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

Delgado, N. ; Nunes, F. ; Seco, G.

GPS Solutions Vol. 21, Nº 1, pp. 1139 - 1147, January, 2017.

ISSN (print): 1080-5370
ISSN (online):

Journal Impact Factor: 2,991 (in 2015)

Digital Object Identifier: 10.1007/s.10291-016-0592-3

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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 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.