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AbstractThe multivariate Fay-Herriot model has been shown to be useful in various applications when there are multiple response variables. Therefore, several studies of the model have been pursued specially the study of estimation techniques of the variance components. The two benchmark methods for the variance component estimation are the profile maximum likelihood method and the residual maximum likelihood method. However, it has been shown in literature that these methods can produce zero estimates of the variance components. This leads to unfavorable results since the direct estimates do not contribute to the EBLUPs. In this paper, we propose alternative estimation methods based on the EM algorithm for the variance components of the multivariate Fay-Herriot model. In our study, we illustrate the procedures of the EM algorithms for the profile likelihood and the residual likelihood. Moreover, we perform a Monte Carlo simulation to investigate the performances of the proposed methods comparing with some existing methods. The simulation results suggest that the EM algorithm improves those existing methods in certain cases particularly for the cases of small number of areas which are commonly found in applications. Finally, we apply the proposed estimates to the average household income and average household expenditure in Thailand. [ABSTRACT FROM AUTHOR]

Hydrological models are crucial for characterizing large-scale water quantity variations and correcting GNSS reference station vertical displacements. We evaluated the robustness of multiple models, such as the Global Land Data Assimilation System (GLDAS), the Famine Early Warning System Network Land Data Assimilation System (FLDAS), the National Centers for Environmental Prediction (NCEP), and the WaterGAP Global Hydrology Model (WGHM). Inter-model and outer comparisons with Global Positioning System (GPS) coordinate time series, satellite gravity field Mascon solutions, and Global Precipitation Climatology Centre (GPCC) guide our assessment. Results confirm WGHM's 26% greater effectiveness in correcting nonlinear variations in GPS height time series compared to NCEP. In the Amazon River Basin, a 5-month lag between FLDAS, GLDAS, and satellite gravity results is observed. In eastern Asia and Australia, NCEP's Terrestrial Water Storage Changes (TWSC)-derived surface displacements correlate differently with precipitation compared to other models. Three combined hydrological models (H-VCE, H-EWM, and H-CVM) utilizing Variance Component Estimation (VCE), Entropy Weight Method (EWM), and Coefficient of Variation Method (CVM) are formulated. Correcting nonlinear variations with combined models enhances global GPS height scatter by 15%–17%. Correlation with precipitation increases by 25%–30%, and with satellite gravity, rises from 0.2 to 0.8 at maximum. The combined model eliminates time lag in the Amazon Basin TWSC analysis, exhibiting a four times higher signal-to-noise ratio than single models. H-VCE demonstrates the highest accuracy. In summary, the combined hydrological model minimizes discrepancies among individual models, significantly improving accuracy for monitoring large-scale TWSC.

The combination of satellite laser ranging (SLR) observations to various low earth orbit (LEO) satellites can enhance the accuracy and robustness of SLR-derived geodetic parameters, benefiting the realization of the International terrestrial reference frames. Observation stochastic models play a critical role in the integrated processing of SLR observations to multiple LEO satellites. The consideration of precision in heterogeneous SLR observations from various satellites is essential. In this study, we aim to improve the combination of multi-LEO SLR observations for geodetic parameters determination by optimizing the stochastic model using variance component estimation (VCE). We perform weekly estimates of the geodetic parameters, including station coordinates, Earth rotation parameters, and geocenter coordinates (GCC), using three years of SLR observations to seven LEO satellites at different orbits. The satellite-dependent, station-dependent, and satellite–station-dependent variance components are separately estimated through VCE processing to refine the stochastic models. Given the fact that the precision of SLR observations significantly differs in satellites and stations, the multiple LEO combination can be significantly improved with the implementation of VCE. Satellite–station-pair-dependent variance components are more suitable to the SLR VCE and the accuracy of station coordinates, pole coordinates, and length of day can be averagely improved by 8.4, 22.6, and 21.9%, respectively, compared to the equal-weight solution. Our result also indicates that the observation insufficiency for some stations may result in an unreliable VCE estimation, and eventually leads to an accuracy degradation for station coordinates. To overcome this deficiency, we adopt the variance components derived from the monthly solutions to build the stochastic model in the weekly solutions. The application of monthly weights can effectively mitigate the accuracy deterioration of station coordinates, improving the repeatability of the station coordinates by 15.9, 14.6, and 9.2% with respect to the equal-weight solution in E, N, and U components. The global geodetic parameters also benefit from this processing. The import of monthly weight decreases the outliers in the GCC series, especially in the X and Y components. [ABSTRACT FROM AUTHOR]

Large-effect loci-those statistically significant loci discovered by genome-wide association studies or linkage mapping-associated with key traits segregate amidst a background of minor, often undetectable, genetic effects in wild and domesticated plants and animals. Accurately attributing mean differences and variance explained to the correct components in the linear mixed model analysis is vital for selecting superior progeny and parents in plant and animal breeding, gene therapy, and medical genetics in humans. Marker-assisted prediction and its successor, genomic prediction, have many advantages for selecting superior individuals and understanding disease risk. However, these two approaches are less often integrated to study complex traits with different genetic architectures. This simulation study demonstrates that the average semivariance can be applied to models incorporating Mendelian, oligogenic, and polygenic terms simultaneously and yields accurate estimates of the variance explained for all relevant variables. Our previous research focused on large-effect loci and polygenic variance separately. This work aims to synthesize and expand the average semivariance framework to various genetic architectures and the corresponding mixed models. This framework independently accounts for the effects of large-effect loci and the polygenic genetic background and is universally applicable to genetics studies in humans, plants, animals, and microbes.

When conducting coseismic slip distribution inversion with interferometric synthetic aperture radar (InSAR) data, there is no universal method to objectively determine the appropriate size of InSAR data. Currently, little is also known about the computing efficiency of variance component estimation implemented in the inversion. Therefore, we develop a variance component adaptive estimation algorithm to determine the optimal sampling number of InSAR data for the slip distribution inversion. We derived more concise variation formulae than conventional simplified formulae for the variance component estimation. Based on multiple sampling data sets with different sampling numbers, the proposed algorithm determines the optimal sampling number by the changing behaviors of variance component estimates themselves. In three simulation cases, four evaluation indicators at low levels corresponding to the obtained optimal sampling number validate the feasibility and effectiveness of the proposed algorithm. Compared with the conventional slip distribution inversion strategy with the standard downsampling algorithm, the simulation cases and practical applications of five earthquakes suggest that the developed algorithm is more flexible and robust to yield appropriate size of InSAR data, thus provide a reasonable estimate of slip distribution. Computation time analyses indicate that the computational advantage of variation formulae is dependent of the ratio of the number of data to the number of fault patches and can be effectively suitable for cases with the ratio smaller than five, facilitating the rapid estimation of coseismic slip distribution inversion. [ABSTRACT FROM AUTHOR]

