Probabilistic Methods for Initial Orbit Determination and Orbit Determination in Cislunar Space

Abstract

In orbital mechanics, Gauss's method for orbit determination (OD) is a popular, minimal assumption solution for obtaining the initial state estimate of a passing resident space object (RSO). Since much of the cislunar domain relies on three-body dynamics, a key assumption of Gauss's method is rendered incompatible, creating a need for a new, minimal assumption method for initial orbit determination (IOD). In this work, we present a framework for short and long term probabilistic target tracking in cislunar space which produces an initial state estimate with as few assumptions as possible. Specifically, we propose an IOD method involving the kinematic fitting of several series of noisy, consecutive ground-based observations. Once a probabilistic initial state estimate in the form of a particle cloud is formed, we apply the powerful Particle Gaussian Mixture (PGM) Filter to reduce the uncertainty of our state estimate over time. This combined IOD/OD framework is demonstrated for several classes of trajectories in cislunar space and compared to better-known filtering frameworks.