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Sensing with sound: acoustic tomography and underwater sensor networks

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Sensing with sound: acoustic tomography and underwater sensor networks

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Content SENSING WITH SOUND:
ACOUSTIC TOMOGRAPHY AND UNDERWATER SENSOR NETWORKS
by
Andrew P. Goodney
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(COMPUTER SCIENCE)
May 2015
Copyright 2015 Andrew P. Goodney
Acknowledgments
An advisor once warned me about how much of a solo endeavor earning a PhD could
be. And while the body of work presented in this dissertation was indeed the result of
countless hours alone, I could not have completed it without the support of a multitude
of people along the way. Those mentioned below are surely not an exhaustive list, but
do represent friends, family, colleagues and collaborators that made significant contri-
butions in some way that helped me reach the finish line. Thank you.
Faculty and staff at USC and ISI
Terry Benzel, Matthew Binkley, Michael Crowley, Lizsl De Leon, Michael Elkins,
Ted Faber, Shahram Ghandeharizadeh, John Heidemann, John Hickey, Joe Kemp, Erik
Kline, Sameera Poduri, Alba Regalado-Palacios, Steve Schrader, Joe Touch, John Wro-
clawski, Jeanine Yamazaki
Chevron and CiSoft
Brian Batiste, Iraj Ershaghi, Gregory LaFramboise, Juli Legat, Lanre Olabinjo, Ken
Porche, Brian Thigpen, Charlie Webb
ii
Fellow USC graduate students
Vivek Bhandwalkar, Siddharth Bhargav, Dirk Hovy, Ritu Jain, Kunal Joshi, Jinho
Jung, Shawn Kailath, Philippe Kassouf, Saurabh Kumar, Charisse L’Pree, Adam Lam-
mert, Emily Mower, Shailesh Narayan, Scott Needham, Devang Negandhi, Rishvanth
Prabakar, Lin Quan, Akshay Ravi, Marta Recasens, Mahyar Salek, Shahin Shayandeh,
Mark Shirley, Affan Syed, Chengjie Zhang, Kaidi Zhou
Members of my qualification and defense committees
Pedro Diniz, Bhaskar Krishnamachari, Jelena Mirkovic, Antonio Ortega, Paul Rosen-
bloom, Shanghua Teng
My advisor
Young H. Cho
Friends and family
Jonathan Chikhale, Cece Chikhale, Ben Coates, Susan Goodney, David Goodney,
Kalindi Lake, Jim Lake, Abby Phoenix, Evan Phoenix, Biren Shah, Alison Stoner, Jane
Stoner, Todd Ulman, Angela Ulman
Dedicated to
Ashley, Margaret and William
iii
Funding
Portions of this work were funded by grants from the NSF. CNS-0821750, “MRI: Develop-
ment of an Always-Available Testbed for Underwater Networking Research” and CNS-0708946,
“Open Research Testbed for Underwater Ad Hoc and Sensor Networks”. Additional funding
provided by a grant under the USC Viterbi School of Engineering Research Innovation Fund,
Spring 2011.
iv
Contents
Acknowledgments ii
List of Tables viii
List of Figures ix
Chapter 1 Introduction 1
Chapter 2 An Overview of Related Work 9
2.1 Travel Time Tomography Techniques . . . . . . . . . . . . . . . . . . . 9
2.1.1 Ocean Acoustic Tomography . . . . . . . . . . . . . . . . . . . 9
2.1.2 Atmospheric Acoustic Tomography . . . . . . . . . . . . . . . 12
2.2 Underwater Acoustics: Sensing, Ranging, and Communications . . . . 15
2.2.1 Underwater Sensor Networks . . . . . . . . . . . . . . . . . . . 15
2.2.2 Underwater Ranging Systems . . . . . . . . . . . . . . . . . . 19
2.2.3 Robotic Temperature Sampling . . . . . . . . . . . . . . . . . . 19
2.2.4 Acoustic Ranging for Sensor Networks . . . . . . . . . . . . . 20
Chapter 3 Sensor Network Acoustic Tomography 21
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 Underwater Acoustic Sensor Node . . . . . . . . . . . . . . . . 23
3.2.2 Precise Timing . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Microtomography Simulator . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
v
3.3.2 Simulator Features . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Multi-Node Tomography Simulation . . . . . . . . . . . . . . . . . . . 32
3.4.1 Weighted Linear System . . . . . . . . . . . . . . . . . . . . . 33
3.4.2 Radial Basis Functions . . . . . . . . . . . . . . . . . . . . . . 35
3.5 Underwater Time-of-Flight Experiments . . . . . . . . . . . . . . . . . 36
3.5.1 Time-of-Flight using GPS time synchronization . . . . . . . . . 37
3.5.2 Time-of-Flight without time synchronization . . . . . . . . . . 39
3.5.3 5 Node Tomography . . . . . . . . . . . . . . . . . . . . . . . 40
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Chapter 4 Combined Data and Sensing Using Long Pseudo Noise Codes 42
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2 Signal Design for Simultaneous Data and Sensing Transmissions . . . . 43
4.2.1 Existing Methods . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.2 Overcoming Noise in the Underwater Channel . . . . . . . . . . 45
4.2.3 Medium Access Control . . . . . . . . . . . . . . . . . . . . . 46
4.2.4 Simultaneous Data and Sensing . . . . . . . . . . . . . . . . . 47
4.3 System Design Summary . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.4 System Verification Experiment . . . . . . . . . . . . . . . . . . . . . . 50
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Chapter 5 Multipulse Acoustic Tomography 53
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Multipulse Acoustic Tomography . . . . . . . . . . . . . . . . . . . . . 56
5.2.1 System Description . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . 57
5.2.3 Extension to an arbitrary number of segments . . . . . . . . . . 60
5.2.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2.5 1D Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2.6 2D Simulation and Reconstruction . . . . . . . . . . . . . . . . 63
5.2.7 Design Constraints . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2.8 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
vi
Chapter 6 Extending Multipulse Tomography to Other Domains 72
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.2 Multipulse Tomography for Atmospheric Temperature Monitoring . . . 72
6.3 Multipulse Tomography for Temperature Monitoring of Electrical Power
Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
References 76
Appendix A Calculating Sub-Sample Arrival Times for High Precision
Time-of-Flight 83
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
A.2 Detecting Arrival Time With Cross-correlation . . . . . . . . . . . . . . 84
A.3 Sampling Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
A.4 Signal Processing Details . . . . . . . . . . . . . . . . . . . . . . . . . 86
A.5 In-air Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
A.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Appendix B Construction of
Guohua and Quan Sequences 90
vii
List of Tables
3.1 Parameters and equation for the MacKenzie approximation for speed of
sound in sea water as a function of temperature (T ), salinity (S) and
depth (z) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 System of Equations for 5 Node Tomography . . . . . . . . . . . . . . 34
viii
List of Figures
3.1 Underwater Acoustic Sensor Node . . . . . . . . . . . . . . . . . . . . 24
3.2 Precise Timing using PPS . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Precise Timing without time synchronization . . . . . . . . . . . . . . . 28
3.4 Marina Del Rey Testbed . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5 SeaSim Ocean Acoustics Research Simulator GUI . . . . . . . . . . . . 30
3.6 Five Node Tomography Simulation . . . . . . . . . . . . . . . . . . . . 33
3.7 Radial Basis Function Tomography Simulation with 16 Nodes . . . . . 35
3.8 GPS Time of Flight Experiment . . . . . . . . . . . . . . . . . . . . . 38
3.9 Time of Flight Experiment . . . . . . . . . . . . . . . . . . . . . . . . 39
3.10 2D Tomography Reconstruction . . . . . . . . . . . . . . . . . . . . . 40
4.1 Block diagram of FSK Receive Chain . . . . . . . . . . . . . . . . . . 43
4.2 Ideal ACF of ‘Guohua and Quan’ pseudo noise sequence . . . . . . . . 44
4.3 Received Audio Signal . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.4 Ideal CCF of ‘Guohua and Quan’ pseudo noise sequence . . . . . . . . 47
4.5 Coding System Design Overview . . . . . . . . . . . . . . . . . . . . . 49
4.6 Received Audio Channel at Node A . . . . . . . . . . . . . . . . . . . 50
4.7 Detection of ‘q1’ at Node A . . . . . . . . . . . . . . . . . . . . . . . . 51
4.8 Detection of ‘q3’ at Node A . . . . . . . . . . . . . . . . . . . . . . . . 51
5.1 Two sender/receiver nodes . . . . . . . . . . . . . . . . . . . . . . . . 57
ix
5.2 Multipuse tomography with four segments . . . . . . . . . . . . . . . . 58
5.3 1D simulation of multipulse acoustic tomography with four segments . . 62
5.4 Schematic layout of six node 2D simulation . . . . . . . . . . . . . . . 63
5.5 2D Simulation - Target . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.6 2D Simulation - Least-squares . . . . . . . . . . . . . . . . . . . . . . 65
5.7 2D Simulation - Multipulse . . . . . . . . . . . . . . . . . . . . . . . . 66
A.1 Sampled Sine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
A.2 Sample sine with different sample offsets . . . . . . . . . . . . . . . . 86
A.3 Signal Processing Block Diagram . . . . . . . . . . . . . . . . . . . . . 87
A.4 Experiment block diagram . . . . . . . . . . . . . . . . . . . . . . . . 88
A.5 Experiment results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
x
Chapter 1
Introduction
The term tomography is a widely used in science and engineering to describe sensing
techniques that allow for the study of an object or area by placing sensors around the
object or at the periphery of the area. ‘Tomo’ means ‘to cut (through)’ and thus tomog-
raphy means to map by cutting through an object or medium of interest. The basic
principal shared by all tomography systems is that transmission of a signal (here the
term ‘signal’ is used very generically) through a medium alters the signal in some way
such that information about the medium is carried along with the signal. Analysis of the
received signals allows for this information to be recovered and mapped (typically spa-
tially in a 2D or 3D sense). Tomography is applied in medicine with various techniques
taking advantage of the transmission properties of X-rays or ultrasonic sound through
the body to study the health of the tissues. Geologists use tomography techniques to
learn about the subterranean structure of the Earth (useful for studying earthquakes or
performing oil exploration). Tomography is even performed on the Sun by exploiting
the way a solar event on one side of the Sun sends vibrations and magnetic shock waves
through the star where they can be observed reaching the other side.
The tomography techniques discussed in this dissertation fall into the ‘travel-time’
subclass of tomography techniques. Travel time tomography techniques exploit changes
in the speed of a signal traveling through a medium as the information modulating
characteristic. For example, in many mediums (air, water, rocks, etc.) the speed of
an acoustic signal depends on a property of the medium e.g. temperature for air and
1
water and density for rock. It is obvious that the average speed of the signal in such a
medium can be found by dividing the distance travelled by the travel-time. If a number
of sender-receiver pairs are arranged around a region of interest, the set of pair-wise
travel times can be used algorithmically to model or to reconstruct the signal-speed field
inside the region. Travel-time tomography systems are used at various scales from atmo-
spheric and geological distances measured in kilometers to non-invasive evaluation of
tree trunks with distances measured at less than one meter.
The inspiration for this dissertation is a travel time tomography technique known
as ocean acoustic tomography. With typical sender-receiver distances measured in the
100’s if not 1000’s of kilometers, the technique has traditionally been used for large scale
oceanographic experiments wherein the distribution of water temperature and current
flows is studied. As discussed later in this introduction, one goal of this dissertation is to
reduce by two to three orders of magnitude the distance between sender-receiver pairs in
ocean acoustic tomography systems. First proposed by Munk et al circa 1980 [37], the
technique aims to model the speed-of-sound field in the ocean. As the speed of sound in
water is predominately a function of temperature, depth and current, the speed-of-sound
field can be used to learn about the distribution of temperature and current flow in the
oceans. Several successful, large scale ocean acoustic tomography experiments have
been carried out and have shown that the technique can yield interesting data about the
temperature variations found in the Earths oceans.
Ocean acoustic tomography techniques have two clear advantages when compared to
systems that can only make measurements at the location of the sensor platforms. First,
stand-alone measurement systems must place sensors at the locations of interest. Doing
so can be difficult if the area is large or generally inhospitable to buoys or other fixed
platforms. Ocean acoustic tomography deployments place the sensors at the periphery,
2
and thus the sensor platforms can be located near shore or out of the way of marine
traffic. Second for a given number (N) of sensor platforms (if each acts as a sender-
receiver), then tomography systems can yield up to approximatelyN
2
measurements.
The work for this PhD dissertation was performed at a time when it became a widely
accepted scientific fact that human behavior is causing climate change on a global scale.
In light of this context, we noted that scientists must study bodies of water of various
size (not just large scale) to monitor the effects of ecological change on the plants and
animals living in these waters. In order for such studies to be impactful, new technolo-
gies are required so that ocean monitoring experiments return accurate, high resolution
data. In addition, the industrial exploitation of marine environments for commercial
purposes (e.g. farming, oil and gas extraction, mining) is also increasing as technology
makes profitable processes that were once impractical, and as such, systems for small
scale ocean monitoring are needed both to facilitate new exploration and as a check on
harm caused by industrial accidents and malfeasance.
For many such experiments the size of the body of water under study might be
measured in kilometers or even meters (e.g lakes, bays, coastal channels). In the context
of ocean acoustic tomography this implies sender-reciever distances on the order of a
kilometer. For the purposes of this dissertation we consider water sensing data collected
at kilometer scale to be high resolution. We can illustrate the motivation for our research
by examples from three areas: industry, defense and ecology.
The oil and gas industry operates numerous off-shore platforms and pipelines.
The environmental and monetary costs from an accident are extremely large. High-
resolution water temperature sensing could increase situational awareness around under-
water wells and pipelines by detecting leaks or other anomalies that might change the
3
water temperature in subtle ways. Such early detection could be the difference between
a safe shutdown and a Deepwater Horizon type accident.
For defense purposes submarine detection and monitoring is an obvious applica-
tion that now requires high-resolution water temperature sensing. With the advent of
extremely quiet ‘Shark’ class submarines and materials with negative index of refrac-
tion for sound waves, both passive and active SONAR will soon be insufficient to detect
submarine activity. However, submarines must heat up the water around them, and
therefore leave a heat signature that could be detected by an underwater temperature
sensing system with sufficient precision.
Ecologically, the risks to fisheries from global warming is dire. For example,
research has shown that the health of coral reefs greatly impacts the surrounding fish-
eries [26]. In a similar way, the health of salmon fisheries in Alaska has been impacted in
a devastating way with rising water temperatures. The formation and evolution of harm-
ful algal blooms touched off by the upwelling of nutrient rich cool water is another area
where the health of the marine environment is impacted by water temperature. Keeping
track of water temperature changes at high resolution will give marine biologists and
other scientists a deeper understanding of the dynamic processes that lead to harmful
conditions in the underwater environment.
There are many approaches to solving the problem of high-resolution underwater
temperature sensing, for example cabled buoys and ocean floor mounted monitoring
stations can be used. However, the cost of connecting such equipment with power and
networking cables is prohibitively large for many applications. Robotic boats and AUVs
may also work for some applications, however by their nature they sample only at their
current location and thus might miss dynamic temperature events that occur nearby, but
4
not at their current location. Acquisition, maintenance and deployment costs for robots
and AUVs are also quite high.
The fact oceanographic studies must be done at different scales presents an opportu-
nity for computer scientists to contribute to solving problems in underwater sensing by
using sensor networks. A sensor network is a network of computers that are deployed
to perform a distributed sensing task. A key feature of sensor networks that ties into our
oceanographic monitoring problem is that sensor networks are typically deployed with
the distance between nodes measured at less than one kilometer.
Sensor networks are made up of low cost nodes distributed spatially about an area
used primarily for environmental monitoring. Research in this area has shown that by
aggregating observations across time and space, sensor networks often yield data of
equal or higher quality as compared to single expensive sensor platforms. Underwater
sensor networks therefore provide an opportunity to achieve high-resolution temperature
sensing by distributing a number of low cost sensor nodes around the body of water
under study.
In this dissertation we thus assume that we will be building an underwater sensor
network from a set of spatially distributed nodes connected by a network. Further we
assume that the nodes will have local sensing capabilities (e.g. temperature, salinity,
dissolved gasses, etc.) that depend on the specific application and will need to relay this
data to an uplink node for delivery to a monitoring and logging facility. Because of the
favorable propagation properties of acoustic signals underwater (as compared to RF or
optical signals), underwater communication networks are typically build with acoustic
transducers.
Deploying a sensor network with spatially distributed nodes as depicted obviously
increases the spatial sensing resolution as compared to a single sensor, however there
5
is always a practical limit to the number of sensors that can be deployed. Thus we ask
the following question which motivates the rest of this dissertation: using the acoustic
communications facility of an underwater sensor network, can we increase the spatial
sensing resolution of an underwater sensor network by learning something about the
water temperature in-between nodes?
In this dissertation we turn to ocean acoustic tomography as the answer to this ques-
tion. With nodes situated in and around a body of water, we say that ocean acoustic
tomography is a natural application for underwater sensor networks. Adapting ocean
acoustic tomography to underwater sensor networks is not simply a straight forward
task. Building an underwater sensor network required us to overcome several challeng-
ing implementation questions.
With large scale ocean acoustic tomography the time of flight for a signal is mea-
sured in seconds (if not minutes) with changes in time-of-flight caused by temperature
changes on the order of milliseconds. Measuring times-of-flight with sufficient accu-
racy and precision to perform large scale acoustic tomography is not difficult, however
with inter-node distances on the order of 1 kilometer (and thus times-of-flight measured
in milliseconds and changes due to temperature measured in microseconds) perform-
ing acoustic topography with a sensor network presents significant challenges related
to accurately and precisely measuring acoustic time-of-flight, we can not assume that
a technique exists that will provide time-of-flight measurements that are 3 to 4 orders
of magnitude more precise that what is required for ocean acoustic tomography. Chap-
ter 3 provides the details of our first contribution: a time-of-flight measurement system
and experiments that show high-resolution water temperature sensing is possible by per-
forming acoustic tomography with an underwater sensor network.
6
Additionally, the underwater environment is extremely energy constrained, espe-
cially deep underwater where sunlight does not reach. Batteries are the most common
form of energy storage due to the lack of sources for energy harvesting. When build-
ing underwater wireless sensor networks operating efficiently is extremely important.
Conversely, acoustic communications underwater is very expensive power-wise. Trans-
missions are on the order of 10’s of Watts. In our underwater sensor network we assume
that the sensor nodes have data that needs to be relayed across the network. We observe
then that it is wasteful to have an acoustic signal for performing acoustic tomography
and a signal for data transmissions. Ideally, we would be able to use the data trans-
missions for acoustic tomography as well. However, there are several reasons why the
typical underwater data transmission signals are not suitable for acoustic tomography.
Chapter 4 details our second contribution which is a coding technique and transmission
scheme that allows for simultaneous data transmissions and acoustic tomography.
These two chapters present the first real-world sensor network acoustic tomography
results to appear in the literature (originally published in [24, 25]). In common with
all travel-time tomography systems prior to this dissertation, the travel time for a signal
is taken as a single data point: the spatial average over the path between sender and
receiver. Doing so limits the spatial resolution of an acoustic tomography system, as the
resolution is dependent on the number of nodes and their placement. This observation
led us to ask whether there is a way to derive some information about the spatial dis-
tribution of temperatures along the path between a single sender-receiver pair. If this is
possible, the information could be used to increase the spatial resolution and accuracy
of tomographic reconstructions.
7
This brings us to multi-pulse tomography, the third and primary contribution of this
dissertation (chapter 5). Multi-pulse tomography is a new travel time tomography tech-
nique that sends multiple bi-directional signals (‘pulses’) back-to-back such that several
are in flight between a sender and receiver at the same time. We show that under a
reasonable set of constraints, the travel-time information contained in the pulses can be
used to derive the spatial distribution of water temperature changes along the path. With
this system we show how the spatial resolution of a single sender-receiver path depends
not on the node spacing, but on the precision to which time-of-flight can be measured.
This allows for reconstructions to take place in the absence of priori assumptions about
the spatial distribution of temperatures in the area of water under study. In the overall
context of this dissertation we introduce the technique for sensor network ocean acoustic
tomography, however we also discuss how the technique is general and can be applied
to any travel tomography technique and we propose several interesting applications that
warrant future work.
8
Chapter 2
An Overview of Related Work
2.1 Travel Time Tomography Techniques
Of use for many scientific and practical domains, travel time tomography techniques
are found where the speed of a signal through a region or material of interest depends
on some property of the material. The speed of seismic waves depends on the density
of rock and thus travel time tomography techniques are used in geology and oil/gas
exploration to model the subterranean structure of the earth [41]. On a much smaller
scale, but using the same property, travel time tomography is used to study the structural
integrity of priceless statues [10] and potentially dangerous trees [2]. Solar observations
have been used to perform travel time tomography of the Sun as solar events on the
surface cause acoustic waves to travel through the star where the time it takes the waves
to travel to other parts of the star can be measured [34]. However, of most relevance to
the topic of this paper are travel time acoustic tomography techniques used to study the
oceans and the atmosphere.
2.1.1 Ocean Acoustic Tomography
The technology from which we derive our inspiration is ocean acoustic tomography.
First proposed by Munk and Wunsch in 1978 [37] as a large scale (1000’s of km) ocean
monitoring technique, ocean acoustic tomography relies on the principal that the speed
of sound in water is proportional to the temperature and salinity of the water as well as
9
being affected by the currents. By measuring the time-of-flight required for an acous-
tic signal to travel between sender and one or more receivers, the average temperature
along the path can be measured. If there are multiple sender and receiver pairs, tomo-
graphic inversion techniques can be used to reconstruct the 2D or 3D field bounded by
the senders and receivers.
Ocean acoustic tomography techniques can be divided into two classes: vertical
slice or horizontal slice. Vertical slice techniques aim to reconstruct or model over some
area the sound-speed profile of the water as it varies by depth. Vertical slice techniques
use the time delay between multi path arrivals of the same signal to model the depth
dependent sound speed profile. Horizontal slice techniques aim to reconstruct or model
the sound speed-profile as it varies over the area at constant depth. Deployments and
demonstrations of both types of technique have been performed at various scales since
ocean acoustic tomography was first proposed by Munk. Large scale experiments have
been performed across the Pacific Basin, while other experiments have been performed
at medium scale in the Atlantic Ocean, Mediterranean Sea and else where. At the small
scale, costal experiments have been performed near shore, while our work with sensor
network acoustic tomography has shown the technique at the sub-kilometer scale.
A good review of several experiments across the Norway Sea and Mediterranean
Sea is in [12] while for the Mid-Atlantic Ocean see[59]. In the very large scale a vari-
