The Future of Single-Frequency Integer Ambiguity Resolution

  • Sandra VerhagenEmail author
  • Peter J. G. Teunissen
  • Dennis Odijk
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 137)


The coming decade will bring a proliferation of Global Navigation Satellite Systems (GNSSs) that are likely to enable a much wider range of demanding applications compared to the current GPS-only situation. One such important area of application is single-frequency real-time kinematic (RTK) positioning. Presently, however, such systems lack real-time performance. In this contribution we analyze the ambiguity resolution performance of the single-frequency RTK model for different next generation GNSS configurations and positioning scenarios. For this purpose, a closed form expression of the single-frequency Ambiguity Dilution of Precision (ADOP) is derived. This form gives a clear insight into how and to what extent the various factors of the underlying model contribute to the overall performance. Analytical and simulation results will be presented for different measurement scenarios. The results indicate that low-cost, single-frequency Galileo+GPS RTK will become a serious competitor to its more expensive dual-frequency cousin.


ADOP Ambiguity resolution Single-frequency RTK 



The research of Sandra Verhagen is supported by the Dutch Technology Foundation STW, applied science division of NWO and the Technology Program of the Ministry of Economic Affairs.

Professor Teunissen is the recipient of an Australian Research Council Federation Fellowship (project number FF0883188). This support is greatly acknowledged.


  1. Denham JL, Whitlock AK, Yule D (2006) Contemporary position and navigation needs of precision agriculture and victoria’s GPSnet CORS network. In: Proceedings of IGNSS symposium, Holiday Inn Surfers Paradise, AustraliaGoogle Scholar
  2. Milbert D (2005) Influence of pseudorange accuracy on phase ambiguity resolution in various GPS modernization scenarios. Navigation 52(1):29–38Google Scholar
  3. Millner J, Hale M, Standen P, Talbot N (2004) The development and enhancement of a GNSS/GPS infrastructure to support location based service positioning systems in Victoria. In: Proceedings of international symposium on GNSS/GPS, Sydney, AustraliaGoogle Scholar
  4. Odijk D (2002) Fast precise GPS positioning in the presence of ionospheric delays. Ph.D. thesis, Publications on Geodesy, 52, Netherlands Geodetic Commission, DelftGoogle Scholar
  5. Odijk D, Teunissen PJG (2007) Sensititvity of ADOP to changes in the single-baseline GNSS model. Artificial Satellites 42(2):71–96CrossRefGoogle Scholar
  6. Odijk D, Teunissen PJG (2008) ADOP in closed form for a hierarchy of multi-frequency single-baseline GNSS models. J Geodes 82(8):473–492CrossRefGoogle Scholar
  7. Odijk D, Traugott J, Sachs G, Montenbruck O, Tiberius C (2007) Two approaches to precise kinematic GPS positioning with miniaturized L1 receivers. In: Proceedings of ION GNSS 2007, Fort Worth TX, pp 827–838Google Scholar
  8. Saeki M, Hori M (2006) Positioning system using low-cost L1 GPS receivers. Comput Aided Civ Infrastruct Eng 21(4):258–267CrossRefGoogle Scholar
  9. Simsky A, Sleewaegen JM, Hollreiser M, Crisci M (2006) Performance assessment of Galileo ranging signals transmitted by GSTB-V2 satellites. In: Proceedings of ION GNSS 2006, Fort Worth TXGoogle Scholar
  10. Takasu T, Yasuda A (2008) Evaluation of RTK-GPS performance with low-cost single-frequency GPS receivers. In: Proceedings of international symposium on GPS/GNSS 2008 Tokyo, Japan, pp 852–861Google Scholar
  11. Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geodes 70(1-2):65–82CrossRefGoogle Scholar
  12. Teunissen PJG (1997) A canonical theory for short GPS baselines. Part IV: Precision versus reliability. J Geodes 71: 513–525Google Scholar
  13. Teunissen PJG (1999) An optimality property of the integer least-squares estimator. J Geodes 73(11):587– 593CrossRefGoogle Scholar
  14. Verhagen S (2005) On the reliability of integer ambiguity resolution. Navigation 52(2):99–110Google Scholar
  15. Wirola L, Alanen K, Kappi J, Syrjarinne J (2006) Bringing RTK to cellular terminals using a low-cost single-frequency AGPS receiver and inertial sensors. In: Proceedings IEEE/ION PLANS 2006, San Diego CA, pp 645–652Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sandra Verhagen
    • 1
    Email author
  • Peter J. G. Teunissen
    • 2
    • 1
  • Dennis Odijk
    • 2
  1. 1.Delft Institute of Earth Observation and Space SystemsDelft University of TechnologyDelftThe Netherlands
  2. 2.Department of Spatial SciencesCurtin University of TechnologyPerthAustralia

Personalised recommendations