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High Dimensional Integer Ambiguity Resolution: A First Comparison between LAMBDA and Bernese

  • Bofeng Li (a1) and Peter J.G. Teunissen (a1)

The LAMBDA method for integer least-squares ambiguity resolution has been widely used in a great variety of Global Navigation Satellite System (GNSS) applications. The popularity of this method stems from its numerical efficiency and its guaranteed optimality in the sense of maximising the success probability of integer ambiguity estimation. In the past two decades, the LAMBDA method has been typically used in cases where the number of ambiguities is less than several tens. With the advent of denser network processing and the availability of multi-frequency, multi-GNSS systems, it is important to understand LAMBDA's performance in high dimensional spaces. In this contribution, we will address this issue using real GPS data based on the Bernese software. We have embedded the LAMBDA method into the Bernese software and compared their ambiguity resolution performances. Twelve day dual-frequency GPS data with a sampling interval of 30 s was used in the experiment, which was collected from a network of 19 stations in the Perth area of Western Australia with an average baseline length of 380 km. Different experimental scenarios were examined and tested with different observation spans, which represent the different ambiguity dimensions. The results showed that LAMBDA is still efficient even when the number of ambiguities is more than 100, and that the baseline repeatability obtained with the ambiguities resolved from the LAMBDA method agreed well with that of Bernese. Therefore, for future dense network processing, the easy-to-use LAMBDA method should be considered as an alternative to baseline-per-baseline methods as those used in e.g. the Bernese software.

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Blewitt, G. (1989). Carrier Phase Ambiguity Resolution for the Global Positioning System Applied to Geodetic Baselines up to 2000 km. Journal of Geophysical Research, 94, 135151.
Counselman, C. and Gourevitch, S. (1981). Miniature Interferometer Terminals for Earth Surveying: Ambiguity and Multipath with the Global Positioning System. IEEE Transaction on Geosciences and Remote Sensing, 19(4), 244252.
Chang, X., Yang, X. and Zhou, T. (2005). MLAMBDA: a Modified LAMBDA Method for Integer Least-Squares Estimation. Journal of Geodesy, 79, 552565.
Dach, R., Hugentobler, U., Fridez, P. and Meindl, M. (2007). Bernese GPS Software: Version 5.0. Astronomical Institute, University of Bern.
Euler, H. and Landau, H. (1992). Fast Ambiguity Resolution on-the-fly for Real-Time Applications. Proceedings of the 6th international geodesy symposium on satellite positioning, Columbus, Ohio, 17–20 March, 650659.
Frei, E. and Beulter, G. (1990). Rapid Static Positioning Based on the Fast Ambiguity Resolution Approach ‘FARA’: Theory and First Results. Manuscripta Geodaetica, 15, 326356.
De Jonge, P., Teunissen, P., Jonkman, N. and Joosten, P. (2000). The Distributional Dependence of the Range on Triple Frequency GPS Ambiguity Resolution. Proceedings of ION-NTM, Anaheim, CA, USA, 605612.
De Jonge, P. and Tiberius, C. (1996). The LAMBDA Method for Integer Ambiguity Estimation: Implementation Aspects. LGR-Series, No 12. Technical report.
Ge, M., Gendt, G., Rothacher, M., Shi, C. and Liu, J. (2008). Resolution of GPS Carrier-Phase Ambiguities in Precise Point Positioning (PPP) with Daily Observations. Journal of Geodesy, 82, 389399.
Hatch, R. (1990). Instantaneous Ambiguity Resolution. Proceedings of KIS'90, Banff, Canada, 299308.
Hofmann-Wellenhof, B., Lichtenegger, H. and Collins, J. (2001). Global Positioning System: Theory and Practice. 5th edn. Springer Berlin Heidelberg, New York.
Leick, A. (2004). GPS Satellite Surveying. 3rd edn. John Wiley, New York.
Strang, G. and Borre, K. (1997). Linear Algebra, Geodesy, and GPS. Wellesley-Cambridge Press.
Teunissen, P. (1993). Least-Squares Estimation of Integer GPS Ambiguities. Invited Lecture on Sect. IV Theory and Methodology, IAG General Meeting, Beijing, China.
Teunissen, P. (1995a). The Invertible GPS Ambiguity Transformations. Manuscripta Geodaetica, 20, 489497.
Teunissen, P. (1995b). The Least-Squares Ambiguity Decorrelation Adjustment: a Method for Fast GPS Integer Ambiguity Estimation. Journal of Geodesy, 70, 6582.
Teunissen, P. (1999). An Optimality Property of the Integer Least-Squares Estimator. Journal of Geodesy, 73, 587593.
Teunissen, P., de Jonge, P. and Tiberius, C. (1996). The Volume of the GPS Ambiguity Search Space and Its Relevance for Integer Ambiguity Resolution. Proceedings of ION-GPS-1996, Kansas City MO, 889898.
Teunissen, P., de Jonge, P. and Tiberius, C. (1997). The Least-Squares Ambiguity Decorrelation Adjustment: Its Performance on Short GPS Baselines and Short Observation Spans. Journal of Geodesy, 71, 589602.
Teunissen, P. and Kleusberg, A. (1998). GPS for Geodesy. 2nd edn. Springer Berlin Heidelberg New York.
Teunissen, P. and Verhagen, S. (2009). The GNSS Ambiguity Ratio-Test Revisited: a Better Way of Using It. Survey Review, 41, (312), 138151.
Wübbena, G. (1989). The GPS Adjustment Software Package-GEONAP Concepts and Models. Proceedings of the 5th Geodesy Symposium on Satellite Positioning, 452461.
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The Journal of Navigation
  • ISSN: 0373-4633
  • EISSN: 1469-7785
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