ation on ocean acoustic tomography was performed over the North Pacific Ocean [17].
These experiments validated the technique and showed that it is possible to perform
tomography in the ocean using acoustics.
While based on the same principal there are several key differences between the
techniques we have introduced of the course of the research perfumed for this thesis
and ocean scale acoustic tomography. At ocean scales, sound travels in multiple paths
10
(‘rays’) between sender and receivers. This is caused by the bending of sound due to
the speed of sound changing with depth and temperature. Since the rays are of dif-
ferent length, multiple signal arrivals are expected at a receiver, which allow for the
tomographic inversion to infer data about the ocean at different depths. With sensor net-
work acoustic tomography the distances are such that we can assume the sound travels
directly over the shortest path. Making this assumption also allows for simpler inversion
algorithms.
We are able to simplify the tomographic inversions because at distances of less
than 5 km we can assume that sound is taking a direct path between transmitter and
receiver[45]. On the other hand we must develop a highly precise time-of-flight mea-
surement system because the travel time for an acoustic signal at short distances is mea-
sured on the order of 10’s of milliseconds with changes due to temperature on the order
of 10’s to 100’s of microseconds. Therefore, developing a timing system with sufficient
accuracy and precision is a major contribution of this work.
Although monitoring large scale changes are essential for conducting high impact
ecological research, studies often use data collected on a smaller scale to extrapolate and
justify their large scale conclusions. For example, in a highly cited work by Graham and
Wilson et al. [26] on ecological responses to climate change, the authors support their
thesis by showing the migration of schools of fish and plankton. The study was based
on data which was manually collected over a long period of time.
There is clear motivation for studying underwater environments of much smaller
scale and we are not the first to turn to tomography. Most similar to our work, Yamoaka
et al. have devised and deployed an acoustic tomography system for costal waters [62].
Their system is designed to detect the current flows in a turbulent costal environment.
Their experiment is conducted in such a way as to negate temperature variances, and
11
thus by starting with a model of ideal (current-less) sound propagation they can detect
currents by changes in time-of-flight.
Also similar to our system, D’Antona proposed a system [15, 16] to perform acoustic
tomography in lakes. However, it does not appear any further work towards implemen-
tation and experimentation was performed. A GPS based system similar to our work
first published in [22] was used in the UNCAT test of 2011 [29] to map currents near
the Sizihwan Bay in Kaohsiung, Taiwan.
2.1.2 Atmospheric Acoustic Tomography
As the speed of sound in air varies with temperature and wind speed, travel time acoustic
tomography techniques for the atmosphere have also been developed. As early as 1955
investigations into the propagation properties of the pressure waves caused by artillery
shell burst were carried out to see how temperature and winds effected the sound propa-
gation [49]. More recently, Ziemann et al. [64] proposed and carried out experiments to
evaluate the feasibility of performing acoustic tomography in the atmosphere at the scale
of 200 m. In [43] Osashev provides a good overview of the topic, while Jovanovi´ c [31]
discusses travel time tomography techniques for reconstructing a combined scalar and
vector field, with the application to air temperature and wind speed. Several real-world
experiments have been performed as well [44, 48].
These techniques are similar in operating principal to our work, and the recon-
struction techniques can be modified to work with our short-range underwater acoustic
tomography system. However, in contrast to the ocean acoustic tomography problem,
atmospheric tomography systems are usually constructed over an area small enough to
allow all senders and receivers to be connected by wire to a central recording station and
thus these techniques do not use a sensor network. As the signals from the senders and
12
receivers are brought back to a central data recorder, highly accurate timing is also not
required. Setting up such a system underwater is possible, however working in marine
environments presents challenges when attempting to use long cables spread over a body
of water.
Reconstruction Methods
A reconstruction method or algorithm is used in travel time tomography to invert (or
reconstruct) the sound speed field that is representative of the set of average travel times
as measured between the senders and receivers. Many travel time tomography systems
[32, 64] use a straight forward reconstruction method whereby the area under study
is divided into a grid which may not be uniform. Then each ray or path between a
sender and receiver is divided into sections along the grid and used with the set of
travel times to form a system of equations where the unknowns are the speed-of-sound
in each grid section. Known as grid-based reconstruction methods, standard matrix
solving techniques can then be used to find the speed-of-sound for each grid section.
More advanced grid-based reconstruction methods have been proposed [33, 43] that use
statistical models of wind and temperature variation to improve the reconstruction. Of
most interest to the proposed multi-pulse tomography technique is the TDSI method
of [43], because the technique uses several back-to-back time-of-flight measurements.
In contrast to our technique, the consecutive measurements are used to better inform
the statistical models used for reconstruction, not to directly measure spatial changes
in the sound-speed field. Grid based reconstruction methods can lead to adjacent grid
sections having large discontinuities in the reconstructed parameters. For fluids like air
and water, such large discontinuities are not generally found in natural settings.
13
Therefore, in order to reconstruct a smooth sound-speed field, several other recon-
struction techniques have been proposed. Wiens [58] proposed using a set of radial basis
functions placed over the area to model the sound-speed parameters. Chosen properly,
radial basis functions create a continuous and smooth reconstructed sound-speed field
while also offering the advantageous property that the basis functions are linear in their
parameters, i.e. the parameters can be found using linear matrix solving methods. In
their atmospheric tomography literature Jovanovi´ c et al propose a similar method [30]
based on the idea of compressive sensing where the times-of-flight sample some smooth,
but sparse functions over the area under study.
We observe here that these tomographic reconstruction algorithms treat each time-
of-flight as a single data point representing the average speed-of-sound encountered
along the ray-path. As such, a single data point carries no spatial information except
for the starting and ending points. This often yields under determined solutions. In
order to reduce the resulting solution space the reconstruction algorithms must make
assumptions about the spatial distribution of the sound-speed field.
Reconstructions based on such assumptions often yield good solutions, however as
Wilson and Thomson note in [33] including a priori statistical information in the inverse
operator will bias the results. Said another way, including assumptions is another way
of saying that you know what you are looking for. Wien’s radial basis function work and
Jovanovi´ c compressive sensing methods make these spatial assumptions very explicit.
However, in smaller scale marine environments, in particular when trying to detect
temperature anomalies we would like to have accurate reconstructions without needing
any prior assumptions. In chapter 5 we describe our multipulse acoustic tomography
algorithm that builds spatial temperature distributions without prior assumptions about
14
the distributions themselves and show how having high resolution spatial distributions
leads to more accurate and higher resolution reconstructions.
2.2 Underwater Acoustics: Sensing, Ranging, and
Communications
Because of their positive propagation properties, underwater acoustic signals are also
used in several other technical capacities that are related to the research presented in this
thesis. Increasing the sensing capabilities of underwater sensor networks is a top-level
goal for this work and thus form the platform on which we started our work. We also
consider the acoustic communications infrastructure that provides networking capabil-
ities to underwater nodes. Related to travel-time acoustic tomography, but inverse in
a sense, are underwater acoustic ranging techniques that use time-of-flight to infer dis-
tance as opposed to speed-of-sound.
2.2.1 Underwater Sensor Networks
‘Sensor network’ is a term of art used to describe a network of nodes built to perform a
sensing function, typically environmental. By using a network of inexpensive nodes, a
sensor network can perform the sensing function of more sophisticated sensing equip-
ment by combining temporally and spatially distributed readings. Terrestrially, using
RF for communications the field is mature and research has turned to development of
commercial products. The underwater environment is a perfect fit to the sensor network
paradigm, however, due to several challenges, research into underwater sensor networks
has not progressed as quickly [7, 28, 46].
15
Underwater acoustic communications is a well studied field with a plethora of aca-
demic papers published on modems, modulation techniques and media access control
schemes[9, 18, 50, 55]. These academic researchers offer details on how to construct
specific components from the transducers to DSP or FPGA based modems. There are
also several commercial underwater modems systems that offer varying bit rates and
modulation schemes. For several reasons the main challenge is the acoustic communi-
cations required to build the underwater network. Inexpensive, short to moderate range
underwater modems and hydrophones do not currently exist. Commercial modems
exist, however their cost is usually prohibitive.
Two modulation methods are worth discussing here, frequency shift keying (FSK)
and direct sequence spread spectrum (DSSS).
Frequency-shift keying has been shown to have good properties under a wide range
of conditions in underwater communications and is therefore offered as a modulation
technique on most underwater modems. FSK offers reliable communication and sim-
ple modulator/demodulator design, however it does not perform well in the presence of
multi-path interference, and is thus most suited to open or deep waters. We are specifi-
cally targeting (but not limited to) shallow coastal waters, or even lakes, and thus need
a system that performs well in the presence of multi-path interference and low signal to
noise ratio.
A well cited example modem is the WHOI MicroModem. The feature most similar
to our system is the wide-band REMUS compatible navigation system. This system
use a coded PSK signal to interrogate transponders. Using the known locations of the
transponders and the round-trip-times, the modems can perform ranging. If the locations
of the nodes in a sensor network is known and fixed, ranging is equivalent to performing
tomography, however due to system design the WHOI MicroModem allows for 125s
16
in temporal resolution. Our system is capable of delivering approximately 10 times the
temporal resolution.
Direct sequence spread spectrum communications systems draw on the advanta-
geous mathematical properties of long pseudo-noise codes to improve noise immunity
(spreading gain) and resistance to multi-path interference. DSSS systems include a syn-
chronization method that can be used for precise time-of-flight mechanisms, however
the spreading gain may not be enough to overcome a noisy channel with very low trans-
mit powers.
More importantly, the propagation properties of an acoustic signal underwater differ
so drastically from terrestrial RF that the basic network algorithms and protocols must be
redesigned as the signal propagation is no longer negligible. Therefore, a large amount
of research has been performed to develop new modulation techniques, MAC protocols,
routing schemes and other fundamental network protocols (a small sample: [50, 54,
60]). However, since these algorithms and protocols can be evaluated in simulation and
given the difficulty of deploying and testing equipment in a marine environment most of
this work has not been tested in a real-world environment.
Despite these challenges, there have been a few underwater sensor network deploy-
ments to date. In 2002 Codiga et al. [14] deployed a number of acoustic Doppler current
profilers (ADCP). Data from the ADCP were relayed by underwater modem to a central
buoy for uplink. Similar to our testbed research, the Woods Hole Oceanographic Insti-
tution maintains a testbed in the ocean near the Quissett campus [19]. Vasilescu et al.
performed a sensor networking and data muling experiment in rivers and lakes, explor-
ing the feasibility of using acoustic as well as short-range infrared optical networking
underwater [57].
17
The SOLO-TREC [5] project has produced a Lagrangrian buoy that is capable of
repeated dives up to 500 m, however it does not contain any acoustic sensors. The
ARGO [3] project has deployed a large number of floats to profile ocean temperature
and salinity. These floats operate on the oceans at large and do not use any acoustic
sensing. The ORCA Kilroy network [56] aims to provide temperature, salinity and
water flow data on costal bodies of water similar to our system. However, it does so
by deploying a dense network of sensor nodes that only act locally (i.e. they do not
communicate through the water). Kilroy does use very short range (< 1 m) acoustic
signals to sense the water flowing past a node.
Performing specialized acoustic tomography, an inverted echo sounder (IES) [] is a
device that measures the average temperature of a water column at a point location in
the ocean. The device is placed on the sea floor and transmits a ping to the surface. This
ping is reflected off the surface of the water and when received back, the round-trip-time
is calculated. Given the depth of the water at the IES, the average temperature of the
water column can be calculated. This technique operates at the same distances as our
system, however we envision a sensor network of active transmitters and receivers at
different depths which can provide 2D or 3D temperature maps.
In 2002, Codigaetal. [14] deployed a network of acoustic Doppler current profilers
(ADCP) on the ocean bottom near Montauk Point, NY . ACDP’s use acoustic signals to
develop a depth-current profile by sending signals upwards towards the surface. The
amount of Doppler effect measured is used to compute the current. This experiment
also used acoustic modems to relay the ACDP data in real-time to the shore.
18
2.2.2 Underwater Ranging Systems
Underwater positioning systems such as long or short baseline navigation systems use
a set of fixed location transponders that reply with fixed delay to interrogation signals.
Given the round-trip time and fixed delay, the acoustic propagation time and thus dis-
tance to the transponder can be calculated. With adaptation, such a system could be
used to perform tomography. However, existing systems are designed for a specific
positional accuracy which dictates the required time-of-flight accuracy. Thus, the time-
of-flight accuracy required to obtain the positional accuracy specified by current under-
water ranging systems is typically insufficient for use as a tomography system.
2.2.3 Robotic Temperature Sampling
An alternate method proposed by several groups to improve the spatial resolution of an
aquatic temperature map involves using robotic vehicles. Either surface or underwater
vehicles may be employed and they may be controlled or autonomous. Zhang [63]
proposed and deployed a system using fixed nodes and a small remote controlled boat
to survey the temperature map on the surface of a lake. The temperature is taken at
the fixed nodes and then a path is constructed for the boat to follow. The boat takes
temperature measurements along the way and the resulting temperature data is used to
interpolate the temperature map across the surface of the lake. While this system can
yield high resolution maps, the time required for the boat to traverse the lake surface is
considerable, and the authors assume the temperature profile does not change while the
boat is surveying the lake. We will show that the system presented here is capable of
producing maps of comparable resolution in near real-time.
The REMUS project [52] from the Wood-Hole Oceanographic Institute deploys
autonomous underwater vehicles of various sizes. Using acoustic signals from surface
19
buoys as navigation aids, the AUVs are capable of surveying the temperature and cur-
rent profile of bodies of water. Some versions of the REMUS AUV deploy ADCP and
acoustic modems for communications; however, they do not perform any tomographic
acoustic sensing.
2.2.4 Acoustic Ranging for Sensor Networks
In the context of terrestrial (i.e not underwater) sensor networks, work has been done on
using acoustic signals for ranging and localization. Directly of interest to this work is
the work by Girod while at UCLA CENS[20]. In order to locate multiple sensor nodes,
Girod constructed orthogonal chirps using BPSK. Like our system, in order to get robust
detection in a noisy environment, long PN codes with good ACF and CCF properties are
required. However, Girod’s method for finding such codes is ad-hoc and the difficulty
of finding a large set of codes grows exponentially with code length. In appendix B we
describe how Legendre sequences can be transformed into PN codes with the required
properties with no restriction on length or increasing difficulty.
20
Chapter 3
Sensor Network Acoustic Tomography
3.1 Introduction
Data collected by monitoring marine environments with instruments that measure var-
ious ecological conditions (e.g. temperature, salinity, oxygen concentration, current
flow) form the core around which scientific research about our oceans is built. Scientists
almost always prefer data at the highest resolution possible, both temporally and spa-
tially. In order to obtain high spatial resolution, a number of sensors must be deployed,
even when monitoring relatively small bodies of water like bays, channels or marinas.
Furthermore, in order to use this data, it must be easily collected and made available
to scientists. Easy collection of spatially distributed data is a main feature provided by
sensor networks, therefore computer scientists and engineers are creating underwater
sensor networks using a distributed network of inexpensive sensing nodes.
To easily collect the sensed data, the nodes must join a communications network.
Due to well known constraints on underwater communication, the physical layer of an
underwater communications network is implemented using acoustics. However, due to
the properties of underwater acoustic propagation, sound can also be used to perform
tomography, i.e sense the physical properties of the medium through which the sound
is traveling. This observation, that the same equipment that allows for underwater com-
munication can also be used for sensing, is the reason why acoustic tomography is an
ideal application for an underwater sensor network.
21
Using a sensor network for acoustic tomography enhances or enables a number of
ecological and defense applications. Many marine organisms are temperature sensitive;
however, the dynamic spatial and temporal temperature changes that can occur in small
bodies of water are difficult to study due to the expense of buoys, floats or robotic probes.
By performing acoustic tomography between shore or buoy mounted nodes, the spatial
resolution of a system can be increased for little or no additional cost. As a defense
application, sensor network acoustic tomography can detect the heat signatures of boats
or submarines even if these water craft are equipped with sophisticated SONAR avoiding
materials.
In this chapter we present the construction of an underwater sensor network that
uses sound for sensing. First we present our UwASN hardware system designed for
prototyping underwater sensor networks. We then present our simulation efforts that
verify in theory that acoustic tomography with a sensor network is possible. Finally, we
present results and experiences from a five node acoustic tomography sensor network
deployed in a marina. We are able to show an increase in spatial resolution as compared
to sensing locally at the node locations.
Acoustic tomography is typically performed at large scales, from hundreds to thou-
sands of kilometers. However, underwater sensor networks are usually envisioned as
being deployed at very small scales, from tens of meters to perhaps one kilometer
between nodes. In order to implement an acoustic tomography system at such scales,
several challenges must be over come. Acoustic tomography principally operates by
measuring the time-of-flight for acoustic signals sent through the water. In our work we
are targeting an inter-node distance of 50 m. Thus to measure changes in time-of-flight
caused by temperature fluctuations over 50 m, we need time-of-flight measurements
22
accurate to approximately 10 s. We discuss how to build an underwater sensor net-
work using two recently published techniques we developed that provide sufficiently
accurate timing and thus enable acoustic tomography. One of the techniques discussed
does not require time synchronization across the nodes and is thus appropriate for use
deep underwater.
We also believe that sensor network research has the most impact when real-world
deployments are used to test algorithms and equipment. Such deployments often provide
challenges that are difficult to anticipate in the lab or simulation. In order to be viable,
sensor networks must be constructed from inexpensive, easily available sensors and
equipment. Therefore, using off-the-shelf components we constructed and deployed a
five node underwater sensor network in a marina and used it to perform acoustic tomog-
raphy. We present the details of our deployment and show that we can create water
temperature maps with higher spatial resolution than one would obtain using sensors
locally at each node.
3.2 System Design
3.2.1 Underwater Acoustic Sensor Node
Sensor networks are typically built using small, low cost, ‘embedded’ systems. How-
ever, as a research platform such systems can be inflexible and thus difficult to rapidly
modify during the development and prototyping of signal processing and network algo-
rithms. In [23] we presented the Underwater Acoustic Sensor Node (UwASN), a PC
based platform that allows for rapid prototyping and deployment of signal processing
and other algorithms into a marine environment.
The UwASN is comprised of several components:
23
(a) UwASN Components Inside Dock Box (b) Marina Testbed Node
!"#$ %"#$
&'()*+,-*$
./$012$ 3/$012$
%"&$
%4)4-,5$"(-2'64$!'12(74-$
&4-8,5$
""&$
./$.-,)6*(+4-$ 3/$.-,)6*(+4-$
(c) UwASN Diagram
Figure 3.1: Underwater Acoustic Sensor Node
Small Form Factor PC providing CPU and GPU resources for signal processing
algorithms.
On board, or external 96 kHz sampling frequency sound card for capture and
playback of acoustic signals into the water.
Receive hydrophone with suitable pre-amplifier
Transmit hydrophone with suitable power amplifier
GPS receiver with Pulse-per-Second
Network (Internet) connectivity for control and data collection
24
Figures 3.1(a) — 3.1(c) show a diagram and pictures of a deployed UwASN.
These components can typically be assembled for approximately $500 in 2012.
However, it is important to note that the cost of the hydrophones can be a major contribu-
tor to this cost. Until a inexpensive hydrophone capable of sending and receiving signals
at distances on the order of 1 km is developed, underwater sensor network deployments
will be limited. We find the low cost hydrophones ($175) by Aquarian Audio [1] to
work at distances of up to 75 m, while hydrophones by Benthowave [4] will work at
much greater distance, albeit at approximately two times the cost.
The other components of the UwASN are selected to ease development and experi-
mentation in underwater signal processing and network algorithms. The general purpose
CPU and GPU provide the signal processing resources, without the cumbersome devel-
opment cycle typical of DSP or FPGA based systems. If DSP or FPGA resources are
needed, the UwASN can also host such boards in PCI-Express expansion slots or over
USB.
Using the built-in sound card or a higher quality add-on sound card gives the ability
to sample the audio signal from the hydrophone at high sample rates. If ultra-sonic
signals are needed for an application, they system can be tested at lower frequencies
using the UwASN before developing specialized hardware that operates at ultra-sonic
frequencies.
Using both a send and receive hydrophone instead one hydrophone with a TX/RX
switch has several advantages during development and testing of underwater algorithms.
For example, we can employ self-listening to monitor or ‘loop-back’ the local acoustic
signal while also transmitting. Section 3.2.2 shows how this technique, when combined
with the GPS PPS signal described below, is used to enable precise measurement of the
acoustic time-of-flight for a signal in the water.
25
The GPS receiver is used to synchronize the operating system clock on the UwASN
and allows experimental data to be time stamped with a globally accurate time, while
the pulse-per-second (PPS) signal provided by some GPS receivers can be used to times-
tamp data with an accuracy under 1s.
3.2.2 Precise Timing
It is obvious from the physical principals behind acoustic tomography that the precision
to which time-of-flight is measured defines the resolution at which a tomography system
operates. Put another way we are asking “just how precise do we need to be?” Given
an equation for the speed of sound in water and the smallest inter-node distance we
can estimate the temperature resolution of our system. To a first order approximation
using the equation from [36], the speed of sound in water changes 4.59m=s per degree
Celsius. At a nominal speed of 1500 m=s, over a distance of 50 m the time of flight
is 33 ms and the change in time-of-flight observed over a one degree change in water
temperature is 100s.
Thus, if an acoustic tomography system is to have a temperature resolution of 0:1

