Journal of Geodesy

, Volume 93, Issue 7, pp 1011–1024 | Cite as

PPP-RTK based on undifferenced and uncombined observations: theoretical and practical aspects

  • Baocheng ZhangEmail author
  • Yongchang Chen
  • Yunbin Yuan
Original Article


A synthesis of two prevailing global navigation satellite system positioning technologies, namely the precise point positioning and the network-based real-time kinematic, results in the emergence of the PPP-RTK, enabling single-receiver users to achieve high positioning accuracy with reasonable timeliness through integer ambiguity resolution. The realization of PPP-RTK needs to accomplish two sequential tasks. The first task is to determine a class of corrections including, among others, the satellite phase biases (SPBs) at the network level. With these corrections, the second task, then, is to solve for the ambiguity-fixed, absolute position at the user level. In this contribution, we revisit three variants (geometry-free, geometry-fixed and geometry-plus-satellite-clock-fixed) of the undifferenced and uncombined PPP-RTK network model and then point out their implications for practical use. We also carry out a case study using multi-day, dual-frequency global positioning system data from the crustal movement observation network of China stations, aiming to figure out what are the most appropriate linear combinations of the SPBs to be transmitted to the users from the viewpoint of decorrelation, and to assess the static and kinematic positioning performance.


Global navigation satellite system (GNSS) PPP-RTK Integer ambiguity resolution (IAR) S-system theory Satellite phase bias (SPB) Crustal movement observation network of China (CMONOC) 



This work was partially funded by the National Natural Science Foundation of China (Nos. 41604031, 41774042, 41621091). The first author is supported by the CAS Pioneer Hundred Talents Program. The third author acknowledges LU JIAXI International team program supported by the K.C. Wong Education Foundation and CAS. The GPS data used in this work are kindly provided by Crustal Movement Observation Network of China.


