Abstract
Precise point positioning (PPP) can currently achieve time transfer to a precision of one hundred picoseconds. However, the long convergence time is the main drawback of this popular time and frequency transfer method. It is well known that the convergence of position and receiver clock offset parameters in PPP solution is related to the satellite geometry, in which the receiver clock offset is the key parameter in time and frequency transfer and its performance could be reflected by the time dilution of precision (TDOP). This study applies tropospheric augmentation to accelerate PPP initialization and improve PPP frequency transfer performance during the convergence period. With the tropospheric augmentation applied to BDS-3 PPP, the convergence speed of receiver clock offset has been greatly improved when there are few visible satellites. Since GPS and BDS-3/GPS combined PPP, the satellite geometry and TDOP are better than that of BDS-3, the improvement in convergence speed is limited correspondingly. In addition, due to a more stable receiver clock offset estimated with the tropospheric information constraints, the short-term stability of frequency transfer during the convergence period has been greatly improved for GPS, BDS-3 and BDS-3/GPS combined PPP. For the two time links selected in this study, the short-term stability has been improved by more than 60, 45 and 40% in BDS-3, GPS and BDS-3/GPS combined PPP frequency transfer, respectively. However, the contribution of tropospheric augmentation to PPP frequency transfer is no longer significant after convergence.
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Data Availability
GNSS data are provided by the EPN data center at ftp://epncb.oma.be/. The GBM precise orbit and clock products are released by the IGS products center at https://cddis.nasa.gov/archive. And the CNES real-time products can be downloaded at http://www.ppp-wizard.net/products/REAL_TIME/.
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Acknowledgements
The authors show great gratitude to EPN Central Bureau and IGS for providing GNSS data and products. Also, acknowledgments go to the reviewers and editors whose suggestions helped us to significantly improve the manuscript. This study is supported by the National Key Research and Development Plan (Grant Nos. 2021YFB3900703) and the National Nature Science Foundation of China (Grant Nos. 42004026)
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Appendix
Appendix
In order to verify the contribution of our methods to real-time clock comparison and frequency transfer in PPP solution, the real-time orbit and clock products released by CNES (Centre National d’Etudes Spatiales) are adopted in the following analysis. As described in the above results, the same stations and processing strategies are used for the tropospheric modeling and clock comparison in DOY 189, 2022. Compared with the ZTD obtained with real-time GPS PPP processing, the RMS of RTGP model at CEBR, ONSA and REDU are 0.84, 0.74 and 1.08 cm, respectively. Then two time slots (15:00–16:00 and 20:00–21:00) with fewer BDS-3 satellites are selected for the clock comparison and frequency transfer of T-link1 and T-link2, respectively.
As shown in Fig. 13, when the high-accuracy prior tropospheric information is used, the STD of clock comparison results for BDS-3 PPP during the convergence period has been reduced by 4.11 ns and 0.94 ns for T-link1 and T-link2, respectively. This shows that our method can improve the convergence speed of clock comparison in real-time PPP solution. Due to the better satellite geometry, GPS standard PPP shows better performance than BDS-3 standard PPP for clock comparison. After the tropospheric augmentation is applied, the STDs of clock comparison results using GPS PPP are improved by 0.02 and 0.38 ns for two time links, respectively. For the BDS-3/GPS PPP with tropospheric augmentation, the STD during the convergence period has been improved by 0.38 and 0.35 ns for T-link1 and T-link2, respectively.
Real-time clock comparison results of T-link1 (left column) and T-link2 (right column) with and without tropospheric augmentation
Due to the faster convergence speed and mitigation of fluctuation on the clock comparison results by using tropospheric augmentation, a great improvement has been achieved for BDS-3, GPS and BDS-3/GPS real-time PPP frequency transfer. As shown in Fig. 14, all of the MDEV at different averaging times have been significantly improved for the two time links. For the different averaging time on T-link1, the stability of BDS-3 frequency transfer has been improved by 45–92%, while the stability of GPS and BDS-3/GPS frequency transfer are improved by 16.9–56.9% and 16.1–68.7%, respectively. In terms of frequency stability on T-link2 results, the improvements in BDS-3 PPP range from 49.4 to 62.4%, and the improvements in GPS and BDS-3/GPS PPP are 22.6–68.2 and 6.9–58.3%, respectively.
MDEV of real-time frequency transfer of T-link1 (left column) and T-link2 (right column)
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Zhang, D., Shi, C., Zheng, F. et al. Rapid frequency transfer by BDS-3/GPS PPP with tropospheric augmentation. GPS Solut 27, 41 (2023). https://doi.org/10.1007/s10291-022-01376-3
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DOI: https://doi.org/10.1007/s10291-022-01376-3