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 on the basis of 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 use of time that usually must be accounted for to improve 
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 constraint that can be imposed, and also in this case a polynomial system is obtained. 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.
Committee
•  Dr. John A. Christian – School of Aerospace Engineering (advisor)
•  Dr. Brian C. Gunter– School of Aerospace Engineering
•  Dr. Anton Leykin – School of Mathematics