Angles-only orbit determination using hamiltonian monte carlo

The lack of observability inherent in the linearized dynamics model for angles-only relative navigation between two satellites in close proximity has been well established by numerous studies, showing that an infinite set of possible relative orbits satisfy the observations. This work seeks a probabilistic method of angles-only orbit determination and to study this problem using the full nonlinear formulation. The lack of range observability in the problem makes Gaussian approximations a poor representation of the solution probability density, and motivates higher fidelity approaches than typical Markov Chain Monte Carlo approaches for probability distribution sampling. In order to achieve this, Hamiltonian Monte Carlo sampling of a theoretical probability distribution of possible solutions is explored, which is known to be more successful for high dimensional problems. The technique is performed on several angles-only measurement cases with increasingly difficult observability, including close proximity and coplanar cases. It is observed that when tuned correctly, Hamiltonian Monte Carlo sampling can successfully resolve the probability distributions of the possible deputy states, showing increasingly non-Gaussian behavior as observability is limited. Additionally, Hamiltonian Monte Carlo achieves this much more efficiently than traditional Markov Chain Monte Carlo techniques.