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.

中文翻译：

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GPS-BDS-Galileo基于最小二乘方差分量估计的双差分随机模型细化

随机模型对于全球导航卫星系统 (GNSS) 的精确导航和定位至关重要。随机模型可以影响模糊度的分辨率，这是 GNSS 定位的关键步骤。现有的多GNSS随机模型大多基于GPS经验模型，没有考虑不同系统间观测精度的差异。本文提出了基于最小二乘方差分量的三个细化随机模型，即系统间方差分量（RSM1）、不同类型观测值方差（RSM2）和每颗卫星观测值方差（RSM3）。估计（LS-VCE）。零基线和短基线 GNSS 实验数据用于验证所提出的三个改进的随机模型。结果表明，与传统的仰角依赖模型（EDM）相比，提出的模型虽然没有显着提高模糊度解析成功率，但三种模型的定位精度都有所提高。RSM3对数据本身比较真实，表现最好，仰角掩膜角20°、30°、40°、50°精度可提升4⋅6%、7⋅6%、13⋅2 L1-B1-E1 为 %, 73⋅0%，L2-B2-E5a 分别为 1⋅1%, 4⋅8%, 16⋅3%, 64⋅5%。