3D affine coordinate transformations

Abstract: This thesis investigates the three-dimensional (3D) coordinate transformation from a globalgeocentric coordinate system to a national terrestrial coordinate system. Numerical studies arecarried out using the Swedish geodetic data SWEREF 93 and RT90/RH70. Based on theHelmert transformation model with 7-parameters, two new models have been studied: firstly ageneral 3D affine transformation model has been developed using 9-parameters (threetranslations, three rotations and three scale factors) and secondly the model with 8-parameters(three translations, three rotations and two scale factors) has been derived. To estimate the 3Dtransformation parameters from given coordinates in the two systems, the linearizedobservation equations were derived. Numerical tests were carried out using a local (North,East, Up) topocentric coordinate system derived from the given global geocentric system. Thetransformation parameters and the residuals of the coordinates of the common points werecomputed. The investigation shows the horizontal scale factor is significantly different by thevertical scale factor. The residuals of the control points were expressed in a separate (North,East, Up) coordinate system for each control point. Some investigations on the weightingprocess between horizontal and vertical components were also carried out, and an optimalweighting model was derived in order to reduce the residuals in horizontal componentswithout changing the coordinates.