C,
the time-of-flight measurements must be accurate to approximately 10s.
In building a sensor network implementation of underwater acoustic tomography,
it is desirable to use as simple and low cost equipment as possible. Yet to perform
tomography we must measure as exactly as possible when the signal enters the water at
one node, and when it is received at another. When considering the timing requirements,
a naive implementation would use the system clock and timing facilities provided by
the operating system running on an underwater sensor node. However, due to the non-
deterministic nature of interrupts and process scheduling on commodity hardware it is
very difficult to obtain accurate timestamps. In addition, trying to measure the time at
26
Acoustic Signal Start
PPS Signal
Figure 3.2: Precise Timing using PPS
which a signal is actually sent into the water, versus when the system call was made to
start playing the audio would probably require modifications to the operating system.
Therefore, our system utilizes self-listening and the GPS PPS signal to obtain glob-
ally accurate timestamps on the order of 10 s. The key to doing so is the GPS PPS
signal (although we’ll later relax this restriction). The GPS PPS signal is a logic-level
signal output from some GPS receivers that identifies the start of each second accurate
to about 1 s. This signal is input to one channel of a two-channel sound card and
the output from the receive hydrophone is connected to the other channel. Whenever
an underwater signal is detected in the received audio signal, the number of samples
elapsed since the previous transition of the PPS signal gives the time position of one
sample within that second accurate to the inverse of the sampling frequency. Since it is
quite easy to know in which absolute second the arrival was detected, these two numbers
can be combined to provide a globally correct timestamp for the arrival time accurate
to 10s (at 96 kHz sampling rate). Figure 3.2 illustrates this method. At the receiving
node this technique gives the arrival time. Since the transmitting node is self-listening
27
clk
b
clk
a
T
A
T
B
T
C
T
D
t
d
t
ba
t
ab
Figure 3.3: Precise Timing without time synchronization
the same technique will give an accurate send timestamp. Subtracting these two times-
tamps gives time-of-flight.
However, relying on GPS PPS restricts the system to nodes that are at or near the
surface. The potential applications for sensor network acoustic tomography will require
nodes operate deep underwater, and thus we have developed another time-of-flight mea-
surement technique that does not rely on GPS PPS. Similar to the technique in [47] used
for acoustic ranging between mobile phones, we send a signal from node A to node B
and then a short-time later from node B to node A. By using only the sample counts
between the arrivals, we can also obtain time-of-flight accurate to approximately one
sample, and presented this result in [24]. Figure 3.3 illustrates this method, where the
final time-of-flight is calculated as ((T
D
T
A
) (T
C
T
B
))=2. This technique requires
round-trip transmission and assumes that no current is present along the acoustic path.
3.3 Microtomography Simulator
In order to better understand sensor network acoustic tomography and the results we
might expect from real-world experimentation we used simulation to evaluate the effec-
tiveness of our proposed system. There are existing underwater sensor network sim-
ulators, such as the AquaSim [61] project from University of Connecticut. AquaSim
28
(a) Aerial View
A
B
C
D
E
°
°
°
°
°
(b) Schematic View
Figure 3.4: Marina Del Rey Testbed
aims to provide a complete physical layer to application layer simulation of underwa-
ter acoustic networks. While it supports a high-fidelity acoustic propagation model, in
order to simulate tomography we need only to calculate time of flight for a signal sent
between two nodes. More importantly, the speed of sound in water for AquaSim is fixed
at 1500 m/s. At this time we believe there is no other underwater communications simu-
lator that includes variations in speed of sound in the propagation model. Thus, we have
developed an underwater sensing simulator called SeaSim. Designed to simulate acous-
tic propagation from the physical layer up, SeaSim is able to simulate the propagation
of sound through water in which the temperature and current vary spatially.
3.3.1 Architecture
SeaSim is an event based simulator written in Java and includes the GUI shown in Figure
3.5(a). The GUI allows the user to set up a grid over an area of simulated ocean. The
water in each tile defined by the grid can be set to a different temperature, salinity
and current speed and direction. Nodes may be placed in the simulation at arbitrary
29
(a) Full View of Main GUI
(b) Arrows Indicate Current Direction and Magnitude (c) Close-up Showing Node Place-
ment and Current Gradient
Figure 3.5: SeaSim Ocean Acoustics Research Simulator GUI
points. A timeline of messages is then specified to tell the simulator from which node
and at what time to send a message. The speed of sound for each tile is calculated
using the temperature, salinity and current information. By tracking the propagation of
sound through the various tiles, the time at which the signal reaches the other nodes is
calculated.
When calculating the speed of sound in water given temperature and salinity for our
simulator we use the MacKenzie equation [36]. The equation is shown in (3.1) and the
parameters are described in table 3.1. Using this equation allows us to model accurately
the speed of sound as the signal propagates across the tiles. In tiles that specify a current
30
Table 3.1: Parameters and equation for the MacKenzie approximation for speed of sound
in sea water as a function of temperature (T ), salinity (S) and depth (z)
a1 1448:96
a2 4:59
a3 5:304 10
2
a4 2:374 10
4
a5 1:34
a6 1:630 10
2
a7 1:675 10
7
a8 1:025 10
2
a9 7:139 10
13
c(T;S;z) =a
1
+a
2
T +a
3
T
2
+a
4
T
3
+
a
5
(S 35) +a
6
z +a
7
z
2
+
a
8
T (S 35) +a
9
Tz
3
(3.1)
speed and direction, the component of current in the direction of travel for the acoustic
signal is calculated. This component is then added or subtracted to the speed of sound
for that tile.
3.3.2 Simulator Features
SeaSim includes a full set of features that let the user define the simulation parameters.
Users may:
Define Physical Parameters: Users enter the size of the water area for the sim-
ulation, along with the default water temperature, salinity and current vector for
each tile in the simulation
Modify Physical Parameters: The user may then modify the temperature,
salinity or current vector for individual tiles or groups of tiles selected together.
31
This allows the user to set up gradients of the physical parameters across the
simulated area. The gradients may be smoothed out using a Gaussian blur filter.
Add Nodes: Users then add nodes of three types: transmitters, receivers or
transceivers. The nodes are be placed by clicking on the GUI, and their location
may be fine tuned by right-clicking on an individual node.
Run Simulation: A series of messages is defined to be sent at a particular time
from a particular node, the simulation then reports when these messages arrive
at the other receiver or transceiver nodes. The simulator also has a tomography
mode, where the simulator calculates the average temperature along the pair-wise
paths (using the time-of-flight). The simulator solves the tomography system to
obtain the temperature at all nodes and intersections. A 2D cubic interpolation is
performed and a temperature map is displayed.
3.4 Multi-Node Tomography Simulation
The goal of microtomography is to provide a temperature map for a small body of water.
To generate such a map, one must perform a tomographic inversion on the time-of-flight
data (also called a reconstruction). Tomography in general is a mature field, and there
are many methods to choose from when calculating the inversion. In this section we
present two methods of reconstructing the temperature map given time-of-flight data.
We generate the time-of-flight data by sending tomography signals from each node
and thus obtain the time-of-flight for each pair-wise set of nodes. These time-of-flight
measurements are then turned into a temperature using equation 3.1. This temperature
represents the average water temperature along the path between each pair of nodes.
32
(a) Input Heat Map for Tomography
Simulation
A
B
C
D E
F G
H
I
J
!"#$
!"#$
(b) Schematic Diagram for 5 Node
Tomography System
(c) Heat Map Interpolated From 5
Points
(d) Heat Map Interpolated from 10
Points
Figure 3.6: Five Node Tomography Simulation
3.4.1 Weighted Linear System
We first start with a simple system using just five nodes. Figure 3.6(b) shows a
schematic. For this method we try to reconstruct the temperature at the signal cross-
ing points by assuming that the average temperature observed is a weighted average of
the temperature at the crossing points. If we denoteT (p
1
;p
2
) as the average tempera-
ture as calculated using time-of-flight between pointsp
1
andp
2
,d(p
1
;p
2
) as the distance
between pointsp
1
andp
2
, andP as the temperature at pointp (the unknown tempera-
tures: A;B, etc.), then we can form the system of 10 equations as shown in table 3.2.
33
Table 3.2: System of Equations for 5 Node Tomography
A +B = 2T(A;B) d(A;F) (A +F) +d(F;G) (F +G) +d(G;C) (G +C) = 2T(A;C)d(A;C)
B +C = 2T(B;C) d(B;G) (B +G) +d(G;H) (G +H) +d(H;D) (H +D) = 2T(B;D)d(B;D)
C +D = 2T(C;D) d(C;H) (C +H) +d(H;I) (H +I) +d(I;E) (I +E) = 2T(I;E)d(C;E)
D +E = 2T(D;E) d(D;I) (D +I) +d(I;J) (I +J) +d(J;A) (J +A) = 2T(D;A)d(D;A)
E +A = 2T(E;A) d(E;J) (E +J) +d(J;F) (J +F) +d(F;B) (F +B) = 2T(E;B)d(E;B)
Solving this system will yield the temperature at the five nodes and the five intersection
points.
As described in [38], tomography networks with more than five nodes result in a
rank-deficient linear system. Solving a tomography system with more than five nodes is
possible as an optimization problem; however for simplicity, we focus here on the five
node system which has a direct solution. Given 10 temperature points, we can then use a
suitable interpolation method to draw a map of the temperature distribution in the body
of water under study.
Using SeaSim we performed several simulations to illustrate the remote sensing
capabilities of microtomography. Figure 3.6(a) shows the heat map for a 50 meter square
simulation. The temperature of an area in the middle is set to two degrees lower than
the surrounding water. Figure 3.6(c) shows the temperature map that is possible if just
the temperature at the five nodes is known. Note that the blue areas around the edges of
the figure are outside the convex hull formed by the nodes and are thus not appropriate
for interpolation. Figure 3.6(d) shows the temperature map obtained using information
from all 10 points. Here we see the advantage of an underwater sensor network that
deploys microtomography. Previously, knowledge of the water would be limited to tem-
perature readings at the nodes themselves. With microtomography we are able to greatly
34
−100 −80 −60 −40 −20 0 20 40 60 80 100
−100
−80
−60
−40
−20
0
20
40
60
80
100
x (m)
y (m)
Target

