Thesis
Estimation in linear networks: algebraic and graph-theoretic results
Washington State University
Master of Science (MS), Washington State University
2012
Handle:
https://hdl.handle.net/2376/100402
Abstract
In this thesis, we examine the effect of having multiple observations in the estimation of non–random modes of linear dynamical systems from noisy impulse response data. Specifically, for this estimation problem, we develop an explicit algebraic characterization of the Fisher information matrix and hence Cramer-Rao bound in terms of the eigenvalues and residues of the transfer function, and so develop some simple bounds on the minimum possible error variance for eigenvalue estimates in terms of the eigenvalues’ locations. We focus especially on developing a relationship between the Cramer-Rao bound on pole estimates for the multiobservation case, and those when each single observation is used separately for estimation. We are particularly interested in characterizing mode-estimation performance in linear dynamical network models. For these network models, our aim is to tie estimator performance to the network’s underlying graph structure. Applying structural-decomposition concepts for linear systems allows connection of a network’s graph topology with its system (pole-zero) structure, and hence with estimation performance. Here, we examine the structural decomposition or special coordinate basis (SCB) for a class of canonical network models, in which actuation is provided at one network component and measurements are made at another. Specifically, we develop a non singular transformation that explicitly connects the network’s graph structure (and input/output locations) to its zero structure. Through this particular transformation, we explore the importance of the stimulus-observation location in the relative degree of the system, and the finite zero structure’s dependence on the network’s corresponding weighted undirected graph.
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Details
- Title
- Estimation in linear networks
- Creators
- Jackeline Abad Torres
- Contributors
- Sandip Roy (Degree Supervisor)
- Awarding Institution
- Washington State University
- Academic Unit
- Electrical Engineering and Computer Science, School of
- Theses and Dissertations
- Master of Science (MS), Washington State University
- Publisher
- Washington State University; Pullman, Wash. :
- Identifiers
- 99900525400901842
- Language
- English
- Resource Type
- Thesis