The International GNSS Service (IGS) provides combined satellite and station clock products, which are generated from the individual clock solutions produced by the analysis centers (ACs). Combinations for GPS and GLONASS are currently available, but there is still a lack of combined products for the new constellations such as Galileo, BeiDou, and QZSS. This study presents a combination framework based on least squares variance component estimation using the ACs' aligned clock solutions. We present the various alignments required to harmonize the solutions from the ACs, namely the radial correction derived from the differences of the associated orbits, the alignment of the AC clocks to compensate for different reference clocks within each AC solution, and the inter-system bias (ISB) alignment to correct for different AC ISB definitions when multiple constellations are used. The combination scheme is tested with IGS MGEX and repro3 products. The RMS computed between the combined product and the aligned ACs' solutions differ for each constellation, where the lowest values are obtained for Galileo and GPS with on average below 45 psec (13 mm) and reaching more than 150 psec (45 mm) for QZSS. The same behavior is repeated when the process is performed with the repro3 products. A clock and orbit combination validation is done using precise point positioning (PPP) that shows ionosphere-free phase residuals below 10 mm for all constellations, comparable with the AC solutions that are in the same level. [ABSTRACT FROM AUTHOR]

A robust GNSS/UWB integration algorithm is proposed for the indoor-outdoor cross region to control the influences of observation outliers of both GNSS and UWB. An important attempt in this paper is to re-estimate the uncertainty of the virtual observations derived from the kinematic model predicted information, and the GNSS satellites as well as the UWB anchors observations by using variance component estimation. Due to the correlations of the derived observations from estimated state parameters at previous epoch, a bi-factor inflated covariance model is employed to reduce the influences of the predicted correlated observations. Accordingly, a signal variance inflation factor is employed for independent measurements. Semi-simulation and field tests are carried out to validate and analyze the performance of the proposed algorithms in terms of positioning accuracy. The simulation demonstrates that the proposed algorithm improves the positioning accuracy when outliers exist in the measurements and the correlated predicted information. The field test results show that the positioning accuracy by using the proposed methods is improved by about 56% in average of E, N, and U components compared to that of the least squares positioning strategy, and about 40% in the average of E, N, and U components compared to that of integrated positioning by EKF without companying the variance component estimation. [ABSTRACT FROM AUTHOR]

ABSTRACT: Residual feed intake is viewed as an important trait in breeding programs that could be used to enhance genetic progress in feed efficiency. In particular, improving feed efficiency could improve both economic and environmental sustainability in the dairy cattle industry. However, data remain sparse, limiting the development of reliable genomic evaluations across lactation and parity for residual feed intake. Here, we estimated novel genetic parameters for genetic residual feed intake (gRFI) across the first, second, and third parity, using a random regression model. Research data on the measured feed intake, milk production, and body weight of 7,379 cows (271,080 records) from 6 countries in 2 continents were shared through the Horizon 2020 project Genomic Management Tools to Optimise Resilience and Efficiency, and the Resilient Dairy Genome Project. The countries included Canada (1,053 cows with 47,130 weekly records), Denmark (1,045 cows with 72,760 weekly records), France (329 cows with 16,888 weekly records), Germany (938 cows with 32,614 weekly records), the Netherlands (2,051 cows with 57,830 weekly records), and United States (1,963 cows with 43,858 weekly records). Each trait had variance components estimated from first to third parity, using a random regression model across countries. Genetic residual feed intake was found to be heritable in all 3 parities, with first parity being predominant (range: 22–34%). Genetic residual feed intake was highly correlated across parities for mid- to late lactation; however, genetic correlation across parities was lower during early lactation, especially when comparing first and third parity. We estimated a genetic correlation of 0.77 ± 0.37 between North America and Europe for dry matter intake at first parity. Published literature on genetic correlations between high input countries/continents for dry matter intake support a high genetic correlation for dry matter intake. In conclusion, our results demonstrate the feasibility of estimating variance components for gRFI across parities, and the value of sharing data on scarce phenotypes across countries. These results can potentially be implemented in genetic evaluations for gRFI in dairy cattle.

Geodetic functional models, stochastic models, and model parameter estimation theory are fundamental for geodetic data processing. In the past five years, through the unremitting efforts of Chinese scholars in the field of geodetic data processing, according to the application and practice of geodesy, they have made significant contributions in the fields of hypothesis testing theory, un-modeled error, outlier detection, and robust estimation, variance component estimation, complex least squares, and ill-posed problems treatment. Many functional models such as the nonlinear adjustment model, EIV model, and mixed additive and multiplicative random error model are also constructed and improved. Geodetic data inversion is an important part of geodetic data processing, and Chinese scholars have done a lot of work in geodetic data inversion in the past five years, such as seismic slide distribution inversion, intelligent inversion algorithm, multi-source data joint inversion, water reserve change and satellite gravity inversion. This paper introduces the achievements of Chinese scholars in the field of geodetic data processing in the past five years, analyzes the methods used by scholars and the problems solved, and looks forward to the unsolved problems in geodetic data processing and the direction that needs further research in the future.

Stochastic models play an important role in achieving high accuracy in positioning, the ideal estimator in the least-squares (LS) can be obtained only by using the suitable stochastic model. This study investigates the role of variance component estimation (VCE) in the LS method for Precise Point Positioning (PPP). This estimation is performed by considering the ionospheric-free (IF) functional model for code and the phase observation of Global Positioning System (GPS). The strategy for estimating the accuracy of these observations was evaluated to check the effect of the stochastic model in four modes: a) antenna type, b) receiver type, c) the tropospheric effect, and d) the ionosphere effect. The results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unknown components in the PPP model. This is because a constant empirical variance may not be suitable for various receivers and antennas under different conditions. Coordinates were compared in two cases using the stochastic model of nominal weight and weight estimated by LS-VCE. The position error difference for the east-west, north-south, and height components was 1.5 cm, 4 mm, and 1.8 cm, respectively. Therefore, weight estimation with LS-VCE can provide more appropriate results. Eventually, the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE weight. According to the results, the LS-VCE has a higher convergence rate than the nominal weight. The weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11, 13, 12, and 9 min, respectively.

Residual feed intake is viewed as an important trait in breeding programs that could be used to enhance genetic progress in feed efficiency. In particular, improving feed efficiency could improve both economic and environmental sustainability in the dairy cattle industry. However, data remain sparse, limiting the development of reliable genomic evaluations across lactation and parity for residual feed intake. Here, we estimated novel genetic parameters for genetic residual feed intake (gRFI) across the first, second, and third parity, using a random regression model. Research data on the measured feed intake, milk production, and body weight of 7,379 cows (271,080 records) from 6 countries in 2 continents were shared through the Horizon 2020 project Genomic Management Tools to Optimise Resilience and Efficiency, and the Resilient Dairy Genome Project. The countries included Canada (1,053 cows with 47,130 weekly records), Denmark (1,045 cows with 72,760 weekly records), France (329 cows with 16,888 weekly records), Germany (938 cows with 32,614 weekly records), the Netherlands (2,051 cows with 57,830 weekly records), and United States (1,963 cows with 43,858 weekly records). Each trait had variance components estimated from first to third parity, using a random regression model across countries. Genetic residual feed intake was found to be heritable in all 3 parities, with first parity being predominant (range: 22–34%). Genetic residual feed intake was highly correlated across parities for mid- to late lactation; however, genetic correlation across parities was lower during early lactation, especially when comparing first and third parity. We estimated a genetic correlation of 0.77 ± 0.37 between North America and Europe for dry matter intake at first parity. Published literature on genetic correlations between high input countries/continents for dry matter intake support a high genetic correlation for dry matter intake. In conclusion, our results demonstrate the feasibility of estimating variance components for gRFI across parities, and the value of sharing data on scarce phenotypes across countries. These results can potentially be implemented in genetic evaluations for gRFI in dairy cattle. [ABSTRACT FROM AUTHOR]

