helmert

seven

parameters

parameter

transformation

The program produces a set with seven parameters of the sapatial Helmert transformation valid for an specific area, with which then arbitrary coordinates of the area can be transformed from one reference system into another with high accuracy. The seven transformation parameters are computed with a set of individual identical points. Those are points with known coordinates in both reference systems. For the computation at least three identical points must be present. In practice you will be anxious to use more identical points than those three necessities. The program supports upto 10.000 identical points. Cartesian coordinates or geographical coordinates with ellipsoidal height using the ellipsoid dimensions are suitable. Identical measuring points of higher order can be usually inquired or referred by the official institutions for measurement. The necessary ellipsoid half-axis are available in the program for the selection from lists. There are altogether to determine seven parameters, i.e. three translations, three rotations and a scale constant. The parameters are calculated by the compensation according to the method of the smallest squares (L2 norm, Helmert transformation). Therefore must be dissolved a formula system with seven equations and seven unknown quantities. The coordinates of the identical points are tested intensively on outliers and deviations by different statistic procedures. The quality of the computed seven parameters of the Helmert transformation is documented by a residual matrix and by the computation of the middle, maximum and root mean square (RMS) deviations. The seven parameters are presented in the three most usual standards. Those are the Coordinate Frame Rotation, the Position Vector Transformation and the European Standard ISO 19111.