ABSTRACT Stochastic models play a crucial role in high-precision global navigation satellite system (GNSS) positioning. They have enormous influence on parameter estimation and hypothesis testing, especially when multi-GNSS multi-frequency observables are used. In this contribution, by means of reasonably simplified variance-covariance component estimation (VCE) formulas, the precision, cross-correlation, as well as the time correlation of GPS, BDS and Galileo multi-frequency observables collected from different types of receivers are analysed. The results show that the STDs of observables are GNSS-, receiver- and elevation-dependent. The precision of Galileo observables is better than that of GPS and BDS observables, whereas the GPS and BDS observables possess comparable precision. The STDs of observables computed are found to be stable over a period as long as one year. Larger STDs are estimated and more significant time correlations are presented when an ultra-short baseline is used, compared to the results of a zero baseline.

中文翻译：

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不同类型接收机下GPS/BDS/Galileo多频观测的随机特性分析

摘要 随机模型在高精度全球导航卫星系统 (GNSS) 定位中起着至关重要的作用。它们对参数估计和假设检验具有巨大的影响，尤其是在使用多 GNSS 多频观测值时。在这篇贡献中，通过合理简化的方差-协方差分量估计（VCE）公式，分析了从不同类型接收机收集的 GPS、BDS 和伽利略多频观测的精度、互相关以及时间相关. 结果表明，可观测的 STD 与 GNSS、接收器和海拔相关。伽利略观测值的精度优于 GPS 和 BDS 观测值，而 GPS 和 BDS 观测值具有可比的精度。计算出的可观测值的 STD 在长达一年的时间段内是稳定的。与零基线的结果相比，当使用超短基线时，估计更大的 STD 并呈现更显着的时间相关性。