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

Nuria Blanco-Delgado; Fernando Duarte Nunes; Gonzalo Seco-Granados

doi:10.1007/s10291-016-0592-3

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

Nuria Blanco-Delgado, Fernando Duarte Nunes, Gonzalo Seco-Granados

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Resum

La dilució geomètrica de precisió (GDOP) està relacionada amb la geometria del satèl·lit. Fins ara, les investigacions s'han centrat en minimitzar el GDOP seleccionant un conjunt de satèl·lits que maximitzi el volum abastat pels vectors unitat usuari-satèl·lit. Tanmateix, aquesta relació només s'ha analitzat quan s'utilitzen quatre satèl·lits per a calcular la posició tridimensional, i la relació és gairebé directa. L'anàlisi aplicable a qualsevol nombre de satèl·lits es presenta aquí. Els resultats mostren que la relació entre el GDOP i el volum abastat pels vectors unitat usuari-satèl·lit no garanteix l'obtenció del valor òptim del GDOP mitjançant la maximització del volum. La distribució dels satèl·lits també s'ha de considerar de manera que afavoreixi les geometries més properes a un politop regular. © 2017, The Author(s)

Idioma original	Anglès
Pàgines (de-a)	1139-1147
Revista	GPS Solutions
Volum	21
Número	3
DOIs	https://doi.org/10.1007/s10291-016-0592-3
Estat de la publicació	Publicada - 1 de jul. 2017

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10.1007/s10291-016-0592-3

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https://www.scopus.com/pages/publications/85009291678

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

abstract = "{\textcopyright} 2017, The Author(s). 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.",

keywords = "GNSS, Geometric dilution of precision, Maximum volume, Satellite selection",

author = "Nuria Blanco-Delgado and \{Duarte Nunes\}, Fernando and Gonzalo Seco-Granados",

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doi = "10.1007/s10291-016-0592-3",

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TY - JOUR

T1 - On the relation between GDOP and the volume described by the user-to-satellite unit vectors for GNSS positioning

AU - Blanco-Delgado, Nuria

AU - Duarte Nunes, Fernando

AU - Seco-Granados, Gonzalo

PY - 2017/7/1

Y1 - 2017/7/1

N2 - © 2017, The Author(s). 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.

AB - © 2017, The Author(s). 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.

KW - GNSS

KW - Geometric dilution of precision

KW - Maximum volume

KW - Satellite selection

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

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