Monte Carlo Method for Collision Probability Calculations using 3D Satellite Models

Details Monte Carlo Method for Collision Probability Calculations using 3D Satellite Models Monte Carlo Method for Collision Probability Calculations using 3D Satellite Models

Sep 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010amos.confe..11d&link_type=abstract

Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, held in Wailea, Maui, Hawaii, September

Statistics

Computation

Scientific paper

We developed an efficient method for calculating the collision probability using a Monte Carlo approach. The method requires knowledge of the full 6x6 covariance matrix information for each of the objects under consideration, and is capable of incorporating not just the positional uncertainty information, but also the velocity component of the uncertainties in its calculation. This ensures a higher level of accuracy and robustness over strictly analytic methods, albeit at the cost of a larger computational load. It is part of the Testbed Environment for Space Situational Awareness (TESSA) development effort at Lawrence Livermore National Laboratory (LLNL).
This paper will describe our implementation as well as an overview of the capabilities and expectations for the cases where orbital refinement has reduced the size of the uncertainty ellipsoids to much less than a kilometer. Under this regime a spherical approximation of the collision cross-section is not utilizing the full potential of the available information. The combination of direct or indirect attitude information of the satellites, their detailed 3D mesh models, and the relatively accurate information on the size, shape, and separations of the uncertainty ellipsoids can be used to not only refine the collision calculation, but also allow for detailed assessment of the relative likelihood of various impact scenarios. The distribution of Monte Carlo trajectories that form the collection of collision cases is, provided the uncertainties are small enough, distinctly non uniform across the combined satellite cross-section shape. This can significantly modify the relative collision rates based on surface area alone (for instance, the collision geometry and relative positions of the uncertainties may make a hit on the main body more likely than an impact on the solar panels, even though the latter are larger). In cases where a satellite might survive a collision (e.g., a small piece of debris puncturing a solar panel), we can now augment the probability of collision with the odds of survival given a collision. Furthermore, this information allows us to constrain the possible impact scenarios a-posteriori, reducing the number of computationally costly hydro-code simulations we have to run for our detailed debris modeling capabilities (cf. K. Springer et al. in these proceedings for a report on our Cosmos - Iridium analysis).

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