Abstract
As a basic service of global navigation satellite system (GNSS), the timing technique tends to be processed based on precise point positioning (PPP) with the advantages of convenience and high-precision combined. The increasing demand for real-time PPP promotes the development of real-time satellite clock estimation. In real-time satellite clock estimation, the phase white noise model is widely adopted. Nevertheless, the white noise may mask the short-term characteristic of satellite atomic clocks, thus affecting the performance of the timing service. Therefore, we developed a clock model to characterize atomic clocks for GPS, GLONASS, BDS, and Galileo satellites based on Hadamard deviation analysis of 90-week multi-GNSS final clock products generated from GeoForschungsZentrum (GFZ). The results suggest that GPS Block IIF/III, BDS-3, and Galileo clocks have relatively outstanding frequency stabilities. And for the product of these satellite clocks, the simulated real-time clock estimation indicates that the clock model can provide better stabilities than the white noise model and even GFZ final products. Moreover, the clock model can provide a short-term prediction service during the period of data interruption and accelerate the convergence of clock offsets once the data recovered in real-time applications. Finally, PPP one-way timing was performed with five MGEX stations linked with external time sources. When employing the clock products with the clock model, the average improvement rates in stabilities over intervals from 30 to 10,260 s are 59.8%, 68.2%, 74.7%, and 66.6% for GPS, GLONASS, BDS-3, and Galileo PPP one-way timing, respectively, in comparison with that of the white noise model.
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Data availability
The multi-GNSS datasets analyzed during the current study are available from ftp://igs.gnsswhu.cn/.
References
Agrotis L, Schönemann E, Enderle W, et al (2017) The IGS Real Time Service. In: GNSS 2017—DVW-Seminar Kompetenz für die Zukunft. Potsdam
Allan DW (1987) Time and frequency (time-domain) characterization, estimation, and prediction of precision clocks and oscillators. IEEE Trans Ultrason Ferroelect,freq Contr 34:647–654. https://doi.org/10.1109/T-UFFC.1987.26997
Allan DW, Weiss MA (1980) Accurate time and frequency transfer during common-view of a GPS satellite. In: 34th Annual symposium on frequency control. IEEE, pp 334–346
Beard R, Senior K (2017) Clocks. In: Teunissen PJG, Montenbruck O (eds) Springer Handbook of global navigation satellite systems. Springer, Cham, pp 121–164
Bock H, Dach R, Yoon Y, Montenbruck O (2009) GPS clock correction estimation for near real-time orbit determination applications. Aerosp Sci Technol 13:415–422. https://doi.org/10.1016/j.ast.2009.08.003
Cerretto G, Tavella P, Lahaye F, et al (2011) PPP using NRCan ultra rapid products (EMU): near real-time comparison and monitoring of time scales generated in time and frequency laboratories. In: 2011 Joint conference of the IEEE international frequency control and the European frequency and time forum (FCS) proceedings. IEEE, San Francisco, pp 1–6
Dai X, Gong X, Li C et al (2022) Real-time precise orbit and clock estimation of multi-GNSS satellites with undifferenced ambiguity resolution. J Geod 96:73. https://doi.org/10.1007/s00190-022-01664-3
Defraigne P (2017) GNSS time and frequency transfer. In: Teunissen PJG, Montenbruck O (eds) Springer handbook of global navigation satellite systems. Springer, Cham, pp 1187–1206
Defraigne P, Aerts W, Pottiaux E (2015) Monitoring of UTC(k)’s using PPP and IGS real-time products. GPS Solut 19:165–172. https://doi.org/10.1007/s10291-014-0377-5
Gong X, Gu S, Lou Y et al (2018) An efficient solution of real-time data processing for multi-GNSS network. J Geod 92:797–809. https://doi.org/10.1007/s00190-017-1095-x
Gong X, Zheng F, Gu S et al (2022) The long-term characteristics of GNSS signal distortion biases and their empirical corrections. GPS Solut 26:52. https://doi.org/10.1007/s10291-022-01238-y
Gu S, Shi C, Lou Y, Liu J (2015) Ionospheric effects in uncalibrated phase delay estimation and ambiguity-fixed PPP based on raw observable model. J Geod 89:447–457. https://doi.org/10.1007/s00190-015-0789-1
Gu S, Dai C, Fang W et al (2021) Multi-GNSS PPP/INS tightly coupled integration with atmospheric augmentation and its application in urban vehicle navigation. J Geod 95:64. https://doi.org/10.1007/s00190-021-01514-8
Guo J, Xu X, Zhao Q, Liu J (2016) Precise orbit determination for quad-constellation satellites at Wuhan University: strategy, result validation, and comparison. J Geod 90:143–159. https://doi.org/10.1007/s00190-015-0862-9
Guo W, Song W, Niu X et al (2019) Foundation and performance evaluation of real-time GNSS high-precision one-way timing system. GPS Solut 23:23. https://doi.org/10.1007/s10291-018-0811-1
Guo W, Zuo H, Mao F et al (2022) On the satellite clock datum stability of RT-PPP product and its application in one-way timing and time synchronization. J Geod 96:52. https://doi.org/10.1007/s00190-022-01638-5
