Minimum Safety Distance Study On Stochastic Differential Equations In Free Flight

In free flight, the pilots could choose their own aircraft path and speed in a given airspace. Therefore, contrast to the current flight, the free flight is able to save time, save the cost of airlines and improve airspace capacity. The interval is defined as the distance between two aircraft in free flight. For the sake of ensuring the plane's security, we must to study the minimum safety distance in free flight.The main work of this paper is as following: Firstly analysis the plane's motion law in free flight, establish the random kinematics model in view of Cartesian coordinate.Considering the factors of CNS performance and winds aloft, a collision risk model based on stochastic differential equations is created. When the distance between the aircraft is less than the minimum safety distance, it proves collision occurring. The minimum safe distance between flights can be optimized with Newton iterative method. Then studying on the influence factors: CNS performance, velocity distribution in free flight. The plane Cartesian coordinate system, using the Kalman filter theory estimate of relative distance between aircrafts. Then build the horizontal projection plane collision risk model; In the vertical projection plane, found random kinematics pattern. Making the two projection surface relative distance integrated into the same space coordinate system, the distance between the aircraft is less than the minimum safety distance, the collision happens. Finally building the collision risk model in view of establish air rotary overpass, adjust the plane conflict, joining the rotary or rise?descend the height.Considering the CNS performances, velocity distribution, human factors and the collision avoidance system, affect on aircraft collision risk. Set up the establishment of three-dimensional coordinates to calculation the minimum safety distance.