When we talk about GPS, we immediately think about going from point A to B. Technologies similar to GPS have been used to track patient remotely. The basic idea is that these devices, which are, most of the time, attached to the patient, report the location information to a central location and if the movement patterns deviate from the normal patterns, they detect an anomaly. That anomaly could be something good (for example, a patient who is recovering making some movement could be a positive sign, no movement at all could be a negative sign).
There have been commercial as well as research projects in this regard. For example,
Remotely monitory elderly location: here here
A research project to track the recovery from a surgery: here
A device to track dangerous psychiatric patients: here
And many more
Even though these devices/techniques are designed/deployed with good intension, one concern here is people who are being monitored have no control over their own data, i.e. their movement information. And they don't have control over who can view their data. Hence, it could lead to serious privacy breaches. I'd like to see a system where it gives more control to the target (to someone on behalf of the target) over their information.