Efficient 4D Trajectory Conflict-Detection for Large Scale ATM Simulations Using Bounding-Volume Hierarchies and Time-Spatial Indexing

We propose a new method for collision detection of large sets of 4D flight-trajectories. A two phase approach is used, that is based on time and spatial indexing techniques to reduce the number of pairwise trajectory comparisons and bounding volume hierarchies to increase the runtime efficiency of pairwise interference tests. Within a so called broad phase two space decomposition data structures, R-tree and Interval-tree, are used to filter the set of given trajectories for possibly intersecting ones, which are then used as input for a second processing step, the so called narrow phase. A bounding volume type called k-dops that has been introduced in prior projects is extended for the regarded spacetime problem domain and applied within the narrow phase to increase the performance of pairwise trajectory intersection tests. Experiments with different sets of an average of 30000 randomly generated trajectories based on real traffic demand data for the European airspace and the BADA aircraft performance model are used to measure the performance of the investigated algorithms in application on realistic data. The empirical findings prove the expectations raised by the theoretical considerations. A significant improvement in runtime efficiency is achieved that would enable an automation tool running on a standard PC to check more than 60 trajectories for conflicts against a set of 30000 others within one second whereas the additional working memory consumption is moderate.

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