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

2021 ◽  
Author(s):  
Leyang Wang ◽  
Jianqiang Sun ◽  
Qiwen Wu
Keyword(s):  
Least Squares ◽  
Variance Component ◽  
Total Least Squares ◽  
Variance Component Estimation ◽  
Component Estimation

GPS-BDS-Galileo double-differenced stochastic model refinement based on least-squares variance component estimation

2021 ◽  
pp. 1-16
Author(s):  
Hong Hu ◽  
Xuefeng Xie ◽  
Jingxiang Gao ◽  
Shuanggen Jin ◽  
Peng Jiang
Keyword(s):  
Stochastic Model ◽  
Least Squares ◽  
Stochastic Models ◽  
Variance Component ◽  
Satellite System ◽  
Variance Component Estimation ◽  
Short Baseline ◽  
Component Estimation ◽  
Zero Baseline ◽  
Global Navigation Satellite

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.

Application of Least-Squares Variance Component Estimation to GPS Observables

2009 ◽  
Vol 135 (4) ◽  
pp. 149-160 ◽  
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

scholarly journals Combination of GNSS orbits using variance component estimation

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.  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>

scholarly journals Least-squares variance component estimation

2007 ◽  
Vol 82 (2) ◽  
pp. 65-82 ◽  
Author(s):  
P. J. G. Teunissen ◽  
A. R. Amiri-Simkooei
Keyword(s):  
Least Squares ◽  
Variance Component ◽  
Variance Component Estimation ◽  
Component Estimation
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