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Physics-Informed Neural Networks for Satellite State Estimation

Jacob Varey, Jessica D. Ruprecht, Michael Tierney, Ryan Sullenberger

TL;DR

The application of PINNs to estimate the orbital state and a continuous, low-amplitude anomalous acceleration profile for satellites and the performance of pure physics models with PINNs is evaluated in terms of their observation residuals and their propagation accuracy beyond the fit span of the observations.

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).

Physics-Informed Neural Networks for Satellite State Estimation

TL;DR

The application of PINNs to estimate the orbital state and a continuous, low-amplitude anomalous acceleration profile for satellites and the performance of pure physics models with PINNs is evaluated in terms of their observation residuals and their propagation accuracy beyond the fit span of the observations.

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 , 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).
Paper Structure (11 sections, 4 equations, 9 figures, 2 tables)

This paper contains 11 sections, 4 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Orbit State Fitting and Propagation
  3. Simulating Observation Data
  4. Technical Approach
  5. Model Training
  6. DNN Architecture and Hyper-Parameter Tuning
  7. Results
  8. Observation Residuals
  9. Extrapolation Error
  10. DNN Evaluation
  11. Summary

Figures (9)

  • Figure 1: A diagram illustrating orbital state changes using impulsive and continuous thrust maneuvers. The regions shown by straight blue lines represent times in which the satellite is not thrusting, and is thus on a constant-energy orbit that is well-modeled by current propagators. The regions shown in red are those in which the satellite is thrusting and the assumption of the propagators is violated.
  • Figure 2: Simulated RA and declination observations of the satellite over the 48 hour time span used for training both the PINN and the physics-only models.
  • Figure 3: A random periodic acceleration is generated and applied to the satellite in inertial coordinates to simulate an arbitrary thrust profile. The magnitude of the integrated thrust is chosen to lie within the capability of modern electric propulsion systems.
  • Figure 4: PyTorch- and TorchDiffEq-based pseudocode for the coupled model architecture, orbit propagation, and loss computation. The low-level details of computing observations and the loss function are abstracted.
  • Figure 5: Training loss as a function of training epoch.
  • ...and 4 more figures