Date of Award

3-2007

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Electrical and Computer Engineering

First Advisor

Peter S. Maybeck, PhD

Abstract

Kalman filtering and multiple model adaptive estimation (MMAE) methods have been applied by researchers in several engineering disciplines to a multitude of problems featuring a linear (or mildly nonlinear) model based on finite-dimensional differential (or difference) equations perturbed by random inputs. However, many real-world systems are more naturally modeled using an infinite-dimensional continuous-time linear systems model, such as those most naturally modeled as partial differential equations or time-delayed differential equations along with a possibly infinite-dimensional measurement model. The Kalman filtering technique was extended to encompass infinite-dimensional continuous-time systems with sampled-data measurements and a technique to approximate an infinite-dimensional continuous-time system model with an essentially equivalent finite-dimensional discrete-time model upon which a filtering algorithm could be based was developed. The tools developed during this research were demonstrated using an estimation problem based on a stochastic partial differential equation with an unknown noise environment.

AFIT Designator

AFIT-DS-ENG-07-08

DTIC Accession Number

ADA464767

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