dT (C)
−0.5
0
0.5
1
1.5
(a) Target Heat Map for 16 Node Simulation
−100 −80 −60 −40 −20 0 20 40 60 80 100
−100
−80
−60
−40
−20
0
20
40
60
80
100
x (m)
y (m)
Reconstruction

dT
hat
(C)
−0.5
0
0.5
1
1.5
(b) Reconstructed Heat Map for 16 Node Simula-
tion
Figure 3.7: Radial Basis Function Tomography Simulation with 16 Nodes
improve the spatial resolution of the sensor network without adding additional nodes nor
by adding mobile nodes.
The advantage of using this method is simplicity and speed. A small fixed number
of calculations are performed, with no iterations for optimization. Such a system of
equations can be solved quickly even if the system were built using mote-class hardware.
3.4.2 Radial Basis Functions
However, depending on the size of deployed system, more complex reconstruction tech-
niques may be required. Weins presents an interesting method in [58] that uses radial
basis functions to model acoustic propagation in the air. A radial basis function can be
used to describe a non-linear parametric surface which is linear in the parameters. A set
of several radial basis functions distributed spatially form a smooth surface which can
be fit to data using standard least squares techniques. We adapted the method to work
with a simulated marine environment.
In this example we show how more transducers can produce higher resolution
results. Here we assume a 200 meter square area. Sixteen nodes are distributed around
35
the edges of the area. We place two heat sources that generate an increase of two degrees
Celcius in their immediate vicinity. Figures 3.7(a) and 3.7(b) show the target and recon-
struction, respectively. With this method we again see that microtomography provides
better spatial resolution versus temperature sampling at the node locations alone.
3.5 Underwater Time-of-Flight Experiments
In order to provide a location for real-world, underwater sensor network experiments,
USC/ISI has developed an underwater testbed. The testbed is located in Marina Del
Rey directly across the street from ISI at the Pier 44 Marina. Equipment is deployed as
required in various locations on the marina boat docks. See Figure 3.4 for an overhead
view of the testbed. For this experiment two UwASN prototype nodes are deployed at
a distance of 55 m. As described in previous sections, the prototypes are designed to
continually obtain highly precise global time from GPS units and time-stamp the acous-
tic input signal. In this section we describe two experiments, one using GPS signals
for time synchronization and one which does not require time synchronization (only a
locally accurate sample clock).
In these experiments we make several assumptions. First, except in the immediate
vicinity of fresh water mixing, the salinity of the ocean is very homogenous (even more
so at small scales) [8]. Therefore, we do not consider salinity changes as affecting the
time-of-flight. Second, the speed of sound in water does depend on depth; however our
current experiments are conducted in 2D with all transducers lying in a plane. Even
in the case of a 3D system, changes in speed of sound due to depth are more than
two orders of magnitude less than those caused by distance. Since we also assume the
positions of the transducers are known, differences in speed of sound caused by depth
can be incorporated into the reconstruction algorithms. Third, Ostashev shows in [45]
36
that for short distances (< 5km), refraction may be ignored and thus we may assume
that our acoustic signals follow the straight path between two nodes.
3.5.1 Time-of-Flight using GPS time synchronization
First we performed an experiment where the acoustic signal was only sent from one
side (traveling from East to West as shown on the testbed map). This experiment was
performed using the above system to validate that the system design can indeed detect
sub-degree changes in water temperature. An acoustic tomography ‘chirp’ signal was
played once a minute over the course of a week. Both sender and receiver recorded
the inputs of their sound card at a sampling rate of 96 kHz. A USB temperature probe
sampled the water temperature at one minute intervals to provide ground truth. The
resulting 9000 sound files and temperature log were later retrieved and processed.
Figure 3.8(a) is a plot of the time-of-flight for an acoustic signal traveling between
the two nodes. Figure 3.8(b) is a plot of the USB temperature data. We first note that
the error bars on the time-of-flight measurements are on average += one sample with
one-half sample of error coming from each measurement (departure and arrival). This
indicates the desired precision for our measurement technique has been achieved.
The correlation between the time-of-flight and temperature data is clear and can be
analyzed further. Figure 3.8(c) shows the time-of-flight data vs. temperature with a
linear regression. In section 3.3 we will discuss equation (3.1), which is an approxima-
tion used to relate the speed of sound in water to the temperature, salinity and depth.
Here we note that over a small temperature range (with constant salinity and depth), the
change in speed of sound in water (and thus time-of-flight as well) is linear with the
temperature change. TheR
2
value of 0:93 on the linear-fit in Figure 3.8(c) indicates our
data is measuring changes in time-of-flight caused by changes in water temperature.
37
35.5
35.55
35.6
35.65
35.7
0 1 2 3 4 5 6 7
Time-of-flight (ms)
Expreiment day
Acoustic Time-of-Flight
(a) Time-of-flght as measured over one week
17
17.5
18
18.5
19
0 1 2 3 4 5 6 7
Temperature (C)
Expreiment day
USB Temperature Probe
(b) USB temperature data as measured over one
week
(c) Linear Regression of Time-of-Flight vs. USB
Temperature
0.0355 0.0355 0.0355 0.0356 0.0356 0.0356
0
0.5
1
1.5
2
2.5
3
3.5
x 10
4
Time−of−Flight

