Detail Explanation of Coordinate Transformation Procedures Used in Geodesy and Geoinformatics on the Example of the Territory of the Republic of Croatia

Abstract

With strong technology improvement, especially GNSS, coordinate transformation has become an essential tool in everyday practice. For this reason, it is beneficial to have a good understanding of the mathematical process of coordinate transformation, as well as the method for calculating transformation parameters. The purpose of this article is to provide a detailed explanation of the coordinate transformation procedure and the calculation of transformation parameters for seven transformation models: 3-parameter, 5-parameter standard and abridged, 7-parameter, 8-parameter, 9-parameter, and 12-parameter. For each transformation model, a basic transformation equation, a procedure for calculating transformation parameters, inverse expression for reversible transformation, as well as characteristics of each model are provided. As an addition, for each model, a numerical example of calculating transformation parameters for the territory of the Republic of Croatia is provided. Additionally, for the example of the 7-parameter transformation, importance of reversible transformation, rotation convention, as well as the form of the rotation matrix used during transformation are demonstrated.