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constraint violation of P =0.1. It is easy to see that there exists a maneuver in the set of optimization parameters that gives negligible conflict probability. Therefore, based on inequality (7), we select A = 10 in the optimization criterion.
The results of the optimization procedure are illustrated in Figures 4(b-d). Each figure shows the scatter plot of the accepted parameters during MCMC simulation for different choices of J and search distribution g. In all cases the first 10% of accepted parameters was discarded as a burn in period, to allow convergence of the Markov chain to its stationary distribution.
Figure 4(b) illustrates the case J = 10. Regions characterized by a low density of accepted parameters can be clearly seen in the figure. These are parameters which correspond to nominal paths with high probability of conflict. The figure also shows distinct “clouds” of accepted maneuvers. They correspond to different sequences of arrivals at the
1 In the TMA of large airports horizontal minimal separation is sometimes reduced to 3nmi, but this fact is ignored here.
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本文鏈接地址：Monte Carlo Optimization for Conflict Resolution in Air Traffic Control(11)