Date of Award

Fall 2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mechanical & Aerospace Engineering

Program/Concentration

Aerospace Engineering

Committee Director

Brett Newman

Committee Member

Robert Ash

Committee Member

T. Alan Lovell

Call Number for Print

Special Collections; LD4331.E56 P728 2014

Abstract

An approximate second order nonlinear closed-form solution for three-dimensional relative motion assuming Keplerian dynamics and a circular reference track are applied to the relative initial orbit determination problem. A series of azimuth-elevation angular measurements locating a deputy satellite with respect to a chief satellite are coupled through the observation geometry with the nonlinear dynamics model for the relative motion in terms of linear, quadratic, and bilinear combinations of the deputy initial conditions and chief orbital elements. The resulting set of nonlinear measurement equations are analyzed, formulated, and solved using three separate non-iterative methods. By using a nonlinear dynamics model with angular measurements, the problem of unobservable states when using a linear model is avoided. One method is a reformulation as an equivalent set of linear equations with constraints solved by matrix decomposition and computation of an unknown scaling factor. A method requiring a reduced number of measurements uses linear dynamics to solve for an unscaled state and then applies the full nonlinear dynamics equations to scale the solution. The final method employs Macaulay resultant theory to directly solve the system of multivariate polynomial measurement equations. Performance of the initial relative orbit determination procedures is evaluated with computer simulation while varying factors such as noise level, sample rate, and along-track drift rate. Overall, the procedures facilitate recovery of the deputy relative orbital state with requisite accuracy such that the information could be passed on to a refined precision orbit detem1ination procedure.

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In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).

DOI

10.25777/8m48-9w86

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