Primitive navigation system
You could use some kind of beacons in the room. For example, IR beacons, radio beacons or maybe even sonic beacons. If you can estimate the distance to your robot from three beacons (and you only need to estimate, you don't need to know the exact position) you can apply simple trigonometry to figure out your position. This has the advantage that errors do not accumulate.

INS systems are not very useful except for short runs. For example, assume you have an accelerometer has an offset of +0.1%, that is, its measurements are all 0.1% greater than they should be (which would be a top spec accelerometer) and your robot runs for 30 minutes taking five samples per second, it would lead to an overall position error of +8066%.