When are police allowed to track you via GPS?

I woke up last night/this morning to find that my father (in Tennessee) was arrested for domestic abuse. My mother and father are going through a divorce, are selling their house, and without bothering with the story, it is pretty clear (even just from my mother's side of the story) that the whole thing was nonsense. After a 12 hour cool off period at the local police station, he was to be released. Apparently, he is being fitted with a tracking device. This seems pretty unconstitutional to me, or at least wasteful and unneccesary. I've had a great deal of difficulty finding the legal rules for attaching a tracking device and cannot understand why you need to track someone for such a reason when they share an address.

There was no physical violence and my mother asked to not press charges (ploy for the court proceedings), but the police ran with it. So, without any emotional response, is this allowed? Can cops just track whoever they want for any reason?