利用相对论精密单点定位时间比较确定地球位差：模拟观测实例研究
Determining geopotential difference via relativistic precise point positioning time comparison: A case study using simulated observations
摘要：
根据广义相对论（GRT），通过使用精密单点定位（PPP）时间传递技术（称为相对论PPP时间比较方法）比较精密时钟之间的时差变化，可以确定地球电势差（GD）。重点研究了利用相对论PPP时间传递确定GD的两个精密钟之间的高精度时间比对，并进行了仿真实验验证。在实验中，我们考虑了三种情况来评估该方法的性能，使用不同的稳定度的时钟，即，在三个选定的地面站配备的时钟的频率稳定度分别为（情况1），（情况2），和（情况3）在时间段。从实验结果中得出结论。首先，高精度时钟可以显著提高PPP时间传递的精度，但这种提高受到测量噪声的限制。与病例1相比，病例2和病例3中OPMT-BRUX以及PTBB-BRUX的长期稳定性得到改善。在OPMT-BRUX的10天平均时间，情况1-3的频率稳定度分别约为4.28*10-16、4.00*10-17和3.22*10-17，而对于PTBB-BRUX，这些值约为3.73*10-16、8.17*10-17和4.64*10-17。第二，可以在分米级确定任意两个站之间的位势差，其精度与情况1-3中的时间链路的稳定性一致。在情况3中，OPMT和BRUX之间确定的地球位势差偏离EIGEN-6C 4模型值-0.64 m2/s2，不确定度为1.11 m2/s2，而PTBB和BRUX之间的偏差误差为0.76 m2/s2，不确定度为1.79 m2/s2。本研究所提出的方法也可以应用于测试GRT。
英文摘要：
According to general relativity theory (GRT), the geopotential difference (GD) can be determined by comparing the change in time difference between precise clocks using the precise point positioning (PPP) time transfer technique, referred to as the relativistic PPP time comparison approach. We focused on high-precision time comparison between two precise clocks for determining the GD using the relativistic PPP time transfer,and conducted simulation experiments to validate the approach. In the experiments, we consider three cases to evaluate the performance of the approach using clocks with different stabilities, namely, the frequency stabilities of the clocks equipped at three selected ground stations are respectively (Case 1), (Case 2), and (Case 3) at time period. Conclusions are drawn from the experimental results. First, high-precision clocks can significantly improve the accuracy for PPP time transfer, but the improvement is limited by measurement noises. Compared to Case 1, the long-term stabilities of OPMT-BRUX as well as PTBB-BRUX are improved in Cases 2 and 3. The frequency stabilities of Cases 1-3 are approximately 4.28*10-16, 4.00*10-17, and 3.22*10-17 at 10-day averaging time for OPMT-BRUX, respectively, and for PTBB-BRUX, these values are approximately 3.73*10-16, 8.17*10-17, and 4.64*10-17. Second, the geopotential difference between any two stations can be determined at the decimeter level, with its accuracy being consistent with the stabilities of the time links in Cases 1-3. In Case 3, the determined geopotential differences between OPMT and BRUX deviate from the EIGEN-6C4 model values by -0.64 m2/s2 with an uncertainty of 1.11 m2/s2, whereas the deviation error between PTBB and BRUX is 0.76 m2/s2 with an uncertainty of 1.79 m2/s2. The approach proposed in this study can be also applied to testing GRT.
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