative position vectors using the segregated magnetic field. Relation between the magnetic field and relative position vector is derived analytically in this article for the initial position estimator. The unscented Kalman filter refines the estimation accuracy by initializing the filter with the estimate by the initial position estimator. It is shown that a spacecraft can conduct relative position vector estimation using the magnetic field of a target spacecraft, provided that a few conditions clarified in the article are satisfied. Finally, the proposed estimators are evaluated numerically via simulations.

Phase nonlinearity–weighted optical flow for enhanced full-field displacement measurement and vibration imaging

In this study, we developed a technique to utilize phase nonlinearity as a quantifiable confidence measure of the reliability of component displacement vectors extracted from multi-scale and multi-direction phases. The proposed approach includes three novel concepts. First, relative confidence values are established based on phase nonlinearity to quantify the reliability of the displacement components across various environmental conditions. Second, by analyzing the distribution of the relative confidence values, adaptive confidence measures are extracted and are used to reject unreliable displacement components; these confidence measures can dynamically adapt to various environmental conditions, such as varying image noise and large amplitudes of motion. Third, phase nonlinearity–weighted motion integration is conducted to ensure accurate estimation of the full displacement vector from the component vectors. By integrating these three approaches, a remarkable enhancement was achieved in full-field displacement measurement in terms of accuracy, robustness, and signal-to-noise ratio, especially in environments with high noise levels. The capability of the proposed technique was evaluated through numerical experiments using artificial patterns that simulate identical motions under varying noise levels. Experimental validation was also performed on an air compressor to substantiate the accuracy and robustness of the proposed technique. The findings verify its improvements over conventional techniques for full-field displacement measurement.

Deep inelastic scattering in the capture of dark matter by neutron stars

Because of the dense environment, neutron stars (NSs) can serve as an ideal laboratory for studying the interactions between dark matter (DM) and ordinary matter. In the process of DM capture, deep inelastic scattering may dominate over elastic scattering, especially for the DM with a large momentum transfer. In this work, we calculate DM-nucleon deep inelastic scattering via a vector mediator and estimate its contribution to the capture rate. Using the surface temperature of the NSs, we derive the exclusion limits for the DM-nucleon scattering cross section in the mass range 1 GeV<mχ<105 GeV. We find the bounds for DM with the mass ≳1 GeV can be changed several times after including the deep inelastic scattering contribution. Published by the American Physical Society 2024

Inference about a Common Mean Vector from Several Independent Multinormal Populations with Unequal and Unknown Dispersion Matrices

This paper addresses the problem of making inferences about a common mean vector from several independent multivariate normal populations with unknown and unequal dispersion matrices. We propose an unbiased estimator of the common mean vector, along with its asymptotic estimated variance, which can be used to test hypotheses and construct confidence ellipsoids, both of which are valid for large samples. Additionally, we discuss an approximate method based on generalized p-values. The paper also presents exact test procedures and methods for constructing exact confidence sets for the common mean vector, with a comparison of the local power of these exact tests. The performance of the proposed methods is demonstrated through a simulation study and an application to data from the Current Population Survey (CPS) Annual Social and Economic (ASEC) Supplement 2021 conducted by the U.S. Census Bureau for the Bureau of Labor Statistics.

CAWE-ACNN Algorithm for Coprime Sensor Array Adaptive Beamforming.

This paper presents a robust adaptive beamforming algorithm based on an attention convolutional neural network (ACNN) for coprime sensor arrays, named the CAWE-ACNN algorithm. In the proposed algorithm, via a spatial and channel attention unit, an ACNN model is constructed to enhance the features contributing to beamforming weight vector estimation and to improve the signal-to-interference-plus-noise ratio (SINR) performance, respectively. Then, an interference-plus-noise covariance matrix reconstruction algorithm is used to obtain an appropriate label for the proposed ACNN model. By the calculated label and the sample signals received from the coprime sensor arrays, the ACNN is well-trained and capable of accurately and efficiently outputting the beamforming weight vector. The simulation results verify that the proposed algorithm achieves excellent SINR performance and high computation efficiency.

