System and method in lane departure warning with full nonlinear kinematics and curvature

An apparatus, comprising:

• at least one camera configured to capture an image of a traffic lane in front of a vehicle;
• and
• a vehicle behavior prediction controller configured to:
• determine lane boundaries for a segment of a traffic lane occupied by the vehicle from the captured image of the traffic lane in front of the vehicle and prior captured images of the traffic lane in front of the vehicle,
• determine a rate of road curvature for the segment of the traffic lane occupied by the vehicle from the captured image of the traffic lane in front of the vehicle and prior captured images of the traffic lane in front of the vehicle,
• determine lateral distances of the vehicle from the lane boundaries and a rate of departure of the vehicle from the occupied traffic lane that is accurate for the determined road curvature,
• determine a time to line crossing for the vehicle from the lateral distances and the rate of departure, and
• activate a lane departure warning indicator based on the determined time to line crossing.