Realistic Uncertainty Measures for GPS Observations
The classical concept in geodesy of an exclusively stochastic assessment of the total error budget of observation data is extended. Uncertainty due to remaining systematics (imprecision) is treated consistently by interval mathematics. The superposition of both random variability (stochasticity) and imprecision yields uncertainty measures such as extended point confidence regions which are more realistic. The new concept is applied to GPS phase measurements. It is exemplarily discussed for a synthetic GPS network.
KeywordsSystematic Errors Imprecision Interval Mathematics GPS
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- Brunner F. and M. Gu (1991): An improved model for the dual frequemcy ionospheric correction of GPS observations. manuscript geodaetica, 16:205–214.Google Scholar
- Henk M., J. Richter-Gebert and G. Ziegler (1997): Basic Properties of convex Polytopes. In: J. Goodman and J. O’Rourke, editors. Handbook of Discrete and Computational Geometry, CRC Press, Boca Raton, pp.243–270.Google Scholar
- ISO (1995): Guide to the Expression of Uncertainty in Measurements. International Organization of Standardization.Google Scholar
- Koch K.-R. (1999): Parameter Estimation and Hypothesis Testing in Linear Models. Springer Berlin.Google Scholar
- Klobuchar J. (1996): Ionospheric effects on GPS. In: B. Parkinson and J. Spilker, editors. Global Positioning System: Theory and Applications, American Society of Aeronautics and Astronautics, Vol.163:485–502.Google Scholar
- Kutterer H. (2002): Joint treatment of random variability and imprecision in GPS data analysis. Journal of Global Positioning Systems, 1(2):96–105.Google Scholar
- Saastamoinen J. (1973): Contribution to the theory of atmospheric refraction. Bulletin Géodésique, 107:13–34.Google Scholar
- Schön S. and H. Kutterer (2001a): Interval-based Description of Measurement Uncertainties and Network Optimization. In: A. Carosio and H. Kutterer, editors. Proceedings of the First International Symposium on Robust Statistics and Fuzzy Techniques in Geodesy and GIS. Report No.295, Swiss Federal Institute of Technology Zurich (ETH), Institute of Geodesy and Photogrammetry, pp.41–46.Google Scholar
- Schön S. and H. Kutterer (2001b): Optimal Design of Geodetic Monitoring Networks by means of Interval Mathematics. Proceedings of the 10th FIG International Symposium on Deformation Measurements held in Anaheim California, March 19–22 2001, pp.362–371.Google Scholar
- Teunissen P. and A. Kleusberg (1998): GPS Observation Equations and Positioning Concepts. In: P. Teunissen and A. Kleusberg (editors). GPSfor Geodesy, 2nd ed.. Springer Berlin, pp.187–230.Google Scholar