LOCALIZATION ALGORITHMS FOR WIRELESS SENSOR …

The Pennsylvania State University

The Graduate School

Department of Computer Science and Engineering

LOCALIZATION ALGORITHMS FOR WIRELESS SENSOR

NETWORK SYSTEMS

A Thesis in

Computer Science and Engineering

by

Xiang Ji

c© 2004 Xiang Ji

Submitted in Partial Fulfillmentof the Requirements

for the Degree of

Doctor of Philosophy

August 2004

The thesis of Xiang Ji was reviewed and approved∗ by the following:

Hongyuan ZhaAssociate Professor of Computer Science and EngineeringThesis AdviserChair of Committee

John J. MetznerProfessor of Computer Science and Engineering

Wang-Chien LeeAssociate Professor of Computer Science and Engineering

Peng LiuAssistant Professor of Information Science and Technology

Raj AcharyaProfessor of Computer Science and EngineeringChairman, Department of Computer Science and Engineering

∗Signatures are on file in the Graduate School.

iii

Abstract

Advances in the micro-electro-mechanical system and wireless communication

technology have enabled researchers to develop large-scale wireless sensor networks with a

large number of inexpensive and small sensors. Many applications are developed based on

wireless sensor networks, such as habitat monitoring, navigation, and objects detection

and tracking. By its nature, location awareness is indispensable for the implementation

of these applications.

In this dissertation, we study two issues related to sensor and object localization

in wireless sensor networks. We first examine the sensor localization algorithms, which

are used to determine sensors’ positions in ad-hoc sensor networks. Most existing sen-

sor localization methods suffer from various location estimation errors that result from

ranging errors, complex network topologies and anisotropic terrain, etc. We explore

the characteristics of dimensionality reduction techniques and propose three sensor lo-

calization algorithms based on the multidimensional scaling techniques. They include

a centralized sensor localization algorithm, a distributed sensor localization algorithm,

and a robust sensor location algorithm based on multidimensional scaling. The results

of our experiment demonstrate that these algorithms are effective in positioning sensors

Positioning all sensors in a sensor network usually consumes a large amount of

time and energy. In many applications based on sensor networks, there is no need to

estimate the location of all sensors in a sensor network. Sometimes, only sensors within

a given direction or region need to be located. We propose the concept of differentiated

iv

sensor localization. Three differentiated sensor localization methods are also proposed,

which can selectively locate only one or a specific set of sensors.

Given the sensor location information known, many surveillance tasks may then

be carried out with sensor networks. One of the major applications of sensor networks

is locating objects and tracking their movement. We investigate the problem of using

large-scale sensor network to locate large continuous objects and track their boundary

movement. The large continuous objects, such as wild fire and bio-chemical materials,

are different from the traditional single or multiple discrete targets in that they are

continuously distributed across a region and usually occupy a large area. Detecting

and tracking the large continuous objects poses many challenging research issues which

have not been adequately addressed in previous research. Capturing their spread and

boundary information is usually an efficient approach for monitoring them. A distributed

algorithm is proposed in this research to locate the boundary of continuous objects. A

dynamic structure is proposed to track the movement of boundaries and to facilitate

the fusion and dissemination of boundary information in a sensor network. Simulation

results show the efficiency of the proposed algorithms.

v

Table of Contents

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Applications of Sensor Networks . . . . . . . . . . . . . . . . . . . . 2

1.3 Location-aware Computing . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Localization in Sensor Networks . . . . . . . . . . . . . . . . . . . . . 5

1.5 Dissertation Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Chapter 2. Background and Related Research . . . . . . . . . . . . . . . . . . . 10

2.1 Wireless Sensor Network Model . . . . . . . . . . . . . . . . . . . . . 10

2.2 Elements of Localization . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Received Signal Strength Indication . . . . . . . . . . . . . . 14

2.2.2 Time of Arrival . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.3 Time Difference of Arrival . . . . . . . . . . . . . . . . . . . . 16

2.2.4 Angle of Arrival . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.5 Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.6 Trilateration . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.7 Multilateration . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Related Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

vi

2.4 Challenges of Localization . . . . . . . . . . . . . . . . . . . . . . . . 26

Chapter 3. Sensor Localization with Multidimensional Scaling . . . . . . . . . . 29

3.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Overview of The Centralized Sensor Localization . . . . . . . . . . . 30

3.3 Multidimensional Scaling . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3.1 Classical Multidimensional Scaling . . . . . . . . . . . . . . . 32

3.3.2 Iterative Multidimensional Scaling . . . . . . . . . . . . . . . 35

3.4 Ranging Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.5 Pairwise Distance Collection . . . . . . . . . . . . . . . . . . . . . . . 39

3.6 Performance Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Chapter 4. Distributed and Robust Sensor Localization . . . . . . . . . . . . . . 51

4.1 Distributed Sensor Localization . . . . . . . . . . . . . . . . . . . . . 51

4.1.1 Calculating Relative Positions . . . . . . . . . . . . . . . . . . 51

4.1.2 Aligning Relative Positions . . . . . . . . . . . . . . . . . . . 52

4.2 Robust Sensor Localization . . . . . . . . . . . . . . . . . . . . . . . 54

4.3 Performance Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.3.1 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Chapter 5. Differentiated Sensor Localization . . . . . . . . . . . . . . . . . . . . 63

vii

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.3 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.4 Differentiated Sensor Localization Methods . . . . . . . . . . . . . . 66

5.4.1 The Localization-Along-Curve Method . . . . . . . . . . . . 66

5.4.2 The Localization-Within-Region Method . . . . . . . . . . . 69

5.4.3 On Demand Sensor Localization Method . . . . . . . . . . . . 69

5.5 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.5.1 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Chapter 6. Large Continuous Object Detection and Tracking . . . . . . . . . . . 77

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.3 Model Assumptions and Challenges . . . . . . . . . . . . . . . . . . . 81

6.4 Boundary Localization . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.4.1 Boundary Sensors Selection . . . . . . . . . . . . . . . . . . . 85

6.4.2 Distributed Boundary Localization . . . . . . . . . . . . . . . 88

6.5 Boundary Movement Tracking . . . . . . . . . . . . . . . . . . . . . . 89

6.5.1 Curvilinear Belt Structure and Its Partitioning . . . . . . . . 91

6.5.2 Tracking Boundaries . . . . . . . . . . . . . . . . . . . . . . . 100

6.6 Performance Evaluations . . . . . . . . . . . . . . . . . . . . . . . . . 106

viii

6.6.1 Simulation model . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.6.2 Evaluation criteria . . . . . . . . . . . . . . . . . . . . . . . . 107

6.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Chapter 7. Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . 119

7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

7.2 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

ix

List of Figures

2.1 Example of tiny wireless sensor node [41]. . . . . . . . . . . . . . . . . . 11

2.2 Sensors deployed in the mountain area form an ad-hoc sensor network

and monitor the environment. . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Soldiers with receivers scout the enemy tanks’ information with the as-

sistance of a distributed sensor network [101]. . . . . . . . . . . . . . . . 13

2.4 The power of the received radio signal strength attenuates exponentially

with the increase of distance between the transmitter and receiver. . . . 15

2.5 Triangulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.6 Trilateration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.7 Multilateration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.8 A sensor network deployed in a square area with obstacles . . . . . . . . 23

2.9 A sensor network in non-square area . . . . . . . . . . . . . . . . . . . . 24

2.10 Irregular radio pattern of a sensor . . . . . . . . . . . . . . . . . . . . . 25

2.11 Anisotropic terrain condition leading to different radio ranges . . . . . . 25

3.1 Hop distance and signal strength . . . . . . . . . . . . . . . . . . . . . . 39

3.2 Routes of a flooding initialized by node S . . . . . . . . . . . . . . . . . 40

3.3 Flooding routes from a source node of a sensor network . . . . . . . . . 43

3.4 A broadcast initialized by node S collects 34 pairwise distances . . . . . 43



x

3.7 (a)The physical positions of sensors in an adjacent area.(b) The recovered

relative positions of sensors in the adjacent area based on classical MDS.

(c) These sensors’ physical positions after alignment. (d)When the error

of measured distances for pairwise adjacent sensors increases, the error

rates of estimated sensor positions increase. . . . . . . . . . . . . . . . . 47

3.8 (a)Error rates of sensor localization increase when the percentage of sen-

sor pairwise distances collected and the number of iteration increase.

(b)When the collected pairwise distance and the number of iteration are

fixed, the error rates of sensor localization increase with the increase of

distance measurement error. . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.9 Error rates when varying the percentage of collected pairwise distances . 49

3.10 Percentage of collected pairwise distances when increasing the number of

source nodes and broadcasts . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.1 Flooding from a starting anchor to the whole network. Red nodes are

anchor nodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.2 Position estimation in the adjacent area of a starting anchor sensor. . . 56

4.3 The propagation of position estimation . . . . . . . . . . . . . . . . . . . 57

4.4 Classical multidimensional scaling . . . . . . . . . . . . . . . . . . . . . 58

4.5 Iterative multidimensional scaling . . . . . . . . . . . . . . . . . . . . . . 59

4.6 Error rates when applying the robust localization method with anchor

sensors to all sensors in a square region with an uniform radio range and

different distance measurement errors . . . . . . . . . . . . . . . . . . . 60

xi

4.7 Errors when applying the robust localization method with anchor sensors

to all sensors in a square region with different signal attenuation factors

(radio ranges) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.1 The propagation of sensor localization along the route from sensor A to

sensor B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.2 Position estimation in the adjacent area of a sensor without position known. 70

5.3 Localization error rates within an isotropic square area. . . . . . . . . . 73

5.4 Localization error rates within an anisotropic square area. . . . . . . . . 74

5.5 Localization error rates within a T -shape area. . . . . . . . . . . . . . . 74

5.6 Errors when applying the distributed on demand localization method

to one sensor in two square regions with uniform and different signal

attenuation factors, respectively. . . . . . . . . . . . . . . . . . . . . . . 76

6.1 Large continuous objects and their boundaries; The boundary informa-

tion may either be collected by a fixed sink or be scouted/queried by

mobile users, such as a soldier . . . . . . . . . . . . . . . . . . . . . . . . 83

