Machine learning (ML) prediction of cislunar family and period on non-uniformly sampled line of sight time series
Gregory P. Badura, Ebenezer Arunkumar, Miguel Vélez-Reyes, Koki Ho · 2025
Angles-only Initial Orbit Determination (IOD) techniques developed for near-Earth objects do not readily extend to the cislunar domain due to their reliance on two-body gravitational assumptions. For objects that are beyond Geostationary Orbit (GEO), the Moon’s gravitational influence becomes significant and requires three-body gravitational models. Under three-body dynamics, many near-Earth IOD assumptions fail: orbits are not necessarily periodic, planar, or elliptical. Emerging Machine Learning (ML) algorithms such as Physics Informed Neural Networks (PINNs) have recently demonstrated promise for accomplishing cislunar IOD using line of sight measurements. PINNs perform supervised prediction of cislunar satellite position while simultaneously respecting laws of orbital dynamics that are approximated using automatic differentiation algorithms. Unfortunately, recent research has shown that PINNs are sensitive to the initial trajectory estimate. For example, research has shown that if a PINN’s initial trajectory estimate is in the wrong pseudopotential zone, the PINN can fail to converge due to the network’s dynamics loss spiking as it’s trajectory estimate traverses the cislunar volume. In order to improve the convergence rate of PINNs for performing IOD, the weights of the NN component must be initialized such that the initial trajectory estimate exhibits similarity in terms of the cislunar family and period to the true trajectory. As a means of aiding ML-based IOD methods, we therefore test two architectures for classification of cislunar family and intra-family period from irregularly sampled line of sight measurements. The first is a Residual Network (ResNet)-based architecture, which uses several residual blocks of convolutional filters in order to extract a feature embedding. The second is a time-variant encoder architecture that relies on Recurrent Neural Networks (RNNs) to extract a time-flattened feature embedding. Our results indicate that both architectures performed well at predicting cislunar family. The time-variant encoder model and ResNet models achieved 94% and 95% accuracy, respectively, in cislunar family classification depending on the number of line of sight measurements (Nt) available to the classifier. Our results also show that both architectures can accomplish the goal of intra-family period estimation. The time-variant encoder model and ResNet model both achieved ≤ 1% error in average period estimation across cislunar families as the number of line of sight measurements increased to a maximum of Nt = 36. By merging these classification systems with a PINN for IOD, we demonstrate that a repeatable and accurate end-to-end ML system for performing cislunar OD can be attained.