Abstract
The real-time service (RTS) of satellite clock offsets is one of the main routine tasks for real-time precise point positioning (PPP). The quadratic polynomial coefficients of the GPS satellite clock corrections in the International GNSS Service (IGS) RTS are updated every 5 s. This frequent updating of the satellite clock correction coefficients means that the quadratic polynomial adopted in IGS RTS is inadequate if a lack of connectivity necessitates extrapolation over minutes instead of seconds. An improved RTS, using a polynomial and harmonic-based function, is proposed to address this concern. Its functions are constructed based on the periodic variations in the GPS satellite clock corrections observed from the differences between the estimated satellite clock corrections and those of the broadcast ephemeris over one year. The eighth-order harmonic coefficients are updated in the improved RTS every 6 h. Extrapolation results show that the combined results of a quadratic polynomial plus an eighth-order harmonic-based function are better than those of a quadratic polynomial plus a fourth-order harmonic-based function. The 6 h extrapolation accuracy of the combined quadratic polynomial and eighth-order harmonic-based function reaches 0.81 ns and is significantly improved over that of the current IGS ultra-rapid products. Under good connectivity condition and eighth-order harmonic coefficients at 6 h intervals, which transmits linear polynomial coefficients at 1 min intervals, is better than the IGS RTS product, with a 5-day averaged root mean square of 0.10 ns. Although the update interval of the improved RTS is 12 times larger than that of the current IGS RTS, its 5-day static and kinematic PPP performances are better at all 55 IGS stations tested. Even if connectivity is interrupted for several minutes, the improved method can reach centimeter and even millimeter accuracy.
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Data availability
The experimental data used in this manuscript are all public data and can be downloaded from the IGS website (cddis.nasa.gov/archive/gps/products/).
References
Böse M, Heaton T (2010) Probabilistic prediction of rupture length, slip and seismic ground motions for an ongoing rupture: implications for early warning for large earthquakes: early warning for large earthquakes. Geophys J Int 183:1014–1030. https://doi.org/10.1111/j.1365-246X.2010.04774.x
Cai C, Gao Y, Pan L, Zhu J (2015) Precise point positioning with quad-constellations: GPS, BeiDou, GLONASS and Galileo. Adv Space Res 56:133–143. https://doi.org/10.1016/j.asr.2015.04.001
Chang G (2015) On least-squares solution to 3D similarity transformation problem under Gauss–Helmert model. J Geodesy 89(6):573–576. https://doi.org/10.1007/s00190-015-0799-z
Du Y, Wang J, Rizos C, El-Mowafy A (2021) Vulnerabilities and integrity of precise point positioning for intelligent transport systems: overview and analysis. Satell Navig 2:3. https://doi.org/10.1186/s43020-020-00034-8
El-Mowafy A, Deo M, Kubo N (2017) Maintaining real-time precise point positioning during outages of orbit and clock corrections. GPS Solut 21:937–947. https://doi.org/10.1007/s10291-016-0583-4
Elsobeiey M, Al-Harbi S (2016) Performance of real-time Precise Point Positioning using IGS real-time service. GPS Solut 20:565–571. https://doi.org/10.1007/s10291-015-0467-z
Hadas T, Bosy J (2015) IGS RTS precise orbits and clocks verification and quality degradation over time. GPS Solut 19:93–105. https://doi.org/10.1007/s10291-014-0369-5
Heo Y, Cho J, Heo MB (2010) Improving prediction accuracy of GPS satellite clocks with periodic variation behaviour. Meas Sci Technol 21:073001. https://doi.org/10.1088/0957-0233/21/7/073001
Huang G, Zhang Q, Xu G (2014) Real-time clock offset prediction with an improved model. GPS Solut 18:95–104. https://doi.org/10.1007/s10291-013-0313-0
Huang L, Zhu G, Liu L, Chen H, Jiang W (2021) A global grid model for the correction of the vertical zenith total delay based on a sliding window algorithm. GPS Solut 25(3):98. https://doi.org/10.1007/s10291-021-01138-7