Hauschild A, Montenbruck O (2009) Kalman-filter-based GPS clock estimation for near real-time positioning. GPS Solut 13:173–182. https://doi.org/10.1007/s10291-008-0110-3
Hutsell ST (1995) Relating the Hadamard variance to MCS kalman filter clock estimation. In: Proceedings of the 27th annual precise time and time interval systems and applications meeting. San Diego, pp 291–302
Hutsell ST, Reid WG, Mobbs HS (1996) Operational use of the hadamard variance in GPS. In: 28th Annual precise time and time interval (PTTI) systems and applications meeting. Reston, USA
Kouba J, Héroux P (2001) Precise point positioning using IGS orbit and clock products. GPS Solut 5:12–28. https://doi.org/10.1007/PL00012883
Lou Y, Gong X, Gu S et al (2017) Assessment of code bias variations of BDS triple-frequency signals and their impacts on ambiguity resolution for long baselines. GPS Solut 21:177–186. https://doi.org/10.1007/s10291-016-0514-4
Luo X, Gu S, Lou Y et al (2020) Amplitude scintillation index derived from C/N0 measurements released by common geodetic GNSS receivers operating at 1 Hz. J Geod 94:27. https://doi.org/10.1007/s00190-020-01359-7
Montenbruck O, Hugentobler U, Dach R et al (2012) Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite. GPS Solut 16:303–313. https://doi.org/10.1007/s10291-011-0232-x
Montenbruck O, Hauschild A, Häberling S et al (2017) High-rate clock variations of the Galileo IOV-1/2 satellites and their impact on carrier tracking by geodetic receivers. GPS Solut 21:43–52. https://doi.org/10.1007/s10291-015-0503-z
Orgiazzi D, Tavella P, Lahaye F (2005) Experimental assessment of the time transfer capability of precise point positioning (PPP). In: Proceedings of the 2005 IEEE international frequency control symposium and exposition, 2005. IEEE, Vancouver, pp 337–345
Petit G, Jiang Z (2008) GPS all in view time transfer for TAI computation. Metrologia 45:35–45. https://doi.org/10.1088/0026-1394/45/1/006
Ren Z, Gong H, Lyu D et al (2023) Time transfer with BDS-3 signals: CV, PPP and IPPP. Meas Sci Technol 34:045007. https://doi.org/10.1088/1361-6501/acaf96
Riley WJ (2008) Handbook of frequency stability analysis. National Institute of Standards and Technology, Gaithersburg
Senior KL (2012) International GNSS Service technical report 2011—Report of the IGS working group on clock products. IGS
Senior K, Koppang P, Ray J (2003) Developing an IGS time scale. IEEE Trans Ultrason Ferroelectr Freq Control 50:585–593. https://doi.org/10.1109/TUFFC.2003.1209545
Senior KL, Ray JR, Beard RL (2008) Characterization of periodic variations in the GPS satellite clocks. GPS Solut 12:211–225. https://doi.org/10.1007/s10291-008-0089-9
Shi C, Guo S, Gu S et al (2019) Multi-GNSS satellite clock estimation constrained with oscillator noise model in the existence of data discontinuity. J Geod 93:515–528. https://doi.org/10.1007/s00190-018-1178-3
Stein SR, Filler RL (1988) Kalman filter analysis for real time applications of clocks and oscillators. In: Proceedings of the 42nd annual frequency control symposium, 1988. IEEE, Baltimore, pp 447–452
van Bree RJP, Tiberius CCJM (2012) Real-time single-frequency precise point positioning: accuracy assessment. GPS Solut 16:259–266. https://doi.org/10.1007/s10291-011-0228-6
Vannicola F, Beard R, White J, et al (2010) GPS block IIF atomic frequency standard analysis. pp 181–196
Verhasselt K, Defraigne P (2019) Multi-GNSS time transfer based on the CGGTTS. Metrologia 56:065003. https://doi.org/10.1088/1681-7575/ab3ed7
Yang X, Gu S, Gong X et al (2019) Regional BDS satellite clock estimation with triple-frequency ambiguity resolution based on undifferenced observation. GPS Solut 23:33. https://doi.org/10.1007/s10291-019-0828-0
Zhang Z, Lou Y, Zheng F, Gu S (2021) ON GLONASS pseudo-range inter-frequency bias solution with ionospheric delay modeling and the undifferenced uncombined PPP. J Geod 95:32. https://doi.org/10.1007/s00190-021-01480-1
Zheng F, Lou Y, Gu S et al (2018) Modeling tropospheric wet delays with national GNSS reference network in China for BeiDou precise point positioning. J Geod 92:545–560. https://doi.org/10.1007/s00190-017-1080-4
Zumberge JF, Heflin MB, Jefferson DC et al (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res Solid Earth 102:5005–5017. https://doi.org/10.1029/96JB03860
Acknowledgements
Thanks for the data support of MGEX. This study is partially supported by the National Key Research and Development Plan (No. 2021YFB3900703), the National Natural Science Foundation of China (42274023, 41904016) and Young Elite Scientists Sponsorship Program by CAST (No. YESS20210184).
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GS and MF designed and performed this research; MF and GX analyzed data; MF wrote the paper; all authors provided critical feedback and reviewed the paper.
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Gu, S., Mao, F., Gong, X. et al. Improved short-term stability for real-time GNSS satellite clock estimation with clock model. J Geod 97, 61 (2023). https://doi.org/10.1007/s00190-023-01747-9
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DOI: https://doi.org/10.1007/s00190-023-01747-9