Gross-Error Detection in GNSS Networks Using Spanning Trees
Publication: Journal of Surveying Engineering
Volume 142, Issue 3
Abstract
Many methods and techniques have been developed to detect gross errors in geodetic measurements, but none seems to have prevailed. Statistical tests and robust methods are the most common approaches for detecting outliers in geodetic measurements. Least-squares adjustment and iterative attitudes are the essence of those methods. In this paper, closing loops in Global Navigation Satellite System (GNSS) networks are used to detect gross errors. Spanning trees are used to define a set of independent loops in the network. Careful examination of the misclosure of loops assists in defining the faulty vectors. The method is very effective and delivers another alternative for outlier detection without using adjustment computation and statistical tests. The method of outlier detection by means of spanning trees is presented and tested against well-known methods like convectional statistical tests (w-test, τ-test, and t-test) and robust M-estimation methods (Andrews, Huber, and Danish). A number of tests were performed on a GNSS network that contains 115 points and 917 vectors to detect gross errors in different scenarios, and the results are presented in the paper. Based on the results of the presented tests, it is seen that the w-test and the M-estimation methods correctly detect all outliers in the GNSS network, whereas τ-tests and t-tests do not always detect the correct errors. The new method for detection of gross errors by means of spanning trees performs quite well and can correctly exclude all outliers with only one iteration.
Get full access to this article
View all available purchase options and get full access to this article.
References
Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H., and Tukey, J. W. (1972). Robust estimates of location: Surveys and advances, Princeton University Press, Princeton, NJ.
Baarda, W. (1968). A testing procedure for use in geodetic networks, Vol. 2, No. 5, Netherlands Geodetic Commission Publications on Geodesy, New Series, Delft, Netherlands.
Baselga, S. (2007). “Critical limitation in use of τ test for gross error detection.” J. Surv. Eng., 52–55.
Chen, Y. Q., Kavouras, M., and Chrzanowski, A. (1987). “A strategy for the detection of outlying observations in measurements of high precision.” Can. Surveyor, 41(4), 527–40.
Delcev S., Gucevic J., and Ogrizovic V. (2015). “Comparison of different software for GPS network adjustment.” FIG Working Week, Sofia, Bulgaria.
Eckl, M. C., Snay, R. A., Soler, T., Cline, M. W., and Mader, G. L. (2001) “Accuracy of GPS-derived relative positions as a function of interstation distance and observing-session duration.” J. Geod., 75(12), 633–640.
Ethrog, U. (1991). “Statistical test of significance for testing outlying observations.” Surv. Rev., 31(240), 62–70.
Euler, L. (1736). “Solution problematis ad geometrian situs pertinantis.” Academimae Petropolitanae, 8, 128–140.
Even-Tzur, G. (2001). “Graph theory applications to GPS networks.” GPS Solutions, 5(1), 31–38.
Even-Tzur, G., Salmon, E., Kozakov, M., and Rosenblum, M. (2004). “Designing a geodetic-geodynamic network: a comparative study of data processing tools.” GPS Solutions, 8(1), 30–35.
Gökalp E., Güngör O., and Boz, Y. (2008). “Evaluation of different outlier detection methods for GPS networks.” Sensors, 8(11), 7344–7358.
Gullu, M., and Yilmaz, I. (2010) “Outlier detection for geodetic nets using ADALINE learning algorithm.” Sci Res Essays, 5(5), 440–447.
Heck, B. (1981). “Der Einfluss einzelner Beobachtungen auf das Ergebnis einer Ausleichung und die Suche nach Ausreissern in den Beobachtungen.” AVN, 88(1), 17–34.
Hekimoglu, S., Erdogan, B., Soycan, M., and Durdag, U. (2014). “Univariate approach for detecting outliers in geodetic networks.” J. Surv. Eng., 04014006.
Huber, P. J. (1964). “Robust estimation of a location parameter.” Ann. Math. Stat., 35(1), 73–101.
Huber, P. J. (1981). Robust statistics, Wiley, New York.
Jureckova, J., and Sen, P. K. (1996). Robust statistical procedures asymptotics and interrelations, Wiley, New York.
Kavouras, M. (1982). “On the detection of outliers and the determination of reliability geodetic networks.” Technical Rep. 87, Dept. of Surveying Engineering, University of New Brunswick, New Brunswick, Canada.
Kepner, J., and Gilbert, J. eds. (2011). Graph algorithms in the language of linear algebra, Vol. 22, Society for Industrial and Applied Mathematics, Philadelphia.
Knight, N. L., and Wang, J. (2009). “A comparison of outlier detection procedures and robust estimation methods in GPS positioning.” J. Navig., 62(04), 699–709.
Koch, K. R. (1985). “Test von Ausreissern in Beobachtungspaaren.” Z. Vermess, 110, 34–38.
Koch, K. R. (1999). Parameter estimation and hypothesis testing in linear models, 2nd Ed., Springer, New York.
Kok, J. J. (1984). “On data snooping and multiple outlier testing.” NOAA Tech. Report NOS NGS 30, National Geodetic Survey, Rockville, Md.
Krarup, T., Juhl, J., and Kubik, K. (1980). “Götterdaemmerung over least squares adjustment.” Proc., 14th Cong. of the int. Soc. Photogr., International archives of Photogrammetry, Hamburg, Germany, 369–378.
Pope, A. J. (1976). “The statistics of residuals and the outlier detection of outliers.” NOAA Tech. Rep. NOS 65, NGS 1, National Geodetic Survey, Rockville, MD.
Sisman, Y. (2010). “Outlier measurement analysis with the robust estimation.” Sci. Res. Essays, 5(7), 668–678.
Snow, K., and Schaffrin, B. (2003). “Three-dimensional outlier detection for GPS networks and their densification via the BLIMPBE approach.” GPS Solutions, 7(2), 130–139.
Teunissen, P. J. G. (2003). Adjustment theory: An introduction, Delft University Press, Delft, Netherlands.
Trimble Total Control 2.73 [Computer software]. Trimble Navigation, Sunnyvale, CA.
Wieser A., and Brunner F. K. (2002). “Short static GPS sessions: Robust estimation results.” GPS Solutions, 5(3), 70–79.
Information & Authors
Information
Published In
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jan 26, 2015
Accepted: Nov 24, 2015
Published online: Jan 28, 2016
Discussion open until: Jun 28, 2016
Published in print: Aug 1, 2016
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.