Jin S, Komjathy A (2010) GNSS reflectometry and remote sensing: new objectives and results. Adv Space Res 46:111–117. https://doi.org/10.1016/j.asr.2010.01.014
Leick A, Rapoport L, Tatarnikov D (2015) GPS satellite surveying, 4th edn. Wiley, New York
Li H, Zhou X, Wu B (2013) Fast estimation and analysis of the inter-frequency clock bias for Block IIF satellites. GPS Solut 17:347–355. https://doi.org/10.1007/s10291-012-0283-7
Li X, Ge M, Dai X, Ren X, Fritsche M, Wickert J, Schuh H (2015) Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo. J Geod 89:607–635. https://doi.org/10.1007/s00190-015-0802-8
Li H, Li B, Lou L, Yang L, Wang J (2017) Impact of GPS differential code bias in dual- and triple-frequency positioning and satellite clock estimation. GPS Solut 21:897–903. https://doi.org/10.1007/s10291-016-0578-1
Li H, Liao X, Li B, Yang L (2018) Modeling of the GPS satellite clock error and its performance evaluation in precise point positioning. Adv Space Res 62:845–854. https://doi.org/10.1016/j.asr.2018.05.025
Li X, Chen X, Ge M, Schuh H (2019) Improving multi-GNSS ultra-rapid orbit determination for real-time precise point positioning. J Geod 93:45–64. https://doi.org/10.1007/s00190-018-1138-y
Malys S, Jensen P (1990) Geodetic point positioning with GPS carrier beat phase data from the CASA UNO experiment. Geophys Res Lett 17:651–654. https://doi.org/10.1029/GL017i005p00651
Montenbruck O et al (2017) The multi-GNSS experiment (MGEX) of the international GNSS service (IGS)—achievements, prospects and challenges. Adv Space Res 59:1671–1697. https://doi.org/10.1016/j.asr.2017.01.011
Nie Z, Gao Y, Wang Z, Ji S, Yang H (2018) An approach to GPS clock prediction for real-time PPP during outages of RTS stream. GPS Solut 22:14. https://doi.org/10.1007/s10291-017-0681-y
Panfilo G, Tavella P (2008) Atomic clock prediction based on stochastic differential equations. Metrologia 45:S108–S116. https://doi.org/10.1088/0026-1394/45/6/S16
Petit G, Luzum B (2010) IERS Conventions (2010). IERS technical note
Senior K, Ray J, Beard R (2008) Characterization of periodic variations in the GPS satellite clocks. GPS Solut 12:211–225. https://doi.org/10.1007/s10291-008-0089-9
Vigny C et al (2005) Insight into the 2004 Sumatra-Andaman earthquake from GPS measurements in southeast Asia. Nature 436:201–206. https://doi.org/10.1038/nature03937
Wang Y, Shen J (2020) Real-time integrity monitoring for a wide area precise positioning system. Satell Navig 1:24. https://doi.org/10.1186/s43020-020-00018-8
Wang B, Lou Y, Liu J, Zhao Q, Su X (2016) Analysis of BDS satellite clocks in orbit. GPS Solut 20:783–794. https://doi.org/10.1007/s10291-015-0488-7
Yan X, Li W, Yang Y, Pan X (2020) BDS satellite clock offset prediction based on a semiparametric adjustment model considering model errors. Satell Navig 1:11. https://doi.org/10.1186/s43020-019-0007-z
Ye Z, Li H, Wang S (2021) Characteristic analysis of the GNSS satellite clock. Adv Space Res 68:3314–3326. https://doi.org/10.1016/j.asr.2021.06.030
Zhang L, Yang H, Yao Y, Gao Y, Xu C (2019) A new datum jump detection and mitigation method of Real-Time Service (RTS) clock products. GPS Solut 23:67. https://doi.org/10.1007/s10291-019-0859-6
Zhao X, Ge Y, Ke F, Liu C, Li F (2020) Investigation of real-time kinematic multi-GNSS precise point positioning with the CNES products. Measurement 166:108231. https://doi.org/10.1016/j.measurement.2020.108231
Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res 102:5005–5017. https://doi.org/10.1029/96JB03860
Acknowledgements
This research was supported by the National Natural Science Foundation of China (NSFC) (Nos. 41974025 and 42174019), a Shanghai Industrial Collaborative Science and Technology Innovation Project (2021-cyxt2-kj10), a Shanghai Municipal Science and Technology Major Project (2021SHZDZX0100) and the Fundamental Research Funds for the Central Universities.
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Li, H., Li, X. & Gong, X. Improved method for the GPS high-precision real-time satellite clock error service. GPS Solut 26, 136 (2022). https://doi.org/10.1007/s10291-022-01327-y
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DOI: https://doi.org/10.1007/s10291-022-01327-y