Density
acoustic data
Normal fit
(d) Distribution of Time-of-Flight at Fixed
Temperature
Figure 3.8: GPS Time of Flight Experiment
Figure 3.8(d) shows the distribution of time-of-flight observations for a given tem-
perature. This data is a good fit with a normal distribution (tested with the chi-squared
goodness-of-fit metric), and thus in a fully deployed system we can send several signals
over a short time period and average the results to overcome the observed uncertainties
in calculated time-of-flight.
38
35.22
35.24
35.26
35.28
35.3
35.32
35.34
35.36
35.38
35.4
0 1 2 3 4 5 6 7
Temperature (C)
Experiment Days
Acoustic Signal
(a) Time-of-flght as measured over one week, with-
out GPS
18.5
19
19.5
20
20.5
21
0 1 2 3 4 5 6 7
Temperature (C)
Experiment Days
USB Temperature Probe
(b) USB temperature data as measured over one
week
Figure 3.9: Time of Flight Experiment
3.5.2 Time-of-Flight without time synchronization
Requiring GPS time synchronization is a severe limitation in situations when a micro-
tomography system is to be deployed deep underwater. Therefore using a similar tech-
nique to [47] we can use bi-directional signals to perform microtomography without
network wide time synchronization. To calculate time-of-flight without network wide
time sync, we only require the local audio sample clock at each node (operating at fre-
quencyf
s
).
Figure 3.3 shows the signal flow between two nodes. Node A sends a signal at
time T
A
and records the sample number. Node B receives the signal at time T
B
and
records the sample number. Sometime later node B sends a signal at timeT
C
and records
the sample number. Node A then receives the signal at sample time T
D
. The sample
numbers forT
B
andT
C
are then sent to node A, which can then calculate the time-of-
flight as ((T
D
T
A
) (T
C
T
B
))=(2f
s
). This result holds given t
d
= T
C
T
B
is sufficiently small and there is no current (and thus t
ab
= t
ba
). It can be seen from
equation 3.1 that the error in absolute temperature caused by a 1m=s current is of the
39
(a) Change from baseline after 3 hours (b) Change from baseline after 6 hours
Figure 3.10: 2D Tomography Reconstruction
order of 0:5 degree C and that current does not affect the ability to detect temperature
changes.
We performed a second similar experiment with bi-directional signals. On analysis,
the calculations described above were performed without considering the GPS PPS sig-
nal. Figure 3.9(a) shows these results. Again we show a clear correlation between the
calculated time-of-flight and water temperature. The error bars on this plot are twice
(+= two samples) what was measured with GPS and this is exactly as expected given
that we are now making four measurements to calculate time-of-flight.
3.5.3 5 Node Tomography
Given that our time-of-flight measurement techniques can measure water temperature
changes between two points, we performed further experiments to draw 2D maps of
the water temperature in the marina testbed. We sent and received acoustic signals
between all five nodes of our testbed and calculated the time-of-flight for each of the
10 pair-wise paths. Since we know the positions of each node we can use the time-of-
flight to calculate the average speed of sound and thus average water temperature along
each path. Using the linear system of equations as a reconstruction algorithm we can
40
then calculate a 2D temperature map. We chose 10 am on the 5th experimental day
as a baseline calculated the temperature change from baseline after 3 hours and after
6 hours. Figures 3.10(a) and 3.10(b) show the changes from the baseline. We observe
that the shallower, eastern end of the marina heats up faster, while the deeper channel
in the middle of the marina remains relatively cooler. These results show that acoustic
tomography is possible with an underwater sensor network at kilometer scale. Such an
acoustic tomography system increases the spatial resolution of the water temperature
sensing compared to only sensing at the node locations.
3.6 Conclusion
In this chapter we have detailed the hardware and software systems and techniques
required to perform acoustic tomography at kilometer scale with an underwater sensor
network. Additionally, we have presented SeaSim-2D, an acoustic tomography simula-
tor for underwater sensor networks along with two reconstruction algorithms useful for
drawing 2D temperature maps. We presented experimental results that show our system
can measure water temperature changes along a path between two nodes using acoustic
signals with high precision. We then present results using a five node system to draw
2D maps of the water temperature in the marina.
41
Chapter 4
Combined Data and Sensing Using
Long Pseudo Noise Codes
4.1 Introduction
In the previous chapter we have developed an acoustic tomography system using an
underwater sensor network. For sensor network deployments energy is an important
constraint. Throughout this thesis we are assuming that the sensor nodes in the network
must relay local measurement data across the network, and that acoustic tomography
is also used to sense the water temperature between the nodes. If our network nodes
were not energy constrained we could support separate sensing and data transmissions.
However, such a network is not realistic and thus we assume constraints on the amount
of energy available to the sensor nodes.
The obvious way to maintain the usefulness of the network is to use the data trans-
missions themselves to do the acoustic tomography function. The questions we must
answer is then do existing underwater data transmission schemes support the precise
time-of-flight measurements required for acoustic tomography and if not can we develop
a coding and transmission scheme that will support both data transmissions and acoustic
tomography simultaneously? The following sections of this chapter identify four sub-
questions that must be overcome when designing an acoustic signal capable of simulta-
neous data and sensing.
42
Information Sciences Institute
1. Can existing methods be used?
• Frequency Shift Keying (FSK)
– Commonly used modulation technique
BP @ Mark
BP @ Space
FSK Signal
4kHz BW at baseband
Sampled at Nyquist for baseband
1
0
e.g. WHOI baseband is sampled at 8kHz = 125µs
Temperature resolution @ 50 m of 1.5 °C
Figure 4.1: Block diagram of FSK Receive Chain
4.2 Signal Design for Simultaneous Data and Sensing
Transmissions
4.2.1 Existing Methods
Underwater acoustic communications is a fairly mature field with several research and
commercial modems available. Therefore we must first evaluate whether the modula-
tion techniques used by existing modems can be used for acoustic tomography. Figure
4.1 shows a block diagram for a modem using frequency shift keying (FSK) as the mod-
ulation technique. The precision to which the arrival time of an acoustic signal can be
resolved is determined by the sampling frequency of the baseband signal. In the WHOI
modem [] this sampling rate is 8 kHz (the Nyquist rate for the 4 kHz of baseband band-
width). Using the equations described in chapter 3 it is straight forward to calculate
that a 8 kHz sampling rate yields a temperature precision of 1.5

C. Given the 2 degree
temperature swings also described in chapter 3, 1.5

is not useful.
Therefore, due to their design, existing underwater modulation techniques do yield
sufficient arrival-time precision to be used for acoustic tomography. Our solution to this
problem is two fold: we sample the incoming audio signal at high sampling rates and
we send a signal with properties that yield highly precise arrival time measurements,
43
Information Sciences Institute
Solution #1: precise timing
6700 6750 6800 6850 6900 6950 7000 7050 7100
−600
−400
−200
0
200
400
600
800
1000
1200
One sample wide peak in ACF
Adjacent samples
are negative
Figure 4.2: Ideal ACF of ‘Guohua and Quan’ pseudo noise sequence
typically accurate to += 1 sample. Other modulation techniques used in advanced
underwater modems such as direct sequence spread spectrum (DSSS) and orthogonal
frequency division multiplexing (OFDM) share the baseband sampling limitation with
FSK. In our implementation we sample the underwater acoustic channel at high rate (96
kHz) so that we can achieve approximately 10s of precision when determining signal
arrival time.
Previous work has identified pseudo noise sequences as good signal to use when
the application requires determining precise arrival time [20]. For use in this manner,
the sequences are typically binary phase shift keying (BPSK) modulated at appropriate
carrier frequency. For detection, correlation with the known signal is performed (auto-
correlation). Ideally, the auto-correlation function (ACF) for a pseudo noise sequence
will have a large central peak, with low side lobes resembling noise away from the peak.
The narrow peak allows the point of maximum correlation to be fixed precisely in time,
even in the presence of noise. Figure 4.2 shows the ideal auto-correlation function of a
selected pseudo noise sequence. The peak in the ACF is one sample wide, thus yielding
+= one sample precision for arrival time measurements.
44
Figure 4.3: Received Audio Signal
4.2.2 Overcoming Noise in the Underwater Channel
The underwater acoustic channel is considered to be a very noisy channel, especially in
shallow water [6, 51]. Figure 4.3 shows a small recording of the underwater channel
in our Marina Del Rey testbed. The signal-to-noise ratio (SNR) at the receiver was
measured to be -35 dB. In order to receive data and perform acoustic tomography we
must robustly detect the modulated signal at the receiver. This means overcoming low
signal-to-noise ratios with gain.
G = 10log
10
(L) (4.1)
A naive approach would be to overcome the noise at the receiver by increasing the ampli-
tude at the transmitter. However, to overcome a SNR of' -40 dB at the receiver, the
transmitter would need to increase the output amplitude by a factor of 100. In most sce-
narios increasing the transmit amplitude by such a large amount is impractical. To over-
come this problem we note that auto correlation function for pseudo noise sequences
concentrates the received signal energy into the central peak. This phenomenon is
known and de-spreading, and thus detecting signals with correlation is said to achieve
‘spreading gain’ related to the length of the signal. Equation 4.1 shows the formula for
45
spreading gain in dB as a function of the signal length. By measuring or estimating the
worst-case SNR for any transmitter-receiver pair in our network, we can choose a length
for our pseudo-noise sequences that will yield adequate spreading gain to overcome the
channel noise.
4.2.3 Medium Access Control
When transmitting acoustic signals the underwater channel is clearly a shared medium.
When building a network where the physical layer is a shared medium some method of
medium access control is needed so that signals from multiple senders do not interfere
with each other. For underwater communications medium access control methods like
frequency division or time division multiple access (FDMA, TDMA) can be employed,
however both have limitations. For FDMA there is a limit to the number of slots that can
be obtained by splitting up the usable frequency band. This limits the number of nodes
that can be deployed in a network. For TDMA to operate efficiently, very tight time syn-
chronization must be maintained across the network. Underwater time synchronization
has been addressed, but may not provided the accuracy and stability needed [13, 53] and
thus TDMA is not a good choice for our system. We then look to code division multiple
access (CDMA) for a solution to medium access control for combined data and sens-
ing transmissions. CDMA uses pseudo random sequences to modulate digital signals in
such a way that they are mathematically orthogonal. This allows several transmitters to
share the transmission medium. Since we are using pseudo noise sequences, to allow
for simultaneous transmissions we only need to ensure that are pseudo noise sequences
are drawn from an orthogonal set. Figure 4.4 shows the cross-correlation function for
orthogonal pseudo noise sequences. The near-zero CCF compared to the peak in the
46
Information Sciences Institute
Solution 3: obtain orthogonality with
pseudo-noise sequences
• If chosen properly sets of PNS can have this property
• Use Legendre sequences to generate classes of arbitrary
length PSNs with orthogonality
– Based on prime numbers p = 3 mod 4, airity of class = (p-1)/2
6700 6750 6800 6850 6900 6950 7000 7050 7100
−600
−400
−200
0
200
400
600
800
1000
1200
0 2000 4000 6000 8000 10000 12000 14000
−600
−400
−200
0
200
400
600
800
1000
1200
ACF
Figure 4.4: Ideal CCF of ‘Guohua and Quan’ pseudo noise sequence
ACF allows the receiver to determine which of a set of signals is present in the received
signal.
4.2.4 Simultaneous Data and Sensing
At this point we have determined that properly designed pseudo noise sequences can
support precise time-of-flight measurement, over come channel noise and provide
medium access control. Thus to enable simultaneous sensing and data transmissions
we must identity a method to carry data with such a signal. We have assumed that the
sensor nodes need to send a small amount of local data across the network. If we struc-
ture our packet format into a fixed length (e.g. < NODEID >< SENSOR1 ><
SENSOR2 >< STATUS >) the there are a fixed number of possible messages. To
complete the system design we determine the maximum message size in bits (N), then
generate a set of orthogonal pseudo noise codes of size 2
N
. This allows for each pseudo
noise sequence in the set to represent one possible message.
Thus we need a method to generate pseudo noise codes with the following proper-
ties:
47
Generate signals of at least L to generate spreading gain to overcome channel
noise
Generate orthogonal sequences
Generate a set of size at leastM = 2
N
to represent all possible messages of length
N in bits
We then chooseP as the required length of our sequences as the greater ofL orM.
Gold, Bent or No [21, 40, 42] codes are several examples of algorithms that can be
used to generate sets of orthogonal pseudo noise sequences. However, by their con-
structionP = 2
n
1 withn increasing by a minimum of two when increasing the code
length. This severely limits the flexibility in code length. For example, if we needed
a code length ofP = 600 thenP = 511 is too short, but the next two available code
lengths would beP = 2047 andP = 8191.
Girod [20] generated similar sequences to be used for acoustic ranging in air by
using a genetic algorithm to find sets of pseudo noise codes with adequate ACF and
CCF properties. However, the code lengths used in his system were fairly short (< 512)
and of fixed length. Also, as the sequences were not used to carry data the set size
required was also small (< 32). In our system we will need to generate sequences with
long length (> 1000) and large set size (' 2000). Generating pseudo noise sequences
by a computational method like genetic algorithms is likely to be impractical.
Helpfully, Guohua and Quan [27] provide an algorithm based on the Legendre
sequence where the restriction on code length is that P is a prime number where
P = 3 mod 4 i.e the length is a prime number where P + 1 is a multiple of 4. The
sets of sequences generated by this method are of size (P 1)=2, have good ACF and
48
Information Sciences Institute
Solution Overview
8/14/13&
Copyright&USC/ISI.&All&rights&reserved.&
36&
10101101………1011101!
01010010………0011011!
00011110………0000111!
…!
11111001………0010100!
10101010………1000001!
Length p = 3 mod 4 (e.g. 6173)
Spreading gain = 10 log (p)
Class size = (p-1)/2
Message bits log
2
((p-1)/2)
BPSK&
modulate&
Transmit hydrophone
Input parameters:
(message bits, spreading gain) = p

