Not long ago, we have announced GPS Navigation, a navigation software for Ubuntu Touch that works only online and is built on OpenStreetMap.
But there is also an offline GPS application called OSMScout (OpenStreetMap Scout), ideal for users without internet connection, permitting them to download the app at home and use it outdoors.
The application requires special access to the SD card (not permissible on the phone) and so, the users need to bypass this with the Open App Store, but this limitation should be passed soon.
See the below demo video of OSMScout, for more information: