Detection of Outliers in GPS Measurements by Using Functional-Data Analysis
Publication: Journal of Surveying Engineering
Volume 137, Issue 4
Abstract
The identification of outliers in global positioning system (GPS) observations—to compare equipment, positioning methods, or working conditions—has traditionally been performed using univariate or multivariate statistics. However, these methods have certain drawbacks when processing data collected by GPS receivers. Such data can be more suitably handled as observations at discrete points of a smooth stochastic process and, consequently, other statistical approaches to the analysis of functional data may prove more suitable. We analyzed the applicability of the concept of functional depth to the identification of outliers in GPS observations. The proposed method was applied to 12 series of GPS receiver data collected in an open space and in similar signal reception conditions. The results obtained adapted better to the expected results, given the signal-reception conditions, than those obtained by the classical statistical approaches used by other writers to compare GPS observations.
Get full access to this article
View all available purchase options and get full access to this article.
References
Cuevas, A., Febrero, M., and Fraiman, R. (2006). “On the use of the bootstrap for estimating functions with functional data.” Comput. Stat. Data Anal., 51(2), 1063–1074.
Cuevas, A., and Fraiman, R. (1997). “A plug-in approach to support estimation.” Ann. Stat., 25(6), 2300–2312.
Febrero, M., Galeano, P., and González-Manteiga, W. (2008). “Outlier detection in functional data by depth measures, with application to identify abnormal NOx levels.” Environmetrics, 19(4), 331–345.
Fraiman, R., and Muniz, G. (2001). “Trimmed means for functional data.” Test, 10(2), 419–440.
Guochang, X. (2003). GPS: Theory, algorithms, and applications, Springer, Berlin.
Hasegawa, H., and Yoshimura, T. (2003). “Application of dual-frequency GPS receivers for static surveying under tree canopies.” J. For. Res., 8(2), 103–110.
Hollander, M., and Wolfe, D. A. (1999). Nonparametric statistical methods, Wiley, New York.
López-Pintado, S., and Romo, J. (2007). “Depth-based inference for functional data.” Comput. Stat. Data Anal., 51(10), 4957–4968.
Naesset, E., and Jonmeister, T. (2002). “Assessing point accuracy of DGPS under forest canopy before data acquisition, in the field and after postprocessing.” Scand. J. For. Res., 17(4), 351–358.
Nickitopoulou, A., Protopsalti, K., and Stiros, S. (2006). “Monitoring dynamic and quasi-static deformations of large flexible engineering structures with GPS: Accuracy, limitations and promises.” Eng. Struct., 28(10), 1471–1482.
Peng, L., and Qi, Y. (2008). “Bootstrap approximation of tail dependence function.” J. Multivariate Anal., 99(8), 1807–1824.
Psimoulis, P., and Stiros, S. (2008). “Experimental assessment of the accuracy of GPS and RTS for the determination of the parameters of oscillation of major structures.” Comput. Aided Civ. Infrastruct. Eng., 23(5), 389–403.
Ramsay, J. O., and Silverman, B. W. (2005). Functional data analysis, Springer, New York.
Regional GNSS Network. (2007). “Red de Estaciones GNSS de Castilla y León.” 〈http://gnss.itacyl.es/〉 (Aug. 25, 2007).
Rodríguez-Pérez, J. R., Álvarez, M. F., and Sanz-Ablanedo, E. (2007). “Assessment of low-cost GPS receiver accuracy and precision in forest environments.” J. Surv. Eng., 133(4), 159–167.
Serr, K., Windholz, T., and Weber, K. (2006). “Comparing GPS receivers: A field study.” URISA J., 18(2), 19–23.
Tiberius, C., and Kenselaar, F. (2003). “Variance component estimation and precise GPS positioning: Case study.” J. Surv. Eng., 129(1), 11–18.
Van Sickle, J. (1996). GPS for land surveyors, Ann Arbor Press, Chelsea, MI.
Wdowinski, S., Bock, Y., Zhang, J., Fang, P., and Genrich, J. (1997). “Southern California permanent GPS geodetic array: Spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake.” J. Geophys. Res. [Solid Earth Planets], 102(B8), 18057–18070.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 137 • Issue 4 • November 2011
Pages: 150 - 155
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Jul 19, 2010
Accepted: Jan 19, 2011
Published online: Jan 20, 2011
Published in print: Nov 1, 2011
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.