Figure 4.5: Coding System Design Overview
CCF properties and the generation algorithm is computationally simple. See appendix
B for a summary of their construction.
4.3 System Design Summary
Figure 4.5 is a summary of the system design we have developed here to create an under-
water acoustic signal capable of supporting data transmissions and acoustic tomography
simultaneously. The steps are as follows:
1. Measure or estimate the spreading gainG necessary to overcome channel noise.
2. SetL = 10
(G=10)
3. SetM = 2
N
whereN is the maximum message size in bits.
4. SetP
0
equal to the greater of 2L or 2M.
5. FindP as a 3mod 4 prime number greater thanP
0
49
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Audio Signal
Figure 4.6: Received Audio Channel at Node A
6. Use the construction method detailed in appendix B to generate a set of of size
(P 1)=2 containing orthogonal pseudo noise sequences with sequence lengthP
7. Assign the set of sequences to unencoded messages as required by the specifics of
then deployed network.
4.4 System Verification Experiment
To verify that our system works as designed we performed an experiment to show that
the same signal allows for precise timing, data transmission and overlapping orthogonal
transmission. We set P = 6173 to obtain 37 dB of spreading gain. Two orthogonal
codes ‘q1’ and ’q3’ were generated. We performed the experiment in our Marina Del
Rey testbed as shown in figure 3.4. The code ‘q1’ was transmitted from node C while
node D transmitted code ‘q3.’ Each code was repeated 9 times exactly 1 second apart.
The codes were BPSK modulated with a 12 kHz carrier and the acoustic channel was
sampled at 96 kHz. The transmissions were coordinated so that the signal arrived over-
lapping at node A. Figure 4.6 shows the raw acoustic signal recorded at node A, showing
50
0 100000 200000 300000 400000 500000 600000 700000 800000 900000
Sample Time
q1 arrivals at node 3603
Figure 4.7: Detection of ‘q1’ at Node A
0 100000 200000 300000 400000 500000 600000 700000 800000 900000
Sample Time
q3 arrivals at node 3603
Figure 4.8: Detection of ‘q3’ at Node A
high levels of impulse noise. Signal ‘q1’ is assigned as the< NODEID > message
for node C and ‘q3’ is assigned as the < NODEID > message for node D. Figure
4.7 shows the detection of code ‘q1’ from the acoustic signal while similarly figure 4.8
shows the detection of code ‘q3.’ The spikes representing the detected signal are exactly
96,000 samples apart, indicating += one sample precision on arrival time. Since the
51
signal is also recorded and detected at the transmitter, these precise arrival times can be
used to precisely calculate travel time.
The same figures can also be seen as confirmation of data transmission and orthog-
onality. The messages were transmitted so that they overlapped at the receiver, and
thus since we can clearly detect two district messages in the audio signal, the message
< NODEID > was successfully received from both senders even though the signals
overlapped at the receiver.
4.5 Conclusion
In this chapter we have presented a coding technique for underwater sensor networks
that allows for simultaneous data and sensing transmissions by supporting precise arrival
time measurements and robust decoding in the presence of noise. The coding scheme
supports low-bandwidth data transmissions by considering message formats of fixed
length. Medium access control is supported because the codes used are orthogonal
therefore allowing overlapping transmissions. The coding scheme is parameterized by
the channel conditions observed between nodes and thus can be deployed in a wide
variety of situations. We presented experimental results showing successful data trans-
mission and precise arrival time measurements.
52
Chapter 5
Multipulse Acoustic Tomography
5.1 Introduction
Ocean acoustic tomography is a well known technique for studying the distribution of
water properties in the ocean. Ocean acoustic tomography techniques are travel time
tomography techniques that measure the time-of-flight for an acoustic signal travel-
ing between a sender and one or more receivers. The speed-of-sound in ocean water
is dependent on temperature, salinity, depth and current flow and various tomography
techniques have been demonstrated that reconstruct one or more of these parameters.
Ocean acoustic tomography techniques can be divided into two classes: vertical
slice or horizontal slice. Vertical slice techniques aim to reconstruct or model over some
area the sound-speed profile of the water as it varies by depth. Vertical slice techniques
use the time delay between multi path arrivals of the same signal to model the depth
dependent sound speed profile. Horizontal slice techniques aim to reconstruct or model
the sound speed-profile as it varies over the area at constant depth. Deployments and
demonstrations of both types of technique have been performed at various scales since
ocean acoustic tomography was first proposed by Munk et al circa 1980. Large scale
experiments have been performed across the Pacific Basin, while other experiments have
been performed at medium scale in the Atlantic Ocean, Mediterranean Sea and else
where. At the small scale, costal experiments have been performed near shore, while
53
our work with sensor network acoustic tomography has shown the technique at the sub-
kilometer scale.
Our sensor network acoustic tomography technique is a horizontal slice tomogra-
phy technique that shows high-resolution water temperature sensing is possible using
a sensor network. We developed the technique to improve the spatial sampling resolu-
tion of underwater sensor networks by using acoustic communications to do acoustic
tomography between the nodes.
In a horizontal slice acoustic tomography system nodes are arranged in and around
the area of water under study. Acoustic signals are sent between the nodes. Tradition-
ally, for each node pair an average temperature along the path can be determined. In
order to measure water temperatures spatially around a region, multiple sender-receiver
pairs are arrayed around the region. Using tomographic inversion techniques the set
of pair-wise average temperatures can be turned into a 2D map of water temperature.
The number of intersection points between the pair-wise paths roughly determines the
spatial resolution of the map. Thus, in order to obtain high resolution maps there must
be a sufficient number of sender-receiver pairs and they must be arranged strategically
around the region. These constraints effectively limit the spatial resolution of the water
temperature maps to be some constant factor of the number of deployed nodes, which
in turn is generally limited by the cost of deploying and maintaining an ocean asset.
Adding more nodes to increase spatial resolution is not always practical, therefore,
another aspect of travel-time tomography systems must be found that can be modified
to increase spatial resolution. In this chapter we focus on removing the limitation that
each travel-time measurement represents only the average of the water conditions along
the path by introducing a new travel-time acoustic tomography technique we are calling
multipulse acoustic tomography. Initially we are focusing on tracking speed-of-sound
54
changes caused by changes in water temperature. By sending multiple, bi-directional
acoustic signals (pulses) back-to-back and carefully keeping track of the differences in
travel time between the pulses, we show that as the water temperature changes, the distri-
bution of the changes along the acoustic path can be determined. We divide the acoustic
path into sub-regions and derive the relative temperature change for each region. We
show that the number of regions (and thus spatial resolution) is limited by the timing
precision of the time-of-flight measurements. We provide a parameterized equation that
will help system designers understand the spatial and temporal resolution constraints
given the locations of the nodes and timing precision of their acoustic transceivers.
To understand conceptually how this is possible, imagine a scenario where the region
between two nodes (node 0, node 1) is divided into two parts (region A and region B).
We constrain the problem by requiring that the water temperature changes slowly com-
pared to the total time of flight (a good assumption for natural environments). Pulses are
sent simultaneously from both nodes towards the other node. If the water temperature
in region A changes after the pulses have crossed the center line, then only the pulse
traveling from node 1 to node 0 will see any change in time-of-flight. Thus, we can
convert the change in time-of-flight to a change in temperature and assign this tempera-
ture change to region 1. The process is repeated continuously and thus the distribution
of temperature changes over the path is determined. This simple thought experiment
forms the core of our technique and we are able to expand the number of sub-regions to
any even number under the further constraint that at a minimum there must be the same
number of pulses in flight as sub-regions.
Mutlipulse acoustic tomography changes the assumption that only an average tem-
perature reading can be obtained for each sender-reciever pair. In section 5.2.2 we show
55
that the spatial resolution that can be obtained along the path is dependent on the preci-
sion to which times-of-flight can be measured. With a multipulse acoustic tomography
system the input to the reconstruction and modeling algorithms is a high resolution, spa-
tial distribution of water temperature along each path. This increases the accuracy and
resolution of the 2D water temperature maps that are the ultimate goal for horizontal
slice acoustic tomography systems. System designers can also trade resolution for node
density, achieving similar resolution with fewer nodes, or covering larger areas at the
same resolution with the same number of nodes.
In this chapter we introduce the system design of multipulse acoustic tomography
(section 5.2) and discuss the design constraints that are imposed. We introduce an algo-
rithm for deriving the spatial distribution of water temperature changes along a single
path (section 5.2.2) and through simulation (section 5.2.4) show that the algorithm works
under a set of constraints that are reasonable when targeting real-world phenomenon.
Finally, we briefly discuss the generality of our system (section 5.3) and propose several
other domains in which travel-time tomography techniques can be adapted to a multi-
pulse configuration.
5.2 Multipulse Acoustic Tomography
5.2.1 System Description
While ocean acoustic tomography systems generally have many nodes acting as senders
and/or recovers, we will introduce the multipulse acoustic tomography technique by
considering the simple case of two nodes, each acting as a sender and receiver (see
figure 5.1). We will also assume the following constraints: current flow between the
nodes is negligible, and the salinity and depth are constant. The sender/receiver nodes
56
N1

N0

N3

N4

Midpoint!
Pulses t
e
apart!
Segment A! Segment B!
Figure 5.1: Two sender/receiver nodes
are equipped with acoustic transceivers and use GPS or some other method to precisely
measure the time-of-flight for acoustic signals.
5.2.2 Problem Formulation
We desire to map out the distribution of temperatures along the acoustic path between
the two nodes by sending acoustic signals between the two nodes using only the time-of-
flight information to calculate the distribution. The time-of-flight for an acoustic signal
is representative of the average speed-of-sound along the path travelled by the signal,
with the speed-of-sound at a particular point along the path varying with time. Thus, if
we section the acoustic path intoN segments of lengthd, then we have the spatially and
temporally varying speed-of-sound fieldc(i;t) and the time-of-flight for thei
th
segment
is:

i
=
d
c(i;t)
(5.1)
To find the total time-of-flight we calculate the time-of-flight for each segment and sum:
=
N1
X
i=0
d
i
c(i;t =t
0
+
P
i1
j=0

j
)
(5.2)
57
The recursive term in the denominator accounts for the travel-time up to the point the
signal reaches segmenti, witht
0
being the start time. If we assume that the travel time
for each segment is nominally somet
e
then this equation can be simplified to:
N1

N0

N3

N4

Pulses t
e
apart!
Segment A!
Segments! A! B! C! D!
System 1!
System 2!
System 3!
Figure 5.2: Multipuse tomography with four segments
=
N1
X
i=0
d
i
c(i;t =t
0
+it
e
)
(5.3)
Given the discretized model for the average-speed of sound, and a number of obser-
vations of the time-of-flight for an acoustic signal, we seek a way to use the observed
changes in time-of-flight to assign these changes as changes in the sound-speed field.
To understand our solution to this problem we build up from the simple case where the
acoustic path is sectioned in two pieces. We simultaneously send signals from each node
with the signals spaced in time such that a new signal is generated when the previous
signal reaches the half-way point between the two nodes (we will call this time interval
t
e
). See figure 5.1 for a schematic representation.
Using the idea that the total time-of-flight can be broken into a time-dependent sum-
mation, we denote the time-of-flight for a signal through path section m at time t as
58

m
(t) and the time-of-flight for pulse n from node N0 to N1 as
+
n
= , where the
plus sign indicates the direction (from lower numbered node to higher is denoted as +,
higher node to lower). We can then write the following equations for the observed
times-of-flight for the first pulse from each node:
8
>
>
<
>
>
:

+
0
=
A
(0) +
B
(t
e
)

0
=
B
(0) +
A
(t
e
)
(5.4)
After timet
e
each node again transmits a pulse at the point in time the previous pulses
are crossing at the middle. We write the equation for the second set of pulses:
8
>
>
<
>
>
:

+
0
=
A
(t
e
) +
B
(2t
e
)

0
=
B
(t
e
) +
A
(2t
e
)
(5.5)
Notice how the right-most elements in equation 5.4 appear in equation 5.5. We now
combine the time-of-flight equations from 5.4 and 5.5 into one system of equations:
8
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
:

+
0
=
A
(0) +
B
(t
e
)

0
=
B
(0) +
A
(t
e
)

+
1
=
A
(t
e
) +
B
(2t
e
)

1
=
B
(t
e
) +
A
(2t
e
)
(5.6)
We now have the four time-of-flight observations and six unknown sub-section times-
of-flight. We now make the assumption that we know a priori the initial conditions
(i.e.
A
(0) and
B
(0)), and under this assumption the system of equations can be solved
for
A
and
B
att = t
e
andt = 2t
e
. To continue to track the distribution of water
59
temperature changes over time a new system of equations can then be formed for the
next two pulses using
A
(2t
e
) and
B
(2t
e
) as the initial conditions and the process
repeated, or the system of equation can be extended by an arbitrary number of pulses
and solved all at once. Setting up the model for temperature changes in this manner
assumes that the water temperature is constant over eacht
e
interval, which is obviously
not the case in realistic scenarios. However, when the rate of water temperature change
is small, such that there is only a small increase or decrease over the time interval t
e
,
then this assumption can be considered valid. In section 5.2.8 we will discuss the system
design equations and examine how slowly the temperature must be changing for this
assumption to remain valid.
5.2.3 Extension to an arbitrary number of segments
It is intuitive to see that multipulse acoustic tomography can split the acoustic path in
two pieces because for each bi-directional exchange of pulses we measure two travel-
times. This presents a problem, however, when considering how to extend the technique
to more than two sub-sections. The answer to the problem is found by changing the
phase between the transmission of the two pulses. This changes the point where the two
signals cross and thus changes the geometry of the sub-sections. If we transmitN pairs
of pulses with the proper phase we can divide the acoustic path into N sections. We
build up the system of equations as before, however the initial conditions are adjusted
to account for the relative size of each side of the system. What results is a set of
overlapping temperature distributions. If we then subtract the distributions properly we
can arrive at the total distribution across allN sections. Figure 5.2 shows how we do
this for N = 4. In the figure each system is divided into a left-side and a right-side.
60
In order to calculate the speed-of-sound in segment A, we subtract the left-hand side of
system 2 from system 1. Similarly we find the speed-of-sound for each segment.
Conceptually the pulse pairs can be thought of separately, however, the result of this
procedure is that a bi-directional pulse train ofN signals separated byt
e
can be used to
map the distribution of water temperature changes overN sub-sections of the acoustic
path.
5.2.4 Simulation Results
To examine the feasibility of multipulse acoustic tomography we built an event-based
simulator that can simulate the travel time for acoustic pulses traveling between two
underwater nodes. The simulated water through which the pulses travel can be pro-
gramed to change temperature over time. The number of segments, rate of water tem-
perature change and time between pulses are fully configurable. The resulting times-of-
flight are then used with the system-of-equations algorithm described in section 5.2.2 to
track the distribution of temperature changes over time.
5.2.5 1D Simulation
The setup for the simulation presented here was as follows. The distance between the
nodesD is 6km and we sub-divided the acoustic path intoN = 4 segments. This gives
D
S
= 1:5 km. We selected a nominal (starting) speed-of-sound of 1500 m=s, which
gives t
e
= 1 s. This means that each node will transmit a pulse into the water every
one second, which as discussed in section 5.2.7 gives us the required N = 4 pulses
in-flight bi-directionally from each node. The goal then for this simulation is to derive
the average speed-of-sound in each segment as the water temperature in each segment
is changed independently of the other segments.
61

0
0.05
0.1
0.15
0.2
0.25
Segments! A! B! C! D!
Time!
Temperature Change (degrees C)!
(a) Target Water Temperature Distribution vs. Time

0
0.05
0.1
0.15
0.2
0.25
Segments! A! B! C! D!
Time!
Temperature Change (degrees C)!
(b) Reconstructed Water Temperature Distribution
vs. Time
Figure 5.3: 1D simulation of multipulse acoustic tomography with four segments
Starting from the nominal state we programmed a scenario where each water seg-
ment will heat and then cool over the course of 12 minutes starting with segment A. The
heating and cooling is staggered such that when segment A reaches peak temperature,
segment B begins to heat. Similarly, when segment B reaches peak temperature, seg-
ment A has returned to nominal and segment C begins to heat. This pattern is repeated
for segment D as well. The rate of temperature change is 0:6

