*IF* the precision is actually that good (5km), then taking into account known wind drift and making assumption on a/p settings (FMC versus HDG - Thanks aerobat77 ) and TAS I would expect you can come up with some pretty precise estimations of the flight path.
Am I missing something here?
Surely these additional pings would just give us a series of extra arcs that tell us nothing more than the average speed for each hourly portion of the flight and whether the aircraft was traveling away from or towards the satellite?