Abstract: An apparatus for compensating a magnetic heading as indicated by a vehicle's magnetic compass so that the magnetic heading corresponds to a true heading as indicated by signals received in the vehicle from the Global Positioning System. The apparatus includes a computer for calculating compensation factors from successive positions occupied by the vehicle as it travels.

Abstract: When a vehicle has deviated from a computer-determined optimal route from a starting point to a destination, a navigation system warns the vehicle driver that he is off the optimal route, picks an appropriate direction for continued travel, selects a new starting point, and computes a new optimal route from the new starting point to the destination. By selecting the new starting point based on the vehicle's present location and the time to recompute a new optimal route, the system eliminates the necessity for a driver either to go back to the original optimal route, to recompute the optimal route by a manual operation, or to recompute a new optimal route more than once.