I have been trying out a variety of power sources. One is the 4xAA battery holder to female USB Verbatim 97928 available for about $10. It seems to have a well regulated 5.0 volt output.
The red arrow points to the side of the “74″ diode that comes right off the micro USB connector. I measured 5.00 Volts there with the Edison running on the Verbatim 97928. On the other side (downstream) of the diode I measured 4.72 Volts with the Edison idling. This voltage drop is expected due to the forward bias diode voltage drop.
Under 100% of one core CPU load, I measured 4.98V on the USB side, and 4.66V on the Edison side of this diode while powering from the USB port on the Verbatim 97928. The miniscule apparent 20mV voltage drop on the battery/USB side of the diode is likely to come from ohmic losses in the USB connector and cable.
Based on measurements of Intel Edison power consumption, and assuming 2000mAh, I estimate 10-12 hours of battery life on 4xAA alkaline batteries assuming continuous 100% CPU of one of the two CPU cores (other core idle). Normally the Edison will be mostly resting, drawing perhaps 100mW.
Thus with mixed use, I might expect to get up to 4-5 days of continuous mixed use operation on 4xAA batteries for the Intel Edison.