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Probability of collision between space objects including model uncertainty

机译：空间物体之间碰撞的可能性，包括模型不确定性

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An adaptive Collision Risk Assessment Tool (CRATER) is introduced in order to analyze conjunctions featuring non Gaussian distributions, long encounter times, and considerable model uncertainty. The algorithm makes use of the Fokker Planck equation to quantify the error in various assumptions, refine approximations of the propagated probability density functions (PDFs), and assess the need for external validation in some scenarios. A Local Gaussian approximation of the non-Gaussian propagated PDFs is introduced and shown to be comparable to Gaussian Mixture methods (GMM) in terms of accuracy, while exhibiting superior performance in terms of speed. The algorithm is made adaptive through the use of a non linearity index, which is used to determine the number of mixture components needed in a GMM or the spacing of local Gaussians when approximating the propagated PDFs. Coppola's method for calculating the probability of collision (PC) between space objects is modified to considering parametric model uncertainty. The PC integral is then incorporated into CRATER. CRATER is then used to compute the PC for 8 different test cases and is compared to Monte Carlo results.
机译：引入了一种自适应碰撞风险评估工具（CRATER），以分析具有非高斯分布，较长相遇时间和相当大的模型不确定性的合取。该算法利用Fokker Planck方程来量化各种假设下的误差，细化传播概率密度函数（PDF）的近似值，并在某些情况下评估对外部验证的需求。引入了非高斯传播PDF的局部高斯近似，并在准确性方面可与高斯混合方法（GMM）媲美，同时在速度方面表现出优异的性能。通过使用非线性指数使该算法具有自适应性，该非线性指数用于确定GMM中所需的混合组分的数量或在近似传播的PDF时确定局部高斯分布的间距。修改了Coppola用于计算空间物体之间碰撞概率（PC）的方法，以考虑参数模型的不确定性。然后将PC集成到CRATER中。然后使用CRATER计算8个不同测试用例的PC，并将其与Monte Carlo结果进行比较。

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