Coordinate Systems: How to Get Your Position Very Precise and Completely Wrong

Abstract

Positioning by navigation satellites is carried out in three-dimensional geocentric cartesian coordinates, X, Y, Z. This applies to both the Transit System, which has now been in operation for over 20 years, and the Global Positioning System which is being tested and is due to become operational in 1988. Traditionally, the cartographer, the seafaring navigator and the geodetic surveyor have always expressed their coordinates in geographical terms, i.e. latitude and longtitude, whereas the land-based civil engineer, surveyor and the foot (or mechanized) soldier preferred theirs in terms of projection grid coordinates, i.e. northings and eastings. Transformations between these various coordinate systems involve not only complex algebraical formulae, but also some very specific numerical parameters, which are appropriate for different countries and continents and which can only be determined empirically. Moreover, the treatment and interpretation of the different systems of coordinates may frequently involve some very basic conceptual misunderstandings. These include confusing astronomical latitudes and longitudes with their geodetic counterparts, treating projection northings and eastings as if they were ordinary plane coordinates and, in the case of positions derived from observations to Transit satellites, applying the wrong set of transformation parameters or using inappropriate geoidal contour maps. These are typical examples of the sort of common misconceptions leading to gross errors and affecting even the most precisely determined absolute positions. Relative positioning, with respect to another point or a framework of points with known coordinates, eliminates some of the worst effects of these systematic sources of error, and is commonly used in geodetic surveying. However, instantaneous navigation (especially by using satellites) is most likely to be based on continuously determined, successive absolute positions and will therefore inevitably be affected by reference system errors. This is particularly important in the case of land navigation where much higher accuracies will be expected. This is a review paper with definitions and descriptions of the various types of coordinate systems and their mutual relationships. Geographical and geodetic coordinates are discussed in section 2, and projection grid coordinates in section 3. This is followed, in section 5, by a description of three-dimensional cartesian coordinates used in conjunction with navigation satellites. A brief discussion on current and proposed navigation satellite systems is given in section 6 and the paper is concluded in section 7.