The precise orbit determination (POD) of Global Navigation Satellite System (GNSS) satellites and low Earth orbiters (LEOs) are usually performed independently. It is a potential way to improve the GNSS orbits by integrating LEOs onboard observations into the processing, especially for the developing GNSS, e.g., Galileo with a sparse sensor station network and Beidou with a regional distributed operating network. In recent years, few studies combined the processing of ground- and space-based GNSS observations. The integrated POD of GPS satellites and seven LEOs, including GRACE-A/B, OSTM/Jason-2, Jason-3 and, Swarm-A/B/C, is discussed in this study. GPS code and phase observations obtained by onboard GPS receivers of LEOs and ground-based receivers of the International GNSS Service (IGS) tracking network are used together in one least-squares adjustment. The POD solutions of the integrated processing with different subsets of LEOs and ground stations are analyzed in detail. The derived GPS satellite orbits are validated by comparing with the official IGS products and internal comparison based on the differences of overlapping orbits and satellite positions at the day-boundary epoch. The differences between the GPS satellite orbits derived based on a 26-station network and the official IGS products decrease from 37.5 to 23.9 mm (34%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$34\%$$\end{document} improvement) in 1D-mean RMS when adding seven LEOs. Both the number of the space-based observations and the LEO orbit geometry affect the GPS satellite orbits derived in the integrated processing. In this study, the latter one is proved to be more critical. By including three LEOs in three different orbital planes, the GPS satellite orbits improve more than from adding seven well-selected additional stations to the network. Experiments with a ten-station and regional network show an improvement of the GPS satellite orbits from about 25 cm to less than five centimeters in 1D-mean RMS after integrating the seven LEOs.

中文翻译：

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地基和空基 GPS 观测的综合处理：改进用稀疏地面网络观测的 GPS 卫星轨道

全球导航卫星系统 (GNSS) 卫星和低地球轨道器 (LEO) 的精确定轨 (POD) 通常是独立执行的。通过将 LEO 机载观测整合到处理中来改进 GNSS 轨道是一种潜在的方式，特别是对于发展中的 GNSS，例如具有稀疏传感器站网络的伽利略和具有区域分布式操作网络的北斗。近年来，很少有研究将地基和空基 GNSS 观测的处理结合起来。本研究讨论了 GPS 卫星和 7 个 LEO 的集成 POD，包括 GRACE-A/B、OSTM/Jason-2、Jason-3 和 Swarm-A/B/C。由 LEO 的机载 GPS 接收器和国际 GNSS 服务 (IGS) 跟踪网络的地面接收器获得的 GPS 代码和相位观测值一起用于一个最小二乘平差。详细分析了具有不同LEO子集和地面站的集成处理的POD解决方案。推导出的 GPS 卫星轨道通过与官方 IGS 产品的对比和基于日界时期重叠轨道和卫星位置差异的内部对比进行验证。基于26站网络得出的GPS卫星轨道与IGS官方产品的差异从37.5减少到23。9 毫米（34%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength {\oddsidemargin}{-69pt} \begin{document}$$34\%$$\end{document} 改进）在添加七个 LEO 时一维均值 RMS。天基观测的数量和 LEO 轨道几何形状都会影响综合处理中导出的 GPS 卫星轨道。在本研究中，后者被证明更为关键。通过在三个不同的轨道平面中包含三个 LEO，GPS 卫星轨道的改进比向网络添加七个精心挑选的附加站要好得多。