C=hr, which corresponds
to a speed-of-sound rate-of-change of 7:5 10
4
m=s
2
. Figure A.2(a) shows the target
as a series of stacked maps showing the distribution of water temperature as a function
of distance and time. Figure 5.3(b) show the simulation results, also as a function of
distance and time, but calculated by the multipulse algorithm described in section 5.2.2.
The heating and cooling cycles can be seen moving across the segments. A traditional
tomography system does not yield an interesting graphic for this scenario, such a system
would only return a single value at each time step representing the average temperature
62
N0
N1
N2
N3
N4
N5
Figure 5.4: Schematic layout of six node 2D simulation
along the path.. As compared to only measuring the average speed-of-sound over the
6km acoustic path, multipulse acoustic tomography provides a detailed map of how the
water temperature changes have accumulated spatially.
5.2.6 2D Simulation and Reconstruction
The 1D simulation presented in section 5.2.5 shows that multipulse acoustic tomogra-
phy can detect changes in speed-of-sound caused by changing water temperature and
correctly assign the change to one or more segments. However, as the top-level goal of
the work presented in this dissertation is to increase the resolution of water temperature
sensing, we designed a 2D simulation to showcase the increase in spatial resolution and
reconstruction accuracy possible with multipulse acoustic tomography.
The geometry of the simulation is show in figure 5.4, where the simulated water area
is 4 km x 4 km. Six nodes were arranged on the ‘east’ and ‘west’ side of the simulation.
Each of the nine acoustic paths were split into four segments using multipulse acoustic
tomography. A complex heating and cooling geometry was simulated by dividing the
water area into a 100 x 100 grid where the water temperature in each grid section could
63
(a) Target t=0 (b) Target t=15 minutes
(c) Target t=30 minutes (d) Target t=45 minutes
(e) Target t=60 minutes
Figure 5.5: 2D Simulation - Target
64
(a) Least-squares t=0 (b) Least-squares t=15 minutes
(c) Least-squares t=30 minutes (d) Least-squares t=45 minutes
(e) Least-squares t=60 minutes
Figure 5.6: 2D Simulation - Least-squares
65
(a) Least-squares t=0 (b) Multipulse t=15 minutes
(c) Multipulse t=30 minutes (d) Multipulse t=45 minutes
(e) Multipulse t=60 minutes
Figure 5.7: 2D Simulation - Multipulse
66
be individually varied. The hot and cold spots grew and then shrank over the course of
a simulated hour. A time series of the target is presented in figure 5.5.
In order to compare to how standard acoustic tomography would perform on such a
simulation we also used the time-of-flight data with a least-squares based reconstruction
algorithm. A time series of the least-squares reconstruction is presented in figure 5.6
and shows very poor reconstruction performance. The poor reconstruction performance
is due to the fact that the average temperatures measured by the times-of-flight do not
carry any spatial information and the heating and cooling geometry leads to spatially
ambiguous results. This simulation highlights how traditional tomography techniques
require additional assumptions or nodes to disambiguate the data.
To reconstruct the simulated heating and cooling profile with the multipulse algo-
rithm we use the spatial location of the 36 midpoints and fit a surface to the spatial
distribution given as the result of the multipulse algorithm. A time series of the multi-
pulse reconstruction is shown in figure 5.7. Over the course of the simulation the least
squares method has a maximum error of 2:9

C, with a RMS error of 1:6

C. In compar-
ison, the multipluse based reconstruction has a maximum error of 0:38

C, with a RMS
error of 0:12

C. These simulation results demonstrate that multipulse acoustic tomog-
raphy enables reconstruction algorithms to return more accurate and higher resolution
reconstructions of the underlying data.
5.2.7 Design Constraints
In order for multipulse acoustic tomography to be of practical use system designers
must understand the constraints put on an implementation by the described algorithm.
For this analysis we start with the timing precision or time resolution of the acoustic
communications provided by the underwater sensor nodes (t) the internode distance
67
(D) and the number of desired segments (N). We also use c
o
to indicate the nominal
speed-of-sound in water and as the coefficient of the linear term in the relation between
speed-of-sound in water and temperature. Using these variables we will then describe
the equation that governs that spatial and temperature resolution of a multipulse acoustic
tomography system.
The key observation to make when considering the design of a multipulse acoustic
tomography system is that there exists a trade-off between spatial resolution and tem-
perature resolution. Intuitively, this can been seen by observing that for longer segments
a small change in average temperature has more time to act, thus it can effect a greater
change on the total time-of-flight for an acoustic signal traveling through the segment.
Using our notation, the segment distance is:
D
s
=D=N (5.7)
Since the terms of interest (D
s
and T ) are intimately related by the timing precision
(t) of a multipulse system we derive the design equation in terms of the minimum seg-
ment size. We do this because we assume that the timing precision will be fixed by the
equipment available when designing the system and the desired temperature resolution
will be dictated by scientific or industrial requirements.
We derive the equation forD
s
by calculating the minimum distance required such
that a T change in temperature will result in a detectable amount of change in time-
of-flight (i.e 1t):
D
s
=
t

1
co

1
co+T
(5.8)
Thus in sea-water with a nominal c
o
= 1500 m=s and = 4:591, timing precision
of t = 10 s and a desired temperature resolution of T = 0:1

C, the minimum
68
segment size is found to be 49 m. The sanity check for this result is found in our
sensor network acoustic tomography results (presented in chapter 3) where sub-degree
temperature resolution was obtained down to 50m internode distance.
Of course, if dictating the spatial resolution is more important equation 5.8 can be re-
arranged and solved for T in terms of the spatial resolution (D
s
) and timing precision
(t):
T =
1

1
1
co

t
Ds
c
o
!
(5.9)
This form of the design equation will give system designers the temperature resolution
they can expect from a multipulse tomography system given a predetermined spatial
resolution.
5.2.8 Error Analysis
If the water under study were so well behaved as to change temperature in discrete
steps synchronously with every pulse cycle, then the equations in section 5.2.2 would
be exact and thus there would be no error. Alas, since we study natural, poorly behaved
phenomenon we must analyze the assumptions that underly our multipulse tomography
system in order to understand the sources of error.
We make one main assumption that we find dominate the error analysis. We assume
that the pulses cross at a fixed location (i.e. in the middle of the acoustic path), sub-
dividing the acoustic path into well defined pieces. In reality the mid-point that defines
the sub-sections will vary as the average water temperature changes on either side of
the nominal mid-point. In effect it will ‘wander’ back-and-forth changing the size of
the sub-sections. Therefore, the pulses can be seen as being ‘out of phase’ and thus
measuring the speed-of-sound of a sub-section at slightly different times. The pulses
can become out of phase due to slowly accumulating temperature differences on either
69
side of a section boundary, or due to rapidly changing water temperatures (with the
correspondingly rapid change in speed-of-sound).
To understand the magnitude of the error caused by the mid-point shifting, we start
with equation 5.6, however we slightly change the notation to indicate the direction a
pulse is traveling for each segment:
8
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
:

+
0
=
+
A
(0) +
+
B
(t
e
)

0
=

B
(0) +

A
(t
e
)

+
1
=
+
A
(t
e
) +
+
B
(2t
e
)

+
1
=
+
B
(t
e
) +

A
(2t
e
)
(5.10)
In order to solve the system of equations we assume that
+
B
(t
e
)

B
(t
e
) and

A
(t
e
)
+
A
(t
e
). This is the same as saying the pulse traveling one direction mea-
sures the same conditions as the pulse traveling the opposite direction, because they
arrive at the segment at the same time. However, if the pulses are out of phase (i.e. the
mid-point has shifted), then these equivalencies do not hold and the error in the solution
for
A
(2t
e
) and
B
(2t
e
) is

A
(t
e
)
+
A
(t
e
) and
+
B
(t
e
)

B
(t
e
), respectively.
Given this result we can examine the expected magnitude of this error. The error is
exactly the difference in average speed-of-sound for a given segment as measured by the
two out-of-phase pulses. If we denote the time-offset between the pulses, or phase as
then the difference in average speed-of-sound (and thus the error seen above) is the rate
of change in speed-of-sound times, or
c
t
. If we have two nodes separated by 3km,
and the speed-of-sound difference between the two 1.5 km sections is 15 m/s, then the
mid-point will have shifted 7.5 m. At a nominal speed of 1500 m/s, this gives = 0:005
70
s. If we use a realistic rate of change of 2

C=12hr = 5 10
5
C=s 1 10
5
m=s=s,
then the error per pulse cycle is 5 10
8
m=s.
The second case we consider is that of phase offset caused by rapidly changing water
temperatures. Here the phase offset occurs because pulses that enter a water section
spaced byt
e
do not exit the water section with that spacing, their relative phase is shifted
by the difference in time-of-flight accumulated overt
e
. This can then be similarly used
to approximate the error caused by rapidly changing water temperatures.
5.3 Conclusion
This chapter introduces multipulse acoustic tomography as a novel travel-time acous-
tic tomography technique for the under water environment. The technique improves
existing travel time tomography techniques by breaking the assumption that for each
sender-receiver pair only the average signal speed along the path can be determined.
By using multiple, bi-directional signals (pulses) we show that changes in time-of-flight
(and therefore average speed-of-sound) can be allocated to sub-sections of the acoustic
path. Thus, for each sender-receiver we now obtain the distribution in speed-of-sound
along the acoustic path. We presented the system design and design constraints that
can be used to determined the spatial and temperature resolution possible with mul-
tipulse acoustic tomography. The simulation results we presented showed that multi-
pulse acoustic tomography yields high-resolution water temperature maps and does not
require any sophisticated statistical or spatial assumptions be made a priori for recon-
struction.
71
Chapter 6
Extending Multipulse Tomography to
Other Domains
6.1 Introduction
Multipulse acoustic tomography was presented in chapter 5 in the context of underwater
sensor networks for performing high-resolution water temperature measurements. How-
ever, nothing in the system design is specific to signals traveling in sea water, except for
the coefficient that accounts for the relation between temperature and speed-of-sound in
water.
Therefore, in this chapter we explore other travel-time domains where multipulse
tomography can be applied. Using the design constraints discussed in chapter 5 we
examine several domains so that we can understand the temperature and spatial resolu-
tion that can be obtained.
6.2 Multipulse Tomography for Atmospheric Tempera-
ture Monitoring
Discussed in chapter 2 atmospheric acoustic tomography is a similar technique to ocean
acoustic tomography as it relies on the dependance of speed-of-sound in air and the air
temperature and the relation between speed-of-sound in air and air temperature is also
72
linear. Of interest to an implementation of multipulse acoustic tomography in air is the
overall slower speed-of-sound (c
o
= 330m=s in air vs. c
o
= 1500m=s for sea water).
This implies that the timing constraints for multipulse acoustic tomography will be more
relaxed, however the coefficient for the linear relationship between temperature and
sound speed is smaller and thus for a given temperature change we expect less change
in speed-of-sound than is seen in sea water. The design constraints developed in chapter
5 are therefore helpful to understand the relationship between temperature resolution,
spatial resolution and time-of-flight precision that can be expected if mutlipulse acoustic
tomography is implement in air.
For the range of temperatures seen in the lower atmosphere the speed-of-sound in
air can be approximated by the following relation [35]:
c(T ) = 331:4 + 0:6T m=s (6.1)
Therefore we can see that = 0:6. If we have nominalc
o
= 330m=s, sample at 96
kHz, and would like to have 0:1

C temperature resolution then we can use equation 5.8
(included again here):
D
s
=
t

1
co

1
co+T

to calculate the minimum segment size. Using the above parameters we find the min-
imum segment size to be 18.9 m. Such a segment size is reasonable and implies that
one could successfully implement multipulse tomography for atmospheric temperature
monitoring.
73
6.3 Multipulse Tomography for Temperature Monitor-
ing of Electrical Power Lines
Electrical power lines are a critical piece of infrastructure because failures that lead to
large or small blackouts can have wide ranging consequences. In 2003 a large portion
of the eastern United States and some small parts of Canada were blacked out when
a cascade of failures caused a grid collapse [39]. The root cause of the initial failure
was a power line that sagged when it over heated, causing it to come in contact with
tree branches. Monitoring of power lines with high spatial resolution would allow such
failures to be detected in advance or even avoided all together. As power lines lose effi-
ciency as they heat, such fine grained temperature monitoring would also allow operators
to better manage the power flowing through their lines. Many power lines run for many
10’s if not 100’s of kilometers and thus power line systems engineers do not have a good
solution for monitoring the temperature of power lines with high spatial resolution due
to the high cost of installing and maintaining the large number of sensors that would be
required.
Thus if multipulse tomography can be adapted to work on power lines, a system
could be designed that would monitor the temperature of the power line in segments
along its length. The existence of time-domain reflectometers shows that the speed
of a signal in an electrical power line is a measurable quantity. In order to implement
multipulse tomography on a power line, we then need to understand the relation between
signal speed and temperature. The speed of a signal on a power line is related to the
inductance per unit length and the capacitance per unit length. It can be shown that the
unit capacitance does not vary significantly with temperature and thus the variation in
signal speed with temperature depends on changes in unit inductance [11].
74
Using parameters also found in [11] we can choosec
o
= 810
7
m=s and = 210
5
.
For this example we again use equation 5.8, but with T = 1

