As far as I can tell, Galileo has nothing like this. They have a small buffer of future ephemeris data, but the ground segment failure here was so long that it completely ran out. Their approach seems to be full accuracy or why even bother.
Seems only marginally worth it...
It's probably easier to say "our system being down won't be catastrophic" when it's one of 4+ systems rather than one of one, like GPS was.
Also probably not inaccurate to say that the US military cares more about what happens after the nukes start falling than the ESA does.
Indeed, Galileo has nothing like this. The GPS solution sounds exceptionally fancy, and it may go a long way to explaining where all those billions of USD/year go :-) Do you know if it has ever been tried for real? Thanks!
Also, satellites are in direct view of one another and can easily receive each others signals. A rather simple software radio could receive the signals from a basic omnidirectional antenna. The only challenge is subtracting out the very strong local signal before digitising, but considering the very strong coding gain in GPS, it should be doable.
I'd think that would be rather a phase accurate software radio.
Incidentally, it seems like the EU is looking at developing their own version of Autonav for the next generation of Galileo, quite possibly with optical rather than radio links between the satellites.