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Fault tolerant algorithm for matching sequence of road segments

I am trying to design a system for determining the absolute position of a vehicle without using GPS. The idea is that I will record data from sensors onboard a vehicle at specified time intervals, primarily the altitude, heading, and distance traveled, and use this to create some model of the route driven (note: the absolute heading itself cannot be trusted, but I can rely on the change in heading between data captures). I then would like to compare this against data extracted from open street maps in order to locate the vehicle.