insight - Satellite Orbit Estimation - # Modeling Satellite Thrust Profiles using Physics-Informed Neural Networks

Core Concepts

Physics-Informed Neural Networks (PINNs) can effectively model the total dynamics of a continuously thrusting satellite, including both the natural forces and the active thrust, by combining astrodynamics models with deep neural networks. This approach outperforms pure physics models in fitting observation data and extrapolating the satellite's future state.

Abstract

The paper presents a methodology for using Physics-Informed Neural Networks (PINNs) to model the dynamics of continuously thrusting satellites. Key highlights:
Satellites employing electric propulsion for slow orbital maneuvers are difficult to maintain using pure physics models, as the models do not account for the active thrusting.
The PINN approach combines astrodynamics models with a deep neural network to learn the satellite's thrust profile directly from observation data.
The PINN model is able to fit the simulated observation data with much lower residuals (1.00 arcsec RMSE) compared to a pure physics model (123 arcsec RMSE).
When extrapolating the satellite state beyond the observation fit span, the PINN model significantly outperforms the pure physics model, with position errors of 164 km vs 3860 km after 5 days.
The DNN component of the PINN is able to reasonably estimate the underlying thrust profile applied to the satellite, demonstrating the model's ability to learn the unmodeled dynamics.
The PINN approach offers a flexible and effective way to model the total dynamics of thrusting satellites, improving upon the limitations of pure physics-based models.

Stats

The simulated satellite experienced a total ΔV of approximately 10 m/s over the 2-day observation period, which would require only 10 mN of thrust for a 180 kg ESPA-class satellite.

Quotes

"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."
"For a two-day simulation of a GEO satellite using an unmodeled acceleration profile on the order of 10^-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 PINN had an error of 1.00 arcsec, comparable to the measurement noise."
"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."

Key Insights Distilled From

by Jacob Varey,... at **arxiv.org** 04-01-2024

Deeper Inquiries

The performance of the Physics-Informed Neural Network (PINN) model would likely be impacted if the simulated thrust profile had different characteristics.
Magnitude: A higher magnitude thrust profile would introduce larger deviations from the physics-based model, potentially making it more challenging for the PINN to accurately capture these deviations. Conversely, a lower magnitude thrust profile might be harder to detect amidst the noise in the observations, requiring the PINN to be more sensitive to subtle changes.
Duration: A longer duration thrust profile would lead to sustained deviations from the physics model, which could be easier for the PINN to learn over time. On the other hand, a shorter duration thrust profile might require the PINN to quickly adapt to rapid changes in the satellite's dynamics.
Frequency: A higher frequency thrust profile, with more rapid changes in acceleration, could pose challenges for the PINN in capturing the dynamic nature of the thrust accurately. Conversely, a lower frequency thrust profile might be easier for the PINN to model due to more gradual changes in acceleration.
In summary, the performance of the PINN model would depend on how well it can adapt to different magnitudes, durations, and frequencies of the thrust profile, with potential trade-offs in accuracy and computational complexity.

Applying the PINN approach to real-world observation data of thrusting satellites, where the true thrust profile is unknown, could present several challenges:
Complexity of Real Data: Real-world observation data may be noisier and more complex than simulated data, making it harder to discern the effects of the thrust profile accurately. The PINN would need to be robust to handle this variability.
Limited Training Data: Obtaining sufficient training data for diverse thrust profiles and observation modalities could be challenging. The model might struggle to generalize well to unseen scenarios without a comprehensive dataset.
Model Interpretability: Interpreting the results of the PINN in real-world scenarios, where the true thrust profile is unknown, could be challenging. Understanding the learned dynamics and ensuring the model's predictions align with physical constraints would be crucial.
Computational Resources: Real-time estimation of the satellite's state and thrust profile from diverse observation modalities could require significant computational resources, especially for complex models like PINNs.
Addressing these challenges would involve careful data collection, model validation, and continuous refinement to ensure the PINN framework can effectively handle the uncertainties in real-world scenarios.

Extending the PINN framework to simultaneously estimate the satellite's state and thrust profile from a diverse set of observation modalities could offer several advantages:
Improved Accuracy: By incorporating multiple observation modalities such as angles, range, and range-rate, the PINN could leverage complementary information to enhance the accuracy of the estimated state and thrust profile.
Robustness: Using a diverse set of observation modalities would make the model more robust to uncertainties or noise in any single modality. It could help in capturing a more comprehensive understanding of the satellite's dynamics.
Enhanced Generalization: Training the PINN on a diverse set of observation modalities could improve its generalization capabilities, enabling it to adapt to different types of data and scenarios.
However, this extension would also introduce challenges such as increased model complexity, the need for larger and more diverse datasets, and potential difficulties in interpreting the combined results. Balancing these factors would be essential in successfully implementing a multi-modal PINN framework for satellite state and thrust estimation.

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