6.2 (a) Possible cases of boundary estimation by boundary sensors, among

which pair (S1, B) and (S1, C) are error prone. We try to eliminate the

two pairs by reducing the range of neighborhood to adc. (b) Selecting

boundary sensors: Only sensors are covered by the continuous object and

marked by the small ellipses are boundary sensors. . . . . . . . . . . . 87

xii

6.3 Distributed boundary estimation: E, F , G, and H are boundary sensors;

They form five boundary pairs with non-boundary sensors A, B, C, and

D, respectively; Five position marked with small circles are estimated as

the boundary locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.4 Curvilinear belt structure for object boundary and its partition: The

large continuous object is on the left side of the object boundary. Black

dots are sensors that detect the object, and those dark dots along the

entity boundary (A, B, C) are boundary sensors. Small circles are sensors

that do not detect the object. Most boundary sensors are connected

to the backbone (B, A, D, C). Boundary sensor A is the head of the

partition. A and C are two boundary sensors, and they are out of each

others radio range. An ellipse is formed with A and C as foci, and α is

its eccentricity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

6.5 Ellipse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

6.6 α values for a randomly and uniformly deployed sensor network tend to

be a constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.7 Curvilinear belt partition reconstruction and dr; Boundary moves to left

with speed V . When boundary is close enough to the margin of the

current partition, head A will select sensor B as a new head to construct

a new partition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

xiii

6.8 (a)When the number of sensors deployed in the 1000m-by-1000m field

increases from 1000 to 4000, the error rates of estimated boundary de-

crease. (b)When the number of sensors deployed in the 1000m-by-1000m

field increases from 1000 to 4000, the total number of boundary sensors

involved in boundary estimation increases. . . . . . . . . . . . . . . . . 107

6.9 (a)When hop distance of sensors increases from 30m to 70m, the error

rates of estimated boundary decrease. (b)When hop distance of sen-

sors increases from 30m to 70m, the number of selected boundary sen-

sors keeps constant with compactness distance applied. The number of

boundary sensors increase if they are selected based on hop distance. . . 110

6.10 (a)When the rectangle object’s right boundary moves from 300 to 600,

the error rates of estimated boundary are stable. (b)When the rectangle

object’s right boundary moves from 300 to 600, the numbers of boundary

sensors of estimated boundary are stable. . . . . . . . . . . . . . . . . . 112

6.11 (a)The error rates of the estimated boundary for a circle object are rel-

atively constant when its radius increase. (b)The number of boundary

sensors involved in a circle object boundary estimation are increasing

approximately linearly with the length of the boundary. . . . . . . . . . 112

6.12 (a)When a increases from 1 to 2, error rates of estimated boundary in-

crease. (b) When a increases from 1 to 2, the number of boundary sensors

involved in boundary estimation increases. . . . . . . . . . . . . . . . . . 113

6.13 Shortest path from sensors to the sink in the baseline case. . . . . . . . 115

xiv

6.14 (a)Total message costs during boundary travelling from 0 to 300 with

different speeds. (b)Total message costs during boundary travelling from

0 to 180 with different number of partitions of the curvilinear belt struc-

ture. (c)Total message costs during boundary travelling from 0 to 180

with different hop distances. (d)Total message costs during boundary

travelling from 0 to 180 with curvilinear belt structure in different width. 117

xv

Acknowledgments

No words in the world can be used to express my gratitude to my thesis advisor,

Dr. Hongyuan Zha. The work presented here could not possibly have been accomplished

without the help and encouragement of my advisor. He gave me the opportunity to jump

into an amazing research field with a rare chance to discover the truth of the world. He

gave me a great deal of freedom in my research, but I am never lacked for help when it

was needed. I am especially indebted for the financial support which he has provided to

me over the years.

Dr. Hongyuan Zha has guided and influenced me. He is an excellent researcher

and maintains the highest standards for himself and his students. He is also an awesome

advisor and grants me his careful teaching, large doses of guidance, patience, encourage-

ment. He has developed me the spirit of always pursuing for high quality research. He

taught me how to identify a problem that will substantially impact the current state-of-

the-art research, the society, the industry and the ecology. He also showed me that strong

theoretical foundation and cross-discipline knowledge are indispensable to perform solid

research. Under his edification, I finally found my career. I hope I can inherit and live

up to his high standards in my future career.

I also feel very grateful to other committee members, Dr. John J. Metzner, Dr.

Wang-Chien Lee and Dr. Peng Liu. I thank them for serving on my qualifying exam

and dissertation committees. Their suggestions have greatly improved my dissertation

work.

xvi

I would like to specially thank Dr. John J. Metzner, for his inspiration and

enlightening discussions on a wide variety of topics. His invaluable insight on my research

work has helped me make significant improvements on this dissertation work. He is very

attentive, responsive, always has the best interests of his students at heart. He is always

very kind to me.

Special thanks also due to Dr. Wang-Chien Lee. He gave me many important

suggestions some leading to a research topic in my dissertation. He also carefully polished

my papers and gave me very valuable comments. I appreciate Dr. Wang-Chien Lee for

his comprehensive and insightful knowledge on mobile data management research and

other related fields. I always enjoy the discussion with him and the classes he offered.

Dr. Peng Liu has been extremely generous with his time, patient and support

than I probably deserve. He thoughtfully asked questions which made me look at my

proposed research from different perspectives. My appreciation for his sharp mind in

research grows each time I interact with him. I feel very grateful and indebted to him.

I would like to thank lots of people for having contributed, in one way or another,

to the completion of this thesis.

Last but not least, I thank my parents, my brother, my sister and my wife for

their love and support, their unconditional encouragement and belief during these years.

1

Chapter 1

Introduction

1.1 Wireless Sensor Networks

With the advances in the miniaturization and integration of sensing and com-

munication technologies, large-scale wireless sensor networks with a large number of

low-cost and low-power sensors have been developed. In a wireless sensor network, hun-

dreds or even thousands of tiny, battery-powered sensor nodes are scattered throughout

a physical area. Each sensor in the sensor network collects data, for instance, sensing

vibration, temperature, radiation and other environmental factors. These sensors relay

the collected data to their neighboring sensors and then to a specified destination where

the data are processed. This sensory input is used to describe the surroundings in real

time. One typical application scenario is that hundreds or thousands of sensors are ran-

domly deployed within a battle field or urban area to detect intrusion or to monitor

the distribution of target objects and materials, such as animals, vehicles, wild fire, or

bio-chemical materials.

In the last decade, we have witnessed the bloom of the Internet, which provides

us with the ability to transfer diverse forms of information readily and thus revolution-

izes business, industry, science, education, and our lifestyles. Wireless sensor networks

represent a new way of computing. They have been envisioned as a proactive computing

world in which networked computing nodes automatically acquire real-time data about a

2

physical environment. They may, in the long run, be equally significant as the Internet by

providing measurements of our physical environment, leading to our understanding and

ultimately, to the utilization of this information for a wide range of applications. These

sensor networks will eventually help us to improve lives, promote a better understanding

of the world and make people more productive.

1.2 Applications of Sensor Networks

Wireless sensor networks have the unique features of easy deployment, self organi-

zation and fault tolerance. Emerging as a new information-gathering paradigm, wireless

sensor networks have been used in a broad range of applications relating to health care,

environmental control, energy, food safety, and manufacturing [6, 5, 28, 54].

During the past several years, there have been many to turn the vision of sensor

networks into a reality. Some prototypes of sensor nodes have been developed, including

Motes [39, 42] at Berkeley, uAMPS [35, 68] at MIT, and GNOMES [98] at Rice. The

elementary functions of sensor networks include localization, detection, tracking, and

targeting. Besides military applications, civilian applications have been developed based

on these elementary functions, which can be classed into habitat monitoring, environment

observation, health and other commercial applications. In addition, Sibley et al. have

recently developed mobile sensors, known as Robomote, which are equipped with wheels

and are able to move within a field [88]. Applications in sensor deployment and coverage

are studies based on mobile sensors [45, 46].

As one of the first efforts of utilize sensor networks for civil applications, Berkeley

and Intel Research Laboratory used a Mote sensor network to monitor storm petrels on

3

Great Duck Island, Maine [65] in the summer of 2002. Thirty-two sensor nodes were

deployed on a small island off the coast of Maine to collect useful live data onto the world

wide web. The system operated for over four months and provided data for two months

after researchers had left the island for the winter due to poor weather conditions. This

habitat monitoring application represents an important class of sensor network appli-

cations. Most importantly, sensor networks are able to collect data under hazardous

conditions which are not directly accessible to human beings. During the storm pe-

trel monitoring research, a set of system design requirements were raised, including the

hardware design of the nodes, the design of the sensor network, and the capabilities for

remote data access and management. Many efforts have been made to address these

system design requirements, which have led to the development of a set of prototype

sensor network systems. The sensor network used in the Berkeley and Intel research,

although still primitive, efficiently collected the interesting habitat data and provided

researchers studying storm petrel with valuable information.

Sensor networks have found their application in environment observation and

forecasting. A real-world example of such an application is the system of Automated

Local Evaluation in Real-Time (ALERT) developed by the National Weather Service

with wireless sensor networks [1]. Equipped with a meteorological/hydrological sensing

device, the sensors in this system usually measure several properties of the local weather,

such as water level, temperature, and wind. Data are transmitted via line-of-sight radio

communication from the sensors to the base station. A Flood Forecast Model has been

adopted to process these data and issue an automatic warning. Web-based query is

available, so that the system is able to provide important real-time rainfall and water level

4

information to evaluate the possibility of potential blooding anywhere in the country.

Currently ALERT is deployed across most of the western United States, and it is heavily

used for flood warnings in California and Arizona.

Sensor networks have recently been introduced to health care with applications

ranging from patients and doctors tracking and monitoring [5], glucose level monitors,

cancer detectors, even to artificial organ [87, 86, 12, 93]. Scientists have proposed that

biomedical sensors are implanted into human body for different purposes. These sensors

communicate with an external computer system through wireless interface. Multiple

biomedical sensors are networked into an application-specific solution to diagnose and

treat diseases. The biomedical sensors offer the promise of significantly advances in

medical care.

1.3 Location-aware Computing

The paradigm of context-aware computing [94, 75, 8] has become increasingly in-

teresting to researchers lately. Context-aware computing systems aim to autonomously

change their function based on their observation of the environment around them. By

determining the context or environment, the computing devices are able to adjust them-

selves to the current computing demands, customize their behavior according to their

location, or even actively react to their surroundings. The paradigm of context-aware

computing represents a significant step towards the vision of ubiquitous computing

[37, 95, 58].

Location-aware computing [38] is an important and practical subset of the context-

aware computing paradigm. Fundamental to the computing in these systems is location

5

awareness. By detecting and tracking the locations of objects, it is feasible to derive

other useful location related information, such as the objects’ orientation and mobility.

The behavior of location-aware computing systems depends heavily on these types of lo-

cation information. Since these location-aware computing systems are usually embedded

into the physical world, it is necessary to establish spatial relationships between these

computing devices and their physical environment. For example, many of these sensor

network systems are designed to monitor or control the behavior of the physical world

where they are deployed, which means that the sensor nodes of these systems often need

to determine their actions based on their physical locations or spatial relationship with

the particular objects. Therefore, the location information of the sensors and target

objects is indispensable for the management and operation of sensor networks.

1.4 Localization in Sensor Networks

The issue of localization has been raised and addressed in many research fields,

including the autonomous robot and vehicle navigation [43, 97] for mobile robotics [91],

virtual reality systems [96], and user location and tracking in cellular networks [89].

Determining the physical positions of sensors is a fundamental and crucial issue

for wireless ad-hoc sensor network operations for several reasons. Sensor networks are

often developed in the form of a layered network protocol stack. In the application layer,

sensor localization is necessary for location-aware applications that process data based

on location [32]. In order to use the data collected by sensors, it is often necessary to have

their position information stamped. For example, to detect and track objects with sensor

networks, the physical position of each sensor is needed for identifying the positions of

6

detected objects. In the network layer, many communication protocols of sensor networks

are built upon the knowledge of the geographic positions of sensors [15, 17, 101]. For

example, knowledge of location information and transmission range enables geographic

routing algorithms that propagate information through multi-hop sensor networks [78,

77, 57].

However, in most cases, sensors are deployed without their position information

being known in advance, so there is no supporting infrastructure available to locate them

after deployment. It is therefore necessary to find some approaches for identifying the

location of each sensor in wireless sensor networks after their deployment.

One of the most well known and widely used technologies for localization is the

Global Positioning System (GPS) [97]. Many applications have been developed based

on GPS. Although it is possible to find the position of each sensor in a wireless sensor

network with the aid of GPS installed in each sensor, it is not practical to use GPS for

sensor localization for three reasons.

Firstly, GPS is not always available because of the line of sight conditions. For

instance, it does not work indoors, under water, or in a subway. Secondly, since a typical

GPS receiver costs approximately one hundred dollars, it is too expensive to equip each

sensor with a GPS receiver, considering that these sensors are usually designed to be low

cost and disposable. Finally, the GPS receivers are highly power-consuming while the

sensors are designed to require low-power and therefore to ensure their greater longevity.

