Date of Award

Spring 4-2023

Access Type

Dissertation - Open Access

Degree Name

Doctor of Philosophy in Aerospace Engineering

Department

Aerospace Engineering

Committee Chair

Dr. Troy Henderson

First Committee Member

Dr. Richard Prazenica

Second Committee Member

Dr. Morad Nazari

Third Committee Member

Dr. Ted von Hippel

Fourth Committee Member

Dr. Alex Sizemore

Fifth Committee Member

Dr. Alan Lovell

College Dean

Dr. James Gregory

Abstract

Space is becoming increasingly congested every day and the task of accurately tracking satellites is paramount for the continued safe operation of both manned and unmanned space missions. In addition to new spacecraft launches, satellite break-up events and collisions generate large amounts of orbital debris dramatically increasing the number of orbiting objects with each such event. In order to prevent collisions and protect both life and property in orbit, accurate knowledge of the position of orbiting objects is necessary. Space Domain Awareness (SDA) used interchangeably with Space Situational Awareness (SSA), are the names given to the daunting task of tracking all orbiting objects. In addition to myriad objects in low-earth-orbit (LEO) up to Geostationary (GEO) orbit, there are a growing number of spacecraft in cislunar space expanding the task of cataloguing and tracking space objects to include the whole of the earth-moon system.

This research proposes a series of algorithms to be used in autonomous SSA for earth-orbiting and cislunar objects. The algorithms are autonomous in the sense that once a set of raw measurements (images in this case) are input to the algorithms, no human in the loop input is required to produce an orbit estimate. There are two main components to this research, an image processing and satellite detection component, and a dynamics modeling component for three-body relative motion.

For the image processing component, resident space objects, (commonly referred to as RSOs) which are satellites or orbiting debris are identified in optical images. Two methods of identifying RSOs in a set of images are presented. The first method autonomously builds a template image to match a constellation of satellites and proceeds to match RSOs across a set of images. The second method utilizes optical flow to use the image velocities of objects to differentiate between stars and RSOs. Once RSOs have been detected, measurements are generated from the detected RSO locations to estimate the orbit of the observed object. The orbit determination component includes multiple methods capable of handling both earth-orbiting and cislunar observations. The methods used include batch-least squares and unscented Kalman filtering for earth-orbiting objects. For cislunar objects, a novel application of a particle swarm optimizer (PSO) is used to estimate the observed satellite orbit. The PSO algorithm ingests a set of measurements and attempts to match a set of virtual particle measurements to the truth measurements. The PSO orbit determination method is tested using both MATLAB and Python implementations.

The second main component of this research develops a novel linear dynamics model of relative motion for satellites in cislunar space. A set of novel linear relative equations of motion are developed with a semi-analytical matrix exponential method. The motion models are tested on various cislunar orbit geometries for both the elliptical restricted three-body problem (ER3BP) and the circular restricted three-body problem (CR3BP) through MATLAB simulations. The linear solution method's accuracy is compared to the non-linear equations of relative motion and are seen to hold to meter level accuracy for deputy position for a variety of orbits and time-spans.

Two applications of the linearized motion models are then developed. The first application defines a differential corrector to compute closed relative motion trajectories in a relative three-body frame. The second application uses the exponential matrix solution for the linearized equations of relative motion to develop a method of initial relative orbit determination (IROD) for the CR3BP.

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