|
Previous work on refining orbital states and/or physical object characteristics has used either semi-empirical or statistical regression techniques. Semi-empirical techniques have been applied to objects whose orbital states and/or physical object characteristics are already known to high degree and do provide academically interesting observations on object-specific perturbative phenomena. However, semi-empirical techniques cannot be extrapolated and applied to the wider orbital population, whose orbital states and/or physical object characteristics are known to a lesser degree and may operate in orbital regimes substantially different from those studied. The refinement solutions provided by statistical regression techniques are ’best-fit’ rather than unique, because they do not attempt to narrow the solution space using fundamental physical principles such as the conservation of energy and momentum. s thesis aims to extend the work of orbital refinement by exploiting additional strategies and techniques, including (1) the replacement of semi-empirical or statistical regression techniques with multivariate optimisation; (2) the application of fundamental physics, particularly celestial mechanics, as constraints to the solution process; and (3) the addition of a stochastic discrepancy function to represent natural or non-natural forces that are not represented in the perturbative models employed. Multivariate optimisation creates the opportunity to correct all states, physical object characteristics, and natural and non-natural forces simultaneously. The application of celestial mechanics principles narrows the family of solutions returned to those that adhere to the laws of conservation of energy and momentum. Forces represented by a stochastic discrepancy function are designed to account for the inability to exploit the full accuracy of geophysical, planetary and atmospheric models due to the amount of high-performance computing capability available to this work. The method is tested against three of the accidental orbital conjunctions that have occurred to date. These test scenarios provide further determinism to the system of equations for development and evaluation purposes and offer new forensic details on the cases not seen in previous literature. It is anticipated that subsequent works which expand on the lessons learned from implementing these strategies will deliver a method capable of correcting the states, physical characteristics and natural or non-natural forces of objects considered individually. |
|