AN IMAGE COMPRESSION APPROACH TO COOPERATIVE PROCESSING FOR SWARMING AUTONOMOUS UNDERWATER

VEHICLES

Caroline A. Hutchison

Thesis submitted to the faculty of Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Science

in Mechanical Engineering

Dr. Michael J. Roan, Committee Chair

Dr. Martin Johnson, Committee Member Dr. Daniel Inman, Committee Member

26 August 2008

Blacksburg, Virginia

Keywords: Compression, Underwater Communication

Copyright by Caroline Anne Hutchison, 2008.

An Image Compression Approach to Cooperative Processing for Swarming

Autonomous Underwater Vehicles

Caroline A. Hutchison

Abstract

Current wireless underwater communication technologies—i.e. underwater

acoustic modems—are extremely bandwidth limited as compared to land-based wireless

technologies. Additionally, acoustic modem technologies are not advancing at the same

high rate as computing technologies. Therefore, it is proposed that image compression

techniques be applied to sonar maps. This will both reduce the amount of information

that must be transferred by these modems which in turn reduces the amount of time

required to send information across acoustic channels. After compression is performed

on one platform’s map, the information is transformed into the coordinate system of the

uncompressed second, non-collocated platform’s map and the two maps are additively

compared. If returns are common in both maps, they will be show up with higher energy

than the individual maps’ returns. This thesis proves that application of image

compression techniques on range-angle maps allow for target detection, down to a

minimum target strength value of 0 dB, independent of target return strength.

All images and figures are the property of Caroline Anne Hutchison and were captured or created between August 2006 and August 2008.

Acknowledgements

I would like to first thank my graduate advisor and committee chair, Dr. Michael

Roan, for allowing me the opportunity to work on this graduate research project. His

guidance and support helped me to push myself to learn about and to create new ideas.

Dr. Martin Johnson and Dr. Daniel Inman also deserve my sincere thanks for serving on

my review committee, offering support, and providing constructive criticism.

I would also like to thank my sponsors at The Office of Naval Research (ONR)

University Laboratory Initiative (ULI), Dr. David Drumheller and Mrs. Maria Medeiros.

Without their sponsorship, this project would not have been possible. In addition, I

would like to convey my appreciation to Mr. Michael Roeckel, my mentor at The

Applied Research Laboratory of Penn State University (ARL). Steven Rice and Dr.

Jeffrey Weinschenk, also at ARL, were extremely supportive.

Finally, I must recognize my family. I would not be where I am today without the

love and encouragement of my parents, Mary and Danny Hutchison, throughout my

college career. And my brother, Adam Hutchison, who has provided endless support

throughout our college careers.

Carpe Diem.

iii

Table of Contents

Acknowledgements iii

Table of Contents iv

Nomenclature vii

Acronyms viii

List of Figures ix

List of Tables xii

Chapter 1: Introduction 1

1.1 Motivation & Objective 1

1.2 Previous Contributions 2

1.3 Significance 4

1.4 Organization 8

Chapter 2: Background 10

2.1 Acoustics Review 10

2.1.1 A Basic Understanding of Acoustic Properties 11

2.1.2 The Simple Linear Array 12

iv

2.2 Underwater Signal Processing Review 15

2.2.1 Sonar Basics 15

2.2.2 Underwater Sound Propagation 16

2.2.3 The Doppler Effect 18

2.2.4 Current Wireless Underwater Communication Capabilities 21

2.2.5 Other Underwater Communication Capabilities 25

2.3 Image Compression Review 27

2.3.1 Introduction 27

2.3.2 Current Image Compression Strategies 28

2.3.3 Image Compression Using Wavelets 32

Chapter 3: Computer Simulated Tests 34

3.1 Presentation of Data 34

3.1.1 Sound Simulation Toolset 34

3.1.2 Test Configuration 38

3.1.3 The Simulated Sonar Data 39

3.2 Range-Doppler Map Sharing 41

3.2.1 The Image Compression Approach Algorithm 41

3.2.2 Definition of Variables 43

3.2.3 The Best Theoretical Capability 43

3.2.4 Filtering Techniques 49

3.2.5 Application of the Image Compression Approach 60

3.2.6 Comparison with Other Image Compression Techniques 64

Chapter 4: Conclusions 67

v

4.1 Conclusions & Applications 67

4.2 Future Research 69

Appendix A: Presentation of Raw Data 72

Appendix B: Intersection Maps 74

Appendix C: Filtered Range-Angle Maps 70

Appendix D: Compressed Maps 72

References 74

vi

Nomenclature

c Speed of Sound in a Fluid, m/s

EL Echo Level, dB

f Frequency, Hz

k Wave Number, m-1

NL Noise Level, dB

p Acoustic Pressure, μPa

P Gauge Pressure, Atmospheres

S Water Salinity, ppt

SL Source Level, dB

t Time, s

T Temperature, °C

TL Transmission Loss

λ Wavelength, m

θ Angle of Incidence, degrees

ω Angular Frequency, rad/s

NOTE: Units are assumed to be used in those mentioned above unless otherwise noted.

vii

Acronyms

ARL The Applied Research Laboratory of Penn State University

AUV Autonomous Underwater Vehicle

DCT Discrete Cosine Transform

DOD The United States Department of Defense

FOV Field of View

FFT Fast Fourier Transform

GIF Graphics Interface Format

IFFT Inverse Fast Fourier Transform

JPEG Joint Photographic Experts Group standard

JPEG2000 Joint Photographic Experts Group updated standard

LOS Line of Site

ONR Office of Naval Research

ppt Parts per Thousand

STFT Short Time Fourier Transform

TIFF Tagged Image File Format

ULI University Laboratory Initiative

UUV Unmanned Underwater Vehicle

viii

List of Figures

Figure 1.3.1 A simulated-data example of a range-Doppler map. 8

Figure 2.1.1 An illustration of the three regions of sound propagation. 12

Figure 2.1.2 The geometry of a line array. 13

Figure 2.1.3 An illustration of broadside and end-fire definitions. 14

Figure 2.2.1 An illustration of active and passive sonar pursuing a school of fish. 16

Figure 2.2.2 The geometry used in the calculation of Doppler shifted velocities. 20

Figure 2.2.3 An example configuration of the WHOI acoustic micro-modem. 23

Figure 2.2.4 An illustration of UUVs using radio waves to communicate. 26

Figure 2.3.1 An example illustrating linear prediction pixel residuals. 29

Figure 3.1.1 An example of a target-only range-Doppler map. 36

Figure 3.1.2 An example of broadband noise only return range-Doppler map. 37

Figure 3.1.3 An example of a reverberation-only return range-Doppler map. 37

Figure 3.1.4 An example of a total output range-Doppler map. 38

Figure 3.1.5 Test configuration geometry. 39

Figure 3.1.6 Time series from both sonar for the +40 dB target return case. 40

Figure 3.2.1 The flowchart for Image Compression Approach algorithm. 42

Figure 3.2.2 The range-angle map for Sonar 1 in the +40 dB case. 44

ix

Figure 3.2.3 The range-angle map for Sonar 2 in the +40 dB case. 45

Figure 3.2.4 The Cartesian rang-angle map for Sonar 1 in the +40 dB case. 46

Figure 3.2.5 The Cartesian rang-angle map for Sonar 2 in the +40 dB case. 47

Figure 3.2.6 The common environmental map for Sonar 1 in the +40 dB case. 47

Figure 3.2.7 The common environmental map for Sonar 2 in the +40 dB case. 48

Figure 3.2.8 The intersection map for the +40 dB case. 48

Figure 3.2.9 True frequency plotted as a function of aliasing frequency. 50

Figure 3.2.10 An example of an aliased range-Doppler map. 50

Figure 3.2.11 The split window normalization method. 51

Figure 3.2.12 Split window normalization output; guard band=lagging window=4. 52

Figure 3.2.13 Split window normalization output; guard band=20, lagging window=4. 52

Figure 3.2.14 A comparison of the original range-Doppler map and two scaling factors. 54

Figure 3.2.15 The original & reconstructed output for Channel 2, Sonar 1, +40 dB case. 56

Figure 3.2.16 The original & post-filtered output for Channel 2, Sonar 1, 0 dB case. 57

Figure 3.2.17 The original & post-filtered output for Channel 2, Sonar 1, +40 dB case. 57

Figure 3.2.18 A post-filter-and-inversed range-angle map for Sonar 1 in the 0 dB case. 58

Figure 3.2.19 A post-normalization range-angle map for Sonar 1 in the 0 dB case. 59

Figure 3.2.20 A post-normalization range-angle map for Sonar 1 in the +40 dB case. 59

Figure 3.2.21 An example of the grid applied to a XY map for compression. 61

Figure 3.2.22 An example of the grid applied to a XY map for compression. 61

Figure 3.2.23 Percent compression and time elapsed as a function of grid rate. 63

Figure 3.2.24 Filtered, compressed, & combined range-angle map for the 0 dB case. 64

Figure 3.2.25. An uncompressed bitmap image for the +40 dB case. 65

x

Figure 3.2.26. An 8-bit compressed bitmap image for the +40 dB case. 65

Figure 3.2.27. An losslessly compressed JPEG image for the +40 dB case. 66

xi

List of Tables

Table 1.3.1 Two-way traveling ranges for various operating frequencies. 7

Table 2.3.1 The eight linear prediction schemes for lossless JPEG compression. 30

Table 3.3.1 Results for various grid rates for the 0 dB case. 62

Table 3.3.2 A comparison of the image compression techniques. 66

xii

Chapter 1: Introduction

This chapter provides an introduction to An Image Compression Approach to

Cooperative Processing for Swarming Autonomous Underwater Vehicles. The following

sections describe the motivation and objective for this research, briefly discuss previous

contributions in this area of study, and explain the significance of this research. A final

section describes the organization for the remainder of this thesis.

1.1 Motivation & Objective

When multiple sonar platforms are used to analyze underwater environments, the

ability to share information between vehicles is vital. Even more important is the need to

quickly transfer information, via images, between several platforms without losing

significant image detail and information. Such communication is essential for

applications where self-navigation and object detection are necessary. Areas of

application include: 1) image communication from satellite captures to ground based

systems, 2) image sharing between unmanned aerial and/or ground vehicle platforms, and

3) image comparisons from data gathered in underwater environments. This last

application leads to the focus of this thesis: using image compression techniques to

1

facilitate improved swarmed autonomous underwater vehicle (AUV) communication,

navigation, and target pursuit.

This research can be directly applied to many applications encountered by the

United States Navy’s unmanned underwater vehicles (UUV) including homeland

security, underwater mine detection, mapping, and navigation as well as civilian

applications such as boat recovery and inspection of ship hulls and oil rigs. The objective

of this thesis is to develop a method for compressing sonar maps such that key features

are preserved while enabling faster, more reliable and faster data transmission assuming a

fixed acoustic modem bandwidth.