For over two decades, an essential information about global monthly gravity variations is provided by the GRACE mission and its successor, the GRACE Follow-On (GRACE-FO) mission. The temporal variations in gravity field from GRACE/GRACEFO are determined based on the measurement of distance changes between two identical satellites using microwave ranging instruments. This process is carried out by various processing centers, which adopt different processing strategies and background models. This causes discrepancies in the resulting gravity fields.We address this problem by determining a monthly homogenous GRACE-FO gravity field solutions from June 2018 to November 2022 as provided by different processing centers included in the Science Data System (SDS) project, i.e. the Center for Space Research (CSR), the German Research Center for Geosciences (GFZ) and the Jet Propulsion Laboratory (JPL). We test three different weighting schemes. We show that for the last 4 years, at least 65% of continental areas are characterized by water decrease. We show that proposed merged solutions contain more signal information than individual ones based on the square root of the degree variance values.We note that the largest signal differences between individual and combined solutions occur for sectoral coefficients up to degree 40, and for zonal coefficients, the signal differences are twice as small.We also present that the differences in the spherical harmonic coefficients cause differences in global and local equivalent water height (EWH) changes. For example, the proposed merged solutions reduce root mean square scatter ofEWHby 5–15% comparing to individual solutions.

Large-effect loci--those statistically significant loci discovered by genome-wide association studies or linkage mapping--associated with key traits segregate amidst a background of minor, often undetectable, genetic effects in wild and domesticated plants and animals. Accurately attributing mean differences and variance explained to the correct components in the linear mixed model analysis is vital for selecting superior progeny and parents in plant and animal breeding, gene therapy, and medical genetics in humans. Marker-assisted prediction and its successor, genomic prediction, have many advantages for selecting superior individuals and understanding disease risk. However, these two approaches are less often integrated to study complex traits with different genetic architectures. This simulation study demonstrates that the average semivariance can be applied to models incorporating Mendelian, oligogenic, and polygenic terms simultaneously and yields accurate estimates of the variance explained for all relevant variables. Our previous research focused on largeeffect loci and polygenic variance separately. This work aims to synthesize and expand the average semivariance framework to various genetic architectures and the corresponding mixed models. This framework independently accounts for the effects of large-effect loci and the polygenic genetic background and is universally applicable to genetics studies in humans, plants, animals, and microbes. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

For over two decades, an essential information about global monthly gravity variations is provided by the GRACE mission and its successor, the GRACE Follow-On (GRACE-FO) mission. The temporal variations in gravity field from GRACE/GRACEFO are determined based on the measurement of distance changes between two identical satellites using microwave ranging instruments. This process is carried out by various processing centers, which adopt different processing strategies and background models. This causes discrepancies in the resulting gravity fields. We address this problem by determining a monthly homogenous GRACE-FO gravity field solutions from June 2018 to November 2022 as provided by different processing centers included in the Science Data System (SDS) project, i.e. the Center for Space Research (CSR), the German Research Center for Geosciences (GFZ) and the Jet Propulsion Laboratory (JPL). We test three different weighting schemes. We show that for the last 4 years, at least 65% of continental areas are characterized by water decrease. We show that proposed merged solutions contain more signal information than individual ones based on the square root of the degree variance values. We note that the largest signal differences between individual and combined solutions occur for sectoral coefficients up to degree 40, and for zonal coefficients, the signal differences are twice as small. We also present that the differences in the spherical harmonic coefficients cause differences in global and local equivalent water height (EWH) changes. For example, the proposed merged solutions reduce root mean square scatter of EWH by 5-15% comparing to individual solutions. [ABSTRACT FROM AUTHOR]

ABSTRACT: The dairy industry is moving toward selecting animals with better fertility to decrease the economic losses linked to reproductive issues. The reproductive tract size and position score (SPS) was recently developed in physiological studies as an indicator of pregnancy rate and the number of services to conception. Cows are scored as SPS 1, 2, or 3 based on the size of their reproductive tract and its position in the pelvis, as determined by transrectal palpation. The objective of this study was to estimate genetic parameters for SPS to assess its potential as a novel fertility trait. Phenotypes were collected at the University of British Columbia's research herd from 2017 to 2020, consisting of 3,247 within- and across-lactation SPS records from 490 Holstein cows. A univariate animal model was used to estimate the variance components for SPS. Both threshold and linear models were fit under a Bayesian approach and the results were compared using the Spearman rank correlation (r) between the estimated breeding values. The 2 models ranked the animals very similarly (r = 0.99), and the linear model was selected for further analysis. Genetic correlations with other currently evaluated traits were estimated using a bivariate animal model. The posterior means (± posterior standard deviation) for heritability and repeatability within- and across-lactation were 0.113 (± 0.013), 0.242 (± 0.012), and 0.134 (± 0.014), respectively. The SPS showed null correlations with production traits and favorable correlations with traditional fertility traits, varying from −0.730 (nonreturn rate) to 0.931 (number of services). Although preliminary, these results are encouraging because SPS seems to be more heritable than and strongly genetically correlated with number of services, nonreturn rate, and first service to conception, indicating potential for effective indirect selection response on these traits from SPS genetic selection. Therefore, further studies with larger data sets to validate these findings are warranted.

To suppress the correlated noise of Gravity Recovery and Climate Experiment (GRACE) spherical harmonic (SH) solutions, we developed a series of constrained monthly gravity field solutions named WHU‐GRACE‐GPD01s from August 2002 to July 2016 using GRACE‐based geopotential differences. The constrained solutions were estimated using Kaula regularization, and the optimal regularization parameters were adaptively determined from the GRACE data itself through variance component estimation. The performance of the constrained WHU‐GRACE‐GPD01s solutions was validated against the official SH solutions (GFZ, JPL, and CSR RL06) and mass concentration (mascon) solutions (CSR RL06M) at global and regional scales. The results demonstrate that mass changes derived from the constrained solutions and official SH solutions with DDK4 filtering are in good agreement, but the constrained solutions present weaker longitudinal stripes and have a lower noise level at regional scales (e.g., in the Middle Pacific Ocean and Sahara Desert). Furthermore, regional mass changes (e.g., major river basins, Greenland, and Antarctic ice sheet) inferred from the constrained solutions agree with the ones derived from the official SH solutions with DDK4 filtering. The constrained solutions also have a higher signal intensity and smaller spatial leakages as compared to the CSR RL06 SH solutions with spatial filtering (Gaussian filtering plus de‐striping). For the problematic months, the constrained solutions are more reliable than the official SH solutions using spatial filtering or DDK4 filtering, and are closer to CSR RL06M mascon solutions. These validations demonstrate that our constrained solutions are comparable to the official SH solutions and can be used without postprocessing. Key Points: The constrained WHU‐GRACE‐GPD01s solutions are estimated based on Kaula regularization using GRACE‐based geopotential differencesOptimal regularization parameters are adaptively determined from the GRACE data itself based on variance component estimationPerformance of the constrained solutions is validated with comparisons of the official spherical harmonic solutions and mascon solutions [ABSTRACT FROM AUTHOR]

