A novel subset simulation-based technique for calculating the probability of collision

Analytically computed value of Probability of Collision for long term engagements between two space objects using traditional schemes, which only consider some time span around the time of closet approach, can sometimes be incorrect by orders of magnitude. Sampling based methods are presented as a robust alternative to analytical schemes. To decrease the computational burden of simulating a large number of particles, a novel subset simulation based MCMC scheme is introduced to compute in-orbit space-object collision probability. The collision probability is expressed as a product of larger conditional failure probabilities by introducing intermediate failure events. Well-chosen large (relative to collision probability) values of nested conditional failure probabilities can be estimated by means of simulating only a limited number of samples. The resulting efficiency and accuracy of the suggested scheme are demonstrated against independent benchmarks that use other techniques for calculating the probability of collision.