Jordan Maxwell, Scout Space Inc; Ryan Blay, Scout Space LLC; David Lujan, Scout Space Inc; Jordan Marshall, Scout Space LLC
Keywords: conjunction analysis, spacecraft collisions, astrodynamics, space domain awareness, spacecraft self-protect
Abstract:
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.
Once a collision has been identified given up-to-date estimates of two objects’ orbits, the novel theory presented also allows for a rigorous and exact collision likelihood analysis given the orbit state uncertainty of the two colliders. The fully-analytic nature of the new collision location determination tool described above allows for transformation of uncertainty in the individual orbit elements for each object directly into uncertainty in the collision locations. A key benefit of the presented approach is that the collision location is determined via a constraint on the true anomalies of the colliders: essentially reducing the dimensionality of the problem relative to modern position-differencing approaches by incorporating orbital dynamics constraints. Existing collision analysis methodologies apply the propagate-and-check method described above to find collisions by identifying when near-miss distances fall below a threshold. Once the location has been determined, up-to-date ephemerides and associated uncertainties are propagated to the collision time and (applying assumptions) the full 3D position covariance ellipsoid for each object is flattened into a 2D projection in the collision-plane. The collision likelihood is then determined numerically through calculation of the overlap area of these two shapes, potentially requiring comparisons of hundreds or thousands of grid points in a single simulation timestep. As more observations are made of the colliders, the ephemerides will be updated, requiring many iterations of both the propagate-and-check location determination as well as the ellipsoid-overlap calculation described. In contrast, the novel framework presented in this paper applies orbital constraints to determine collision locations through a simple trigonometric expression, and likelihood through convolution of uncertainty transformed through the fully-analytic framework. Both of these improvements promise significant computational savings relative to the state-of-the-art, and are feasible for deployment given modern spacecraft compute resources.
The final paper and presentation will include a detailed derivation of both the collision location and likelihood determination algorithms. An analysis with commercial partners will also be presented demonstrating the predicted improvements using real SDA data for an apples-to-apples comparison. Finally, follow-on analyses will be discussed, potentially including nominal avoidance maneuver definition given predicted collision geometries.
Date of Conference: September 17-20, 2024
Track: Conjunction/RPO