1.2 Previous Contributions

Image compression is not a novel idea. In fact, since the dawn of the so-called

‘digital age,’ compression techniques have been developed, improved, and tailored to

optimize the compression ratio relative to each data set’s unique characteristics. These

algorithms aid in improved digital data storage and transmission. Examples where image

compression techniques are useful include: 1) compression of high-resolution

photographs to reduce the storage space required, and 2) reducing the size of these same

images so data transmission and downloading time are optimized—especially when high

speed internet connections or satellite relays are not available. Two widely-used

compression algorithms include the JPEG and the JPEG2000 IEEE standards. The JPEG

algorithms are based on linear prediction models and discrete cosine transforms [1],

while the JPEG2000 code uses discrete wavelet transforms [2] to facilitate image

compression. In addition to the wavelet-based JPEG2000 standard, methods to reduce

2

data size exist including wavelet packets, multiwavelets, and multiwavelet packets [3, 4].

Some of these techniques will be discussed in greater detail later in this thesis.

Other image compression techniques have been developed over the years. The

Laplacian Pyramid—a multiresolution image representation technique—was developed

by Burt and Adelson in 1983. While this method provides “a technique for removing

image correlation that combines features of predictive and transform methods,” it “is

noncausal, yet computations are relatively simple and local [5].” This research was

furthered by Do and Vetterli in 2003 through their method of Framing Pyramids. Their

technique can process signals of any size or dimension and their algorithm can

accommodate image borders. This is important because image borders often contain high

pixel discrepancies, which can lead to blurry edges and thus less detailed borders in

compressed images [6].

In addition to advancements in image compression, there are other methods for

reducing the data size. These include algorithms that are capable of isolating viable

‘snippets’ of information as discussed in Grimmett’s paper. This method of ‘detection

cueing’ was developed to reduce communication requirements with a multistatic setup

and aims to reduce the number of false target positives by “selectively [extracting] data

[that] is stored locally [at] individual sonar nodes” at a fusion center [7]. (The term

‘multistatic’ refers to the case where “there can be any number of sound sources,

receivers, and targets on any number of platforms [32].) Further, “the main [advantages]

of this approach [are] to greatly reduce the false alert rate, sensor communication

requirements, and operator loading [7].” Although new acoustic communication

techniques and technologies are not discussed in this thesis, it is important to realize the

3

current capabilities in order to understand where signal processing advancements can be

made.

Similar to the focus of this thesis is the concept of compressing satellite-based

imagery data prior to sending information to ground stations on Earth either directly or

indirectly via transmission to satellite(s) within line of site (LOS). According to Guzmán

and Beltrán, this need arises from the fact that “the next generation of earth observation

satellites will exceed their downlink capability” so image size reduction is essential.

Much like sonar platforms, satellites can gather large amounts of information with their

high-resolution technology but are limited in available bandwidth and the time-in-contact

with other platforms or base stations. Accounting for these points, Guzmán and Beltrán

suggest an on-board image compression system adviser that can distinguish between the

need for lossless or lossy image compression using an algorithm based on the JPEG2000

standard. Their system statistically analyzes captured images and selects the compression

method that “will be more profitable to use in terms of storage and bandwidth resource

utilization [8].”

1.3 Significance

This section presents the significance of this research. First, a general background

into the issues encountered in underwater communications is discussed. This leads into a

brief introduction into acoustic modems, sonar systems, and sonar returns.

There are unique challenges associated with underwater communication, ranging

from the vehicle design to communication technology to the specific characteristics of

underwater sound propagation through a varying medium. The design of the vehicle

4

platform, often referred to as a “towfish,” is limited by the high pressures encountered as

depth increases. Pre-deployment testing and evaluation is required to ensure a vessel can

perform under these pressure demands. Platform buoyancy and drag (i.e. hydrodynamic

characteristics) are also considered during the design process. Risks due to the potential

for water damage and electrical shortages can also be mitigated using demonstrated

materials and sealing techniques.

The aforementioned points are minor obstacles compared to the challenges

encountered by sensors in an underwater environment. Unlike planar land environments,

unmanned systems often require the ability to search in every direction; that is,

spherically about the exterior of the vehicle. This presents an additional challenge for

sonar arrays—which often have well-defined beam patterns that focus their search in a

single direction; forward looking and side-scan sonar are two examples. In deeper water

(i.e. that under the photic zone—the uppermost zone of water where light is still present,

extends from the surface to approximately 200m in depth [9]), passive vision sensors

cannot be used. Additionally, light and radio waves are not optimal underwater sensor

and communication device choices because of their attenuation characteristics [21]; these

two sensing options are greatly restricted by the diffraction characteristics of

thermoclines—vertical layers of rapidly changing water temperatures [10], signal

degradation due to multipath propagation, and variances in underwater bathymetry [11].

Communication between an underwater vehicle and other non water-based

platforms is limited because the propagation characteristics of water and air differ

significantly. Any radio communication would require the towfish to surface for data

transmission to satellites and/or base stations. Tethering the towfish to a boat or base

5

station allows for water-to-air communication without surfacing but presents additional

constraints. Two examples include: (1) the vehicle is limited in travel to the length of the

tethering cable and (2) the weight of the cable itself can adversely affect the buoyancy

and mobility of the towfish especially as the cable length increases. Leakage, water

damage, and electrical shortages are also a concern for transmission cables [12].

Current commercially available acoustic modems can be used for wireless

underwater communication. However, these modems are primarily limited by their

bandwidth, some having bandwidths between 80 and 5000 bits per second. Examples

include the Wood’s Hole Oceanographic Institute (WHOI) micro-modem [13],

DSPComm’s AquaNetwork—an underwater acoustic modem that also has networking

capabilities [14], and LinkQuest Inc.’s SoundLink underwater acoustic modems [15].

The WHOI model will be addressed later in this thesis.

Due to the limitations previously discussed, sonar—SOund, NAvigation, and

Ranging [20]—is the most widely used underwater sensing and communications

technology today. Sonar applies the principles of acoustic propagation to overcome the

lack of visibility in underwater environments. Sonar will also be discussed in further

detail in a later chapter.

Each sonar return, such as the acoustic signatures seen in range-Doppler or range-

angle maps, depends on the physical characteristics of the target(s) in its field-of-view

(FOV). (A FOV can be defined as the area that a map covers; the range axis is dependant

on the physical characteristics of the underwater environment as well as the sonar’s

frequency of operation.) According to Fish and Carr, low frequencies traveling through

seawater are able to propagate much further than higher frequencies [10]. This

6

phenomenon is presented in Table 1.3.1, showing a comparison of two-way traveling

ranges for various frequencies of operation. Sonar maps can be decomposed to identify

target features including speed, direction, size, and location all relative to the sensing

platform’s speed, direction, size, and location.

Table 1.3.1. Two-way traveling ranges for various operating frequencies [10].

Frequency of Operation Wavelength Two-way Traveling Range 100 Hz 15 m ≥ 1000 km 1 kHz 1.5 m ≥ 100 km

10 kHz 15 cm 10 km 25 kHz 6 cm 3 km 50 kHz 3 cm 1 km

100 kHz 1.5 cm 600 m 500 kHz 3 mm 150 m 1 MHz 1.5 mm 50 m

There are a few different ways to present the data collected at a sonar platform.

For this research, range-Doppler and range-angle maps were selected to differentiate a

moving target in a high-clutter environment. Range-Doppler maps can be used to locate

and track moving target(s) from extraneous background noise. Similarly, range-angle

maps present the target(s) angle of arrival with respect to a sensor’s bore sight. An

example of a range-Doppler map is presented in Figure 1.3.1. The strong return along the

entire range centered on zero-Doppler is environmental reverberation from the ocean

surface and bottom while the identified target is circled in red.

In a number of situations that UUVs may encounter, it is useful to employ two or

more sonar platforms to survey underwater. Once data is collected at each platform, the

data can be combined to determine similar FOV detections. This allows for a method to

identify mutual information, which because of correlation rises above the background

noise. Because of lower correlation, the background noise in combined maps is reduced.

7

Thus when two or more maps are combined, a higher certainty is established that a hot-

spot is a target is a true, positive detection. This certainty may be increased with

additional sonar information sets. However, because of the low bandwidths—leading to

high transmission times—available in wireless underwater communication, a method to

reduce the amount of information must be devised. To overcome these limitations, the

use of compression techniques for underwater data transmission is proposed.

Figure 1.3.1. A simulated-data example of a range-Doppler map.

1.4 Organization

The remainder of this thesis is organized as follows. Chapter 2 discusses

background information and is divided into several sections. These include 1) a review

of acoustics for a basic understanding, 2) a review of underwater signal processing

technologies, and 3) information on image compression. Chapter 3 provides background

into the compressed map sharing algorithm along with processed simulated underwater

Ran

ge (m

)

Doppler (m/s)

Sonar1total

-20 -10 0 10 200

500

1000

1500

2000

40

50

60

70

80

90

100

110

8

data results. This chapter finishes with a discussion of the viability of applying image

compression techniques to cooperative processing between multiple autonomous

underwater vehicles. Chapter 4 provides a conclusion to this thesis as well as

recommendations for future research in the area of underwater signal processing.

9

Chapter 2: Background

To establish a clear understanding of this research, a brief summary of

fundamental acoustic properties, underwater signal processing, and underwater

communication capabilities are provided in this chapter.

2.1 Acoustics Review

This section discusses concepts in underwater acoustics directly relevant to the

data analyzed in the next chapter. In the definition of acoustics, sound is responsible for

noises that can be heard by humans as well as those out of the audible range; all sounds

are governed by similar physical principles [19]. Sound is classified as mechanical

energy, specifically mechanical wave motion, and can propagate through a variety of

mediums including fluids, gases, and solids [19, 21]. In the following subsections, a brief

review of general acoustics equations, underwater acoustic properties, and line array

derivations are provided.

10

2.1.1 A Basic Understanding of Acoustic Properties

The new work developed in this thesis relies on the assumption of plane wave

acoustic propagation in the underwater environment. This subsection reviews the

acoustic wave equation and a plane wave solution to that equation. To provide a

complete foundation to this body of work, the acoustic wave equation and a plane wave

solution to that equation are introduced. The basic linear wave equation as presented in

Equation 1:

2

2

22

2

2

2

2

22 1

tp

cp

zyxp

∂∂

=⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

+∂∂

=∇ (1)

where ∇ is defined as “the sum of all unmixed partial derivatives [22],” p is the acoustic

pressure in μPa, and c is the speed of sound in the medium in units of m/s. If used to

analyze three-dimensional space, this nabla symbol (i.e. the del operator) [23] is referred

to as the three-dimensional Laplacian [20]. Moving further from Equation 1, a three-

dimensional equation for the acoustic pressure of a plane wave moving in some direction

in (x, y, z) space can be derived, and i shown in Equation 2:

( ) ( )zkykxktjzkykxktj zyxzyx BeAep +++−−− −= ωω (2)

where A and B are amplitudes of some value and the natural frequency, ω in rad/s, is

equal to the frequency, , in Hz multiplied by a factor off π2 . Finally, the wave

numbers—kx, ky, and kz each for their respective plane—are defined as the natural

frequency over the speed of sound and are recorded in units of m-1. The speed of sound

may alternatively be calculated by multiplying a sound’s wavelength, λ, by its frequency

[20].

11

There are three regions of sound propagation: 1) near field, 2) a transition region,

and 3) far field as shown in the illustration in Figure 2.1.1, adapted from Urick [21]. In

this figure, a sound originates at a distance r = 0 meters and travels through the medium.

