### Abstract

The paper presents four different non-intrusive approaches to the propagation of uncertainty in orbital dynamics with particular application to space debris orbit analysis. Intrusive approaches are generally understood as those methods that require a modification of the original problem by introducing a new algebra or by directly embedding high-order polynomial expansions of the uncertain quantities in the governing equations. Non-intrusive approaches are instead based on a polynomial representations built on sparse samples of the system response to the uncertain quantities. The paper will present a standard Polynomial Chaos Expansion, an Uncertain Quantification-High Dimensional Model Representation, a Generalised Kriging model and an expansion with Tchebycheff polynomials on sparse grids. The work will assess the computational cost and the suitability of these methods to propagate different type of orbits.

Original language | English |
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Title of host publication | Astrodynamics 2015 |

Subtitle of host publication | Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A. |

Editors | Manoranjan Majji, James D. Turner, Geoff G. Wawrzyniak, William Todd Cerven |

Place of Publication | San Diego, California |

Pages | 3979-3992 |

Number of pages | 14 |

Publication status | Published - 9 Aug 2015 |

Event | AAS/AIAA Astrodynamics Specialist Conference 2015 - Colorado, Vail, United States Duration: 9 Aug 2015 → 13 Aug 2015 |

### Publication series

Name | Advances in Astrnautical Sciences |
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Publisher | American Astronautical Society |

Volume | 156 |

ISSN (Print) | 0065-3438 |

### Conference

Conference | AAS/AIAA Astrodynamics Specialist Conference 2015 |
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Country | United States |

City | Vail |

Period | 9/08/15 → 13/08/15 |

### Fingerprint

### Keywords

- space debris
- orbit analysis
- polynomial chaos expansion
- sparse grids
- uncertainty
- non-intrusive
- kriging model
- Tchebycheff polynomials

### Cite this

*Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A.*(pp. 3979-3992). [AAS 15-545] (Advances in Astrnautical Sciences; Vol. 156). San Diego, California.

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*Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A..*, AAS 15-545, Advances in Astrnautical Sciences, vol. 156, San Diego, California, pp. 3979-3992, AAS/AIAA Astrodynamics Specialist Conference 2015, Vail, United States, 9/08/15.

**Comparison of non-intrusive approaches to uncertainty propagation in orbital mechanics.** / Tardioli, Chiara; Kubicek, Martin; Vasile, Massimiliano; Minisci, Edmondo; Riccardi, Annalisa.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - Comparison of non-intrusive approaches to uncertainty propagation in orbital mechanics

AU - Tardioli, Chiara

AU - Kubicek, Martin

AU - Vasile, Massimiliano

AU - Minisci, Edmondo

AU - Riccardi, Annalisa

N1 - This paper was originally presented at the AAS/AIAA Astrodynamics Specialist Conference held August 9-13, 2015, Vail, Colorado, U.S.A., and was originally published in the American Astronautical Society (AAS) publication Astrodynamics 2015, edited by Manoranjan Majji, James D. Turner, Geoff G. Wawrzyniak and William Todd Cerven, American Astronautical Society (AAS) Advances in the Astronautical Sciences, Volume 156, 2016, pp. 4205-4220 (Copyright © 2016 by American Astronautical Society Publications Office, P.O. Box 28130, San Diego, CA 92198, U.S.A.; Web Site: http://www.univelt.com

PY - 2015/8/9

Y1 - 2015/8/9

N2 - The paper presents four different non-intrusive approaches to the propagation of uncertainty in orbital dynamics with particular application to space debris orbit analysis. Intrusive approaches are generally understood as those methods that require a modification of the original problem by introducing a new algebra or by directly embedding high-order polynomial expansions of the uncertain quantities in the governing equations. Non-intrusive approaches are instead based on a polynomial representations built on sparse samples of the system response to the uncertain quantities. The paper will present a standard Polynomial Chaos Expansion, an Uncertain Quantification-High Dimensional Model Representation, a Generalised Kriging model and an expansion with Tchebycheff polynomials on sparse grids. The work will assess the computational cost and the suitability of these methods to propagate different type of orbits.

AB - The paper presents four different non-intrusive approaches to the propagation of uncertainty in orbital dynamics with particular application to space debris orbit analysis. Intrusive approaches are generally understood as those methods that require a modification of the original problem by introducing a new algebra or by directly embedding high-order polynomial expansions of the uncertain quantities in the governing equations. Non-intrusive approaches are instead based on a polynomial representations built on sparse samples of the system response to the uncertain quantities. The paper will present a standard Polynomial Chaos Expansion, an Uncertain Quantification-High Dimensional Model Representation, a Generalised Kriging model and an expansion with Tchebycheff polynomials on sparse grids. The work will assess the computational cost and the suitability of these methods to propagate different type of orbits.

KW - space debris

KW - orbit analysis

KW - polynomial chaos expansion

KW - sparse grids

KW - uncertainty

KW - non-intrusive

KW - kriging model

KW - Tchebycheff polynomials

UR - http://www.scopus.com/inward/record.url?scp=85007374238&partnerID=8YFLogxK

UR - http://www.space-flight.org/docs/2015_astro/2015_astro.html

UR - http://www.univelt.com/book=5315

M3 - Conference contribution book

SN - 9780877036296

T3 - Advances in Astrnautical Sciences

SP - 3979

EP - 3992

BT - Astrodynamics 2015

A2 - Majji, Manoranjan

A2 - Turner, James D.

A2 - Wawrzyniak, Geoff G.

A2 - Cerven, William Todd

CY - San Diego, California

ER -