引用本文: 桑吉章, 李彬, 刘宏康. 空间碎片轨道协方差传播及其动态校正[J]. 武汉大学学报 ( 信息科学版), 2018, 43(12): 2139-2146.
SANG Jizhang, LI Bin, LIU Hongkang. Orbital Covariance Propagation of Space Debris and Its Dynamic Calibration[J]. Geomatics and Information Science of Wuhan University, 2018, 43(12): 2139-2146.
 Citation: SANG Jizhang, LI Bin, LIU Hongkang. Orbital Covariance Propagation of Space Debris and Its Dynamic Calibration[J]. Geomatics and Information Science of Wuhan University, 2018, 43(12): 2139-2146.

## Orbital Covariance Propagation of Space Debris and Its Dynamic Calibration

• 摘要: 轨道误差传播研究在空间碰撞风险分析、任务规划等空间态势感知领域具有重要作用。轨道误差常用误差协方差矩阵表达，其传播方式主要有线性传播模型与非线性传播模型两种。线性传播模型通过状态转移矩阵外推初始协方差矩阵，计算快速，但因将高度非线性化的轨道动力学问题线性化描述，导致传播精度随时间快速降低。非线性传播模型精度高但计算慢，难以进行大规模碎片群的轨道误差传播。在轨道误差传播特性分析的基础上，提出了一种获得较为真实的空间碎片轨道预报误差的方法，分3步进行：初始协方差矩阵的构建、初始轨道协方差线性传播以及基于实测数据对轨道预报协方差的动态校正。经大量案例统计分析，结果表明，校正后的轨道预报协方差，相较于线性传播结果，精度提高了60%以上，可服务于空间碰撞风险分析等高精度空间任务。

Abstract: Orbital covariance propagation plays a vital role in the space situation awareness tasks such as the space conjunction analysis and space mission planning. Orbital errors, usually expressed by the orbital covariance matrix, can be propagated with linear models or non-linear models. Linear models are analytical and computationally fast since only the state transition matrix is needed. However, the propagation accuracy declines quickly with the time due to the linearization of highly nonlinear orbital dynamic systems. The non-linear models are accurate but computationally intensive, and thus are less attractive in the orbital covariance propagation for massive space debris. On the basis of the analysis of the propagated orbital errors, this paper proposes a dynamic calibration method to improve the accuracy of orbit error propagation. The method has three steps:the generation of realistic initial orbit covariance matrix, the linear propagation of the covariance matrix, and dynamic calibration of the propagated covariance using past observations. Experiments of real data processing show that the accuracy of calibrated orbit covariance can be improved by more than 60% compared to the linearly propagated covariance, and can provide more accurate propagated covariance for many space applications require high-accuracy such as the space collision probability computation.

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