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This thesis is concerned with measuring and predicting the performance and effectiveness of a data fusion process. Its central proposition is that information entropy may be used to quantify concisely the effectiveness of the process. The personal and original contribution to that subject which is contained in this thesis is summarised as follows: The mixture of performance behaviours that occur in a data fusion system are described and modelled as the states of an ergodic Markov process. An new analytic approach to combining the entropy of discrete and continuous information is defined. A new simple and accurate model of data association performance is proposed. A new model is proposed for the propagation of information entropy in an minimum mean square combination of track estimates. A new model is proposed for the propagation of the information entropy of object classification belief as new observations are incorporated in a recursive Bayesian classifier. A new model to quantify the information entropy of the penalty of ignorance is proposed. New formulations of the steady state solution of the matrix Riccati equation to model tracker performance are proposed.

The asymptotic properties of discrete time stochastic systems operating under feedback is addressed. It is assumed that a Markov chain $ Phi$ evolving on Euclidean space exists, and that the input and output processes appear as functions of $ Phi$. The main objectives of the thesis are (i) to extend various asymptotic properties of Markov chains to hold for arbitrary initial distributions; and (ii) to develop a robustness theory for Markovian systems. / A condition called local stochastic controllability, a generalization of the concept of controllability from linear system theory, is introduced and is shown to be sufficient to ensure that the first objective is met. The second objective is explored by introducing a notion of convergence for stochastic systems and investigating the behavior of the invariant probabilities corresponding to a convergent sequence of stochastic systems. / These general results are applied to two previously unsolved problems: The asymptotic behavior of linear state space systems operating under nonlinear feedback, and the stability and asymptotic behavior of a class of random parameter AR (p) stochastic systems under optimal control.

The Hamiltonian cycle problem (HCP) can be succinctly stated as: "Given a graph, find a cycle that passes through every single vertex exactly once, or determine that this cannot be achieved". Such a cycle is called a Hamiltonian cycle. The HCP is a special case of the better known Travelling salesman problem, both of which are computationally difficult to solve. An efficient solution to the HCP would help solving the TSP effectively, and therefore would have a great impact in various fields such as computer science and operations research. In this thesis, we obtain novel theoretical results that approach this discrete, deterministic, problem using tools from stochastic processes, matrix analysis, and graph theory. / PhD Doctorate

Project report (M.S.)--Virginia Polytechnic Institute and State University, 1990. / Abstract. Includes bibliographical references (leaves 99-100). Also available via the Internet.

Thesis (Ph.D.) -- University of Adelaide, Dept. of Statistics, 1978.

Thesis (Ph. D.)--Duke University, 2007.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 89-93). Also available via the Internet.

Thesis (m.s.)--University of Kentucky, 2004. / Title from document title page (viewed Jan. 5, 2005). Document formatted into pages; contains vii, 32p. : ill. Includes abstract and vita. Includes bibliographical references (p. 30-31).