Based on the previous discussion, alternative sensor localization systems are re-

quired. Considering the application scenarios of sensor networks, designing localization

systems for sensor networks is more challenging than designing localization systems for

7

applications in many other domains. Sensors are designed to be small and to require low

computation power and a limited power supply. They are usually randomly and densely

deployed within a large region. After being deployed, these sensors self-organize into a

distributed ad-hoc sensor network. The ideal sensor localization system is also required

to have a low computation and a low power cost. The localization system should be

able to tolerate ad-hoc deployment without infrastructure support for localization, and

should be able to perform self-localization. The localization system is expected to scale to

include a large number of sensor nodes, and must accommodate a dynamic environment

and system.

1.5 Dissertation Overview

The rest of this dissertation is divided into six chapters.

In Chapter 2, we present the necessary background information and related re-

search for sensor localization in distributed ad-hoc sensor networks. The challenges for

effective and robust sensor localization are also discussed.

In Chapter 3, we present a centralized sensor location method based on multidi-

mensional scaling technique. It utilizes pairwise sensor distances to recover locations of

sensors in two (or three) dimensions. If pairwise distances between all sensors are known,

a simple eigen-decomposition will generate the sensors’ locations. In this chapter, we

focus on the case of only a portion of pairwise sensor distances known and an iterative

calculation of the optimal sensors’ locations. The method yields competitive location

results.

8

In Chapter 4, the centralized sensor localization method is extended to a dis-

tributed sensor localization algorithm and a robust sensor localization algorithm. They

are developed based on multidimensional scaling technique to deal with diverse challeng-

ing conditions. In the distributed sensor localization algorithm, multidimensional scaling

and coordinate alignment techniques are applied to recover positions of adjacent sensors.

The estimated positions of the anchors are compared with their true physical positions

and corrected to achieve robust sensor localization. This method is demonstrated to be

able to achieve robust sensor localization under diverse challenging conditions such as

complex terrain.

In Chapter 5, we propose the concept of differentiated sensor localization in dis-

tributed ad-hoc sensor networks. The application demands for differentiated sensor

localization are identified. Then, three differentiated sensor localization methods based

on multidimensional scaling techniques are proposed to get accurate position estimation

and to reduce computation and communication costs. They are able to locate only one

or a specific set of sensors based on demand.

In Chapter 6, the application of locating large continuous objects and tracking

their movement is proposed and investigated. Large continuous objects are different from

collections of discrete targets such as a group of vehicles in that they are continuously

distributed across a region and occupy a large area. Locating their spatial extents

and related boundary information represents a class of very challenging tasks in sensor

network research. We first propose a distributed algorithm for locating the boundary

information of large continuous objects covered by a sensor network. Further, a dynamic

curvilinear belt structure is proposed to track the movement of boundaries in real-time

9

manner and to facilitate the fusion and dissemination of boundary information in a sensor

network.

In Chapter 7, we first summarize the contributions of this dissertation on lo-

calization algorithms for wireless sensor network systems. Then, we examine potential

extension based on the proposed approaches. Finally, we discuss some directions for

future work.

10

Chapter 2

Background and Related Research

2.1 Wireless Sensor Network Model

Advances in the miniaturization and integration of sensing and communication

technologies have facilitated the development of large-scale wireless sensor networks with

hundreds or even thousands of tiny, battery-powered sensors. Figure 2.1 shows the tiny

sensors [39, 42, 41].

In a sensor network, hundreds or even thousands of such kind of sensors are

scattered throughout a physical area. Each sensor in the sensor network collects data,

for instance, sensing vibration, temperature, humidity and other environmental factors.

The sensor relays the collected data to its neighboring sensors and then to a specified

destination where they are processed. For example, the Figure 2.2 illustrates that sensors

are deployed in the mountain area to monitor the environment.

Another typical application scenario is that of a large number of sensors deployed

within some battle fields or urban areas to monitor the intrusion or distribution of

target objects and materials, such as enemy vehicles, wild fire, or bio-chemical spill

materials. In Figure 2.3, soldiers scout the enemy tanks’ information with the assistance

of a distributed sensor network [101].

In the general model of wireless ad-hoc sensor networks, a large number of sensors

are deployed within a given area without pre-assigning their locations. Each sensor

11

Fig. 2.1. Example of tiny wireless sensor node [41].

usually combines the functionality of sensing, radioing and processing, and it typically

has a limited power supply and low mobility. Communications between the sensors

are through omni-directional radioing. Since each sensor has limited signal strength,

only neighboring sensors within a specific hop distance are able to directly communicate

with each other. Non-neighboring sensors communicate through hop-by-hop relay. In

general, the costs for computation locally are much lower than those for communication

among sensors. In order to prolong the life of a wireless sensor network, it is desirable to

minimize the communication costs in designing sensor network protocols and algorithms.

The distance between a pair of sensors can be estimated based on radio signal

strength measurement (RSSI), time of arrival for ultrasound (TOA), time difference of

arrival (TDOA), and angle of arrival (AoA) with smart antenna. Based on the measured

distances, sensors have their locations estimated with some localization algorithms, such

12

as trilateration, multilateration, or other location bound information [14, 17, 33, 71, 83,

80].

In a sensor network, there are usually one or a few sensors that have a strong radio

signal and can communicate with a distant base station. These are named as sinks and

play the role of gateway for information exchange between the sensor networks and the

outside world. Collected information by the sensor network may either be aggregated

by several sinks and relayed to external servers or the Internet, or be queried by some

mobile users in the network. In the following parts of the dissertation, we use sink to

represent both fixed sinks and mobile users. In the general model of wireless ad-hoc

Fig. 2.2. Sensors deployed in the mountain area form an ad-hoc sensor network andmonitor the environment.

sensor network, there are usually some landmarks or nodes named anchor nodes, whose

13

position information is known, within the area to facilitate locating all sensors in a sensor

network.

Fig. 2.3. Soldiers with receivers scout the enemy tanks’ information with the assistanceof a distributed sensor network [101].

2.2 Elements of Localization

Most localization methods first estimate distances or angles between unknown

sensors and anchor sensors, then the location of unknown sensors are calculated with

some geometry algorithms. Thus, the most important elements for sensor localization are

distance measurement, angle measurement, and geometry constraints. In the following

section, we discuss available techniques for each of them.

14

2.2.1 Received Signal Strength Indication

During radio propagation, an important characteristic is that the radio signal

attenuates as the distance between the transmitter and receiver increases. The power of

the received radio signal falls off exponentially with distance increasing, and the receiver

can measure this attenuation based on Received Signal Strength Indication (RSSI) in

order to estimate the distance to the sender. RSSI measures the power of the signal at

the receiver. Based on the transmit power, the propagation loss is calculated and the

loss can be translated into distance estimate. This method has been used mainly for

radio frequency (RF) signals.

In [76], radio propagation models are well researched, and they are used to pre-

dict the average RSSI at a given distance away from the transmitter. An ideal radio

propagation model,

Pr(d) =PλGtGrλ

2

4π2dnL, (2.1)

predicts the received signal power as a function of the distance between the transmitter

and the receiver. In the ideal model, Pλ is the transmitted power, Gt is the antenna

gains of the transmitter, Gr is the receiver, L is the system loss, and λ is the system

wavelength. Usually Gt, Gr, and L can be set as 1 [13, 15, 16, 14].

In [83], the distance estimation with received RF signal strength using the WINS

sensor nodes [3] is studied. In the experiments, different configuration strategies, includ-

ing different power levels in transmitters and deployment strategies of sensors, are used to

estimate the relation between received signal strength and distance between transmitter

15

and receiver. The power of the received radio signal strength attenuates exponentially

with the increase in distance as seen in Figure 2.4.

Fig. 2.4. The power of the received radio signal strength attenuates exponentially withthe increase of distance between the transmitter and receiver.

2.2.2 Time of Arrival

The distance between the transmitter and the receiver may be estimated based

on the speed of the wave propagation and the measured time for a radio signal to travel

between two sensor nodes. The method may be applied to many different signals, such

as RF, acoustic, infrared and ultrasound. The implementation of the technique depends

on the measurement of time of arrival (ToA). The ToA may be measured with some

advanced timing techniques.

16

The Global Positioning System (GPS) uses the technique for distance estimation

[97]. In GPS, each satellite (transmitter) transmits a unique code. On the receiver side, a

copy of the code is created. The receiver gradually shifts its internal clock to correspond

to the received code, which is called lock-on. Once a receiver has locked-on to a satellite,

the receiver determines the exact time of receiving radio signal from the satellite. Based

on the time, the ToA can be determined by subtracting the known transmission time

from the calculated receive time.

ToA offers a high level of accuracy, but also requires relatively fast processing

capabilities in sensor nodes to resolve many timing differences for fine-grained measure-

ments.

2.2.3 Time Difference of Arrival

The distance from transmitter to receiver may be measured by the time difference

of arrival (TDoA) of different communication media at different speeds. For example,

the measurement for time of arrival (ToA) is made based on two different modalities

of communication, ultrasound and radio, in sensor nodes. The propagation speeds for

ultrasound and radio are considerably different. Then, the radio signal is used for syn-

chronization between the transmitter and the receiver and the ultrasound signal is used

to estimate the distance between them. The TDoA technique is used in projects of

Active Bat [92], AHLoS [83], Cricket [74], and Cricket Compass [75].

17

2.2.4 Angle of Arrival

Angle of Arrival (AoA) means the angle at which signals are received by the

receiver from the transmitter. An Angle of Arrival system is able to estimate the angle

at which signals are received and to use simple geometric relationships to estimate the

relative locations of transmitter and receiver. Angles of Arrival may also be combined

with distance estimates to derive relative locations.

The implementation of the AoA system relies on smart antenna with antenna

arrays to measure the angle at which the signal arrives. A smart antenna is an array of

antenna elements connected to a digital signal processor. Such a configuration will not

only enable AoA estimation, but also will dramatically enhance the capacity of wireless

links through the combination of diversity gain, array gain, and interference suppression.

There are two major disadvantages of the AoA techniques which make it inappli-

cable to sensor networks, however. First, the cost of the complex antenna array is high.

Second, the AoA techniques will not scale well for systems with a large number of such

nodes.

2.2.5 Triangulation

Triangulation is a geometric technique that uses the angles of arrival to determine

the location of sensors. With the angle of each anchor sensor, with respect to the

unknown sensor node in some reference frame, the unknown sensor node’s locations

are calculated with the trigonometry laws of sines and cosines. The computation of

triangulation is illustrated by Figure 2.5 [80].

18

Fig. 2.5. Triangulation.

2.2.6 Trilateration

Trilateration is a geometric technique that uses distances between three anchor

sensors and one unknown sensor to determine the unknown sensor’s location. An un-

known sensor is uniquely located when at least three reference points are associated with

it in a two-dimensional space. The location of the unknown sensor is estimated by calcu-

lating the intersection of three circles. Figure 2.6 illustrates the computation geometry

constraint [83].

2.2.7 Multilateration

An unknown sensor’s location may also be estimated with multilateration with its

distances to more than three anchor sensors. In [9], Beutel studied the multilateration

with the least square algorithm.

19

Fig. 2.6. Trilateration.

For n anchor sensors in three dimensional space and their distances to the un-

known sensor, we have

d21

d22

.

.

.

d2n

=

(x1 − ux)2 + (y1 − uy)2

(x2 − ux)2 + (y2 − uy)2

.

.

.

(xn − ux)2 + (yn − uy)2

, (2.2)

where di is the distance between the ith anchor sensor and the unknown sensor, (xi, yi, zi)

is the location of ith anchor sensor in three-dimensional space, and (ux, uy, uz) is the

location of unknown sensor in three-dimensional space.

