Under free flight, an aircrew has both the freedom to select their trajectory and the responsibility of resolving conflicts with other aircraft. The general belief is that free flight can be made safe under low traffic conditions. Increasing traffic, however, raises safety verification issues. This problem is formulated as one of estimating for a large scale stochastic hybrid system the probability of reaching a small collision set. The huge state space prohibits the use of existing numerical approaches to solve this safety verification problem. As an alternative we study randomization methods, the simplest of which would be to run many Monte Carlo simulations with a stochastic model of free flight operations, and count the number of runs during which a collision between two or more aircraft occurs. The huge state space prohibits such a straightforward MC simulation approach. By exploiting recent particle system theory by Del Moral and co-workers, this paper develops a sequential Monte Carlo simulation approach for the estimation of collision risk in a future air traffic scenario. The working of the resulting particle system is demonstrated for an eight aircraft scenario under free flight air traffic conditions.
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