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Figure 22-2. Satellite coordinate system
The equations of the three circles are therefore:
r 2 1 = x 2 +y 2
r 2 2 = (x-d) 2 +y 2
r 2 3 = (x-i) 2 +(y-j) 2
Each radius is found by subtracting the transmission time, t i , from the current time and
multiplying by the speed of light. As the speed of light is very large, and our current
time is only a rough estimate, these radii are commonly referred to as pseudoranges to
remind us they are still approximate. The x and y values that satisfy these equations are
our current location in two-dimensional space. We now subtract the second equation
from the first:
r 1 2 - r 2 2 = x 2 + y 2 - (x-d) 2 - y 2
r 1 2 - r 2 2 = x 2 - (x-d) 2
Solving for x gives:
x = (r 1 2 - r 2 2 +d 2 ) / 2d
 
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