In predicting the collision of space debris, the propagated orbital uncertainty may not follow a Gaussian distribution if the initial orbital uncertainty is large or the propagation time is long. In this paper, a Gaussian mixture uncertainty propagation method developed by (Psiaki et al., 2015) is used to calculate the collision probability. The initial Gaussian distribution is fitted by the weighted Gaussian mixture components. The linear matrix inequality is optimized to prevent the covariance matrix of Gaussian mixture components from being too small, and an appropriate number of Gaussian mixture components is used to approximate the initial orbital covariance. At the same time, this paper provides a method to calculate the collision probability of two objects in which a Gaussian mixture is used to represent the distribution of orbital uncertainty. The linear method and the unscented Kalman filter (UKF) method for propagating the Gaussian covariance are analysed. The results of numerical simulations show that compared with the linear covariance propagation method, UKF method, and high-precision Monte Carlo covariance propagation method for space objects with a large initial orbital uncertainty, the Gaussian mixture method can be effectively applied to capture the non-Gaussian characteristics of the predicted nonlinear orbital dynamic uncertainty. Compared with the univariate splitting method, the advantage of this Gaussian mixture method is that it does not need to search for the most nonlinear direction. The accuracy of the collision probability calculation is improved from 1.460 × 10⁻³ to 1.663 × 10⁻³. A comparison of the computational burden between the Gaussian mixture algorithm and Vittaldev’s algorithm to achieve the same results is presented. The calculation burden of the Gaussian mixture method is approximately 3 times that of the univariate Gaussian method.

在预测空间碎片碰撞时，如果初始轨道不确定度大或传播时间长，传播的轨道不确定度可能不服从高斯分布。在本文中，使用 (Psiaki et al., 2015) 开发的高斯混合不确定性传播方法来计算碰撞概率。初始高斯分布由加权高斯混合分量拟合。对线性矩阵不等式进行优化，防止高斯混合分量的协方差矩阵过小，并使用适当数量的高斯混合分量来逼近初始轨道协方差。同时，本文提供了一种计算两个物体碰撞概率的方法，其中使用高斯混合来表示轨道不确定性的分布。分析了传播高斯协方差的线性方法和无迹卡尔曼滤波器(UKF)方法。数值模拟结果表明，对于初始轨道不确定性较大的空间物体，与线性协方差传播方法、UKF方法和高精度蒙特卡罗协方差传播方法相比，高斯混合方法可以有效地捕获非预测的非线性轨道动态不确定性的高斯特性。与单变量分裂方法相比，这种高斯混合方法的优点是不需要搜索最非线性的方向。^-3到 1.663 × 10 ^-3。给出了高斯混合算法和 Vittaldev 算法之间计算负担的比较，以实现相同的结果。高斯混合方法的计算负担大约是单变量高斯方法的 3 倍。