Title:
Mahalanobis Shell Sampling (MSS) method for collision
probability computation
Mahalanobis Shell Sampling (MSS) method for collision
probability computation
Author(s)
Núñez Garzón, Ulises E.
Advisor(s)
Lightsey, E. Glenn
Editor(s)
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Abstract
Motivated by desire for collision avoidance in spacecraft formations, and by the need for
accurately computing low kinematic probabilities of collision (KPC) in spacecraft collision
risk analysis, this work introduces an algorithm for sampling from non-degenerate, multidi mensional normal random variables. In this algorithm, the analytical relationship between
certain probability density integrals of such random variables and the chi-square distribution
is leveraged in order to provide weights to sample points. In so doing, this algorithm allows
direct sampling from probability density “tails” without unduly penalizing sample size, as
would occur with Monte Carlo-based methods. The primary motivation for the development
of this algorithm is to help in the efficient computation of collision probability measures for
relative dynamic systems. Performance of this method in approximating KPC waveforms is
examined for a low-dimensionality dynamic example. However, this method could be applied
to other dynamic systems and for probability density integrals other than collision probability
measures, allowing for efficient computation of such integrals for problems where analytical
results do not exist. Therefore, this method is suggested as an alternative to random sampling
algorithms such as Monte Carlo methods or the Unscented Transform.
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Date Issued
2019-12-01
Extent
Resource Type
Text
Resource Subtype
Masters Project
Rights Statement
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