Abstract
A time transfer model with Global Navigation Satellite System (GNSS) carrier phase using precise point positioning (PPP), integer PPP (IPPP), single-difference (SD) and integer SD (ISD) modes between two stations is studied. To overcome the difficulty of being unable to fix the SD ambiguity due to the influence of the uncalibrated phase delay (UPD) at the receivers, the SD ambiguity is resolved with the constraint of the fixed double-difference (DD) ambiguity among several stations and satellites. Here the SD and ISD time transfer algorithms are extended to Global Positioning System (GPS), BeiDou Navigation Satellite System (BDS), Galileo Navigation Satellite System (Galileo), and Global Navigation Satellite System (GLONASS). As an example, taking four long-baseline links between pairs of ground stations, BRUX–OPMT, BRUX–PTBB, BRUX–WTZR and BRUX–CEBR, the performances of the carrier-phase ISD, IPPP, SD, and the PPP time transfer of the GPS, BDS, Galileo, and GLONASS systems are compared and analyzed. The results show that the SD and PPP time transfer precisions are equivalent, and the performances of GPS and Galileo are better than those of BDS and GLONASS. With an ambiguity resolution, the frequency instability in time transfer can reach sub 10–16 level after 5 days. The positioning accuracies of fixed solutions are improved compared with float solutions, and the positioning accuracies of ISD are slightly better than that of IPPP. Although the short-term frequency stabilities of IPPP and ISD did not improve over PPP and SD, the long-term frequency stabilities of IPPP and ISD all improved roughly 15% on average. The ISD is suitable for short and middle-long baselines time transfer, while IPPP is suitable for ultra-long baseline time transfer. The time transfer model provided in this study could be applied to gravity potential determination.
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Data availability
The observation data from MGEX networks are available at https://gdc.cddis.eosdis.nasa.gov/gps/data/daily/. The precise orbit and clock products are available at https://gdc.cddis.eosdis.nasa.gov/gps/products/mgex/. The DCBs are provided at the http://ftp.gipp.org.cn/product/dcb/mgex/.
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Acknowledgements
The authors gratefully acknowledge IGS MGEX for providing GNSS data. We also acknowledge the GFZ and CNES/CLS for providing precise satellite orbit, clock bias, and WSB products. We would like to express our sincere thanks to the anonymous reviewers and D. Matsakis for their careful corrections, valuable comments, and suggestions, which greatly improved the manuscript. This study is supported by the National Natural Science Foundations of China (Nos. 41721003, 42030105, 41804012, 41974034, 41631072, 41874023), Space Station Project (2020) (No. 228), and the Natural Science Foundation of Hubei Province of China (No. 2019CFB611).
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Xu, W., Shen, W., Cai, C. et al. Comparison and evaluation of carrier phase PPP and single difference time transfer with multi-GNSS ambiguity resolution. GPS Solut 26, 58 (2022). https://doi.org/10.1007/s10291-022-01242-2
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DOI: https://doi.org/10.1007/s10291-022-01242-2