GNSS Elevation-Dependent Stochastic Modeling and Its Impacts on the Statistic Testing
Publication: Journal of Surveying Engineering
Volume 142, Issue 2
Abstract
Only the correct stochastic model can be applied to derive the optimal parameter estimation and then realize the precision global navigation satellite system (GNSS) positioning. The key for refining the GNSS stochastic model is to establish the easy-to-use stochastic model that should capture the error characteristics adequately based on the estimated precisions from the real observations. In this paper, the authors study the GNSS elevation-dependent precision modeling and analyze its impact on the statistic testing involved in the adjustment reliability. With the zero-baseline dual-frequency Global Positioning System (GPS) data, the authors first estimate the elevation-dependent precisions and establish the stochastic models by fitting them with three predefined functions, including the unique precision function and the sine and exponential types of elevation-dependent functions. Three established models are then evaluated by their performance in the overall and w-statistic testing. The results indicated that the GNSS observation precisions are indeed elevation dependent, but this dependence differed from the observation types. The inadequate elevation-dependent model will result in the incorrect statistics and lead to larger wrong decisions, for instance, larger false alarms.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work is supported by the National Natural Science Funds of China (41374031, 41574023, and 41274035), the State Key Laboratory of Geo-information Engineering (SKLGIE2013-M-2-2), and the China Special Fund for Surveying, Mapping and Geo-information Research in the Public Interest (HY14122136).
References
Bona, P. (2000). “Precision, cross correlation, and time correlation of GPS phase and code observations.” GPS Solutions, 4(2), 3–13.
Dach, R., Hugentobler, U., Fridez, P., and Meindl, M. (2007). User’s manual of Bernese GPS software: version 5.0, Astronomical Institute, Univ. of Bern, Bern, Switzerland.
Eueler, H.-J., and Goad, C. (1991). “On optimal filtering of GPS dual frequency observations without using orbit information.” Bull. Géod. 65(2), 130–143.
Herring, T. A., King, R. W., and McClusky, S. C. (2010). Gamit reference manual: GPS analysis at MIT, Release 10.4, Dept. of Earth, Atmospheric, and Planetary Sciences, MIT, Cambridge, MA.
Koch, K. (1988). Parameter estimation and hypothesis testing in linear models, Springer, New York.
Koch, K. R., and Kusche, J. (2002). “Regularization of geopotential determination from satellite data by variance components.” J. Geod., 76(5), 259–268.
Li, B., Shen, Y., and Lou, L. (2011). “Efficient estimation of variance and covariance components: A case study for GPS stochastic model evaluation.” IEEE Trans. Geosci. Remote Sens., 49(1), 203–210.
Li, B., Shen, Y., and Xu, P. (2008). “Assessment of stochastic models for GPS measurements with different types of receivers.” Chin. Sci. Bull., 53(20), 3219–3225.
Liu, X. (2002). “A comparison of stochastic models for GPS single differential kinematic positioning.” 15th Int. Technical Meeting, ION GPS 2002, Portland, OR.
Teunissen, P. J. G. (1995). “The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation.” J. Geod., 70(1), 65–82.
Teunissen, P. J. G. (1998). “Success probability of integer GPS ambiguity rounding and bootstrapping.” J. Geod., 72(10), 606–612.
Teunissen, P. J. G. (2000). “The success rate and precision of GPS ambiguities.” J. Geod., 74(3), 321–326.
Teunissen, P. J. G. (2006). Testing theory: An introduction, 2nd Ed., Delft University Press, Delft, The Netherlands.
Teunissen, P. J. G. (2007). “Influence of ambiguity precision on the success rate of GNSS integer ambiguity bootstrapping.” J. Geod., 81(5), 351–358.
Teunissen, P. J. G., Simons, D., and Tiberius, C. C. J. M. (2008). Probability and observation theory, Lecture Notes AE2-EO1, Faculty of Aerospace Engineering, Delft Univ. of Technology, Delft, The Netherlands.
Tiberius, C., and Kenselaar, F. (2000). “Estimation of the stochastic model for GPS code and phase observables.” Surv. Rev., 35(277), 441–454.
Verhagen, S., and Li, B. (2012). LAMBDA software package: MATLAB implementation, Version 3.0. Delft Univ. of Technology and Curtin Univ., Perth, Australia.
Wang, J., Stewart, M., and Sakiri, M. (1998). “Stochastic modeling for static GPS baseline data processing.” J. Surv. Eng., 171–181.
Yang, Y., Zeng, A., and Zhang, J. (2009). “Adaptive collocation with application in height system transformation.” J. Geod., 83(5), 403–410.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 142 • Issue 2 • May 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Mar 5, 2014
Accepted: Sep 15, 2015
Published online: Dec 30, 2015
Published in print: May 1, 2016
Discussion open until: May 30, 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.