Here are a couple of web sources on how the course of MH370 was determined.
Some of these transponder-based, distance analyses reminds me a bit of the Oboe navigation system used during WW2.
The Doppler shift work is interesting and I quote here from the Wikipedia. One good aspect of this approach is that it is easily testable using actual aircraft tracking data.
After establishing the "corridors" where the aircraft may have been located at the time of the final handshake, Inmarsat proceeded to further analyze the signals received by its ground stations during the handshakes with Flight 370. This analysis focused on the frequency of the signal expected from the aircraft and the actual frequency of the signal received, known as the burst frequency offset. The burst frequency offset results from the change in frequency of an electromagnetic wave to an observer due to the motion of the source, known as the doppler effect. A baseline of system characteristics for the aircraft, satellite, and ground station could be calculated from several messages sent by Flight 370 while on the ground in Kuala Lumpur and during the early stage of the flight when its location was known.The burst frequency offset would change not only based on the aircraft's airspeed, but also its position along the identified arcs and direction. To test its theory, Inmarsat calculated positions for six Boeing 777 aircraft flying in various directions on the same day and compared those calculations to actual positions, resulting in a good match. Using the results of that analysis, there was a good correlation of the expected and actual burst frequency offsets with the aircraft flying south over the Indian Ocean (along the southern corridor at the time of last transmission) and poor correlation if the aircraft flew north. After factoring in the satellite's small movements in relation to the earth, which were not taken into account in the earlier calculations, the northern corridor was ruled out completely.