Single-Frequency PPP-RTK: Theory and Experimental Results

  • Dennis OdijkEmail author
  • Peter J. G. Teunissen
  • Amir Khodabandeh
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 139)


Integer ambiguity resolution enabled Precise (cm-level) Point Positioning (PPP) is feasible if corrections from a GPS network of CORS stations are applied to the single-receiver phase and code data of a user. The concept of PPP-RTK requires a proper definition and quality of the PPP-user network corrections, which are satellite clocks, satellite phase biases and ionospheric delays interpolated to the approximate location of the user. The availability of the satellite phase bias corrections enables the user to carry out integer resolution of ambiguities that are double-differenced, i.e., relative to those of the pivot receiver in the network. The availability of the interpolated ionospheric corrections is not absolutely required, however PPP-RTK for single-frequency users would virtually be impossible without them. A proper handling of the network corrections implies that the PPP-user should take their uncertainty into account as well. In order to limit the amount of information to be transmitted to the user, in this contribution we provide a closed-form analytical expression for the variance matrix of the network corrections which a single-frequency user can apply in his processing. Experimental results of single-frequency PPP-RTK for both a high-grade geodetic receiver as well as a low-grade mass-market receiver demonstrate that although single-epoch integer ambiguity resolution is not possible, single-frequency ambiguity resolution enabled cm-level PPP is feasible based on an accumulation of less than 10 min of observations plus network corrections on average.


GPS PPP-RTK Single frequency Integer ambiguity resolution Closed-form variance matrix 



This work has been executed in the framework of the Positioning Program Project 1.01 of the Cooperative Research Centre for Spatial Information (CRC-SI2). Peter J.G. Teunissen is the recipient of an Australian Research Council (ARC) Federation Fellowship (project number FF0883188). The CORS network data in this study have been provided by the GPS Network Perth. All this support is gratefully acknowledged.


  1. van Bree RJP, Tiberius CCJM (2012) Real-time single-frequency precise point positioning: accuracy assessment. GPS Solut 16(2):259–266CrossRefGoogle Scholar
  2. Chen X, Allison T, Cao W, Ferguson K, Gruenig S, Gromez V, Kipka A, Koehler J, Landau H, Leandro R, Lu G, Stolz R, Talbot N (2011) Trimble RTX, an innovative new approach for network RTK. In: Proceedings of ION GNSS-2011, pp 2214–2219, Portland, OR, 19–23 September 2011Google Scholar
  3. Collins P, Lahaye F, Heroux P, Bisnath S (2008) Precise point positioning with ambiguity resolution using the decoupled clock model. In: Proceedings of ION GNSS-2008, pp 1315–1322, Savannah, GA, 16–19 September 2008Google Scholar
  4. Dow JM, Neilan RE, Rizos C (2009) The international GNSS service in a changing landscape of global navigation satellite systems. J Geodes 83:191–198CrossRefGoogle Scholar
  5. 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 Geodes 82:389–399CrossRefGoogle Scholar
  6. Geng J, Teferle FN, Meng X, Dodson AH (2011) Towards PPP-RTK: ambiguity resolution in real-time precise point positioning. Adv Space Res 47:1664–1673CrossRefGoogle Scholar
  7. Huisman L, Teunissen PJG, Hu C (2012) GNSS precise point positioning in regional reference frames using real-time broadcast corrections. J Appl Geodes 6:15–23CrossRefGoogle Scholar
  8. Kouba J, Heroux P (2001) Precise point positioning using IGS orbit products. GPS Solut 5(2):12–28CrossRefGoogle Scholar
  9. Lannes A, Teunissen PJG (2011) GNSS algebraic structures. J Geodes 85:273–290CrossRefGoogle Scholar
  10. Laurichesse D, Mercier F (2007) Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP. In: Proceedings of ION GNSS-2007, pp 839–848, Fort Worth, TX, 25–28 September 2007Google Scholar
  11. Li X, Zhang X, Ge M (2011) Regional reference network augmented precise point positioning for instantaneous ambiguity resolution. J Geodes 85:151–158Google Scholar
  12. Loyer S, Perosanz F, Mercier F, Capdeville H, Marty JC (2012) Zero difference GPS ambiguity resolution at CNES-CLS IGS analysis center. J Geodes. doi:10.1007/s00190-012-0559-2Google Scholar
  13. Odijk D, Teunissen PJG (2008) ADOP in closed form for a hierarchy of multi-frequency single-baseline GNSS models. J Geodes 82:473–492CrossRefGoogle Scholar
  14. Schaer S (1999) Mapping and predicting the Earth’s ionosphere using the global positioning system. Ph.D. thesisGoogle Scholar
  15. Teunissen PJG, 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
  16. Vollath U, Buecherl A, Landau H, Pagels C, Wagner B (2000) Multi-base RTK positioning using virtual reference stations. In: Proceedings of ION GPS-2000, pp 123–131, Salt Lake City, UT, 19–22 September 2000Google Scholar
  17. Wackernagel H (2003) Multivariate geostatistics: an introduction with applications. Springer, BerlinGoogle Scholar
  18. Wuebbena G, Schmitz M, Bagge A (2005) PPP-RTK: precise point positioning using state-space reprentation in RTK networks. In: Proceedings of ION GNSS-2005, pp 2584–2594, Long Beach, CA, 13–16 September 2005Google Scholar
  19. 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 102:5005–5017Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Dennis Odijk
    • 1
    Email author
  • Peter J. G. Teunissen
    • 1
  • Amir Khodabandeh
    • 1
  1. 1.Curtin UniversityPerthAustralia

Personalised recommendations