Journal of Geodesy

, 82:473 | Cite as

ADOP in closed form for a hierarchy of multi-frequency single-baseline GNSS models

Open Access
Original Article

Abstract

Successful carrier phase ambiguity resolution is the key to high-precision positioning with Global Navigation Satellite Systems (GNSS). The ambiguity dilution of precision (ADOP) is a well-known scalar measure which can be used to infer the strength of the GNSS model for carrier phase ambiguity resolution. In this contribution we present analytical closed-form expressions for the ADOP. This will be done for a whole class of different multi- frequency single baseline models. These models include the geometry-fixed, the geometry-free and the geometry-based models, respectively. And within the class of geometry-based models, we discriminate between short and long observation time spans, and between stationary and moving receivers. The easy-to-use ADOP expressions can be applied to infer the contribution of various GNSS model factors. They comprise, for instance, the type, the number and the precision of the GNSS observations, the number and selection of frequencies, the presence of atmospheric disturbances, the length of the observation time span and the length of the baseline.

Keywords

ADOP GNSS GPS Ambiguity resolution 

References

  1. Barrena V, Colmenarejo P (2002) Ambiguity dilution of precision for radio frequency based relative navigation determination. In: Proc 5th Int. ESA Conf on Spacecraft Guidance, Navigation and Control Systems. Frascati, October 22–25, pp 603–607Google Scholar
  2. Bock Y, Gourevitch SA, Counselman CC III, King RW and Abbot RI (1986). Interferometric analysis of GPS phase observations. Manus Geod 11: 282–288 Google Scholar
  3. Chen X, Vollath U, Landau H, Sauer K (2004) Will Galileo/modernized GPS obsolete network RTK? In: Proc ENC-GNSS 2004. Rotterdam, May 16–19Google Scholar
  4. Chmielewsky MA (1981). Elliptically symmetric distributions: a review and bibliography. Int Statist Rev 49: 67–74 CrossRefGoogle Scholar
  5. Euler HJ and Goad CC (1991). On optimal filtering of GPS dual frequency observations without using orbit information. Bull Géod 65: 130–143 CrossRefGoogle Scholar
  6. Goad CC, Yang M (1994) On automatic precision airborne GPS positioning. In: Proc KIS94. Banff, August 30–September 2, pp 131–138Google Scholar
  7. Ji S, Chen W, Zhao C, Ding X and Chen Y (2007). Single epoch ambiguity resolution for Galileo with the CAR and LAMBDA methods. GPS Solutions. doi:10.1007/s10291-007-0057-9 Google Scholar
  8. Koch K-R (1999). Parameter estimation and hypothesis testing in linear models, 2nd edn. Springer, Heidelberg Google Scholar
  9. Lee HK, Wang J, Rizos C, Barnes J, Tsujii T, Soon BKH (2002) Analysis of pseudolite augmentation for GPS airborne applications. In: Proc ION GPS-2002. Portland, September 24–27, pp 2610–2618Google Scholar
  10. Lee HK, Wang J and Rizos C (2005). An integer ambiguity resolution procedure for GPS/pseudolite/INS integration. J Geod 79: 242–255 CrossRefGoogle Scholar
  11. Liu GC (2001) Ionosphere-weighted Global Positioning System carrier phase ambiguity resolution. MSc. thesis, Department of Geomatics Engineering, University of CalgaryGoogle Scholar
  12. Mathematical Geodesy and Positioning (MGP), Delft University of Technology (2007) http://www.lr.tudelft.nl/mgp
  13. Milbert D (2005). Influence of pseudorange accuracy on phase ambiguity resolution in various GPS modernization scenarios. Navigation 5(1): 29–38 Google Scholar
  14. Moore M, Rizos C, Wang J, Boyd G, Mathews K, Williams W, Smith R (2003) Issues concerning the implementation of a low cost attitude solution for an unmanned airborne vehicle (UAV) (2003). In: Proc SatNav 2003. Melbourne, July 22–25, CD-ROMGoogle Scholar
  15. Odijk D (2000) Weighting ionospheric corrections to improve fast GPS positioning over medium distances. In: Proc ION GPS-2000. Salt Lake City, September 19–22, pp 1113–1123Google Scholar
