Shadoko wrote
But, you can't deduce a speed of the a/c from F1, only a "couple" [speed + direction of flight]. There are an infinity of couples which are in accordance with F1, thus with the BFO, but you have a minimum speed (flight direction exactly away from the satellite) and a maximum angle between the direction of flight and the line of sight of the satellite given by the maximum speed of the a/c. This error is also very small, so the incertitude about the "couple" is pretty large.
This is an important point. Further comments:
(1) Conceptually, it is tidier to separate out:
(a) the velocity component along the axis between the satellite and the aircraft location (i.e. notional point at sea level below aircraft) due to satellite motion relative to earth. This component can be computed precisely for any given time and (assumed) aircraft location.
(b) the total velocity component along the axis between the aircraft and the satellite due to the combination of aircraft and satellite motion. This component is equivalent to the doppler shift between the aircraft and the satellite which contributes to the overall BFO value.
(2) The BFO correction value is apparently derived based on measurement of the frequency deviation of the incoming signal received from the satellite. The idea is that the a/c system pre-compensates for Doppler shift such that the signal received by the satellite appears at the nominal channel frequency.