Gregory Badura, Georgia Tech Research Institute; Miguel Velez-Reyes, University of Texas at El Paso; Brian Gunter, Georgia Institute of Technology; Christopher Valenta, Georgia Tech Research Institute; Koki Ho, Georgia Institute of Technology
Keywords: Machine Learning, Physics-Informed Machine Learning, Cislunar, Space Domain Awareness, Orbit Determination
Abstract:
Orbit Determination (OD) is critical for monitoring spacecraft state over time. When utilizing electro-optical telescopes to perform OD, the object’s state is estimated with respect to passive Line of Sight (LoS) measurements. Historical methods of performing angles-only OD on near-earth objects do not extend to cislunar objects due to the challenges of propagating objects under three body dynamics. Therefore, new paradigms of performing cislunar OD must be explored.
One recently introduced method is Physics Informed Neural Networks (PINNs). PINNs perform supervised prediction of cislunar satellite position while simultaneously respecting laws of orbital dynamics as described by nonlinear partial differential equations. PINNs accept time as the input variable and output estimated satellite positions. The parameters of the PINN are trained to minimize a mean squared error loss that is a summation of (1) dynamics errors expressed under Circular Restricted 3 Body (CR3B) dynamics, and (2) measurement (i.e. LoS) errors. The measurement error is a function of ancillary information (time and telescope location) and predicted satellite location, meaning that the true position of the observed satellite is not available to the PINN during the training phase.
Due to lack of true state information, there can be no initial or bounding constraints placed on satellite position. Consequently, there is a high likelihood that a PINN gets trapped in a dynamically unstable gravitational region from which it cannot escape. We propose a repeatable method for training PINNs such that they avoid drifting into gravitationally unstable solutions: transfer learning. Transfer learning in this context means training the PINN to predict the position and velocity of a similar cislunar family prior to performing full training on observed LoS measurements. Transfer learning, therefore, primes the PINN parameters such that network biases and weights are not randomized at the beginning of training.
Our research shows that transfer learning results in more repeatable, faster, and more dynamically stable training of PINNs for OD. Qualitatively, we demonstrate the problem of poor parameter initialization of PINNs causing them to predict gravitationally unstable solutions and show how they are unable to escape due to explosion of the dynamical loss term. We also qualitatively show how transfer learning produces repeatable OD outcomes even when the initial state vector is randomized across the full span of a cislunar family’s trajectory. Quantitatively, we demonstrate that transfer learning increases the percentage of runs for which acceptable OD trajectories are obtained. Our results show that transfer learning yields OD solutions that are within a 0.1 degree Field of View (FoV) of the true line of sight for the full trajectory at ~12X the rate of PINNs that have randomized initial weights (46% for transfer learning vs 4% for randomized weights). Furthermore, the mean position error of transfer learned solutions is ~1 km after training for 2000 epochs, as opposed to >50 kms for PINNs trained from randomized weights after >5000 epochs at the same learning rate.
This research has numerous applications to cislunar OD. The repeatable nature of transfer learned PINNs allows for training of networks to predict the optimal trajectory in the context of a given family and stability index; this allows researchers to explore trajectory solutions that produced a sequence of LoS measurements for a specific cislunar family. The potential of transfer learning also opens up the door to utilizing novel light curve classification methods in OD. Recent research has shown that neural networks can predict cislunar family from visual magnitude time series with high accuracy. If merged with a transfer learning PINN system, it is possible that fully Machine Learning (ML) based OD systems can be realized.
Date of Conference: September 17-20, 2024
Track: Machine Learning for SDA Applications