Journal of Geodesy

, Volume 88, Issue 4, pp 363–376 | Cite as

GNSS antenna array-aided CORS ambiguity resolution

  • Bofeng LiEmail author
  • Peter J. G. Teunissen
Original Article


Array-aided precise point positioning is a measurement concept that uses GNSS data, from multiple antennas in an array of known geometry, to realize improved GNSS parameter estimation proposed by Teunissen (IEEE Trans Signal Process 60:2870–2881, 2012). In this contribution, the benefits of array-aided CORS ambiguity resolution are explored. The mathematical model is formulated to show how the platform-array data can be reduced and how the variance matrix of the between-platform ambiguities can profit from the increased precision of the reduced platform data. The ambiguity resolution performance will be demonstrated for varying scenarios using simulation. We consider single-, dual- and triple-frequency scenarios of geometry-based and geometry-free models for different number of antennas and different standard deviations of the ionosphere-weighted constraints. The performances of both full and partial ambiguity resolution (PAR) are presented for these different scenarios. As the study shows, when full advantage is taken of the array antennas, both full and partial ambiguity resolution can be significantly improved, in some important cases even enabling instantaneous ambiguity resolution. PAR widelaning and its suboptimal character are hereby also illustrated.


Global navigation satellite system (GNSS) Integer ambiguity resolution (IAR) Continuously operating reference station (CORS) Array-aided precise point positioning (A-PPP) Full ambiguity resolution (FAR) Partial ambiguity resolution (PAR) 



This work has been executed in the framework of the Positioning Program Project 1.01 ‘New carrier phase processing strategies for achieving precise and reliable multi-satellite, multi-frequency GNSS/RNSS positioning in Australia’ of the Cooperative Research Centre for Spatial Information. PJG Teunissen is the recipient of an Australian Research Council (ARC) Federation Fellowship (FF0883188). This support is gratefully acknowledged. This work is also supported by the National Natural Science Funds of China (41374031), the State Key Laboratory of Geo-information Engineering (SKLGIE2013-M-2-2) and the Key Laboratory of Geo-informatics of State Bureau of Surveying and Mapping (201306).


