Conjunction Time and Collision Probability Calculation Based on Bayesian Optimization

Abstract

Collision probability calculation is critical to space situational awareness or space traffic management. To determine the collision probability, the conjunction time needs to be determined first, but both collision probability and conjunction time usually exist large uncertainties. In this paper, a continuous representation of the polynomial chaos expansion (PCE)-based surrogate model is used to describe the uncertainty of space objects along with time. This PCE model facilitates the propagation of sampling points representing orbital uncertainty at any time. A machine learning-based Bayesian optimization method is employed to determine the conjunction time and then the collision probability. A data-driven Gaussian process regression model is built to approximate the Hausdorff distance, which is a distance metric between two space objects with uncertainty and is used as an objective function for Bayesian optimization. The proposed PCE model and Bayesian optimization do not require the Gaussian assumption and provide a general framework to calculate the conjunction time and collision probability. Two numerical experiments are used to show the effectiveness of the proposed algorithm and its close performance to the traditional Monte Carlo sampling-based method.