While the sound wave in this illustration is shown as non-decaying, the real-world sound

amplitude decays due to spreading & absorption. While near-field sound propagation is

not impossible to evaluate, it tends to require additional details and therefore requires

increased processing time. Conversely, sound sources in the far field reach sensors as

plane waves which are much easier to model. The shift from near to far field propagation

occurs at some distance, ro, away from the sensor. The calculation of ro will be defined in

the next section.

Transition Zone

Figure 2.1.1. An illustration of the three regions of sound propagation.

2.1.2 The Simple Linear Array

In his book, Kinsler developed equations to evaluate a ‘simple line array.’ A

depiction of this array is shown in Figure 2.1.2. Some clarification about this illustration

should be made. First, the sound source originates at a considerable distance from an

array; such a source is referred to as a ‘far field source’ as mentioned above. Second, it is

assumed that the length of the line array, L, is much smaller than the distance, r, from the

sound source. Finally, within the array of length L, there are a number, N, listening

r

ro

Sound Source

Far FieldNear Field

12

microphones (or hydrophones in the case of underwater sound collection) in a straight

line configuration and are separated by a constant distance, d. This constant spacing

allows a user to assume that waves arrive at each respective hydrophone at a constant

interval [20].

Figure 2.1.2. The geometry of a line array [20].

In practice, a user will come across the terms ‘broadside’ and ‘endfire.’ As

depicted in Figure 2.1.3, broadside refers “to the direction perpendicular to the length of

the array [24],” while endfire indicates the direction parallel to the length of the array.

For a broadside array, which will be referred to as ‘array’ for the remainder of this thesis,

a positive (+) angle, θ, originates clockwise from normal in the direction the hydrophones

are facing and a negative (−) return angle originates counterclockwise from this direction.

While a linear array is a useful tool for sound collection, there is uncertainty between

whether a sound is emanating from the ‘front’ or ‘back’ side of the array—referred to as

front-back ambiguity. By using more than one array and knowing the locations and

1

θ

θsindr =Δ

'2r

'1r

N6543 2

( )r θ,To

d

( )dNL 1−=

13

orientations of each array with respect to one another, front-back ambiguity can be

resolved as will be shown with the data presented in Chapter 3 [24].

Broadside

+θ

Figure 2.1.3. An illustration of broadside and end-fire definitions.

Taking into account the far field restriction, the sound waves are said to be

parallel to each other. Through this, the equation in Figure 2.1.2, θsindr =Δ in units of

meters, can be used to estimate the difference in arrival time, ∆t, from element to

element, as given in Equation 3 [24]:

c

dcrt θsin=

Δ=Δ (3)

where all variables have been previously defined and ∆t is reported in seconds.

As discussed in the previous section, the transition between near- and far-field

sound propagation can be mathematically determined once an array’s parameters are

known. For a line array, the formula to determine the distance at which this shift occurs,

ro, is presented in Equation 4:

λ

22Lro = (4)

where all variables have been previously defined [25]. In order to make calculations less

complicated, sources considered must meet the far-field assumption. That is, the

distance, r, between a sound source and an array should be greater than the calculated ro

distance. Gathering from all of the above notations, the remainder of this thesis will

End-fire1 2 3 4 5 6

14

assume the following: 1) all sources originate in the far-field so 2) all sources (direct

waves, reflections, reverberations, etc.) arrive at hydrophones as plane waves.

2.2 Underwater Signal Processing Review

This section discusses important concepts in the area of underwater signal

processing. The following subsections describe the basics of sonar use, the

characteristics of underwater sound propagation and the Doppler effect, and give a

summary of the current underwater communication capabilities.

2.2.1 Sonar Basics

As previously mentioned, sonar is an acronym for SOund, NAvigation, and

Ranging [20]. There are two sonar configurations: active and passive. A simple

illustration of these two types of sonar systems pursuing a target, illustrated as a school of

fish, is presented in Figure 2.2.1. Shown with ‘ping’ graphics originating at the front end,

Array A is considered active. Characteristics that classify active sonar include a projector

that sends a known sound—also referred to as a ping—and an array of hydrophones that

listen for and record target(s) echo return(s). Passive sonar systems, illustrated as Array

B in the figure below, consist of hydrophone arrays that listen for radiated sound and/or

reflections along with a processing unit; they are considered listen-only devices as they

do not project sound [10, 21].

15

A

B

Targets Sensing Platforms (Arrays)

Figure 2.2.1. An illustration of active and passive sonar pursuing a school of fish.

In classifying sonar types, there are other important terms. Monostatic refers to

sonar systems with the sound projector and hydrophone array on the same unit, as is the

case with active sonar systems. On the other hand, a bistatic sonar system exists when

the sound projector and hydrophone arrays are not collocated, such as with passive sonar

systems [21].

2.2.2 Underwater Sound Propagation

Evolving from basic underwater range and depth finding created to mitigate sea

vessels running aground, the use of underwater sound has grown in application and

complexity. Today, its uses include military applications such as underwater navigation,

mapping, and tracking through various sonar platforms and civilian applications such as

fish-finding. As one may expect, the acoustic properties of Earth’s atmosphere and water

differ significantly. In fact, sound propagates much faster in water than in air. The speed

of sound in air may be estimated at 343 m/s [20]. In contrast, an estimate for the speed of

sound for saltwater is presented in Equation 5:

16

( ) ( )

( ) ( )⎥⎦⎤

⎢⎣⎡ −

+−−⎥⎦

⎤⎢⎣⎡ −

+

−⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+−

×++

−++=

1035

202540035

1200

1203606.89

1046.11522.0

3533.157.408.1449,,

2

STST

TTT

OCEAN

ePPe

eSTePSTc (5)

and is a function of the water’s 1) temperature, T, reported in degrees Celsius, 2) salinity,

S, in parts per thousand (ppt), and 3) gauge pressure, P, in atmospheres. Similarly, the

speed of sound in non-saline water is a function of temperature and pressure.

Substituting in a few sets of values into this highly involved ocean speed of sound

calculation, one can arrive at a change of approximately 4m/s for every 1°C while a 1%

variation in salinity results in a 1m/s change [20].

Sound propagation in water not only depends on the variables defined above, but

can also vary with thermoclines, salinity and pressure gradients (summed up in the term

‘refraction’ [20]) and bathymetry—otherwise known as underwater topography [10].

According to Kinsler, these variations are much more significant in the vertical direction

than in the horizontal direction. For purpose of continuity, the remainder of this thesis

will use a speed of sound of 1500 m/s. This value assumes readings are taken in seawater

and there is no variation due to the aforementioned variables [20].

Sound behaves differently depending on the characteristics of the propagation

medium and decays from its point of origin. Accounting for this weakened sound level

are several types of losses that are often grouped together in what are called the sonar

equations [20, 21]. These equations combine “the effects of the medium, the target, and

the equipment [21].” Included within this set of equations are several important variables

referred to as sonar parameters [21].

To establish basic understanding of these parameters, a brief synopsis follows.

Urick divides his sonar parameters into three groups: 1) those governed by the sonar

17

equipment, 2) those characterized by the propagation medium, and 3) those established

by the target [21]. In the first group are the projector’s source level (SL), the receiver’s

directivity index (DI), and the detection threshold (DT). The second group includes the

medium’s transmission loss (TL), reverberation level (RL), and background noise level

(NL). These two groups encompass the loss terms in the sonar equations with the

exception of SL. The final group defines the target’s strength (TS), which tends to be an

additive term [20, 21].

These variables establish a basis for separating undesirable noise from the

important target signal. The ideal situation has a target level greater than the combination

of the loss terms. The active sonar equation is presented in Equation 6:

DTDINLTSTLSL +−=+− 2 (6)

where all terms have been previously defined [21]. Similarly, the passive sonar equation

is defined in Equation 7:

DTDINLTLSL +−=− (7)

where, once again, all terms have been previously defined [21]. While these equations

are not used directly in the scope of this research, they are important concepts to explain

the calculations commonly used in underwater sound propagation analysis. The research

for this thesis uses a different technique that will be discussed in a later chapter.

2.2.3 The Doppler Effect

In this thesis, range-Doppler maps are used as a means of filtering specific

frequencies from sonar time series. A range-Doppler map shows range from a receiver—

a function of time—in m on one axis and Doppler shift—a function of frequency—in m/s

18

on the other axis. Figure 2.2.2 presents an illustration of the geometry used in the

following calculations. An equation for the Doppler shift is shown in Equation 8:

fc

f vu +=Δ (8)

where u is the speed of the transmitter, v is the speed of the receiver, and is the

original transmitted frequency. This equation assumes that both u and

f

v are much

smaller than the speed of sound [20]. For passive sonar, this equation can be further

refined as seen in Equation 9:

⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛ +=Δ

ccff βα cosv1cosv1 TT (9)

where is the magnitude of the target’s velocity, α is the projection angle of the target

velocity onto the transmission sonar’s line of sight, and β is the projection angle of the

target velocity onto the passive sonar’s line of sight [20]. For active sonar, Equation 5 is

modified as presented in Equation 10:

Tv

⎟⎠⎞

⎜⎝⎛ +=Δ

cff αcos2v1 T (10)

where all variables have been previously defined and the factor of two accounts for the

sound returning to the same sonar array as it was transmitted [20].

19

Figure 2.2.2. The geometry used in the calculations of Doppler shifted velocities [20].

To generate a range-Doppler map, time series must first be converted into the

frequency domain. Analysis in the frequency domain can be used as a tool to determine

the frequency content (i.e. the returns at specific frequencies within a discrete signal).

The fast Fourier transform (FFT) and short-time Fourier transform (STFT) can be used to

accomplish this using Equation 11:

( ) ( )∑−

=

−

=1

0

21 N

n

Nknj

enxN

kXπ

(11)

where values are calculated for each frequency bin, k, based on the input signal, ,

from where

( )nx

( )1:0 −= Nn N the length of the input vector. The STFT uses the same

formula, only performing the FFT on small portions of data, defined by some window

length. After one portion is analyzed, the window is moved over by some amount,

commonly a 50% overlap of the previously analyzed portion, and then done over and

over until the entire input signal’s frequency content is determined [28, 33, 34].

To return to the time domain, an inverse Fourier transform (IFFT) is performed,

which can be calculated using Equation 12:

α

Passive Sonar

Active Sonar

βTvTarget

20

( ) ( )∑−

=

=1

0

2N

n

Nknj

ekXnxπ

(12)

where all variables have been previously defined. As it is not available as a MATLAB

function, an inverse short-time Fourier transform program was created during the course

of this research to accomplish the goal of generating a time series after frequency domain

filtering was performed; this program, called ‘inverseSpecgram,’ will be discussed in a

later chapter [28, 33, 34].

