Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T05:02:32.707Z Has data issue: false hasContentIssue false

A Comparison of Outlier Detection Procedures and Robust Estimation Methods in GPS Positioning

Published online by Cambridge University Press:  07 October 2009

Nathan L. Knight*
Affiliation:
(The University of New South Wales, Sydney, Australia)
Jinling Wang
Affiliation:
(The University of New South Wales, Sydney, Australia)
*

Abstract

With more satellite systems becoming available there is currently a need for Receiver Autonomous Integrity Monitoring (RAIM) to exclude multiple outliers. While the single outlier test can be applied iteratively, in the field of statistics robust methods are preferred when multiple outliers exist. This study compares the outlier test and numerous robust methods with simulated GPS measurements to identify which methods have the greatest ability to correctly exclude outliers. It was found that no method could correctly exclude outliers 100% of the time. However, for a single outlier the outlier test achieved the highest rates of correct exclusion followed by the MM-estimator and the L1-norm. As the number of outliers increased MM-estimators and the L1-norm obtained the highest rates of normal exclusion, which were up to ten percent higher than the outlier test.

Type
Research Article
Copyright
Copyright © The Royal Institute of Navigation 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andersen, R. (2008) Modern Methods for Robust Regression. Sage Publications, London.CrossRefGoogle Scholar
Baarda, W. (1968) A Testing procedure for use in geodetic networks. Netherlands Geodetic Commission, Publications on Geodesy, New Series 2, No. 5, Delft, Netherlands.CrossRefGoogle Scholar
Brenner, M. (1990) Implementation of a RAIM Monitor in a GPS Receiver and an Integrated GPS/INS. Proceedings of ION GPS 1990, 19–21 September 1990, Colorado Springs, Colorado, 397414.Google Scholar
Caspary, W. F. (1987) Concepts of Network and Deformation Analysis. Monograph 11, School of Geomatic Engineering, The University of New South Wales, Sydney.Google Scholar
Donoho, D. L. and Huber, P. J. (1983) The Notion of Breakdown Point. A Festschrift For Erich L. Lehmann, Editors Bickel, P. J., Doksum, K. and Hodges, J. L., Wadsworth, Belmont, California, 157185.Google Scholar
Edgeworth, F. Y. (1887) On Observations Relating to Several Quantities. Hermathena, 6, 279285.Google Scholar
Ferguson, T. S. (1961) On the Rejection of Outliers. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, California, 1, 253287.Google Scholar
Hampel, F. R. (1971) A General Qualitative Definition of Robustness. The Annals of Mathematical Statistics, 42, 18871896.CrossRefGoogle Scholar
Hampel, F. R., Ronchetti, E. Z., Rousseeuw, P. J. and Stahel, W. A. (1986) Robust Statistics: The Approach Based on Influence Functions. Wiley, New York.Google Scholar
Hewitson, S. and Wang, J. (2006) GNSS Receiver Autonomous Integrity Monitoring (RAIM) Performance Analysis. GPS Solutions, 10(3), 155170.CrossRefGoogle Scholar
Hewitson, S. and Wang, J. (2007) GNSS Receiver Autonomous Integrity Monitoring with a Dynamic Model. Journal of Navigation, 60(2), 247263.CrossRefGoogle Scholar
Hewitson, S.Lee, H. K. and Wang, J. (2004) Localizability Analysis for GPS/Galileo Receiver Autonomus Integrity Monitoring. Journal of Navigation, 57(2), 245259.CrossRefGoogle Scholar
Huber, P. J. (1964) Robust Estimation of Location Parameters. Annals of Mathematical Statistics, 35, 73101.CrossRefGoogle Scholar
Jaeckel, L. A. (1972) Estimating Regression Coefficients by Minimising the Dispersion of the Residuals. Annals of Mathematical Statistics, 43, 14491458.CrossRefGoogle Scholar
Kelly, R. J. (1998) The Linear Model, RNP, and the Near-Optimum Fault Detection and Exclusion Algorithm. Global Positioning System: Papers Published in NAVIGATION, The Institute of Navigation, Fairfax, Virginia, 5, 227260.Google Scholar
Krarup, T., Kubik, K. and Juhl, J. (1980) Götterdämmerung Over Least Squares. Proceedings of International Society for Photogrammetry 14th Congress, Hamburg, 370378.Google Scholar
Kuter, M. H., Nachtsheim, C. J., Neter, J. and Li, W. (2005) Applied Linear Statistical Models. 5th Edn., McGraw-Hill Irwin, New York.Google Scholar
Lee, Y. C. (1986) Analysis of Range and Position Comparison Methods as a Means to Provide GPS Integrity in the User Receiver. Global Positioning System: Papers Published in NAVIGATION, The Institute of Navigation, Fairfax, Virginia, 5, 519.Google Scholar
Parkinson, B. W. and Axelrad, P. (1988) Autonomous GPS Integrity Monitoring Using the Pseudorange Residual. Navigation, 35(2), 4968.CrossRefGoogle Scholar
Pervan, B. S., Lawrence, D. G., Cohen, C. E. and Parkinson, B. W. (1996) Parity Space Methods For Autonomous Fault Detection and Exclusion Algorithms Using Carrier Phase. Proceedings of ION PLANS 1996, 22–16 April 1996, Atlanta, Georgia, 649656.Google Scholar
Rousseeuw, P. J. (1984) Least Median of Squares Regression. Journal of the American Statistical Association, 79, 871880.CrossRefGoogle Scholar
Rousseeuw, P. J. and Leroy, A. M. (1987) Robust Regression and Outlier Detection. John Wiley and Sons, New York.CrossRefGoogle Scholar
Sturza, M. A. (1988) Navigation system Integrity Monitoring Using Redundant Measurements. Navigation, 35(4), 6987.CrossRefGoogle Scholar
Wang, J. and Chen, Y. Q. (1994a) On the Reliability Measures of Observations. Acta Geodaetica et Cartographica Sinica (English Edition), Journal of Chinese Society of Geodesy, Photogrammetry and Cartography, 4251.Google Scholar
Wang, J. and Chen, Y. Q. (1994b) On the Localizability of Blunders in Correlated Coordinates of Junction Points in Densification Networks. Australian Journal of Geodesy, Photogrammetry and Surveying, 60, 109119.Google Scholar
Wang, J. and Ober, P. B. (2009) On the Availability of Fault Detection and Exclusion in GNSS Receiver Autonomous Integrity Monitoring. Journal of Navigation, 62(2), 111.CrossRefGoogle Scholar
Wang, J. and Wang, J. (2007) Mitigation the Effects of Multiple Outliers on GNSS Navigation with M-Estimation Schemes. Proceedings of IGNSS Symposium 2007, 4–6 December 2007, Sydney, 19.Google Scholar
Yang, Y., Cheng, M. K., Shum, C. K. and Tapley, B. D. (1999) Robust Estimation of Systematic Errors of Satellite Laser Range. Journal of Geodesy, 73, 345349.CrossRefGoogle Scholar
Yohai, V. J. (1987) High Breakdown Point and High Efficiency Robust Estimates for Regression. The Annals of Statistics, 15, 642656.CrossRefGoogle Scholar
Yohai, V. J. and Rousseeuw, P. J. (1984) Robust and Nonlinear Time Series Analysis. Lecture Notes in Statistics, No. 26, Editors Franke, J., Härdle, W. and Martin, D., Springer-Verlag, New York, 256272.Google Scholar