Abstract Navigation augmentation based on Low Earth Orbit (LEO) satellites has become a hot topic in recent years. The orbital design of LEO augmentation constellations and the analysis of their performance are essential issues for the development of LEO augmentation systems. In this paper, LEO constellations for navigation are designed with the constraint that they augment the BeiDou Navigation Satellite System (BDS) in independent and combined modes. First, the calculation of the dilution of precision (DOP) values in different augmentation work modes is derived. Second, some numerical simulations of LEO constellations with different altitudes and inclinations are carried out. Based on the designed constellations, the coverage performance in typical regions and the global DOP values are analyzed, the suitable constellations with the orbital altitude of 500 km, 1000 km, 1500 km and 2000 km are derived. Finally, the suitable LEO constellations combined with the BDS in a time synchronized scenario and a non-synchronized scenario are demonstrated. The results show that 320/16/1:500 km, 80°, 144/12/1:1000 km, 70°, 100/10/1:1500 km, 70° and 80/8/1:2000 km, 60° are the suitable constellations, and the average GDOP values of these constellations are all below 5. In the combined work mode, the amplitude and stability of the DOP are improved significantly in the time-synchronized scenario of LEO navigation system and the BDS compared with only applying the BDS. The GDOP and TDOP values are improved by up to 22.46–44.41% and 29.06–60.62% respectively. When the non-synchronized scenario is considered, i.e. the LEO navigation system and the BDS are independent systems, the improvement of the DOP value is relatively limited because a new LEO clock error parameter has to be introduced in the positioning estimation. In that case, the improvement of the GDOP values is only 3.11–22.28%, and the TDOP values become worse at medium and low latitudes.

中文翻译：

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LEO 导航星座的轨道设计及其对 BDS 的增强评估

摘要 基于低地球轨道（LEO）卫星的导航增强是近年来的热门话题。LEO 增强星座的轨道设计及其性能分析是 LEO 增强系统发展的基本问题。在本文中，LEO 导航星座的设计约束条件是它们以独立和组合模式增强北斗导航卫星系统（BDS）。首先，推导出不同增强工作模式下精度稀释 (DOP) 值的计算。其次，对不同高度和倾角的LEO星座进行了一些数值模拟。基于所设计的星座，分析了典型区域的覆盖性能和全球DOP值，推导出轨道高度为500km、1000km、1500km、2000km的合适星座。最后，在时间同步场景和非同步场景中展示了合适的低轨星座与北斗系统的结合。结果显示，320/16/1:500 km、80°、144/12/1:1000 km、70°、100/10/1:1500 km、70°和80/8/1:2000 km、60 °为合适的星座，这些星座的平均GDOP值均在5以下。在组合工作模式下，LEO导航系统与北斗系统时间同步场景下DOP的幅度和稳定性较北斗系统有显着提升只应用 BDS。GDOP 和 TDOP 值分别提高了 22.46-44.41% 和 29.06-60.62%。当考虑非同步场景时，即 LEO 导航系统和 BDS 是独立的系统，DOP 值的提高相对有限，因为在定位估计中必须引入新的 LEO 时钟误差参数。在这种情况下，GDOP 值的提高只有 3.11-22.28%，而 TDOP 值在中低纬度变得更糟。