Coordinate Transformation Using the Least Squares Method: A Case Study on Trabzon, Türkiye

The ED50 datum uses the Hayford ellipsoid and the Greenwich meridian as the prime meridian. In Turkey, the ED50 datum with the Hayford ellipsoid was used until 2001, after which the ITRF datum with the GRS80 ellipsoid became the standard. To utilize coordinate systems across different datums, these systems must be associated and transformed accordingly. This study determines 2D transformation parameters for converting the ED50 datum to the ITRF-96 datum. For this transformation, common points in both the ED50 and ITRF systems were selected in the Maçka and Ortahisar districts of Trabzon province. The two-dimensional similarity (Helmert) and Affine transformation methods were applied to these common points to establish the relationship between the two systems within the study area. Statistical data was gathered to evaluate the performance of the transformation parameters and process. Additionally, test points within the study areas were selected, and their ED50 datum coordinates were transformed to ITRF-96 coordinates using these parameters. The differences between the transformed coordinates and the current coordinates of these test points were analyzed, with root mean square error (RMSE), minimum and maximum errors, and mean absolute error (MAE) values calculated. In this study, a total of 197 points were used in Değirmendere, and 106 points were used in Maçka. It was observed that the sensitivity parameters of the transformation in the Maçka region are better than those in Değirmendere, potentially due to the number of common points. When comparing the Affine and Similarity transformations, the similarity transformation yielded significantly better results. All calculations were conducted using MATLAB R2022b software.