##Version #1
I used a combination of the TI stick, Intel Edison and Sparkfun base board, a battery that has pass-through charging (so you can charger it will keeping your Edison up and running), along with a few other tools and connectors. See V1 Page for photos and details
##Version #2 Version 1 seemed to have a crappy (2-3 hour) battery life. So for v2, I tried reduce consumption by moving from 2 USB connections (battery and TI stick) down to 1. I did this by switching to this 2000mAu LiPo battery. The result was a smaller form factor photo coming soon, but battery life did not improve at all. The next try was to move my loop time from once a minute to once every five. Still, the battery life was only 2-3 hours. So, I have decided to move on to v3.
##Version #3 I am going to try the Edison board + ERF stick setup - stay tuned!