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Integrity Monitoring for Carrier Phase Ambiguities

Published online by Cambridge University Press:  25 November 2011

Shaojun Feng ,
Washington Ochieng ,
Jaron Samson ,
Michel Tossaint ,
Manuel Hernandez-Pajares ,
J. Miguel Juan ,
Jaume Sanz ,
Àngela Aragón-Àngel ,
Pere Ramos-Bosch  and
Marti Jofre
Shaojun Feng*
Affiliation:
Centre for Transport Studies, Department of Civil & Environmental Engineering Imperial College London
Washington Ochieng
Affiliation:
Centre for Transport Studies, Department of Civil & Environmental Engineering Imperial College London
Jaron Samson
Affiliation:
ESA (ESTEC/TEC-ETN), The Netherlands
Michel Tossaint
Affiliation:
ESA (ESTEC/TEC-ETN), The Netherlands
Manuel Hernandez-Pajares
Affiliation:
Research Group of Astronomy and Geomatics (gAGE), Universitat Politècnica de Catalunya (UPC), Barcelona (Spain)
J. Miguel Juan
Affiliation:
Research Group of Astronomy and Geomatics (gAGE), Universitat Politècnica de Catalunya (UPC), Barcelona (Spain)
Jaume Sanz
Affiliation:
Research Group of Astronomy and Geomatics (gAGE), Universitat Politècnica de Catalunya (UPC), Barcelona (Spain)
Àngela Aragón-Àngel
Affiliation:
Research Group of Astronomy and Geomatics (gAGE), Universitat Politècnica de Catalunya (UPC), Barcelona (Spain)
Pere Ramos-Bosch
Affiliation:
Research Group of Astronomy and Geomatics (gAGE), Universitat Politècnica de Catalunya (UPC), Barcelona (Spain)
Marti Jofre
Affiliation:
CTAE - Aerospace Research & Technology Centre, Barcelona, Spain
*
(E-mail: [email protected])
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Abstract

The determination of the correct integer number of carrier cycles (integer ambiguity) is the key to high accuracy positioning with carrier phase measurements from Global Navigation Satellite Systems (GNSS). There are a number of current methods for resolving ambiguities including the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method, which is a combination of least-squares and a transformation to reduce the search space. The current techniques to determine the level of confidence (integrity) of the resolved ambiguities (i.e. ambiguity validation), usually involve the construction of test statistics, characterisation of their distribution and definition of thresholds. Example tests applied include ratio, F-distribution, t-distribution and Chi-square distribution. However, the assumptions that underpin these tests have weaknesses. These include the application of a fixed threshold for all scenarios, and therefore, not always able to provide an acceptable integrity level in the computed ambiguities. A relatively recent technique referred to as Integer Aperture (IA) based on the ratio test with a large number of simulated samples of float ambiguities requires significant computational resources. This precludes the application of IA in real time.

This paper proposes and demonstrates the power of an integrity monitoring technique that is applied at the ambiguity resolution and positioning stages. The technique has the important benefit of facilitating early detection of any potential threat to the position solution, originating in the ambiguity space, while at the same time giving overall protection in the position domain based on the required navigation performance. The proposed method uses the conventional test statistic for ratio testing together with a doubly non-central F distribution to compute the level of confidence (integrity) of the ambiguities. Specifically, this is determined as a function of geometry and the ambiguity residuals from least squares based ambiguity resolution algorithms including LAMBDA. A numerical method is implemented to compute the level of confidence in real time.

The results for Precise Point Positioning (PPP) with simulated and real data demonstrate the power and efficiency of the proposed method in monitoring both the integrity of the ambiguity computation and position solution processes. Furthermore, due to the fact that the method only requires information from least squares based ambiguity resolution algorithms, it is easily transferable to conventional Real Time Kinematic (RTK) positioning.

