### Abstract

This paper describes the quantification of uncertainty in a dynamical system by efficiently evaluating the moments of the state probability density function using the recently developed Conjugate Unscented Transform Method. The Conjugate Unscented Transform is a method by which one can evaluate the multidimensional expectation integrals, involving the Gaussian or Uniform probability density function, with fewer points than the equivalent Gaussian Quadratures. The efficacy of the proposed Conjugate Unscented Transform in capturing the higher order moments when compared to Unscented Transform, Gauss-Hermite Quadrature and Monte Carlo random samples is illustrated by means of a simple Two Body Problem involving the Earth and a satellite. Furthermore, these higher order moments are used to capture the non-Gaussian nature of the state probability density function at the required times by the Principle of Maximum Entropy.

Original language | English (US) |
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Title of host publication | Astrodynamics 2013 - Advances in the Astronautical Sciences |

Subtitle of host publication | Proceedings of the AAS/AIAA Astrodynamics Specialist Conference |

Publisher | Univelt Inc. |

Pages | 1841-1857 |

Number of pages | 17 |

ISBN (Print) | 9780877036050 |

State | Published - Jan 1 2014 |

Event | 2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013 - Hilton Head Island, SC, United States Duration: Aug 11 2013 → Aug 15 2013 |

### Publication series

Name | Advances in the Astronautical Sciences |
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Volume | 150 |

ISSN (Print) | 0065-3438 |

### Other

Other | 2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013 |
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Country | United States |

City | Hilton Head Island, SC |

Period | 8/11/13 → 8/15/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Astrodynamics 2013 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference*(pp. 1841-1857). (Advances in the Astronautical Sciences; Vol. 150). Univelt Inc..

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*Astrodynamics 2013 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference.*Advances in the Astronautical Sciences, vol. 150, Univelt Inc., pp. 1841-1857, 2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013, Hilton Head Island, SC, United States, 8/11/13.

**The conjugate unscented transform and the principle of maximum entropy for probability density reconstruction : An application to the two body problem.** / Adurthi, Nagavenkat; Singla, Puneet.

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

TY - GEN

T1 - The conjugate unscented transform and the principle of maximum entropy for probability density reconstruction

T2 - An application to the two body problem

AU - Adurthi, Nagavenkat

AU - Singla, Puneet

PY - 2014/1/1

Y1 - 2014/1/1

N2 - This paper describes the quantification of uncertainty in a dynamical system by efficiently evaluating the moments of the state probability density function using the recently developed Conjugate Unscented Transform Method. The Conjugate Unscented Transform is a method by which one can evaluate the multidimensional expectation integrals, involving the Gaussian or Uniform probability density function, with fewer points than the equivalent Gaussian Quadratures. The efficacy of the proposed Conjugate Unscented Transform in capturing the higher order moments when compared to Unscented Transform, Gauss-Hermite Quadrature and Monte Carlo random samples is illustrated by means of a simple Two Body Problem involving the Earth and a satellite. Furthermore, these higher order moments are used to capture the non-Gaussian nature of the state probability density function at the required times by the Principle of Maximum Entropy.

AB - This paper describes the quantification of uncertainty in a dynamical system by efficiently evaluating the moments of the state probability density function using the recently developed Conjugate Unscented Transform Method. The Conjugate Unscented Transform is a method by which one can evaluate the multidimensional expectation integrals, involving the Gaussian or Uniform probability density function, with fewer points than the equivalent Gaussian Quadratures. The efficacy of the proposed Conjugate Unscented Transform in capturing the higher order moments when compared to Unscented Transform, Gauss-Hermite Quadrature and Monte Carlo random samples is illustrated by means of a simple Two Body Problem involving the Earth and a satellite. Furthermore, these higher order moments are used to capture the non-Gaussian nature of the state probability density function at the required times by the Principle of Maximum Entropy.

UR - http://www.scopus.com/inward/record.url?scp=84899007210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899007210&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84899007210

SN - 9780877036050

T3 - Advances in the Astronautical Sciences

SP - 1841

EP - 1857

BT - Astrodynamics 2013 - Advances in the Astronautical Sciences

PB - Univelt Inc.

ER -