I am not quite sure if this discussion is about how sat pinging is/was used for a/c positioning (a lot of inputs, harder and harder to follow).
However, pretty clear explained here:
Help from above: Satellite signals can confirm a plane's identity - CNN.com
The purpose of the hourly "handshakes" is to allow the satellite to know the approximate location of the aircraft so that it can efficiently relay any messages. For this, the satellite needs to know the angle of the aircraft from the satellite. An aircraft directly under the satellite would be at a 90 degree angle to the satellite; an aircraft at the poles would be at 0 degrees. (Inmarsat Official via CNN)
The probable track was obtained (backwards) starting from the last estimated position, using the know position of the (stationary) sat, the ground reference and the computed angle between the emitter (plane) and receiver (sat) when last ping has been sent - that is, not by time delay means (as GPS works). Which is straightforward...
They also said that's new territory:
"We're trying to get up to speed on what that means and how to interpret it," one U.S. official told reporters. "It's sort of a new technology for us."
regards,