Basically, the telemetry data from the 777’s motors was subjected to additional analysis, and Doppler shift allowed them to locate the track of the plane to southwest of Perth, Australia:

Inmarsat leveraged a “groundbreaking but traditional mathematics-based process” to analyze data from other flights that use its satellite network and establish a pattern that helped investigators nail down Malaysia Airlines Flight 370’s (MH370) final flight path as traveling south over the Indian Ocean, an Inmarsat executive explains.

Inmarsat’s initial analysis, handed over to investigators on March 11, helped investigators establish the now-famous northern and southern arcs as possible flight corridors for MH370 after it dropped off radar on March 8 over the Andaman Sea.

Inmarsat VP External Communications Chris McLaughlin says the company continued to analyze its data, and concluded on March 23 that the aircraft’s last known position was in the middle of the Indian Ocean, well southwest of Perth.

“What we discovered and what we passed to the investigation … is that the southern path predicted fits very well with the path that’s been indicated by our pings,” McLaughlin says. “To all intents and purposes, there’s no way [the aircraft] went north.”

A key calculation done by Inmarsat was determining the “Doppler shift” in the ping, or the slight change in the frequency of the signal caused by the movement of the aircraft relative to the satellite in space.

“From that process – a compression or an expansion of the wavelengths – you can determine whether the aircraft is getting closer or farther away,” McLaughlin explains. “It’s been a groundbreaking but traditional mathematics-based process that was then peer-reviewed by others in the space industry, and indeed contributed to by Boeing.”

It increasingly looks to be some sort of horrible accident, and not malice, with the most rational theory being an electrical fire followed by a diversion to the nearest airport, and then extended operation on autopilot: (The author is a pilot, and it is the only explanation that makes sense)

There has been a lot of speculation about Malaysia Airlines Flight 370. Terrorism, hijacking, meteors. I cannot believe the analysis on CNN; it’s almost disturbing. I tend to look for a simpler explanation, and I find it with the 13,000-foot runway at Pulau Langkawi.

We know the story of MH370: A loaded Boeing 777 departs at midnight from Kuala Lampur, headed to Beijing. A hot night. A heavy aircraft. About an hour out, across the gulf toward Vietnam, the plane goes dark, meaning the transponder and secondary radar tracking go off. Two days later we hear reports that Malaysian military radar (which is a primary radar, meaning the plane is tracked by reflection rather than by transponder interrogation response) has tracked the plane on a southwesterly course back across the Malay Peninsula into the Strait of Malacca.

The left turn is the key here. Zaharie Ahmad Shah1 was a very experienced senior captain with 18,000 hours of flight time. We old pilots were drilled to know what is the closest airport of safe harbor while in cruise. Airports behind us, airports abeam us, and airports ahead of us. They’re always in our head. Always. If something happens, you don’t want to be thinking about what are you going to do–you already know what you are going to do. When I saw that left turn with a direct heading, I instinctively knew he was heading for an airport. He was taking a direct route to Palau Langkawi, a 13,000-foot airstrip with an approach over water and no obstacles. The captain did not turn back to Kuala Lampur because he knew he had 8,000-foot ridges to cross. He knew the terrain was friendlier toward Langkawi, which also was closer.

………

For me, the loss of transponders and communications makes perfect sense in a fire. And there most likely was an electrical fire. In the case of a fire, the first response is to pull the main busses and restore circuits one by one until you have isolated the bad one. If they pulled the busses, the plane would go silent. It probably was a serious event and the flight crew was occupied with controlling the plane and trying to fight the fire. Aviate, navigate, and lastly, communicate is the mantra in such situations.