That's the point. I think the Inmarsat spokesman, who is a PR guy and probably not a satellite enginer, misspoke.
We have an aircraft moving at say 500 miles an hour across the surface of the earth.
We have a satellite that is basically stationary with respect to the surface of the earth.
It is not the movement of the satellite with respect to the earth, which is what the spokesman suggested, that is causing the bulk of the Doppler effect.
Signal Doppler can be caused by motion of the transmitter, motion of the receiver, or both. There would be little to no Doppler shift with regards to a satellite in geosynchronous orbit. Assuming that the satellite was near the same longitude there would only be Doppler shift if the plane were moving up or down relative to the surface of the earth, and hence, the satellite. If the geosynch satellite was near the horizon, a Doppler shift would only be generated based on the East-West motion of the aircraft. If the aircraft was on a mostly North-South track, as has been proposed, the Doppler shift would be VERY small.
If the satellite was in low earth orbit you could get significant up or down Doppler shift depending on positions and relative motion of the satellite and the aircraft. Doppler shift would be the greatest if they were on or near the same track and less or none if the tracks were perpendicular.
If the satellite had the ability to determine the bearing of the signal (unlikely) then you could use target motion analysis to generate a series of likely tracks (and general position) depending on the assumed speed of the aircraft.
Hope this helps.
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