Applying transformation parameters for 3D transformation between systems WGS 84 and RES (B)

Abstract

Coordinate transformation between 3D cartesian systems: the Reference Elipsoidical System for Bessel’s Ellipsoid - RES(B) (with coordinates C R(B)), and the World geodetic system – WGS 84 (with coordinates C w) are used for transformations C W→ C R(B) as well for coordinates C J in the System S-JTSK and also in reverse order C J→ C R(B)→ C W. These coordinate transformation are necessary for GPS measurements, i. e. when C J coordinates are to be determined for points, or in opposite cases, when coordinates C J must be transformed to values C W(e. g. aerial and ship navigation, development of Š GIS and others). These transformations can be done using various transformation models (depending on the number of points and the area size), from which Molodenskij - Badekas´model (MBM) is preferred for smaller point sets.This contribution gives an overview of the mathematical and geometrical relations between both coordinate systems, the approach for the development of the basic transformation model, its adaptation to MBM and its linearisation. Applying the transformation equations demands for a knowledge of 6 or 7 transformation parameters that are know or one can determine them for a certain area using some identical (homological) points with known coordinates C W and C R(B). For the determination parameters needed, it is recommended to apply optimally selected identical points from its given set using a numerical optimization for the selection. It is required for a first – rate transformation, that the points used must give the minimal value of the quadratic form of transformation residuals.

Keywords

• 3D Coordinate systems RES (B) and WGS 84
• similarity transformation models
• linearisation of models
• Molodenskij - Badekas´ transformation approach parameters
• transformation quality