Computers are very far away from understanding where they are from context alone. Hell most humans don't know where they are. So if you have a short GPS outage they will be able to continue navigating due to other sensors, but the longer the GPS outage/issues persist the more unlikely it is that they still know where they are.
There should definitely be a safety to drive to the side of the road and wait though.
In any case, aren't all self-driving vehicles equipped with lidars and work in pre-mapped regions? I would 100% expect they are able to just use those maps with lidar to precisely geolocate themselves, probably more precisely than with GPS. And, indeed, GPS itself can at times be inaccurate or simply not available due to obstructions.
So what I'm saying, maybe it's wasn't the GPS.
I believe Tesla has made a lot of noise about not using lidar.[0]
[0]: https://venturebeat.com/2021/07/03/tesla-ai-chief-explains-w...
I imagine these robotaxi vehicles would not have stayed on the road had they have had a safety driver in them :).
"Where on Earth am I" on the other hand is basically irrelevant to safety. Run it on the entertainment console or whatever. Interpolate position, come up with heuristics, whatever. I mean, it should be like two reasonably competent people on a road-trip -- if you are the driver and I'm the map guy, you aren't going to just stomp on the brakes when I inevitable lose track of where we are (I'm bad at navigating). You'd probably just go along the road while I worked it out, unless I was really confused, in which case you'd presumably pull over somewhere.
If local sensors tell you the road is blocked, fine. But if remote data tells you one thing, and local sensors tell you something else, the fail safe should be pulling over to the side of the road.