Michela Mancini 
(Advisor: Dr. John Christian]

will defend a doctoral thesis entitled,

Algebraic Methods in Spacecraft Navigation

On

Thursday, April 17 at 10:30 a.m. 
Coda C1015 Vinings

Abstract
The technological advancements of recent decades, coupled with the ever-existing interest in expanding the boundaries of our knowledge of the universe, are enabling new types of space missions, each presenting its own unique challenges. Deep space missions increasingly demand autonomous navigation capabilities, and Optical Navigation(OPNAV) has proven to be a promising response to this need. Developing new navigation solutions, and refining existing ones, is a thriving area of research. 
      When developing algorithms for OPNAV, a convenient mathematical framework is provided by algebraic geometry. Algebraic geometry studies polynomial equations, and its connection with navigation becomes evident when realizing how many features and physical phenomena in the world of spacecraft navigation can be described in polynomial form. Keplerian orbits, elliptical crater rims, ellipsoidal celestial bodies, atmospheric bands, planetary rings, and the path traced by any object bound to the surface of a spinning body are all curves and surfaces that can be described in terms of polynomials of degree two. Furthermore, the Doppler effect, stellar aberration, image distortion, the line-of-sight observation of an orbiting body are only some examples of phenomena or constraints which are either represented or well-modeled in terms of polynomials. This dissertation explores the application of some techniques from algebraic and projective geometry to address multiple navigation-related challenges. 
      The first part of this work explores how analytical tools can be leveraged to obtain the closed form expression of the projection of a crater rim imaged with a pushbroom camera. Crater rims are often visible in the images captured by such sensors, and the knowledge of their analytical shape enables interesting capabilities, such as crater reconstruction and spacecraft state estimation. 
      After that, projective geometry will be used to develop an analytical framework for the representation of Keplerian orbits. This framework led to a novel velocity propagation technique, and to a solution to the problem of fitting a conic with constrained focus location to three points. 
      Finally, algebraic geometry will be used to address two image analysis tasks. First, a new technique for partially calibrating a camera from a single celestial body is presented. Then, the conic intersection problem, encountered when identifying craters in a digital image, is revisited and an algorithmic framework providing a simpler solution compared with current techniques is developed.

Committee

• Dr. John A. Christian – School of Aerospace Engineering (advisor)
• Dr. Koki Ho – School of Aerospace Engineering
• Dr. Brian C. Gunter – School of Aerospace Engineering
• Dr. Glenn E. Lightsey – School of Aerospace Engineering
• Dr. Timothy Duff – Department of Mathematics, University of Missouri