Abstract To suppress the correlated noise of Gravity Recovery and Climate Experiment (GRACE) spherical harmonic (SH) solutions, we developed a series of constrained monthly gravity field solutions named WHU‐GRACE‐GPD01s from August 2002 to July 2016 using GRACE‐based geopotential differences. The constrained solutions were estimated using Kaula regularization, and the optimal regularization parameters were adaptively determined from the GRACE data itself through variance component estimation. The performance of the constrained WHU‐GRACE‐GPD01s solutions was validated against the official SH solutions (GFZ, JPL, and CSR RL06) and mass concentration (mascon) solutions (CSR RL06M) at global and regional scales. The results demonstrate that mass changes derived from the constrained solutions and official SH solutions with DDK4 filtering are in good agreement, but the constrained solutions present weaker longitudinal stripes and have a lower noise level at regional scales (e.g., in the Middle Pacific Ocean and Sahara Desert). Furthermore, regional mass changes (e.g., major river basins, Greenland, and Antarctic ice sheet) inferred from the constrained solutions agree with the ones derived from the official SH solutions with DDK4 filtering. The constrained solutions also have a higher signal intensity and smaller spatial leakages as compared to the CSR RL06 SH solutions with spatial filtering (Gaussian filtering plus de‐striping). For the problematic months, the constrained solutions are more reliable than the official SH solutions using spatial filtering or DDK4 filtering, and are closer to CSR RL06M mascon solutions. These validations demonstrate that our constrained solutions are comparable to the official SH solutions and can be used without postprocessing.

For slip distribution inversion with Bayesian theory, traditionally, the Markov Chain Monte Carlo (MCMC) method is well applied to generate a posterior probability density function with a sampling strategy. However, its computational cost may be expensive, and it fails to accommodate large volume data sets and estimate higher dimensional parameters of interest. In this study, we introduce variational inference theory into the study of coseismic slip distribution, and present a variational Bayesian slip distribution inversion approach. Furthermore, synthetic tests show that the variational Bayesian approach can efficiently and accurately invert the designed slip distribution; therefore, we conclude that the proposed algorithm is appropriate to invert the slip distribution parameters, which might be superior to MCMC sampling due to its excellent convergence speed and low computational burden. Taking the Dingri earthquake on March 20, 2020, as an example, we further verify the practicability of the variational Bayesian method in actual earthquakes. Additionally, the inversion results show that the main fault slip region of the Dingri earthquake occurs at depths of 2 ~ 8 km on the surface, the maximum slip amount is 0.54 m, and the coseismic release seismic moment is 5.58 × 1017 Nm, corresponding to a moment magnitude of Mw 5.79. [ABSTRACT FROM AUTHOR]

We fitted statistical models, which assumed single-nucleotide polymorphism (SNP) marker effects differing across the fattened steers marketed into different prefectures, to the records for cold carcass weight (CW) and marbling score (MS) of 1036, 733, and 279 Japanese Black fattened steers marketed into Tottori, Hiroshima, and Hyogo prefectures in Japan, respectively. Genotype data on 33,059 SNPs was used. Five models that assume only common SNP effects to all the steers (model 1), common effects plus SNP effects differing between the steers marketed into Hyogo prefecture and others (model 2), only the SNP effects differing between Hyogo steers and others (model 3), common effects plus SNP effects specific to each prefecture (model 4), and only the effects specific to each prefecture (model 5) were exploited. For both traits, slightly lower values of residual variance than that of model 1 were estimated when fitting all other models. Estimated genetic correlation among the prefectures in models 2 and 4 ranged to 0.53 to 0.71, all <0.8. These results might support that the SNP effects differ among the prefectures to some degree, although we discussed the necessity of careful consideration to interpret the current results. [ABSTRACT FROM AUTHOR]

Over the past years, the International GNSS Service (IGS) has been putting efforts into extending its service by setting up and running the Multi-GNSS experiment and pilot project (MGEX). Several MGEX analysis centers (ACs) contribute by providing solutions containing not only GPS and GLONASS but also Galileo, BeiDou, and QZSS. As the current IGS combination software can only handle the orbits of one constellation at a time, it requires substantial modifications to obtain a consistent MGEX orbit product. In this contribution, we present a least-squares framework for a Multi-GNSS orbit combination, where the weights used to combine the ACs’ orbits are determined by least-squares variance component estimation. We introduce and compare two weighting strategies, where either AC-specific weights or AC and constellation-specific weights are used. An automated Z-score test is implemented yielding a common set of core satellites that are used to determine the weights. Both strategies are tested using MGEX orbit solutions for a period of two and a half years. They yield similar results with an agreement with the ACs’ orbits at the one centimeter level for GPS and up to a few centimeters for the other constellations. The 3D-RMS is generally slightly better with the AC and constellation weighting. A comparison of our combination approach with the official IGS combination using three years of GPS and GLONASS orbits shows an agreement of better than 5 mm and 12 mm for GPS and GLONASS, respectively, while the agreement of the official IGS combination with the ACs’ GPS solutions is only around 15 mm . An external validation using satellite laser ranging shows that the mean residuals of our combined products are around - 3 mm for Galileo, 6 mm for GLONASS, - 8 mm for BeiDou, and - 31 mm for QZSS. [ABSTRACT FROM AUTHOR]

Genotype x environment (GxE) interaction for production traits in Fleckvieh cattle was assessed by means of various environmental descriptors (EDs). It was also of particular interest to search for EDs useful for studying differing robustness or resilience of individuals which implies reasonable GxE interaction. The set of studied EDs included farm/herd environment (e.g. herd size, housing/feeding regimes, herd production level), geographical location (e.g. height above sea level), temperature humidity index and fat‐to‐protein ratio. Milk, fat and protein yield deviations for the first test day, the first 100 days and the 305‐day‐yield of the first lactation were used as phenotypes. Genetic correlations were estimated with bi‐ and multivariate sire models in case of categorical EDs and reaction norm sire models in case of continuous EDs. Further, rank correlations of bulls' estimated breeding values were calculated for different environmental levels/classes. Almost all estimated genetic correlations were significantly different from 1, but not <0.93. There were some exceptions for extremely different classes/levels of some EDs (e.g. average herd‐year production, organic vs conventional farm systems, way of concentrated feed supply). Rank correlations were rarely below 0.95. In summary, no substantial GxE interactions for milk production traits were found with the studied EDs. [ABSTRACT FROM AUTHOR]

Land use regression (LUR) models are one of the standard methods for estimating air pollution concentration in urban areas. These models are usually low accurate due to inappropriate stochastic models (weight matrix). Furthermore, the measurement or modeling of dependent and independent variables used in LUR models is affected by various errors, which indicates the need to use an efficient stochastic and functional model to achieve the best estimation. This study proposes a locally weighted total least-squares variance component estimation (LW-TLS-VCE) for modeling urban air pollution. In the proposed method, in the first step, a locally weighted total least-squares (LW-TLS) regression is developed to simultaneously considers the non-stationary effects and errors of dependent and independent variables. In the second step, the variance components of the stochastic model are estimated to achieve the best linear unbiased estimation of unknowns. The efficiency of the proposed method is evaluated by modeling PM2.5 concentrations via meteorological, land use, and traffic variables in Isfahan, Iran. The benefits provided by the proposed method, including considering non-stationary effects and random errors of all variables, besides estimating the actual variance of observations, are evaluated by comparing four consecutive methods. The obtained results demonstrate that using a suitable stochastic and functional model will significantly increase the proposed method's efficiency in PM2.5 modeling. [ABSTRACT FROM AUTHOR]

