Hybrid Particle Gaussian Mixture (H-PGM) Solution for Cislunar Target Tracking

Gauss's method of orbit determination (OD) is one of the most popular, minimal assumption target tracking techniques in astrodynamics, especially for generating an initial state estimate. However, due to Gauss's method's assumption of Keplerian motion (part of the larger two-body problem), this method cannot be applied in a cislunar environment, where three body, non-planar effects dominate. In this work, we showcase a hybrid Particle Gaussian Mixture (H-PGM) filtering method, a purely recursive probabilistic OD framework that relies upon a sequential combination of the Markov Chain Monte Carlo (MCMC) based Particle Gaussian Mixture-II (PGM-II) and Kalman update based Particle Gaussian Mixture-I (PGM-I) filters. This method allows us to fuse probabilistic information with angles-only observations from terrestrial telescopes for short- and long-term cislunar target tracking. This method also allows us to fuse other target \textit{a priori} information in an effort to reduce target uncertainty in the short term. This hybrid filtering technique is demonstrated for several popular and important cislunar orbit regimes and compared with several homogeneous and hybrid filtering frameworks.