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

D. Odijk; P. J. G. Teunissen

doi:10.1007/s00190-007-0197-2

Download PDF

Journal of Geodesy

August 2008, 82:473

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

Authors
Authors and affiliations

D. OdijkEmail author
P. J. G. Teunissen

Open Access

Original Article

First Online:: 29 January 2008

Received:: 07 August 2007
Accepted:: 07 November 2007

DOI: 10.1007/s00190-007-0197-2

Cite this article as:: Odijk, D. & Teunissen, P.J.G. J Geod (2008) 82: 473. doi:10.1007/s00190-007-0197-2

25 Citations
512 Downloads

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

Download to read the full article text

References

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 603–607
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
Chen X, Vollath U, Landau H, Sauer K (2004) Will Galileo/modernized GPS obsolete network RTK? In: Proc ENC-GNSS 2004. Rotterdam, May 16–19
Chmielewsky MA (1981). Elliptically symmetric distributions: a review and bibliography. Int Statist Rev 49: 67–74 CrossRefGoogle Scholar
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
Goad CC, Yang M (1994) On automatic precision airborne GPS positioning. In: Proc KIS94. Banff, August 30–September 2, pp 131–138
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
Koch K-R (1999). Parameter estimation and hypothesis testing in linear models, 2nd edn. Springer, Heidelberg Google Scholar
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 2610–2618
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
Liu GC (2001) Ionosphere-weighted Global Positioning System carrier phase ambiguity resolution. MSc. thesis, Department of Geomatics Engineering, University of Calgary
Mathematical Geodesy and Positioning (MGP), Delft University of Technology (2007) http://www.lr.tudelft.nl/mgp
Milbert D (2005). Influence of pseudorange accuracy on phase ambiguity resolution in various GPS modernization scenarios. Navigation 5(1): 29–38 Google Scholar
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-ROM
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 1113–1123
Odijk D (2002) Fast precise GPS positioning in the presence of ionospheric delays. Publications on Geodesy 52, Netherlands Geodetic Commission, 242 p
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
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
Rao CR (1973). Linear statistical inference and its applications, 2nd edn. Wiley, New York Google Scholar
Richtert T, El-Sheimy N (2005) Ionospheric modeling: the key to GNSS ambiguity resolution. GPS World. June 2005, pp 35–40
Schaer S (1994). Stochastische Ionosphärenmodellierung beim ‘Rapid Static Positioning’ mit GPS. Astronomical Institute, University of Berne, Switzerland Google Scholar
Schaffrin B and Bock Y (1988). A unified scheme for processing GPS dual-band phase observations. Bull Géod 62: 142–160 CrossRefGoogle Scholar
Scherzinger BM (2000) Precise robust positioning with inertial/GPS RTK. In: Proc ION GPS-2000. Salt Lake City, September 19–22, pp 155–162
Scherzinger BM (2001) Robust inertially-aided RTK position measurement. In: Proc KIS2001. Banff, June 5–8, 8p CD-ROM
Skaloud J (1998) Reducing the GPS ambiguity search space by including inertial data. In: Proc ION GPS-1998. Nashville, September 15–18, pp 2073–2080
Teunissen PJG (1993) Least-squares estimation of the integer GPS ambiguities. Invited lecture, Sect. IV Theory and Methodology, IAG General Meeting, Beijing
Teunissen PJG (1995). The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation. J Geod 70: 65–82 CrossRefGoogle Scholar
Teunissen PJG (1997a). A canonical theory for short GPS baselines. Part I: The baseline precision. J Geod 71: 320–336 Google Scholar
Teunissen PJG (1997b). A canonical theory for short GPS baselines. Part IV: Precision versus reliability. J Geod 71: 513–525 Google Scholar
Teunissen PJG (1998). The ionosphere-weighted GPS baseline precision in canonical form. J Geod 72: 107–117 CrossRefGoogle Scholar
Teunissen PJG (1999). An optimality property of the integer least-squares estimator. J Geod 73: 587–593 CrossRefGoogle Scholar
Teunissen PJG, Kleusberg A (eds) (1998). GPS for geodesy, 2nd edn. Springer, Heidelberg Google Scholar
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 891–899
Verhagen S (2005). On the reliability of integer ambiguity resolution. Navigation 5(2): 99–110 Google Scholar
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 1470–1477
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 6–8
Wu H (2003) On-the-fly ambiguity resolution with inertial aiding. Master’s thesis, University of Calgary, Canada, 171 p
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
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 2–14

Copyright information

Authors and Affiliations

D. Odijk
- 1
Email author
P. J. G. Teunissen
- 1

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

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

Abstract

Keywords

Copyright information

Authors and Affiliations

Personalised recommendations

Cookies