Physics-Guided Machine Learning for Satellite Spin Property Estimation from Light Curves

Knowledge of the spin state of space objects is critical for effectively planning operations such as collision avoidance and debris removal. One such passive method for assessing the spin rate and spin-axis of debris is through the use of passive brightness measurements known as "light curves." Astronomers have derived physics-based algorithms for retrieving spin state via light curve analysis. These algorithms convert the relative spin state into an inertial spin state by accounting for the motions of the observation telescope, the space object, and the sun. A major downside of these theories, however, is that the resulting cost functions for operational deployment are highly non-linear. The intractable nature of the spin state estimation problem opens the door for solution via Machine Learning (ML) models. Typical "black box" ML algorithms do not rely on scientific theory, but rather are trained on large data-bases to learn how to solve a task in a manner that is obscured from the operator. While ML models can be effective for making predictions that out-perform human-derived algorithms, they also have the potential to derive solutions that either violate known physical constraints or are non-generalizable to new data instances. This is in particular a concern for many Space Domain Awareness (SDA) problems that are rooted in the physical theory of the motions of orbiting bodies. To overcome the limitations of both physical theory and "black box" ML models for spin state retrieval, we leverage a hybrid approach: the physics-guided ML model. This concept uses a physics-based loss function in the learning objective of the ML model in order to guide the model towards making predictions that not only exhibit low prediction error with respect to training data but are also physically consistent with astronomer-derived theories. Towards this end, we introduce a new physically derived equation for relating the inertial spin state to observations of relative spin rates. We then show that this equation can be used as a loss function for training ML models. We present a time-variant ML model for the retrieval of spin state that substantially outperforms both randomized numerical optimization approaches as well as temporally-invariant ML methods such as Convolutional Neural Networks. Finally, we provide initial evidence that training of the time-variant ML model with our physics-based loss function is more stable and generalizes more effectively to unseen (i.e. "out-of-distribution") data instances. We believe that this paper provides promising avenues for merging big-data ML approaches with the robust physical theory of the SDA field.