2d Helmert and Affine Coordinate Transformation Using the Least Squares Method: Trabzon Province in Turkey

Abstract

ED50 datum uses Hayford ellipsoid and Greenwich meridian as the prime meridian. In Turkey, ED-50 datum using Hayford ellipsoid was used until 2001, and ITRF datum using GRS80 ellipsoid was used after 2001. In order to use coordinate systems in different datums, different systems must be associated and transformed to each other. In this study, 2D transformation parameters from ED-50 datum to ITRF-96 datum have been determined. For transformation, common points from both the ED-50 and ITRF systems have been selected in Maçka and Ortahisar districts of Trabzon province. The two-dimensional similarity (Helmert) and the Affine transformation methods have been applied through common points with the aim at defining the relationship between the two systems in the study area. Some statistical information has been obtained representing the sensitivity of the transformation parameters and the transformation process. In addition, test points have been selected in the study areas and the ED-50 datum coordinates of test points have been transformed to the ITRF-96 coordinates through transformation parameters. The differences between the transformed coordinates and current coordinates of these test points have been taken. The root mean square error (RMSE), minimum and maximum errors and the mean absolute errors (MAE) values have been calculated for differences. All calculations in the study have been made using the MATLAB R2022b program.