The introduction of the new concepts of air traffic management (ATM) and transition from centralized to decentralized air traffic control (ATC) with the change of traditional ATM to Cooperative ATM sets new tasks and opens new capabilities for air traffic safety systems. This paper is devoted to the problem of evaluating the probability of aircraft collision under the condition of Cooperative ATM, when the necessary information is available to the subjects involved in the decision‐making process. The generalized stochastic conflict probability evaluation method is developed. This method is based on the generalized conflict probability equation for evaluation of potential conflict probability and aircraft collision probability that is derived by taking into account stochastic nature and time correlation of deviation from planned flight trajectory in controlled air traffic. This equation is described as a multi‐dimensional parabolic partial differential equation using a differential (infinitesimal) operator of the multi‐dimensional stochastic process of relative aircraft movement. The common procedure for the prediction of conflict probability is given, and the practical application of the generalized method presented is shown. All equational coefficients of a differential operator for a practical solution of a parabolic partial differential equation are derived. For some conditions, the numerical solution of the conflict probability equation is obtained and illustrated graphically.
Ulam-Hyers stability of a parabolic partial differential equation
