How creative are you?
Just for fun, I am putting together a list of every known way that an indoor robot can tell where its absolute position in a room is. I am excluding relative position solutions such as wheel odometers unless someone can show that they don't drift. I will post a summary of all the answers when the ideas stop coming in.
Here is my start:
Ultrasonic range finders pointing in all directions.
Follow a line on the floor made with UV ink.
Use a camera and figure out where you are from what it sees.
Three bike reflectors on the ceiling, and a scanning beam of light with a photodetector to see the reflections.
Optical mouse technology, looking at the floor or at the ceiling (or does this technology drift?)
Any other ideas?