Originally Posted by
ackfoo
Quoting lakedude:
Triangulation doesn't require the points of measurement to be in a triangle, or even for there to be three of them
You might want to look up trilateration. Indeed in 3-space, with 3 origins, if the origins of the spheres lie in a straight line with one another then you are not able to narrow your search down to two possible positions, which in the case with space-based geolocation is really only one since the other will be in space.
Trilateration is not what they were doing with these SATCOM pings. Knowing the difference between tx/rx time and the height of the satellite above ground at that exact point in time, it is possible to calculate a rough angle down to the surface of the earth. This creates a circle. By rejecting points on this circle that lie outside of the a/c's possible range, in combination with PSR data collected, allow you to narrow down the position to a point on an arc.
This will be *approximate* since millisecond differences can result in hundreds of kilometres of error when the receiver is in geostationary orbit.
Insulting the other poster by suggesting he take an elementary school math class is rude and asinine. None of this is grade school mathematics. This is advanced stuff (although perhaps not advanced in theory). I should know, I studied Mathematics.