Abstract The present work deals with an important theoretical problem of geodesy: we are looking for a mathematical dependency between two spatial coordinate systems utilizing common pairs of points whose coordinates are given in both systems. In geodesy and photogrammetry the most often used procedure to move from one coordinate system to the other is the 3D, 7 parameter (Helmert) transformation. Up to recent times this task was solved either by iteration, or by applying the Bursa–Wolf model. Producers of GPS/GNSS receivers install these algorithms in their systems to achieve a quick processing of data. But nowadays algebraic methods of mathematics give closed form solutions of this problem, which require high level computer technology background. In everyday usage, the closed form solutions are much more simple and have a higher precision than earlier procedures and thus it can be predicted that these new solutions will find their place in the practice. The paper discusses various methods for calculating the scale factor and it also compares solutions based on quaternion with those that are based on rotation matrix making use of skew-symmetric matrix.
"Acta Geodaetica et Geophysica" – Springer Journals
Published: Jun 1, 2016