20

The equation can be converted into the following relations through linear opera-

tions:

Au = b, (2.3)

A = −2 ∗

(x1 − xn) (y1 − yn)

(x2 − xn) (y2 − yn)

. .

. .

. .

(xn−1 − xn) (yn−1 − yn),

(2.4)

u =

ux

uy

, (2.5)

b =

d21− d2

n− x2

1+ x2

n− y2

1+ y2

n

d22− d2

n− x2

2+ x2

n− y2

2+ y2

n

.

.

.

d2n−1

− d2n− x2

n−1+ x2

n− y2

n−1+ y2

n

. (2.6)

21

The u can be derived with [29, 34]

u = (A′A)−1 × A′b. (2.7)

Figure 2.7 illustrates the computation geometry constraint [83].

Fig. 2.7. Multilateration.

2.3 Related Research

In the robotics research community, many methods have been discovered for

robotic localization. Howard et al. used maximum likelihood to estimate a mobile

22

robot’s location [44]. Roumeliotis et al. proposed a distributed Kalman filter for co-

operative localization [79]. Fox et al. proposed probabilistic collaborative localization

[27].

There have been many efforts to deal with the sensor localization problem. They

mainly fall into one of the following four classes or a combinations of them. The first

class of methods improved the accuracy of distance estimation by using different signal

techniques. The Received Signal Strength Indicator (RSSI) technique was employed to

measure the power of the signal at the receiver. Relatively low accuracy is achieved in this

way. However, because of its simplicity, RSSI has been widely used in previous research.

Later, Time of Arrival (ToA) and Time Difference of Arrival (TDoA) were used by

Savvides et al. [83, 19] and Priyantha et al. [74] to reduce the errors of range estimation,

but these methods require equipping each sensor node with a powerful computation

capability. Recently, Niculescu et al. used Angle of Arrival (AoA) to measure the

positions of sensors [71]. The AoA sensing requires each sensor node to be installed

with an antenna array or ultrasound receivers.

The second class of sensor localization methods relies on a large number of sensor

nodes with positions known densely distributed in a sensor network [15, 16, 14]. These

nodes with positions known, which are also named as beacons or anchor nodes, are

arranged in a grid across the network to estimate other nodes’ positions nearby them.

The third class of localization methods employs distance vector exchange to find

the distances from the non-anchor nodes to the anchor nodes. Based on these dis-

tances, each node can estimate its position by performing a trilateration or multilater-

ation [70, 83]. The performance of the algorithms is deteriorated by range estimation

23

errors and inaccurate distance measures, which are caused by complex terrain and the

anisotropic topology of the sensor network. Savarese [80] tried to improve the above

approach by iteratively computing. However, this method adds a large deal to the com-

munication cost of the algorithm and still cannot generate a good position estimation

in some circumstances. Moreover, the accuracy of this class of algorithms relies on the

average radio range estimation, and it tends to deteriorate when the topology of a sensor

network is anisotropic. For example, in Figure 2.8, sensors are deployed in a square area.

��

��

��

��

��

��

��

��

A

Building

B

C

C’

Fig. 2.8. A sensor network deployed in a square area with obstacles

But there are some buildings that are marked by shadowed rectangle areas, and sensors

cannot access them. Thus, the routes between a pair of sensors are severely detoured

severely by the buildings in the square area, and the estimated distances of AC and BC

are increased significantly. There is a similar situation happens to the case in Figure

2.9, when sensors are deployed in a T -shape area, instead of in a square area which is

24

C’

C

BA

Fig. 2.9. A sensor network in non-square area

assumed and used as the fundamental condition by most existing research works. A and

B are two anchors, A may estimate radio range with the distance of AB and hop count

in the route from A to B. If A and B estimate their distances to C with the estimated

radio range, the estimated distances will be increased a lot by error. Another example

is that the ideal radio range of a sensor is a circle centered in the sensor. However, a

sensor usually has an irregular radio pattern, which is represented with the black curve

in Figure 2.10, in real world. This meas that the radio range of a sensor is different

at different directions. In Figure 2.11, sensors are deployed on a square area with deep

grass or bushes on the left-hand part and clear ground on the right. The complexity of

the terrain leads to different signal attenuation factors and radio ranges in the field.

The last class of methods [17, 70, 81] locally calculates maps of adjacent nodes

with trilateration or multilateration and pieces them together to estimate the nodes’

25

sensor

maximum radio range

Fig. 2.10. Irregular radio pattern of a sensor

��

��

r12r

A

Clear ground

B

C

Grass

D

Fig. 2.11. Anisotropic terrain condition leading to different radio ranges

26

physical or relative positions. The performance of these algorithms relies heavily on the

average radio range estimation and suffers from the cumulative range error during the

map stitching.

Recently, there has been some research on the error characteristics of sensor lo-

calization [82, 72] and computation complexity [7]. Chintalapudi analyzed factors that

impact the performance of the system and then proposed ad-hoc localization systems

with ranging and either bearing or imprecise bearing information [21]. Eren applied

graph rigidity theory to locate sensors [25]. Range constraints [24] and area constraints

[33] are used to locate sensors in coarse granularity as well.

2.4 Challenges of Localization

Considering the real sensor network application scenario, there are several chal-

lenges in designing effective and robust sensor localization algorithms.

Firstly, since a large number of sensors are generally used when they are randomly

deployed across an given area, we hope to achieve good position estimation as well as

keep the hardware design of sensors simple and inexpensive.

Secondly, in many circumstances it is impossible to get a large number of anchor

nodes deployed uniformly across the area to assist the location estimation of non-anchor

nodes. Thus, it is desirable to design a sensor localization method that is able to generate

accurate localization estimation with as few anchors as possible.

Thirdly, sensors may be deployed in battle fields or in urban areas with complex

terrain and vegetation (Figure 2.8, Figure 2.9). The sensor network may have a high

level of anisotropicity (Figure 2.11). However, most existing research studies that have

27

explored sensor localization algorithms are based on isotropic network topology in a

square area. Neither their algorithms nor their experimental environment dealt with a

sensor network that has had an anisotropic topology as seen in Figure 2.8, Figure 2.9,

Figure 2.10, and Figure 2.11.

Fourthly, most of previous methods estimate an average hop distance and broad-

cast it to whole network. In many cases, sensors may be deployed on an area with

anisotropic vegetation and terrain conditions (Figure 2.11). Thus, sensors at different

locations in the area may have different radio ranges, and using a uniform radio range

calculation will lead to serious errors during sensor localization (in [70, 83, 80]) and such

errors may propagate throughout the sensors in the network [17, 81].

Finally, as we have mentioned, most existing sensor localization research tries

to provide accurate location estimation for a network of sensors. Wireless sensor net-

works have limited energy availability, while sensor localization usually involves energy-

consuming computation and communication. Therefore, it is always desirable to reduce

the energy costs for sensor localization. Among many approaches that have been used

to reduce energy caused by sensor localization, one of the most effective method is to

eliminate sensor localization or to reduce the times of localization. So, it is necessary to

develop localization methods that are able to locate sensors only on demand for energy-

efficiency concerns. We also noticed that many applications and operations in sensor

networks only require the location information of some sensors. This situation enables

on demand sensor localization. Some sensor networks are mobile or deployed in a dy-

namic environment, for example, sensor networks deployed in a river or sea to monitor

fish activities or water pollution. They tend to slowly and constantly drift with water

28

current. Estimated locations of sensors are invalidated quickly. In this case, it is difficult

to locate all sensors in the sensor network. Instead, it is preferable to locate the “right”

sensors at the “right” time.

29

Chapter 3

Sensor Localization with Multidimensional Scaling

Most existing localization algorithms make use of trilateration or multilateration

based on range measurements obtained from TOA, TDOA and RSSI. We explore the

idea of using dimensionality reduction techniques to estimate sensors coordinates in two

(or three) dimensional space. In this chapter, we present a centralized sensor localization

algorithm based on a dimensionality reduction technique - Multidimensional Scaling. It

utilizes pairwise sensor distances to recover locations of sensors in two (or three) dimen-

sions. If pairwise distances between all sensors are known, a simple eigen-decomposition

will generate sensors’ locations. In this chapter, we focus on the case of only a por-

tion of pairwise sensor distances known and iterative calculation of the optimal sensors’

locations. The method yields competitive location results and has the feature of pro-

viding location estimations with various accuracies according to users’ requirement or

power-budget.

3.1 Problem Definition

In order to estimate all sensors’ location in a distributed wireless ad-hoc sensor

network, a small percentage of sensors have their location information known either

30

through manual configuration or equipped with GPS. These sensors with location infor-

mation known are referred as anchor sensors and other sensors without location informa-

tion are defined as unknown sensors. We hope to estimate all sensors’ locations with the

assistance of anchor sensors. In general, the anchor sensors broadcast their locations to

their neighbors. Neighboring unknown sensors measure their spatial relation from their

neighbors and use the broadcasted anchor sensor locations to estimate their own posi-

tions. For an unknown sensor, once an unknown node estimates its position, it becomes

an anchor sensor and is able to assist other unknown sensors to estimate their locations.

3.2 Overview of The Centralized Sensor Localization

In addition to improving the accuracy of location estimation and reducing algo-

rithm costs as previous research, a requirement-aware and power-aware sensor location

algorithm based on multidimensional scaling technique is proposed, which provides loca-

tion estimation with various accuracies based on power budget and application require-

ment.

Firstly, a portion of pairwise distances of sensors are collected through flooding in

a sensor network. Then, an iterative multivariate optimization algorithm is performed

based on these pairwise distances to generate relative locations for nodes. The accuracy

of the locations depends on the number of pairwise distances collected. If more pairwise

distances are collected, higher accuracy is achieved when calculating nodes’ relative lo-

cation while less pairwise distances lead to more errors in sensor location. We can collect

more pairwise distance by initializing more flooding operation in sensor networks, which

31

will consume more power of sensors in the network. So there is tradeoff between the ac-

curacy of the location estimation and the power consumption of the sensor network. The

users may determine the accuracy based on their requirements and the current power

budget of the sensor network. At last, three anchor nodes within the network are used

to convert the relative positions computed above into physical positions. The location

algorithm requires centralized computation, which means some sensors collecting and

transmitting pairwise distance information to a computer or sensor. The paradigm is

supported by sensor system design [40] or fly-over base-station, and has been used by

Doherty et al. [24] in their sensor position algorithm. In the work, we focus on the

location estimation aspect instead of communication protocol details.

The advantages of our approach are: various accuracies of sensor locations can be

achieved based on different power budget and accuracy requirement for a wireless sensor

networks by launching different number of broadcasting through the network. For each

node whose location is unknown, instead of utilizing its distances to limited number of

anchor nodes or neighboring nodes in previous research, we use its distances to many

other nodes to optimally locate it and reduce errors in distance measurement.

Second, instead of finding the location of nodes one by one with tendency of error

cumulation, we calculate the locations of nodes simultaneously and globally with high

tolerance of range estimation error and inaccurate distance measures.

At last, three anchor nodes that are not in a line are enough for our algorithm to

identify absolute positions of all nodes. In this dissertation, we illustrate the algorithm

with planar networks and it can be easily adapted into 3-D cases.

32

The main steps in our method are collecting pairwise distances and estimating

sensor locations with multidimensional scaling technique.

