There are numerous uses of the GPS for uses of police tracking, from potentially tracking a former criminal's every move to making sure someone sticks with their restraining order. Similar cases stem all the way back to 1983, where secretive warrantless tracking (here with “bird dog trackers”, not GPS) was said to be OK—as long as police only tracked anything while it was on public, not private property. Rulings regarding the use of bird dog trackers and other pre-GPS tracking devices have largely been extended to GPS devices.
The court verdicts have been a mixed bag on this, from entirely permissive to hostile. A recent 2009 case in Wisconsin ruled that the police can use GPS to track anyone, without probable cause, without a warrant, without consent, without anything at all. The logic used here was that GPS tracking was not any more invasive than normal police tracking, and did not constitute of a “search and seizure.” A similar case occurred in 2005 in New York, which was later more-or-less overturned in 2009. Another recent 2009 case in Massachusetts ruled that, while GPS tracking was perfectly acceptable on public property, the moment that the device strayed into private property, the police needed a warrant to continue tracking. The examples are numerous.
The general trend in court cases seems to be one of approval for use of warrantless, secretive GPS tracking of criminals and suspects, as long as the device remains on public property and does not stray. However, the rulings are erratic enough that anything can really happen.