Efficient Evaluation of 2-D Collision Probability Derivatives for Uncertain k-scaled Covariances: A PcMax Case Study

Denis Arzelier (1) , Mioara Joldeş (1) , Matthieu Masson (1)

1 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes

This paper focuses on efficiently evaluating derivatives of the 2-D collision probability, treated as a function of parameters, which appear as linear forms in the entries of the covariance matrix. This boils down to computing moments of the associated Gaussian measure restricted to a disk. Specifically, we propose an optimization-based solution to computing the maximum collision probability when the covariance data is unreliable, implementing an alternative method to the traditional k-scaled covariance approach. Preliminary results indicate our method's potential for improving the understanding of Pc's validity as a measure of conjunction likelihood.

Mots clés: Covariance Matrices; Gaussian measure; Collision Avoidance; Collision probability; Space Debris; Space Applications

Domaines: Automatique; Analyse numérique [cs.NA]; Optimisation et contrôle [math.OC]

Denis Arzelier, Mioara Joldeş, Matthieu Masson. Efficient Evaluation of 2-D Collision Probability Derivatives for Uncertain k-scaled Covariances: A PcMax Case Study. 2024. ⟨hal-04710373⟩