3.3 Multidimensional Scaling

The multidimensional scaling (MDS) refers to a set of methods that is widely used

in behavioral, econometric, and social sciences to analyze subjective evaluations [11, 30,

84]. We use it as a data-analytic approach to discover the dimensions that underlie the

judgements of distance and model data in a geometric space. The main advantages in

using the MDS for position estimation is that once calculation with MDS generates all

involved sensors location information, and it always generates relatively high accurate

position estimation even based on limited and error-prone distance information. There

are several varieties of MDS. We focus on classical MDS and the iterative optimization

of MDS, the basic idea of which is to assume that the dissimilarity of data are distances

and then deduce their coordinates.

3.3.1 Classical Multidimensional Scaling

If all pairwise distances of sensors in an ad-hoc sensor network are collected,

we can use the classical multidimensional scaling method to estimate the positions of

sensors.

T = [tij ]n×2 denotes the true locations of the set of n sensor nodes in 2-dimensional

space. dij(T ) stands for the distance between sensor i and j based on their position in

T and

dij(T ) = (2

∑

a=1

(tia − tja)2)1/2. (3.1)

33

If we define

H = TT ′,

then

dij(T )2 =∑

t2ik

+∑

t2ik

− 2∑

tiktjk

= Hii + Hjj − 2Hij . (3.2)

Without loss of generality, we center the data at the coordinate matrix T . Then,

n∑

i=1

Hij = 0.

By sum equation 3.2 over i, over j, and over both i and j, we get:

1

n

n∑

i=1

d2ij

=1

n

n∑

i=1

Hii + Hjj , (3.3)

1

n

n∑

i=1

d2ij

=1

n

n∑

j=1

Hjj + Hii, (3.4)

1

n2

n∑

i=1

n∑

j=1

d2ij

=2

n

n∑

i=1

Hii. (3.5)

Now from equation 3.2, we get

Hij =1

2[Hii + Hjj − d2

ij]

=1

2[1

n

∑

j

d2ij

+1

n

∑

i

d2ij

− d2ij

−1

n2

∑

i

∑

j

d2ij

] (3.6)

34

That means the H can be calculated with dij . Since H = TT ′, H is needed to

be factorized. With eigen-decomposition,

H = UV U ′, (3.7)

where U = [u1, u2, ..., un] and V = diag(v1, v2, ..., vn]). In order to get equation 3.7, A

is re-scaled as

X = UV1

2 = [u1v1

2

1 , u2v1

2

2 , ..., unv1

2n

], (3.8)

and

H = XX ′.

The X is different from T in that X is n × n and T is n × 2. Just take the first two

coordinates in X as T .

Based on the above, the classical multidimensional scaling method is summarized

as:

1. Compute the matrix of squared distance D2, where D = [dij ]n×n;

2. Compute the matrix J with J = I − e ∗ eT /n, where e = (1, 1, . . . , 1);

3. Apply double centering to this matrix with H = −12JD2J ;

4. Compute the eigen-decomposition H = UV UT ;

5. Suppose we want to get the i dimensions of the solution (i = 2 in 2-D case), we

denote the matrix of largest i eigenvalues by Vi and Ui the first i columns of U .

The coordinate matrix of classical scaling is X = UiV1

2

i .

35

The computation complexity of classical MDS is an O(N3) [11].

3.3.2 Iterative Multidimensional Scaling

If only a portion of pairwise distances for sensors in an ad-hoc sensor network

are collected, we can use the iterative multidimensional scaling method to estimate the

positions of sensors.

T = [tij ]n×2 denote the true locations of the set of n sensor nodes in 2-dimensional

space. If not all pairwise distances of sensors in T are collected, we use the iterative

multidimensional scaling algorithm to estimate sensors’ location. dij(T ) stands for the

distance between sensor i and j based on their position in T and

dij(T ) = (

2∑

a=1

(tia − tja)2)1/2. (3.9)

The collected distance between node i and j is δij . If we ignore the errors in

distance measurement, δij is equal to dij(T ). We will discuss the error effects to location

estimation caused by differences between δij and dij(T ) later. If only a portion of

pairwise distances are collected, some δij are undefined for some i, j. In order to assist

computation, we define weights wij with value 1 if δij is known and 0 if δij is unknown

and assume

δij = dij(T )

in the following induction. X = [xij ]n×2 denotes the estimated locations of the set of

n sensor nodes in 2-dimensional space. X is randomly initialized as X [0] and will be

updated into X [1], X [2], X [3] . . . to approximate T with our iterative algorithm. dij(X)

36

means the calculated distance between sensor i and j based on their estimated positions

in X and

dij(X) = (m∑

a=1

(xia − xja)2)1/2. (3.10)

We hope to find the a position matrix X to approximate T by minimizing

σ(X) =∑

i<j

wij(dij(X) − δij)2. (3.11)

This is a quadratic function without constraints. The minimum value of such functions

is reached when its gradient is equal to 0. For our problem, we have the following

observations:

σ(X) =∑

i<j

wijδ2ij

+∑

i<j

wijd2ij

(X) − 2∑

i<j

wijδijdij(X), (3.12)

∑

i<j

wijd2ij

(X) =∑

i<j

tr(X ′(wijAij)X) = tr(X ′(∑

i<j

wijAij)X) = tr(X ′V X) (3.13)

where where Aij is a matrix with aii = ajj = 1, aij = aji = −1, and all other elements

zeros, V =∑

i<j wijAij , tr the trace function and

−∑

wijδijdij(X) =

−∑

wijδij(∑m

a=1(xia − xja)2)1/2(

∑ma=1

(tia − tja)2)1/2

dij(T )

37

≤ −∑

wijδij(∑m

a=1(xia − xja)(tia − tja))

dij(T )

= −∑

wijδijtr(X ′AijT )

dij(T )= tr(X ′(

wijδij

dij(T )Aij)T )

where the equality achieved when X = T . Thus, we get

σ(X) =∑

i<j

wijδ2ij

+ tr(X ′V X) − 2tr(X ′(wijδij

dij(X)Aij)X)

≤∑

i<j

wijδ2ij

+ tr(X ′V X) − 2tr(X ′(wijδij

dij(T )Aij)T ),

and the equality is achieved when X = T . This means that the derivative of the right

side of the inequation is zero when the equality is achieved. Based on the above idea,

we easily induce the update formular of the SMACOF algorithm

V X = (wijδij

dij(T )Aij)T, (3.14)

or

X = V −1(wijδij

dij(T )Aij)T. (3.15)

If V −1 does not exist, we should replace it with Moore-Penrose inverse of V given by

V − = (V + 11′

)−1 − n−211′

. (3.16)

38

In summary, the distances between some pairs of sensors in the local area are not

available. When this happens, the iterative MDS is employed to compute the relative

coordinates of adjacent sensors. We summarize the iteration steps as:

1. Initialize X [0] as random start configuration, set T = X [0] and k = 0, and compute

σ(X [0]);

2. Increase the k by one;

3. Compute X [k] with the above update formula and σ(X [k]);

4. If σ(X [k−1])−σ(X [k]) < ǫ, which is a small positive constant, then stop; Otherwise

set T = X [k] and go to step 2.

The ǫ is an empirical threshold based on accuracy requirement. We usually set it as

5% of the average radio range. This algorithm generates the relative positions of sensor

nodes in X [k]. The computation complexity of iterative MDS is an O(N2) [11, 69].

The above methods can estimate the relative locations of sensor nodes based

on their pairwise distances. We also need position alignment techniques to map the

relative coordinates to physical coordinates based on three or more anchor sensors. The

alignment techniques will be discussed in the next chapter.

3.4 Ranging Estimation

We employ the widely used distance measurement model of Received Signal

Strength Indication (RSSI). A circle centered in a sensor node bounds the maximal

range for direct communication, which is called the hop distance, of the sensor’s radio

39

C

B

A

D

r r

rh h

ad

Fig. 3.1. Hop distance and signal strength

signal. Nodes within one hop distance can directly communicate with each other, while

nodes that are in more than one hop away relay messages hop by hop. The power of

the radio signal attenuates exponentially with distance, and this property enables the

receiver to estimate the distance to the sender by measuring the attenuation in radio

signal strength between sender and receiver. For example, there are four sensor nodes

A, B, C, and D in Figure 3.1. Hop distance is rh. rad is the distance between A and D

and it can be induced with A’s signal strength at location of D.

3.5 Pairwise Distance Collection

Usually, a network of sensors are randomly, densely distributed. They are suf-

ficiently connected and previous research indicates the average connection degree of a

node is between 5 and 15 in a general sensor network model.

The essential operation in pairwise distance collection is flooding by several se-

lected sensor nodes. We describe the procedure as below. An anchor node is selected

as source sensor to initialize a broadcast containing its ID, location, and hop count

40

rA

B

C

DEFG

S

Fig. 3.2. Routes of a flooding initialized by node S

equal to 0. Each of its one-hop neighbors hears the broadcast, appends its ID to the

message, increases the hop count by one, and then rebroadcasts it. Every other node

that hears broadcast but did not hear the previous broadcasts with lower hop count will

append its ID, increase the hop count by one, and then rebroadcast. The process con-

tinues until all nodes in the sensor network get the message broadcasted by the original

source node. Each node that is far away from the source node usually keeps a route

from source node to it. An example broadcast is illustrated in Figure 3.2 , where node S

initializes a broadcast and the average hop distance is r. Each route found is indicated

with connected arrow lines. Nodes A, B, C, D, E, F, G each keep the corresponding route

information from node S to them, respectively. The distance of any pair of nodes on one

of the routes can be calculated by multiplying the average hop distance (calculated by

following operation) by the number of hop count between them on the route. Usually, a

41

source node’s broadcast only collects the pairwise distances of nodes for which the route

information is available. When there is another anchor node hears the broadcast, it uses

the information in the received message to induce the average hop distance. The anchor

node is then selected as a new source node and it initializes another broadcast later to

collect more pairwise distances as well as publish the average hop distance. Similarly,

we can select some other nodes as source nodes to broadcast.

For n sensors in a sensor network, there are n(n − 1)/2 pairwise distances in

total. Our experimental results indicate that a source node broadcasts to all other nodes

usually collects 3% − 8% of all pairwise distances depending on the relative location of

the source node in the network, connection degree of nodes and hop distance. As we have

mentioned, the following iterative location algorithm will generate location estimation

with various accuracies depending on the percentage of the pairwise distances collected

to all pairwise distances. Usually, we need more than 10% pairwise distances collected for

an accurate location estimation. Thus, a certain amount of source nodes (anchor nodes

or general nodes without location know) should be selected and initialize broadcasts.

However, the total number of pairwise distances collected does not increase linearly with

the number of source nodes selected, since there are a lot of overlaps among the sets

of broadcast routes, which determine the pairwise distance obtained, by every source

nodes’ broadcast.

In order to reduce the total number of messages (or power consumption) sent or

received by all nodes during source nodes’ broadcasts in the sensor network, we hope

to initialize as few source sensors to broadcast as possible and collect as many pairwise

distances as possible. This requires that broadcast from each source sensor can collect

42

relatively more pairwise distances and the overlap among sets of pairwise distances col-

lected by every source node’s broadcast should be small. Figure 3.3 illustrate a typical

network of sensors (dots) and broadcast routes (lines) from a source node (the trian-

gle in the left-up corner). There are 400 sensor nodes, average hop distance 1.2, and

3.1% sensor pairwise distances collected in the network. We take a heuristic analysis

of source nodes selection with approximating the topology of a network of sensors with

grids. An approximated topology of a sensor network with 37 sensor nodes is plotted in

Figure 3.4. Node S initializes the broadcast and the circle centered with S represents

the range of signal. Some routes marked by arrow lines are selected to connect 16 nodes,

while other routes are omitted. These selected routes contain relatively more nodes than

other routes. Based on the route information in nodes A, B, C, D, E, F, G, we induce 34

pairwise distance. With the grid model, we have the observations:

1. A broadcast initialized by a source node located at the outer part of the network

usually collects a larger number of pairwise distances than that of a source node

located at the inner part of the network;

2. Broadcasts initialized by source nodes geodesic far away from each other tend to

generate pairwise distance sets with less overlap.

