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Bayesian Fault-Tolerant Position Estimator and Integrity Risk Bound for GNSS Navigation

Published online by Cambridge University Press:  17 April 2014

Fang-Cheng Chan ,
Mathieu Joerger ,
Samer Khanafseh  and
Boris Pervan
Fang-Cheng Chan*
Affiliation:
(Illinois Institute of Technology)
Mathieu Joerger
Affiliation:
(Illinois Institute of Technology)
Samer Khanafseh
Affiliation:
(Illinois Institute of Technology)
Boris Pervan
Affiliation:
(Illinois Institute of Technology)
*
(E-mail: [email protected])
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Abstract

The advent of multiple Global Navigation Satellite System (GNSS) constellations will result in a considerable increase in the number of satellites for positioning worldwide. This substantial improvement in measurement redundancy has the potential to radically advance receiver autonomous integrity monitoring (RAIM) performance. However, regardless of the number of satellites, the performance of existing RAIM methods is sensitive to the assumed prior probabilities of individual fault hypotheses. In this paper, a new method is developed using Bayes’ theorem to generate upper bounds on posterior probabilities of individual fault hypotheses given current user measurements. These bounds are used in a Bayesian fault-tolerant position estimator (FTE) that minimizes integrity risk. The detection test statistic is a measurement-based integrity risk bound, which is directly compared with a pre-specified risk requirement. The associated challenge of quantifying continuity risk is resolved using a bounding approach, which is also detailed in this work. The new Bayesian FTE method is shown to be more robust to uncertainty in prior probability of fault occurrence than existing RAIM methods.

Keywords

Global Navigation Satellite Systems (GNSS)Bayesian probabilityFault-tolerance position estimationRAIMNavigation integrity
Type
Research Article
Information
The Journal of Navigation , Volume 67 , Issue 5 , September 2014 , pp. 753 - 775
Copyright
Copyright © The Royal Institute of Navigation 2014 

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References

REFERENCES

Berger, J.O. (1985). Statistical decision theory and Bayesian analysis, Springer.Google Scholar
Blanch, J., Ene, A., Walter, T. and Enge, P. (2007). An Optimized Multiple Hypothesis RAIM Algorithm for Vertical Guidance. ION GNSS 20th International Technical Meeting of the Satellite Division, Fort Worth, TX, 2924–2933.Google Scholar
Blanch, J., Walter, T. and Enge, P. (2012). Optimal Positioning for Advanced RAIM. Proceeding of ION ITM, Newport Beach, CA, 1624–1647.Google Scholar
Blanch, J., Walter, T., Enge, P., Wallner, S., Amarillo Fernandez, F., Dellago, R., Ioannides, R., Hernandes, I.F., Belabbas, B., Spletter, A. and Rippl, M. (2013). Critical Elements for a Multi-Constellation Advanced RAIM. NAVIGATION, 60(1), 53–69.CrossRefGoogle Scholar
Brown, R.G. (1996). Receiver Autonomous Integrity Monitoring. Global Positioning System: Theory and Applications, Vol. II, 143–165.Google Scholar
Chan, F.-C. and Pervan, B. (2010). A Practical Approach to RAIM-based Fault-Tolerant Position Estimation. Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR, 3181–3190.Google Scholar
FAA. (2007). Program Requirements for the Wide Area Augmentation System (WAAS), FAA doc. WAAS070030, Jun. 5 2007.Google Scholar
FAA. (2011). Phase II of the GNSS Evolutionary Architecture Study. FAA report, Feb. 2011. http://www.faa.gov/about/office_org/headquarters_offices/ato/service_units/techops/navservices/gnss/library/documents/media/GEASPhaseII_Final.pdfGoogle Scholar
Frank, R. and Weston, M. (1997). A survey of Venn diagrams. Electronic Journal of Combinatorics. http://www.combinatorics.org/files/Surveys/ds5/VennEJC.htmlGoogle Scholar
Hwang, P. and Brown, R.G. (2006). RAIM FDE Revisited: A new Breakthrough in Availability Performance With NIORAIM (Novel Integrity-Optimized RAIM). NAVIGATION, 53(1), 654–665.Google Scholar
Joerger, M., Chan, F.-C., Langel, S. and Pervan, B. (2012). RAIM Detector and Estimator Design to Minimize the Integrity Risk. ION GNSS 25th International Technical Meeting of the Satellite Division, Nashville, TN, 2785–2807.Google Scholar
Lee, Y.C. and McLaughlin, M.P. (2007). Feasibility Analysis of RAIM to Provide LPV-200 Approaches with Future GPS. ION GNSS 20th International Technical Meeting of the Satellite Division, Fort Worth, TX, 2898–2919.Google Scholar
Luenberger, D.G. (2003). Linear and nonlinear programming. Springer, 198.Google Scholar
Ober, P.B. (2003). Integrity Predication and Monitoring of Navigation Systems. PhD Dissertation, TU Delft, 93–99.Google Scholar
Parkinson, B.W. and Axelrad, P. (1988). Autonomous GPS Integrity Monitoring Using the Pseudorange Residual. NAVIGATION, 35(2), 225–274.Google Scholar
Pervan, B., Lawrence, D.G., Cohen, C.E. and Parkinson, B.W. (1996). Parity Space Methods for Autonomous Fault Detection and Exclusion using GPS Carrier Phase. IEEE 1996 Position Location and Navigation Symposium, 649–656.CrossRefGoogle Scholar
Pervan, B., Pullen, S. and Christie, J. (1998). A Multiple Hypothesis Approach to Satellite Navigation Integrity. NAVIGATION, 45(1), 61–84.CrossRefGoogle Scholar
Sturza, M.A. (1989). Navigation System Integrity Monitoring Using Redundant Measurements. NAVIGATION, 35(4), 483–502.Google Scholar
US DOD. (2001). Global positioning system standard positioning service performance standard. Assistant secretary of Defense for Command, Control, Communications, and Intelligence.Google Scholar
Walter, T., Enge, P., Blanch, J. and Pervan, B. (2008). Worldwide Vertical Guidance of Aircraft Based on Modernized GPS and New Integrity Augmentations. Proceedings of the IEEE Special Issue on Aviation Information Systems, 96(12), 1918–1935.Google Scholar
Young, C.L. (2006). A New Improved RAIM Method Based on the Optimally Weighted Average Solution (OWAS) Under the Assumption of a Single Fault. Proceedings of the ION National Technical Meeting, Monterey, CA, 574–586.Google Scholar
Zandbergen, R., Dinwiddy, S., Hahn, J., Breeuwer, J. and Blonski, D. (2004). Galileo Orbit Selection. Proceedings of the 17th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2004), Long Beach, CA, 616–623.Google Scholar