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Probability of collision between space objects including model uncertainty

机译：空间对象之间的碰撞概率，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：引入了自适应碰撞风险评估工具（火山口），以分析具有非高斯分布的连词，长期遇到次数和相当大的模型不确定性。该算法利用Fokker普朗克方程来量化各种假设中的错误，细化传播概率密度函数（PDF）的近似，并在某些情况下评估外部验证的需要。引入了非高斯传播的PDF的局部高斯近似，并显示与高斯混合方法（GMM）在精度方面相当，同时在速度方面表现出卓越的性能。通过使用非线性指数，该算法用于自适应，该非线性指数用于确定GMM中所需的混合组分的数量或当地高斯在近似传播的PDF时的间隔。 CopPola用于计算空间对象之间的碰撞（PC）概率的方法，以考虑参数模型不确定性。然后将PC整体结合到火山口中。然后使用火山口来计算PC 8不同的测试用例，并与Monte Carlo结果进行比较。

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