Samuel, Richard2020-08-10http://hdl.handle.net/1885/207348A multivariate optimisation technique for refining the physical characteristics and non-natural behaviours of near-earth orbiting objects is being developed. The technique uses a series of initial arbitrary precision state vectors whose covariances form a system of equations composed of partial derivatives, which is iteratively solved until the residuals are minimised. The technique is similar to least-squares orbit determination but occurs over much longer time scales. The technique also has similarities with computational fluid dynamics analysis in that it is solved through linear algebraic techniques but relies on orbital geometry continuity rather than mass continuity as a constituent quantity. Geophysical and atmospheric models can be user-selected and the technique is likely to be extended to accommodate non-spherical geometric shape as it relates to drag and solar radiation pressure, and non-natural force production. At the present stage of development, the constituent equations are predominantly derived from geometry continuity and are not fully determined. Convergence to a theoretically valid solution occurs however the solution is not unique and varies with infinitesimal changes to the partial derivatives; a consequence of a non-linear system with limited diversity. Constituent diversity can possibly be added to the system of equations through the use of Galilean invariance of energy and momentum, akin to its classical employment in ten-integral celestial mechanics problems. The opportunities and challenges of this approach will be examined in this paper.application/pdfen-AU© 2018 National Aeronautics and Space Administration20182020-04-19