Probability of collision in nonlinear dynamics by moment propagation
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910914308997120 |
|---|---|
| author | Verhelst, Théo Acciarini, Giacomo Izzo, Dario Biscani, Francesco |
| author_facet | Verhelst, Théo Acciarini, Giacomo Izzo, Dario Biscani, Francesco |
| contents | Estimating the probability of collision between spacecraft is crucial for risk management and collision-avoidance strategies. Current methods often rely on Gaussian assumptions and simplifications, which can be inaccurate in highly nonlinear scenarios. This paper presents a general and efficient approach for computing collision probabilities without relying on such assumptions. Using high-order multivariate Taylor polynomials, we propagate statistical moments of initial uncertainties to the point of closest approach between the spacecraft. To compute the probability of collision, we derive a semi-analytical expression for the probability density function (PDF) of the closest approach distance, inferred from the propagated moments using orthogonal polynomials. Tested on various short-term and long-term encounters in low-Earth orbit, our method accurately handles nonlinear dynamics, non-Gaussian uncertainties, and irregular distributions. This versatile framework advances space situational awareness by providing precise collision probability estimates in complex dynamical environments. Moreover, our methodology applies to any dynamical system with uncertainty in its initial state and is therefore not restricted to collision probability estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probability of collision in nonlinear dynamics by moment propagation Verhelst, Théo Acciarini, Giacomo Izzo, Dario Biscani, Francesco Systems and Control Data Analysis, Statistics and Probability Space Physics I.2.8; G.3; J.2 Estimating the probability of collision between spacecraft is crucial for risk management and collision-avoidance strategies. Current methods often rely on Gaussian assumptions and simplifications, which can be inaccurate in highly nonlinear scenarios. This paper presents a general and efficient approach for computing collision probabilities without relying on such assumptions. Using high-order multivariate Taylor polynomials, we propagate statistical moments of initial uncertainties to the point of closest approach between the spacecraft. To compute the probability of collision, we derive a semi-analytical expression for the probability density function (PDF) of the closest approach distance, inferred from the propagated moments using orthogonal polynomials. Tested on various short-term and long-term encounters in low-Earth orbit, our method accurately handles nonlinear dynamics, non-Gaussian uncertainties, and irregular distributions. This versatile framework advances space situational awareness by providing precise collision probability estimates in complex dynamical environments. Moreover, our methodology applies to any dynamical system with uncertainty in its initial state and is therefore not restricted to collision probability estimation. |
| title | Probability of collision in nonlinear dynamics by moment propagation |
| topic | Systems and Control Data Analysis, Statistics and Probability Space Physics I.2.8; G.3; J.2 |
| url | https://arxiv.org/abs/2504.13935 |