标题： 非线性动力学中碰撞的概率通过矩传播 显示英文标题

标题： Probability of collision in nonlinear dynamics by moment propagation

摘要： 估算航天器之间碰撞的概率对于风险管理及规避策略至关重要。目前的方法通常依赖于高斯假设和简化，这在高度非线性场景中可能不够准确。本文提出了一种通用且高效的方法来计算碰撞概率，而无需依赖此类假设。通过使用高阶多元泰勒多项式，我们将初始不确定性的统计矩传播到航天器最近接近点处。为了计算碰撞概率，我们推导出一个半解析表达式，用于从传播的矩中推断最近接近距离的概率密度函数（PDF），利用正交多项式实现这一过程。在低地球轨道的各种短期和长期交会测试中，我们的方法能够准确处理非线性动力学、非高斯不确定性以及不规则分布。这一多功能框架通过在复杂动态环境中提供精确的碰撞概率估计，推进了空间态势感知能力。此外，我们的方法适用于初始状态存在不确定性的任何动力系统，因此不仅限于碰撞概率估计。 显示英文摘要

摘要： 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.