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The app should use the accelerometer and other sensors (including GPS, although it may be mainly unavailable) to create a 3d 'track'. The track will start with a GPS location, but then may have perhaps 10 minutes / 1km with no GPS. The app will need to estimate the position of the phone continually throughout this period using inertial navigation / accelerometer etc.
Ideally, the app could record a low speed track (walking), mid speed (cycling) or high speed (car). The key is that the track needs to be recorded once per second and with no GPS for upto 10 minutes at a time (maybe more).
The track should then be exportable as a GPX or KML or other 3d route.
The app does not need to be publishable to the public in the first instance - it could just run via testflight for internal use. We may then have a second stage when it is published.