The risk of collision between resident space objects has significantly increased in recent years. As a result, spacecraft collision avoidance procedures have become an essential part of satellite operations. To ensure safe and effective space activities, satellite owners and operators rely on constantly updated estimates of encounters. These estimates include the uncertainty associated with the position of each object at the expected TCA. These estimates are crucial in planning risk mitigation measures, such as collision avoidance manoeuvres. As the TCA approaches, the accuracy of these estimates improves, as both objects' orbit determination and propagation procedures are made for increasingly shorter time intervals. However, this improvement comes at the cost of taking place close to the critical decision moment. This means that safe avoidance manoeuvres might not be possible or could incur significant costs. Therefore, knowing the evolution of this variable in advance can be crucial for operators. This work proposes a machine learning model based on diffusion models to forecast the position uncertainty of objects involved in a close encounter, particularly for the secondary object (usually debris), which tends to be more unpredictable. We compare the performance of our model with other state-of-the-art solutions and a na\"ive baseline approach, showing that the proposed solution has the potential to significantly improve the safety and effectiveness of spacecraft operations.

翻译：近年来，在轨空间物体间的碰撞风险显著增加，航天器避碰程序已成为卫星运行的关键环节。为确保安全高效的空间活动，卫星所有者和运营商需依赖持续更新的交会估计数据。这些估计值包含每个物体在预期最接近时刻（TCA）的位置不确定性信息，对规划碰撞规避机动等风险缓解措施至关重要。随着TCA临近，轨道确定和传播过程的时间间隔缩短，估计精度逐步提升。但这种精度提升以接近关键决策时刻为代价，可能导致安全规避机动不可行或产生重大成本。因此，提前预知该变量的演变趋势对运营方至关重要。本研究提出一种基于扩散模型（diffusion models）的机器学习方法，用以预测近距离交会中物体（尤其是通常更为不可预测的次级物体，如空间碎片）的位置不确定性。我们将该模型与现有最优解决方案及朴素基线方法进行性能对比，结果表明本方案具有显著提升航天器运行安全性与有效性的潜力。