Differential corrections algorithm for initial orbit determination in the cislunar region using angle-only measurements

Abstract

As space traffic continues to increase in the cislunar region, accurately determining the trajectories of objects operating within this domain becomes critical. However, due to the combined gravitational influences of the Earth and Moon, orbital dynamics in this region are highly nonlinear and often exhibit chaotic behavior, posing significant challenges for trajectory determination. Many existing methods attempt to address this complexity using machine learning models, advanced optimization techniques, or sensors that directly measure distance to the target, approaches that often increase computational burden and system complexity. This work presents a novel initial orbit determination (IOD) algorithm for cislunar objects based solely on three angle-only measurements taken at three discrete times. The core methodology builds upon a differential corrections framework which iteratively refines the target’s trajectory to satisfy line-of-sight constraints. Numerical simulations show that the algorithm achieves accurate IOD with minimal observational data. Its simplicity and efficiency make it well suited for onboard implementation in resource-constrained cislunar missions, owing to its lightweight correction scheme and limited data requirements.