Abstract
Precise satellite clock product is an important prerequisite to support the real-time precise positioning service. In this contribution, the multi-GNSS integer recovery clock (MIRC) model is developed to improve both the accuracy and efficiency of real-time clock estimates. In the proposed method, the undifferenced ambiguities of GPS, BDS, Galileo and GLONASS are fixed to integers, and thus the integer properties of the ambiguities are recovered and the accuracy of the clock estimates is also improved. In addition, benefiting from the removal of large quantities of ambiguity parameters, the computation time is greatly reduced which can guarantee the high processing efficiency of real-time clock estimates. Multi-GNSS observations from 151 globally distributed Multi-GNSS Experiment tracking stations are processed with the proposed MIRC model over a one-month period (DOY 240–270, 2018). Compared to the float satellite clocks, the precision (standard deviation, STD) of the real-time MIRC with respect to CODE 30 s final multi-GNSS satellite clock products was improved by 53.0% from 0.046 to 0.022 ns for GPS, 42.7% from 0.096 to 0.055 ns for BDS, 63.7% from 0.097 to 0.035 ns for Galileo and 33.9% from 0.153 to 0.101 ns for GLONASS, respectively. With the proposed method, the average computation time per epoch with multi-GNSS observations for 50-, 100- and 150-station networks was improved by 7.3%, 82.7% and 97.1% compared to that of standard float clock estimation. Multi-GNSS kinematic precise point positioning (PPP) ambiguity resolution was also performed with the derived real-time MIRC products. Compared to the float PPP solutions, the position accuracy of the multi-GNSS MIRC-based fixed solutions was improved by 77.2%, 49.7% and 52.7% from 24.2, 13.3 and 30.7 mm to 5.5, 6.7 and 14.5 mm for the east, north and up components, respectively.
Similar content being viewed by others
Data availability
The GNSS observations are available in the IGS repository, ftp://cddis.gsfc.nasa.gov/pub/gps/data. The precise orbits are provided by Center for Orbit Determination in Europe (CODE). The IGS weekly combined solutions are available in the IGS repository, ftp://cddis.gsfc.nasa.gov/pub/gps/products.
References
Bock H, Dach R, Jäggi A, Beutler G (2009) High-rate GPS clock corrections from CODE: support of 1 Hz applications. J Geod 83(11):1083–1094. https://doi.org/10.1007/s00190-009-0326-1
Boehm J, Niell A, Tregoning P et al (2006) Global Mapping Function (GMF): a new empirical mapping function based on numerical weather model data. Geophys Res Lett 33(7):L07304. https://doi.org/10.1029/2005gl025546
Chen H, Jiang W, Ge M, Wickert J, Schuh H (2014) Efficient high-rate satellite clock estimation for PPP ambiguity resolution using carrier-ranges. Sensors 14(1):22300–22312. https://doi.org/10.3390/s141222300
Collins P (2008) Isolating and estimating undifferenced GPS integer ambiguities. In: Proceedings of ION national technical meeting of the Institute of Navigation, San Diego, USA, 28–30 January, pp 720–732
Collins P, Bisnath S, Francois L, Héroux P (2010) Undifferenced GPS ambiguity resolution using the decoupled clock model and ambiguity datum fixing. Navigation 57(2):123–135
CSNO (2019) BeiDou navigation satellite system signal in space interface control document-open service signal B1I, version 3.0. China Satellite Navigation Office, Feb 2019. http://www.beidou.gov.cn/xt/gfxz/201902/P020190227593621142475.pdf
Dach R, Schaer S, Hugentobler U (2006) Combined multi-system GNSS analysis for time and frequency transfer. In: Proceedings of the European Frequency and Time Forum, pp 530–537
Dow JM, Neilan RE, Rizos C (2009) The international GNSS service in a changing landscape of global navigation satellite systems. J Geod 83(3–4):191–198. https://doi.org/10.1007/s00190-008-0300-3
Falcone M, Hahn J, Burger T (2017) Galileo. In: Teunissen PJG, Montenbruck O (eds) Springer hand-book of global navigation satellite systems. Springer, Berlin, pp 247–271
Fu W, Yang Y, Zhang Q, Huang G (2018) Real-time estimation of BDS/GPS high-rate satellite clock offsets using sequential least squares. Adv Space Res 62(2):477–487. https://doi.org/10.1016/j.asr.2018.04.025
Ge M, Gendt G, Dick G, Zhang FP (2005) Improving carrier-phase ambiguity resolution in global GPS network solutions. J Geod 79(1–3):103–110. https://doi.org/10.1007/s00190-005-0447-0
Ge M, Gendt G, Rothacher M, Shi C, Liu J (2008) Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations. J Geod 82(7):389–399. https://doi.org/10.1007/s00190-007-0187-4
Ge M, Chen J, Douša J, Gendt G, Wickert J (2012) A computationally efficient approach for estimating high-rate satellite clock corrections in realtime. GPS Solut 16(1):9–17. https://doi.org/10.1007/s10291-011-0206-z
Geng J, Bock Y (2016) GLONASS fractional-cycle bias estimation across inhomogeneous receivers for PPP ambiguity resolution. J Geod 90(4):379–396. https://doi.org/10.1007/s00190-015-0879-0
Geng J, Meng X, Dodson A, Teferle F (2010) Integer ambiguity resolution in precise point positioning: method comparison. J Geod 84(9):569–581. https://doi.org/10.1007/s00190-010-0399-x
