Some Results on Biased Linear Estimation Applied to Variance Component Estimation

1980 ◽  
pp. 266-274 ◽  
Author(s):  
Lynn Roy LaMotte
Keyword(s):  
Variance Component ◽  
Variance Component Estimation ◽  
Linear 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.

scholarly journals An overview of variance component estimation

Metrika ◽  
1995 ◽  
Vol 42 (1) ◽  
pp. 215-230 ◽  
Author(s):  
Shayle R. Searle
Keyword(s):  
Variance Component ◽  
Variance Component Estimation ◽  
Component Estimation

scholarly journals Relationships between longevity and conformation traits in Czech Fleckvieh cows

2009 ◽  
Vol 54 (No. 9) ◽  
pp. 385-394 ◽  
Author(s):  
L. Zavadilová ◽  
E. Němcová ◽  
M. Štípková ◽  
J. Bouška
Keyword(s):  
Variance Component ◽  
Genetic Relationships ◽  
Genetic Correlations ◽  
Variance Component Estimation ◽  
Body Measurements ◽  
Linear Type ◽  
Zero Correlation ◽  
Type Traits ◽  
Component Estimation

The relationships between conformation and longevity traits were analysed in 58 493 Czech Fleckvieh cows first calved from 1994 to 2003. All cows were scored for conformation during the first lactation. Genetic correlations between longevity and conformation traits were estimated by bivariate runs using the VCE 4.0 program for variance component estimation. The values of heritability for conformation traits were in the range from 0.06 to 0.63 and for longevity traits from 0.04 to 0.05. Low or intermediate genetic relationships between recorded linear traits and longevity trait were found. The correlations were lower for functional longevity. Body measurements showed negative genetic correlations with real as well as functional longevity (–0.12 to –0.29). The dairy character negatively correlated with longevity traits (–0.18 to –0.26). The muscularity and udder showed a zero correlation with functional longevity, while the feet and legs were not correlated with real longevity. The highest positive genetic correlations between real longevity and objectively scored linear type traits were found for hock (0.24), rear udder attachment (0.28), fore udder length (0.16) and central ligament (0.11). On the contrary, the correlation between the udder depth and the milk-corrected longevity was positive (0.28) and higher than in the case of real longevity.

scholarly journals Helmert Variance Component Estimation for Multi-GNSS Relative Positioning

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 669 ◽  
Author(s):  
Mowen Li ◽  
Wenfeng Nie ◽  
Tianhe Xu ◽  
Adria Rovira-Garcia ◽  
Zhenlong Fang ◽  
...  
Keyword(s):  
Variance Component ◽  
Computation Time ◽  
Satellite System ◽  
Unit Weight ◽  
Variance Component Estimation ◽  
Positioning Accuracy ◽  
Gnss Positioning ◽  
Component Estimation ◽  
Weighting Strategy ◽  
Gnss Constellation

The Multi-constellation Global Navigation Satellite System (Multi-GNSS) has become the standard implementation of high accuracy positioning and navigation applications. It is well known that the noise of code and phase measurements depend on GNSS constellation. Then, Helmert variance component estimation (HVCE) is usually used to adjust the contributions of different GNSS constellations by determining their individual variances of unit weight. However, HVCE requires a heavy computation load. In this study, the HVCE posterior weighting was employed to carry out a kinematic relative Multi-GNSS positioning experiment with six short-baselines from day of year (DoY) 171 to 200 in 2019. As a result, the HVCE posterior weighting strategy improved Multi-GNSS positioning accuracy by 20.5%, 15.7% and 13.2% in east-north-up (ENU) components, compared to an elevation-dependent (ED) priori weighting strategy. We observed that the weight proportion of both code and phase observations for each GNSS constellation were consistent during the entire 30 days, which indicates that the weight proportions of both code and phase observations are stable over a long period of time. It was also found that the quality of a phase observation is almost equivalent in each baseline and GNSS constellation, whereas that of a code observation is different. In order to reduce the time consumption of the HVCE method without sacrificing positioning accuracy, the stable variances of unit weights of both phase and code observations obtained over 30 days were averaged and then frozen as a priori information in the positioning experiment. The result demonstrated similar ENU improvements of 20.0%, 14.1% and 11.1% with respect to the ED method but saving 88% of the computation time of the HCVE strategy. Our study concludes with the observations that the frozen variances of unit weight (FVUW) could be applied to the positioning experiment for the next 30 days, that is, from DoY 201 to 230 in 2019, improving the positioning ENU accuracy of the ED method by 18.1%, 13.2% and 10.6%, indicating the effectiveness of the FVUW.

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