2.2.4 Current Wireless Underwater Communication Capabilities

Many of today’s unmanned underwater applications require real-time data

transmission for communication between submarines, autonomous underwater vehicles,

base stations, surface vessels, and/or relay stations [11]. Acoustic modems can be

employed to accomplish this communication. An acoustic modem is defined as a modem

that uses acoustic waves (i.e. sounds) to communicate information between two or more

underwater vehicles or platforms [30]. In other words, a signal—either preset or

determined on-the-fly via the data collected—is sent through a projector. The signal then

propagates through the medium—in this case seawater—to another platform or node

where it can be analyzed and/or retransmitted. These modems vary in range, networking,

and bandwidth capabilities, as well as size and cost and can be tailored for use in a

variety of situations.

Although useful, underwater communication is limited by a number of factors.

These include reverberation and propagation off of a myriad of underwater

environmental characteristics—such as wildlife, mountain ranges, coral reefs, other

21

water-based vessels, the surface and the ocean floor—otherwise referred to as multipath,

the requirement of long propagation times relative to those required in air, and combating

diffraction due to temperature and salinity gradients. It is important to note that

multipath propagations “vary with time and are highly dependent on the location of the

transmitter and receiver [11].” This means that a sensor (i.e. a transmitter or receiver)

placed in a large, deep, open body of water will behave quite differently than if it were

placed in shallow water or in close proximity to the ocean floor where reverberation

characteristics are much more prominent. Another limitation placed on underwater

communication is the bandwidth of operation available to a user. Such bandwidth is also

hindered by the losses and noise as previously defined in the section on Underwater

Sound Propagation [10, 11].

WHOI micro-modems are commonly used for communication between unmanned

underwater vehicles. An example configuration is shown in Figure 2.2.3. The WHOI

micro-modem is divided into three parts: 1) the main board, 2) a power amplifier, and 3)

a floating point coprocessor. The main board has up to a 1 GHz processor, two RS-232

serial ports—one for user control and a second for tertiary instrument control, a 12-bit

A/D low-pass anti-aliasing filter, and a real-time clock. Typical sampling rate for the

low-pass anti-aliasing filter is 80 kHz. In addition to providing a time monitoring system,

the real-time clock also permits system hibernation for power conservation. Although

operation at full-power consumes 180mW, the majority of processing occurs at a mere

80mW. Easy-to-upgrade flash memory is used for internal data storage. A ceramic

pinger is driven by a one-channel Class D power amplifier, which also provides signal

conditioning and can be easily modified for a variety of vehicle power systems. The

22

floating point coprocessor, developed in conjunction with the Naval Undersea Warfare

Center Newport Division, is used to process “computationally complex [phase-shift

keying (PSK)] equalization algorithms.” The final part of the micro-modem system is a

surface-based RF-acoustic gateway buoy. This buoy allows underwater network traffic

for up to 16 vehicle platforms to be transmitted to an offsite processing center [13].

Figure 2.2.3. An example configuration of the WHOI acoustic micro-modem [13].

Used with permission from Woods Hole Oceanographic Institute, 2006.

While the WHOI micro-modem is a useful tool for underwater communication, it

does have some limitations. For shallow water applications, there are two main issues: 1)

time-varying multipath returns and 2) non-Gaussian noise. When signal returns are

observed by an array in shallow water, there are often multiple high-energy returns. Such

returns can be reflected from the surface, sea floor, coral reefs, fish, and surface vessels

and can vary with temperature, salinity, and turbulence such as waves, among other

factors. These multipath returns can lead to false-positives and ambiguities in processed

data. Unlike Guassian noise, which can be predicted and filtered out, non-Gaussian noise

is not easy to overcome in the post-processing stage. To get around these two issues, the

WHOI micro-modem operates using frequency-hopping frequency-shift keying. There

23

are three 4kHz frequency bands centered at 10, 15, and 25 kHz; a fourth band is in the

range of 3-30kHz, but was not specified by WHOI [11, 13].

On a side note, the frequencies for marine-based wireless communication does not

have the same restrictions as surface- or space-based communication systems—both of

which are strictly controlled by the U.S. Department of Commerce’s National

Telecommunications and Information Administration (NTIA) and/or the Federal

Communication Commission (FCC). This is important for design engineers because the

entire acoustic spectrum is available for use in underwater communications.

Additionally, frequency bandwidths can be selected to optimize acoustic communication

without constraint by these governing agencies. Finally, interference with commercial

applications is not an issue underwater [16, 17].

Typical data rates for the WHOI micro-modem range between 80-5400bps.

Compared to ‘slow’ 56K land-based dial-up modems, underwater communication is

significantly more limited. Despite this, transmission distances up to 4km and range

estimation errors of less than 10cm have been shown in WHOI test results. It should be

noted that transmission range and range estimation are related to the frequency band of

operation [10, 13].

The WHOI micro-modem can be utilized for a myriad of applications.

Unmanned underwater systems have become popular in the push for underwater terrain

mapping, mine hunting, and could even be applied in commercial fishing applications. In

a similar manner, this micro-modem can be used for recovery efforts for lost ships,

divers, aircraft, or any other occurrence where manned dive teams would prove

24

inefficient or impossible. These are all areas of application important to the United States

Department of Defense including both the Navy and Coast Guard.

A primary focus for future enhancements of the WHOI micro-modem should be

to expand the data rate beyond 5400bps. With the data rate being the largest drawback to

micro-modem use, any increase in data transfer speed will greatly expand its potential

utilization. In addition, increasingly efficient and more intelligent post-processing

techniques are being developed to overcome micro-modem hardware limitations.

2.2.5 Other Underwater Communication Capabilities

Because of the extreme bandwidth limitations of wireless underwater

communication technologies, other communications options must be explored. As

previously mentioned, these include radio and/or satellite communication as well as

utilizing fiber optic cables to allow for communication between vehicles. While

radio/satellite communication will allow higher data transfer rates, the platforms must

make contact with the surface to commence transfer. Vehicle surfacing may not be

practical in cases where platforms are submerged at significant depths, where currents

and/or waves may put the vehicle at risk, or when stealth is desired. Similarly, fiber optic

cable(s) connecting two or more platforms may not be realistic in a situation that risks

irreversible damage to the fragile cable including: 1) extremely long separation distances

between vehicles, and 2) extreme environmental conditions such as strong current.

However, if used in combination, these two options may be the optimal way to

communicate between vehicles. An example of a combination is a fiber optic cable

connecting a radio communication unit on the surface to the submerged vehicle platform.

25

Figure 2.2.4 shows a representation of this configuration where two deployed buoys may

share information. Platform A gathers data and sends it up a fiber optic cable to a buoy

where it is transmitted via radio waves. This information is collected by platform B’s

buoy, travels down the second fiber option cable and arrives at platform B for further

processing.

Transmit/Receive Buoys

Figure 2.2.4. An illustration of UUVs using radio waves to communicate.

Acoustic modems serve as the transponders of underwater data collected at sonar

platforms. This information can be analyzed—either at surface-based command and

control stations or at one ‘home base’ underwater platform—for decision making and

target tracking. The later of these two analysis options is the situation assumed in the

development of the algorithms presented in Chapter 3.

Ocean

A

Sensing Platforms (Arrays)

BA

Air

Fiber Optic Cables

26

2.3 Image Compression Review

This section discusses important developments in the area of image compression

in order to give insight into the methods used for the compression strategy employed in

this thesis. The following subsections describe current image compression strategies to

provide an introduction to those used in the Image Compression Approach algorithm

which will be explained in Chapter 3.

2.3.1 Introduction

There are two primary classifications in image compression: lossless and lossy.

Lossless compression decreases the size of an image without compromising the

information contained in an image. Because of this characteristic, data that has been

compressed using lossless algorithms can be restored back into to its original form

without any artifacts. Common applications for lossless compression techniques include

facsimile encoding for transmission, progressive image transmission (sometimes

encountered when downloading pictures from the internet), and for storing image and

video information [27].

Lossy compression does involve some loss of information between an original

data set or image and the compressed data set or image. However, one of the payoffs of

using lossy compression is that much higher compression ratios can be achieved as

compared to lossless algorithms [27]. A user can specify the amount of compression best

suited for a particular application in order to optimize the compression and loss

characteristics. Speech, video, and image data can all be compressed using lossy

27

techniques depending on the desired output [27]. The most important benefit for this

research is reduced data transmission packets, translating to faster transmission times.

2.3.2 Current Image Compression Strategies

A number of image compression strategies have been developed over the last two

decades. These include, but are not limited to, the Joint Photographic Experts Group

format (JPEG) standard, a newer JPEG standard (JPEG2000), the Graphics Interchange

Format (GIF), and the Tagged Image File Format (TIFF). While the GIF format can only

perform lossless image compression, the other three techniques can accomplish both

lossless and lossy image compression depending on user specifications [28]. The JPEG

and JPEG2000 methods of image compression will be introduced for the purpose of

defining a baseline image compression method.

Established in 1992, the first compression standard is known as JPEG and is a set

of international standards for both grayscale and color image compression strategies. The

name JPEG came from the abbreviation for the team—the Joint Photographic Experts

Group—which developed this technology. Within the JPEG standard are “two basic

compression methods.” The first routine, centered around discrete cosine transforms

(DCTs), allows for lossy compression while the second uses linear prediction techniques

for lossless compression; the latter method is more commonly used. The lossless method

is also referred to as the Baseline Method [1, 27].

Linear prediction techniques are used to accomplish lossless JPEG image

compression. Linear prediction models assume that one cell or pixel will have a value

“close to that of its neighbors” in order to calculate the values of a cell and to “remove

28

any structure that might” exist within an image [27]. ‘One-dimensional schemes’ use a

cell neighboring on one side, say the cell above, to predict the value, or residual, of the

cell of interest. As its name implies, ‘two-dimensional predictive schemes’ use two cells,

say the cell above and the cell to the left, to predict the residual of the cell of interest. An

example, adapted from Khalid Sayood’s linear prediction model illustration, of an

original image and the residual values of this image is presented in Figure 2.3.1 [27]. As

explained by Khalid Sayood, the large number of residuals taking the value of zero will

enable compressed image sizes with “far fewer bits than the original image [27].”

Original Values Residual Values

Figure 2.3.1. An example illustrating linear prediction pixel residuals .

Lossless JPEG compression has eight user-selected linear prediction methods for

application. One scheme does not predict values, while the remaining options allow

either one- or two-dimensional predictions. The first method assumes that the cell of

interest, , can be determined solely by cell ( jiI ,∧

) ( )jiI , of the original image where ( )ji,

are the x- and y-coordinates of a specific pixel within both the original and compressed

images. In a similar fashion, the other seven schemes use various combinations of

neighboring cells. Because the patterns are chosen by a user, optimization of both

resolution and quality for the compressed images can be achieved. The patterns for all

eight predicting schemes are presented in Table 2.3.1 [27].

29

Table 2.3.1. The eight linear prediction schemes for lossless JPEG compression.

