Maximum Likelihood Time-Domain Beamforming Using Simulated Annealing

112 Pages·2013·7.56 MB·English

Maximum Likelihood Time-Domain Beamforming
Using Simulated Annealing
by
Kevin Xu
Submitted in partial fulfillment of the
requirements for the degree of
Master of Science in Oceanographic Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
and the ENG'
WOODS HOLE OCEANOGRAPHIC INSTITUTION MAssj
September 1999
@ Kevin Xu, 1999. All Rights Reserved.
L
The author hereby grants to MIT and WHOI permission to repro-
duce and distribute copies of this thesis document in whole or part.
A uthor .................... ..................
Department of Ocean Engineering, MIT
and the MIT-WHOI Joint Program in Oceanographic Engineering
August 22, 1999
Certified by ........ ............
Nicholas C. Makris
Assistant Professor, Massachusetts Institute of Technology
Thesis Supervisor
Acce ted bh
p. y... ..... ....................
Michael S. Triantafyllou
Chairman, Joint Committee for Oceanographic Engineering, Massachusetts
Institute of Technology and Woods Hole Oceanographic Institution
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Maximum Likelihood Time-Domain Beamforming
Using Simulated Annealing
by
Kevin Xu
Submitted to the Department of Ocean Engineering on August 22,
1999, in partial fulfillment of the requirements for the degree of
Master of Science in Oceanographic Engineering
Abstract
An algorithm is developed for underwater acoustic signal processing with an array of
hydrophones. With various acoustic signals coming from different directions, the maxi-
mum likelihood approach is used to estimate the source bearings and time series. Simu-
lated annealing is used to implement the resulting time-domain beamformer. Broadband
signals in spatially correlated noise are treated. Previous time-domain beamformers did
not consider the correlation between random noise, and they did not use the concept of
maximum likelihood, which is asymptotically optimal. We show that improved resolution
can be achieved using this new method.
Thesis Supervisor: Nicholas C. Makris
Title: Assistant Professor, MIT
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Acknowledgements
It is with deep appreciation that I express my thanks to my academic and research advisor, Dr.
Nicholas C. Makris, who with his clear guidance provided me this excellent opportunity and led
me to the completion of the thesis. I also appreciate his support and mentorship during the past
two years, and his encouragement and patience when I struggled and made mistakes. The time,
effort and care which he has taken to shape my research career will be appreciated forever.
I am especially grateful to Mr. Wen Xu for all kinds of help, from courses to research, from
FrameMaker to Matlab.
My thanks also go to the Ocean Acoustics Group graduate students at MIT Room 5-435 and other
friends. They are Yi-San Lai, Vicent Lupien, Peter Daly, Chin-Swee Chia, Brian Sperry, Kyle
Becker, Yanwu Zhang, Yuriy Dudko, Pierre Elisseeff, Dianne Egnor, and Irena Veljkovic.
I would like to thank Ms. Jean Sucharewicz at MIT Ocean Engineering Administration Office,
who assisted me in many ways during this work.
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Contents
1 Introduc tion .............................................................................................................. 13
1.1 Beamforming .............................................................................................. 13
1.2 Time-domain beamforming .......................................................................... 13
1.3 Maximum likelihood and least squares estimation...................14
1.4 Simulated annealing......................................................................................14
1.5 Thesis overview ............................................................................................ 14
2 Problem and Data Model ........................................................................................ 17
2.1 Problem definition ........................................................................................... 17
2.2 Data model and signal model...................................................................... 18
3 Maximum Likelihood Estimation...........................................................................23
3.1 Ocean ambient noise ................................................................................... 23
3.2 Maximum likelihood parameter estimation.....................................................27
3.3 Maximum likelihood time-domain beamforming....................31
4 Fast Simulated Annealing Algorithm ................................................................ 35
4.1 Simulated annealing algorithms....................................................................35
4.2 Fast simulated annealing algorithm ............................................................ 39
5 Simulation Results .............................................................................................. 45
5.1 In spatially correlated Gaussian noise......................................................... 46
5.1.1 The diagonal elements of the covariance matrix are inhomogeneous.......46
5.1.1.1 Source signal is an impulse...............................................................50
5.1.1.2 Source signal is a short pulse ............................................................ 54
5.1.1.3 Source signal is a long pulse.............................................................59
5.1.1.4 Source is a sinusoidal signal ............................................................ 63
5.1.1.4.1 Source is a low frequency sinusoidal signal .............................. 63
5.1.1.4.2 Source is a higher frequency sinusoidal signal..........................67
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5.1.1.4.3 Source is a general broadband signal........................................ 71
5.1.2 The diagonal elements of the covariance matrix are homogeneous .......... 75
5.1.2.1 Source is a broadband signal............................................................. 77
5.1.2.2 Source is m ulti-im pulse ................................................................... 80
5.1.2.3 M ulti-source...................................................................................... 84
5.1.2.3.1 An array of 5 hydrophones is used ............................................. 85
5.1.2.3.2 An array of 25 hydrophones is used ......................................... 90
5.2 Surface generated noise in a w aveguide ...................................................... 98
5.3 In spatially uncorrelated noise ....................................................................... 105
6 Conclusions and Discussions.................................................................................109
6.1 Conclusions....................................................................................................109