Keywords

GNSSPPPRNPCRAIM
Type
Research Article
Information
The Journal of Navigation , Volume 65 , Issue 1 , January 2012 , pp. 41 - 58
Copyright
Copyright © The Royal Institute of Navigation 2011

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References

REFERENCES

Bulgren, W. G. (1971). On Representations of the Doubly Non-Central F Distribution. Journal of American Statistical Association, 66(333), 184–186.Google Scholar
Chen, Y. (1997). An approach to validate the resolved ambiguities in GPS rapid positioning. Proceedings of the International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, Banff, Canada.Google Scholar
Diesel, J. and Luu, S. (1995). GPS/IRS AIME: Calculation of thresholds and protection radius using Chi-square methods. Proceedings of ION GPS 1995, Palm Springs, CA.Google Scholar
Euler, H. J. and Schaffrin, B. (1991). On a measure for the discernability between different ambiguity solutions in the static-kinematic GPS-mode. IAG Symposia 107, Kinematic Systems in Geodesy, Surveying, and Remote Sensing. Springer.Google Scholar
Feng, S., Ochieng, W. Y., Walsh, D. and Ioannides, R. (2006). A Measurement Domain Receiver Autonomous Integrity Monitoring Algorithm. GPS Solutions, Springer, 10(2), 85–96.CrossRefGoogle Scholar
Feng, S., Ochieng, W. Y., Moore, T., Hill, C. and Hide, C. (2009). Carrier-Phase Based Integrity Monitoring for High Accuracy Positioning. GPS Solutions, DOI 10.1007/s10291-008-0093-0, 13–22.CrossRefGoogle Scholar
Laurichesse, D. and Mercier, F. (2007). Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP. Proceedings of 20th Int. Tech. Meet. Satellite Div. Inst. Navigation GNSS.Google Scholar
Lee, Y. C. and Laughlin, D. G. (1999). A performance analysis of a tightly coupled GPS/inertial system for two integrity monitoring method. Proceedings of ION GPS, Nashville, TN.Google Scholar
Leick, A. (2003). GPS Satellite Surveying. John Wiley and Sons, New York, 3rd edition.Google Scholar
Hernández-Pajares, M., Juan, J. M., Sanz, J., Aragón, A., Ramos, P., Samson, J., Tossaint, M., Albertazzi, M. A., Odijk, D., Teunissen, P., de Bakker, P., Verhagen, S. and van der Marel, H. (2010). Wide-Area RTK High Precision Positioning on a Continental Scale. Inside GNSS, March/April, 35–46.Google Scholar
Sauer, K. (2003). Integrated High Precision Kinematic Positioning Using GPS and EGNOS Observations.PhD thesis, Imperial College London, July, 2003.Google Scholar
Teunissen, P. J. G. (1993). Least-Squares Estimation of the Integer GPS Ambiguities. Invited lecture, Section IV: Theory and Methodology. IAG General Meeting, Beijing, China.Google Scholar
Teunissen, P. J. G. (2003). Integer Aperture GNSS Ambiguity Resolution. Artificial Satellites, 38(3), 79–88.Google Scholar
Teunissen, P. J. G. and Verhagen, S. (2004). On the foundation of the Popular Ratio Test for GNSS Ambiguity Resolution. Proceeding of the ION GNSS, Long Beach, CA.Google Scholar
Teunissen, P. J. G. (2005). Integer Aperture Bootstrapping: A New GNSS Ambiguity Estimator with Controllable Fail-Rate. Journal of Geodesy, 79(6&7), 389–397.CrossRefGoogle Scholar
Teunissen, P. J. G. and Verhagen, S. (2009a). GNSS carrier phase ambiguity resolution:challenges and open problems. Springer Berlin Heidelberg: Observing our Changing Earth, 133(4), 785–792.Google Scholar
Teunissen, P. J. G. and Verhagen, S. (2009b). The GNSS ambiguity ratio-test revisited: a better way of using it. Survey Review, 41(312), 138–151.CrossRefGoogle Scholar
Tiberius, C. and De, J. (1995). Fast positioning using the LAMBDA method, Proceeding of DSNS, Bergen, Norway.Google Scholar
Verhagen, S. (2004). Integer ambiguity validation: an open problem? GPS Solutions, 8(1), 36–43.CrossRefGoogle Scholar
Wang, J., Stewart, M. P. and Tsakiri, M. (2000). A comparative study of the integer ambiguity validation procedures. Earth Planets Space, 52, 813–817.CrossRefGoogle Scholar
Wang, M. and Gao, Y. (2006). GPS Un-differenced Ambiguity Resolution and Validation. Proceedings of ION GNSS 2006, Fort Worth, Texas.Google Scholar
Wei, M. and Schwarz, K. P. (1995). Fast ambiguity resolution using an integer nonlinear programming method. Proceedings of ION GPS, Palm Springs CA.Google Scholar