Theses and Dissertations

Issuing Body

Mississippi State University


Cheng, Yang

Committee Member

Koenig, Keith

Committee Member

Xin, Ming

Date of Degree


Original embargo terms

MSU Only Indefinitely

Document Type

Graduate Thesis - Campus Access Only


Aerospace Engineering

Degree Name

Master of Science


James Worth Bagley College of Engineering


Department of Aerospace Engineering


The system of sparse gridpoints was used to propagate uncertainty forward in time through orbital mechanics simulations. Propagation of initial uncertainty through a nonlinear dynamic model is examined in regards to the uncertainty of orbit estimation. The necessary underlying mechanics of orbital mechanics, probability, and nonlinear estimation theory are reviewed to allow greater understanding of the problem. The sparse grid method itself and its implementation is covered in detail, along with the necessary properties and how to best it to a given problem based on inputs and desired outputs. Three test cases were run in the form of a restricted two-body problem, a perturbed two-body problem, and a three-body problem in which the orbiting body is positioned at a Lagrange point. It is shown that the sparse grid method shows sufficient accuracy for all mean calculations in the given problems and that higher accuracy levels allow for accurate estimation of higher moments such as the covariance.



uncertainty||orbit propagation||uncertainty propagation||sparse grid||smolyak