BBC News:

Android phones can be tracked without using their GPS or wi-fi data by studying their power use over time, a study has found.

A smartphone uses more power the further away it is from a cellular base and the more obstacles are in its way as it reaches for a signal.

Additional power use by other activities could be factored out with algorithms, the researchers found.

The key here is that a malicious app can track your movement without getting permission to access your GPS info. Just tracking your power usage can help malware track your location. [Hat tip, Rob Richman]