Vehicular driving assistance system with vehicle state estimation

A vehicular driving assistance system includes a camera disposed at a vehicle and an electronic control unit (ECU). The vehicular driving assistance system, responsive to processing at the ECU of image data captured by the camera, determines lane markers for a traffic lane along which the vehicle is traveling. The system, using a first Kalman filter and based on the determined lane markers, a lateral lane offset of the vehicle. The vehicular driving assistance system, responsive to processing by the data processor of GPS data, determines, using a second Kalman filter different from the first Kalman filter, a geographical location of the vehicle. The vehicular driving assistance system, based on the determined lateral lane offset of the vehicle and based on the determined geographical location of the vehicle, controls at least one selected from the group consisting of (i) steering of the vehicle and (ii) velocity of the vehicle.