Deformation Detection in the GPS Real-Time Series by the Multiple Kalman Filters Model
Publication: Journal of Surveying Engineering
Volume 136, Issue 4
Abstract
Global Positioning System (GPS) is widely used for monitoring some natural phenomena and man-made structures. The detection of the deformation epoch in real time is of great importance in these applications. This study is concerned with designing algorithms to detect the deformation epoch in order to improve the quality of GPS measurements for the real-time deformation applications. In this regard, the multiple Kalman filters model based on the idea of model selection is proposed to improve the reliability of the detection of the deformation epoch. For the model selection, the proposed model makes use of the statistical criterion comparison in each case instead of the hypothesis test. The model with the lower value of the statistical criterion is to be preferred. According to the statistical criterion, the optimal Kalman filter model can be selected to describe the time series and to identify the deformation epoch at each epoch. The simulated data and the GPS kinematic time series are used to verify the effectiveness of the multiple Kalman filters model.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers would like to thank Professor Foerstner at the University of Bonn for his valuable suggestions and detailed discussion. They also thank two anonymous reviewers for their helpful comments that greatly improved the paper.
References
Brown, R. G., and Hwang, P. Y. (1992). Introduction to random signals and applied Kalman filtering, 2nd Ed., Wiley, New York.
Cai, J., Wang, J., Wu, J., Hu, C., Grafarend, E., and Chen, J. (2008). “Horizontal deformation rate analysis based on multiepoch GPS measurements in Shanghai.” J. Surv. Eng., 134(4), 132–137.
Gelb, A. (1974). Applied optimal estimation, The MIT Press, Cambridge, Mass. and London.
Grewal, M. S., and Andrews, A. P. (2001). Kalman filtering: Theory and practice using Matlab, 2nd Ed., Wiley, New York.
Ince, C. D., and Sahin, M. (2000). “Real-time deformation monitoring with GPS and Kalman filter.” Earth, Planets Space, 52(10), 837–840.
Kalman R. E. (1960). “A new approach to linear filtering and prediction problems.” Trans. ASME J. Basic Engineering, 82, 35–45.
Kim, D., Langley, R. B., Bond, J., and Chrzanowski, A. (2003). “Local deformation monitoring using GPS in an open pit mine: Initial study.” GPS Solutions, 7(3), 176–185.
Mertikas, S. P. (2001). “Automatic and online detection of small but persistent shifts in GPS station coordinates by statistical process control.” GPS Solutions, 5(1), 39–50.
Mertikas, S. P., and Rizos, C. (1997). “Online detection of abrupt changes in the carrier-phase measurements of GPS.” J. Geodesy, Berlin, 71(8), 469–482.
Mikhail, E. M. (1976). Observations and least squares, IEP-A DUN-Donnelley, New York.
Okatan, A., Hajiyev, C., and Hajiyeva, U. (2007). “Kalman filter innovation sequence based fault detection in LEO satellite attitude determination and control system.” 3rd Int. Conf. on Recent Advances in Space Technologies 2007, Proc. IEEE RAST, Istanbul, Turkey, 411–416.
Rissanen, J. (1983). “A universal prior for integers and estimation by minimum description length.” Ann. Stat., 11(2), 416–431.
Schön, S. (2007). “Affine distortion of small GPS networks with large height.” GPS Solutions, 11(2), 107–117.
Strang, G., and Borre, K. (1997). Linear algebra, geodesy, and GPS, Wellesley-Cambridge Press, Wellesley, Mass.
Teunissen, P. J. G. (1990). “Quality control in integrated navigation systems.” Proc., IEEE PLANS, Position Location and Navigation Symp., Las Vegas, 158–165.
Welch, G., and Bishop, G. (2006). “An introduction to the Kalman filter.” TR95-041, Univ. of North Carolina at Chapel Hill, Chapel Hill, N.C.
Willsky, A. S. (1976). “A survey of design methods for failure detection in dynamic systems.” Automatica, 12, 601–611.
Yang, Y., He, H., and Xu, G. (2001). “Adaptively robust filtering for kinematic geodetic positioning.” J. Geodesy, Berlin, 75(2–3), 109–116.
Information & Authors
Information
Published In
Copyright
© 2010 ASCE.
History
Received: Sep 9, 2009
Accepted: Jan 7, 2010
Published online: Oct 15, 2010
Published in print: Nov 2010
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.