Helmert Variance Component Estimation for Multi-GNSS Relative Positioning

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

Journal of Navigation ◽

10.1017/s0373463321000564 ◽

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.

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A Robust Method for GPS/BDS Pseudorange Differential Positioning Based on the Helmert Variance Component Estimation

Journal of Sensors ◽

10.1155/2017/8172342 ◽

2017 ◽

Vol 2017 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Jian Deng ◽

Xingwang Zhao ◽

Aiguo Zhang ◽

Fuyang Ke

Keyword(s):

Real Time ◽

Variance Component ◽

Large Deviation ◽

Satellite System ◽

Observation Data ◽

Variance Component Estimation ◽

Relative Positioning ◽

Long Baseline ◽

Component Estimation ◽

Global Navigation Satellite

The use of global navigation satellite system (GNSS) is entering a new era of joint positioning based on the use of multifrequencies and multimodes. Ensuring the correct weighting of observations from each system and satellite has become a key problem during real-time positioning. This paper addresses the issue of weights of observations as well as the quality control of GPS/BDS pseudoranges in the context of real-time relative positioning. Thus, in the first place, the Helmert variance component estimation (VCE) is used to determine the relative weighting of observations from the two systems, and then, we introduce robustness estimation theory and construct a new method. The method is resistant to the influence of outliers in the observations by selecting weight iterations. To do this, we selected GPS/BDS observation data at baseline lengths of 40 km, 46 km, and 64 km for verification and analysis. Experimental results show that, in terms of the relative positioning of medium-to-long baseline based on GPS/BDS pseudorange observations, when observed values incorporate large gross errors, our method can reduce the weighting of suspicious or abnormal values and weaken their impact on positioning solutions, so that the positioning results will not appear to have large deviation.

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