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Figure 2: Screen shot of a simulation of all flights using the Barcelona airport on a given day.
4.3 Sequencing aircraft in Terminal Maneuvering Areas
We consider the problem of sequencing two aircraft. This is a typical task of ATC in TMA where aircraft descend from cruising altitude and need to be sequenced and separated by a certain time interval before entering in the final Approach Sector. In Figure 3 several possible trajectory realizations of a descending aircraft corresponding to the same nominal path are displayed. In this figure, the aircraft descends from FL350 to FL100. In addition to stochastic wind terms, uncertainty about the mass of the aircraft is introduced as a uniform distribution between two extreme values. The figure suggests that the resulting uncertainty in the position of aircraft is of the order of magnitude of some kilometers.
We consider the problem of sequencing two descending aircraft as illustrated in Figure 4(a). The initial position of the first aircraft (A1) is (−100000, 100000) (where coordinates are expressed in meters) and FL350. The path of this aircraft is fixed: The aircraft proceeds to way-point (−90000, 90000) where it will start a descent to FL150. The trajectory of A1, while descending, is determined by an intermediate way-point in (0, 0) and a final way-point in (100000, 0), where the aircraft is assumed to exit the TMA and enter the approach sector. The second aircraft (A2) is initially at (−100000, −100000) and FL350. This aircraft proceeds to way-point (−90000, −90000) where it will start its
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Positions after 10 minutes
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Positions after 20 minutes
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Figure 3: Several trajectory realizations of aircraft descent
descent to FL150. The intermediate way-point ω =(ω1,ω2) must be selected in the range ω1 ,ω2 ∀ [−90000, 90000]. The aircraft will then proceed to way-point (90000, 0) and then to the exit way-point (100000, 0).
We assume that the objective is to obtain a time separation of 300 seconds between the arrivals of the two aircraft at the exit way-point, (10000, 0). Performance in this sense is measured by perf = e−a·(|T1 −T2 |−300) where T1 and T2 are the arrival times of A1 and A2 at the exit way-point and a =5 · 10−3 . The constraint is that the trajectories of the two aircraft should not be conflicting. In our simulations we define a conflict as the situation in which two aircraft have less than 5nmi of horizontal separation and less than 1000ft of vertical separation1 . We optimize initially with an upper bound on the probability of
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Monte Carlo Optimization for Conflict Resolution in Air Traffic Control(10)
