I have heard of some sort of chip that gets implanted under the skin, I noticed a sign on the local vet's office that said tracking chips installed here. I guess it is GPS involved.
there is no GPS but the tech is cool, we use them on deer captures to mark deer for later recapture or when they are harvest to see how big they grow. It's called a PIT tag (Personal Id Tag) and it uses the barcode tech like in the Supermarket. When you see your dog, there is a special scanner you pass over the animal and each PIT has a number assigned to it. So dog #1 is #2569984, Dog #2 is #7951366 etc. etc.
When you see your dog (lets say #2), take the documentation to the Sheriffs Dept. and ask the person with the dog to let you scan him. when it reads the PIT it will show #7951366 on the screen and you got them red-headed.