Satellite Safe Margin: Fast Solutions for Conjunction Analysis

The amount of debris in orbit has increased significantly over the years. With the recent growth of interest in space exploration, conjunction assessment has become a central issue. One important metric to evaluate conjunction risk is the miss distance. However, this metric does not intrinsically take into account uncertainty distributions. Some work has been developed to consider the uncertainty associated with the position of the orbiting objects, in particular, to know if these uncertainty distributions overlap (e.g., ellipsoids when considering Gaussian distributions). This work presents two fast solutions to not only check if the ellipsoids overlap but to compute the distance between them, referred to as margin. One solution computes the margin when the best-known data from both objects can be centralized (e.g., debris/satellite conjunctions). The second solution is applied in the decentralized case when the most precise covariances cannot be shared (conjunctions of satellites owned by different operators). These methods are both accurate and fast, being able to process 15,000 conjunctions per minute with the centralized solution and approximately 490 conjunctions per minute with the distributed solution.