Iterative bayesian estimation of navigation performance modeled by a mixture of Gaussian and laplace distributions for the application of collision risk modeling

Abstract

Collision risk modeling is a methodology to estimate the risk of aircraft collisions under given route spacing/separation minima. Both pre-implementation risk estimation and continuous long-term risk monitoring are encouraged by the International Civil Aviation Organization. Collision risk modeling is an often-used methodology for that purpose. Mixture distribution models of Gaussian and Laplace distributions are often used for the modeling of lateral deviations of aircraft from the center line of air routes. We developed an iterative Bayesian parameter estimation algorithm of the mixture distributions which is classified as a variational Bayesian method. It is a heuristic algorithm which estimates the model parameters from observation data. We select the appropriate family of prior distributions so that the posterior distributions have the same form of the prior distributions. This feature enables iterative application of the algorithm. The algorithm also enables interval estimation of statistics such as lateral overlap probabilities, which is a key parameter of the collision risk model of route spacing. It can be used for long-term monitoring of lateral deviation of aircraft. We also applied the algorithm to the data of lateral deviations observed in Japanese oceanic airspace. The application example showed that our algorithm can be applied for real data. © 2013 The Japan Society for Aeronautical and Space Sciences.