Deriving the course from the Inmarsat pings
I have done some simulations of whether the route of the flight could be determined if the arcs from the interim Inmarsat pings were available. So far we only have the final arcs (the north and south 'corridors').
I used the final published arc as the set of possible ‘destinations’ of the flight. One example destination on this arc was chosen, this determines the speed and heading from the last recorded radar position to achieve that final position, and hence where the hourly pings would be emitted over the 7 hours of the flight (and thus the distance from the Inmarsat sub-satellite point, which is what Inmarsat measures). A constant speed and heading was used as a first approximation.
The results of this example can be compared with the same calculation for each point along the published final arc, each of which requires a different heading and speed from the last recorded radar position and generates a different set of predicted ping arcs (distances from the sub-satellite point). An overall error can be calculated for each point along the published final arc.
The result is that there is only one constant heading course from the last recorded radar position that matches the example set of ping arcs, that is the destination is uniquely defined by the interim and final ping arcs (if interim arcs exist). There is a (rough) mirror course in the southern hemisphere which may be hard to distinguish as the last recorded radar position was close to the equator.
I also added a random error (noise) to the ping signals derived from course to the example destination, with the magnitude of the error being 50km on the ground (Gaussian, one sigma). This increases the error in deriving the final course giving an uncertainty of around plus/minus 100km in recovering the final destination – but it does not invalidate the technique.
I haven’t yet tried putting in a course with a change of heading along the route, but the method seems quite sensitive so I suspect such a course change could be recovered from the data. Many headings or speed changes would increase the final error, obviously.
So if the interim pings are available (to someone), and hence their arcs, it is very likely that the destination (or at least one in each hemisphere) could be derived with reasonable errors, at least up to the final ping.
Notes:
1. This is a rough piece of work done quickly to see whether the concept works. I have made a few assumptions that seem reasonable.
2. in this first try I have used simple Cartesian geometry (flat plane) rather than spherical geometry. The differences are relatively small as the area covered is reasonably close to the equator. A full spherical interpretation will not change the conclusion that the set of arcs define a single destination (or rather one in each hemisphere) but obviously would be needed to interpret the actual interim ping arcs.