Bradley Ebinger

Date Approved

9-10-2015

Embargo Period

3-3-2020

Document Type

Thesis

Degree Name

M.S. Electrical and Computer Engineering

Department

Electrical and Computer Engineering

College

Henry M. Rowan College of Engineering

Advisor

Bouaynaya, Nidhal

Subject(s)

Electroencephalography; State-space methods

Disciplines

Electrical and Computer Engineering

Abstract

Particle Filters (PFs) have a unique ability to perform asymptotically optimal estimation for non-linear and non-Gaussian state-space models. However, the numerical nature of PFs cause them to have major weakness in two important areas: (1) handling constraints on the state, and (2) dealing with high-dimensional states. In the first area, handling constraints within the PF framework is crucial in dynamical systems, which are often required to satisfy constraints that arise from basic physical laws or other considerations. The current trend in constrained particle filtering is to enforce the constraints on all particles of the PF. We show that this approach leads to more stringent conditions on the posterior density that can cause incorrect state estimates. We subsequently describe a novel algorithm that restricts the mean estimate without restricting the posterior pdf, thus providing a more accurate state estimate. In the second area, we tackle the "curse of dimensionality," which causes the PF to require an exponential increase in computational complexity as the dimension of the state increases. The application of interest is localization of the brain neural generators that create the Electroencephalogram (EEG) signal. Specifically, we describe a state-space model that tracks the position and moments of multiple dynamic dipoles and apply the marginalized PF, which alleviates the "curse of dimensionality" for tracking multiple dynamic dipoles. This modified framework allows us to consider dynamic dipoles, which were historically considered time-invariant.

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