The dairy industry is moving toward selecting animals with better fertility to decrease the economic losses linked to reproductive issues. The reproductive tract size and position score (SPS) was recently developed in physiological studies as an indicator of pregnancy rate and the number of services to conception. Cows are scored as SPS 1, 2, or 3 based on the size of their reproductive tract and its position in the pelvis, as determined by transrectal palpation. The objective of this study was to estimate genetic parameters for SPS to assess its potential as a novel fertility trait. Phenotypes were collected at the University of British Columbia's research herd from 2017 to 2020, consisting of 3,247 within- and across-lactation SPS records from 490 Holstein cows. A univariate animal model was used to estimate the variance components for SPS. Both threshold and linear models were fit under a Bayesian approach and the results were compared using the Spearman rank correlation (r) between the estimated breeding values. The 2 models ranked the animals very similarly (r = 0.99), and the linear model was selected for further analysis. Genetic correlations with other currently evaluated traits were estimated using a bivariate animal model. The posterior means (± posterior standard deviation) for heritability and repeatability within- and across-lactation were 0.113 (± 0.013), 0.242 (± 0.012), and 0.134 (± 0.014), respectively. The SPS showed null correlations with production traits and favorable correlations with traditional fertility traits, varying from −0.730 (nonreturn rate) to 0.931 (number of services). Although preliminary, these results are encouraging because SPS seems to be more heritable than and strongly genetically correlated with number of services, nonreturn rate, and first service to conception, indicating potential for effective indirect selection response on these traits from SPS genetic selection. Therefore, further studies with larger data sets to validate these findings are warranted. [ABSTRACT FROM AUTHOR]

In view of the defects of total station and laser tracker in the construction of three-dimensional control network, a construction method of three-dimensional control network is proposed by combining total station and laser tracker. Total stations and laser trackers are utilized separately to observe the control points according to the free-stationing method. In data processing, the weights of different types of observations of total station and laser tracker are reasonably determined based on the Helmert variance component estimation. The high-precision horizontal direction observations of total station, which are better than 0. 5 ″ , and the ultra-high-precision ranging observations of laser tracker, which are better than 10 μm, are effectively combined in order to obtain more precise adjustment results. The experimental results show that the positional precision of the combined adjustment is better than that of the adjustment results of a single measurement system, and the precision of three-dimensional control network can be further improved by employing Helmert variance component estimation to determine the weight reasonably. [ABSTRACT FROM AUTHOR]

For the Fay–Herriot model, the empirical best linear unbiased predictor (EBLUP) is the weighted sum of direct estimate and regression-synthetic estimate, where the weight depends on the estimate of variance component of random area effects. However, in some cases, the weight of direct survey estimator is zero and the EBLUP reduces to regression-synthetic estimator. This leads to unfavourable estimates. Therefore, Lahiri and Li (2009) introduced the concept of adjusted maximum likelihood method for linear mixed models. The method was then generalized in Li and Lahiri (2010) and Yoshimori and Lahiri (2014) to develop adjusted maximum likelihood consistent variance estimators with positive variance estimates. These adjustments prevent zero weight of direct estimate. In this paper, we extend their methods to propose adjusted maximum likelihood estimates for multivariate Fay–Herriot models. Moreover, we derive their asymptotic properties and perform numerical results to investigate performances of the proposed estimates. • Adjusted Maximum Likelihood Estimators. • Multivariate Fay–Herriot Models. • Empirical Best Linear Unbiased Predictor. • Second–order unbiased MSE estimator. • Non zero estimates of variance components in the Multivariate Fay–Herriot models. [ABSTRACT FROM AUTHOR]

Understanding and modelling the properties of the stochastic variations in geodetic time series is crucial to obtain realistic uncertainties for deterministic parameters, e.g., long-term velocities, and helpful in characterizing non-modelled processes. With the increasing span of geodetic time series, it is expected that additional observations would help better understand the low-frequency properties of these stochastic variations. In the meantime, recent studies evidenced that the choice of the functional model for the time series biases the assessment of these low-frequency stochastic properties. In particular, frequent offsets in position time series can hinder the evaluation of the noise level at low frequencies and prevent the detection of possible random-walk-type variability. This study investigates the ability of the Maximum Likelihood Estimation (MLE) method to correctly retrieve low-frequency stochastic properties of geodetic time series in the presence of frequent offsets. We show that part of the influence of offsets reported by previous studies results from the MLE method estimation biases. These biases occur even when all offset epochs are correctly identified and accounted for in the trajectory model. They can cause a dramatic underestimation of deterministic parameter uncertainties. We show that one can avoid biases using the Restricted Maximum Likelihood Estimation (RMLE) method. Yet, even when using the RMLE method or equivalent, adding offsets to the trajectory model inevitably blurs the estimated low-frequency properties of geodetic time series by increasing low-frequency stochastic parameter uncertainties more than other stochastic parameters. [ABSTRACT FROM AUTHOR]

Precise orbits are required for real-time precise point positioning (PPP). Nowadays, real-time orbit corrections with respect to broadcast ephemerides are normally transmitted to the users with an update interval between 5 and 60 s. Due to time latency, users extrapolate to calculate the satellite positions at the needed epochs. However, since the original satellite orbits change rapidly, users have to extrapolate the orbit corrections. Nevertheless, the correction accuracy of GLONASS decreases faster over time than GPS, Galileo, and Beidou, in addition, the calculation efficiency of the satellite position seems not perfect. In this study, an improved polynomial fitting method was proposed to improve the orbit extrapolation ability of polynomial by introducing the satellite velocities and accelerations into the fitting model. Experimental results of GPS, GLONASS, Galileo, and Beidou show that the accuracy of extrapolated orbits could be within a few centimeters when the time latency is approximate 10 min and 40 min for eclipsing and non-eclipsing satellites, respectively. And these results also have been confirmed through the PPP experiments from eight global distribution stations with multi-GNSS observation data on 2019–1-1. Thus, by utilizing the new method, it is possible to directly extrapolate the original satellite orbits, which suggests that the application of real-time precise orbits can be independent of broadcast ephemeris. [ABSTRACT FROM AUTHOR]

In recent years, single-frequency precise point positioning (SF-PPP) has taken increasing attention from the GNSS community owing to its operational simplicity and cost-effectiveness. Thanks to the real-time service (RTS) products of the International GNSS Service (IGS), it is possible to use SF-PPP solutions in real-time tropospheric delay retrieval. Moreover, the advent of newly-emerged satellite systems, such as Galileo and BeiDou, offers significant opportunities to enhance its performance in real-time tropospheric delay estimation. Still, to take advantage of the potential benefits of multi-GNSS combinations, it is required to consider the stochastic properties of observations from different navigation systems. Therefore, the main objective of this study is to improve the tropospheric delay estimation performance of the multi-GNSS SF-PPP solution, including GPS, GLONASS, Galileo, and BeiDou, with advanced stochastic approaches. For this purpose, this study proposes an advanced weighting strategy that employs the variance component estimation method to specify the weights of multi-GNSS observations in the real-time SF-PPP process. The experimental tests reveal that the employment of the advanced weighting strategy in the multi-GNSS solution provides an accuracy of 2.18 cm in tropospheric delay estimation, which means an improvement of 17.4% on average compared with the conventional weighting approach. Besides, separately analyzing the recent performance of each navigation system is another objective of this study. The results indicate that within single-system SF-PPP solutions, Galileo provides the highest accuracy for the zenith total delay (ZTD) estimation with an average RMS error of 3.22 cm which is better than that of GPS solution by 8.3%. [ABSTRACT FROM AUTHOR]