  1. Arnold D et al (2015) CODE’s new solar radiation pressure model for GNSS orbit determination. J Geod 89(8):775–791CrossRefGoogle Scholar
  2. Bertiger W, Desai SD, Haines B, Harvey N, Moore AW, Owen S, Weiss JP (2010) Single receiver phase ambiguity resolution with GPS data. J Geod 84(5):327–337CrossRefGoogle Scholar
  3. Collins P, Bisnath S, Lahaye F, Héroux P (2010) Undifferenced GPS ambiguity resolution using the decoupled clock model and ambiguity datum fixing. Navigation 57(2):123–135CrossRefGoogle Scholar
  4. 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):191–198CrossRefGoogle Scholar
  5. Gao Y, Shen X (2002) A new method for carrier-phase-based precise point positioning. Navigation 49(2):109–116CrossRefGoogle Scholar
  6. Ge M, Gendt G, Ma Rothacher, Shi C, Liu J (2008) Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations. J Geod 82(7):389–399CrossRefGoogle Scholar
  7. Geng J, Teferle FN, Meng X, Dodson A (2011) Towards PPP-RTK: ambiguity resolution in real-time precise point positioning. Adv Space Res 47(10):1664–1673CrossRefGoogle Scholar
  8. 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):579–589CrossRefGoogle Scholar
  9. Hofmann-Wellenhof B, Lichtenegger H, Wasle E (2008) GNSS–Global Navigation Satellite Systems: GPS, GLONASS, Galileo & more. Springer, New YorkGoogle Scholar
  10. Khodabandeh A, Teunissen P (2014) Array-based satellite phase bias sensing: theory and GPS/BeiDou/QZSS results. Meas Sci Technol 25(9):095801CrossRefGoogle Scholar
  11. Khodabandeh A, Teunissen P (2015) An analytical study of PPP-RTK corrections: precision, correlation and user-impact. J Geod 89(11):1109–1132CrossRefGoogle Scholar
  12. Khodabandeh A, Teunissen P (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):837–851CrossRefGoogle Scholar
  13. Kouba J, Heroux P (2001) Precise point positioning using IGS orbit and clock products. GPS Solut 5(2):12–28CrossRefGoogle Scholar
  14. Landau H, Vollath U, Chen X (2003) Virtual reference stations versus broadcast solutions in network RTK: advantages and limitations. The European GNSS 2003, GrazGoogle Scholar
  15. 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):135–149CrossRefGoogle Scholar
  16. Leick A, Rapoport L, Tatarnikov D (2015) GPS satellite surveying. Wiley, HobokenCrossRefGoogle Scholar
  17. Li B (2016) Stochastic modeling of triple-frequency BeiDou signals: estimation, assessment and impact analysis. J Geod 90(7):593–610CrossRefGoogle Scholar
  18. Li B, Shen Y, Xu P (2008) Assessment of stochastic models for GPS measurements with different types of receivers. Chin Sci Bull 53(20):3219–3225Google Scholar
  19. Li X, Zhang X, Ge M (2011) Regional reference network augmented precise point positioning for instantaneous ambiguity resolution. J Geod 85(3):151–158CrossRefGoogle Scholar
  20. Mervart L, Lukes Z, Rocken C, Iwabuchi T (2008) Precise point positioning with ambiguity resolution in realtime. In: Proceedings of ION GNSS 2008, 16–19 Sept 2008, Savannah, GA, USA, pp 397–405Google Scholar
  21. Montenbruck O, Schmid R, Mercier F et al (2015) GNSS satellite geometry and attitude models. Adv Space Res 56(5):1015–1029CrossRefGoogle Scholar
  22. Nadarajah N, Khodabandeh A, Wang K, Choudhury M, Teunissen PJ (2018) Multi-GNSS PPP-RTK: from large-to small-scale networks. Sensors 18(4):1078CrossRefGoogle Scholar
  23. Nardo A et al (2015) Experiences with trimble CenterPoint RTX with fast convergence. Trimble TerraSat GmbH, Haringstrasse 19:85635Google Scholar
  24. Odijk D, Teunissen PJ, Zhang B (2012) Single-frequency integer ambiguity resolution enabled GPS precise point positioning. J Surv Eng 138(4):193–202CrossRefGoogle Scholar
  25. Odijk D, Khodabandeh A, Nadarajah N, Choudhury M, Zhang B, Li W, Teunissen PJ (2016a) PPP-RTK by means of S-system theory: Australian network and user demonstration. J Spat Sci 62(1):3–27CrossRefGoogle Scholar
  26. Odijk D, Zhang B, Khodabandeh A, Odolinski R, Teunissen PJ (2016b) 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):15–44CrossRefGoogle Scholar
  27. Rizos C (2002) Network RTK research and implementation: a geodetic perspective. J Glob Position Syst 1(2):144–150CrossRefGoogle Scholar
  28. Schönemann E, Becker M, Springer T (2011) A new approach for GNSS analysis in a multi-GNSS and multi-signal environment. J Geod Sci 1(3):204–214Google Scholar
  29. Springer T, Hugentobler U (2001) IGS ultra rapid products for (near-) real-time applications. Phys Chem Earth Part A 26(6–8):623–628CrossRefGoogle Scholar
  30. Teferle F, Orliac E, Bingley R (2007) An assessment of Bernese GPS software precise point positioning using IGS final products for global site velocities. GPS Solut 11(3):205–213CrossRefGoogle Scholar
  31. Teunissen P (1985) Generalized inverses, adjustment, the datum problem and S-transformations. In: Grafarend EW, Sanso F (eds) Optimization of geodetic networks. Springer, Berlin, pp 11–55CrossRefGoogle Scholar
  32. Teunissen P (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70(1–2):65–82CrossRefGoogle Scholar
  33. Teunissen P (1997) On the GPS widelane and its decorrelating property. J Geod 71(9):577–587CrossRefGoogle Scholar
  34. Teunissen P (2018) Distributional theory for the DIA method. J Geod 92(1):59–80CrossRefGoogle Scholar
  35. Teunissen P, Khodabandeh A (2015) Review and principles of PPP-RTK methods. J Geod 89(3):217–240CrossRefGoogle Scholar
  36. Teunissen P, Montenbruck O (eds) (2017) Springer handbook of global navigation satellite systems. Springer, BerlinGoogle Scholar
  37. Teunissen P, Verhagen S (2009) The GNSS ambiguity ratio-test revisited: a better way of using it. Surv Rev 41(312):138–151CrossRefGoogle Scholar
  38. Teunissen P, Odijk D, Zhang B (2010) PPP-RTK: results of CORS network-based PPP with integer ambiguity resolution. J Aeronaut Astronaut Aviat Ser A 42(4):223–230Google Scholar
  39. Teunissen P, Odolinski R, Odijk D (2014) Instantaneous BeiDou+GPS RTK positioning with high cut-off elevation angles. J Geod 88(4):335–350CrossRefGoogle Scholar
  40. Wielgosz P, Kashani I, Grejner-Brzezinska D (2005) Analysis of long-range network RTK during a severe ionospheric storm. J Geod 79(9):524–531CrossRefGoogle Scholar
  41. Wubbena G, Schmitz M, Bagg A (2005) PPP-RTK: precise point positioning using state-space representation in RTK networks. In: Proceedings of ION GNSS, pp 13–16Google Scholar
  42. Zhang B, Teunissen P (2016) Zero-baseline analysis of GPS/BeiDou/Galileo between-receiver differential code biases (BR-DCBs): time-wise retrieval and preliminary characterization. Navigation 63(2):181–191CrossRefGoogle Scholar
  43. Zhang B, Teunissen P, Odijk D (2011) A novel un-differenced PPP-RTK concept. J Navig 64(S1):S180–S191CrossRefGoogle Scholar
  44. Zhang H, Yuan Y, Li W, Zhang B, Ou J (2018) A grid-based tropospheric product for China using a GNSS network. J Geod 92(7):765–777CrossRefGoogle Scholar
  45. Zumberge J, Heflin M, Jefferson D, Watkins M, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res Solid Earth 102(B3):5005–5017CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Geodesy and Earth’s Dynamics, Institute of Geodesy and GeophysicsChinese Academy of SciencesWuhanChina

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