Quasi-Accurate Detection of Outliers for Correlated Observations
Publication: Journal of Surveying Engineering
Volume 133, Issue 3
Abstract
Experience with surveying practices has shown that correlated observations are very often encountered, especially in preprocessed observations. Hence, it is not only of theoretical interest, but also of practical interest, to investigate the detection of outliers for correlated observations. The so-called quasi-accurate detection (QUAD) of outliers for correlated observations is developed. The corresponding computation principle and its implementation are investigated in detail. The key of QUAD is how to select the quasi-accurate observations (QAO) reasonably. A new, distinctive sensitivity-analysis based method is proposed for selecting the QAO. For illustrative purposes, an application to global positioning system network adjustment is analyzed. The numerical results demonstrate that more than one outlier can be correctly identified and localized by using the proposed procedure.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The project that led to this paper was sponsored by the National Natural Science Foundation of China (Grant No. NNSFC40474009) and the China National Science Fund for Distinguished Young Scholars (Grant No. UNSPECIFIED40625013). The first writer is also supported by the BHP Billiton Scholarship at GUCAS. The writers would like to thank the anonymous reviewers for critical comments and suggestions, and for pointing out some references.
References
Baarda, W. (1968). “A testing procedure for use in geodetic networks.” Netherlands Geod. Comm., Publ. on Geodesy, New Series, 2(5), Delft, The Netherlands.
Golub, G. H., and Van Loan, C. F. (1996). Matrix computations, 3rd Ed., Johns Hopkins, Baltimore.
Grafarend, E. W., Heister, H., Kelm, R., Kropff, H., and Schaffrin, B. (1979). Optimierung geodätischer messoperationen, Wichmann-Verlag, Karlsruhe, Germany.
Grafarend, E. W., and Sanso, F. (1985). Optimization and design of geodetic networks, Springer, Heidelberg, Germany.
Grafarend, E. W., and Schaffrin, B. (1993). Ausgleichungsrechnung in linearen modellen, BI-Wissenschaftsverlag, Mannheim, Germany.
Gui, Q., Li, G., and Ou, J. (2005). “Robust-biased estimation based on quasi-accurate detection.” J. Surv. Eng., 131(3), 67–72.
Hampel, F. (2001). “Robust statistics.” Proc., 1st Int. Symp. on Robust Statistics and Fuzzy Techniques in Geodesy and GIS, Zurich, Switzerland, 13–17.
Han, B. M. (2002). “Detection and repair of continuous cycle slips in GPS carrier-phase data using QUAD method.” Proc., ION GPS-2002 Meeting, Portland, Ore., 1353–1360.
Huber, P. J. (1981). Robust statistics, Wiley, New York.
Koch, K. R. (1999). Parameter estimation and hypothesis testing in linear models, 2nd Ed. Springer, Berlin.
Ou, J. K. (1999). “A new method of identifying and locating gross errors: Quasi-accurate detection.” Chin. Sci. Bull., 44(23), 2200–2204.
Ou, J. K. (2001). “Selection of quasi-accurate observations and ‘hive-off’ phenomena about the estimators of real errors.” Proc., 1st Int. Symp. on Robust Statistics and Fuzzy Techniques in Geodesy and GIS, Zurich, Switzerland, 73–78.
Pelzer, H. (1983). “Detection of errors in the functional adjustment model.” Deutsche Geod. Komm., Reihe A, Nr. 98, 61–70, Munich, Germany.
Pope, A. (1976). “The statistics of residuals and detection of outliers.” NOAA Technical Rep. No. 66, NGS 1, Rockville, Md.
Rousseeuw, P. J., and Leroy, A. M. (1987). Robust regression and outlier detection, Wiley, New York.
Schaffrin, B. (1997). “Reliability measures for correlated observations.” J. Surv. Eng., 123(3), 126–137.
Schaffrin, B., and Iz, H. B. (2002). “BLIMPBE and its geodetic applications.” Vistas for geodesy in the new millennium, J. Adam and K. P. Schwarz, eds., Springer, Berlin, 377–381.
Sun, W. P. (1994). “A new method for localization of gross errors.” Surv. Rev., 32(252), 344–358.
Teunissen, P. J. G. (1990). “Quality control in integrated navigation systems.” Proc., IEEE PLANS90, Las Vegas, 158–165.
Teunissen, P. J. G. (1998). “Minimal detectable biases of GPS data.” J. Geodesy, Berlin, 72(4), 236–244.
Wolf, P. R., and Ghilani, C. D. (1997). Adjustment computations: Statistics and least squares in surveying and GIS, 3rd Ed., Wiley, New York.
Xu, P. L. (1989). “On robust estimation with correlated observations.” Bull. Geod., 63(3), 237–252.
Xu, P. L. (2005). “Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness.” J. Geodesy, Berlin, 79(1–3), 146–159.
Xu, P. L., Shimada, S., Fujii, Y., and Tanaka, T. (2000). “Invariant geodynamical information in geometric geodetic measurements.” Geophys. J. Int., 142(2), 586–602.
Yang, Y. X., Song, L. J., and Xu, T. H. (2002). “Robust estimator for correlated observations based on bifactor equivalent weights.” J. Geodesy, Berlin, 76(6–7), 353–358.
Yang, Y., Xu, T., and Song, L. (2005). “Robust estimation of variance components with application in global positioning system network adjustment.” J. Surv. Eng., 131(4), 107–112.
Zhou, J. W. (1980). “Quasi-stable adjustment of monitoring networks (in Chinese).” Spec. Publ., No. 2, Wuhan Inst. Geod. and Geophys., Chinese Acad. of Sci., Wuhan, P.R. China.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 133 • Issue 3 • August 2007
Pages: 129 - 133
Copyright
© 2007 ASCE.
History
Received: Aug 29, 2005
Accepted: Nov 17, 2006
Published online: Aug 1, 2007
Published in print: Aug 2007
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.