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News reports about Flight 370's disappearance have given a sketchy idea of how hourly pings to a satellite have helped build up a picture of where it went.

From a naive intuitive point of view, if all the ping does is tell you the distance from plane to satellite, then it locates the plane on a sphere. Intersecting with the surface of the earth, taken as another sphere, would give you a circle on the earth's surface. So if it were that simple, you'd have a sequence of locating circles.

The altitude of the plane is clearly being neglected in this model. The time spacing of the circles brings up an issue in plausible interpolation. All that said, what is the modelling technique we are being told about, as applied by Inmarsat?

The news stories were talking about "two paths", not a travelling circle quite well. Anyone here know what actually has been going on, as a piece of applied mathematics?

Edit: Edited, given that my first ideas were wrong. To those voting to close, reports speak of research being carried out on the fly.

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    $\begingroup$ Keep in mind that ping times are probably a very unreliable method of determining distance; they are probably intended for measuring network latency, so incorporate unpredictable delays in processing on both the plane and satellite's ends. $\endgroup$ Mar 25 '14 at 7:52
  • $\begingroup$ I suspect that there is no very simple story here. If I understand correctly, the pings were infrequent, and none was received by more than one satellite. I have not seen any clear statement of what data was logged by Inmarsat, which is crucial to understand the possible methods. Reports suggest that the Doppler effect was used somehow, so they must have some kind of frequency data. I also read that Inmarsat built a complex model based on a large dataset of pings from other flights an "did a couple of years worth of research in two weeks". $\endgroup$ Mar 25 '14 at 7:59
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    $\begingroup$ Related: aviation.stackexchange.com/questions/2623/… $\endgroup$
    – Waldemar
    Mar 25 '14 at 9:18
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    $\begingroup$ The altitude of the plane is clearly negligible. No more than 10km, compared to 36 000 km for the satellite: less than 0.03%. You can mollify it by the curvature of the earth, but considering where the satellite is compared to the plane, the altitude still does not matter much. To get the pings 'en route' they had to remove all other pings, I guess $\endgroup$
    – username
    Mar 25 '14 at 14:14
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    $\begingroup$ There is now some reasonably detailed information at mh370.dca.gov.my/information-provided-to-mh370-by-aaib (found via Wikipedia) $\endgroup$ Mar 26 '14 at 9:21