Abstract Human activity in the polar regions is increasing, and as a result of this, the positioning performance of global navigation satellite systems (GNSSs) in these regions is attracting more attention. Since the constellation design of GNSS systems (such as GPS, GLONASS, Galileo, and BDS) only provides superior coverage for human activity in the middle and low latitudes, the elevation angles of GNSS satellites are lower in the polar regions. In this study, the authors first analyzed the availability of GPS, GLONASS, Galileo, and BDS in the polar regions using the classic geometric dilution of precision (GDOP) metric. It was discovered that if only a stand-alone navigation system is employed, satellite visibility in the Arctic and Antarctic regions is excellent, but the GDOP is much higher than in the middle and low latitudes areas. Another interesting phenomenon is that a single navigation system other than GPS (i.e., GLONASS, Galileo, or BDS) will have some areas that cannot be located in the middle and low latitudes and will not appear in the polar regions. A simple solution of this problem is to combine multiple navigation systems to attain better GDOP. In reality, there are currently few achievable or practical solutions for the weight ratio of different satellites in the actual multi-system combined GDOP algorithm. Based on the signal-in-space analysis of different GNSS satellites, the authors propose a NEW WDOP metric for the spatial constellation configuration of multi-GNSSs, including detailed mathematical models and algorithms. The NEW WDOP metric was then used to assess the availability of multi-GNSSs in the polar regions with dual-system, three-system, and four-system combinations. This study thus draws some conclusions using the NEW WDOP model and measured data. In particular, when navigating and positioning in polar regions with a stand-alone GNSS, the mean of the NEW WDOP values is approximately 2.5, and there are many outlier values. Meanwhile, the mean of the NEW WDOP values with the dual GNSS combinations is

中文翻译：

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极地地区多 GNSS 星座可用性评估的精细度量

摘要 极地地区的人类活动日益增加，因此，这些地区的全球导航卫星系统（GNSS）的定位性能越来越受到关注。由于GNSS系统（如GPS、GLONASS、Galileo、BDS）的星座设计只为中低纬度地区的人类活动提供优越的覆盖，因此GNSS卫星在极地地区的仰角较低。在这项研究中，作者首先使用经典几何精度稀释 (GDOP) 指标分析了极地地区 GPS、GLONASS、Galileo 和 BDS 的可用性。发现如果仅采用独立导航系统，在北极和南极地区的卫星能见度很好，但GDOP远高于中低纬度地区。另一个有趣的现象是，除了GPS之外的单一导航系统（即GLONASS、Galileo或BDS），都会有一些区域无法定位在中低纬度，也不会出现在极地地区。这个问题的一个简单解决方案是组合多个导航系统以获得更好的 GDOP。现实中，目前在实际多系统组合GDOP算法中，对于不同卫星的权重比，可实现的或实用的解决方案很少。基于对不同 GNSS 卫星的空间信号分析，作者提出了一种新的 WDOP 度量，用于多 GNSS 的空间星座配置，包括详细的数学模型和算法。然后使用新的 WDOP 指标来评估具有双系统、三系统、和四系统组合。因此，本研究使用 NEW WDOP 模型和测量数据得出了一些结论。尤其是在极地地区使用独立的GNSS导航定位时，NEW WDOP值的平均值约为2.5，异常值较多。同时，具有双 GNSS 组合的 NEW WDOP 值的平均值为