Robust sequential Monte-Carlo estimation methods

Seymen, Niyazi Burak
This thesis addresses the robust system modeling, analysis and state estimation problem for uncertain systems. In the first part of the thesis, polynomial chaos based system representations and some of their important properties such as stability and controllability are studied. A novel relation between the the eigenvalues of the affine uncertain system matrix and the eigenvalues of the polynomial chaos (PC) transformed system is derived. A necessary and sufficient condition that relates stability of the PC transformed system to the original uncertain system is also obtained as a corollary. A necessary condition for the stability of the more general PC transformed systems is obtained in terms of the one-norm matrix measure identity. Furthermore, some necessary conditions for the controllability are obtained. A set-valued estimation problem and its solution for the state estimation of PC transformed system is proposed. The performances of the proposed estimation technique and a technique proposed in literature including an ad-hoc measurement model are evaluated by three framework examples that are used in literature. An observability analysis is also performed for these models. In the second part of the thesis, an extended and robust particle filtering methods are proposed to the solution of the robust nonlinear estimation problem for uncertain systems with cumulative relative entropy constraint. Additionally, robust estimation problem for instantaneous type relative entropy constraint is studied by referring the recent results in literature. Some numerical solutions are proposed for the related problems utilizing particle filtering and unscented Kalman filtering.
Citation Formats
N. B. Seymen, “Robust sequential Monte-Carlo estimation methods,” Ph.D. - Doctoral Program, Middle East Technical University, 2013.