Enhancing Precision in Population Variance Vector Estimation: A Two-Phase Sampling Approach with Multi-Auxiliary Information

To enhance precision in estimating unknown population parameters, an auxiliary variable is often used. However, in scenarios where required information on an auxiliary variable is partially or fully unavailable, two-phase sampling is commonly employed. The challenge of estimating the variance vector using multi-auxiliary variables is a less explored area in current literature. This paper addresses the estimation of vector of unknown population variances for multiple study variables by using an estimated vector of variances derived from multi-auxiliary information. This approach is particularly relevant when population variances for the multi-auxiliary variables are not known prior to the survey. The paper introduces a generalized variance and a vector of biases for the proposed multivariate estimator. Special cases of the proposed multivariate variance estimator are provided, accompanied by expressions for mean square errors. Theoretical mathematical conditions are discussed to guide the preference for the proposed estimator. Through the analysis of real-world application-based data, the applicability and efficiency of the proposed multivariate variance estimator are demonstrated, outperforming modified versions of multivariate variance estimators. Additionally, a simulation study validates the superior performance of the proposed estimator compared to its modified estimators.

Music Sentiment Analysis and its Application in Music Therapy Based on AI Technology

Music therapy, enriched by the integration of AI technology, represents a cutting-edge approach to harnessing the therapeutic power of music for mental and emotional well-being. AI algorithms are employed to analyze individual preferences, emotional states, and physiological responses, enabling the creation of personalized music interventions. These interventions can range from mood-enhancing playlists to dynamically generated compositions tailored to the specific needs of the listener. This paper introduces an Optimized Sentimental n-gram Classifier (OSC) model tailored for application in the context of music therapy. Leveraging artificial intelligence (AI) technology and sentiment analysis techniques, the OSC model aims to enhance the understanding and classification of sentiments expressed during music therapy sessions. The OSC model uses the n-gram classifier for the estimation of the feature vector in the music speech signal. The classifier model comprises of the Artificial Intelligence (AI) for the evaluation of the music therapy for the sentimental analysis. Through extensive experimentation and evaluation, the OSC model demonstrates high accuracy, precision, recall, and F1 scores across multiple iterations, indicating its effectiveness in accurately predicting sentiments and classifying sessions. The model's robust performance suggests its potential to assist therapists in better understanding participants' emotional states and tailoring interventions accordingly. By providing a valuable tool for sentiment analysis in music therapy, the OSC model contributes to advancing the integration of AI technology into healthcare practices, with implications for improving patient outcomes and well-being.

A note on trigonometric regression in the presence of Berkson‐type measurement error

In this note, we study how parameter vector estimation for a trigonometric regression model and the expected squared residual error computed from an estimated model are affected by Berkson‐type measurement error. Closed‐form expressions for the parameter vector and the expected squared residual error are obtained by assuming that the observed covariate data are sampled from an equispaced design and that measurement error is generated from a symmetric probability distribution with a mean of zero. Notably, these results indicate that estimates of the amplitude parameters for a trigonometric regression model suffer from attenuation bias when covariate data are mis‐measured, and that estimates of the phase‐shift parameters are unbiased.

Robust Bayesian target vector optimization for multi-stage manufacturing processes

This research focuses on optimizing multi-stage manufacturing processes using Bayesian optimization (BO) with a robust Expected Improvement (EI) acquisition function. The aim is to optimize towards pre-selected target vectors, not to just minimize or maximize a function. To achieve this, we minimize the Euclidean distance between the actual and target output vectors, which requires transforming the Gaussian surrogate model posterior distribution into a non-central χ2(NCχ2) distribution. Furthermore, the distance measure additionally uses aleatoric uncertainty estimates of the actual output vectors to achieve robustness. We use a cascaded method that also considers the optimization results of intermediate stages, whereby optimization results are propagated from the last stage towards the first stage in each optimization iteration. By considering intermediate process outputs and aleatoric effects, our approach provides a robust optimization method for multi-stage manufacturing processes. To validate our method and to evaluate its properties, we use two artificial use cases. Moreover, we evaluate our approach in an industrial multi-stage forging process for the manufacturing of a nickel basis superalloy turbine disk, where involved stages are represented by corresponding 2D finite element method (FEM) DEFORM simulations. Evaluation suggests that our approach is superior in optimizing multi-stage manufacturing processes by considering all stage outcomes, robust distance measures, and the use of appropriate uncertainty distributions.