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Acoustic tomography of the atmosphere using iterated unscented Kalman filter




Kolouri, Soheil, author
Azimi-Sadjadi, Mahmood R., advisor
Chong, Edwin K. P., committee member
Cooley, Daniel S., committee member

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Tomography approaches are of great interests because of their non-intrusive nature and their ability to generate a significantly larger amount of data in comparison to the in-situ measurement method. Acoustic tomography is an approach which reconstructs the unknown parameters that affect the propagation of acoustic rays in a field of interest by studying the temporal characteristics of the propagation. Acoustic tomography has been used in several different disciplines such as biomedical imaging, oceanographic studies and atmospheric studies. The focus of this thesis is to study acoustic tomography of the atmosphere in order to reconstruct the temperature and wind velocity fields in the atmospheric surface layer using the travel-times collected from several pairs of transmitter and receiver sensors distributed in the field. Our work consists of three main parts. The first part of this thesis is dedicated to reviewing the existing methods for acoustic tomography of the atmosphere, namely statistical inversion (SI), time dependent statistical inversion (TDSI), simultaneous iterative reconstruction technique (SIRT), and sparse recovery framework. The properties of these methods are then explained extensively and their shortcomings are also mentioned. In the second part of this thesis, a new acoustic tomography method based on Unscented Kalman Filter (UKF) is introduced in order to address some of the shortcomings of the existing methods. Using the UKF, the problem is cast as a state estimation problem in which the temperature and wind velocity fields are the desired states to be reconstructed. The field is discretized into several grids in which the temperature and wind velocity fields are assumed to be constant. Different models, namely random walk, first order 3-D autoregressive (AR) model, and 1-D temporal AR model are used to capture the state evolution in time-space . Given the time of arrival (TOA) equation for acoustic propagation as the observation equation, the temperature and wind velocity fields are then reconstructed using a fixed point iterative UKF. The focus in the third part of this thesis is on generating a meaningful synthetic data for the temperature and wind velocity fields to test the proposed algorithms. A 2-D Fractal Brownian motion (fBm)-based method is used in order to generate realizations of the temperature and wind velocity fields. The synthetic data is generated for 500 subsequent snapshots of wind velocity and temperature field realizations with spatial resolution of one meter and temporal resolution of 12 seconds. Given the location of acoustic sensors the TOA&rsquos are calculated for all the acoustic paths. In addition, white Gaussian noise is added to the calculated TOAs in order to simulate the measurement error. The synthetic data is then used to test the proposed method and the results are compared to those of the TDSI method. This comparison attests to the superiority of the proposed method in terms of accuracy of reconstruction, real-time processing and the ability to track the temporal changes in the data.


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acoustic tomography
unscented Kalman filter
Fractal Brownian motion


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