Currently, Global Navigation Satellite Systems (GNSS) do not contribute to the realization of origin and scale of combined global terrestrial reference frame (TRF) solutions due to present system design limitations. The future Galileo-like medium Earth orbit (MEO) constellation, called “Kepler”, proposed by the German Aerospace Center DLR, is characterized by a low Earth orbit (LEO) segment and the innovative key features of optical inter-satellite links (ISL) delivering highly precise range measurements and of optical frequency references enabling a perfect time synchronization within the complete constellation. In this study, the potential improvements of the Kepler constellation on the TRF origin and scale are assessed by simulations. The fully developed Kepler system allows significant improvements of the geocenter estimates (realized TRF origin in long-term). In particular, we find improvements by factors of 43 for the Z and of 8 for the X and Y component w. r. t. a contemporary MEO-only constellation. Furthermore, the Kepler constellation increases the reliability due to a complete de-correlation of the geocenter coordinates and the orbit parameters related to the solar radiation pressure modeling (SRP). However, biases in SRP modeling cause biased geocenter estimates and the ISL of Kepler can only partly compensate this effect. The realized scale enabling all Kepler features improves by 34% w. r. t. MEO-only. The dependency of the estimated satellite antenna phase center offsets (PCOs) upon the underlying TRF impedes a scale realization by GNSS. In order to realize the network scale with 1 mm accuracy, the PCOs have to be known within 2 cm for the MEO and 4 mm for the LEO satellites. Independently, the scale can be realized by estimating the MEO PCOs and by simultaneously fixing the LEO PCOs. This requires very accurate LEO PCOs; the simulations suggest them to be smaller than 1 mm in order to keep scale changes below 1 mm.

中文翻译：

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未来 GNSS 星座“开普勒”中的参考系统起源和比例实现

目前，由于目前的系统设计限制，全球导航卫星系统 (GNSS) 对组合全球地面参考框架 (TRF) 解决方案的起源和规模的实现没有贡献。德国航空航天中心 DLR 提出的未来类伽利略中地球轨道 (MEO) 星座称为“开普勒”，其特点是低地球轨道 (LEO) 段和光学星间链路 (ISL) 的创新关键特征) 提供高精度的距离测量和光频参考，从而在整个星座内实现完美的时间同步。在这项研究中，开普勒星座在 TRF 起源和尺度上的潜在改进是通过模拟来评估的。完全开发的开普勒系统可以显着改进地心估计（长期实现的 TRF 原点）。特别是，我们发现在现代仅 MEO 星座中，Z 分量提高了 43 倍，X 和 Y 分量提高了 8 倍。此外，由于地心坐标和与太阳辐射压力建模 (SRP) 相关的轨道参数的完全去相关，开普勒星座提高了可靠性。然而，SRP 建模中的偏差会导致地心估计有偏差，而开普勒的 ISL 只能部分补偿这种影响。启用所有开普勒功能的已实现规模比仅 MEO 提高了 34%。估计的卫星天线相位中心偏移 (PCO) 对基础 TRF 的依赖性阻碍了 GNSS 的规模实现。为了实现 1 mm 精度的网络规模，MEO 和 LEO 卫星的 PCO 必须在 2 cm 内已知。独立地，可以通过估计 MEO PCO 和同时固定 LEO PCO 来实现规模。这需要非常准确的 LEO PCO；模拟表明它们小于 1 毫米，以便将比例变化保持在 1 毫米以下。