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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.29388 |
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| _version_ | 1866911556644634624 |
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| author | Rebollo, Jose Antonio Vazquez, Rafael Bombardelli, Claudio |
| author_facet | Rebollo, Jose Antonio Vazquez, Rafael Bombardelli, Claudio |
| contents | Non-Gaussian tails dominate collision probability estimates in conjunction assessment, yet capturing them without Monte Carlo sampling is challenging, especially when process noise is included. We present a closed-form, grid-free solution to the Fokker-Planck equation by proving that an exponential-of-quadratic-form ansatz is structurally preserved under advection and diffusion. The probability density function propagates via a compact ODE system, significantly cheaper than Monte Carlo and without spatial discretization. As an application, the method performs orbit uncertainty propagation under stochastic forcing representative of atmospheric drag. Results demonstrate the method faithfully captures non-Gaussian features, asymmetric tails, and stochastic broadening, matching a Monte Carlo benchmark. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29388 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Closed-Form Solutions to the Fokker-Planck Equation for Orbital Uncertainty Propagation Rebollo, Jose Antonio Vazquez, Rafael Bombardelli, Claudio Space Physics Numerical Analysis Non-Gaussian tails dominate collision probability estimates in conjunction assessment, yet capturing them without Monte Carlo sampling is challenging, especially when process noise is included. We present a closed-form, grid-free solution to the Fokker-Planck equation by proving that an exponential-of-quadratic-form ansatz is structurally preserved under advection and diffusion. The probability density function propagates via a compact ODE system, significantly cheaper than Monte Carlo and without spatial discretization. As an application, the method performs orbit uncertainty propagation under stochastic forcing representative of atmospheric drag. Results demonstrate the method faithfully captures non-Gaussian features, asymmetric tails, and stochastic broadening, matching a Monte Carlo benchmark. |
| title | Closed-Form Solutions to the Fokker-Planck Equation for Orbital Uncertainty Propagation |
| topic | Space Physics Numerical Analysis |
| url | https://arxiv.org/abs/2603.29388 |