Aircraft collision avoidance using statistical decision theory

Collision avoidance involves the detection of impending collisions of an aircraft with either another aircraft or the ground from radar data and the timely alert of the danger to the pilot or air-traffic controller. The challenge is to provide sufficient warning (timely detections) with minimal false alarms. Radar measurement uncertainties degrade collision detection performance and must be accounted for in the algorithm design. This paper describes a method which uses statistical decision theory to control both missed or late detections and false alarms. The key to the technique is the mathematical description of the aircraft corridor uncertainty region. The corridor uncertainty region is derived from the position and velocity confidence ellipsoid associated with the aircraft radar track via a mapping from six dimensional space to three. By careful choice of the mapping, the minimum volume corridor uncertainty region is derived. This allows for the definition of the optimal collision avoidance decision rule. Since the method is based solely on the statistical properties of an aircraft's position and velocity track, it may be adapted to a variety of collision avoidance or guidance problems involving a radar or beacon-type sensors such as Mode C or Mode S.