We illustrate the above principle with Figure 3.5 and Figure 3.6. Both of them

illustrate broadcast routes from different source nodes on the same sensor network as

that in Figure 3.2. The source node in Figure 3.2 and 3.6 is more far away from the center

of the network than that in Figure 5. There are 24 pairwise distances collected in Figure

5 and 34 in Figure 4 and 6, respectively. If Figure 4 indicates the first broadcast and

43

0

1

2

3

4

5

6

7

8

9

100 1 2 3 4 5 6 7 8 9 10

Fig. 3.3. Flooding routes from a source node of a sensor network

rA

B

C

DEFG

S

Fig. 3.4. A broadcast initialized by node S collects 34 pairwise distances

44

A

B

C

DEFG

S

r


B

A

C

GD

F E

rS


45

Figure 5 indicates the second broadcast, then the second broadcast in Figure 5 collect

extra 24 pairwise distances, while the broadcast in Figure 6 only collect extra 6 pairwise

distances. Thus, during pairwise distance collection, we should select new source node

which is far way from most of previous source nodes and the center of the network.

3.6 Performance Study

We measure the performance of the algorithm with mean error, which is widely

used in previous research works:

error =

∑ni=m+1

‖xiest

− xireal

‖2

(n − m) × (radio − range), (3.17)

where n and m are the total number of sensors and the number of anchors, respectively.

A low error means good performance of the method.

During our simulation, 400 nodes are randomly and uniformly placed in a square

region of side length 10. If distance of a pair of nodes is less than 1, the nodes are labelled

as directly connected.

In order to understand how the classic MDS and iterative MDS work, we first

study the performance of classic MDS and iterative MDS in recovering sensors’ position.

Figure 3.7(a), (b), and (c) show the procedure of recovering sensors positions within

a small area with classical MDS. Sensors A, B, and C are the three anchor senors.

The Figure 3.7(c) shows the estimated physical position for all sensors within the area.

Figure 3.7(d) indicates that when the error of measured distances for pairwise adjacent

sensors increase, the error rates of sensor positioning increases. We vary the density of

46

sensor deployment so that different number of sensors are enclosed in the area. When the

number of sensors in the area is small, the error rates barely increase even as the measured

distance error increases. When there are more sensors in the area, the error rates of

sensor positioning increase faster. The increase of error rates under different conditions

is always slower than the increase of distance measurement error. This indicates the

classical MDS is robust in tolerating measurement errors of sensor distance. Based on

the experiments, we get the observation that it is preferred to estimate positions for less

number of sensors within a small area, which tends to generate more accurate sensor

positioning.

Figure 3.8 is the experimental results about recovering sensors’ location with iter-

ative MDS. When the number of iterations increase, the error rates of sensor localization

decrease. But, a large number of iteration steps mean high computation costs and com-

putation time. In Figure 3.8(a), the three curves correspond to error rates with different

percentage of pairwise distances collected during sensor localization. When more pair-

wise distances collected for sensor localization based on iterative MDS, the error rates

decrease as well. The error rates of sensor localization with iterative MDS is larger than

that with classical MDS. In Figure 3.8(b), when the collected pairwise distance and the

number of iteration are fixed, the error rates of sensor localization increase with the

increase of distance measurement error. The increase of sensor localization error rates

are slower than the increase of distance measurement. This indicates the iterative MDS

is also robust in tolerating errors of pairwise sensor distance measurement.

47

2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.50

1

2

3

4

5

6

7

8

9

10

A

B

C

−6 −4 −2 0 2 4 6−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

A

B

C

(a) (b)

1 2 3 4 5 6 7 8−2

0

2

4

6

8

10

A

B

C

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Measured range error

Loca

tion

erro

r ra

tes

5 sensors 10 sensors 20 sensors

(c) (d)

Fig. 3.7. (a)The physical positions of sensors in an adjacent area.(b) The recoveredrelative positions of sensors in the adjacent area based on classical MDS. (c) Thesesensors’ physical positions after alignment. (d)When the error of measured distances forpairwise adjacent sensors increases, the error rates of estimated sensor positions increase.

48

5 10 15 20 25 30 35 400.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Number of Interation

Loca

tion

erro

r ra

tes

all pairwise distance collected 90% pairwise distances collected 70% pairwise distances collected

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Range measure error

Loca

tion

erro

r ra

tes

(a) (b)

Fig. 3.8. (a)Error rates of sensor localization increase when the percentage of sensorpairwise distances collected and the number of iteration increase. (b)When the col-lected pairwise distance and the number of iteration are fixed, the error rates of sensorlocalization increase with the increase of distance measurement error.

49

We utilize the DV-distance propagation method [70] to control flooding as well

as our flooding scheme (hop distance). Simulation results shown in Figure 3.9 are com-

petitive with previous research.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

1

2

3

4

5

6

7

8

Percentage of Pairwise Distances Collected

Ave

rage

Err

or

DV−distancehop distance

Fig. 3.9. Error rates when varying the percentage of collected pairwise distances

In order to demonstrate the scheme we proposed for source nodes selection, we

compare the number of collected pairwise distances based on random source nodes selec-

tion and our selection scheme. The results are shown in Figure 3.10 and indicates that

our source nodes selection scheme is efficient in pairwise distance collection.

3.7 Summary

In this chapter, we explore the idea of using multidimensional scaling technique to

compute relative positions of sensors in a wireless sensor network. A centralized sensor

50

1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Number of Source Nodes

Per

cent

age

of C

olle

cted

Pai

rwis

e D

ista

nces

Our selection principleRandom selection

Fig. 3.10. Percentage of collected pairwise distances when increasing the number ofsource nodes and broadcasts

localization algorithm is proposed to get the accurate position estimation and reduce

error cumulation. In order to support the implementation of the algorithm, we also

study the pairwise sensor distances collection with flooding.

51

Chapter 4

Distributed and Robust Sensor Localization

In the chapter, we extend the centralized sensor localization algorithm into a

distributed sensor localization algorithm and a robust sensor localization method based

on multidimensional scaling technique. In the distributed sensor localization algorithms,

multidimensional scaling is used to estimate location of adjacent sensors in small regions

to form local maps. Then, these local maps are aligned to form a global map that

describe location information of all sensors in the network.

In the robust sensor localization algorithm, local maps are calculated for sensor

nodes along the flooding route from one anchor sensor to another anchor sensor only.

The estimated positions of the anchors are compared with their physical positions and

corrected. The positions of other sensors are corrected accordingly. With iterative

adjustment, the robust localization algorithm is able to overcome adverse network and

terrain conditions, and generate accurate sensor position.

4.1 Distributed Sensor Localization

4.1.1 Calculating Relative Positions

In our distributed sensor localization method, the above MDS techniques are used

in a distributed manner to estimate a local map for each group of adjacent sensors, and

52

then these maps are aligned together based on the alignment method. In this section,

the details of distributed sensor localization method are presented.

We employ the widely used distance measurement model of Received Signal

Strength Indication (RSSI). It is necessary to point out that some other distance mea-

sure approaches, such as TOA, TDOA, AoA, and Ultrasound, can also be applied here.

They even generate more accurate distance measure than RSSI, but they usually need

complex hardware equipped in each sensor. In the dissertation, we intend to use RSSI

and simple hardware configuration to achieve competitive performance.

Based on the analysis of the challenges of sensor localization problem in real

applications, the conditions that most existing sensor positioning methods fail to perform

well are the anisotropic topology of the sensor networks and complex terrain where the

sensor networks are deployed. In order to accurately position sensors in anisotropic

network and complex terrain, the distributed sensor localization algorithm computes a

series of local maps which are computed with multidimensional scaling. These local maps

are then pieced together to get the approximation of the physical positions of the sensor

nodes.

The method estimates the relative locations of sensor nodes based on their pair-

wise distances. We also need position alignment techniques to map the relative coordi-

nates to physical coordinates based on three or more anchor sensors.

4.1.2 Aligning Relative Positions

Since we hope to compute the physical positions of sensors eventually, it is nec-

essary to align the relative positions to physical positions with the aid of sensors with

53

positions known. For an adjacent group of sensors, at least three sensors’ physical po-

sitions are needed in order to identify the physical positions of remaining nodes in the

group in 2-D case. Thus, each group of adjacent sensors must contain at least three nodes

with physical positions known, which may be anchors or nodes with physical positions

calculated previously.

The alignment usually includes shift, rotation, and reflection of coordinates. R =

[rij ]2×n = (R1, R2, . . . , Rn) denotes the relative positions of the set of n sensor nodes in

2-dimensional space. T = [tij ]2×n = (T1, T2, . . . , Tn) denotes the true positions of the

set of n sensor nodes in 2-dimensional space. In following explanation, we assume the

nodes 1,2,3 are anchors. A vector Ri may be shifted to R(1)i by R

(1)i = Ri + X, where

X = R(1)i −Ri. It may be rotated counterclockwise through an angle α to R

(2)i = Q1Ri,

where

Q1 =

cos(α) − sin(α)

sin(α) cos(α)

.

It may also be reflected across a line

S =

cos(β/2)

sin(β/2)

to R(3)i = Q2Ri, where

Q2 =

cos(β) sin(β)

sin(β) − cos(β)

.

54

Before alignment, we only know R and three or more anchor sensors’ physical positions

T1, T2, T3. Based on them, we computer T4, T5, . . . , Tn. Based on the above rules, we

have

(T1 − T1, T2 − T1, T3 − T1) = Q1Q2(R1 − R1, R2 − R1,

R3 − R1). (4.1)

With R1, R2, R3, T1, T2, and T3 known, we can compute

Q = Q1Q2 = (R1 − R1, R2 − R1, R3 − R1)/(T1 − T1,

T2 − T1, T3 − T1). (4.2)

Then, (T4, T5, . . . , Tn) can be calculated with

(T4 − T1, T5 − T1, . . . , Tn − T1) = Q(R4 − R1, R5 − R1,

. . . , Rn − R1), (4.3)

(T4, T5, . . . , Tn) = Q(R4 − R1, R5 − R1, . . . , Rn − R1)

+(T1, T1, . . . , T1). (4.4)

4.2 Robust Sensor Localization

An anchor node named as starting anchor initializes flooding to the whole net-

work. When other anchor nodes, named ending anchors, get the flooding message, they

55

pass their positions back to the starting anchor along the reverse routes from starting

anchor to each of them. Then, the starting anchor knows the positions of ending anchors

and routes to each of them. The average radio ranges in different directions from the

starting anchor to different ending anchors can be estimated with the hop counts and

physical distances between the starting sensor to these anchor sensors. Figure 4.1 shows

a flooding initialized by the starting anchor in up-left corner of the square area. Black

lines are the routes that the flooding passed, and blue circles represent the adjacent areas

where sensors position will be estimated with MDS.

Starting

EndingAnchor

Anchor

Fig. 4.1. Flooding from a starting anchor to the whole network. Red nodes are anchornodes.

After the flooding, the starting anchor will initialize sensor localization for sensors

along the routes from the starting anchor to each ending anchor.

56

A

B C

D

E

FG

B’

E’

G’

D’

C’

F’

H

K

Fig. 4.2. Position estimation in the adjacent area of a starting anchor sensor.

Starting anchor first estimates the positions of those sensors that are on these

routes and one hop away from it. Figure 4.2 illustrates the procedure: A is the starting

anchor, D and H are the ending anchors. A knows the positions of D and H as well as

the routes to them, which are (A, B, C, D) and (A, E, F, G, H), respectively. A estimates

that the position of B is B′ on dashed line AD and the position of E is E′ on dashed

line AH. A also estimates the average radio ranges in the direction of AD and AH,

respectively.