  16. Odijk D (2002) Fast precise GPS positioning in the presence of ionospheric delays. Publications on Geodesy 52, Netherlands Geodetic Commission, 242 pGoogle Scholar
  17. O’Keefe K, Julien O, Cannon ME and Lachapelle G (2005). Availability, accuracy, reliability and carrier-phase ambiguity resolution with Galileo and GPS. Acta Astron 58: 422–434 CrossRefGoogle Scholar
  18. Priestley MB (1981). Spectral analysis and time series. Probability and mathematical statistics, a series of monographs and textbooks, vols. 1 and 2. Academic, London Google Scholar
  19. Rao CR (1973). Linear statistical inference and its applications, 2nd edn. Wiley, New York Google Scholar
  20. Richtert T, El-Sheimy N (2005) Ionospheric modeling: the key to GNSS ambiguity resolution. GPS World. June 2005, pp 35–40Google Scholar
  21. Schaer S (1994). Stochastische Ionosphärenmodellierung beim ‘Rapid Static Positioning’ mit GPS. Astronomical Institute, University of Berne, Switzerland Google Scholar
  22. Schaffrin B and Bock Y (1988). A unified scheme for processing GPS dual-band phase observations. Bull Géod 62: 142–160 CrossRefGoogle Scholar
  23. Scherzinger BM (2000) Precise robust positioning with inertial/GPS RTK. In: Proc ION GPS-2000. Salt Lake City, September 19–22, pp 155–162Google Scholar
  24. Scherzinger BM (2001) Robust inertially-aided RTK position measurement. In: Proc KIS2001. Banff, June 5–8, 8p CD-ROMGoogle Scholar
  25. Skaloud J (1998) Reducing the GPS ambiguity search space by including inertial data. In: Proc ION GPS-1998. Nashville, September 15–18, pp 2073–2080Google Scholar
  26. Teunissen PJG (1993) Least-squares estimation of the integer GPS ambiguities. Invited lecture, Sect. IV Theory and Methodology, IAG General Meeting, BeijingGoogle Scholar
  27. Teunissen PJG (1995). The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation. J Geod 70: 65–82 CrossRefGoogle Scholar
  28. Teunissen PJG (1997a). A canonical theory for short GPS baselines. Part I: The baseline precision. J Geod 71: 320–336 Google Scholar
  29. Teunissen PJG (1997b). A canonical theory for short GPS baselines. Part IV: Precision versus reliability. J Geod 71: 513–525 Google Scholar
  30. Teunissen PJG (1998). The ionosphere-weighted GPS baseline precision in canonical form. J Geod 72: 107–117 CrossRefGoogle Scholar
  31. Teunissen PJG (1999). An optimality property of the integer least-squares estimator. J Geod 73: 587–593 CrossRefGoogle Scholar
  32. Teunissen PJG, Kleusberg A (eds) (1998). GPS for geodesy, 2nd edn. Springer, Heidelberg Google Scholar
  33. Teunissen PJG, Odijk D (1997) Ambiguity dilution of precision: definition, properties and application. In: Proc of ION GPS-1997. Kansas City, September 16–19, pp 891–899Google Scholar
  34. Verhagen S (2005). On the reliability of integer ambiguity resolution. Navigation 5(2): 99–110 Google Scholar
  35. Vollath U, Sauer K, Amarillo F, Pereira J (2003) Three or four carriers—how many are enough? In: Proc of ION GPS/GNSS 2003. Portland, September 9–12, pp 1470–1477Google Scholar
  36. Wang J, Lee HK, Lee YJ, Musa T, Rizos C (2004) Online stochastic modelling for network-based GPS real-time kinematic positioning. In: Proceedings of GNSS 2004, The 2004 International Symposium on GNSS/GPS. Sydney, December 6–8Google Scholar
  37. Wu H (2003) On-the-fly ambiguity resolution with inertial aiding. Master’s thesis, University of Calgary, Canada, 171 pGoogle Scholar
  38. Wu F, Kubo N and Yasuda A (2004). Performance evaluation of GPS augmentation using quasi-zenith satellite system. IEEE Trans Aeros Electron Systems 40(4): 1249–1261 CrossRefGoogle Scholar
  39. Xu P, Cannon ME, Lachapelle G (1995) Mixed integer programming for the resolution of the GPS carrier phase ambiguities. Paper presented at IUGG95 Assembly. Boulder, July 2–14Google Scholar

Copyright information

© The Author(s) 2008

Authors and Affiliations

  1. 1.Delft Institute of Earth Observation and Space Systems (DEOS)Delft University of TechnologyDelftThe Netherlands

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