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.

中文翻译：

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多GNSS相对定位的Helmert方差分量估计。

多星座全球导航卫星系统（Multi-GNSS）已成为高精度定位和导航应用程序的标准实现。众所周知，代码和相位测量的噪声取决于GNSS星座图。然后，通常使用Helmert方差分量估计（HVCE）通过确定它们各自的单位权重方差来调整不同GNSS星座的贡献。但是，HVCE需要繁重的计算工作。在这项研究中，采用HVCE后加权来进行运动学相对Multi-GNSS定位实验，该运动以6个短基线为基准，从每年的日（DoY）171到2019年的200个。因此，HVCE后加权策略改进了Multi -在北东向上（ENU）组件中，GNSS定位精度提高了20.5％，15.7％和13.2％，与依海拔高度（ED）先验加权策略相比。我们观察到，在整个30天内，每个GNSS星座的代码和相位观测值的重量比例都是一致的，这表明代码和相位观测值的重量比例在很长一段时间内都是稳定的。还发现，在每个基线和GNSS星座中，相位观测的质量几乎相等，而代码观测的质量则不同。为了在不牺牲定位精度的情况下减少HVCE方法的时间消耗，将在30天内获得的相位和代码观测值的单位权重的稳定方差求平均值，然后将其冻结，作为定位实验中的先验信息。结果表明ENU的改善分别为20.0％，14.1％和11。相对于ED方法为1％，但是节省了HCVE策略的88％的计算时间。我们的研究得出的结论是，冻结的单位重量方差（FVUW）可以用于未来30天的定位实验，即从2019年的DoY 201到230，从而通过以下方法提高ED方法的定位ENU准确性： 18.1％，13.2％和10.6％，表明FVUW的有效性。