The present Global Navigation Satellite System (GNSS) can provide at least double-frequency observations, and especially the Galileo Navigation Satellite System (Galileo) can provide five-frequency observations for all constellation satellites. In this contribution, precision point positioning (PPP) models with Galileo E1, E5a, E5b, E5 and E6 frequency observations are established, including a dual-frequency (DF) ionospheric-free (IF) combination model, triple-frequency (TF) IF combination model, quad-frequency (QF) IF combination model, four five-frequency (FF) IF com-bination models and an FF uncombined (UC) model. The observation data of five stations for seven days are selected from the multi-GNSS experiment (MGEX) network, forming four time-frequency links ranging from 454.6 km to 5991.2 km. The positioning and time-frequency transfer performances of Galileo multi-frequency PPP are compared and evaluated using GBM (which denotes precise satellite orbit and clock bias products provided by Geo Forschung Zentrum (GFZ)), WUM (which denotes precise satellite orbit and clock bias products provided by Wuhan University (WHU)) and GRG (which denotes precise satellite orbit and clock bias products provided by the Centre National d’Etudes Spatiales (CNES)) precise products. The results show that the performances of the DF, TF, QF and FF PPP models are basically the same, the frequency stabilities of most links can reach sub10⁻¹⁶ level at 120,000 s, and the average three-dimensional (3D) root mean square (RMS) of position and average frequency stability (120,000 s) can reach 1.82 cm and 1.18 × 10⁻¹⁵, respectively. The differences of 3D RMS among all models are within 0.17 cm, and the differences in frequency stabilities (in 120,000 s) among all models are within 0.08 × 10⁻¹⁵. Using the GRG precise product, the solution performance is slightly better than that of the GBM or WUM precise product, the average 3D RMS values obtained using the WUM and GRG precise products are 1.85 cm and 1.77 cm, respectively, and the average frequency stabilities at 120,000 s can reach 1.13 × 10⁻¹⁵ and 1.06 × 10⁻¹⁵, respectively.

中文翻译：

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利用伽利略五频观测对精确定位和时频传递进行建模和性能评估

目前的全球导航卫星系统（GNSS）至少可以提供双频观测，尤其是伽利略导航卫星系统（Galileo）可以为所有星座卫星提供五频观测。在此贡献中，建立了具有伽利略 E1、E5a、E5b、E5 和 E6 频率观测的精密点定位 (PPP) 模型，包括双频 (DF) 无电离层 (IF) 组合模型、三频 (TF)中频组合模型、四频（QF）中频组合模型、四个五频（FF）中频组合模型和一个FF非组合（UC）模型。从多GNSS实验（MGEX）网络中选取了5个站7天的观测数据，形成了454.6公里至5991.2公里的4条时频链路。使用GBM（Geo Forschung Zentrum（GFZ）提供的精确卫星轨道和时钟偏差产品）、WUM（表示精确卫星轨道和时钟偏差产品）比较和评估Galileo多频PPP的定位和时频传输性能武汉大学（WHU）提供的产品）和GRG（表示精密卫星轨道和时钟偏差产品，由国家空间研究中心（CNES）提供）精密产品。结果表明，DF、TF、QF和FF PPP模型的性能基本一致，大部分链路的频率稳定度可以达到10以下 WUM（武汉大学提供的精密卫星轨道和钟差产品）和GRG（国家空间研究中心（CNES）提供的精密卫星轨道和钟差产品）精密产品。结果表明，DF、TF、QF和FF PPP模型的性能基本一致，大部分链路的频率稳定度可以达到10以下 WUM（武汉大学提供的精密卫星轨道和钟差产品）和GRG（国家空间研究中心（CNES）提供的精密卫星轨道和钟差产品）精密产品。结果表明，DF、TF、QF和FF PPP模型的性能基本一致，大部分链路的频率稳定度可以达到10以下^-16级在 120,000 s，位置和平均频率稳定性（120,000 s）的平均三维（3D）均方根（RMS）分别可以达到 1.82 cm 和 1.18 × 10 ^-15。各型号3D RMS差异在0.17 cm以内，各型号频率稳定性（120,000 s）差异在0.08 × 10 ^-15以内。使用 GRG 精密产品，求解性能略优于 GBM 或 WUM 精密产品，使用 WUM 和 GRG 精密产品获得的平均 3D RMS 值分别为 1.85 cm 和 1.77 cm，平均频率稳定性在120,000 s 可以分别达到1.13 × 10 ^-15和1.06 × 10 ^-15。