Bayesian Methods in the Search for MH370

MH370 was a flight of Malaysian Airlines that on 07 March 2014 disappeared en route from Kuala Lumpur to Beijing. Air traffic controllers lost radio contact with the aircraft half an hour into the flight, and it appeared from military radar data that the aircraft changed course and flew southwest  and then northwest for several hours before disappearing from radar, presumably falling into south Indian Ocean when its fuel ran out. The reasons for the aircraft’s behavior are still unknown, as the flight recorders have not been recovered and in fact the crash location remains unknown, with only a little bit of debris washing ashore. The underwater search was suspended on 17 January 2017.

The present book, released online in November 2015 and published in print in July 2016, is a case study of how Bayesian statistics were used to estimate the crash location so that an efficient search could be organized. It is written by five scientists at the Defense Science and Technology Group in Australia (the Australian government took responsibility for coordinating the search among the several nations involved).

Bayesian methods were also used in the search for Air France flight 447, that went down over the ocean in 2009. That story had a happier ending, when the black box was found two years later in the area predicted by the models.

The book is especially valuable because it concentrates on the modeling rather than the mechanics of applying statistics. Surprisingly little information is available to the outside world about an aircraft in flight. The researchers developed a set of Bayesian filters using the military radar data as priors. An airplane of this size (a Boeing 777) is almost never flown manually, so a key point was to discover the autopilot settings it was using. This was done by validating the models against actual flight data taken earlier on the same aircraft and on similar aircraft that were flying the same route. There were also useful satellite-aircraft communications and C-channel ground-to-air telephone calls (automatic equipment continued operating even though there was no human communication). This additional data did not give position information but the timing delays were useful in calibrating the model. The telephone calls, although unanswered, still involved a handshake and that data turned out to be crucial in correcting the models. This additional data is called metadata, in that it’s not the actual message but data that accompanies the message. (Metadata is a term we often in connection with NSA wiretapping, usually accompanied by a government explanation that attempts to downplay how much it reveals.)

These models eventually produced a most-likely search area, although a large one: about 100,000 square kilometers, versus a much smaller area of 17,000 square kilometers in the Air France case. The search area is consistent with a piece of debris (flaperon) that washed up on Reunion Island, and everyone seems happy with the accuracy of the model. Unfortunately the effort was ultimately unsuccessful, and MH370 remains a mystery.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His personal web page is allenstenger.com. His mathematical interests are number theory and classical analysis.