C. Also we will solve
for the minimum segment size with varioust to understand the segment sizes possible.
Using these parameters we find the following:
t = 1s;D
s
= 33km
t = 30ns;D
s
= 1km
t = 3ns;D
s
= 100m
At of 3 ns corresponds to a sampling rate of approximately 300 MHz. While much
more precise than required for air or sea water, measuring the time-of-flight for an elec-
trical signal to a precision of 3 ns is technically feasible.
75
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[3] URLhttp://www.argo.ucsd.edu/.
[4] URLhttp://www.benthowave.com/.
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Appendix A
Calculating Sub-Sample Arrival Times
for High Precision Time-of-Flight
A.1 Introduction
The basic measurement for acoustic tomography is the time-of-flight for a signal sent
between two points. In both sensor network acoustic tomography and multipulse acous-
tic tomography highly precise time-of-flight measurements are required. As described
in chapter 3 we obtain the time-of-flight by making two ‘arrival’ time observations: at
the sender (using self-listening) and at the receiver. We describe how a combination of
GPS and an audio sampling rate of 96 kHz will give arrival time precision of1 sample
period, or 10s.
For standard tomography techniques at kilometer scale 10s time-of-flight precision
will yield quite good results. However, in chapter 5 we show how the interconnected val-
ues of segment size and temperature precision are related by the time-of-flight precision
and thus to improve either quantity without sacrificing the other, better time-of-flight
precision must be obtained.
A simple solution is to simply use a higher sampling rate, however for several rea-
sons this may not always be practical. For example analog-to-digital converters gener-
ally get more expensive as the sampling rate increases, while also decreasing in dynamic
83
range (i.e. such an ADC would have a worse signal-to-noise ratio). Therefore the pur-
pose of this appendix is to describe a signal processing technique that can be used to
obtain time-of-arrivals with precision of less than one sample period.
A.2 Detecting Arrival Time With Cross-correlation
The most widely used signal processing technique for detecting a signal arrival in a dig-
ital signal is cross-correlation: the captured samples are cross-correlated with a known
signal. If the known signal is present in the incoming data, then the cross-correlation
exhibits a narrow peak. The location, or sample offset, of the peak in the captured sam-
ples indicates the arrival time of the signal at the receiver. Since the known signal and
incoming signal are sampled at the same rate, the location of the peak gives an arrival
time accurate to1 sample period.
This technique is in theory well documented in the literature, however, in practice
most examples simply state that cross-correlation provided the requisite results. While
developing the acoustic tomography techniques that are the subject of this dissertation,
we postulated that signal processing techniques such as up-sampling could be used to
detect the arrival of the signal with subsample precision. Again, in reading the literature
we found it lacking in specific examples that addressed this issue.
Thus we are including this appendix in this dissertation to document a signal pro-
cessing technique that detects signal arrivals with sub-sample precision. Specifically,
the example shown has a precision of
1
12
th
of a sample. This is of course equivalent to
the arrival time precision that would be obtained with an ADC running at 12 times the
sampling rate. We hope that this documentation will be useful to readers who need to
implement similar signal detection schemes.
84
-1
-0.5
0
0.5
1
0 1 2 3 4 5 6 7 8 9 10 11 12
Figure A.1: Sampled Sine
A.3 Sampling Phase
Consider the simple signal shown in figure A.1, which is of course one period of a sine
signal. The circles represent the sample points that would constitute the ‘known’ signal
as described above. Assuming Nyquist conditions are met, when the signal is output
through an digital-to-analog converter (DAC) and played into the transmission medium
(for this example the air), the analog signal (i.e the pressure wave) will be a very close
representation of the solid line in figure A.1. When the signal arrives at the analog-
to-digital converter (ADC) at the receiver, we can not guarantee that the phase of the
sampling will match that of the signal stored as the ‘known’ signal. Two examples of
how the signal might be sampled at the receiver are shown in figure A.2(b). Generally
the cross-correlation function will return the peak at the location of samples
0
, however
this could be almost one sample later than the actual arrival time.
85
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8 9 10 11 12
(a) Sine sampled with
1
2
sample offset
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8 9 10 11 12
(b) Sine sampled with
9
10
sample offset
Figure A.2: Sample sine with different sample offsets
Therefore, we are looking for a way to transform the received signal and perform the
cross-correlation in such a way that the peak will be returned at the actual arrival time,
even if this does not fall exactly on a sample.
A.4 Signal Processing Details
By careful application of up sampling we can achieve the desired results. The signal
processing described in this section may seem obvious, however we found no specific,
experimentally documented implementation described in the travel-time tomography
(and related) literature.
In order to obtain sub-sample time of arrival the following signal processing chain
is implemented, with block diagram shown in figure A.3.
If the sampling rate of the DAC and ADC at the sender and receiver are bothF
s
,
then determine the up sampling factorN
Construct the known signals with a sampling rate ofNF
s
, stores at the receiver.
Down-samples by a factor ofN to create ~ s
86
↓1/N
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8 9 10 11 12
(a) Sine sampled with
1
2
sample offset
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8 9 10 11 12
(b) Sine sampled with
9
10
sample offset
Figure A.2: Sample sine with different sample offsets
Therefore,wearelookingforawaytotransformthereceivedsignalandperformthe
cross-correlation in such a way that the peak will be returned at the actual arrival time,
even if this does not fall exactly on a sample.
A.4 Signal Processing Details
By careful application of up sampling we can achieve the desired results. The signal
processing described in this section may seem obvious, however we found no specific,
experimentally documented implementation described in the travel-time tomography
(and related) literature.
In order to obtain sub-sample time of arrival the following signal processing chain
is implemented, with block diagram shown in figure ??.
• If the sampling rate of the DAC and ADC at the sender and receiver are bothF
s
,
then determine the up sampling factorN
• ConstructtheknownsignalswithasamplingrateofN⇤ F
s
,storesatthereceiver.
• Down-samples by a factor ofN to create ˜ s
75
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8 9 10 11 12
(a) Sine sampled with
1
2
sample offset
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8 9 10 11 12
(b) Sine sampled with
9
10
sample offset
Figure A.2: Sample sine with different sample offsets
Therefore,wearelookingforawaytotransformthereceivedsignalandperformthe
cross-correlation in such a way that the peak will be returned at the actual arrival time,
even if this does not fall exactly on a sample.
A.4 Signal Processing Details
By careful application of up sampling we can achieve the desired results. The signal
processing described in this section may seem obvious, however we found no specific,
experimentally documented implementation described in the travel-time tomography
(and related) literature.
In order to obtain sub-sample time of arrival the following signal processing chain
is implemented, with block diagram shown in figure ??.
• If the sampling rate of the DAC and ADC at the sender and receiver are bothF
s
,
then determine the up sampling factorN
• ConstructtheknownsignalswithasamplingrateofN⇤ F
s
,storesatthereceiver.
• Down-samples by a factor ofN to create ˜ s
75
DAC
Sender
ADC
• Use ˜ s with the DAC at the sender when required to transmit the signal.
• At the receiver a long sequence of samples ˆ x is received with sampling rateF
s
• Up sample ˆ x by a factor ofN to obtainx with a sampling rate ofN ⇤ F
s
• Cross-correlate s with x. The peak in the CCF will occur at some sample offset
M
• Compute the arrival time as a fractional sample offsett =
M
N
The result of these signal processing operations ist, which is now a fractional value
that represents the arrival time with sub-sample precision.
A.5 In-air Experiment
In order to verify our signal processing technique we constructed an in-air experiment.
A sound file with a known signal was created atN ⇤ F
s
=96 kHz. The sound file was
then down-sampled by a factor of N =12 to give a file with F
s
=8 kHz. The sound
file contained 2 channels and the signal was present in both channels. On a ‘transmit’
laptop, channel 1 was played into a speaker, while channel 2 was electrically connected
directly to the channel 2 input on a ‘receive’ laptop. A microphone was mounted to
an adjustable stage directly opposite the speaker and the output of the microphone was
connected to channel 1 input of the receive laptop. A block diagram of the experiment
is presented in figure ??,
The receive laptop was recording with F
s
=8 kHz. The signal was repeated at
five second intervals, between which the stage was adjusted to move the microphone
closer to the speaker by approximately0.5 cm. The signal was repeated 30 times which
corresponds to a total stage travel distance of approximately 2.5 samples.
76
↑N
• Use ˜ s with the DAC at the sender when required to transmit the signal.
• At the receiver a long sequence of samples ˆ x is received with sampling rateF
s
• Up sample ˆ x by a factor ofN to obtainx with a sampling rate ofN ⇤ F
s
• Cross-correlate s with x. The peak in the CCF will occur at some sample offset
M
• Compute the arrival time as a fractional sample offsett =
M
N
The result of these signal processing operations ist, which is now a fractional value
that represents the arrival time with sub-sample precision.
A.5 In-air Experiment
In order to verify our signal processing technique we constructed an in-air experiment.
A sound file with a known signal was created atN ⇤ F
s
=96 kHz. The sound file was
then down-sampled by a factor of N =12 to give a file with F
s
=8 kHz. The sound
file contained 2 channels and the signal was present in both channels. On a ‘transmit’
laptop, channel 1 was played into a speaker, while channel 2 was electrically connected
directly to the channel 2 input on a ‘receive’ laptop. A microphone was mounted to
an adjustable stage directly opposite the speaker and the output of the microphone was
connected to channel 1 input of the receive laptop. A block diagram of the experiment
is presented in figure ??,
The receive laptop was recording with F
s
=8 kHz. The signal was repeated at
five second intervals, between which the stage was adjusted to move the microphone
closer to the speaker by approximately0.5 cm. The signal was repeated 30 times which
corresponds to a total stage travel distance of approximately 2.5 samples.
76
XCORR
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8 9 10 11 12
(a) Sine sampled with
1
2
sample offset
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8 9 10 11 12
(b) Sine sampled with
9
10
sample offset
Figure A.2: Sample sine with different sample offsets
Therefore,wearelookingforawaytotransformthereceivedsignalandperformthe
cross-correlation in such a way that the peak will be returned at the actual arrival time,
even if this does not fall exactly on a sample.
A.4 Signal Processing Details
By careful application of up sampling we can achieve the desired results. The signal
processing described in this section may seem obvious, however we found no specific,
experimentally documented implementation described in the travel-time tomography
(and related) literature.
In order to obtain sub-sample time of arrival the following signal processing chain
is implemented, with block diagram shown in figure ??.
• If the sampling rate of the DAC and ADC at the sender and receiver are bothF
s
,
then determine the up sampling factorN
• ConstructtheknownsignalswithasamplingrateofN⇤ F
s
,storesatthereceiver.
• Down-samples by a factor ofN to create ˜ s
75
peak find
divide by
N
M
t Receiver
to receiver
from
sender
Figure A.3: Signal Processing Block Diagram
Use ~ s with the DAC at the sender when required to transmit the signal.
At the receiver a long sequence of samples ^ x is received with sampling rateF
s
Up sample ^ x by a factor ofN to obtainx with a sampling rate ofNF
s
Cross-correlates withx. The peak in the CCF will occur at some sample offset
M
Compute the arrival time as a fractional sample offsett =
M
N
The result of these signal processing operations ist, which is now a fractional value that
represents the arrival time with sub-sample precision.
A.5 In-air Experiment
In order to verify our signal processing technique we constructed an in-air experiment.
A sound file with a known signal was created atNF
s
= 96 kHz. The sound file was
then down-sampled by a factor ofN = 12 to give a file withF
s
= 8 kHz. The sound
file contained 2 channels and the signal was present in both channels. On a ‘transmit’
87
Laptop with
sound card
ch. 1
ch. 2
Laptop with
sound card
ch. 2
35 cm
microphone on adjustable stage speaker
Figure A.4: Experiment block diagram
laptop, channel 1 was played into a speaker, while channel 2 was electrically connected
directly to the channel 2 input on a ‘receive’ laptop. A microphone was mounted to
an adjustable stage directly opposite the speaker and the output of the microphone was
connected to channel 1 input of the receive laptop. A block diagram of the experiment is
presented in figure A.4. The receive laptop was recording withF
s
= 8 kHz. The signal
was repeated at five second intervals, between which the stage was adjusted to move the
microphone closer to the speaker by approximately 0:5 cm. The signal was repeated 30
times which corresponds to a total stage travel distance of approximately 2.5 samples.
Both channel 1 and channel 2 were processed using our subsample signal process-
ing technique. The arrival time obtained for channel 1 was subtracted from the arrival
obtained for channel 1. The offset between these two values represents the amount of
time in samples that it took for the signal to travel through the air.
The result of the experiment is shown in figure A.5. The y-axis of the graph is the
offset in samples between the arrival in channel 2 (the direct connection) and the arrival
in channel 1 (through the air). The one sample resolution of the conventional technique
can clearly be seen. In fact the travel time is not monotonically decreasing as would be
expected. As the travel time approaches the boundary between two samples the peak in
the cross correlation function will be spread out over two samples and small amounts of
noise may cause the peak to be detected at the incorrect sample offset. In contrast the
88
0 5 10 15 20 25 30
7.5
8
8.5
9
9.5
10
Position #
Sample offset (travel time)

subsample technique
conventional technique
Figure A.5: Experiment results
fractional travel times obtained by our subsample algorithms is monotonically decreas-
ing and shows that we are able to properly obtain travel times with a precision of
1
12
th
sample.
A.6 Discussion
Highly precise time-of-flight measurements on the order of< 1s are required to sup-
port the high-resolution ocean acoustic tomography techniques discussed in this dis-
sertation. In addition, extending multipulse tomography techniques to other domains
will require nano-second precision time-of-flight measurements. The signal processing
technique discussed in this appendix shows that the precision of a time-of-flight mea-
surement system based on digital sampling can be improved by at least one order of
magnitude over the intrinsic precision given by the ADC sampling rate. The technique
is a ‘software-only’ fix to the problem of improving time-of-flight precision that might
otherwise be solved with very expensive analog-to-digital converters.
89
Appendix B
Construction of
Guohua and Quan Sequences
This appendix is a summary of the construction method found in [27]. Arithmetic oper-
ations on the sequences below are performed position-wise modulo 2. First we define a
numberq2Z to be a quadratic residuemodp of some primep if the following holds:
9x2Z :x
2
qmodp (B.1)
We call the set of all suchq,QR
P
.q is called a quadric non-residue if B.1 does not hold,
and we denote the set asQNR
P
.
A Legendre sequenceL(t) of periodP ,P prime is defined as:
L(0) = 0;L(t) = 0;t2QR
P
;L(t) = 1;t2QNR
P
IfL
d
is the decimation byd of the sequenceL(t) (i.e. taking everydth element ofL(t)),
Guohua and Quan show that for Legendre sequences,L
d
(t) takes only one of two forms:
L
d
(t) =L(t);d2QR
P
or
L
d
(t) = 1 +L(t);d2QNR
P
90
Finally we define the operatorT
k
as a cyclic left shift byk positions. Given the above
equations Guohua and Quan construct the following sets:
M =

T
k
L
d
(t) +L(t);t = 0; 1;:::;P 1

;k = 1; 2;:::; (P 1)=2
N
0
=

T
k
L
d
(t) +L(t);t = 0; 1;:::;P 1

;k = (P + 1)=2;:::;P 1
N =N
0
[L
Then for any given sequence inM orN the sequence has the balance property (i.e. the
difference between the number of zeros and ones in the sequence is equal to 1) ifL
d
(t)
takes the first form, or near balance property (one-zero imbalance = 3) ifL
d
(t) takes the
second form. Additionally, it is shown that for any two sequences from within the same
subsetM orN, then the two sequences have good auto and cross correlation properties,
with the maximum of the autocorrelation function approximately equal to 2
p
P .
91

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Asset Metadata

Creator Goodney, Andrew P. (author)

Core Title Sensing with sound: acoustic tomography and underwater sensor networks

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Computer Science

Publication Date 03/06/2015

Defense Date 09/14/2014

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag acoustic sensor networks,acoustic tomography,acoustical oceanography,OAI-PMH Harvest,remote sensing,underwater sensor networks

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Contributor Electronically uploaded by the author (provenance)

Advisor Cho, Young H. (committee chair), Krishnamachari, Bhaskar (committee member), Teng, Shang-Hua (committee member)

Creator Email andrew.goodney@gmail.com,goodney@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-538121

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