An Efficient Collision Analysis Framework Enabling Real-Time Spacecraft Self-Protect

A novel collision analysis framework has been derived to determine collision locations and likelihoods far more efficiently than the current state-of-the-art, enabling onboard self-protect capabilities for spacecraft with Space Domain Awareness (SDA) sensors. One key contribution of this work is a simple, fully-analytic solution for the collision point given two orbit element sets, enabling first-order calculation of the time-horizon for safety maneuvers with negligible computational effort --- an enabling capability for Just-in-time Collision Avoidance (JCA). Additionally, uncertainty in the orbit elements can be transformed through this analytic expression into uncertainty in the location and time horizon. By convolving these distributions, collision likelihood can be calculated without the need for propagation or assumptions on the covariance as in existing techniques. No linearization or other assumptions are made except that spacecraft exhibit Keplerian motion --- an assumption that will be relaxed in future work. Initial simulations with the technique confirm its accuracy and efficiency relative to existing collision analysis toolsets. Further analysis including direct comparison with current collision analysis approaches will be presented. A major differentiator for this novel collision analysis approach is the ability to determine collision locations analytically from two sets of orbit elements. Modern state-of-the-art techniques employ a "propagate-and-check" approach where relative distance is compared at every simulation timestep for every pair of potential colliders. As orbital congestion grows, self-protect capabilities like JCA will become critical to protecting vital assets, necessitating a more efficient means of determining the location of a potential collision. The analysis approach presented in this paper eliminates the need for propagation to assess collision locations --- given the best estimate of two objects' orbit elements, the most likely collision location can be determined through a simple trigonometric expression. In addition to locating the collision, the method enables determination of the expected time horizon for the collision, providing critical data to inform sensing and avoidance opportunities as the potential collision approaches. The sum of these newly-enabled capabilities amounts to an extremely efficient collision screening method that can be deployed in-situ on SDA-enable spacecraft to identify threats and (at a minimum) create alerts for operators with minimal burden given modern spacecraft compute resources.