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There seems to be a problem with some of the data released by the satellite company Inmarsat.

Specifically, the handshake at 00:10:58 on 7/03/2014.

In the left column the difference in time-stamp between the ground station initiating the request and the receipt of the return signal from the aircraft is given as 1.928 seconds. However, the prior handshakes at 19:41, 20:41, 21:41, and 22:41 took 1.996, 1.997, 1.998, and 1.999 seconds.

This would imply that the round trip distance between the ground station and the aircraft changed by about 13,000 miles in 1.5 hours. What gives?

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TL;DR.

  1. Use the BTO not the difference in time-stamps for request & acknowledge.
  2. BTO is an offset in μs, not a round-trip time.
  3. There's a mean bias value (-495,679 μs) that includes the signal processing delays in equipment.
  4. The distance is ground-station to satellite to aircraft to satellite to ground-station.

Inmarsat data

As I understand it, to calculate distance you should be starting with the Burst Timing Offset (BTO) not the difference between time-stamps in the Inmarsat data. There are latencies in various stages in the electronic processing of messages, not all of these are distance related.

Time    BTO(μS)
19:41   11500
20:41   11740
21:41   12780
22:41   14540
00:10   18040

There's an example on page 54 of MH370 - Definition of Underwater Search Areas:

enter image description here enter image description here

The aircraft AND the satellite are in motion in three dimensions

The satellite is at an altitude of around 35,811 km above the earth's surface, the satellite is moving cyclically north and south of the equator and the aircraft is flying over a roughly oblate spheroid so changes in it's distance from the satellite are not a simple function of changes in the aircraft position relative to the surface.


enter image description here
Not to scale. E&OE. etc


References

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  • $\begingroup$ The "R" terms given in the equation (in reply to my question) do not seem to represent the actual distances.For example, using the coordinates 0 degrees N/101.7 Degrees E the distance from the orbiiting satellite to these coordinates is 23,182 miles. And from the satellite to Perth, Australia is another 24,250 miles. But the maximum value for the term to the right of the equal sign is (.014810xC)/2=1379 miles. And since the distance from the orbiting satellite to Perth is much greater than 1379, this would make the the range value (from the aircraft to the satellite) negative. $\endgroup$ – John Mauch Jul 24 '14 at 16:06
  • $\begingroup$ @John: See P54-55 of the second link. The bias value is negative. $\endgroup$ – RedGrittyBrick Jul 24 '14 at 17:11
  • $\begingroup$ I have updated the answer to include the relevant section of the ATSB report that gives examples of the calculations of aircraft range from Inmarsat timing data. $\endgroup$ – RedGrittyBrick Jul 28 '14 at 10:09

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