Title:
Mahalanobis Shell Sampling (MSS) method for collision
probability computation
Mahalanobis Shell Sampling (MSS) method for collision
probability computation
| dc.contributor.advisor | Lightsey, E. Glenn | |
| dc.contributor.author | Núñez Garzón, Ulises E. | |
| dc.contributor.corporatename | Georgia Institute of Technology. Space Systems Design Lab | |
| dc.date.accessioned | 2024-02-16T18:48:54Z | |
| dc.date.available | 2024-02-16T18:48:54Z | |
| dc.date.issued | 2019-12-01 | |
| dc.description | AE 8900 MS Special Problems Report | |
| dc.description.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. | |
| dc.identifier.uri | https://hdl.handle.net/1853/73542 | |
| dc.publisher | Georgia Institute of Technology | |
| dc.rights | Unless otherwise noted, all materials are protected under U.S. Copyright Law and all rights are reserved | |
| dc.rights.metadata | https://creativecommons.org/publicdomain/zero/1.0/ | |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/?language=en | |
| dc.title | Mahalanobis Shell Sampling (MSS) method for collision probability computation | |
| dc.type | Text | |
| dc.type.genre | Masters Project | |
| dspace.entity.type | Publication | |
| local.contributor.advisor | Lightsey, E. Glenn | |
| local.contributor.corporatename | Space Systems Design Laboratory (SSDL) | |
| local.contributor.corporatename | Daniel Guggenheim School of Aerospace Engineering | |
| local.relation.ispartofseries | Master's Projects | |
| local.relation.ispartofseries | Master of Science in Aerospace Engineering | |
| relation.isAdvisorOfPublication | de67be0a-45bb-48db-8b19-e9245f2632da | |
| relation.isOrgUnitOfPublication | dc68da3d-4cfe-4508-a4b0-35ba8de923fb | |
| relation.isOrgUnitOfPublication | a348b767-ea7e-4789-af1f-1f1d5925fb65 | |
| relation.isSeriesOfPublication | 09b1c264-93da-4a60-8e57-4eecff715bc6 | |
| relation.isSeriesOfPublication | 09844fbb-b7d9-45e2-95de-849e434a6abc |
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