Systematical analysis of the transformation

During the 88th and 96th Conferences of the Working Committee of the Surveying Authorities of the States of the Federal Republic of Germany (AdV) in 1991 and 1995 the resolution was passed to introduce the European Terrestrial Reference System 1989 (ETRS89) with the universal transversals Mercator projection (UTM) as map projection of GRS80 Ellipsoid in Germany and Europe uniformly. The task of transferring the existing two-dimensional Gauss-Krüger coordinates in German geodetic reference system (DHDN) into UTM coordinates in the ERTS89 datum arises from these resolutions. For the concrete “Introduction of ETRS89 into Baden-Württemberg” the transformation with the two models of the 7-Parameter Helmert transformation and the 6-Parameter Helmert transformation using the 131 collocated points (131 BWREF points in Baden-Württemberg) are firstly tested and discussed. Because of the special characteristic of the main triangle net of Baden-Württemberg (countrywide variable net scales, inhomogeneous point accuracies and transformation residual in the decimeter level) an alternative transformation procedure with the Total Least-Squares method is also applied in the estimation of the 7-Parameter Helmert transformation and 6-Parameter Affine transformation based on the 131 collocated points. After the review of basis mathematic background of the TLS method, these methods are complemented with MATLAB. Furthermore, 10 selected points are as test points to study the influence on those points after using TLS transformation parameters. The results are analyzed and compared with these results from the conventional LS method, and the advantages and shortcomings of this TLS method are discussed.