Date of Award

Fall 2013

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

Eliza Zoi-Heleni Michalopoulou

Second Advisor

Ali Abdi

Third Advisor

Sunil Kumar Dhar

Fourth Advisor

David James Horntrop

Fifth Advisor

Jonathan H.C. Luke

Abstract

Acoustic signals propagating in the ocean carry information about geometry and environmental parameters within the propagation medium. Accurately retrieving this information leads us to effectively estimate parameters that are of utmost importance in environmental studies, climate monitoring, and defense. This dissertation focuses on the development of sequential Bayesian filtering methods to obtain accurate esti­mates of instantaneous frequencies using Short Term Fourier Transforms within the acoustic field measured at an array of hydrophones, which can be used in a subsequent step for the estimation of propagation related parameters. We develop a particle filter to estimate these frequencies along with modal amplitudes, variance, model order. In the first part of our work, we consider a Gaussian model for the error in the data measurements, which has been the standard approach in instantaneous frequency estimation to date. We here design a filter that identifies the true structure of the data errors and implement a χ2 model to capture this structure appropriately. We demonstrate both with synthetic and real data that our approach is superior to the conventional method, especially for low Signal-to-Noise-Ratios.

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Mathematics Commons

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