An Algorithm of Selecting more than Four Satellites from GNSS

Abstract

-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

Optimized Selection of Satellite Subsets for a Multi-constellation GBAS

“…In this section a brief background on general satellite selection methods shall be given now. As previous studies have shown ([7], [8]) the best possible satellite geometry in terms of achieved DOP (Dilution of Precision) is defined by a number of satellites with the highest possible elevation and all other satellites equally spaced (in azimuth direction) as close to the horizon as possible (Figure 1). This is problematic in that regard that satellites very close to the horizon commonly experience higher multipath as well as more ionospheric and tropospheric disturbances [9].…”

“…They commonly only work with the geometry itself ( [7], [8], [10]- [13]) and therefore assume all ranging signals to be equally precise, which is usually not the case. Furthermore, the way many methods work makes it hard to introduce any kind of weighting in the selection process.…”

Satellite selection in the context of an operational GBAS

“…The common goal is in general to find a subset of all satellites currently in view which provides the best (whereby best depends on the application) navigation performance under given side conditions. Simple and computationally efficient approaches using only satellite elevation and azimuth were presented by Zhang, Song, and Park . Also, the widespread approach of selecting the highest satellites, assuming the best signal quality with highest elevation, falls into this category.…”

Satellite Selection in the Operational GBAS Context

“…The common goal is in general to find a subset of all satellites currently in view which provides the best (whereby best depends on the application) navigation performance under given side conditions. Simple and computationally efficient approaches using only satellite elevation and azimuth were presented by Zhang [1], Song [2] and Park [3]. Also the widespread approach of selecting the highest satellites, assuming the best signal quality with highest elevation, falls into this category.…”