OMG! I have the answer to all our problems...and to think its been under our noses all this time.
PET TRACKING MICROCHIPS
They are the size of a grain of rice, cost next to nothing ($12.00+ in most states) AND come in a variety of models. From transmitting a frequency thats picked up by a hand held scanner, or a GPS enabled model. The possibility's are endless!
All the parts of the equation are solved
1. Self contained power source (batt)
2. Small and light
Just type in "dog GPS tracking chip" in Google and find a model the fits your needs.
WHY REINVENT THE WHEEL WHEN SOMEONE HAS ALREADY INVENTED IT FOR US?
Kuro Neko Neko