Cislunar Orbit Determination Behavior: Processing Observations of Periodic Orbits with Gaussian Mixture Model Estimation Filters

Abstract

Orbits of objects in cislunar space are, in general, non-Keplerian due to the influence of the Moon’s gravity and cannot be generically parameterized by a simple set of characteristics. Objects are also fainter and move relatively more slowly when viewed from Earth. Detection and tracking are expected to be significantly more difficult and, as a consequence, orbit determination becomes more challenging. In this paper we review a subset of possible orbits and their expected astrometric and photometric signatures from the perspective of hypothetical ground-based electro-optical sensors on Earth. Although a multitude of orbits are possible, we focus on special types of orbits that are closed in the synodic frame (i.e., periodic) and emanate from the libration points of the Earth-Moon system. We investigate three separate elemental periodic orbit families that have been differentially corrected in a high-fidelity dynamical system: H1, L1, and W4W5. For each family, we set objects at different locations at different epochs and simulate the expected observational features (e.g., right ascension, declination, visual magnitude) based on faceted satellite models. In this study, we show how Gaussian mixture model estimation filters behave when processing different observation sets, specifically varying data cadence, data density, data quality, and data span. Convergence and uncertainty bounds are shown to have a strong dependence on the observational data composition (affecting the accuracy of fitting orbits) and a notable correlation to orbital stability (affecting the ability to predict/correct orbits).