The triangulated affine transformation parameters and barycentric coordinates of Turkish Permanent GPS Network

There are several computational approaches and methods to produce the complete solutions of geometry problems and they give sufficient computational strength for geodetic networks. Every approach and method has their advantages and drawbacks. Barycentric coordinates, also called areal coordinates, provide a new knock approach for geometry problems of such networks. This coordinate system offers triangular finite elements which are quite different from the usual Cartesian coordinate system. Actually, barycentric coordinates are a natural system of coordinates for the affine geometry. The modified approach for the affine transformation and barycentric coordinate system has been introduced and discussed, respectively in the study whether the affine transformation improves the results deteriorated by geometry of a GPS network. For this aim, general affine transformation of six-parameters between Eurasia Fixed Reference Frame (EUREF) and International Terrestrial Reference Frame (ITRF) for Turkish Permanent Global Positioning System Network (TPGN) has been computed. The affine transformation results show that the effects of the first and second translation parameters are in negative and positive directions, respectively. The third and sixth parameters are almost constant, on the other hand the fourth and fifth have a very small positive effect. Additionally, three triangular networks of GPS stations, at different locations in Turkey as a numerical example of barycentric coordinates, have also been presented. In the numerical example, the coordinate values of EUREF and ITRF have some differences after the decimal point, but the barycentric coordinates have very small amount of differences (sixth digit after decimal) which proves that the modified approach is meaningful.