Jordan Murphy, Slingshot Aerospace; Conner Grey, Slingshot Aerospace; Jason Stauch, Slingshot Aerospace; Navraj Singh, Slingshot Aerospace; Jeffrey Shaddix, Slingshot Aerospace; Belinda Marchand, Slingshot Aerospace
Keywords: Space Weather, Drag Modeling, Scientific Machine Learning, Compressive Sensing
Abstract:
Accurate modeling of Earth’s atmosphere is critical for precise satellite propagation and conjunction analysis, particularly in low Earth orbit (LEO). At low altitudes, atmospheric drag significantly alters trajectories and is often the dominant error source. Existing and widely available models, such as Jacchia-Roberts 1971 (JR71), struggle to capture the full complexity of space weather-driven changes in the upper atmosphere and, as a result, suffer from systemic biases leading to errors in orbital predictions. More advanced models like the High Accuracy Satellite Drag Model (HASDM) offers state-of-the-art corrections and forecasts to density estimates, but it remains protected by the US Air Force and inaccessible to the broader space community. To address these limitations, this work develops a data-driven correction to the JR71 model by leveraging a combination of Universal Differential Equations (UDEs), driven by differentiable programming, and compressive sensing techniques.
At the core of the novel atmospheric model framework is the UDE approach which enables the use of data-driven functions directly inside of differential equation simulations. This seamless integration of data-driven corrections in mechanistic physics-based models better preserves the interpretability and generalizability not typically found in full data-driven approaches. This hybrid model still utilizes the JR71 as a strong foundation, incorporating established scientific theory with data-driven corrections not encapsulated by the traditional parameterization. By leveraging observed satellite trajectories, the UDE framework learns this correction function that mitigates the simulator bias. The UDE frame is then expanded by utilizing compressive sensing techniques and combining multiple exposed trajectories constraining the data-driven correction to only identify the most relevant terms. Compressive sensing enables high-fidelity reconstruction of signals with limited data by exploiting sparse representations. Constraining the model in this fashion allows for learning a global correction without overfitting to any subset of reference trajectories, significantly enhancing drag modelling and orbit prediction.
Integrating observational data into existing physics-based frameworks in a computationally efficient and interpretable manner is a major challenge in improving atmospheric density models. The key enabler of our novel approach is differentiable programming, which provides a flexible mechanism to incorporate both fundamental physics models and data-driven approaches within a single optimization framework. Utilizing automatic differentiation through high-fidelity models permits accurate and efficient gradients of the parameters needed to train the data-driven correction, even when Jacobians are analytically intractable. Differentiable programming also facilitates the use of adjoint sensitivity methods significantly reducing the computational cost for learning the correction from trajectory data. This capability is crucial for the UDE approach and simplifies the optimization to a gradient descent.
The UDE methodology provides a significant advancement over conventional empirical and physics-based modeling by reducing reliance on fixed and inaccurate assumptions and by incorporating actual observational data. It furthermore provides an open and adaptable framework for improving atmospheric density estimates using a variety of data sources, including the massive number of observations produced by modern commercial tracking networks. By mitigating biases in traditional density modeling, this work aims to significantly improve conjunction assessment, reduce covariance in predicted satellite states, and enhance filtering and data association techniques in space situational awareness applications. Enhancing these further trickles down into any analyses relying on predicted or reconstructed states.
The experimental results shown in this paper will demonstrate improved state accuracy when compared against high-accuracy ephemerides and improved covariances while maintaining covariance realism. Furthermore, to demonstrate the techniques are learning an accurate correction, comparisons between the corrected model and a higher fidelity truth density like that of the Jacchia-Bowman 2008 atmospheric model will be shown.
Date of Conference: September 16-19, 2025
Track: Atmospherics/Space Weather