An analysis on the application of algebraic geometry in Initial Orbit Determination problems

dc.contributor.advisor Christian, John A.
dc.contributor.author Mancini, Michela
dc.contributor.committeeMember Gunter, Brian C.
dc.contributor.committeeMember Leykin, Anton
dc.contributor.department Aerospace Engineering
dc.date.accessioned 2023-01-10T16:24:18Z
dc.date.available 2023-01-10T16:24:18Z
dc.date.created 2022-12
dc.date.issued 2022-12-01
dc.date.submitted December 2022
dc.date.updated 2023-01-10T16:24:18Z
dc.description.abstract Initial Orbit Determination (IOD) is a classical problem in astrodynamics. The space around Earth is crowded by a great many objects whose orbits are unknown, and the number of space debris is constantly increasing because of break-up events and collisions. Reconstructing the orbit of a body from observations allows us to create catalogs that are used to avoid collisions and program missions for debris removal. Also, comparing the observations of celestial bodies with predictions of their positions made based on our knowledge of the universe has been in the past, and is still today, one of the most effective means to make improvements in our cosmological model. In this work, a purely geometric solution to the angles-only IOD problem is analyzed, and its performance under various scenarios of observations is tested. The problem formulation is based on a re-parameterization of the orbit as a disk quadric, and relating the observations to the unknowns leads to a polynomial system that can be solved using tools from numerical algebraic geometry. This method is time-free and does not require any type of initialization. This makes it unaffected by the problems related to the estimate of the time-of-flight, that usually affects the accuracy of the solution. A similar approach may be used to analyze the performance of the solver when streaks are used, together with lines of sight, as inputs to the problem. Streaks on digital images form, together with the camera location, planes that are tangent to the orbit. This produces two different types of constraints, that can be written as polynomial equations. The accuracy and the robustness of the solver are decreased by the presence of streaks, but they remain a valid input when diversity in the observed directions guarantees the departure from the singular configuration of almost coplanar observations.
dc.description.degree M.S.
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/70145
dc.language.iso en_US
dc.publisher Georgia Institute of Technology
dc.subject Initial Orbit Determination
dc.subject Algebraic geometry
dc.title An analysis on the application of algebraic geometry in Initial Orbit Determination problems
dc.type Text
dc.type.genre Thesis
dspace.entity.type Publication
local.contributor.advisor Christian, John A.
local.contributor.corporatename College of Engineering
local.contributor.corporatename Daniel Guggenheim School of Aerospace Engineering
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relation.isOrgUnitOfPublication a348b767-ea7e-4789-af1f-1f1d5925fb65
thesis.degree.level Masters
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