The last and final design, the Teensy and GPS is directly powered from 3.7v li-on batt, 39g heights with IP4 box.

Original project: http://www.f4huy.fr/?p=39
Arduino code and pcb layout (ARES) available.
Load the sketch with CPU Speed 8Mhz under Arduino IDE, (i use v1.6.3 without any problems).

Autonomy test:
With a full batt charge, GPS locked, 5hz rate logging, 20 hours continues logging.

Power button in red, black button to enable charging in case of using +5v AC adapter
SDCard socket is mounted at the back of pcb