On the relation between GDOP and the volume described by the user-to-satellite unit vectors for GNSS positioning

Abstract

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 user-to-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.