In further investigation (thanks to PointyOintment's suggestion) it may be simpler to use multiple PS2 mice instead of the belts. You can do deadest reckoning with two mice read http://www.instructables.com/id/Optical-Mouse-Odometer-for-Arduino-Robot/step4/Further-Modifications-and-Finishing-Up/ and https://www.researchgate.net/publication/221645389_Dead_Reckoning_for_Mobile_Robots_Using_Two_Optical_Mice. But this always assumes you haven't cut large lines out of your working surface. This means many mice would have to be used and ignore the extreame values.