Efficient Nonlinear Uncertainty Quantification for Spaceflight Leveraging Nonlinear Expansions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916040932327424 |
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| author | Burnett, Ethan R. Boone, Spencer |
| author_facet | Burnett, Ethan R. Boone, Spencer |
| contents | This paper provides a comparative study of modern uncertainty quantification (UQ) methods. To greatly enhance real-time performance, both differential algebra (DA) and a directional differential algebra (DDA) approach are employed. This can enable fast UQ in the case of non-Gaussian statistics. Higher-order moments, namely skew and kurtosis, can be computed quickly by several means. This motivates their implementation in an analytic approximation of the confidence bounds for the so-called "banana-shaped" non-Gaussian distributions encountered often in nonlinear astrodynamics problems. This method improves greatly on a linear covariance approach, with only 5x its runtime in numerical tests, even before DA methods are employed. Test problems in this work include a restricted three-body cislunar example and an Earth-return aerocapture example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24147 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient Nonlinear Uncertainty Quantification for Spaceflight Leveraging Nonlinear Expansions Burnett, Ethan R. Boone, Spencer Systems and Control Instrumentation and Methods for Astrophysics This paper provides a comparative study of modern uncertainty quantification (UQ) methods. To greatly enhance real-time performance, both differential algebra (DA) and a directional differential algebra (DDA) approach are employed. This can enable fast UQ in the case of non-Gaussian statistics. Higher-order moments, namely skew and kurtosis, can be computed quickly by several means. This motivates their implementation in an analytic approximation of the confidence bounds for the so-called "banana-shaped" non-Gaussian distributions encountered often in nonlinear astrodynamics problems. This method improves greatly on a linear covariance approach, with only 5x its runtime in numerical tests, even before DA methods are employed. Test problems in this work include a restricted three-body cislunar example and an Earth-return aerocapture example. |
| title | Efficient Nonlinear Uncertainty Quantification for Spaceflight Leveraging Nonlinear Expansions |
| topic | Systems and Control Instrumentation and Methods for Astrophysics |
| url | https://arxiv.org/abs/2605.24147 |