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COVARIANCE MODELING AND ESTIMATION FOR
DISTRIBUTED PARAMETER SYSTEMS AND THEIR
APPROXIMATIONS
by
Yan Yang
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
December 2008
Copyright 2008 Yan Yang
Object Description
| Title | Covariance modeling and estimation for distributed parameter systems and their approximations |
| Author | Yang, Yan |
| Author email | yanyang@usc.edu; yanyang@live.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Applied Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2008-09-03 |
| Date submitted | 2008 |
| Restricted until | Unrestricted |
| Date published | 2008-12-04 |
| Advisor (committee chair) | Wang, Chunming |
| Advisor (committee member) |
Rosen, Gary Levi, Anthony F. J. |
| Abstract | In this dissertation, we first established a mathematical framework for approximation of a filtering problem for infinite dimensional systems with random state. Particularly we defined random states for infinite dimension systems. We also established statistical property of finite dimensional approximations and gave a rigorous treatment for the contributions of error in the observation due to approximation. Numerical simulations were performed to validate the results. Secondly, a type of Bayesian approach was developed to select the most appropriate covariance matrix among a finite number of candidates. Monte carlo simulations were conducted to validate this approach. Finally, we applied the results to 3-D estimation problem for plasmasphere electron density. |
| Keyword | random state; representation error; covariance matrix; Bayesian; plasmasphere; 3-D tomography |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m1865 |
| Contributing entity | University of Southern California |
| Rights | Yang, Yan |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Yang-2377 |
| Archival file | uscthesesreloadpub_Volume32/etd-Yang-2377.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Full text | COVARIANCE MODELING AND ESTIMATION FOR DISTRIBUTED PARAMETER SYSTEMS AND THEIR APPROXIMATIONS by Yan Yang A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) December 2008 Copyright 2008 Yan Yang |
