SEVENPAR (Deutsch)

Financial Calculators


Purpose of the program SEVENPAR is to produce a set with seven Helmert transformation parameters valid for an specific area, in which then arbitrary points can be transformed from one coordinate system into another with high accuracy. The Helmert transformation parameters are computed with a set of individual identical points. Those are points with known coordinates in both coordinate 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. 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 Helmert parameters is documented by a cleavage matrix and by the computation of the middle, maximum and root mean square (RMS) deviations. The seven Helmert parameters are calculated in the three most usual standards. Those are the Coordinate Frame Rotation, the Position Vector Transformation and the European Standard ISO 19111.


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