A noncombinatorial approach for efficient conjunction analysis
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Conjunction analysis is the study of possible collisions between objects in space, and is aimed at reducing the number of collisions between manmade objects and debris or- biting the Earth. Standard conjunction analysis requires computing the probability of collision between each and every resident space object and thus, it is a combinatorial problem. Due to this computational burden, real-time conjunction analysis algorithms are infeasible. The main objective of this thesis is to automatically determine which objects should be chosen to perform a detailed analysis, significantly reducing the number of object pairs to be investigated. The heart of the approach lies in the efficient tree code algorithm. It has been found that these methods significantly reduce computational cost to something more tractable such as O(NlogN) , while obtaining comparable results to expensive brute force methods. To account for probabilistic nearest neighbors, the Hellinger distance has been employed. Additionally, this research accounts for non-Gaussian uncertainties via Gaussian Mixture Models. The resulting probabilistic distance computation is effectively reduced to a linear programming problem. It has been found that the favorable computational efficiency of the tree-based approach is maintained, while the applicability of the proposed method is extended.