Probability of Collision of Aircraft with Dissimilar Position Errors

The natural safety metric in air traffic management is the probability of collision between aircraft : due to its extremely low probability of occurrence, it is virtually impossible to measure directly in simulations. It is shown that the rms position error is an indirect safety metric because it specifies an upper bound for the probability of collision. The latter can be calculated from the rms position error of two aircraft, whether it is the same σ (similar aircraft) or different σ 1 and σ 2 (dissimilar aircraft) ; the latter more general case is considered here. The rms position error is easy to implement as a safety metric : it just requires monitoring of the deviation between the actual trajectory and the intended trajectory. The actual trajectory could be specified by real flight data or a real-time or fast-time simulation; it could include en route flying, terminal maneuvers, and ground movements, as long as a minimum separation distance is defined for each phase. It is shown that International Civil Aviation Organization (ICAO) target level of safety (TLS) of low probability of collision is attained if the rms position error σ does not exceed about 1/11 th σ ≤ 0.09L of the minimum separation distance L. This assumes both aircraft have the same rms position error; in this sense they are similar aircraft. In the case of dissimilar aircraft, with distinct rms position errors, σ 1 > σ 2 , the probability of collision will increase by up to a factor of five if σ 1 and σ 2 do not differ by more than a factor of nine. This is a relatively small increase, which remains within ICAO target level of safety (TLS) of5 x 10 -9 per flight hour, if L/σ ≥ 12 is raised, that is, the rms error is about 1/12th of the separation distance.