Abstract
The Space Domain Awareness (SDA) community routinely tracks satellites in orbit by fitting an orbital state to observations made by the Space Surveillance Network (SSN). In order to fit such orbits, an accurate model of the forces that are acting on the satellite is required. Over the past several decades, high-quality, physics-based models have been developed for satellite state estimation and propagation. These models are exceedingly good at estimating and propagating orbital states for non-maneuvering satellites; however, there are several classes of anomalous accelerations that a satellite might experience which are not well-modeled, such as satellites that use low-thrust electric propulsion to modify their orbit. Physics-Informed Neural Networks (PINNs) are a valuable tool for these classes of satellites as they combine physics models with Deep Neural Networks (DNNs), which are highly expressive and versatile function approximators. By combining a physics model with a DNN, the machine learning model need not learn astrodynamics, which results in more efficient and effective utilization of machine learning resources. This paper details the application of PINNs to estimate the orbital state and a continuous, low-amplitude anomalous acceleration profile for satellites. The PINN is trained to learn the unknown acceleration by minimizing the mean square error of observations. We evaluate the performance of pure physics models with PINNs in terms of their observation residuals and their propagation accuracy beyond the fit span of the observations. For a two-day simulation of a GEO satellite using an unmodeled acceleration profile on the order of $10^{-8} \text{ km/s}^2$, the PINN outperformed the best-fit physics model by orders of magnitude for both observation residuals (123 arcsec vs 1.00 arcsec) as well as propagation accuracy (3860 km vs 164 km after five days).
Abstract (translated)
空间领域意识（SDA）社区通常通过将轨道状态拟合到由空间监视网络（SSN）进行的观测结果来跟踪在轨道上的卫星。为了拟合这样的轨道，需要准确地描述对卫星施加的力的模型。在过去的几十年里，已经开发了高质量、基于物理的卫星状态估计和传播模型。这些模型在估计和传播非机动卫星的轨道状态方面非常出色；然而，卫星可能经历的几种异常加速类型（如使用低推力电推进器修改轨道的卫星）并没有被很好地建模，因此这类卫星的模型存在一定的误差。物理启发的神经网络（PINNs）是这类卫星的宝贵工具，因为它们将物理模型与深度神经网络（DNN）相结合，使得机器学习模型无需学习天体动力学，从而实现更高效和有效的机器学习资源利用。本文详细介绍了PINNs在估计卫星轨道状态和连续低幅度异常加速度剖面方面的应用。PINN通过最小化观测结果的均方误差来学习未知加速度。我们评估了使用无建模加速度剖面在GEO卫星上的物理模型与PINN的性能，以及它们在观测残差和观测外推准确性方面的表现。对于使用未建模加速度剖面模拟的GEO卫星的两天模拟，PINN在观测残差（123 arcsec vs 1.00 arcsec）和观测外推准确性（3860 km vs 164 km）方面均优于最佳拟合物理模型。
URL
https://arxiv.org/abs/2403.19736
