Monte Carlo Orbital Conjunction Analysis Using the Cross-Entropy Method

The growing number of active satellites and nonoperational resident space objects has led to an increasingly cluttered space environment that demands fast, accurate, and robust tools for conjunction assessment and mitigation. Current tools for estimating the probability of collision (PC) often rely on simplifying assumptions, resulting in biased estimates that may not always accurately reflect the true risk. When these assumptions fail, operators turn to brute-force Monte Carlo simulations, which are flexible but inefficient for rare events, requiring a massive sample count and hours to days of computation time. We present an accelerated Monte Carlo method using importance sampling together with the cross-entropy method to estimate the PC more efficiently. Two proposal families are considered for the importance sampling distribution: the Gaussian distribution and the Gaussian mixture model, the latter accommodating multimodal collision events. We demonstrate the method’s effectiveness on real and simulated short- and long-duration conjunctions, including cases with multiple repeating encounters. The estimator converges several orders of magnitude faster than brute-force Monte Carlo, reducing computation time from hours to seconds. In contrast to previous work, our method introduces no new restrictive assumptions and yields an unbiased estimate, making it well suited as a drop-in replacement for operational Monte Carlo implementations.