Physics-Informed Neural Networks for Satellite State Estimation

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 have widely varying degrees of fidelity: some only account f or two-body Keplerian motion, while others consider highly accurate Earth gravity models, atmospheric drag, solar radiation pressure (SRP), perturbations from the Sun, Moon, and other celestial bodies, etc. 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. For example, satellites using low-thrust electric propulsion to modify their orbit, or pieces of debris which have extremely High Area-to-Mass Ratios (HAMR) that experience SRP effects beyond what is accounted for in existing models. 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 the fundamental physics of astrodynamics, which results in more efficient and effective utilization of machine learning resources to solve for only the unmodeled dynamics. This paper details the application of PINNs to estimate the orbital state and a continuous, low-amplitude anomalous acceleration profile for satellites. Angles-only observation data is simulated for satellites near Geosynchronous Orbit (GEO). This simulation first propagates the satellite in time using a physics model coupled with an arbitrary acceleration profile, and then simulates realistic, angles-only observations of the satellite as would be measured by a ground-based optical telescope. This arbitrary acceleration profile could represent a low-thrust orbit maneuver or a difficult-to-model SRP effect on a HAMR object, and is used for generating truth data. The PINN is trained to learn the unknown acceleration by minimizing the mean square error of the 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 1 0
⁻⁸
km/s
²
, the best-fit physics model resulted in observation residuals with a root-mean-square error of 123 arcsec, while the best-fit P INN h ad a n e rror o f 1.00 arcsec, comparable to the measurement noise. Similarly, after propagating the best-fit physics model for five days beyond the fit span of the observations, the propagated position of the satellite using the physics-only model was wrong by 3860 km, compared to the PINN which had an error of only 164 km.