Positioning system

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.