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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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