A program and method are disclosed that provide for determining a position of an object, such as a vehicle, relative to a road network represented by a geographic database. An intermediate position density is determined along a plurality of road segments in the road network by shifting a prior position density which had been determined along the plurality of road segments by a distance traveled by the object since the prior position density had been determined. Then, the intermediate position density is modified to take into account sensor-derived data received since the prior position density had been determined to form a new position density. The position of the object is determined to be that location along the plurality of road segments at which the new position density is greatest. Also disclosed is a way to determine whether the object, such as the vehicle, is on or off the road network. A certainty measure of the new position density is computed. If the certainty measure is less than a predetermined threshold, the object is determined not to be located on road network. If the certainty measure is greater than the predetermined threshold, the object is determined to be located on road network and the position reported. Also disclosed is an implementation of the program and method using step functions to approximate the position density along selected road segments.