published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Approved for public release; distribution is unlimited / "Human body motion tracking using inertial sensors requires an attitude estimation filter capable of tracking in all orientations. One way to represent orientation is to use Euler angles, but they have singularities and therefore are not suitable for human body tracking applications. Quaternions can be used to represent orientation without incurring singularities. A quaternion-based Kalman filter has been designed for this purpose and implemented in this thesis. Also, a new suboptimal algorithm to compute the quaternions based on magnetometer and accelerometer data is implemented. This new algorithm called "Factored Quaternion Algorithm" is computationally simpler than previous methods and provides a decoupling property from magnetometer and accelerometer data." p. i. / Lieutenant Junior Grade, Mexican Navy

The purpose of this dissertation is to clarify the emergence of quaternions in order to make the history of quaternions less opaque to teachers and students in mathematics and physics. ‘Quaternion type Rotation Groups’ are important in modern physics. They are usually encountered by students in the form of: Pauli matrices, and SU(2) & SO(4) rotation groups. These objects did not originally appear in the neat form presented to students in modern mathematics or physics courses. What is presented to students by instructors is usually polished and complete due to many years of reworking. Often neither students of physics, mathematics or their instructors have an understanding about how these objects came into existence, or became incorporated into their respected subject in the first place. This study was done to bridge the gaps between the history of quaternions and their associated rotation groups, and the subject matter that students encounter in their course work.

Reproduction de : Thèse de doctorat : Mathématiques : Faculté des sciences de Paris : 1877. / Titre provenant de la page de titre du document numérisé.

Thesis--Ph. D., University of Hong Kong. / Mimeographed.

Thesis (Ph. D.)--University of Alabama at Birmingham, 2007. / Additional advisors: Nikolai Chernov, S. S. Ravindran, Alan Sprague, Min Sun. Description based on contents viewed Feb. 6, 2008; title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--McMaster University (Canada), 1996. / Source: Dissertation Abstracts International, Volume: 58-06, Section: B, page: 3074. Adviser: V.P. Snaith.

Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, September 2004. / Thesis Advisor(s): Xiaoping Yun. Includes bibliographical references (p. 59-60). Also available online.

D.Ing. / Aerial Vehicle (UAV)-based observation system, by using the principles of strapdown inertial measurement and navigation systems. Effort is concentrated around the mathematical implementation thereof and analysis and proof of the concept in a computer simulation environment. Although the principles of the strapdown system approach to camera-to-target vector estimation are universal to any type of airborne platform that can carry the observation payload, the application thereof is specifically tailored for a UAV system. More specifically, the operational scenario and UAV parameters of a typical close-range UAV system that is used for artillery observation, is used in the derivation of the models and equations. The secondary objective of this research is to derive a realizable mathematical implementation for this strapdown system based camera-to-target vector estimation methodology, by performing a systematic tradeoff between the use of Euler angles and quaternions for describing the camera-to-target vector, and by incorporating the principles of Kalman filtering. This dissertation fully describes the approach that was followed in the derivation of the strapdown system equations for the camera-to-target vector estimation. The mathematical models and principles used are universal for any airborne targeting application with a real-time video down-link. The results as presented in this dissertation, prove that the methodology provides satisfactory results in both a pure digital computer simulation environment, as well as in a digital computer simulation that is hybridized with experimentally determined sensor outputs. It has led to a realizable and workable implementation that could form the basis of practical implementation thereof in operational targeting systems. It further proves that the slant range between a camera and a stationary target on the ground, can be estimated effectively without the use of a laser rangefinder.

This investigation is designed to find quaternion operators which will generate selected space groups and which are more convenient to manipulate in some important types of problems.