A Very Short Introduction to Co-ordinate Reference Systems  Collection by Stefan A. Voser

MapRef

31. December 2000

"There exist various co-ordinate reference systems in which a geographic location may be described mathematically by co-ordinates. In each system, the position gets its own co-ordinate values. These values differ in a numerical sense, but represent the same geographic position. 

When collecting data stored in different co-ordinate reference systems, each definition has to be known together with its geometric relationship to a standard system. Only then, it is possible to transfer all data into a standard co-ordinate reference system."

The main co-ordinate reference systems for describing a geographic position mathematically are geodetic reference systems and map projections (Fig. 1). 
Geodetic reference systems are used for describing the figure of the Earth and positions on it: ellipsoids (and the sphere) are used for describing the horizontal position, whereas geoids are the gravity related model for referencing the elevation. Geodetic reference systems have a datum, describing the position and orientation of the model in relation to the Earth and its surface.

Map projections are used to map the curved surface of an ellipsoid to a plane. They have various characteristics, e.g. mathematical properties as different metric deformations, or they are validated for specific geographical extent etc. 

Not considering the correct definition of the systems together with their relations may effort positional errors of hundreds of meters or more.