Method

Scheme Pattern

1

( ) ( jiIjiI ,, =

∧

)

2

( ) ( )jiIjiI ,1, −=

∧

3

( ) ( )1,, −=

∧

jiIjiI

4

( ) ( )1,1, −−=

∧

jiIjiI

5

6

( ) ( ) ( ) ( )1,1,11,, −−−−+−=∧

jiIjiIjiIjiI

7

( ) ( ) ( ) ( )( ) 2/1,1,11,, −−−−+−=∧

jiIjiIjiIjiI

8

( ) ( ) ( ) ( )( ) 2/1,11,,1, −−−−+−=∧

jiIjiIjiIjiI

( ) ( ) ( )( ) 2/,11,, jiIjiIjiI −+−=∧

Two-dimensional DCTs are used to achieve lossy JPEG compression. Dividing

an image into a number of sections of size nn× pixels, , a two-dimensional DCT

coefficient matrix, , for each

xyp

ijG nn× set of pixels may be calculated as presented in

Equation 13:

( ) ( )⎟⎠⎞

⎜⎝⎛ +

⎟⎠⎞

⎜⎝⎛ +

= ∑∑−

=

−

= nix

njypCC

nG

n

x

n

yxyjiij 2

12cos2

12cos21 1

0

1

0

ππ (13)

where i and j take on values from 1:0 −n , and is generally a power of two, to

expedite calculation; common values are

n

16 ,8=n . The values of and are

calculated as shown in Equation 14:

iC jC

⎪⎩

⎪⎨⎧

>

==

0or if ,1

0or if ,2

1,

j i

jiCC ji (14)

30

where i and j have been previously defined. To produce a compressed image, an inverse

DCT is then applied to each of the pixel sections to approximate the original pixel

values, , as presented in Equation 15: xyp∧

( ) ( )⎟⎠⎞

⎜⎝⎛ +

⎟⎠⎞

⎜⎝⎛ +

= ∑∑−

=

−

=

∧

nix

njyGCC

np

n

i

n

jijjixy 2

12cos2

12cos21 1

0

1

0

ππ (15)

where again all values have been previously defined. It should be noted that values

for are calculated based on a quantized matrix by selecting some number of user-

specified, high-entropy values from the coefficient matrices. The number chosen is

decided upon based on the amount of compression versus allowable distortion desired. It

should be noted that the DCT was chosen as the method of compression by the JPEG

committee “because of its good performance, because it does not assume anything about

the structure of the data (the DFT, for example, assumes that the data to be transformed is

periodic in nature), and because there are ways to speed it up [29].” The quantization

step is the main source of information loss and explains why lossy-compressed images

cannot be reconstructed exactly as is the case with losslessly-compressed images [1, 18,

27, 28, 29].

xyp∧

ijG

Since the JPEG standard is commonly used for image compression in many

applications world-wide, it was chosen as a baseline for comparative purposes in this

thesis. An example of an uncompressed range-Doppler map along with lossless and lossy

compressed JPEG versions of the same map will be presented in the next chapter. These

examples serve as reasoning for developing another image compression algorithm for

collected sonar information.

31

2.3.3 Image Compression Using Wavelets

As digital technology—especially that for digital imagery—becomes more

advanced, so too has the technology used for digital storage and transfer. To

accommodate this growth, the wavelet-based JPEG2000 standard was established and

finalized in December 2000. This compression technique is more advanced than the

JPEG standard and can be optimized for efficiency, image size, and the exchange of

information. Capabilities of JPEG2000 include “lossless and lossy coding, embedded

lossy to lossless coding, progression by resolution and quality, high compression

efficiency, error resilience and region-of-interest (RIO) coding [2].” There are many

advantages in using the JPEG2000 technique over the older JPEG standard. These

include higher compression efficiencies, the ability to compresses larger image sizes than

can JPEG, and include error-correcting codes [2, 29].

Perhaps the most notable improvement in JPEG2000 over JPEG “is the

“compress once, decompress many ways” paradigm [29].” In other words, the

JPEG2000 encoder will choose maximum values for image quality, Q, and image

resolution, R, and then compress the image of interest. The decoder can then be set to

extract a decompressed image at any values of Q and R depending on the desired output

and application. For example, an image may be decompressed with a low Q value and a

high R value or with middle-of-the-road Q and R values—both of these examples

produce lossy compressed images. If the highest Q and R values are selected for

decompression, the image is nearly lossless. JPEG2000 compression can be used for

both color and black and white images [29].

32

To compress an image using the JPEG2000 standard, the image is first broken up

into rectangular blocks, or ‘tiles’ as they are commonly referred to in literature. A

discrete wavelet transform is performed on each tile and wavelet coefficients are

determined. The wavelet coefficients are then quantized according to a user-defined

bitrate—a small bitrate corresponds to a lower amount of coefficients as compared to a

large bitrate. As in the JPEG standard, quatization reduces the amount of complexity, or

entropy, within an image. Next, the quantized coefficients are encoded into ‘packets’

(also known as ‘wavelet packets’ which are components within a bitstream) and

‘markers’ are placed to denote the beginning of each packet. Finally, the bitstream is

reconstructed by arranging the packets with corresponding markers. The markers can be

used to overlook some packets in order to speed up decompression or to set up ‘layers’ of

increasing image resolution, so a user can achieve progressive image transmission and/or

decompression. As its name suggests, progressive transmission techniques send the

lowest amount of information first and then increase the resolution with each successive

information layer; this can be seen when downloading some images from the internet.

Progressive transmission can be completed via “resolution, quality, spatial location (i.e.

an area within an image), and component [29].” Image compression using wavelets was

introduced as an alternative technique but will not be further discussed in this thesis.

33

Chapter 3: Computer Simulated Tests

This chapter discusses the data that was generated using Sound Simulation Toolset

(SST)—a computer-aided underwater sound propagation modeling program. The

following sections introduce this program, describe the simulated data, and present the

output from the Image Compression Approach algorithm.

3.1 Presentation of Data

This section presents the data generated by Sound Simulation Toolset (SST). The

following subsections briefly discuss this powerful simulation program and present the

test geometry and data generated within SST.

3.1.1 Sound Simulation Toolset

Developed by Dr. Robert Goddard, et al. at the Applied Physics Lab of The

University of Washington, “[SST] is a computer program that produces simulated sonar

signals as “heard” by a user-specified active or passive sonar in a user-specified ocean

environment [32].” The user-defined SST can be coded to generate a variety of

information. The data in each simulated output channel “consists of a digital

34

representation of the predicted signal in each channel of the sonar receiver’s processing

path [32].” For the case of the data presented in this chapter, three types of output were

collected and then summed for a fourth set of output. The range-Doppler maps presented

in this section show Doppler shifted velocity on the x-axis, while the y-axis presents the

range of the target from the hydrophone arrays.

First, the target’s echo is generated based on the scenario geometry and other

inputs including the speed of sound underwater. The target created for the simulation is

considered an active target (i.e. its echo is returned after a pulse is transmitted from an

active sonar). An example of a target-only range-Doppler map is presented in Figure

3.1.1, where the red square-like shape is the region where the target returns are the

highest; this corresponds to the target’s location. The second type of output generated is

classified as passive noise which includes the broadband noise that is radiated by the

target; an example is provided in Figured 3.1.2. The third generated output classification,

shown in Figure 3.1.3, is referred to as reverberation. This is the noise that echoes off the

“diffuse scatterers, such as the ocean bottom, that sends back overlapping echoes of an

active sonar’s pulse [32].” The reverberation generated is based on a variety of

parameters including wave speed at the surface, the terrain on the ocean floor, and the

marine life and/or other environmental inhomogeneities within the volume of water.

Within SST, it is assumed that the environmental reverberation has a random distribution

following the patterns associated with Gaussian statistics. As may be predicted, the

decibel level of the reverberation decreases as distance from the sonar increases [32].

35

Ran

ge (

m)

Doppler (m/s)

Sonar1target

29 29.5 30 30.50

500

1000

1500

2000

-20

-10

0

10

20

30

40

50

Figure 3.1.1. An example of a target-only range-Doppler map.

The final set of data combines the three previously mentioned types of data to

create a total output set. An example is presented in Figure 3.1.4. The target return,

broadband passive background noise, and the reverberation ridge are all clearly

represented in this figure. Under close inspection, one can see that the decibel levels

(visualized via the color bars on the right hand side of each map) for the target, passive,

and reverberation ridge returns vary, while the total return assumes the maximum value

of the three parameters. The combination of passive background noise and reverberation

will further be referred to as “environmental noise characteristics.” For the analysis in

the remainder of this chapter, only total data sets will be considered.

36

Ran

ge (

m)

Doppler (m/s)

Sonar1passive

29 29.5 30 30.50

500

1000

1500

2000

-50

-40

-30

-20

-10

0

10

20

Figure 3.1.2. An example of broadband noise only return range-Doppler map.

Ran

ge (

m)

Doppler (m/s)

Sonar1reverb

29 29.5 30 30.50

500

1000

1500

2000

10

20

30

40

50

60

70

80

Figure 3.1.3. An example of a reverberation-only return range-Doppler map.

37

Ran

ge (

m)

Doppler (m/s)

Sonar1total

29 29.5 30 30.50

500

1000

1500

2000

10

20

30

40

50

60

70

80

Figure 3.1.4. An example of a total output range-Doppler map.

The next two sections will present the test configuration defined in SST as well as

describe the raw time series generated. For the remainder of this chapter, only ‘total’

data sets will be considered for analysis. The purpose of doing so is to mimic the

analysis of real-world experiments where separate time series for the target,

environmental reverberation, and passive background noise cannot be easily collected.

3.1.2 Test Configuration

The test configuration codes developed to generate data for this thesis were

completed by modifying Dr. Robert Goddard’s ‘pursuit’ example within the SST

program. In all of these scenarios, there are two linear sonar arrays—one monostatic, one

bistatic—and one target. Each array has fifteen cylindrical piston transducers, each

having a 2cm diameter and arranged adjacent to each other in a linear configuration. In

addition to the recorded data at each of the fifteen hydrophones, a sixteenth ‘channel’

38

collects the sum of all actual channels’ signals into a detection beam. The sampling rate

for the arrays is 2000 Hz.

An underwater environmental location map is presented in Figure 3.1.5. Sonar 1

is located at the origin and Sonar 2 is located off-origin; both were setup to ‘look’ due

North. The target is fleeing from the sonar due North at a speed of 10m/s. Both sonar

vehicles and the target are arranged at a common depth of 200m. As it is the monostatic

sonar, Sonar 1 transmits a tone at 30 kHz from its first hydrophone, located exactly at the

origin. This signal hits the target and is reflected back to Sonar 1 as well as Sonar 2—the

bistatic sonar—where the returned signals are recorded. Time series data sets were

generated using this consistent configuration for target return levels of +40, +30, +20,

+10, +5, and 0 dB.

2000

Figure 3.1.5. Test configuration geometry.

3.1.3 The Simulated Sonar Data

To serve as a representative example, time series for both arrays; time series for

the +40 dB case are presented in Figure 3.1.6 where each of the fifteen channels is

-500 0 500 10000

500

1000

1500

Environmental Map

Easting Distance, m

Nor

thin

g D

ista

nce,

m

Sonar1Sonar2Target

39

indicated by a different color line. As expected, the signals recorded at all channels

follow a similar pattern but are slightly offset from one another. Due to the geometry of

the test setup (i.e. Sonar 2 is closer in proximity to the target than Sonar 1), it makes

sense that the bistatic sonar’s first high energy return occurs prior in time to that of the

monostatic sonar.

0 0.5 1 1.5 2 2.5 3 3.50

50

100

150

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 1

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120

140

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 2

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

Target

Figure 3.1.6. Time series from both sonar for the +40 dB target return case.

