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Speeding up PPP ambiguity resolution using triple-frequency GPS/BeiDou/Galileo/QZSS data

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Abstract

Precise point positioning (PPP) has been suffering from slow convergences to ambiguity-fixed solutions. It is expected that this situation can be relieved or even resolved using triple-frequency GNSS data. We therefore attempt an approach where uncombined triple-frequency GPS/BeiDou/Galileo/QZSS (Quasi-zenith satellite system) data are injected into PPP, whereas their raw ambiguities are mapped into the extra-wide-lane, wide-lane and narrow-lane combinations for integer-cycle resolution at a single station (i.e., PPP-AR). Once both extra-wide-lane and wide-lane ambiguities are fixed to integers, the resulting unambiguous (extra-)wide-lane carrier-phase can usually outweigh the raw pseudorange to improve the convergence of positions and narrow-lane ambiguities. We used 31 days of triple-frequency multi-GNSS data from 76 stations over the Asia Oceania regions and divided them into hourly pieces for real-time PPP-AR. We found that the positioning accuracy for the first 10 min of epochs could be improved by about 50% from 0.23, 0.18 and 0.43 m to 0.12, 0.08 and 0.27 m for the east, north and up components, respectively, once wide-lane ambiguity fixing was achieved for triple-frequency PPP. Consequently, 48% of PPP solutions could be initialized successfully with narrow-lane ambiguities resolved within 2 min, in contrast to only 26% for dual-frequency PPP. On average, 6 min of epochs were required to achieve triple-frequency PPP-AR, whereas 9 min for its dual-frequency counterpart. Of particular note, the more satellites contribute to triple-frequency PPP-AR, the faster the initializations will be; as a typical example, the mean initialization time declined to 3 min in case of 20–21 satellites. We therefore envision that only a few minutes of epochs will suffice to reliably initialize real-time PPP once all GPS, BeiDou, Galileo and QZSS constellations emitting triple-frequency signals are complete in the near future.

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References

  • Banville S, Collins P, Zhang W, Langley R (2014) Global and regional ionospheric corrections for faster PPP convergence. Navigation 61(2):115–124

    Article  Google Scholar 

  • Bisnath S, Gao Y (2009) Current state of precise point positioning and future prospects and limitations. In: Sideris MG (ed) Observing our changing Earth. Springer, Berlin, pp 615–623

    Google Scholar 

  • Boehm J, Niell AE, Tregoning P, Schuh H (2006) The Global Mapping Function (GMF): a new empirical mapping function based on data from numerical weather model data. Geophys Res Lett 33:L07304. https://doi.org/10.1029/2005GL025546

    Article  Google Scholar 

  • Dong D, Bock Y (1989) Global positioning system network analysis with phase ambiguity resolution applied to crustal deformation studies in California. J Geophys Res 94(B4):3949–3966

    Article  Google Scholar 

  • Euler HJ, Schaffrin B (1990) On a measure of the discernibility between different ambiguity solutions in the static-kinematic GPS mode. In: Schwarz KP, Lachapelle G (eds) Kinematic systems in geodesy, surveying and remote sensing. Springer, New York, pp 285–295

    Google Scholar 

  • Feng Y (2008) GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals. J Geod 82(12):847–862

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Geng J, Bock Y (2013) Triple-frequency GPS precise point positioning with rapid ambiguity resolution. J Geod 87(5):449–460

    Article  Google Scholar 

  • Geng J, Shi C (2017) Rapid initialization of real-time PPP by resolving undifferenced GPS and GLONASS ambiguities simultaneously. J Geod 91(4):361–374

    Article  Google Scholar 

  • Geng J, Meng X, Dodson AH, Ge M, Teferle FN (2010) Rapid re-convergences to ambiguity-fixed solutions in precise point positioning. J Geod 84(12):705–714

    Article  Google Scholar 

  • Geng J, Teferle FN, Meng X, Dodson AH (2011) Towards PPP-RTK: ambiguity resolution in real-time precise point positioning. Adv Space Res 47(10):1664–1673

    Article  Google Scholar 

  • Geng J, Shi C, Ge M, Dodson AH, Lou Y, Zhao Q, Liu J (2012) Improving the estimation of fractional-cycle biases for ambiguity resolution in precise point positioning. J Geod 86(8):579–589

    Article  Google Scholar 

  • Geng J, Guo J, Chang H, Li X (2018a) Towards global instantaneous decimeter-level positioning using tightly-coupled multi-constellation and multi-frequency GNSS. J Geod. https://doi.org/10.1007/s00190-018-1219-y

    Article  Google Scholar 

  • Geng J, Li X, Zhao Q, Li G (2018b) Inter-system PPP ambiguity resolution between GPS and BeiDou for rapid initialization. J Geod 93(3):383–398. https://doi.org/10.1007/s00190-018-1167-6

    Article  Google Scholar 

  • Geng J, Chen X, Pan Y, Zhao Q (2019) A modified phase clock/bias model to improve PPP ambiguity resolution at Wuhan University. J Geod 93(10):2053–2067

    Article  Google Scholar 

  • Gu S, Lou Y, Shi C, Liu J (2015) BeiDou phase bias estimation and its application in precise point positioning with triple-frequency observable. J Geod 89(10):979–992

    Article  Google Scholar 

  • Guo J, Geng J (2018) GPS satellite clock determination in case of inter-frequency clock biases for triple-frequency precise point positioning. J Geod 92(10):1133–1142

