Relation between GDOP and the geometry of the satellite constellation

The relationship between Geometrical Dilution Of Precision (GDOP) and maximum volume of the polytope expanded by the user-satellite unit vectors endpoints has been used for long as an approach to reduce the time that a receiver devotes to the satellite selection process. Although receivers are able to track all satellites in view, a satellite selection process may still be needed for some applications or when the number of satellites available is large (i.e., due to the availability of several constellations of satellites). This paper evaluates the relationship between the determinant of the GDOP matrix and the maximum volume of the polytope expanded by the user-satellite unit vectors endpoints when any number of satellites is employed for the computation of the position.