I apologize for the fact that this is behind a paywall, but believe it or not, searching "MuPS navigation" in google only gives me one applicable source and this is it.
At higher latitudes, traditional GPS navigation is not reliable, but muons produced when cosmic rays hit Earth’s atmosphere could be used to navigate in the Arctic, as well as underground or in the water
www.newscientist.com
Short version - bear in mind I'm not completely sure how this works so . . . you've been warned.
So, when energetic cosmic rays hit the atmosphere, they create showers of muons. So far, check.
You then install muon counters (they're pretty easy to detect) here, there and everywhere. These will be your "reference" counters. Got it.
Now, on your sub, bathysphere, multi-mile deep mine or tunneling device (used to get to the center of the earth of course), you have another detector. Here it gets fuzzy.
This device compares the difference in time between the reference modules and the one on board. It can then determine your location to within 60mm - even with only intermittent contact with the reference network. Now I'm lost.
The device was originally developed to help supplement GPS sats that tend to orbit at low altitudes when navigating near the poles.
If it is obvious to you how this works, an explanation would be appreciated.
BTW, since muons mostly (but just mostly) pass through normal matter, these types of devices could be useful deep under both ground and water.