A comparison of different solutions of the Bursa–Wolfmodel and of the 3D, 7-parameter datum transformation

Závoti, József and Kalmár, János (2016) A comparison of different solutions of the Bursa–Wolfmodel and of the 3D, 7-parameter datum transformation. ACTA GEODAETICA ET GEOPHYSICA, 51 (2). pp. 245-256. ISSN 2213-5812

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Abstract

Abstract The present work deals with an important theoretical problem of geodesy: we arelooking for a mathematical dependency between two spatial coordinate systems utilizingcommon pairs of points whose coordinates are given in both systems. In geodesy and pho-togrammetry the most often used procedure to move from one coordinate system to the other isthe 3D, 7 parameter (Helmert) transformation. Up to recent times this task was solved either byiteration, or by applying the Bursa–Wolf model. Producers of GPS/GNSS receivers installthese algorithms in their systems to achieve a quick processing of data. But nowadays algebraicmethods of mathematics give closed form solutions of this problem, which require high levelcomputer technology background. In everyday usage, the closed form solutions are much moresimple and have a higher precision than earlier procedures and thus it can be predicted that thesenew solutions will find their place in the practice. The paper discusses various methods forcalculating the scale factor and it also compares solutions based on quaternion with those thatare based on rotation matrix making use of skew-symmetric matrix.

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