A rotational sensor for use with an in-vehicle navigation system , a navigation system that uses the sensor, and a vehicle with the sensor installed. The rotational sensor is created by placing two gravitational accelerometers configured at 90 degrees with respect to one another and mounted at the center of a vehicle wheel. As this resulting sensor is rotated, sine and cosine signals with a quadrature relationship are generated with respect to the earth's gravity vector, from which both rotation and direction of rotation can be determined. These signals may then allow the counting of the turns of the wheel, thus estimating the distance and the rate at which the vehicle has moved. A self-contained version of this device including a transmitter can relay this information to a receiving unit located within the vehicle. When one of these devices is located on each of the steerable wheels of the vehicle, the relative heading-direction of the vehicle may also be estimated.