I have a FP1U and a few weeks ago I reallized that my GPS is searching for a location - i never granted access to the GPS for any app neither did I activate location services etc. It started from one day to another.
After following the related topics here and elswhere, I figured out that it's the data connection triggering the GPS module to activate itself. As long as I only use WiFi or no data connection, it's fine. As soon as I turn on data, GPS is on. Drowning the battery in under 1h.
Thanks for helping, currently I can't really use the phone because I strongly need data connection for work - hope to hear from you soon.