Satellite Collision Avoidance Prediction Using Verified Interval Orbit Propagation

Verified interval integration methods enclose a solution set corresponding to interval initial values and parameters, and bound integration and rounding errors. Verified interval orbit propagation uses verified integration to create guaranteed satellite trajectory enclosures. An orbit propagator has...

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Bibliographic Details
Published in:Journal of guidance, control, and dynamics control, and dynamics, 2013-05, Vol.36 (3), p.821-832
Main Authors: Römgens, Bart, Mooij, Erwin, Naeije, Marc
Format: Article
Language:English
Subjects:
Aerospace engineering
Cartesian coordinates
Collision avoidance
Collision dynamics
Collisions
Constellations
Enclosures
Intersections
Intervals
Iridium network
Mathematical models
Orbits
Propagation
Rounding
Satellite constellations
Satellites
Trajectories
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Summary:Verified interval integration methods enclose a solution set corresponding to interval initial values and parameters, and bound integration and rounding errors. Verified interval orbit propagation uses verified integration to create guaranteed satellite trajectory enclosures. An orbit propagator has been developed using two verified-integration libraries, VNODE-LP and VSPODE, and three state models: Cartesian coordinates, modified equinoctial elements, and unified state model. Earth–satellite trajectories propagated using VSPODE can continue for 2–3 times longer than those propagated using VNODE-LP before the solution enclosures become larger than 109  km3. Furthermore, using a hybrid state model of the unified state model and modified equinoctial elements, the integration can continue a factor 4–10 longer than the Cartesian model. The exact improvements depend on initial interval widths and the orbit type. This propagator is used to develop collision-prediction software, which uses intersections of interval trajectories to detect possible collisions between satellites. Verified collision prediction has successfully been applied to reconstruct the two-satellite collision of Cosmos-2251 and Iridium-33. It was also successfully applied to the 92-satellite Iridium constellation. This demonstrated the feasibility of verified collision prediction and demonstrated the necessary improvements for real applications with a much larger number of objects.
ISSN:0731-5090
1533-3884
DOI:10.2514/1.57888