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Effects of Errors in Coordinates on Transformation Parameters

In the stage of transformation of global positioning system coordinates to a national coordinate system, the transformation parameters computed show local changes depending upon the selection of common points used in the transformation. The coordinates of the common points in both coordinate frames, however, contain various errors, which result in the local changes mentioned above. In this context, finding out the effects of possible errors in the coordinate components on the transformation parameters and determining which coordinate component influences which transformation parameter will help in developing alternate transformation strategies that can reduce the local effects. For this purpose, first the differential relations between the coordinates and transformation parameters are investigated on the basis of the three-dimensional similarity transformation, and then the degree of influencing—in other words, the effect order—is determined by investigating the relationship between parameter and geographic coordinate component. In this study the height component has been found to be the most affected component among the coordinates, which influences five out of seven transformation parameters.