    Article  Google Scholar 

  • Guo F, Zhang X, Wang J, Ren X (2016) Modeling and assessment of triple-frequency BDS precise point positioning. J Geod 90(11):1223–1235

    Article  Google Scholar 

  • Khodabandeh A, Teunissen PJG (2016) PPP-RTK and inter-system biases: the ISB look-up table as a means to support multi-system PPP-RTK. J Geod 90(9):837–851

    Article  Google Scholar 

  • Li B, Verhagen S, Teunissen PJG (2014) Robustness of GNSS integer ambiguity resolution in the presence of atmospheric biases. GPS Solut 18(2):283–296

    Article  Google Scholar 

  • Li P, Zhang X, Guo F (2017) Ambiguity resolved precise point positioning with GPS and BeiDou. J Geod 91(1):25–40

    Article  Google Scholar 

  • Li P, Zhang X, Ge M, Schuh H (2018) Three-frequency BDS precise point positioning ambiguity resolution based on raw observables. J Geod. https://doi.org/10.1007/s00190-018-1125-3

    Article  Google Scholar 

  • Liu Y, Lou Y, Ye S, Zhang R, Song W, Zhang X, Li Q (2017) Assessment of PPP integer ambiguity resolution using GPS, GLONASS and BeiDou (IGSO, MEO) constellations. GPS Solut 21(4):1647–1659

    Article  Google Scholar 

  • Montenbruck O, Hugentobler U, Dach R, Steigenberger P, Hauschild A (2011) Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite. GPS Solut 16(3):303–313

    Article  Google Scholar 

  • Nadarajah N, Khodabandeh A, Wang KMC, Teunissen PJG (2018) Multi-GNSS PPP-RTK: from large- to small-scale networks. Sensors 18(4):1078

    Article  Google Scholar 

  • Odijk D, Zhang B, Khodabandeh A, Odolinski R, Teunissen PJG (2016) On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of S-system theory. J Geod 90(1):15–44

    Article  Google Scholar 

  • Saastamoinen J (1973) Contribution to the theory of atmospheric refraction: refraction corrections in satellite geodesy. Bull Geod 107(1):13–34

    Article  Google Scholar 

  • Schaffrin B, Bock Y (1988) A unified scheme for processing GPS dual-band phase observations. Bulletin Géodésique 62(2):142–160

    Article  Google Scholar 

  • Schmid R, Dach R, Collilieux X, Jäggi A, Schmitz M, Dilssner F (2016) Absolute IGS antenna phase center model igs08.atx: status and potential improvements. J Geod 90(4):343–364

    Article  Google Scholar 

  • Tang W, Deng C, Shi C, Liu J (2014) Triple-frequency carrier ambiguity resolution for BeiDou navigation satellite system. GPS Solut 18(3):335–344

    Article  Google Scholar 

  • Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70(1–2):65–82

    Article  Google Scholar 

  • Teunissen PJG (1997a) The geometry-free GPS ambiguity search space with a weighted ionosphere. J Geod 71(6):370–383

    Article  Google Scholar 

  • Teunissen PJG (1997b) On the GPS widelane and its decorrelating property. J Geod 71(9):577–587

    Article  Google Scholar 

  • Teunissen PJG (1999) An optimality property of the integer least-squares estimator. J Geod 73(11):587–593

    Article  Google Scholar 

  • Teunissen PJG, Khodabandeh A (2015) Review and principles of PPP-RTK methods. J Geod 89(3):217–240

    Article  Google Scholar 

  • Teunissen P, Joosten P, Tiberius C (1999) Geometry-free ambiguity success rates in case of partial fixing. In: Proceedings of the 1999 National Technical Meeting of The Institute of Navigation, San Diego, CA, pp 201–207

  • Vollath U, Birnbach S, Landau H, Fraile-Ordońez JM, Martín-Neira M (1999) Analysis of three-carrier ambiguity resolution technique for precise relative positioning in GNSS-2. J Inst Navig 46(1):13–23

    Article  Google Scholar 

  • Wübbena G, Schmitz M, Bagge A (2005) PPP-RTK: Precise point positioning using state-space representation in RTK networks. In: Proceedings of ION GNSS 18th International Technical Meeting of the Satellite Division, Long Beach, US, pp 2584–2594

  • 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

    Article  Google Scholar 

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Acknowledgements

This study is funded by National Key R&D Program of China (2018YFC1503601 and 2016YFB0501802) and National Science Foundation of China (41674033). We thank IGS (International GNSS Service), ARGN (Australian Regional GNSS Network) for the multi-GNSS data and the high-quality satellite products. The computation work was finished on the high-performance computing facility of Wuhan University.

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Authors and Affiliations

  1. GNSS Research Center, Wuhan University, Wuhan, China

    Jianghui Geng, Jiang Guo & Kefu Gao

  2. Collaborative Innovation Center of Geospatial Technology, Wuhan, China

    Jianghui Geng, Jiang Guo & Kefu Gao

  3. Nottingham Geospatial Institute, University of Nottingham, Nottingham, UK

    Xiaolin Meng

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  1. Jianghui Geng
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  2. Jiang Guo
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  3. Xiaolin Meng
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  4. Kefu Gao
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Correspondence to Jianghui Geng.

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Geng, J., Guo, J., Meng, X. et al. Speeding up PPP ambiguity resolution using triple-frequency GPS/BeiDou/Galileo/QZSS data. J Geod 94, 6 (2020). https://doi.org/10.1007/s00190-019-01330-1

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