Projectivity, affine, similarity and euclidean coordinates transformation parameters from ITRF to EUREF in Turkey
-
Kutubuddin Ansari
,
Ozsen Corumluoglu
Abstract
Today, in geodesy most practical applications is to use a datum to get three dimensional position of a particular point. The geodetic techniques generally provide time dependent coordinates in global datum. The difference between the global datum like international terrestrial reference frame (ITRF) to local datum like Europe fixed reference frame (EUREF) can be up to several centimeters due to different velocity rate of tectonic plates. To get high-precision measurements, there is an increasing need of time dependent transformations from the global level to local level. The present paper treats, this theoretical problem of geodesy by using mathematical dependency between two spatial coordinate systems whose common points are given in both systems. The paper describes four different (projective, affine, similarity and euclidean) modified methodologies for the transformation between global (ITRF) to local (EUREF) by using the Turkish permanent GPS network (TPGN) as an example. The time series from TPGN stations are used to review these transformations from ITRF 2008 to EUREF 2008. The transformation parameters in all cases shows that mostly transform coordinates depends on its counterparts (X to x and Y to y) and others coordinates have very less effect. Finally to show the validity of our model a comparative analysis with standard Bursa-Wolf and Molodensky-Badekas models has been presented. The test shows that our model error is equivalent to standard models, in this view the presented models are acceptable and can improve our understanding in coordinate transformation.
Busra-Wolf model in general form is given by:
where, X is coordinates vector in the first system, x coordinates vector in the second system, I is Identity matrix, T is translation vector and R is rotation matrix. The equation in matrix form:
For n points:
where
The equation in matrix form can be written in following form:
For n points
Appendix II Flowchart of 3D coordinate transformation
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© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Research Articles
- High frequent total station measurements for the monitoring of bridge vibrations
- Satellite-based Estimates of Ground Subsidence in Ordos Basin, China
- Geodetic monitoring of subrosion-induced subsidence processes in urban areas
- Monitoring of vertical deformations by means high-precision geodetic levelling. Test case: The Arenoso dam (South of Spain)
- Choosing the optimal number of B-spline control points (Part 2: Approximation of surfaces and applications)
- Projectivity, affine, similarity and euclidean coordinates transformation parameters from ITRF to EUREF in Turkey
Articles in the same Issue
- Frontmatter
- Research Articles
- High frequent total station measurements for the monitoring of bridge vibrations
- Satellite-based Estimates of Ground Subsidence in Ordos Basin, China
- Geodetic monitoring of subrosion-induced subsidence processes in urban areas
- Monitoring of vertical deformations by means high-precision geodetic levelling. Test case: The Arenoso dam (South of Spain)
- Choosing the optimal number of B-spline control points (Part 2: Approximation of surfaces and applications)
- Projectivity, affine, similarity and euclidean coordinates transformation parameters from ITRF to EUREF in Turkey
