You don't actually need to transmit the data off a backup battery, just store it and ship it out once a proper power supply is reattached. (You lose the data if someone destroys their phone, but that's a much narrower range of scenarios than "turn it off, but for real".) I don't recall GPS recievers being particularly power-intensive, but there's plenty of other sensors to log, most notably the microphone.

You don't use your phone for navigation a lot do you? It drains the battery very quickly.

I mentioned radio, because wifi / cell tower triangulation can be used to infer location.