The conjugate unscented transform and the principle of maximum entropy for probability density reconstruction: An application to the two body problem

Nagavenkat Adurthi, Puneet Singla

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish (US)
Title of host publicationAstrodynamics 2013 - Advances in the Astronautical Sciences
Subtitle of host publicationProceedings of the AAS/AIAA Astrodynamics Specialist Conference
PublisherUnivelt Inc.
Pages1841-1857
Number of pages17
ISBN (Print)9780877036050
StatePublished - Jan 1 2014
Event2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013 - Hilton Head Island, SC, United States
Duration: Aug 11 2013Aug 15 2013

Publication series

NameAdvances in the Astronautical Sciences
Volume150
ISSN (Print)0065-3438

Other

Other2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013
CountryUnited States
CityHilton Head Island, SC
Period8/11/138/15/13

Fingerprint

two body problem
entropy
Entropy
transform
probability density function
probability density functions
Mathematical transformations
Probability density function
moments
quadratures
dynamical systems
Dynamical systems
Earth (planet)
Satellites
method

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science

Cite this

Adurthi, N., & Singla, P. (2014). The conjugate unscented transform and the principle of maximum entropy for probability density reconstruction: An application to the two body problem. In 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..
Adurthi, Nagavenkat ; Singla, Puneet. / The conjugate unscented transform and the principle of maximum entropy for probability density reconstruction : An application to the two body problem. Astrodynamics 2013 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference. Univelt Inc., 2014. pp. 1841-1857 (Advances in the Astronautical Sciences).
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Adurthi, N & Singla, P 2014, The conjugate unscented transform and the principle of maximum entropy for probability density reconstruction: An application to the two body problem. in 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.

Astrodynamics 2013 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference. Univelt Inc., 2014. p. 1841-1857 (Advances in the Astronautical Sciences; Vol. 150).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Adurthi N, Singla P. The conjugate unscented transform and the principle of maximum entropy for probability density reconstruction: An application to the two body problem. In Astrodynamics 2013 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference. Univelt Inc. 2014. p. 1841-1857. (Advances in the Astronautical Sciences).