Once time signals are collected at both arrays for each of the target return

situations, the data is processed using MATLAB to generate range-Doppler and range-

angle maps. Range-angle maps can be generated from time-domain data, while range-

Doppler maps are generated using the same data transformed into the frequency-domain.

The time series data for the 0, +5, +10, +20, and +30 dB target return cases are presented

in Appendix A. As anticipated, the target returns are more distinguishable from the

environmental noise characteristics as the decibel level increases.

40

3.2 Range-Doppler Map Sharing

This section presents the results of the sharing and compression algorithms

developed during the course of this research. The following subsections define the Image

Compression Approach algorithm and variables. In addition, the results from these

algorithms followed by extreme—high and low—theoretical sharing capabilities are

presented.

3.2.1 The Image Compression Approach Algorithm

The goal of this research is to combine maps from two or more sonar platforms in

order to increase the likelihood of a true positive target return as well as to reduce the

amount of extraneous clutter within the raw data. This is accomplished by passing data

through a series of algorithms that include: 1) a method of converting time domain data

into the frequency domain, 2) applying and evaluating two different filtering

techniques—gap window normalization and band-stop filters—to the frequency domain

data, 3) applying an inverse STFT to convert the frequency domain data back into the

time domain, and 4) compressing the filtered time domain data, and finally 5) combining

the output from two sonar.

Figure 3.2.1 presents a flowchart for the Image Compression Approach algorithm.

In this flowchart, there are two paths to follow. The first path, shown in red, does not

apply compression techniques to the data. The second path, presented in blue, analyzes

the data in the frequency domain, reduces the reverberation ridge via one of two filtering

methods, and converts the data back into the time domain where compression techniques

are applied and the data is analyzed. Some of the data is lost in the compression

algorithm but the target returns are preserved; varying amounts of compression are

41

discussed later in this chapter. Data from both Sonar 1 and Sonar 2 are passed through

this same algorithm for analysis.

Figure 3.2.1. The flowchart for Image Compression Approach algorithm.

OR

Raw Time Series Data

Range-Angle Map Convert into Frequency Domain

Range-Doppler Map

Reduce Reverberation Ridge via Split Window

Normalization

Reduce Reverberation Ridge via Traditional

Filtering

Convert Filtered Data Back into Time Domain

Coordinate System Transformation

Range-Angle Map

Resample Data for Image Compression

Plot Maps Separately in a Common Coordinate

System

Combine Both Maps for Comparison

Determine Target Location

42

3.2.2 Definition of Variables

The time series data—represented by an x variable (more specifically, ‘x1’ for

Sonar 1 and ‘x2’ for Sonar 2)—is imported into Matlab. A second variable, y (‘y1’ and

‘y2’ corresponding to ‘x1’ and ‘x2’, respectively) preserves header information from the

SST output. Sub-variables contained within the y variable include: 1) the number of

channels within the file, 2) the number of data points (i.e. samples) collected for each

channel, 3) the sampling frequency, 4) the time the receivers initialized data recording,

and 5) the center frequency of the tone emitted from the first channel of Sonar 1. All of

these sub-variables are used during signal analysis. Other variables must also be defined

prior to analysis including the speed of sound, m/s 1500=c , the window length,

, the range of decibel level displayed in graphs,

, and the size of the fft,

samples 128=thwindowLeng

dB 80=dBrange 256 =nfft , corresponding to the next power of

two greater than the window length. In addition, a Hanning window of

length, , is also specified. thwindowLeng

3.2.3 The Best Theoretical Capability

Following the red path, every data point is used for analysis. Therefore, this is the

best case scenario as far as target detection as no compression is applied to the data. The

first step in the red path processes the data in the time-domain to produce range-angle

maps. Figures 3.2.2 and 3.2.3 present the range-angle maps for both Sonar 1 and Sonar

2, respectively, for the +40 dB case. These maps show returns for the entire data set from

-30 to +30 degrees. In both figures, strong returns over the entire range are detected;

these are the environmental returns from the surface, bottom, and volumetric

43

reverberations. The first figure shows a ‘hot-spot’ return that does not follow the

environmental noise pattern at a range around 1000m. In the second figure, a similar

return is shown around 850m; these two ‘hot spots’ are target returns. The solid blue

portion in Figure 3.2.3 represents empty returns added to the end of Sonar 2’s time series

to make it the same length as Sonar 1’s return for analysis purposes. Such empty returns

are noted within Matlab as ‘NaN’ referring to “not a number” [28]. This time

corresponds to the 0.06 second tone emitted from Sonar 1 when Sonar 2 is not collecting

data.

Range-Angle Map for Sonar 1

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800

Figure 3.2.2. The range-angle map for Sonar 1 in the +40 dB case.

44

Range-Angle Map for Sonar 2

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800

Figure 3.2.3. The range-angle map for Sonar 2 in the +40 dB case.

These range-angle maps are transformed into Cartesian coordinates using

MATLAB’s ‘pol2cart’ function [28] and are presented in Figures 3.2.4 and 3.2.5,

respectively. Each of these plots begins at the location of the sonar in the environment,

as was presented in Figure 3.1.5. The cone-like shape is an artifact of the conversion into

the Cartesian coordinate system (if the returns at angles from 0 to 360 degrees were

generated, the shape would be a complete circle). Just as with the range-angle maps, a

target return can be distinguished from the environmental returns. The target angle and

range centers from the origin of each sonar return corresponds to the angle and range

from the range-angle maps.

The next step in the red path is to plot these Cartesian maps onto a common map

encompassing the entire environment, as shown in Figures 3.2.6 and 3.2.7. The only

difference between this set of maps and the previous step is the empty values have been

inserted into the ‘common’ maps where the sonar detections from the sonar were not

45

evaluated. The final step is to additively compare these maps as shown in Figure 3.2.8.

This manner of determining common returns is similar to the middle portion of a Venn

diagram or the overlapping areas in Doppler radar in weather analysis. Just as any

number multiplied by zero is zero, the addition of a real number and an empty (NaN)

value return equals an empty value. Therefore, only the intersecting areas are shown in

this figure. Following the same procedure, intersection return maps for the remaining

cases are presented in Appendix B. As may be expected, the level of the intersecting

energy return is reduced as the target return level decreases. Additionally, positive

detections are no longer visible below a target level return of +20 dB. It is hypothesized

that this occurs due to the inclusion of the environmental noise characteristics.

Therefore, the data must be manipulated to allow for positive target detections

independent of target return strength.

Distance, m

Dis

tanc

e, m

Sonar 1 Range-Angle Cartesian Coordinate Map

-800 -600 -400 -200 0 200 400 600 8000

200

400

600

800

1000

1200

1400

1600

1800

Figure 3.2.4. The Cartesian range-angle map for Sonar 1 in the +40 dB case.

46

Distance, m

Dis

tanc

e, m

Sonar 2 Range-Angle Cartesian Coordinate Map

-400 -200 0 200 400 600 800 1000 1200 1400200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 3.2.5. The Cartesian range-angle map for Sonar 2 in the +40 dB case.

Distance, m

Dis

tanc

e, m

Comman Map Plot for Sonar 1

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 3.2.6. The common environmental map for Sonar 1 in the +40 dB case.

47

Distance, m

Dis

tanc

e, m

Common Map Plot for Sonar 2

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 3.2.7. The common environmental map for Sonar 2 in the +40 dB case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 3.2.8. The intersection map for the +40 dB case.

48

3.2.4 Filtering Techniques

The blue route in Figure 3.2.1 allows for the raw data to be filtered, significantly

reducing the influence of the reverberation ridge on the signals received at the

hydrophone arrays. In return, targets are more easily identified—even those with low

level return strengths. Because the reverberation ridge return is easily characterized in

the frequency domain, two frequency-based filtering techniques were explored: split

window normalization [35, 36] and traditional filtering.

As one may have previously discovered, the sampling rate of 2000 Hz is

significantly lower than the 30 kHz tone emitted by Sonar 1. Therefore the effects of

aliasing must be considered in post-processing. When aliasing occurs, frequencies higher

than half the sampling rate—1000 Hz for the data discussed here—appear to occur at

lower frequencies as shown in Figure 3.2.9 [34]. It is important to note that aliasing can

be avoided by setting the sampling frequency higher than the highest frequency of

interest—also referred to as the Nyquist frequency. Figure 3.2.10 shows a range-Doppler

map for non-adjusted aliased data set. This map shows a center frequency at half the

sampling frequency but the frequencies included do not reflect the frequencies of interest.

The effects of aliasing can be seen in this figure: the actual frequencies occurring above

the center frequency of 30 kHz are aliased down to lower frequency values and those

below the center frequency are aliased to higher values. Since the phenomenon of

aliasing is understood, the data can be adjusted so the center frequency is 30 kHz rather

than 1000 Hz; this adjustment can be seen in Figure 3.1.4—a presentation of what Figure

3.2.10 should look like after adjusting the aliased frequencies.

49

Figure 3.2.9. True frequency plotted as a function of aliasing frequency.

sf21

f

sf sf2 sf3 sf4

Frequency, Hz

Ran

ge, m

Aliased Range-Doppler Map Example

0 200 400 600 800 1000 1200 1400 1600 18000

500

1000

1500

2000

Figure 3.2.10. An example of an aliased range-Doppler map.

To account for varying oceanographic characteristics and underwater scenarios,

Baldacci and Haralabus suggest applying a split window normalization technique to time

series data. This technique is used to reduce the influence the environmental returns have

on target detection. A flow chart by Balducci and Haralabus explaining the process of

split window normalization is presented in Figure 3.2.11. In this method, a ‘cell of

interest’ is first selected. Next, the user defines the sizes of the ‘guard bands’ and

‘lagging windows;’ these values can be equal or different from each other. The ‘guard

bands’ serve as buffer between the ‘cell of interest’ and the ‘lagging windows.’ The next

step averages the sum of the power within the two lagging windows. Finally, this

50

average value is used to normalize the value of the cell of interest, shown in the flowchart

as ‘normalized data sample.’ This process is completed until the entire map is evaluated.

Although the authors discuss application solely in the time domain, this program has been

applied to data in the frequency domain [35].

Figure 3.2.11. The split window normalization method [35].

Lagging Window

Guard Band

Cell Being Normalized

Guard Band

Lagging Window

Normalized Data Sample

Estimate Time Dependent Noise Background Power

Two example outputs from the split-window normalizer implemented by E.

Hoppe are presented in Figures 3.2.12 and 3.2.13 [36]. These figures reflect the data for

the first channel of Sonar 1 in the 0 dB target return case. This data set is used here

because it is the worst case scenario in terms of the simulated data. In addition, without

filtering techniques, the target cannot be located using the combination map technique

described in the previous section. The first figure uses a guard band and lagging window

both of 4 cells. The second figure uses a guard band of 20 cells and a lagging window of

4 cells. For target strength comparison, both maps reflect the same decibel levels. The

target can be localized in both cases, but at a slightly higher strength in the second map.

The trade off between the amount of false target detections—low in the first map and

51

higher in the second due to the size of the guard bands—must be considered when using

the split window normalization method to manipulate data in real-time applications.