Hadas T, Bosy J (2015) IGS RTS precise orbits and clocks verification and quality degradation over time. GPS Solut 19(1):93–105. https://doi.org/10.1007/s10291-014-0369-5
Hauschild A, Montenbruck O (2009) Kalman-filter-based GPS clock estimation for near real-time positioning. GPS Solut 13(3):173–182. https://doi.org/10.1007/s10291-008-0110-3
Kouba J (2009) A guide to using International GNSS Service (IGS) products. http://igscb.jpl.nasa.gov/igscb/resource/pubs/UsingIGSProductsVer21.pdf. Accessed 10 Dec 2017
Laurichesse D, Mercier F (2007) Integer ambiguity resolution on Undifferenced GPS phase measurements and its application to PPP. In: ION GNSS 20th international technical meeting of the satellite division, 25–28 September 2007, Fort Worth, TX, USA, pp 839–848
Laurichesse D, Mercier F, Berthias JP, Broca P, Cerri L (2009) Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP and satellite precise orbit determination. Navigation 56(2):135–149
Li X, Zhang X (2012) Improving the estimation of uncalibrated fractional phase offsets for PPP ambiguity resolution. Navigation 65(3):513–529. https://doi.org/10.1017/S0373463312000112
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(6):607–635. https://doi.org/10.1007/s00190-015-0802-8
Li X, Li X, Yuan Y, Zhang K, Zhang X, Wickert J (2018) Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo. J Geod 92(6):579–608. https://doi.org/10.1007/s00190-017-1081-3
Liu T, Zhang B, Yuan Y, Zha J, Zhao C (2019) An efficient undifferenced method for estimating multi-GNSS high-rate clock corrections with data streams in real time. J Geod. https://doi.org/10.1007/s00190-019-01255-9
Loyer S, Perosanz F, Mercier F, Capdeville H, Marty J (2012) Zero-difference GPS ambiguity resolution at CNES-CLS IGS analysis center. J Geod 86(11):991–1003. https://doi.org/10.1007/s00190-012-0559-2
Melbourne WG (1985) The case for ranging in GPS-based geodetic systems. In: Proceedings of the first international symposium on precise positioning with the global positioning system, Rockville, MD, USA, 15–19 April
Montenbruck O, Steigenberger P, Khachikyan R, Weber G, Langley RB, Mervart L, Hugentobler U (2014) IGS-MGEX: preparing the ground for multi-constellation GNSS science. Inside GNSS 9(1):42–49
Montenbruck O, Steigenberger P, Prange L, Deng Z, Zhao Q, Perosanz F, Romero I, Noll C, Sturze A, Weber G (2017) The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS)—achievements, prospects and challenges. Adv Space Res 59(7):1671–1697. https://doi.org/10.1016/j.asr.2017.01.011
Rebischung P, Schmid R (2016) IGS14/igs14.atx: a new framework for the IGS products. In: AGU fall meeting, San Francisco, CA
Rizos C, Montenbruck O, Weber R, Neilan R, Hugentobler U (2013) The IGS MGEX experiment as a milestone for a comprehensive multi-GNSS service. In: Proceedings of ION PNT 2013, Institute of Navigation, Honolulu, HI, pp 289–295
Saastamoinen J (1972) Contributions to the theory of atmospheric refraction. Bull Geod 105(1):279–298. https://doi.org/10.1007/BF02521844
Schaer S, Beutler G, Rothacher M, Brockmann E, Wiget A, Wild U (1999) The impact of the atmosphere and other systematic errors on permanent GPS networks. Presented at IAG Symp on Positioning, Birmingham, UK, 19–24 July, p 406
Wu JT, Wu SC, Hajj GA, Bertiger WI, Lichten SM (1993) Effects of antenna orientation on GPS carrier phase. Manuscr Geod 18(2):91–98
Wübbena G (1985) Software developments for geodetic positioning with GPS using TI-4100 code and carrier measurements. In: Proceedings of first international symposium on precise positioning with the global positioning system. U.S. Department of Commerce, Rockville, MD, pp 403–412
Zhang X, Li X, Guo F (2011) Satellite clock estimation at 1 Hz for realtime kinematic PPP applications. GPS Solut 15(4):315–324. https://doi.org/10.1007/s10291-010-0191-7
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(B3):5005–5017. https://doi.org/10.1029/96JB03860
Acknowledgements
We would like to express our gratitude to IGS MGEX for providing multi-GNSS data and products. This study is financially supported by the National Natural Science Foundation of China (Grant No. 41774030), the Hubei Province Natural Science Foundation of China (Grant No. 2018CFA081) and the National Youth Thousand Talents Program. In addition, the numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University.
Author information
Authors and Affiliations
Contributions
XL provided the initial idea and designed the experiments for this study; XL and YX wrote the manuscript; YY, JW, XL, KZ and JH analyzed the data and helped with the writing. All authors reviewed the manuscript.
Corresponding author
Rights and permissions
About this article
Cite this article
Li, X., Xiong, Y., Yuan, Y. et al. Real-time estimation of multi-GNSS integer recovery clock with undifferenced ambiguity resolution. J Geod 93, 2515–2528 (2019). https://doi.org/10.1007/s00190-019-01312-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00190-019-01312-3