航天器轨迹偏差的非线性非高斯预报方法

针对航天器轨道偏差传播问题，提出一种高斯和模型与状态转移张量结合的预报方法。该方法使用多个子高斯分布加权拟合状态偏差分布，再以高阶状态转移张量分别预报每个子高斯分布，以捕获偏差分布的非高斯性，减小预报误差。将其应用到航天器二体轨道问题中，对比分析不同方法的预报结果。仿真结果表明，该方法可以逼近Monte Carlo仿真的预报精度，并显著提高计算效率，对长时间预报问题，效率提高可达数十倍。该方法面向一般的非线性系统状态偏差预报问题，尤其在长时间仿真预报时兼具很好的精度和计算效率。

A Nonlinear and Non Gaussian Propagation Method for Spacecraft Trajectory Uncertainty

For the spacecraft trajectory uncertainty propagation problem, a propagation method is presented, which combines Gaussian mixture model and state transition tensor method. This method approximates the state uncertainty by a weighted sum of Gaussian components, and then propagates each Gaussian component respectively by the high order state transition tensor, in order to capture the non-Gaussian features and decrease the error of linearization. A two-body problem is tested and the results indicate that the proposed method can approach the precision of the Monte Carlo simulation method as well as improve the computation efficiency. Especially, the longer the prediction time is, the larger the ratio of the computation time of the Monte Carlo method to the presented method becomes. Additionally, the presented method faces to the uncertainty propagation problem of a general nonlinear system, and has both a high precision and a good computational efficiency especially for a long-term propagation.