Some mathematical assumptions for accurate transformation parameters between WGS84 and Nord Sahara geodetic systems

Abstract

The transformation of coordinates between different geodetic datums has been a common practice within the geospatial profession. Relating different geodetic datums mostly involves the use of conformal transformation techniques, which could produce results that are not very often satisfactory for certain geodetic, surveying, and mapping purposes. This has been attributed to the inability of the conformal models to resolve the lack (non-exhaustivity) and the heterogeneity of double points existing within the Algerian local geodetic networks. Indeed, the Algerian geodetic network is divided into two main zones completely different in accuracy and points exhaustivity. The North is better and well defined in precision; on the other hand, the South is poorly defined because of the lack of heterogeneity of the points. Mathematical algebraic methods give closed-form solutions to geodetic transformation problems, requiring a high-level computer programming background. In everyday usage, the closed-form solutions are much simpler and have a higher precision than earlier procedures. Thus, it can be predicted that these new solutions will find their place in practice. The present work deals with an important theoretical problem of geodesy: we are looking for a mathematical dependency between two spatial systems using 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 another is the 3D, seven-parameter similarity transformation (Bursa–Wolf, Molodensky–Badekas, and Helmert).

Keywords

• bursa–wolf
• helmert
• spatial coordinates
• similarity
• transformation