Source: https://www.siam.org/news/news.php?id=21...

From a given starting location there are two possible flight paths that cross the arcs at the correct times: one headed south and the other north.On March 25, AAIB released the results of a sophisticated analysis of Doppler-shift data for the relative motion of MH370 and the satellite, which provides strong confirmation that the aircraft took the southerly route. As I will explain in a forthcoming article, the Inmarsat engineering team was able to reach this conclusion only by taking into account a slight elliptical rotation of the satellite about its nominal location above the equator.This new technique developed by the Inmarsat team---a tour de force---is central to their ongoing investigation of the fate of MH370. Recently, I analyzed the technique mathematically and derived a formula for the velocity of a plane at each ping time in terms of the Doppler shift and the angles of the arcs. (Formulae like this are surely well known to experts in the important field of Doppler-based tracking.) In a future pedagogical article, I plan to demonstrate how, with arc angles and Doppler shifts measured at suitably chosen ping times, this formula can be used to determine the flight path of a plane, even if it is not flying along a great circle or at constant speed. It has been challenging for the Inmarsat team to use such a method to completely eliminate the uncertainty in the flight path of MH370 because, at times during the first three hours, the path of the plane was extremely erratic and the plane was not pinged at sufficiently short intervals during that time.