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Dissertation/Thesis Abstract

Chaos, Observability and Symplectic Structure in Optimal Estimation
by Rey, Daniel, Ph.D., University of California, San Diego, 2017, 185; 10281245
Abstract (Summary)

Observation, estimation and prediction are universal challenges that become especially difficult when the system under consideration is dynamical and chaotic. Chaos injects dynamical noise into the estimation process that must be suppressed to satisfy the necessary conditions for success: namely, synchronization of the estimate and the observed data. The ability to control the growth of errors is constrained by the spatiotemporal resolution of the observations, and often exhibits critical thresholds below which the probability of success becomes effectively zero. This thesis examines the connections between these limits and basic issues of complexity, conditioning, and instability in the observation and forecast models. The results suggest several new ideas to improve the collaborative design of combined observation, analysis, and forecast systems. Among these, the most notable is perhaps the fundamental role that symplectic structure plays in the remarkable observational efficiency of Kalman-based estimation methods.

Indexing (document details)
Advisor: Abarbanel, Henry DI
Commitee: Arovas, Daniel, Gill, Philip, Holst, Michael, Leok, Melvin, Paturi, Ramamohan
School: University of California, San Diego
Department: Physics
School Location: United States -- California
Source: DAI-B 79/01(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Biophysics, Computer science
Keywords: Chaos, Data assimilation, Kalman filter, Observability, Optimal estimation, Symplectic structure
Publication Number: 10281245
ISBN: 978-0-355-31365-9
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