Frequency, kHz

Ran

ge, m

Gap Window Normalization Outout for Gaurd Band = 4, Lagging Window = 4

29 29.5 30 30.50

500

1000

1500

2000

0.2

0.4

0.6

0.8

1

1.2

1.4

Figure 3.2.12. Split window normalization output; guard band = lagging window = 4.

29 29.5 30 30.50

500

1000

1500

2000

0.2

0.4

0.6

0.8

1

1.2

1.4

Figure 3.2.13. Split window normalization output; guard band = 20, lagging window = 4.

In parallel with the split window normalization step in the flowchart, the other

option is to perform filtering using more traditional band stop methods. This is done by

52

selecting unwanted frequencies associated with the reverberation ridge and decreasing the

cell values by some scaling factor. (Since passive noise does not have a huge influence

on the target echo returns, only the reverberation ridge returns are considered for

filtering.) For the purposes of this thesis, several scaling values were considered.

Figures 3.2.14 presents the time-series results of such filtering for the 0 dB target return

case for scaling factors of 100 and 1000 as compared to the original range-Doppler map

for the second channel of Sonar 1. All three maps have the same return level values. As

can be seen, the higher the scaling factor, the lower the influence of the reverberation

ridge. While there is a strong discrepancy line between the filtered and unfiltered areas,

the next step in the blue path will prove that this inconsistency is not a factor in the final

outcome of the Image Compression Approach algorithm.

53

Frequency, kHz

Ran

ge, m

Original Range-Doppler Map for Channel 2, 0 dB case

29 29.5 30 30.50

500

1000

1500

2000

20

40

60

80

Frequency, kHz

Ran

ge, m

Scaling Factor = 100 Reverberation Ridge Filtering Results

29 29.5 30 30.50

500

1000

1500

2000

20

40

60

80

Frequency, kHz

Ran

ge, m

Scaling Factor = 1000 Reverberation Ridge Filtering Results

29 29.5 30 30.50

500

1000

1500

2000

20

40

60

80

Figure 3.2.14. A comparison of the original range-Doppler and two scaling factors.

Independent of the filtering method followed, the next step in the blue path

converts the frequency-based range-Doppler maps back into the time domain. This is

accomplished by applying ‘inverseSpecgram’ to the data set; this function does not come

with MATLAB and was developed over the course of research for this thesis. The

inverseSpecgram exploits the fact that range-Doppler maps are generated by taking

STFTs via the ‘spectrogram’ function that comes with MATLAB [28]. The MATLAB

documentation points out that because a signal’s phase is lost after calculating the

spectrogram of a signal, it is not a reversible function [28]. However, inverseSpecgram

overlooks this fact and performs IFFTs on the frequency content at each range in the

54

anticipation that some information may still be gleaned from inversing the effects of the

original spectrogram function. The same inputs used in ‘spectrogram’ are applied in the

new function— , 256 =nfft samples 64=overlap , and samples 128=thwindowLeng .

The fifteen channels are processed through inverseSpecgram individually and

then passed through a time-domain beamforming program to achieve a range-angle map

that reflects the filtered data. Figure 3.2.15 shows a comparison of the original raw data

collected at the second hydrophone in Sonar 1 and the inverseSpecgram output for this

same channel for the +40 dB case. No filtering is performed on the signal in this figure,

proving that the inverse spectrogram program does in fact perform as expected. Notice

that in both of these plots, much of the returned energy in the original output appears to

be occurring at low frequencies while the target return—located just before 3000

samples—is at a higher frequency; this is a time-domain example of the aliasing depicted

in the frequency-domain aliased plot in Figure 3.2.10. In reality, the target is returning

energy at a lower frequency than the environmental noise, just as before. In the inverse

spectrogram’s reconstructed signal output, the noise due to the underwater environment is

rectified to a higher frequency than in the original output.

55

0 1000 2000 3000 4000 5000 6000 7000-5

0

5

10x 10

6

Sample Number

Mag

nitu

de

Original Output from Channel 2, +40dB Case

0 1000 2000 3000 4000 5000 6000 7000-1

-0.5

0

0.5

1x 10

7

Sample Number

Mag

nitu

de

Channel 2 Inverse Spectrogram Output, +40dB Case

Figure 3.2.15. The original & reconstructed output for Channel 2, Sonar 1, +40 dB case.

Referring back to post-filtered data, Figures 3.2.16 and 3.2.17 show this same

comparison for the 0 dB and +40 dB cases, respectively, for Sonar 1’s Channel 2. In the

first figure, the target return is not clearly visible in the original Channel 2 output. But in

the post-filtered inversed output, the target can be clearly distinguished from the

background noise. As expected, the second figure shows that the reverberation ridge

filtering has a greater influence on the data as the target’s return strength increases.

Figure 3.2.18 shows a range-angle map for the 0 dB case using the data presented in

Figure 3.2.16. Again, this data set is presented as the worst-case scenario. There is a

mirroring effect around zero degrees observed in this map. Using the next steps to

combine the maps of two platforms, this mirroring is overcome. Similar post-filter-and-

inversed range-angle maps for all target return level cases are presented in Appendix C.

56

0 1000 2000 3000 4000 5000 6000 7000-5

0

5

10x 10

6

Sample Number

Mag

nitu

de

Original Output from Channel 2, 0 dB Case

0 1000 2000 3000 4000 5000 6000 7000-2

-1

0

1

2x 10

4

Sample Number

Mag

nitu

de

Channel 2 Inverse Spectrogram Output, 0 dB Case

Figure 3.2.16. The original & post-filtered output for Channel 2, Sonar 1, 0 dB.

0 1000 2000 3000 4000 5000 6000 7000-5

0

5

10x 10

6

Sample Number

Mag

nitu

de

Original Output from Channel 2, +40 dB Case

0 1000 2000 3000 4000 5000 6000 7000-1

-0.5

0

0.5

1x 10

6

Sample Number

Mag

nitu

de

Channel 2 Inverse Spectrogram Output, +40 dB Case

Figure 3.2.17. The original & post-filtered output for Channel 2, Sonar 1, +40 dB case.

57

Range-Angle Map for Sonar 1

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800

Figure 3.2.18. A post-filter-and-inversed range-angle map for Sonar 1 in the 0 dB case.

The output from the split window normalization program was also passed through

the inverse spectrogram program, only with non-optimal results. Figures 3.2.19 and

3.2.20 present the post-normalization-and-inversed range-angle map for the 0 dB and +40

dB cases, respectively, for Sonar 1. In the first figure, no target information is even

slightly visible. In the second, the target’s range is preserved but there is no angle

resolution. This occurrence is an artifact of the split window normalization algorithm.

The normalization is completed by using the values—both real and imaginary—from

certain side cells; the normalized cell values are skewed based on the averaged real and

imaginary values generated from the lagging windows. Thus, any reconstruction of the

angle returns becomes pointless using the split window normalization filtering technique.

58

Range-Angle Map for Sonar 1

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800

Figure 3.2.19. A post-normalization range-angle map for Sonar 1 in the 0 dB case.

Range-Angle Map for Sonar 1

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800

Figure 3.2.20. A post-normalization range-angle map for Sonar 1 in the +40 dB case.

While the split window normalization program works well to minimize the

amount of background noise, it will not adapt to accommodate varying data sets. In other

words, the guard band and lagging window inputs used to analyze one map may not

59

necessarily work to accomplish a similar outcome on another map—even if the two maps

collect data from the same target. Finally, split window normalization does not perform

well when trying to reconstruct the time series from a normalized data set because the

averaging method skews the normalized cell values. As a result of the issues encountered

with the split-window normalization method, the remaining data and maps presented will

reflect the data after application of both the traditional filtering method and a scaling

factor that reduces the energy within a set area around the reverberation ridge by a factor

of 1000.

3.2.5 Application of the Image Compression Approach

The next step in the blue route is to combine maps using the same method as the

red path, only with a lossy image compression technique applied to the data. With the

range-angle maps shown in Appendix C, the data for each sonar is broken into a grid

system. An example grid system is shown in Figure 3.2.21. The grid system assigns

three holding variables: x and y coordinates to represent the two ‘Distance, m’ axes

values and the z coordinate to corresponding to the echo return level in decibels. Once

the grid is defined, the compression algorithm allocates new values to the points of grid

line intersection. These revised values are calculated by taking the average of all points

falling within a square centered at the intersection point, as demonstrated in Figure

3.2.22.

60

Figure 3.2.21. An example of the grid applied to a XY map for compression.

Figure 3.2.22. An example of the grid applied to a XY map for compression.

Recalling the goal of reducing the image size to a level where acoustic

transmission is viable, several amounts of compression were investigated. Table 3.2.1

presents the compressed sizes of the combined maps along with the respective

percentages of compression and processing time from the 0 dB target return level case.

Additionally, the transmission time for a 5000 bit per second micro-modem is included.

The compressed and combined map sizes will allow a reduction in transmission time.

However, when using a micro-modem with a maximum bandwidth of 5000 bits per

61

second, the transmission between sonar platforms will not occur instantly. (Note: 1 byte

is equal to 8 bits of information.) Using the largest amount of compression of 1 value per

100 samples, a transmission time of 6.45 seconds is required. Depending on the

situation, this time requirement is acceptable.

Table 3.3.1. Results for various grid rates for the 0 dB case.

Grid Rate, Y (1 value per Y cells)

Combined Map Size (Bytes)

Percent Compression

Time Elapsed for Compression (seconds)

Transmission Time (seconds)

1* 37874088 -- -- -- 2 9477248 74.977 103.40 15163.60 5 1520552 95.985 11.99 2432.88

10 381888 98.992 3.66 611.02 25 61664 99.837 1.67 98.66 50 15416 99.959 1.24 24.67

100 4032 99.989 1.15 6.45 250** 640 99.998 1.03 1.02

*This represents the original unfiltered time series data **At this point, positive target identification is not viable

Figure 3.2.23 presents the two latter values as trend lines for grid rates of 2

through 100 only. The reason for leaving out the end points are: 1) a grid rate of 1 takes

into consideration every data point and no compression takes place, and 2) at a grid rate

of 250, target detection within a certain cell becomes impossible. This second situation

occurs because the size of the simulated target is less than half the size of the grid rate

(i.e. the averaging area for the new allocated value). As can be seen by the blue line in

the figure below, significant compression of 74.997% is seen simply by halving the

amount of considered data. A maximum of 99.989% compression is observed a quadrant

size of 100. The trend line appears to be exponential and approaches an asymptote at

grid rates at and above 1 value per 25 cells. The magenta line shows that the processing

time for compression to take place follows an negative exponential trend and reaches a

somewhat constant slope after a grid rate of 1 value per 25 samples. Figure 3.2.24

62

presents the resulting compressed range-angle map for the grid rate of 1 value per 25

samples. Even with this worst case scenario data, a target is able to be positively

identified. The compressed range-angle maps for the other grid rates at the 0 dB target

return level along with those for the other target return levels at a grid rate of 1 value per

25 sample are presented in Appendix D. Comparing the maps for all of the target return

cases to those when no filtering is completed, the target detection in the compressed maps

is no longer a function of target return level.