6.2 Discussions .................................................................................................... 109
Bibliography ............................................................................................................... 111
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List of Figures
Figure 2.1: Configuration of the array and sources. .................................................. 19
Figure 5.1: The spatially correlated Gaussian noises with different variance ............ 49
Figure 5.2: Plane wave source signal - an impulse.................................................... 50
Figure 5.3: Hydrophone data with an impulse signal ................................................. 51
Figure 5.4: ML E result of the impulse source ............................................................ 51
Figure 5.5: ML E result - Hydrophone data................................................................. 52
Figure 5.6: ML E result of the bearing ....................................................................... 53
Figure 5.7: Energy ..................................................................................................... 53
Figure 5.8: LSE result of the impulse signal............................................................... 54
Figure 5.9: LSE result of the bearing.......................................................................... 55
Figure 5.10: Source is a short pulse ............................................................................ 55
Figure 5.11: Hydrophone data ................................................................................... 56
Figure 5.12: M LE result of the source ........................................................................ 57
Figure 5.13: ML E result of the bearing ..................................................................... 57
Figure 5.14: LSE result of the signal .......................................................................... 58
Figure 5.15: LSE result of the bearing........................................................................ 58
Figure 5.16: LSE Energy ............................................................................................ 59
Figure 5.17: Source is a long pulse............................................................................. 60
Figure 5.18: Hydrophone data ................................................................................... 60
Figure 5.19: M LE result of the source ........................................................................ 61
Figure 5.20: M LE result of the bearing ..................................................................... 61
Figure 5.21: LSE result of the time series.................................................................. 62
Figure 5.22: LSE result of the bearing........................................................................ 63
Figure 5.23: Sinusoidal signal with a low frequency.................................................. 64
Figure 5.24: Hydrophone data when the source is a low frequency sine signal.........64
Figure 5.25: M LE result of the time series ................................................................. 65
Figure 5.26: M LE result of the bearing ..................................................................... 66
Figure 5.27: LSE result of the time series.................................................................. 66
Figure 5.28: LSE result of the bearing........................................................................ 67
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Figure 5.29: Sinusoidal signal with a higher frequency ............................................ 68
Figure 5.30: Hydrophone data when the source is a higher frequency sine signal.........68
Figure 5.31: MLE result of the time series ................................................................. 69
Figure 5.32: MLE result of the bearing ..................................................................... 70
Figure 5.33: LSE result of the time series.................................................................. 70
Figure 5.34: LSE result of the bearing........................................................................71
Figure 5.35: Source is a broadband signal................................................................. 72
Figure 5.36: Hydrophone data when the source is a broadband signal ...................... 72
Figure 5.37: MLE result of the time series ................................................................. 73
Figure 5.38: MLE result of the bearing ..................................................................... 74
Figure 5.39: LSE result of the time series.................................................................. 74
Figure 5.40: LSE result of the bearing........................................................................75
Figure 5.41: The spatially correlated Gaussian noise with same variance ................. 77
Figure 5.42: Hydrophone data when the source is a broadband signal in correlated
n o ise ......................................................................................................... .7 8
Figure 5.43: MLE result of the time series ................................................................. 78
Figure 5.44: MLE result of the bearing ..................................................................... 79
Figure 5.45: LSE result of the time series.................................................................. 79
Figure 5.46: LSE result of the bearing........................................................................80
Figure 5.47: Source is multi-impulse...........................................................................81
Figure 5.48: Hydrophone data when the source is multi-impulse .............................. 81
Figure 5.49: MLE result of the time series ................................................................. 82
Figure 5.50: MLE result of the bearing ...................................................................... 83
Figure 5.51: LSE result of the time series.................................................................. 83
Figure 5.52: LSE result of the bearing........................................................................84
Figure 5.53: Broadband sources ................................................................................. 85
Figure 5.54: Spatially correlated noise (N=5) ............................................................ 86
Figure 5.55: Hydrophone data (N=5) ........................................................................ 87
Figure 5.56: MLE result of the time series (N=5) ..................................................... 88
Figure 5.57: MLE result of the bearings (N=5)..........................................................88
Figure 5.58: LSE result of the time series (N=5)........................................................89
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