Gregory Badura, Georgia Tech Research Institute; Ebenezer Arunkumar, Georgia Tech Research Institute; Miguel Velez-Reyes, The University of Texas at El Paso; Brian Gunter, Georgia Institute of Technology; Koki Ho, Georgia Institute of Technology
Keywords: Machine Learning, Orbit Determination, Angles-Only, Cislunar, Physics Informed Machine Learning
Abstract:
Traditional methods for performing angles-only Orbit Determination (OD) do not directly extend to the cislunar domain due to their reliance on two-body gravitational assumptions. To close this gap, emerging research has shown that Physics Informed Machine Learning (PIML) OD algorithms can overcome the challenge of performing OD under multi-body dynamics by using the high-dimensional embedding of the PIML’s hidden layers. During the training phase, the PIML learns to map this high dimensional embedding to an output trajectory prediction by minimizing a loss function consisting of errors in multi-body dynamics as approximated by automatic differentiation (i.e. the physics loss) and errors in the line-of-sight predictions (i.e. the “big-data” loss). The use of a physics loss term constrains the predictions to match the known dynamics of the cislunar domain while the use of a “big-data” loss term ensures that all predictions match the measured line of sight data. As will be shown, this combination of loss terms allows for convergence to high accuracy trajectory predictions (~1E1 km) even when the PIML is initialized extreme errors in the initial trajectory prediction (~1E6 km).
Unfortunately, current methods for training PIML OD models do not provide a measure of uncertainty in their trajectory predictions. This is a major hindrance towards widespread adoption of ML algorithms because operational Space Situational Awareness (SSA) experts may not be experts in ML; this knowledge gap can lead to difficulties in judging the confidence that should be placed in ML predictions or in diagnosing when a PIML system diverges during training. In order to overcome these operational limitations, we propose a novel PIML training algorithm that generates not only a trajectory prediction but also an epistemic uncertainty of the trajectory prediction, accounting for uncertainty in the trained PIML weights that is non-linearly related to the line of sight measurement uncertainty. This is achieved by treating the trainable PIML weights not as point estimates but rather as Gaussian probability distributions. By solving for the probability distribution of each PIML weight, we show that the uncertainty in the trajectory prediction can be generated by passing the distribution through the high-dimensional hidden layer embedding. In this work, we demonstrate that this training algorithm reliably produces 3σ prediction uncertainty volumes that bound the trajectory prediction errors across a broad range of cislunar orbits ranging from stable cislunar families to chaotic trajectories. We also demonstrate how treating the weights as probability distributions from which to compute weight updates can yield lower overall trajectory errors than by considering the weights as point estimates.
Date of Conference: September 16-19, 2025
Track: Machine Learning for SDA Applications