On the determination of transformation parameters between different ITRS realizations using Procrustes approach in Turkey

Abstract

Abstract The International Terrestrial Reference Frame (ITRF) solutions that are published by the International Earth Rotation and Reference Systems Service (IERS) are annual realizations of the ITRS (International Terrestrial Reference System). The results expressed in two different ITRS realizations can be compared using the transformation parameters that provide a link between different ITRF solutions. Generally, the 7-parameter (the three translation parameters, three rotation parameters and one scale factor) Helmert transformation is employed to compute the transformation parameters. However, the number of transformation parameters can be increased for better understanding. For example, 3 different scale factors may be computed instead of one scale factor. In this paper, the 9-parameter (the three translation parameters, three rotation parameters and three scale factors) transformation model and its solution by Procrustes approach is considered. Transformation parameters between ITRF 05 and ITRF 08 for Turkey have been computed in both 7-parameter model and 9-parameter model and a numerical example has been given to understand the difference between two models in a better way. An explanation about the proposed methodology as a flow chart also has been shown in appendix.