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Uncertainty is introduced in air traffic by the action of wind, incomplete knowledge of the physical coefficients of the aircraft and unavoidable imprecision in the execution of ATC instructions. To perform conflict detection one has to evaluate the possibility of future conflicts given the current state of the airspace and taking into account uncertainty in the future position of aircraft. For this task, one needs a model to predict the future. In a probabilistic setting, the model could be either an empirical distribution of future aircraft positions [18], or a dynamical model, such as a stochastic differential equation (see, for example, [1, 12, 19]), that describes the aircraft motion and defines implicitly a distribution for future aircraft positions. On the basis of the prediction model one can evaluate metrics related to safety. An example of such a metric is conflict probability over a certain time horizon. Several methods have been developed to estimate different metrics related to safety for a number of prediction models, e.g [1, 12, 13, 18, 19]. Among other methods, Monte Carlo methods have the main advantage of allowing flexibility in the complexity of the prediction model since the model is used only as a simulator and, in principle, it is not involved in explicit calculations. In all methods a trade off exists between computational effort (simulation time in the case of Monte Carlo methods) and the accuracy of the model. Techniques to accelerate Monte Carlo methods especially for rare event computations are under development, see for example [14].
For conflict resolution, the objective is to provide suitable maneuvers to avoid a predicted conflict. A number of conflict resolution algorithms have been proposed in the deterministic setting, for example [7, 11, 21]. In the stochastic setting, the research effort has concentrated mainly on conflict detection, and only a few simple resolution strategies have been proposed [18, 19]. The main reason for this is the complexity of stochastic prediction models which makes the quantification of the effects of possible control actions intractable.
In this paper we present a Monte Carlo Markov Chain (MCMC) framework [20] for conflict resolution in a stochastic setting. The aim of the proposed approach is to extend the advantages of Monte Carlo techniques, in terms of flexibility and complexity of the problems that can be tackled, to conflict resolution. The approach is motivated from Bayesian statistics [16, 17]. We consider an expected value resolution criterion that takes into account separation and other factors (e.g. aircraft requests). Then, the MCMC optimization procedure of [16] is employed to estimate the resolution maneuver that optimizes the expected value criterion. The proposed approach is illustrated in simulation, on some realistic benchmark problems, inspired by current ATC practice. The benchmarks were implemented in an air traffic simulator developed in previous work [8, 9, 10].
The material is organized in 5 sections. Section 2 presents the formulation of conflict resolution as an optimization problem. The randomized optimization procedure that we adopt to solve the problem is presented in Section 3. Section 4 is devoted to the benchmark problems used to illustrate our approach. Section 4.1 introduces the problems associated
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Monte Carlo Optimization for Conflict Resolution in Air Traffic Control(2)
