Juan Ojeda Romero, Johns Hopkins Applied Physics Lab; Wayne Schlei, Johns Hopkins University Applied Physics Laboratory; Gene Whipps, Johns Hopkins University Applied Physics Laboratory; Nicholas LaFarge, Johns Hopkins University Applied Physics Laboratory; Gunner Fritsch, Johns Hopkins University Applied Physics Laboratory; Sean Phillips, Johns Hopkins University Applied Physics Laboratory
Keywords: Multibody dynamics, cislunar IOD, Circular Restricted Three Body Problem, Neural Networks, Dynamical Systems Theory, Machine Learning, Classification, Orbit Determination
Abstract:
The desire for cislunar Space Situational Awareness (SSA) beyond GEO has been driven by the increasing number of spacecraft and operators. Optical detection and tracking of cislunar objects are significantly more difficult due to large distances (>300,000 km) and faint lighting conditions. Classical Initial Orbit Determination (IOD) strategies based on Two-Body motion (Gooding, Gauss, and Laplace) are well defined in the vicinity of the Earth and provide an adequate guess to begin the sequential filtering process, e.g., a Kalman filter. However, convergence to a six-dimensional state via these methods within the cislunar regime is non-trivial and presents significant challenges due to the complex multi-body dynamics and the large volume of space. Current research applications to address the cislunar IOD process has implemented existing machine learning techniques, e.g., supervised learning algorithms with Neural Networks (NN); however, their efficacy is dependent on the quality of the training datasets. Therefore, in the absence of an analytic IOD approach, this paper proposes a state-of-the-art cislunar IOD framework that benefits from both a knowledge of the non-Keplerian cislunar dynamics and existing machine learning techniques.
In this investigation, a framework for an end-to-end cislunar IOD process that incorporates angles-only observations is presented. Current traditional methods inherit insights from the Two-Body Problem, however, when considering cislunar objects, these approaches become expensive guess-and-check problems. Current research to provide a proficient solution to the non-trivial cislunar IOD problem has focused on applications of machine learning techniques and corrections algorithms within the higher fidelity Earth-Moon Circular Restricted Three Body Problem (CRTBP) model. Previous authors have investigated classification of astrometric observations to existing dynamical structures, i.e., periodic orbits and invariant manifolds, in cislunar space, however, these studies did not deliver initial state estimates. Additionally, previous research has also focused on reformulating the cislunar IOD process into an optimization problem, although the existence of multiple locally optimal solution basins requires more investigation. In light of this, one of the objectives of this investigation is to provide a six-dimensional state and covariance matrix by training a NN model, i.e., the Machine Classifier for Cislunar Orbit Determination (MCCLOD) model, with periodic orbit information using the dynamics associated with the Earth-Moon CRTBP.
This investigation is focused on the region between the Earth-Moon L1 and L2 Lagrange points with assumed optical measurements from a select set of L1 and L2 halo orbit trajectories. First, a set of periodic orbit families is defined within the context of the Earth-Moon CRTBP model. Periodic orbit states from the simplified model are converted to right-ascension (RA) and declination (DEC) angles and rates, defined in the Earth-Moon rotating frame, and are used as training datasets for the MCCLOD model. For a single measurement, MCCLOD delivers a two-parameter vector (η and τ) that maps to a unique orbit on a periodic orbit family and a point along the specified orbit, respectively. A corrections algorithm maps the η- τ vector to a six-dimensional state. Simulated measurements for optical tracks corresponding to a multi-revolution L2 halo orbit trajectory are processed through MCCLOD and are ingested into a Weighted Batch Least-Squares (WBLS) filter to approximate an initial 6D state and covariance. In the proposed framework, the MCCLOD model is a product of existing machine learning techniques and knowledge of complex multi-body dynamics to address the non-trivial cislunar IOD problem.
Date of Conference: September 17-20, 2024
Track: Cislunar SDA