POSITIONING SYSTEM

1 . A positioning system, said system comprising:

a camera, the camera rendering an image of lane-markings on a roadway ahead of a host-vehicle traveling in a travel-lane of the roadway;

a ranging-sensor, the ranging-sensor detecting a position of an other-vehicle traveling on the roadway behind the host-vehicle; and

one or more controller-circuits in communication with the camera and the ranging-sensor, the one or more controller-circuits:

determining lane-widths of the travel-lane based on the lane-markings at a first-distance ahead of the host-vehicle while the host-vehicle is traveling along the roadway, the lane-widths characterized by pairs of opposed control-points;

tracking relative-positions of the pairs of opposed control-points to the host-vehicle while the host-vehicle is traveling along the roadway;

determining a road-model based on a temporal-history of the relative-positions of the pairs of opposed control-points, the road-model including virtual-lane-markings extending beyond a rear-end of the host-vehicle for a second-distance;

determining a lateral-offset of the other-vehicle based on the road-model, the lateral-offset characterized as a shortest-lateral-distance between the other-vehicle and the virtual-lane-markings; and

operating the host-vehicle in accordance with the lateral-offset.

2 . The system in accordance with claim 1 , wherein the first-distance is about 20-meters ahead of the host-vehicle.

3 . The system in accordance with claim 1 , wherein the one or more controller-circuits further determine the lane-widths at the first-distance ahead of the host-vehicle after the host-vehicle has traveled a distance greater than a distance-threshold.

4 . The system in accordance with claim 3 , wherein the distance-threshold is about 10-meters.

5 . The system in accordance with claim 1 , wherein the second-distance is at least 50-meters beyond the rear-end of the host-vehicle.

6 . The system in accordance with claim 1 , wherein the one or more controller-circuits assign the other-vehicle to an adjacent-lane when the lateral-offset is greater than an offset-threshold.

7 . The system in accordance with claim 6 , wherein the one or more controller-circuits determine a longitudinal-distance between the rear-end of the host-vehicle and a front-end of the other-vehicle, the longitudinal-distance characterized as a distance along a centerline of the adjacent-lane between lateral-projections orthogonal to the virtual-lane-markings.

8 . The system in accordance with claim 1 , wherein the virtual-lane-markings are determined based on a linear-interpolation between the pairs of opposed control-points.

9 . The system in accordance with claim 1 , wherein the one or more controller-circuits further determine a host-vehicle-offset characterized as a lateral-distance between sides of the host-vehicle and the virtual-lane-markings, whereby a total-lateral-distance is determined based on the lateral-offset and the host-vehicle-offset.

10 . A method of operating a positioning system, said method comprising:

rendering an image of lane-markings on a roadway ahead of a host-vehicle traveling in a travel-lane of the roadway with a camera;

detecting a position of an other-vehicle traveling on the roadway behind the host-vehicle with a ranging-sensor;

determining lane-widths of the travel-lane based on the lane-markings at a first-distance ahead of the host-vehicle, with one or more controller-circuits in communication with the camera and the ranging-sensor, while the host-vehicle is traveling along the roadway, the lane-widths characterized by pairs of opposed control-points;

tracking relative-positions of the pairs of opposed control-points to the host-vehicle, with the one or more controller-circuits, while the host-vehicle is traveling along the roadway;

determining a road-model based on a temporal-history of the relative-positions of the pairs of opposed control-points, with the one or more controller-circuits, the road-model including virtual-lane-markings extending beyond a rear-end of the host-vehicle for a second-distance; and

determining a lateral-offset of the other-vehicle based on the road-model, with the one or more controller-circuits, the lateral-offset characterized as a shortest-lateral-distance between the other-vehicle and the virtual-lane-markings; and

operating the host-vehicle in accordance with the lateral-offset.

11 . The method in accordance with claim 10 , further including the step of determining the lane-widths at the first-distance ahead of the host-vehicle after the host-vehicle has traveled a distance greater than a distance-threshold, with the one or more controller-circuits.

12 . The method in accordance with claim 10 , further including the step of assigning the other-vehicle to an adjacent-lane, with the one or more controller-circuits, when the lateral-offset is greater than an offset-threshold.

13 . The method in accordance with claim 12 , further including the step of determining a longitudinal-distance between the rear-end of the host-vehicle and a front-end of the other-vehicle, with the one or more controller-circuits, the longitudinal-distance characterized as a distance along a centerline of the adjacent-lane between lateral-projections orthogonal to the virtual-lane-markings.

14 . The method in accordance with claim 10 , further including the step of determining the virtual-lane-markings based on a linear-interpolation between the pairs of opposed control-points, with the one or more controller-circuits.

15 . The method in accordance with claim 10 , further including the step of determining a host-vehicle-offset characterized as a lateral-distance between sides of the host-vehicle and the virtual-lane-markings, with the one or more controller-circuits, whereby a total-lateral-distance is determined based on the lateral-offset and the host-vehicle-offset.