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Technical Abstract (Limit 2000 characters, approximately 200 words):

Analytically computed value of Probability of Collision for long term engagements between two space objects using traditional schemes, which only consider some time span around the time of closet approach, can sometimes be incorrect by orders of magnitude. Sampling based methods are presented as a robust alternative to analytical schemes. To decrease the computational burden of simulating a large number of particles, a novel subset simulation based MCMC scheme is introduced to compute in-orbit space-object collision probability. The collision probability is expressed as a product of larger conditional failure probabilities by introducing intermediate failure events. Well-chosen large (relative to collision probability) values of nested conditional failure probabilities can be estimated by means of simulating only a limited number of samples. The resulting efficiency and accuracy of the suggested scheme are demonstrated against independent benchmarks that use other techniques for calculating the probability of collision.

Potential NASA Applications (Limit 1500 characters, approximately 150 words):

NASA CARA has a great interest in improving the conjunction assessment processes that are used to protect the scientific and defense satellites. With the addition of many smaller objects (<10cm) to the catalog of tracked objects that are only visible by Space Fence, NASA satellite operators will face more irregular conjunction events that do not follow 2-D PC assumptions. Our solution will reliability and accurately identify such events and help the operators save hours of analysis time or unnecessary avoidance maneuvers.

Potential Non-NASA Applications (Limit 1500 characters, approximately 150 words):

With the dramatic increase in the number of ridesharing activities, more and more spacecraft are released by the launch vehicle into orbit along with tens of other spacecraft, resulting in many long-period encounters that cannot be assessed accurately with conventional methods. Our proposed method can accurately and efficiently quantify the risk associated with long-period conjunctions.

Duration: **6**