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we could reduce the number of unknowns. No such simplification is used here to pro‐
vide you with the most general case.
In our example, we are somewhere on the surface of the two-dimensional earth, shown
in Figure 22-1 as a light gray solid disk. This disk is being orbited by several GPS satellites.
The satellites' orbits are regular, and their positions at any time are tabulated in an
almanac that is stored in the receiver. The time of transmission is encoded in the signal
so that the givens are x i , y i , and t i , with i =1,2,3.
Figure 22-1. Trilateration in 2D
To make things easier for us, we are going to abandon the coordinate system of the earth
and use the coordinate system defined by our three satellites. The origin will be at satellite
1, the x-axis going directly from satellite 1 straight to satellite 2 and the y-axis being
perpendicular to that. This is shown in Figure 22-2 .
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