With the collection of pairwise distances among neighboring nodes by RSSI sens-

ing, MDS computation is performed to calculate the local map (or the relative positions)

for neighboring sensor nodes. In Figure 4.2, the relative positions of neighboring nodes

A, B, E, J, K are calculated by A. Through aligning the relative positions of A, B, E

with their physical positions, the physical positions of J, K can be calculated as well. In

the same way, localized mapping and alignment are performed for sensor nodes along a

57

route from the starting anchor to an ending anchor. Figure 4.3 illustrates the procedure

of propagated position estimation from starting anchor to ending anchor.

E

F

G

H

I

J

D

CB

A

Map iMap j

K

Fig. 4.3. The propagation of position estimation

In Figure 4.3, A is the starting anchor and D is the ending anchor. The remaining

nodes are along the route of flooding from A to D and each local map is represented

with a dash ellipse. Map i contains adjacent sensors E, F, G, H, K. Since the physical

positions of E, F, G are calculated previously, the physical positions of H, K can be

computed with the above MDS and alignment techniques. Then H, K, I, J, and G are

adjacent sensors and build map j to further estimate I and J ’s positions. Figure 4.4

illustrates four adjacent sensors A, B, C, and D. r is the radio range. A, B, and C are

nodes with positions known. D collects the position of A, B, and C, and then calculate

their pairwise distances. D also has its distances to A, B, C, respectively. Thus, D can

perform a classical MDS to compute the local map (or relative positions of the four

sensors).

58

Figure 4.5 illustrates an example of six adjacent sensors A, B, C, D, E, and F . r

is the radio range. Sensors A, B, C, and D know their positions, and sensors E and F

don’t know their positions. E collects the position of A, B and its distances to them.

Then E relays this information to F . F collects the positions of C, D, and its distances

to them. Thus, F can compute the pairwise distances of the six sensors except the

distances of AF, BF, CE, DE. F performs an iterative MDS to compute the local map

(or the relative positions of the six sensors).

r

A

B

D

C

Fig. 4.4. Classical multidimensional scaling

Then, positions of all nodes around a route from a starting anchor to an ending

anchor and the ending anchor itself is estimated. For example, in Figure 4.2, the esti-

mated position of nodes E, F, G are E′, F ′, G′, respectively. With the physical position

of G known in advance, we can compare G′ and G and align them if they are not equal

(rotate ∠G′AG with A as center and then scale AG′ to AG). We can also apply the

same alignment to the coordinates of all sensors along the route, such as E′ and F ′. In

general, the positions of E′ and F ′ are effectively corrected and approximated to their

59

true positions, respectively. The above position estimation procedures are executed iter-

atively on a route from a starting anchor to an ending anchor until estimated positions

converge. Our experimental results indicate that this procedure usually generates ac-

curate position estimation for sensors along a route. Then, those nodes with positions

accurately estimated are viewed as anchor nodes, and they initialize other position esti-

mation for sensors along different routes. The estimation method can be performed on

different portion of sensors in an ad-hoc sensor network simultaneously until all sensors

know their positions.

r r C

D

E FB

A

Fig. 4.5. Iterative multidimensional scaling

4.3 Performance Study

4.3.1 Simulation Model

We simulated our proposed robust sensor localization methods with Matlab [2].

In order to exam the performance of our distributed localization method, different sensor

deployment strategies are considered to model anisotropic network topology and complex

60

terrain. The first strategy is that 400 nodes are randomly placed in a 100-by-100 square

region, and the average radio range is 10. The second strategy is that 400 nodes are

randomly placed in a 100-by-100 square region, and the region is equally divided into

four non-overlapped sub-square regions. Sensors have different radio ranges at different

sub-square regions. The average radio ranges in different small square regions are 7, 8.5,

10, and 11.5.

We also consider the errors of neighboring sensor distance estimation with RSSI.

The measurement error is in the range 0% − 50% of the average radio range, uniformly

distributed.

The performance of the algorithms is evaluated with the criteria of equation 3.17.

4.3.2 Results

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ratio of anchor sensors to sensors

Loca

tion

erro

r ra

tes

0.50 0.25 0.05 0.00

Fig. 4.6. Error rates when applying the robust localization method with anchor sensorsto all sensors in a square region with an uniform radio range and different distancemeasurement errors

61

Figure 4.6 and 4.7 are the experimental results with our proposed robust sensor

localization method with anchor sensors for sensor localization. When 400 sensors are

deployed randomly and uniformly in a square area and their radio ranges are same, the

error rates of sensor localization decrease with the increase of number of anchor sensors

in Figure 4.6. We find that when the total number of anchor sensors in the square area

is small, a little increase of the total number of anchor sensors will improve the error

rates a lot. But, when there are about 10% sensors in the square area are anchor sensors,

the error rates almost reach the minimum. Pure increase of the anchor sensors will not

bring in much improvement of error rates any more. The distance measurement error

rates vary: 0.0, 0.05, 0.25, and 0.50 in Figure 4.6. Small distance measurement error

definitely generates accurate sensor localization.

Similar observations are obtained from Figure 4.7. When 400 sensors are randomly

and uniformly deployed in a square area with different terrain at different portions of the

area. The different terrain generates different radio attenuation ratios and sensor radio

ranges. When we compare the minimum error rates in Figure 4.7 and that in Figure

4.6, we find they are close. This indicates our proposed distributed sensor localization

method is robust in deal with complex terrain and anisotropic network topology. Other

related results are presented in the Chapter 5.

4.4 Summary

In this chapter, we address challenges, which are caused by anisotropic network

topology and complex terrain, of existing sensor localization methods. Then, we explore

the idea of using multidimensional scaling technique to compute relative positions of

62

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Ratio of anchor sensors to sensors

Loca

tion

erro

r ra

tes

0.50 0.25 0.05 0.00

Fig. 4.7. Errors when applying the robust localization method with anchor sensors toall sensors in a square region with different signal attenuation factors (radio ranges)

sensors in a wireless sensor network. A distributed sensor localization algorithm and a

robust sensor localization algorithm based on multidimensional scaling are proposed to

get the accurate position estimation and reduce error cumulation. Comparing with other

positioning methods, with very few anchors, our approach can accurately estimate the

sensors’ positions in network with anisotropic topology and complex terrain as well as

eliminate measurement error cumulation.

63

Chapter 5

Differentiated Sensor Localization

In many applications of sensor networks, there is no need to estimate all sensors

location information in the sensor network. Most times, only sensors within a given di-

rection or region need to be located. For example, sensors in a small area collaboratively

detect intruders into the area. Location of sensors within the small area that surrounds

the intruder need to be estimated only. Positioning all sensors usually consumes a large

amount of time and energy. In this chapter, we study the demand for differentiated sen-

sor localization methods. Three differentiated sensor localization methods are proposed

and they are able to locate only one or a specific set of sensors.

5.1 Introduction

Most existing sensor localization research tries to provide accurate location es-

timation for a whole network of sensors. Wireless sensor networks significantly differ

from classical or ad-hoc networks on their strict limitations on energy consumption, the

simplicity of the processing power of nodes, and possibly high environmental dynamics.

Locating a network of sensors is usually a computation and communication-intensive

task in sensor network. For many high layer applications that rely on sensors’ location

information, only partial sensors’ location information is needed. For example, sensors

either within a given region or along a route need to be located. For mobile sensors or

64

sensors deployed in mobile environment, it is impossible to locate all sensors location

since all sensors location keeps changing. Since most sensor are randomly deployed in

area with complex terrain, sensors at different portions of the area may have different

radio attenuation ratios, and thus radio ranges and connectivity. The sensor networks

topology are anisotropic dramatically. Many sensor networks are deployed in unattended

or mobile environments. So, sensors have different localization requirements and energy

availabilities for localization operation. It is desirable to achieve differentiated sensor

localization for energy saving and meeting different application requirements. By differ-

entiated sensor localization, we mean positioning sensors or not based on requirements.

Based on the above analysis of the gap between real application requirements

and available sensor localization methods and the demands for differentiated localization

service in distributed ad-hoc networks, we propose three distributed differentiated sensor

localization methods. They are the localization-along-curve method, the localization-

within-region method and the on demand localization method.

They are developed based on the multidimensional scaling (MDS) techniques.

MDS is used to compute relative positions of adjacent sensors in a local area to form

local maps. The main advantages of estimating relative locations with MDS is that one

calculation generates all neighboring sensors location information. These local relative

locations are then pieced together to get the approximation of the physical positions

of the sensor nodes. The on demand localization method estimates the position of the

sensor only when it needs to be located. With our proposed localization along curve

method, only sensors along the narrow offset of a curve or line are selectively located,

instead of all sensors are positioned no matter their location information is needed or

65

not. The proposed localization within region method enables sensors within a specified

region to be positioned. With these three localization methods, we are able to perform

differentiated and energy-efficient sensor localization on demand.

5.2 Related Work

Besides sensor localization algorithms and techniques proposed recently, differ-

entiated services and applications in sensor network trigger a lot of research. Yan et

al. study the differentiated surveillance for sensor networks by proposing an adaptable

energy-efficient sensing coverage protocol [99]. Bhatnagar et al. study the delivery ratios

of packets at different priority levels which are affected by the forwarding probability at

intermediate nodes in [10]. Feedback information from the MAC layer are used to reg-

ulate the transmission rate of non-real-time traffic for real-time traffic [4]. In [64], the

RAP was proposed to use velocity monotonic scheduling to prioritize real-time traffic

and enforces such prioritization through a differentiated MAC layer.

5.3 Challenges

As we have mentioned, most existing sensor localization research tries to provide

accurate location estimation for a network of sensors. Wireless sensor networks have

limited energy availability, while sensor localization usually involves energy-consuming

computation and communication. It is always desirable to reduce the energy costs for

sensor localization. Among many approaches to reduce energy caused by sensor localiza-

tion, one of the most effective method is to reduce computation and communication costs

for sensor localization. So, it is necessary to develop localization methods that are able

66

to locate sensors only on demand for energy-efficiency concerning. We also noticed that

many applications and operations in sensor networks only require location information

of a few sensors. Some sensor networks are mobile or deployed in dynamic environment.

For example, sensor networks deployed in river or sea to monitor fish activities or water

pollution. They tend to slowly and constantly drift with water current. Estimated loca-

tions of sensors invalidate quickly. In this case, it is difficult to position all sensors in the

sensor network. Instead, it is preferable to position the “right” sensors at the “right”

time.

Considering the real sensor network application scenario, there are several chal-

lenges in designing differentiated localization algorithm. Since sensors’ location informa-

tion is unknown, it is difficult to selectively locate sensors that meet any location bound,

such as locating sensors within a given region or along a specific route/curve.

5.4 Differentiated Sensor Localization Methods

Sensors are usually randomly and densely distributed within an area. The con-

nectivity of the whole sensor network is guaranteed. We consider a portion of the sen-

sor networks, which is connected and location information is able to exchanged among

neighboring sensors. In this section, we propose three differentiated sensor localization

methods.

5.4.1 The Localization-Along-Curve Method

The localization-along-curve method is proposed to position sensors that are

within the narrow offset region of a line or a curve. In many network protocols, such as

67

routing [70], multicast [47] and object tracking [47], only sensors along a route or a di-

rection are needed to be positioned. Without loss of generality, we model the curvilinear

belt region with a curve function and its offset width constant, β. For example, a line

with slope α starting with the source (x0, y0) is X(t) = x0+t cos(α), Y (t) = y0+t sin(α),

where t describes travelling distance along the line and 0 ≤ t ≤ MAX.

