iPhone 5s GPS no longer working

My iPhone 5s' GPS very suddenly stopped working.

I've been using — and enjoying immensely — the Fog of World app as well as MapMyWalk, so I've been making extensive use of my iPhone's GPS. While I was out last night, I noticed at one point in the Fog of World app that the GPS signal indicator was just one bar and my location was way off in a field with a huge margin-of-error circle, so the phone was clearly just using my cellular signal for location and not GPS.

I thought at the time it may be because my battery was low (it was at 16%) and the iPhone was just trying to save power. So I got home and plugged it in.

After fully charging, this morning it still is not working. I restarted the phone. Still not working.

What do I do?