Accurate and Efficient Orbit Probability Approximation Framework for Space Situational Awareness

Uncertainty Propagation in astrodynamics has gained importance in space situational awareness (SSA) problems such as space debris tracking, collision avoidance, and Cislunar operations. In this dissertation, the technique of Orbit Probability Approximation (OPA) is developed. OPA propagates orbital uncertainty using Liouville’s theorem with different functional approximations. First, OPA is formulated with Chebyshev polynomials to propagate the uncertainty on a geocentric planar orbit problem and then validated using two sources of satellite data: GRACE navigation data from the Jet Propulsion Laboratory (JPL) database, and FireOPAL ground-based observer provided by Lockheed Martin. In this validation process, OPA propagates uncertainty without using any measurements. Results indicate successful validation using GRACE navigation data for a low Earth orbit (LEO), and FireOPAL sensor tracking data for Yamal 202 in geosynchronous Earth orbit (GEO) and a rocket body of the Block-DM satellite in a highly elliptical orbit (HEO). Next, the technique of utilizing Radial Basis Functions (RBF) for uncertainty propagation is formulated and demonstrated on the geocentric planar orbit problem as well as a short-period L4 orbit in Cislunar space. Since RBFs allow the possibility to employ scattered nodes and dimension-wise shape parameters, the optimization of shape parameters and adaptive sampling strategies are explored to mitigate the curse of dimensionality. With cumulative integral as the chief error metric, OPA results show good agreement with Monte-Carlo and polynomial chaos expansion simulations. For example, in GRACE validation, OPA achieves 0.11% error from the true distribution. For the Cislunar orbit problem, OPA uses around 4300 nodes to achieve the same cumulative integral value as that of a Monte-Carlo simulation with 1 million points, a significant reduction in the computational cost. Future work explores the integration of OPA RBF approximation with Mamba, a state-space formulation-based recurrent neural network, to predict the future PDFs of nonlinear dynamical systems.