IR may not be the best approach as you will get lots of interference & reflections in a typical hospital environment - plus what happens if there are several of these patients in the same queue etc. I have been involved in projects like this where even $,$$$,$$$+ couldn't deliver a perfect solution.
RF solutions can suffer from interference also - even between floors or through walls. Using RSSI approaches can be unreliable, even with triangulation.
The best approach is likely to be a hybrid approach.
However, there is a campaign running on Kickstarter or Indiegogo using vision technology to have a robot follow colour coded objects, which is quite impressive & interesting. I think they just sell the camera & board with a standard interface. You will still hit some challenges.
Another approach might be to leverage Kinect or WII type gaming devices...but would need some research.
Let me know if you make any progress it's an topic I am interested in.