Might be coincidence, or maybe not...
But I seem to at least temporarily get the GPS working again if I try to use the compass from Google Maps in the background. Basically turn on Google Maps app, make sure it picks up your current location, then go back to Pokémon GO.
Similarly, I was able to fix my wife's glitch last night by involving her Google Maps app.
As it was a brand new phone, apparently Google Maps needed to be updated. After that it worked fine. OR, possibly, it's because I opened google maps first (but then closed it...) and that made it work. Either way, it was somehow connected to Google Maps functionality.
So, if you're still looking for answers on this one, I suggest tinkering with Google Maps and making sure it's working first.