Abstract

Coordinate transformation is widely used in geodetic application. By a coordinate transformation process, position of points with known coordinates in one coordinate system is transformed into a different coordinate system. Mostly, Helmert (similarity), Affine and Projective transformations are used for two dimensional transformations and Bursa-Wolf transformation is used for 3 dimensional transformations. The orthometric heights are used for heights in the mapping and engineering projects. The determined heights with GPS are ellipsoidal heights. Therefore, the ellipsoidal heights to orthometric heights conversion problem has emerged. For this purpose, fair accuracy of geoid undulations must be known. In this study, a program has been developed that can perform one, two and three-dimensional transformations. With this program, a suitable surface is conveyed by utilizing the basic points of which geoid undulations are known and the x, y coordinates that are proved to be compatible with using orthogonal polynomials in one dimension. Geoid undulations that their x, y coordinates are known at certain points can be calculated with this surface. In two and three dimensional transformation, however, outlier test can be conducted by using the both system coordinates of common points, transformation parameters can be determined and according to outlier and the 2nd system coordinates of the points which their coordinates are known in the 1st system, can be calculated in 2 dimensional and 3 dimensional transformations.

Key words: Coordinate transformations, similarity, affine, projective, Bursa-Wolf, geoid, Global positioning system, ellipsoid height, orthometric height.