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The relationship between Geometrical Dilution Of Precision (GDOP) and maximum volume 1 of the polytope 2 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.

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The geometric dilution of precision (GDOP) is related to the satellite geometry. Thus far, research has focused on minimizing the GDOP by selecting a set of satellites that maximizes the volume spanned by the userto-satellite unit vectors. However, this relation has been only analyzed when four satellites are used for computing the three-dimensional position, for which the relation is nearly direct. The analysis applicable to any number of satellites is presented here. Results show that the relation between GDOP and volume spanned by the user-to-satellite unit vectors does not ensure that the optimal GDOP value is achieved by means of the volume maximization. Satellite distribution should also be considered in such a way that the selection of geometries that are closer to a regular polytope is favored.