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Propagation of large uncertainty sets in orbital dynamics by automatic domain splitting

Propagation of large uncertainty sets in orbital dynamics by automatic domain splitting
Propagation of large uncertainty sets in orbital dynamics by automatic domain splitting
Current approaches to uncertainty propagation in astrodynamics mainly refer to linearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationally intensive. Differential algebra has already proven to be an efficient compromise by replacing thousands of pointwise integrations of Monte Carlo runs with the fast evaluation of the arbitrary order Taylor expansion of the flow of the dynamics. However, the current implementation of the DA-based high-order uncertainty propagator fails when the non-linearities of the dynamics prohibit good convergence of the Taylor expansion in one or more directions. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial expansion of the current state is split into two polynomials whenever its truncation error reaches a predefined threshold. The resulting set of polynomials accurately tracks uncertainties, even in highly nonlinear dynamics. The method is tested on the propagation of (99942) Apophis post-encounter motion.
differential algebra, automatic domain splitting, uncertainty propagation, apophis resonant return
0923-2958
1-23
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201
Di Lizia, Pierluigi
f86916ba-a73b-42a9-8247-558335c21f22
Armellin, Roberto
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Makino, Kyoko
273d1542-a2f6-4c1a-b54c-7a5a493151a0
Bernelli-Zazzera, Franco
4b3eb3b1-d06e-47cd-9676-f465dba2b1e7
Berz, Martin
f8159a81-aa52-4ba3-8b8f-a672aec96b47
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201
Di Lizia, Pierluigi
f86916ba-a73b-42a9-8247-558335c21f22
Armellin, Roberto
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Makino, Kyoko
273d1542-a2f6-4c1a-b54c-7a5a493151a0
Bernelli-Zazzera, Franco
4b3eb3b1-d06e-47cd-9676-f465dba2b1e7
Berz, Martin
f8159a81-aa52-4ba3-8b8f-a672aec96b47

Wittig, Alexander, Di Lizia, Pierluigi, Armellin, Roberto, Makino, Kyoko, Bernelli-Zazzera, Franco and Berz, Martin (2015) Propagation of large uncertainty sets in orbital dynamics by automatic domain splitting. Celestial Mechanics and Dynamical Astronomy, 1-23. (doi:10.1007/s10569-015-9618-3).

Record type: Article

Abstract

Current approaches to uncertainty propagation in astrodynamics mainly refer to linearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationally intensive. Differential algebra has already proven to be an efficient compromise by replacing thousands of pointwise integrations of Monte Carlo runs with the fast evaluation of the arbitrary order Taylor expansion of the flow of the dynamics. However, the current implementation of the DA-based high-order uncertainty propagator fails when the non-linearities of the dynamics prohibit good convergence of the Taylor expansion in one or more directions. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial expansion of the current state is split into two polynomials whenever its truncation error reaches a predefined threshold. The resulting set of polynomials accurately tracks uncertainties, even in highly nonlinear dynamics. The method is tested on the propagation of (99942) Apophis post-encounter motion.

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More information

Accepted/In Press date: 13 April 2015
e-pub ahead of print date: 8 May 2015
Published date: 8 May 2015
Keywords: differential algebra, automatic domain splitting, uncertainty propagation, apophis resonant return
Organisations: Astronautics Group

Identifiers

Local EPrints ID: 377355
URI: http://eprints.soton.ac.uk/id/eprint/377355
ISSN: 0923-2958
PURE UUID: 30a5c8b9-10a7-4832-8224-0c98b91dd036
ORCID for Alexander Wittig: ORCID iD orcid.org/0000-0002-4594-0368

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Date deposited: 03 Jun 2015 14:28
Last modified: 15 Mar 2024 03:58

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Contributors

Author: Pierluigi Di Lizia
Author: Kyoko Makino
Author: Franco Bernelli-Zazzera
Author: Martin Berz

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