Here's some intuition about how the Doppler effect can be used to find location of a transmitter given a single receiver: objects (transmitters) moving in a straight line that are far away from the receiver will have less of a shift in frequency when they "pass" the receiver than objects that are close to the receiver.

What's more, you don't actually have to wait for the transmitter to pass the receiver: the radial velocity is what's important, and if you measure that at several points, you can fit a curve. That will tell you how far the transmitter is from the receiver.

Do this several times, and you can make a constellation of possible locations, and then fit those points to a line.

Globalstar does this with its satellite phones. Their situation is easier than with Inmarsat, because Globalstar uses fast-moving (relative to points on Earth) LEO satellites rather than geostationary satellites. Given a single LEO satellite on a known orbit and assuming that the phone on the ground is stationary, a fix on position can be made relatively quickly using the Doppler effect.

Here's a paper about how Globalstar does it: http://www.eng.tau.ac.il/~nadav/pdf-files/Instant_active_pos...