Abstract
Collocation is a popular method in geodesy for combining heterogeneous data of different kind. It comprises adjustment, interpolation and extrapolation as special cases. Current methods of collocation apply however only if the trend parameters are real valued. In the present contribution we will generalize the theory of collocation by permitting the trend parameters to be integer valued. It will be shown how the collocation formulae change when the integerness of the trend parameters is taken into account. We will also address the problem of evaluating the quality of the collocation results. The quality of the collocation results is usually described by the so-called error covariances. We will show how the error covariances change due to the integerness of the trend. But we also show that the approach based on error covariances does not give an adequate quality description of the collocation results in case of an integer trend. How this approach needs to be generalized is also presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dermanis, A. (1980): Adjustment of geodetic observations in the presence of signals. In: Proceedings of the International School of Advanced Geodesy. Bollettino di Geodesia e Scienze Affini. Vol. 38, pp. 419–445.
de Jonge P.J., C.C.J.M. Tiberius (1996): The LAMBDA method for integer ambiguity estimation: implementation aspects. Publications of the Delft Computing Centre, LGR-Series No. 12.
Krarup, T. (1969): A contribution to the mathematical foundation of physical geodesy. Publ. Danish Geod. Inst. 44, Copenhagen.
Moritz, H. (1973): Least-squares collocation. DGK, A 59, Muenchen.
Moritz, H. (1980): Advanced Physical Geodesy. Herbert Wichmann Verlag Karlsruhe.
Sanso, F. (1986): Statistical methods in physical geodesy. In: Mathematical and numerical techniques in physical geodesy, H. Suenkel Ed., Lecture Notes in Earth Sciences, Springer-Verlag, Vol. 7, 49–156.
Teunissen, P.J.G. (1993): Least-squares estimation of the integer GPS ambiguities. Invited Lecture, Section IV Theory and Methodology, IAG General Meeting, Beijing, China, August 1993. Also in: LGR Series, No. 6, Delft Geodetic Computing Centre.
Teunissen, P.J.G. (1995): The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. Journal of Geodesy, 70: 65–82.
Teunissen, P.J.G. (1999): An optimality property of the integer least-squares estimator. Journal of Geodesy, 73: 587–593.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Teunissen, P. (2008). Collocation with Integer Trend. In: Xu, P., Liu, J., Dermanis, A. (eds) VI Hotine-Marussi Symposium on Theoretical and Computational Geodesy. International Association of Geodesy Symposia, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74584-6_36
Download citation
DOI: https://doi.org/10.1007/978-3-540-74584-6_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74583-9
Online ISBN: 978-3-540-74584-6
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)