Thermospheric density uncertainty propagation based on linearized relative orbital dynamics.
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| Title: | Thermospheric density uncertainty propagation based on linearized relative orbital dynamics. |
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| Authors: | Krückel, Roman1 (AUTHOR) roman.krueckel@ins.uni-stuttgart.de, Hobiger, Thomas1 (AUTHOR) |
| Source: | Advances in Space Research. May2026, Vol. 77 Issue 9, p9088-9104. 17p. |
| Subjects: | Atmospheric density, Relative motion, Uncertainty (Information theory), Gaussian processes, Earth's orbit, Monte Carlo method |
| Abstract: | • Classical mean anomaly methods overestimate short-term density uncertainty. • Relative orbital dynamics improves short-term uncertainty prediction capability. • An analytical model based on the HCW equations is developed. • Numerical covariance propagation supports correlated Gauss–Markov density errors. • Applicability of model was proven for different orbits and physical parameters. Thermospheric density uncertainty is the dominant source of uncertainty for orbit prediction in Low Earth Orbit (LEO) and Very Low Earth Orbit (VLEO). While analytical uncertainty propagation methods based on mean orbital elements accurately capture long-term secular drift, they fail to represent short-term dynamics, leading to a significant overestimation of along-track uncertainty for prediction horizons below one orbital period. These short-term dynamics are characterized by a zero-crossing of the along-track error caused by the initial differential drag acceleration counteracting the secular drift known as the drag paradox. This limitation is addressed in this paper in the form of an uncertainty propagation model based on linearized relative orbit mechanics using the Hill-Clohessy-Wiltshire (HCW) equations. An analytical solution is derived to characterize the zero-crossing phenomenon and evaluate the effect on the along-track uncertainty. To account for time-varying dynamics and temporally correlated atmospheric density errors, the model is extended using Linear Covariance Propagation with a First-Order Gauss–Markov Process (GMP). Validation with Monte Carlo simulations demonstrates that the numerical HCW model accurately reproduces the empirical uncertainty and the zero-crossing effect that the mean element approaches miss. A sensitivity analysis confirms the model's robustness as well as the general zero-crossing behavior across varying altitudes, correlation times and solar activities while identifying valid propagation timeframes and the limiting effects of orbital eccentricity. [ABSTRACT FROM AUTHOR] |
| Copyright of Advances in Space Research is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Thermospheric density uncertainty propagation based on linearized relative orbital dynamics. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Krückel%2C+Roman%22">Krückel, Roman</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> roman.krueckel@ins.uni-stuttgart.de</i><br /><searchLink fieldCode="AR" term="%22Hobiger%2C+Thomas%22">Hobiger, Thomas</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Advances+in+Space+Research%22">Advances in Space Research</searchLink>. May2026, Vol. 77 Issue 9, p9088-9104. 17p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Atmospheric+density%22">Atmospheric density</searchLink><br /><searchLink fieldCode="DE" term="%22Relative+motion%22">Relative motion</searchLink><br /><searchLink fieldCode="DE" term="%22Uncertainty+%28Information+theory%29%22">Uncertainty (Information theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+processes%22">Gaussian processes</searchLink><br /><searchLink fieldCode="DE" term="%22Earth's+orbit%22">Earth's orbit</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: • Classical mean anomaly methods overestimate short-term density uncertainty. • Relative orbital dynamics improves short-term uncertainty prediction capability. • An analytical model based on the HCW equations is developed. • Numerical covariance propagation supports correlated Gauss–Markov density errors. • Applicability of model was proven for different orbits and physical parameters. Thermospheric density uncertainty is the dominant source of uncertainty for orbit prediction in Low Earth Orbit (LEO) and Very Low Earth Orbit (VLEO). While analytical uncertainty propagation methods based on mean orbital elements accurately capture long-term secular drift, they fail to represent short-term dynamics, leading to a significant overestimation of along-track uncertainty for prediction horizons below one orbital period. These short-term dynamics are characterized by a zero-crossing of the along-track error caused by the initial differential drag acceleration counteracting the secular drift known as the drag paradox. This limitation is addressed in this paper in the form of an uncertainty propagation model based on linearized relative orbit mechanics using the Hill-Clohessy-Wiltshire (HCW) equations. An analytical solution is derived to characterize the zero-crossing phenomenon and evaluate the effect on the along-track uncertainty. To account for time-varying dynamics and temporally correlated atmospheric density errors, the model is extended using Linear Covariance Propagation with a First-Order Gauss–Markov Process (GMP). Validation with Monte Carlo simulations demonstrates that the numerical HCW model accurately reproduces the empirical uncertainty and the zero-crossing effect that the mean element approaches miss. A sensitivity analysis confirms the model's robustness as well as the general zero-crossing behavior across varying altitudes, correlation times and solar activities while identifying valid propagation timeframes and the limiting effects of orbital eccentricity. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Advances in Space Research is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.asr.2026.03.043 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 9088 Subjects: – SubjectFull: Atmospheric density Type: general – SubjectFull: Relative motion Type: general – SubjectFull: Uncertainty (Information theory) Type: general – SubjectFull: Gaussian processes Type: general – SubjectFull: Earth's orbit Type: general – SubjectFull: Monte Carlo method Type: general Titles: – TitleFull: Thermospheric density uncertainty propagation based on linearized relative orbital dynamics. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Krückel, Roman – PersonEntity: Name: NameFull: Hobiger, Thomas IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02731177 Numbering: – Type: volume Value: 77 – Type: issue Value: 9 Titles: – TitleFull: Advances in Space Research Type: main |
| ResultId | 1 |