  1. Blewitt G (1989) Carrier phase ambiguity resolution for the global positioning system applied to geodetic baselines up to 2000 km. J Geophys Res 94:135–151Google Scholar
  2. Cocard C, Geiger A (1992) Systematic search for all possible widelanes. In: 6th International Geodetic Symposium on Satellite Positioning. Columbus, Ohio, pp 373–386Google Scholar
  3. Cocard M, Bourgon S, Kamali O, Collins P (2008) A systematic investigation of optimal carrier-phase combinations for modernized triple-frequency GPS. J Geod 82(9):555–564CrossRefGoogle Scholar
  4. Dai L, Eslinger D, Sharpe T (2007) Innovative algorithms to improve long range RTK reliability and availability. In: ION NTM 2007, San Diego CA, pp 860–872.Google Scholar
  5. 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):3949–3966CrossRefGoogle Scholar
  6. Euler H, Landau H (1992) Fast GPS ambiguity resolution on-the-fly for real-time applications. In: 6th International Geodetic Symposium on Satellite Positioning. Columbus, Ohio, pp 650–659Google Scholar
  7. Feng Y (2008) GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals. J Geod 82:847–862CrossRefGoogle Scholar
  8. Giorgi G, Teunissen PJG, Verhagen S, Buist P (2010) Testing a new multivariate gnss carrier phase attitude determination method for remote sensing platforms. Adv Space Res 46(2):118–129CrossRefGoogle Scholar
  9. Goad C (1992) Robust techniques for determining GPS phase ambiguities. In: 6th International Geodetic Symposium on Satellite Positioning. Columbus, Ohio, pp 245–254Google Scholar
  10. Hernández-Pajares M, Zomoza JMJ, Subirana JS, Colombo O (2003) Feasibility of wide-area subdecimeter navigation with GALILEO and modernized GPS. IEEE Trans Geosci Remote Sens 41(9):2128–2131CrossRefGoogle Scholar
  11. Isshiki H (2004) A long baseline kinematic GPS solution of ionosphere-free combination constrained by widelane combination. In: Oceans’04. MTTS/IEEE Techno-Ocean’04, IEEE, vol 4, pp 1807–1814.Google Scholar
  12. Lawrence D (2009) A new method for partial ambiguity resolution. In: ION ITM 2009, Anaheim, CA, pp 652–663.Google Scholar
  13. Li B, Teunissen PJG (2012) Real-time kinematic positioning using fused data from multiple GNSS antennas. In: 15th International Conference on Information Fusion (FUSION), Singapore, pp 933–938.Google Scholar
  14. Li B, Feng Y, Shen Y (2010) Three carrier ambiguity resolution: distance-independent performance demonstrated using semi-generated triple frequency GPS signals. GPS Solut 14(2):177–184CrossRefGoogle Scholar
  15. Li B, Verhagen S, Teunissen PJG (2013) Robustness of GNSS integer ambiguity resolution in the presence of atmospheric biases. GPS Solut doi: 10.1007/s10291-013-0329-5
  16. Liu GC, Lachapelle G (2002) Ionosphere weighted GPS cycle ambiguity resolution. In: ION National Technical Meeting, San Deigo, CA, pp 1–5.Google Scholar
  17. Melbourne WG (1985) The case for ranging in GPS-based geodetic systems. In: 1st International Symposium on Precise Positioning with Global Positioning System, Rockville, Maryland, vol 1, pp 373–386.Google Scholar
  18. Mowlam A (2004) Baseline precision results using triple frequency partial ambiguity sets. In: ION GNSS-2004. Long Beach, CA, pp 2509–2518Google Scholar
  19. Odijk D (2000) Weighting ionospheric corrections to improve fast GPS positioning over medium distances. In: ION GPS 2000. Salt Lake City, UT, pp 1113–1123Google Scholar
  20. Pantoja VDG (2009) Partial ambiguity fixing for precise point positioning with multiple frequencies in the presence of biases. Thesis, Department of Electrical Engineering and Information Technology, Technical University MunichGoogle Scholar
  21. Parkins A (2011) Increasing GNSS RTK availability with a new single-epoch batch partial ambiguity resolution algorithm. GPS Solut 15:391–402CrossRefGoogle Scholar
  22. Rao C (1973) Linear statistical inference and its applications. John Wiley and Sons, New YorkGoogle Scholar
  23. Ray JK, Canon ME, Fenton P (2000) GPS code and carrier multipath mitigation using a multi-antenna system. IEEE Trans Aerosp Electron Syst 37(1):183–195CrossRefGoogle Scholar
  24. Richert T, El-Sheimy N (2007) Optimal linear combinations of triple frequency carrier phase data from future global navigation satellite systems. GPS Solut 11(1):11–19CrossRefGoogle Scholar
  25. Schaffrin B, Bock Y (1988) A unified scheme for processing GPS dual-band phase observations. Bull Géod 62(2):142–160CrossRefGoogle Scholar
  26. Takasu T, Yasuda A (2010) Kalman-filter-based integer ambiguity resolution strategy for long-baseline RTK with ionosphere and troposphere estimation. In: ION GNSS 2010. Portland, Oregon, pp 201–207Google Scholar
  27. Teunissen PJG (1997) On the GPS widelane and its decorrelating property. J Geod 71:577–587CrossRefGoogle Scholar
  28. Teunissen PJG (1998a) Minimal detectable biases of GPS data. J Geod 72:236–244CrossRefGoogle Scholar
  29. Teunissen PJG (1998b) Success probability of integer GPS ambiguity rounding and bootstrapping. J Geod 72(10):606–612CrossRefGoogle Scholar
  30. Teunissen PJG (2003) Adjustment theory: an introduction. Series on mathematical geodesy and positioning. Delft University Press, DelftGoogle Scholar
  31. Teunissen PJG (2012) A-PPP: array-aided precise point positioning with global navigation satellite systems. IEEE Trans Signal Process 60(6):2870–2881CrossRefGoogle Scholar
  32. Teunissen PJG, de Jonge P, Tiberius CCJM (1997) The least-squares ambiguity decorrelation adjustment: its performance on short GPS baselines and short observation spans. J Geod 71:589–602CrossRefGoogle Scholar
  33. Teunissen PJG, Joosten P, Tiberius CCJM (1999) Geometry-free ambiguity success rates in case of partial fixing. In: ION National Technical Meeting 1999 and 19th Biennal Guidance Test Symposium, San Diego CA, pp 201–207. Google Scholar
  34. Teunissen PJG, Joosten P, Tiberius CCJM (2002) A comparison of TCAR, CIR and LAMBDA GNSS ambiguity resolution. In: ION GPS 2002, Portland, OR, pp 2799–2808.Google Scholar
  35. Verhagen S, Li B (2012) LAMBDA software package: Matlab implementation, Version 3.0. Delft University of Technology and Curtin University, Perth, Australia.Google Scholar
  36. Verhagen S, Li B (2013) Ps-LAMBDA software package: Matlab implementation, Version 1.0. Curtin University of Technology, Perth, Australia.Google Scholar
  37. Verhagen S, Li B, Teunissen PJG (2013) Ps-LAMBDA: ambiguity success rate evaluation software for interferometric applications. Comput Geosci 54:361–376CrossRefGoogle Scholar
  38. Werner W, Winkel J (2003) TCAR and MCAR options with Galileo and GPS. In: ION GPS/GNSS 2003, Portland, OR, pp 790–800.Google Scholar
  39. Wübbena G (1991) Zur Modellerung von GPS Beobachtungen fuer die hochgenaue Positionsbestimmung. University Hannover, Germany, (in German).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.College of Surveying and Geo-InformaticsTongji UniversityShanghai People’s Republic of China
  2. 2.GNSS Research CentreCurtin UniversityPerthAustralia
  3. 3.Geoscience and Remote SensingDelft University of TechnologyDelftNetherlands

Personalised recommendations