A probabilistic conflict detection algorithm in terminal area based on three-dimensional Brownian motion

In this paper, two common encounter geometries of aircrafts in terminal area are discussed. Probabilistic modes for aircraft motions are developed based on three-dimensional Brownian motion. The two common encounter geometries can be expressed in the same formula. After the non-orthogonal and orthogonal transformations, three-dimensional Brownian motion is standardized and the formula is simplified to derive the analytical solution. The conflict probability is equal to the probability that a standard three-dimensional Brownian motion hits a time-varying region. An approximation algorithm is given based on Bachelier-Levy theorem to get the analytical expression of conflict probability.