Orbit prediction accuracy is often limited by the underlying physics-based models and estimation methods. Instead of advancing the state-of-the-art from those two aspects, we have recently developed a physics-based machine learning (ML) methodology to discover useful information from historical orbit predictions errors. This paper is posed to answer the next question: how can we fuse the ML approach with classical orbit predictions? The classical method provides valuable and reliable information and should not be abandoned. Using the extended Kalman filter (EKF) as the orbit estimation and prediction method, this paper presents an innovative fusion strategy to incorporate the ML output to the conventional framework. We define the pseudo-physical meaning of the ML output and derive an analytical model for fusion. Using a simulation-based space catalog environment, the paper demonstrates that the proposed fusion strategy can improve both the orbit prediction accuracy and precision. Discussions and insights are presented including the possible causes for some unsatisfying results. Although EKF is used in this paper, the design of the fusion strategy for the ML approach can be generalized to systems with different orbit estimation and prediction methods.

轨道预测的准确性通常受到基础的基于物理的模型和估计方法的限制。我们最近没有开发基于这两个方面的最新技术，而是开发了一种基于物理学的机器学习（ML）方法，以从历史轨道预测错误中发现有用的信息。本文旨在回答下一个问题：如何将ML方法与经典轨道预测融合？经典方法提供了有价值且可靠的信息，因此不应放弃。使用扩展卡尔曼滤波器（EKF）作为轨道估计和预测方法，本文提出了一种创新的融合策略，可将ML输出合并到常规框架中。我们定义了ML输出的伪物理含义，并导出了用于融合的分析模型。利用基于仿真的空间目录环境，本文证明了所提出的融合策略可以提高轨道预测的准确性和精度。提出了讨论和见解，包括导致某些不满意结果的可能原因。尽管在本文中使用了EKF，但是可以将ML方法的融合策略设计推广到具有不同轨道估计和预测方法的系统。