Precise robot

I'm making a robot and I was wandering if it was possible to make a robot that constantly turns at a certain degree in an indoor gym, synthetic floor, for a bit more than 30 meters. How precise can I be because I'd like to be 1 degree precise. I was thinking with a compass or something like that but im not sure if it's precise enough.

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spycatcher2k:
Why would it not me precise? Have you searched for, and investigated the compass modules available?

Yes they all say they're 2 or 3 degrees precise, I havent found one that is really precise.

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Make sure that no external magnetic fields influence the compass in indoor applications.