Compression Results Analysis

0.000

20.000

40.000

60.000

80.000

100.000

120.000

0 20 40 60 80 100 120

Grid Rate, 1 value per n cells

Mag

nitu

de

Percent Compression, %Elapsed Time, seconds

x

Figure 3.2.23. Percent compression and time elapsed as a function of grid rate.

63

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 3.2.24. Filtered, compressed, & combined range-angle map for the 0 dB case.

3.2.6 Comparison with Other Image Compression Techniques

To finalize the Image Compression Approach, these results should be compared

to the JPEG standard. Using the +40 dB data set, a combined-map with a grid-rate of 1

(i.e. uncompressed) was generated as a baseline for comparison. First, this map was

saved as a 24-bit uncompressed bitmap image within Matlab which is presented in Figure

3.2.25. (It should be noted that only lossless JPEG image compression is available within

Matlab.) This file format can store up to 16 million colors and is useful for high-

resolution images. Next, a bitmap image storing only 256 colors was created as shown in

Figure 3.2.26. Finally, a lossless JPEG image, portrayed in Figure 3.2.27, was generated.

Table 3.3.2 shows a comparison of these three images along with combined map results

of the Image Compression Approach grid rate of 25. This table proves that the

algorithms developed in this research do perform slightly better than the lossless JPEG

standard—91.773% vs. 91.257%, and is significantly better than no compression at all.

64

The Image Compression Approach allows for a reduction in image size over that of

traditional image compression techniques.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 3.2.25. An uncompressed bitmap image for the +40 dB case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 3.2.26. An 8-bit compressed bitmap image for the +40 dB case.

65

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 3.2.27. An losslessly compressed JPEG image for the +40 dB case.

Table 3.3.2. A comparison of the image compression techniques.

Algorithm Combined Map Size (Bytes)

Percent Compression over Uncompressed Bitmap

24-bit Bitmap uncompressed image 749568 -- 8-bit Bitmap (256 colors stored) 253952 66.120 24 bit JPEG, lossless 65536 91.257 Image Compression Approach, Grid Rate = 25 61664 91.773

66

Chapter 4: Conclusions

This final chapter draws conclusions from the research completed in the thesis

entitled An Image Compression Approach to Cooperative Processing for Swarming

Autonomous Underwater Vehicles. The following sections list these conclusions and

make suggestions for areas of research that will further this research.

4.1 Conclusions & Applications

Several milestones have been achieved over the course of this research. First,

high fidelity simulated underwater data was generated. The high target strength

simulated data was used as a baseline for algorithm validation runs while the lower target

strengths were analyzed with the Image Compression Approach. For the next milestone,

image compression techniques were applied to sonar data, specifically sonar maps.

Finally, several MATLAB-based algorithms were developed for signal analysis and

target registration.

The two main objectives for this research focus on using image compression

techniques to reduce the required communication bandwidth. The first objective was to

utilize image compression techniques to facilitate improved swarmed AUV

67

communication, navigation, and target pursuit. The second objected was to develop a

method for compressing sonar maps such that key features are preserved while enabling

more reliable and faster data transmission using fixed acoustic modem bandwidth. Both

of these objectives were achieved through the algorithms developed over the course of

this research.

The Image Compression Approach provides a method for accomplishing these

goals. Using this set of algorithms, raw time series from sonar can be manipulated via

filters and lossy compression techniques to achieve the positive target detection. Without

application of the Image Compression Approach to the time series data, it is not possible

to detect targets below a target return level of 30 dB. However, using the filtering and

compression techniques defined in this program, positive target detection is possible—

even at the lowest target strength level of 0 dB! The effects of image degradation due to

image compression techniques were evaluated and quantified. The compression

techniques developed for this thesis allow for a reduction in time required to transmit

maps to cooperative sonar platforms. Additionally, the predicted transmission times

assuming a 5000 bit per second bandwidth were quantified.

There are myriad real world applications for the Image Compression Approach.

In addition to cooperative AUV to AUV communication, these include AUV to sea

vessel communication, cooperative navigation and control, homeland and port security,

cross-domain (water, surface, air, space) communication and other cooperative situations.

Civilian applications are also possible including cooperative search missions and terrain

mapping.

68

4.2 Future Research

There are a few ways in which the work summarized in this thesis can be

furthered. First, other methods of data analysis are suggested. Second, data collected

from in-water experiments will be discussed. Next, for in-water tests, modifications to

the simulated setup are mentioned. Finally, comparisons between predicted versus the

actual data should be evaluated.

While the Image Compression Approach was successful in isolating a target from

a high-clutter simulated underwater environment, it may be of interest to explore other

methods of analysis. In the approach presented in this thesis, image compression

techniques were successfully applied to the intersection maps. To further these results,

the image compression step may be moved around in the flowchart shown in Figure

3.2.1. One idea may be to apply image compression to the range-angle maps prior to

transforming the coordinate system into the x-y plane. Another thought may be to

change the method of image compression. In the Image Compression Approach, the

average values assigned to the grid intersection points during the compression step do not

account for the shape of the sonar return—the data points are more densely packed near

the point of the cone shape in the x-y map and more spaced out towards the opposite end.

A newer image compression technique may be able to account for this difference, thus

allowing for higher compressed resolution closer to the sonar platform. As a final

alternative, it may be beneficial to pass the time series through detection software prior to

image compression. This could further reduce the size of the images transferred by

pinpointing areas of interest (i.e. target detections) and only passing these between sonar

platforms.

69

As the main conclusions were drawn based on simulated underwater data,

experimental tests should be performed to verify the validity of the Image Compression

Approach. Another improvement would be to evaluate—both in simulation and

experiments—the outcome of combining the maps of more than two sonar platforms. In

a similar manner, evaluating situations that include more than one target should be

included in further research plans. In the area of acoustic micro-modems, increases in the

available bandwidth will surely aid in the real-world application of the Image

Compression Approach.

While the focus of this research relied on simulated underwater acoustic data, the

algorithms developed for this thesis can be applied to actual experimental data. It was

hoped that data collected from experiments in Claytor Lake near Radford, VA could be

analyzed with the Image Compression Approach. However, this was not accomplished

due to extenuating circumstances with the vehicles. A future graduate research project

could be to build underwater hydrophone arrays and a target-like UUV, collect data in

Claytor Lake, and then use the Image Compression Approach algorithms for analysis.

Similar to the simulated data presented here, the two hydrophone arrays should be

stationary while the target is moving away from the two arrays in the experiment. Due to

the limitations of Claytor Lake, the experiment should be scaled down significantly both

in the x- and y-coordinates as well as decreasing the depth at which experiments take

place. It should be noted that Claytor Lake is an acoustically noisy underwater

environment due to its underwater topography, so additional adjustments to the Image

Compression Approach may be necessary.

70

Another future area of interest may be to both model and experiment with other

underwater scenarios. These may include target tracking via analysis of multiple ping

returns, setting up autonomous vehicles to follow the target rather than having them

remain stationary, or sending information from two sonar vehicles to a third, fourth, etc.

sonar platforms further down the line. There may also be a case where more detailed

target information—such as surveying the bottom of a ship to check for abnormalities—

may be required. In this case, UUVs should be programmed to first detect a target and

then move in and send multiple pings or even engage an underwater camera with a light

for real-time video. For this case, video compression could also be explored for a method

of sending the footage to a surface vehicle for analysis.

71

Appendix A: Presentation of Raw Data

0 0.5 1 1.5 2 2.5 3 3.50

50

100

150

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 1

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120

140

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 2

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

Figure A.1. Time series data for both sonar for the 0 dB target return case.

0 0.5 1 1.5 2 2.5 3 3.50

50

100

150

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 1

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120

140

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 2

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

Figure A.2. Time series data for both sonar for the +5 dB target return case.

72

0 0.5 1 1.5 2 2.5 3 3.50

50

100

150

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 1

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120

140

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 2

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

Figure A.3. Time series data for both sonar for the +10 dB target return case.

0 0.5 1 1.5 2 2.5 3 3.50

50

100

150

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 1

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120

140

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 2

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

Figure A.4. Time series data for both sonar for the +20 dB target return case.

0 0.5 1 1.5 2 2.5 3 3.50

50

100

150

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 1

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120

140

Time, s

Mag

nitu

de, d

B

Time Series for Sonar 2

Ch1Ch2Ch3Ch4Ch5Ch6Ch7Ch8Ch9Ch10Ch11Ch12Ch13Ch14Ch15

Figure A.5. Time series data for both sonar for the +30 dB target return case.

73

Appendix B: Intersection Maps

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure B.1. The intersection map for the 0 dB

case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure B.2. The intersection map for the +5 dB

case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure B.3. The intersection map for the +10

dB case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure B.4. The intersection map for the +20

dB case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure B.5. The intersection map for the +30

dB case.

74

Appendix C: Filtered Range-Angle Maps

Range-Angle Map for Sonar 1

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800Range-Angle Map for Sonar 2

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800

Figure C.1. Filtered range-angle maps for the 0 dB case.

Range-Angle Map for Sonar 1

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800Range-Angle Map for Sonar 2

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800

Figure C.2. Filtered range-angle maps for the +5 dB case.

Range-Angle Map for Sonar 1

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800Range-Angle Map for Sonar 2

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800

Figure C.3. Filtered range-angle maps for the +10 dB case.

70

Range-Angle Map for Sonar 1

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800Range-Angle Map for Sonar 2

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800

Figure C.4. Filtered range-angle maps for the +20 dB case.

Range-Angle Map for Sonar 1

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800Range-Angle Map for Sonar 2

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800

Figure C.5. Filtered range-angle maps for the +30 dB case.

Range-Angle Map for Sonar 1

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800Range-Angle Map for Sonar 2

Angle, degrees

Ran

ge, m

-30 -20 -10 0 10 20 300

200

400

600

800

1000

1200

1400

1600

1800

Figure C.6. Filtered range-angle maps for the +40 dB case.

71

Appendix D: Compressed Maps

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure D.1. Combined range-angle map for a grid rate of 2

the 0 dB case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure D.2. Combined range-angle map for a grid rate of 5

the 0 dB case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure D.3. Combined range-angle map for a grid rate of 10

the 0 dB case.

Distance, mD

ista

nce,

m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure D.4. Combined range-angle map for a grid rate of 25

the 0 dB case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure D.5. Combined range-angle map for a grid rate of 50

the 0 dB case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure D.6. Combined range-angle map for a grid rate of

100 the 0 dB case.

72

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000

0

200

400

600

800

1000

1200

1400

1600

1800

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 7. Combined range-angle map for a grid rate of 250

for the 0 dB case. Figure D.10. Combined range-angle map for a grid rate of

25 the +20 dB case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure D.8. Combined range-angle map for a grid rate of 25

the +5 dB case. Figure D.11. Combined range-angle map for a grid rate of

25 the +30 dB case.

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Distance, m

Dis

tanc

e, m

Sonar 1 & 2 Intersection Map

-1000 -500 0 500 1000 15000

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure D.9. Combined range-angle map for a grid rate of 25

the +10 dB case. Figure D.12. Combined range-angle map for a grid rate of

25 the +40 dB case.

73

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