Tracking space objects is important for managing space traffic and predicting collisions, but is difficult in part due to data association and orbit model uncertainty. Expectation–maximization (EM) is a commonly used tracking method that has not been widely considered for tracking space objects. The technique consists of iteratively computing data association probabilities with a set of current element estimates, and updating estimates of the elements by solving a nonlinear weighted least-squares regression problem where the weights are the data association probabilities. This paper demonstrates the use of EM for probabilistic data association and orbital-element estimation by applying the technique to simulated data from two angles-only tracking scenarios. In both scenarios, EM provides correct data associations and accurate maximum likelihood estimates of orbital elements. One scenario considers tracking a single object in clutter and quantifies the improvement of the orbital-element estimates and data associations as the detection probability increases. However, standard application of EM requires knowing the number of objects or may fail when a large number of objects are present. To address these issues, this paper employs a multistage version of EM that is applicable when there are a large and possibly unknown number of objects.

跟踪空间物体对于管理空间交通和预测碰撞很重要，但部分由于数据关联和轨道模型不确定性而很难。期望最大化（EM）是一种常用的跟踪方法，尚未广泛考虑用于跟踪空间物体。该技术包括用一组当前元素估计值迭代计算数据关联概率，并通过解决权重为数据关联概率的非线性加权最小二乘回归问题来更新元素的估计值。本文通过将技术应用于仅来自两个角度的跟踪场景中的模拟数据，证明了EM在概率数据关联和轨道元素估计中的应用。在这两种情况下，EM提供正确的数据关联和准确的轨道元素最大似然估计。一种情况是考虑在混乱中跟踪单个物体，并随着检测概率的增加，量化轨道元素估计和数据关联的改进。但是，EM的标准应用程序需要知道对象的数量，否则当存在大量对象时可能会失败。为了解决这些问题，本文采用了EM的多阶段版本，该版本适用于存在大量且可能未知数量的对象的情况。EM的标准应用程序需要知道对象的数量，否则当存在大量对象时可能会失败。为了解决这些问题，本文采用了EM的多阶段版本，该版本适用于存在大量且可能未知数量的对象的情况。EM的标准应用程序需要知道对象的数量，否则当存在大量对象时可能会失败。为了解决这些问题，本文采用了EM的多阶段版本，该版本适用于存在大量且可能未知数量的对象的情况。