A Comparative Study between the 7 and 9 Transformation Models. Case Study: the Algerian North-Sahara System

One of the preoccupations of geodetic sciences is the transformation of coordinates between reference systems (datum). The link between two datum can be the transformation parameters if we use a similarity transformation model such as the Bursa-Wolf model, known also in the literature as the Helmert transformation. In this paper, the simplified and linearized forms of the 7 and 9 parameters transformation models between geodetic datum are compared. The objective of this comparison is the selection of the best form and model for transformation between the World Geodetic System 1984 (WGS84), the reference of the Global Positioning System (GPS), and the Algerian North Sahara 1959 (NS59) local datum. To attain this objective, eleven support points distributed in the north of Algeria between -2.22° to 8.24° in longitude and 27.23° to 36.49° in latitude are used. In order to examine the performance of these parameters, a transformation test is carried out at seven control points located in the Oran region. The results obtained show almost similar values between the simplified and linearized forms of the 7 and 9 transformation models; the simplified form is easy to use and to implement in software but the linearized form is effective when there is a large rotation between geodetic reference systems. Additionally, there are no significant differences between the transformation results obtained by the 7 and 9 transformation models.