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Old 29th Jun 2014, 08:31
  #11214 (permalink)  
OleOle
 
Join Date: Sep 2007
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@Shadoko : I agree that the line in Table 6 must be an error.

Regarding the sensitivity to errors in the BFO I feel that between all the computer simulations one tends to forget the basic facts.

Basically the only independent information in the BFO is the line of sight (LOS) speed of the satellite towards the aircraft. It is what richardC10 calls D2_satellite in his paper.

At a given velocity of the sat, D2_satellite is only a function of the angle between sat velocity vector and the line of sight. I.e. all points of equal D2_satellite are located on a cone around the sat's velocity vector. The intersection of this cone with the surface of the earth gives a line of position.



This principle is used for satellite based location of emergency buoys (e.g.: FAQ - Argos) only that those systems are designed for that purpose and have a much more favorable geometry as opposed to the BFOs measured by inmarsat.

Basically this Doppler derived line of position contains the BFO information which is uncorrelated to the BTO information. The intersection of the BTO line of position (ping arc) with the BFO line of position (doppler cone) defines the position of the aircraft.

On the last ping arc, D2_satellite is greatest due south of the sub-satellite point and it is null on the equator abeam of the satellite. In the middle region between these two extreme ends the variation in D2_satellite can be approximated as linear. According to my calculations at 0:11 UTC D2_satellite is ~12m/s due south of the satellite.

The radius r (not on the surface of earth) of the 0:11 ping arc is ~4000 km
=> the quarter circle section between due south and equator has a length of (pi * r)/2 ~= 6000 km

In the region where MH370 is suspected the variation in D2_satellite can be approximated as linear, then 1 m/s in D2_satellite variation corresponds to
6000 km / (12 m/s) = 500 km per 1 m/s D2_satellite variation.

At 1.6 GHz (L-Band uplink) 1 m/s relative LOS-velocity is equivalent to ~5.3 Hz Doppler shift.

Thus the 1000 km position error for 10 Hz bias error make perfect sense. Actually the error should be much smaller and if it is measurement noise and not fixed bias error, those errors partially cancel out over the series of BFO measurements.
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