Relation between GDOP and the geometry of the satellite constellation

Blanco-Delgado, Nuria; Nunes, Fernando D.

doi:10.1109/icl-gnss.2011.5955282

Cited by 16 publications

(12 citation statements)

References 14 publications

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“…Therefore, the minimum GDOP value and the optimal SRG of n satellites ( 4 n  ) are both of theoretical and practical interest. There have been quite a few research efforts [1,3,4,9], for example, by studying the relationship between the shape of polygon and the GDOP value in 2-D, Nuria [1] proved that the SRG close to a regular polygon is optimal to minimize the GDOP value. However, this theory is only applicable to 2-D. Miaoyan [3] summarized formulas for calculating the minimum GDOP value of n satellites ( 4 n  ) for both 2-D and 3-D positioning.…”

Section: ( *( )*)mentioning

confidence: 99%

“…The GDOP value decreases with the increase of the SRG polygon's area. The minimum GDOP value appears when the area of the polygon is largest [1].…”

Section: The Minimum Gdop Value and The Srg For More Than Four Smentioning

confidence: 99%

“…The smaller the GDOP value is, the higher the positioning accuracy will be [1,2,3,4].GDOP is defined as…”

Section: Introductionmentioning

confidence: 99%

“…Here G is known as the geometry matrix since it characterizes the satellite-receiver geometry (SRG) which is formed with the endpoints of receiver-satellite unit vectors [1] as seen in When the number of satellites is 4, G is a square matrix. Formula (1) can be expressed as ( *( )*) T …”

Section: Introductionmentioning

confidence: 99%

“…As a result, the minimum GDOP value of 4 satellites can be obtained when the SRG tetrahedron's volume reaches maximum. Researchers call the SRG minimizing GDOP value the optimal SRG [1,3,4,5]. So the optimal SRG of 4 satellites is the one which owns the largest volume-one satellite at the zenith and the other three in the horizontal plane to constitute an equilateral triangle [6].…”

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confidence: 99%

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An Algorithm of Selecting more than Four Satellites from GNSS

Song¹,

Zhang²,

Fan³

et al. 2013

Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information

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-By analyzing the relationship between the GDOP value and the area of the polygon formed with the endpoints of the satellite-receiver unit vectors in 2-D, the optimal satellite-receiver geometry (SRG) and the minimum GDOP value of n satellites( 4 n  ) in 3-D were deduced in this paper. Based on the minimum GDOP value and the optimal SRG in 3-D, a satellite selection algorithm is proposed to solve the problem of selecting more than 4 satellites from GNSS (Global Navigation Satellite Systems). The good performance of this algorithm on improving satellite selection efficiency with less sacrifice of the GDOP value is illustrated by simulation.Index Terms -Satellite selection, GDOP, Satellite-receiver geometry (SRG), GNSS. I . IntroductionGDOP (geometric dilution of precision) has been the standard of satellite selection for a long time because it is an important concept to characterize the positioning accuracy. The smaller the GDOP value is, the higher the positioning accuracy will be [1,2,3,4].GDOP is defined asHere G is known as the geometry matrix since it characterizes the satellite-receiver geometry (SRG) which is formed with the endpoints of receiver-satellite unit vectors [1] as seen in When the number of satellites is 4, G is a square matrix. Formula (1) can be expressed as ( *( )*)Where G* is the adjoint matrix of G, and G is the determinant of G. It should be noted that G is six times of the volume of the SRG tetrahedron. ( *( )*)T Trace G G changes little when the value of G increases. Therefore the GDOP value is almost inversely proportional to the SRG tetrahedron's volume [5]. As a result, the minimum GDOP value of 4 satellites can be obtained when the SRG tetrahedron's volume reaches maximum. Researchers call the SRG minimizing GDOP value the optimal SRG [1,3,4,5]. So the optimal SRG of 4 satellites is the one which owns the largest volume-one satellite at the zenith and the other three in the horizontal plane to constitute an equilateral triangle [6]. For decades, it's common to position with selecting four satellites not only because of the scarce of satellite resources (only 6 to 12 satellites for most regions [6]) but also the almost inverse proportionality relationship between the volumes of tetrahedron and the GDOP values [4,6]. It's easy to select 4 satellites with the largest SRG tetrahedron which is closest to the optimal. However，no matter how effective the satellite selection algorithms are, the positioning accuracy of 4 selected satellites can't be further improved due to the limitation of the satellite number. Moreover, thanks to the development of the receiver manufacturing technology, most receivers can receive signal from more than 12 visible satellites. In addition, with the development of GNSS, the number of all-in-view satellites increases rapidly nowadays. After BDS and Galileo System built, there may be more than 40 visible satellites for most regions on the Earth [2,7]. The era of satellite resource

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Section: ( *( )*)mentioning

confidence: 99%

“…The GDOP value decreases with the increase of the SRG polygon's area. The minimum GDOP value appears when the area of the polygon is largest [1].…”

Section: The Minimum Gdop Value and The Srg For More Than Four Smentioning

confidence: 99%

“…The smaller the GDOP value is, the higher the positioning accuracy will be [1,2,3,4].GDOP is defined as…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

An Algorithm of Selecting more than Four Satellites from GNSS

Song¹,

Zhang²,

Fan³

et al. 2013

Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information

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Satellite selection in the context of an operational GBAS

et al. 2019

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When incorporating multiple constellations into future ground based augmentation systems (GBAS), a problem with limited VDB (VHF data broadcast) capacity might arise. Furthermore, the number of airborne receiver tracking channels could be insufficient to use all visible satellites. One way to cope with these issues is to perform a satellite selection to limit the number of used satellites with minor impact on performance. This paper investigates different factors that constrain the approach of simply selecting "the best set in every epoch" and shows how to overcome some limitations. These constraints include limitations in satellite visibility, loss of satellites during approach (i.e. in curves), and convergence times in the airborne processing until satellites are usable. Various protection level simulations are performed to show the influence of the named factors on the nominal performance. Taking into account all these contextual influences, results show satellite selection is still applicable in GBAS ground stations. NAVIGATION. 2019;66:227-238. wileyonlinelibrary.com/journal/navi

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The Satellite Selection Algorithm of GNSS Based on Neural Network

Wei

Zhao

et al. 2016

Lecture Notes in Electrical Engineering

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Relation between GDOP and the geometry of the satellite constellation

Cited by 16 publications

References 14 publications

An Algorithm of Selecting more than Four Satellites from GNSS

An Algorithm of Selecting more than Four Satellites from GNSS

Satellite selection in the context of an operational GBAS

The Satellite Selection Algorithm of GNSS Based on Neural Network

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