Improving Dam Deformation Analysis Using Least-Squares Variance Component Estimation and Tikhonov Regularization

Abstract Stochastic models are essential for precise navigation and positioning of the global navigation satellite system (GNSS). A stochastic model can influence the resolution of ambiguity, which is a key step in GNSS positioning. Most of the existing multi-GNSS stochastic models are based on the GPS empirical model, while differences in the precision of observations among different systems are not considered. In this paper, three refined stochastic models, namely the variance components between systems (RSM1), the variances of different types of observations (RSM2) and the variances of observations for each satellite (RSM3) are proposed based on the least-squares variance component estimation (LS-VCE). Zero-baseline and short-baseline GNSS experimental data were used to verify the proposed three refined stochastic models. The results show that, compared with the traditional elevation-dependent model (EDM), though the proposed models do not significantly improve the ambiguity resolution success rate, the positioning precision of the three proposed models has been improved. RSM3, which is more realistic for the data itself, performs the best, and the precision at elevation mask angles 20°, 30°, 40°, 50° can be improved by 4⋅6%, 7⋅6%, 13⋅2%, 73⋅0% for L1-B1-E1 and 1⋅1%, 4⋅8%, 16⋅3%, 64⋅5% for L2-B2-E5a, respectively.

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Nonlinear total least-squares variance component estimation for GM(1,1) model

Geodesy and Geodynamics ◽

10.1016/j.geog.2021.02.006 ◽

2021 ◽

Author(s):

Leyang Wang ◽

Jianqiang Sun ◽

Qiwen Wu

Keyword(s):

Least Squares ◽

Variance Component ◽

Total Least Squares ◽

Variance Component Estimation ◽

Component Estimation

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Application of Least-Squares Variance Component Estimation to GPS Observables

Journal of Surveying Engineering ◽

10.1061/(asce)0733-9453(2009)135:4(149) ◽

2009 ◽

Vol 135 (4) ◽

pp. 149-160 ◽

Cited By ~ 54

Author(s):

A. R. Amiri-Simkooei ◽

P. J. G. Teunissen ◽

C. C. J. M. Tiberius

Keyword(s):

Least Squares ◽

Variance Component ◽

Variance Component Estimation ◽

Component Estimation

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Combination of GNSS orbits using variance component estimation

10.5194/egusphere-egu21-1102 ◽

2021 ◽

Author(s):

Gustavo Mansur ◽

Pierre Sakic ◽

Andreas Brack ◽

Benjamin Männel ◽

Harald Schuh

Keyword(s):

Least Squares ◽

Variance Component ◽

External Validation ◽

Pilot Project ◽

Variance Component Estimation ◽

International Gnss Service ◽

Consistent Solution ◽

Component Estimation ◽

Combination Approach ◽

Clock Combination

<p>The International GNSS Service (IGS) publishes operationally GPS and GLONASS orbit and clock products with the highest accuracy. These final products result from a combination using as input products determined by the IGS Analysis Centers (ACs). The method to perform the combination was developed in the early nineties by Springer and Beutler and is used until nowadays despite some updates made over the years mainly to improve the clock combination and the alignment with the current ITRF. Over the past years, towards the Multi-GNSS Experiment and Pilot Project (MGEX) the IGS has been putting efforts into extending its service. Several MGEX ACs contribute by providing solutions containing not only GPS and GLONASS but also Galileo, BeiDou, and QZSS. For MGEX an orbit and clock combination is still not consolidated inside the IGS and requires studies in order to provide a consistent solution.</p><p>We will 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. &#160;In this contribution, we will introduce and compare two weighting strategies, where either AC specific weights or AC plus constellation specific weights are used. Both strategies are tested using MGEX orbit solutions for a period of two and a half years. They yield similar results where the agreement between combined and individual products is around one centimeter for GPS and up to a few centimeters for the other constellations. The agreement is generally slightly better using the AC plus constellation weighting. A comparison of our combination approach with the official combined IGS final solution using three years of GPS, and GLONASS orbits from the regular IGS processing show an agreement of better than 5 mm and 12 mm for GPS and GLONASS, respectively. An external validation using Satellite Laser Ranging is performed for our combined MGEX orbit solutions with both weighting schemes and shows offsets values in the millimeter level for all constellations except to QZSS where the values reach a few centimeters.</p>

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An Improved GPS-Inferred Seasonal Terrestrial Water Storage Using Terrain-Corrected Vertical Crustal Displacements Constrained by GRACE

Remote Sensing ◽

10.3390/rs11121433 ◽

2019 ◽

Vol 11 (12) ◽

pp. 1433 ◽

Cited By ~ 4

Author(s):

Hok Sum Fok ◽

Yongxin Liu

Keyword(s):

Tikhonov Regularization ◽

Bayesian Information Criterion ◽

Variance Component ◽

Water Storage ◽

Information Criterion ◽

Variance Component Estimation ◽

Terrestrial Water Storage ◽

Geophysical Model ◽

Terrestrial Water ◽

Component Estimation

Based on a geophysical model for elastic loading, the application potential of Global Positioning System (GPS) vertical crustal displacements for inverting terrestrial water storage has been demonstrated using the Tikhonov regularization and the Helmert variance component estimation since 2014. However, the GPS-inferred terrestrial water storage has larger resulting amplitudes than those inferred from satellite gravimetry (i.e., Gravity Recovery and Climate Experiment (GRACE)) and those simulated from hydrological models (e.g., Global Land Data Assimilation System (GLDAS)). We speculate that the enlarged amplitudes should be partly due to irregularly distributed GPS stations and the neglect of the terrain effect. Within southwest China, covering part of southeastern Tibet as a study region, a novel GPS-inferred terrestrial water storage approach is proposed via terrain-corrected GPS and supplementary vertical crustal displacements inferred from GRACE, serving as "virtual GPS stations" for constraining the inversion. Compared to the Tikhonov regularization and Helmert variance component estimation, we employ Akaike’s Bayesian Information Criterion as an inverse method to prove the effectiveness of our solution. Our results indicate that the combined application of the terrain-corrected GPS vertical crustal displacements and supplementary GRACE spatial data constraints improves the inversion accuracy of the GPS-inferred terrestrial water storage from the Helmert variance component estimation, Tikhonov regularization, and Akaike’s Bayesian Information Criterion, by 55%, 33%, and 41%, respectively, when compared to that of the GLDAS-modeled terrestrial water storage. The solution inverted with Akaike’s Bayesian Information Criterion exhibits more stability regardless of the constraint conditions, when compared to those of other inferred solutions. The best Akaike’s Bayesian Information Criterion inverted solution agrees well with the GLDAS-modeled one, with a root-mean-square error (RMSE) of 3.75 cm, equivalent to a 15.6% relative error, when compared to 39.4% obtained in previous studies. The remaining discrepancy might be due to the difference between GPS and GRACE in sensing different surface water storage components, the remaining effect of the water storage changes in rivers and reservoirs, and the internal error in the geophysical model for elastic loading.

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