I think that we have to remember that Inmarsat and the pings have never before been used to track an aircraft. This isn't an acknowledged or even proven tracking method. It's barely acknowledged now. It may well be total horseshit.
Round trip of an RF signal divided by two is a very common method of determining distance. Its used by a zillion different applications including Radar. Since the satellite knows when it sent the ping to within a few microseconds and they know how long the device takes to respond and the satellite knows when it received the response its basic math to compute the surface of a sphere on which the plane must be. They can even tell the error and compute two spheres. Intersect that sphere's surface with the surface of the earth s
(Solve the two equations) and presto you have an arc or arcs if you factor in the timing error. (Likely well below a microsecond). Thats all very basic hyperbolic trig and identical to what your GPS (except the distance calc is one way in GPS) does so no exotic magic there.
Then to determine if the plane was flying toward or away from the satellite the slight change in frequency can tell you. Good old Doppler effect, same as a police radar.. Again no magic, just basic physics.
A good grade 12 physics student could probably do the math given the data.
Seems pretty solid to me. The only things that could screw you up would be if the satelite clock had a huge error which is unlikely or if the device in the plane took variable amounts of time to respond, also unlikely.
