Hi DenisG and Diversification,
As someone who’s only following this thread superficially, I’m most impressed by the amount of information that you guys are processing − much of which is going over my head, because I haven’t done enough homework at this stage. But perhaps I can intrude briefly to suggest that you may not need to get too exercised about the complexities of the various present-positions computed by the FMC to arrive at its PPOS (present position).
To answer one point, IRS positions are themselves a form of dead-reckoning position, based on the departure position (while stationary), modified by all subsequent accelerations. While the systems were up and running, the three IRS positions are unlikely to have been much apart from either the true position, or each other, after the short flight time (3 hours?). The Mix-IRS position was therefore unlikely − in my opinion − to be more than about 2 nm in error; probably less.
Radio Position updating can only be better than that if a suitable pair of ground-based DME (distance-measuring) stations are available. This would not have been the case, as they are only receivable up to about 200nm at cruising altitudes. So, as is usual over desert and ocean, no Radio Position would have been available for consideration by the FMC.
The most accurate positioning system is, of course, (dual?) GPS. The chances are that it would have been available, and giving a far more accurate position than the Mix-IRS Position. But even if it was not, the FMC position would still have been accurate to within about 2nm. As PJ2 now indicates, the FMC PPOS should be slightly better than Mix-IRS, because it would have incorporated a correction (bias) to it during earlier periods when Radio or GPS Positions were available. So the FMC PPOS is likely to have been accurate to within 2nm while the FMC and IRSs remained powered and serviceable.
In the unlikely event that ACARS happened to transmit a PPOS just before impact, that position should have been accurate enough to send search vessels to the right area. The problem some of you seem to be pursuing is: how far did the flight continue after the last ACARS-transmitted position, and in what direction?
Chris