Stochastic differential equations with application to manifolds and nonlinear filtering
Date
2006-11-03T08:56:08Z
Authors
Rugunanan, Rajesh
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Abstract
This thesis follows a direction of research that deals with the theoretical foundations
of stochastic differential equations on manifolds and a geometric analysis of the
fundamental equations in nonlinear filtering theory. We examine the importance of modern differential geometry in developing an invariant theory of stochastic processes
on manifolds, which allow us to extend current filtering techniques to an important
class of manifolds. Furthermore, these tools provide us with greater insight to the
infinite-dimensional nonlinear filtering problem. In particular, we apply our geometric analysis to the so called unnormalized conditional density approach expounded by M.
Zakai. We exploit the geometric setting to study the geometric and algebraic properties
of the Zakai equation, which is a linear stochastic partial differential equation.
In particular, we investigate the use of Lie algebras and group invariance techniques
for dimension analysis and for the reduction of the Zakai equation. Finally, we utilize simulation to demonstrate the superiority of the Zakai equation over the extended
Kalman filter for a passive radar tracking problem.
Description
Faculty of Science, School of Statistics & Actuarial Science, MSC Dissertation
Keywords
stochastic, nonlinear, filtering