Convergence and Uncertainty of Physics-Informed Machine Learning for Cislunar Orbit Determination

Abstract

Performing initial orbit determination (IOD) using angles-only observations of cislunar objects is intractable via traditional methods due to a reliance on two-body gravitational assumptions. Recent research has suggested that physics-informed machine learning (PIML) IOD algorithms can address this gap via utilization of a regularization term that captures the known differential equations of three-body dynamics. While research has shown that such PIML algorithms can converge on high-accuracy trajectory estimates from a randomized initial state, a detailed study on the operational utility of the trajectory predictions has not been addressed. Toward this end, this paper introduces 1) a method to test the convergence of PIML IOD algorithms as a function of initial state error and 2) a batch estimation routine for the PIML algorithm that allows for the prediction of uncertainty in PIML trajectory estimates. We ultimately find that the PIML’s accuracy is sensitive to the initial trajectory estimate; this sensitivity is a function of both the initial state estimate as well as the pseudopotential region of the truth trajectory. We also find that the trajectory uncertainty derived using the batch estimation routine bounds the error in the trajectory solutions when the model converges on a solution with low line-of-sight error. We discuss how these results provide guidance on future algorithms that must be developed to improve explainability of and confidence in PIML algorithms for operational IOD.