Objectives: When using variance component estimation to determine the relative weight ratio, the least square solution is generally used as the initial value of the iteration. In geodetic joint inversion, the least squares method will cause ill ⁃ posed problems, so the regularized solution is used instead of the least square solution. Regularization introduces bias to reduce variance, but when using variance component estimation to determine the relative weight ratio, the influence of bias is not considered, and the introduction of bias will cause inaccurate variance component estimation. Methods: This paper adopts the bias - corrected variance component estimation method to eliminate the influence of bias introduced by regularization. The residual - based bias - corrected variance component estimation and the variance component estimation method are used for simulation experiments, the Visso earthquake and Norcia earthquake are used for verification. Results and Conclusions: Simulation experimental result shows that the variance component estimation method after bias correction can better reverse the slip distribution. The bias-corrected variance component estimation method takes into account the bias introduced by the iterative initial value, and the theory is more rigorous. Two real earthquakes results show that the bias correction is reasonable and advantageous. [ABSTRACT FROM AUTHOR]

Efficient Variance Component Estimation (VCE) is significant to optimal data combination in large-scale least-squares problems as those encountered in satellite geodesy, where millions of observations are jointly processed to estimate a huge number of unknown parameters. In this paper, an efficient VCE algorithm with rigorous trace calculation is proposed based on the local–global parameters partition scheme in satellite geodesy, which is directly applicable to both the simplified yet common case where local parameters are unique to a single observation group and the generalized case where local parameters are shared by different groups of observations. Moreover, the Monte-Carlo VCE (MCVCE) algorithm, based on the stochastic trace estimation technique, is further extended in this paper to the generalized case. Two numerical simulation cases are investigated for gravity field model recovery to evaluate both the accuracy and efficiency of the proposed algorithm and the extended MCVCE algorithm in terms of trace calculation. Compared to the conventional algorithm, the relative trace calculation errors in the efficient algorithm are all negligibly below 10–7%, while in the MCVCE algorithm they can vary from 0.6 to 37% depending on the number of adopted random vector realizations and the specific applications. The efficient algorithm can achieve computational time reduction rates above 96% compared to the conventional algorithm for all gravity field model sizes considered in the paper. In the MCVCE algorithm, however, the time reduction rates can change from 61 to 99% for different implementations. [ABSTRACT FROM AUTHOR]

A difficulty in variance component estimation (VCE) is that the estimates may become negative, which is not acceptable in practice. This article presents two new methods for non-negative VCE that utilize the expectation maximization algorithm for the partial errors-in-variables model. The former searches for the desired solutions with unconstrained estimation criterion and concludes statistically that the variance components have indeed moved to the edge of the parameter space when negative estimates appear implemented by the other existing VCE methods. We concentrate on the formulation and provide non-negative analysis of this estimator. In particularly, the latter approach, which has greater computational efficiency, would be a practical alternative to the existing VCE-type algorithms. Additionally, this approach is easy to implement, the non-negative variance components are automatically supported by introducing non-negativity constraints. Both algorithms are free from a complex matrix inversion and reduce computational complexity. The results show that our algorithms retrieve well to achieve identical estimates over the other VCE methods, the latter approach can quickly estimate parameters and has practical aspects for the large volume and multisource data processing.

Objectives: Simultaneous and integrated strain tensor estimation from geodetic and satellite deformation measurements(SISTEM) is a popular method in this field due to its advantage of no-need for the interpolation of global navigation satellite system(GNSS) observations. However, the performance of the SISTEM method is greatly limited due to the inaccurate determination of the prior variance. Methods: Variance component estimation(VCE) algorithm is introduced to improve the SISTEM method. The strain model (SM) is used to establish the linear relationship between three-dimensional surface deformation of the target point and those of the neighborhood point. Different from the SISTEM method that only employs the InSAR observations of the target point when constructing the function model, the proposed method not only employs the InSAR observations of the target point, but also exploits an amount of nearest InSAR observations around it. This can improve the reliability of the SISTEM method in the region of lacking GNSS observations. In order to meet the requirement of VCE that the number of all types of observations are roughly equal, the number of both types of InSAR observations (i.e., ascending and descending) are approximately 3 times as that of GNSS observations. Results: Compared with those of the SISTEM method, the root mean square error(RMSE) from the proposed method achieve an improvement of 56.3%, 41.9% and 41.8% in east west(EW), south north(NS), up down(UD) components, respectively. In addition, the average weights of the interferometric synthetic aperture radar(InSAR) and GNSS observations derived from the proposed method is closer to the theoretical value than those from the SISTEM method. The real data experiments were then carried out by using the data acquired from the area near Kilauea Volcano on the island of Hawaii, US, including 29 GNSS observations and two pairs of ALOS PALSAR images in 2007. As expected, the accuracies of the proposed method are also improved by 31.4%, 18.6% and 22.8% in EW, NS, UD components, respectively, compared with those of the SISTEM method. Conclusions: It is found that the proposed method has better resistance to spatial decorrelation in the regions without sufficient GNSS data since more InSAR observations were used to form the observation equation. In addition, the results from the proposed method are less affected by local abrupt deformation. [ABSTRACT FROM AUTHOR]

Offset tracking technology is widely studied to evaluate glacier surface displacements. However, few studies have used a cross-platform to this end. In this study, two heterogeneous data sources, Sentinel-1 and Landsat 8, from January 2019 to January 2021, were used to estimate the offset, and then the optimal estimation of the 3D deformation rate of a Himalayan glacier was obtained based on the joint model of variance component estimation. The results show that the maximum deformation rates of the glacier in the east–west direction, north–south direction, and vertical direction are 85, 126, and 88 mm/day, respectively. The results of the joint model were compared and analyzed with the results of simultaneous optical image pixel offset tracking. The results showed that the accuracy of the joint solution model increased by 41% in the east–west direction and 36% in the south–north direction. The regional flow velocity of the moraine glacier after the joint solution was consistent with the vector boundary of the glacier cataloging data. The time-series results of the glacier displacement were calculated using more images. These results indicate that the joint solution model is feasible for calculating temporal glacier velocity. The model can improve the time resolution of the monitoring results and obtain further information on glacier characteristics. Our results show that the glacier velocity is affected by local terrain slope and temperature. However, there is no absolute positive correlation between glacier velocity and slope. This study provides a reference for the joint acquisition of large-scale three-dimensional displacement of glaciers using multi-source remote sensing data and provides support for the identification and early warning of glacier disasters.

