Basic GPS Concept - Fundamentals of Global Positioning System Receivers: A Software Approach - page 27

four satellites form the optimum constellation. Under this condition the ele-
vation angle is 0 degree and three of the four satellites form an equilateral
triangle. The observer is at the center of the base of the tetrahedron. Under this

condition, the DOP values are: GDOP = √ 3 ≈ 1 . 73, PDOP = 2 √ 2 / 3 ≈ 1 . 63,

HDOP = VDOP = 2 / √ 3 ≈ 1 . 15, and TDOP = 1 / √ 3 ≈ 0 . 58. These values can
be considered as the minimum values (or the limits) of the DOPs. In selecting
satellites, the DOP values should be as small as possible in order to generate the
best user position accuracy.

2.16 SUMMARY

This chapter discusses the basic concept of solving the GPS user position. First
use four or more satellites to solve the user position in terms of latitude, lon-
gitude, altitude, and the user clock bias as discussed in Section 2.5. However,
the solutions obtained through this approach are for a spherical earth. Since the
earth is not a perfect sphere, the latitude and altitude must be modified to reflect
the ellipsoidal shape of the earth. Equations (2.51) and (2.57) are used to derive
the desired values. These results are shown in Figure 2.9 as a quick reference.
Finally, the selection of satellites and the DOP are discussed.

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