Fundamentals of Satellite Navigation - Understanding GPS: Principles and Applications - page 25

Foghorn 3

R3 + ε 3

Estimated
vessel
position

Foghorn 1

Foghorn 2

R2 + ε 2

R1 + ε 1

Figure 2.5 Effect of independent measurement errors on position certainty.

to be synchronized to system time. Timing information is embedded within the satel-
lite ranging signal that enables the receiver to calculate when the signal left the satel-
lite based on the satellite clock time. This is discussed in more detail in Section 2.4.1.
By noting the time when the signal was received, the satellite-to-user propagation
time can be computed. The product of the satellite-to-user propagation time and the
speed of light yields the satellite-to-user range, R . As a result of this measurement
process, the user would be located somewhere on the surface of a sphere centered
about the satellite, as shown in Figure 2.6(a). If a measurement were simultaneously
made using the ranging signal of a second satellite, the user would also be located on
the surface of a second sphere that is concentric about the second satellite. Thus, the
user would then be somewhere on the surface of both spheres, which could be either
on the perimeter of the shaded circle in Figure 2.6(b) that denotes the plane of inter-
section of these spheres or at a single point tangent to both spheres (i.e., where the
spheres just touch). This latter case could only occur if the user were collinear with
the satellites, which is not the typical case. The plane of intersection is perpendicular
to a line connecting the satellites, as shown in Figure 2.6(c).
Repeating the measurement process using a third satellite, the user is at the
intersection of the perimeter of the circle and the surface of the third sphere. This
third sphere intersects the shaded circle perimeter at two points; however, only one
of the points is the correct user position, as shown in Figure 2.6(d). A view of the
intersection is shown in Figure 2.6(e). It can be observed that the candidate loca-
tions are mirror images of one another with respect to the plane of the satellites. For