Objectives: Partial errors⁃in⁃variables (PEIV) model is a more general form of errors in variables (EIV) model. It has been widely used in the data processing of global navigation satellite system (GNSS), coordinate conversion, deformation monitoring and data fitting in the past ten years.Methods: First, the development history of PEIV model is reviewed. Then, five core problems of PEIV model are summarized and analyzed, including parameter estimation algorithm, precision estimation, random model estimation, expansion algorithm and data processing application. Finally, the applications of PEIV model are outlined. Results: We point out three questions for further research, including how to process big data by PEIV parameter estimation method, how to correct the bias of weighted total least squares(WTLS) adjustment by sampling method, and how to derive the formula of higher order parameter estimation covariance matrix are.Conclusions: This review paper aims to further promote the development of surveying and mapping da⁃ ta processing and provide readers with suggestions and references. [ABSTRACT FROM AUTHOR]

A constrained extended Kalman filter (CEKF) based on least-squares variance component estimation (LS-VCE) is generally developed by condition equations since the proper prediction of dispersion matrices is one of the main bottlenecks in the KF algorithms. Here we investigate four problems which have not been simultaneously considered yet. These problems are examination of non-linearty of dynamic model, VCE, general non-linear state constraints and fairly general stochastic model. Although a few contributions proposed some adaptive KF in particular based on Helmert's VCE method, they developed their filters for special problems with some restrictive conditions such as independence of all variables and/or linearity of the dynamic model. Also some of these filters did not apply VCE methods to all parts of the dynamic model. In this contribution, we try to overcome all of these restrictions. Moreover, LS-VCE method gives some added advantages over other VCE methods. First the new formulation of CEKF is developed by condition equations with prediction of all possible cross-covariances as algorithm 1. Then the LS-VCE method is applied to it after some modifications which results in an adaptive constrained extended Kalman filter (ACEKF) as the second algorithm. [ABSTRACT FROM AUTHOR]

Instantaneous velocity is an important variable for navigation and measurement tasks, and its estimation using a stand-alone global navigation satellite system (GNSS) receiver has important theoretical and practical significance for many applications. Adopting a stand-alone receiver to determine the instantaneous velocity in real-time has the advantages of independence of reference station, simple equipment, superior real-time performance and low cost. With these advantages, a new method is proposed to determine the instantaneous velocity by combining Doppler and carrier phase measurements based on online variance component estimation. This is a data fusion problem described by a state space model, in which the uncertainty of the state space model is tuned online through adaptive filtering. The adaptive variables are optimized using the locally best invariant quadrature unbiased estimate (BIQUE), which are directly estimated without iteration. The GNSS velocimetry principle and Doppler and carrier phase combined velocimetry process are provided in the abstract figure. To verify the proposed approach, simulation and real GNSS data with different sampling intervals are used in experiments. All results demonstrate the efficacy and stability of the proposed approach compared to the conventional approaches. [ABSTRACT FROM AUTHOR]

• Under regional GTS, ISL significantly improves BDS-3 orbit determination accuracy. • The initial weight ratio has little effect on the result when VCE algorithm is used. • VCE algorithm has contribute to fusion data processing of L-band and Ka-band. The BeiDou global navigation satellite system (BDS-3) has established the Ka-band inter-satellite link (ISL) to realize a two-way ranging function between satellites, which provides a new observation technology for the orbit determination of BDS-3 satellites. Therefore, this study presents a BDS satellite orbit determination model based on ground tracking station (GTS) observations and ISL ranging observations firstly to analyze the impact of the ISL ranging observations on the orbit determination of BDS-3 satellites. Subsequently, considering the data fusion processing, the variance component estimation (VCE) algorithm is applied to the parameter estimation process of the satellite orbit determination. Finally, using the measured data from China's regional GTS observations and BDS-3 ISL ranging observations, the effects of ISL ranging observations on the orbit determination accuracy of BDS-3 satellites are analyzed. Moreover, the impact of the VCE algorithm on the fusion data processing is evaluated from the aspects of orbit determination accuracy, Ka-band hardware delay parameter stability, and ISL ranging observation residuals. The results show that for China's regional GTSs, the addition of BDS-3 ISL ranging observations can significantly improve the orbit determination accuracy of BDS-3 satellites. The observed orbit determination accuracy of satellite radial component is improved from 48 cm to 4.1 cm. In addition, when the initial weight ratio between GTS observations and ISL ranging observations is not appropriate, the various indicators which include orbit determination accuracy, ISL hardware delay, and ISL observation residuals were observed to have improved after the adjustment of the VCE algorithm. These results validate the effectiveness of the VCE algorithm for the fusion data processing of the GTS observations and ISL ranging observations. [ABSTRACT FROM AUTHOR]

Objectives: To meet the precise coordinate transmission requirement of underground engineering, a measuring and data processing method of high ‐ precision 3D traverse is inspired by the trigeminy tripod method. Methods: The trigeminy total station method is proposed to build 3D traverse. The U buckle is used to fix the adapter of tooling ball reflector on the handle of a total station. The spatial relation between the tooling ball reflector center and instrument center is calibrated to correct the observed values. The lines connecting each two instrument centers constitute a 3D traverse, which avoids the manual measuring error of instrument height and prism height. A practical model for unparalleled plumb lines correction and Helmert variance component estimation are applied to determine the weight of different class observation. These improvements make the data processing of 3D traverse more rigorous.Results: In a tunnel surveying project, a closed 3D traverse is established with 15 sides. Compared to traditional adjustment method, the variance of unit weight of the proposed method is obviously decreased after correction for unparalleled plumb lines and variance component estimation. The precision of traverse points is obviously improved and better than ±0.5 mm. Digital industrial photogrammetry system is utilized to check the adjustment results. The precision of common points transformation between the survey results of digital industrial photogrammetry system and that of 3D traverse is ±0.32 mm.Conclusions: The proposed method has a good performance in severe conditions such as short sides and large vertical angles, so it is worthy of popularization and application. [ABSTRACT FROM AUTHOR]

A difficulty in variance component estimation (VCE) is that the estimates may become negative, which is not acceptable in practice. This article presents two new methods for non-negative VCE that utilize the expectation maximization algorithm for the partial errors-in-variables model. The former searches for the desired solutions with unconstrained estimation criterion and concludes statistically that the variance components have indeed moved to the edge of the parameter space when negative estimates appear implemented by the other existing VCE methods. We concentrate on the formulation and provide non-negative analysis of this estimator. In particularly, the latter approach, which has greater computational efficiency, would be a practical alternative to the existing VCE-type algorithms. Additionally, this approach is easy to implement, the non-negative variance components are automatically supported by introducing non-negativity constraints. Both algorithms are free from a complex matrix inversion and reduce computational complexity. The results show that our algorithms retrieve well to achieve identical estimates over the other VCE methods, the latter approach can quickly estimate parameters and has practical aspects for the large volume and multisource data processing. [ABSTRACT FROM AUTHOR]

To further improve the quality of estimated values based on variance component estimation of the partial errors-in-variables (EIV) model, the jackknife resampling method is introduced in this paper. Focusing on the bias of variance component estimation and combining with the jackknife method, bias calculation and bias correction are performed. Two schemes for parameter estimation are identified, and detailed calculation steps and the whole procedure are given. The jackknife method for variance component estimation of the partial EIV model is evaluated. Meanwhile, these two new algorithms are applied to the straight-line fitting model, space-line fitting model, and plane coordinate transformation model. As shown in the experimental estimation results, both methods proposed can obtain more accurate estimated values than the traditional variance component estimation method, and the method with bias correction can obtain the optimal parameter estimates. The case studies demonstrate the effectiveness and reliability of the proposed procedure, which extends the theory of the jackknife method in parameter estimation and provides resampling insight to further investigate variance component estimation. [ABSTRACT FROM AUTHOR]

