Abstract: A method for calculating a distance between a first point and a second point using linear interpolation is provided. The first point and the second point are located between a first latitude and a second latitude. An interpolated prime vertical radius of curvature value for a point between the first point and the second point is calculated based on a first prime vertical radius of curvature value for the first latitude and a second prime vertical radius of curvature value for the second latitude. An interpolated meridian radius of curvature value for the point between the first point and the second point is calculated based on a first meridian radius of curvature value for the first latitude and a second meridian radius of curvature value for the second latitude. An interpolated cosine value for the point between the first point and the second point is calculated based on a value representing a cosine of the first latitude and a value representing a cosine of the second latitude.

Abstract: A method for calculating a distance between a first point and a second point using linear interpolation is provided. The first point and the second point are located between a first latitude and a second latitude. An interpolated prime vertical radius of curvature value for a point between the first point and the second point is calculated based on a first prime vertical radius of curvature value for the first latitude and a second prime vertical radius of curvature value for the second latitude. An interpolated meridian radius of curvature value for the point between the first point and the second point is calculated based on a first meridian radius of curvature value for the first latitude and a second meridian radius of curvature value for the second latitude. An interpolated cosine value for the point between the first point and the second point is calculated based on a value representing a cosine of the first latitude and a value representing a cosine of the second latitude.

Abstract: A turn detection algorithm is used by a navigation system for determining position and heading of a vehicle relative to a road network represented by a geographic database used by the navigation system. A dead-reckoned position and heading are determined along a plurality of road segments in the road network using sensor measurements of a distance traveled by the vehicle and a change in heading of the vehicle. A vehicle trajectory history is formed and then continuously updated. The vehicle trajectory history includes sensor-derived data representing the vehicle trajectory over a relatively small, chosen distance. The sensor-derived data in the vehicle trajectory history include total turn (i.e., heading change of the vehicle), vehicle state (e.g., travelling straight, turning or reversing in turn direction within a specified small distance) and type of vehicle maneuver. These data represent the trajectory of the vehicle for that distance and are kept in a memory.

Abstract: A program and method are disclosed that provide for determining a position of 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 vehicle 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 sensor-derived data include data indicating three metrics, namely (1) a position of the vehicle, (2) a heading of the vehicle, and (3) a curvature history. The curvature history represents a change of heading of the vehicle as a function of distance.