DjerbaDevil:
"First, it is difficult to imagine that a highly sophisticated and modern nuclear submarine would miss 'hearing' the signals from the black boxes but much more so to accept, that while they were recording sound, they did not record their position relative to the sound recording. "
Actually, detecting these pingers under the conditions encountered in the search is not so simple. Judging from the typical characteristics of the pingers used: (see
Dukane model DK120 and DK100 Underwater acoustic locating beacons), 37kHz and 30 day duration, they are most useful when a plane goes down in shallow water and/or close to shore. After all, most aircraft accidents occur in the takeoff or landing phase, and thus happen in the vicinity of airports. What is needed for deep water recovery are larger/heavier transducers at 9-15kHz (lower attenuation), and transponders (rather than pingers), which only ping when interrogated, so that they don't waste power when no one is listening. This is the usual weight/cost tradeoff that aircraft are so sensitive to.
In this case, the a/c went down in deep water far from shore. This affects the search in two ways: the mid-ocean location takes time to reach, using up part of the 30 days, and the deep water consumes much of the limited range afforded by a high frequency pinger (unless you can deploy a deep receiver).
Consider this calculation:
The source level of the pinger is 160db re 1uPascal @ 1meter.
The deep ocean ambient noise, in a calm sea-state 2-3 (4-10kt wind) at 37kHz is about 37db re 1uPa/sqrt(Hz). The pinger has a 10ms pulse length, giving it roughly a 100Hz bandwidth, so the noise is effectively summed over a 100Hz band: sqrt(100Hz) = 10 times = 20db; so, the total noise in-band is about 57db re 1uPa.
Thus the loss budget is 160-57 = 103db.
Spherical spreading from the source, in db, is 20*log10(R in meters) (because the source level is specified at 1m), and the attenuation loss at 37kHz is greater than 6db/km.
At 5km, the spreading loss is 20*log10(5000) = 74db, and the attenuation is 5km * 6db/km = 30db for a total of 104db. Thus at 5km, the signal power is about equal to the noise power. This ignores other sources of noise, such as higher sea-state, ship self-noise, receiver thermal noise, etc. Normally, a 20db signal-to-noise ratio is required for simple detection, resulting in the commonly quoted 2-3km detectable range.
Now the pingers may be at 4km depth, and the sub can only descend to some classified depth, but a published value for Emeraude of only 300m. That difference may (depending on actual pinger depth) consume over 3km of the detection range.
As for the ambiguity in location, I doubt that it is due to navigational uncertainty, but rather due to acoustic localization uncertainty. I have no idea what signal processing was done to actually extract the signal from the noise, but it would likely have involved integration over long periods of time: as long as the sub, traveling at, say, 3-6knts to minimize self-noise, would have been within a few of km of the pinger. After a long integration, one would only be able to guess the location with a resolution of roughly that integration "distance" (time, times the sensor transit speed), i.e a few km.