As aerospace technology, computer technology, network communication technology and information technology become more and more perfect, a variety of sensors for measurement and remote sensing are constantly emerging, and the ability to acquire remote sensing data is also continuously enhanced. Synthetic Aperture Radar Interferometry (InSAR) technology greatly expands the function and application field of imaging radar. Differential InSAR (DInSAR) developed based on InSAR technology has the advantages of high precision and all-weather compared with traditional measurement methods. However, DInSAR-based deformation monitoring is susceptible to spatiotemporal coherence, orbital errors, atmospheric delays, and elevation errors. Since phase noise is the main error of InSAR, to determine the appropriate filtering parameters, an iterative adaptive filtering method for interferogram is proposed. For the limitation of conventional DInSAR, to improve the accuracy of deformation monitoring as much as possible, this paper proposes a deformation modeling based on ridge estimation and regularization as a constraint condition, and introduces a variance component estimation to optimize the deformation results. The simulation experiment of the iterative adaptive filtering method and the deformation modeling proposed in this paper shows that the deformation information extraction method based on differential synthetic aperture radar has high precision and feasibility. [ABSTRACT FROM AUTHOR]

The detection of deformation is one of the major tasks in surveying engineering. It is meaningful only if the statistical significance of the distortions is correctly investigated, which often underlies a parametric modelization of the object under consideration. So-called regression B-spline approximation can be performed for point clouds of terrestrial laser scanners, allowing the setting of a specific congruence test based on the B-spline surfaces. Such tests are known to be strongly influenced by the underlying stochastic model chosen for the observation errors. The latter has to be correctly specified, which includes accounting for heteroscedasticity and correlations. In this contribution, we justify and make use of a parametric correlation model called the Matérn model to approximate the variance covariance matrix (VCM) of the residuals by performing their empirical mode decomposition. The VCM obtained is integrated into the computation of the congruence test statistics for a more trustworthy test decision. Using a real case study, we estimate the distribution of the test statistics with a bootstrap approach, where no parametric assumptions are made about the underlying population that generated the random sample. This procedure allows us to assess the impact of neglecting correlations on the critical value of the congruence test, highlighting their importance. [ABSTRACT FROM AUTHOR]

Multiple Mobile Robots System (MMRS) has shown many attractive features in lots of real-world applications that motivate their rapid and wide diffusion. In MMRS, the Cooperative Localization (CL) is the basis and premise of its high-performance task. However, the statistical characteristics of the system noise should be already known in traditional CL algorithms, which is difficult to satisfy in actual MMRS because of the numerous of disturbances form the complex external environment. So the CL accuracy will be reduced. To solve this problem, an improved Adaptive Active Cooperative Localization (A2CL) algorithm based on information optimization strategy for MMRS is proposed in this manuscript. In this manuscript, an adaptive information fusion algorithm based on the variance component estimation under Extended Kalman filter (VCEKF) method for MMRS is introduced firstly to enhance the robustness and accuracy of information fusion by estimating the covariance matrix of the system noise or observation noise in real time. Besides, to decrease the effect of observation uncertainty on CL accuracy further, an observation optimization strategy based on information theory, the Model Predictive Control (MPC) strategy, is used here to maximize the information amount from observations. And semi-physical simulation experiments were carried out to verity the A2CL algorithm's performance finally. Results proved that the presented A2CL algorithm based on information optimization strategy for MMRS cannot only enhance the CL accuracy effectively but also have good robustness. [ABSTRACT FROM AUTHOR]

Combining multi-source data can improve the accuracy and the spatial resolution of the three-dimensional (3-D) displacements field. How to effectively integrate multi-source data to obtain high-precision and high spatial resolution 3-D displacements field is worthy of further study. The stochastic model and fusion model of integrating multi-source data affect the accuracy of data fusion. In this paper, based on the least squares method, the effects of different stochastic models and data fusion models on the 3-D displacements field's accuracy are studied. The optimal method for estimating large-scale 3-D displacements field from integrated InSAR, leveling and GPS measurements is obtained. Then we realize the integrating InSAR, leveling and GPS measurements to obtain the high-precision 3-D displacements velocity field in Tianjin (China) from 2016 to 2018. The results are validated with GPS measurements at 6 independent stations, with the root mean squares (RMS) residuals of the discrepancies being 2.39 mm/yr, 2.54 mm/yr and 2.83 mm/yr in eastern, northern and vertical directions, respectively. By comparing different stochastic models, the 3-D displacements field obtained from multi-source data is optimized by the variance component estimation-least squares method, which is better than weighted least squares (WLS) method. By comparing different data fusion models, the accuracy of the horizontal displacements velocity is better than that of interpolated GPS results. The horizontal displacements component has a great influence on the vertical displacements velocity accuracy in the process of acquiring the 3-D displacements velocity by integrating InSAR, GPS and leveling measurements. This study provides a reference method for integrating multi-source data to obtain 3-D displacements field. This method effectively utilizes the advantages of GPS, InSAR and leveling measurements, and extends the limitations of single technical in describing surface-time scale applications. The 3-D displacements information with a large spatial scale and high spatial resolution provide a reliable data basis for studying the crustal movement and its dynamic mechanism. [ABSTRACT FROM AUTHOR]

In the autoregressive (AR) model, random errors in the observation vector are homologous to those in the coefficient matrix. In view of the unreasonable distribution of the observation weight matrix and the inaccuracy of the random model, the random quantities in the augmented matrix consisting of the coeffi- cient matrix and the observation vector are extracted by the variable projection method. Then, we trans- form the errors-in-variables (EIV) model into the nonlinear Gauss-Helmert (GH) model and propose a struc- tural total least squares (STLS) algorithm by the nonlinear least squares adjustment theory. Combined with the least squares variance component estimation (LS - VCE) method, the variance component estimation method of STLS problem is derived. Furthermore, it is applied to the variance component estimation of the AR model. Through the real example, the effectiveness of proposed algorithm is verified. Meanwhile, the results are consistent with those of modified existing variance component estimation methods, but the construction of observation weight matrix is simple, it can also applied to the estimation of covariance factors. [ABSTRACT FROM AUTHOR]

Dimensional variation reduction is critical to assuring high quality in assembly and manufacturing processes. The extent to which data from a multiple-sensor system aids the diagnosis of variation sources depends on the effective placement of the sensors. The diagnostic objective that we consider is to estimate the variance components for potential variation sources. Using a linear structured model to represent the effects of the variation sources on the measurement data, this paper studies the problem of how to add additional sensor(s) to ensure diagnosability and/or improve estimation accuracy. Most prior work on sensor placement focused on automated numerical search algorithms that optimize rather unintuitive mathematical measures of diagnosability and accuracy. Our objective is to translate the measures into expressions that provide better conceptual guidance into how to most appropriately locate additional sensors to improve accuracy and diagnosability. The expressions may be used in conjunction with qualitative judgment and expert knowledge as the basis for locating additional sensors. Alternatively, they can be used in conjunction with existing numerical search routines by providing initial guesses for the sensor location and/or substantially narrowing the space of feasible sensor locations that must be searched during the numerical optimization. The proposed method is illustrated with examples from automotive panel assembly. [ABSTRACT FROM AUTHOR]