are the dogs being stolen for use in experiments
Stealing a dog for experiments is not going to work. For any experiment to be of any use at all you have to know the genetic history of the dog. You don't get that from stealing a dog.
What is getting more common in the UK is stealing a dog for ransom, some how the police do not seem to think it is a crime from what I gathered from one radio phone in program.
In this case the thief is not likely to remove the collar as he hopes to return everything. So you have the problem of transmitting the location. You could do this automatically when you detect that the dog is over some distance away from home, say half a mile. You will get false reports when you take it on a trip but that just assures the owner that it is working.