Investigation on the effects of number of common points in 2D transformation problem

Abstract

Coordinate transformation from one datum to another is the basic problem in geodesy. Generally, the problem may be expressed by converting coordinates in a cartesian coordinate system with defined origin provided by the intersection of two or three axes into another system using mathematical equations. To compute the transformation parameters, a sufficient number of coordinates of the common points should be known in two systems. The problem involves either 2D or 3D coordinate systems. Traditionally the commonly used model for the estimation of the transformation parameters is the Least Squares (LS) method refers as to Helmert Transformation. This study aims to compare the performance of the spatial distribution and quantity of the common points in LS method for coordinate transformation problems. For this purpose, a geodetic network with 25 points, whose coordinates are commonly known in two datum are used to compute the performance of the transformation problem under the different scenarios. To compare the cases, the sum of the absolute coordinate differences is provided by subtracting the original coordinates of test points from computed coordinates by using estimated transformation parameters. The results show that increasing control points one by one to estimate the transformation parameters improve the results of the transformation parameters and reliable transformation parameters have been estimated when a homogeneously distributed 8 points are taken as common points for about a region as 1500 km 2 .