Covariance modeling and estimation for distributed parameter systems and their approximations

UnrestrictedIn 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