Collision avoidance method including determining height of an object fixed to a vehicle

A method of determining a height of an attached object attached to a rear of a vehicle and avoiding a collision between the attached object and an unattached object which is behind and unattached to the rear of the vehicle during reverse maneuvering of the vehicle on a ground surface, comprising:

• determining with an electronic control unit of the vehicle and a rear facing vision system of the vehicle an adjusted top height Hb adjusted Of the attached object wherein the determination of the adjusted top height Hb adjusted of the attached object includes:
• determining with the electronic control unit an angle β which is an angle between a reference plane lying on the ground surface and a line of sight of a camera of the rear facing vision system that is tangent to the attached object by an equation β=arctan(Hc/Da) where Hc is a height of the camera above the reference plane and Da is a lateral distance between a perpendicular plane which extends through the camera and a point where the line of sight intersects the reference plane and determining the lateral distance Da based on distance lines of the rear facing vision system wherein each distance line is indicative of a different distance from the rear of the vehicle;
• determining with the electronic control unit a distance Db that the attached object is away from the camera by using a perspective equation Db=f+f/ABS (yi/y0) where f is a focal length of a lens of the camera of the rear facing vision system which is pre-programmed in the electronic control unit, yi is a height of an image of the attached object seen by the rear facing vision system determined by the electronic control unit, yo is a height of the attached object pre-programmed into the electronic control unit and ABS (yi/y0) is an absolute value of ABS (yi/y0);
• determining with the electronic control unit a height Ha from a top of the attached object to the camera by an equation Ha=Sin (β)*Db;
• determining with the electronic control unit a height Hb that the top of the attached object is above the reference plane by an equation Hb=Hc−Ha;
• and
• adjusting for error (E) with the electronic control unit to determine an adjusted height Hb adjusted that the attached object is above the reference plane by equation Hb adjusted=Hb+E where E is a fixed value;
• determining with the electronic control unit whether the adjusted top height Hb adjusted of the attached object is lower than a clearance height of the unattached object wherein the clearance height of the unattached object is a distance between a bottom of the unattached object and the ground surface,
• upon determining with the electronic control unit that the adjusted top height Hb adjusted of the attached object is not lower than the clearance height of the unattached object, determining with the electronic control unit whether the attached object would collide with the unattached object when the vehicle is reverse maneuvered too close to the unattached object;
• and
• in response to the determining with the electronic control unit that the adjusted top height Hb adjusted of the attached object is not lower than the clearance height of the unattached object and upon determining that the collision would occur, alerting a user of the vehicle by having the electronic control unit display on a display an alert indicating that the collision would occur.