The fitness app [Human](http://human.co/) sits in the background and provide a map of where the user has moved throughout the day, and a timeline of when they moved (for example, that there was a walk from 10-10:30 AM, a jog from 2-:2:14, etc). When apps like this are backgrounded, the iOS permission dialog asks if the user wants to allow the app to continue using their location in the background.

I have no idea what APIs they use, so I'm not sure how hard it is to get this information, but it is at least possible.