  The growing population of man-made objects with the build up of
mega-constellations not only increases the potential danger to all space
vehicles and in-space infrastructures (including space observatories), but
above all poses a serious threat to astronomy and dark skies. Monitoring of
this population requires precise satellite characterization, which is is a
challenging task that involves analyzing observational data such as position,
velocity, and light curves using optimization methods. In this study, we
propose and analyze the application of two optimization procedures to determine
the parameters associated with the dynamics of a satellite: one based on the
Theory of Functional Connections (TFC) and another one based on the Nelder-Mead
heuristic optimization algorithm. The TFC performs linear functional
interpolation to embed the constraints of the problem into a functional. In
this paper, we propose to use this functional to analytically embed the
observational data of a satellite into its equations of dynamics. After that,
any solution will always satisfy the observational data. The second procedure
proposed in this research takes advantage of the Nealder-Mead algorithm, that
does not require the gradient of the objective function, as alternative
solution. The accuracy, efficiency, and dependency on the initial guess of each
method is investigated, analyzed, and compared for several dynamical models.
These methods can be used to obtain the physical parameters of a satellite from
available observational data and for space debris characterization contributing
to follow-up monitoring activities in space and astronomical observatories.
