Study on Free Flight Collision Risk Based on the Error Distribution of Three-Dimensional Position

Abstract

This paper is aimed to evaluate the collision risk in free flight. The collision risk between aircrafts is mostly closely relates to position error, due to which the actual position of the aircraft is different from the displaying position and the former is in the vicinity of the latter. Analyzing error factors closely associated with the risk of collision, such as position error caused by CNS performance, altimeters and CDTI system, and according to the error distribution, the region of actual position of aircraft can be considered as a three-dimensional joint normal probability density ellipsoid. The two adjacent planes can be abstracted into two particles, of which one is based to determine position error ellipsoid, and the other is based to establish collision slab. A free flight collision risk model is established, then simplified by linear transformation according to the principle of relative motion. Using Monte Carlo method of mean of uniform random numbers, given initial state, the collision risk in free flight can be obtained. Numerical results demonstrate the feasibility of this model.