Not GPS, but I did use video surveillance to prove my cat was a scam artist.

We had long suspected this, and the tape bore out that she would lie on the couch all day, then as soon as she heard a car pull into the driveway she'd rush to the kitchen, scarf every bit of food in the dish, and of course once we came in she'd be mewing piteously about how cruel we were to leave her without food.

MyKingdomForYourHorse:

I thought that was already debunked, like they tracked thousands of cats and found that only a scarce quarter of them actually ever caught anything. Basically they proved the modern house cats are shiatty hunters.

I once witnessed the scammer cat mentioned above nail a bird through a window that was open 1", and she had always been an indoor cat. Growing up we had Mort, Lord of Death who... Well, let's just say you always looked before going out on the porch barefoot, as he was prone to leaving gifts like half a rabbit, half a bird, half a snake...

You left out one activity: looking out the window.