Suppose the localization estimation starts from three neighboring sensors with

location information known. The three sensors are within the curvilinear belt region.

They are either anchor sensors or positioned with assistant of mobile GPS-equipped

sensors. One of the three sensors is selected to perform localization for sensors in the

neighborhood region. It collects as many pairwise distances of sensors in its neighborhood

region as possible, and then estimate relative locations of these sensors with MDS. The

relative locations of these sensors are converted into physical locations based on the

physical location information of the three sensors whose physical locations are known.

The sensor that performs localization sends location information of each sensor

to them. For a sensor with location estimated, it first judges whether itself is within the

curvilinear belt region. If it is within the region, it queries and collects all other sensors’

location information in its neighborhood. If there are two or more neighboring sensors

with location known and there also are at least one sensors without location known,

then the sensor performs localization for those sensors with location unknown. With the

collection of pairwise distances among neighboring nodes by RSSI sensing, MDS can be

performed to calculate the local map (or the relative positions) for neighboring sensor

nodes. With each sensors following the protocol, the localization for sensors is able to

propagate along the curve and sensors within the curvilinear belt region are located.

68

E

F

G

H

I

J

D

CB

A

Map iMap j

K

Fig. 5.1. The propagation of sensor localization along the route from sensor A to sensorB.

Figure 5.1 illustrates the localization propagation. Sensors A, B, C, D, E, F ,

G, H, I, J , K are located along the curve. They and the remaining nodes are along

the curve and built up local maps, each represented with a dash ellipse. Map i contains

adjacent sensors E, F, G, H, K. Since the physical positions of E, F, G are calculated

previously, the physical positions of H, K can be computed with the above MDS and

alignment techniques. Then H, K, I, J, and G are adjacent sensors and build map j to

further estimate I and J ’s positions.

During the localization propagation, it is necessary to convert the local relative

locations of sensors into physical locations. It is known that, in an adjacent group of

sensors, at least three sensors’ physical positions are required in order to identify the

physical positions of remaining nodes in the group in 2-D case. Thus, each group of

adjacent sensors must contain at least three nodes with physical positions known, which

69

can be anchors or nodes with physical positions calculated previously. The alignment

techniques are presented in Chapter 4.

5.4.2 The Localization-Within-Region Method

Based on the above two differentiated localization methods, the localization-

within-region method is proposed to position sensor within a specific region, such as

rectangle, circle. It is a generalization of the localization-along-curve method in that

the localization propagation are in all directions.

An anchor within the region first estimates its neighboring sensors location with

MDS. This step can also be implement by a mobile sensor with GPS moving in the

neighboring area of a non-anchor sensor and sampling its distances to the sensor at

three or more different location. Then, the sensors with location estimated keep omni-

directional localization propagation that is similar to that in the localization-along-curve

method. During the sensor localization propagation, the boundary information of the

region is also propagated to sensors. Sensors with location known judge themselves

inside the region or not. If a sensor is within the region and it has neighboring nodes

with location unknown, it locates its neighboring sensors; Otherwise, not.

5.4.3 On Demand Sensor Localization Method

In many applications of sensor networks, there is no need to estimate all sensors

location information in the sensor network. For example, sensors in a small area collab-

oratively detect intruders into the area. Position information of sensors within the small

70

area should be estimated only. Since localization of all sensors usually consumes a large

amount of time and energy, it is desirable to enable on demand sensor localization.

We propose a distributed on demand localization method based on the above

position estimation method with anchor sensors. Without loss of generality, we study

the case that one sensor’s position is needed to be estimated. The sensor (starting sensor)

first initializes flooding to pass its message to three or more anchor sensors, which are

called ending anchors. The ending anchors send their locations and the flooding routes

N (N’)

A

B’

D’

E

H’

C

B

D

F

G

H

F’

G’

E’

C’

J (J’)

K

L

M

Fig. 5.2. Position estimation in the adjacent area of a sensor without position known.

back to the starting sensor. Then, the starting sensor knows the positions of ending

anchors and routes to each of them. The starting sensor first simply estimates its physical

position with a trilateration based on its hop distances to ending anchors, which is similar

to the distance vector exchange based method [70]. Then, it estimates the positions of

71

those sensors that are on these routes and one hop away from it. Figure 5.2 illustrates

the procedure: A is the starting sensor, D , H, and N are the ending anchors. A knows

the positions of D, H, and N as well as the routes to them, which are (A, B, C, D),

(A, E, F, G, H), (A, J, K, L, M, N), respectively. A estimates that the position of B is

B′ on dashed line AD, the position of E is E′ on dashed line AH, and the position of J

is J ′ on dashed line AN .

MDS is used to calculate the local map (or the relative positions) for neighboring

sensor nodes. In Figure 5.2, the relative positions of neighboring nodes A, B, E, J are

calculated by A. As shown in Figure 5.1, localized mapping and alignment are performed

for sensor nodes along a route from the starting sensor to each ending anchor. Eventually,

ending anchors’ physical location are calculated and sent back to the staring sensor.

Then, the starting sensor aligns the estimated three or more ending anchors’ locations

to their physical locations based on the alignment technique presented in Chapter 4.

With the calculated alignment parameters during the alignment, the starting sensor

maps itself from the estimated position to its physical position.

The above position estimation procedures can be executed for several times from a

starting sensor to the ending anchors until estimated positions of starting sensor converge.

At the same time, location information of sensors along the routes from the starting

sensor to all ending anchors are also estimated as bonus.

72

5.5 Performance Evaluation

5.5.1 Simulation Model

In order to exam the performance of our methods, different sensor deployment

strategies are considered to model anisotropic network topology and complex terrain.

The first strategy is that 400 nodes are randomly placed in a 100-by-100 square area,

and the average radio range is 10. The second strategy is that 400 nodes are randomly

placed in a 100-by-100 square area, and the region is equally divided into four non-

overlapped square regions. Sensors have different radio ranges. The average radio ranges

in different small square regions are 7, 8.5, 10, and 11.5. The third strategies that 300

nodes are randomly deployed in a T -shape area as that in Figure 2.9, and the sensor

radio range is 10. The number of anchor sensors is 5% of the total number of sensors

in the areas. We also consider the errors of neighboring sensor distance estimation with

RSSI. The pairwise measurement error is in the range 0% − 40% of the average hop

distance, uniformly distributed.

The performance of the algorithms is evaluated with the criteria of equation 3.17.

5.5.2 Results

Figure 5.3, Figure 5.4 and Figure 5.5 show the experimental results with dif-

ferentiated methods and their comparison with the robust sensor location method. The

x-coordinators are labelled with hop measurement errors. In the plots, localization-

with-correction method denotes the robust sensor localization discussion in Chapter 4.

73

The similarity between the performance of localization-along-curve and localization-

within-region indicates that our algorithm is differentiated in position estimation under

different network topologies and terrain condition. The localization-with-correction is

robust in that it outperforms the other two methods.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Hop Measurement Error

Err

or R

ates

Localization−along−curveLocalization−with−correctionLocalization−within−region

Fig. 5.3. Localization error rates within an isotropic square area.

In order to study the performance of our proposed on demand sensor localization

method, we do experiments on localization one sensor in the square area with uniform

radio attenuation ratio as well that with four different radio attenuation ratio. The

number of anchor sensors are eight, which is 5% of the total number of sensors deployed

in a square area. We also vary the distance measurement error rates to see its effect on

the sensor localization. The error rates with sensors deployed in the square area with

74

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55


Err

or R

ates


Fig. 5.4. Localization error rates within an anisotropic square area.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6


Err

or R

ates


Fig. 5.5. Localization error rates within a T -shape area.

75

an uniform terrain are slightly lower than that in the square area with different terrain

condition. The overall error rates of on demand sensor localization are not as good as

its error rates estimated with distributed sensor localization method.

Since the message costs for localization sensors are proportional to the size of

the area within which we position all sensors with our proposed methods, locating all

sensors in a small region always cause less communication than locating all sensor in a

large region. Based on the observation, the differentiated sensor localization methods

tends to be energy saving.

5.6 Summary

We explore the idea of differentiated sensor localization in distributed ad-hoc

sensor networks. The application demands for differentiated sensor localization are iden-

tified. Then, three differentiated sensor localization method based on MDS are proposed

to get the accurate position estimation and reduce error cumulation. Experimental re-

sults indicate that our differentiated methods are very effective and efficient.

76

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Distance measure error

Loca

tion

erro

r ra

tes

with uniform radio range with different radio range

Fig. 5.6. Errors when applying the distributed on demand localization method toone sensor in two square regions with uniform and different signal attenuation factors,respectively.

77

Chapter 6

Large Continuous Object Detection and Tracking

With the location information of sensors in an wireless ad-hoc sensor network,

many applications related to targets and objects detection and tracking are able to be

implemented. In this chapter, we study the problem of using sensor networks to locate

large continuous objects, such as wild fire and bio-chemical spill materials, and track their

movement. Large continuous objects are different from collections of discrete targets

such as a group of vehicles in that they are continuously distributed across a region and

occupy a large area. Capturing their spatial extents and related boundary information

represents a class of very challenging tasks in sensor network research. It has not been

adequately addressed in previously existing research. We first propose a distributed

algorithm for locating the boundary information of large continuous objects covered by a

sensor network. Since they usually span a large area, the fusion and dissemination of local

boundary information to obtain a global view of the large continuous objects becomes a

very challenging problem. We also propose a dynamic curvilinear belt structure to track

the movement of boundaries real-time manner and facilitate the fusion and dissemination

of boundary information in a sensor network.

78

6.1 Introduction

The tasks of positioning objects and tracking their movements with sensor net-

works generally fall into two classes. The first type of detection and tracking task is to

locate and track one or more individual objects (locations) within the area of deploy-

ment of the sensor network. The discrete set of objects, such as people, animals, and

vehicles, usually have very small special extent comparing with the large area where the

sensor network is deployed. These objects may emit noise, light, and seismic waves etc.,

which may be sensed by sensors around them within a certain distance. Detection and

tracking an individual object is usually performed by one or several sensors close to it

[18, 22, 31, 63, 67].

The second type of detection and tracking task is to position the distribution and

spatial extent of large continuous objects and track their movement. By large continuous

objects we mean objects such as a spreading wild fires, bio-chemical and/or chemical

liquids, poisonous gases etc. which usually possess large spatial extent compared with

sets of discrete objects we discussed before and occupy a significant portion of the area

where sensor network is deployed. Although it is possible to utilize satellite or airplane

to scout the large continuous objects’ location information based on remote sensing

techniques, some large continuous objects may be invisible such as poisonous gases, or

be out of sight of satellites or airplanes. For example, we may want to detect and track

the distribution of some bio-chemical in subway or tunnel. In those cases, it is desirable

to utilize sensor networks to detect and track the large continuous objects. Each sensor

makes local observations (on location and movements) of a portion of the large continuous

79

object. Sometimes, adjacent sensors collaboratively perform signal processing to estimate

the local distribution of the target objects or phenomena. The information may be stored

locally for answering relevant queries by mobile users in the future. It may be further

aggregated at sinks for a global view and relayed to external servers or the Internet. By

locating the targets’ spatial extents and corresponding boundary information, we are

able to efficiently detect and track the large continuous objects. It represents a class of

important and challenging tasks in sensor networks applications [53]. Because this type

of task involves complex information processing and intensive communication of a large

number of sensors spanning a big region, it tends to be more challenging than the first

type of task.

We define boundary sensors as those sensors that detect the object in their vicinity

but have one or more neighboring sensors that do not detect the large continuous object.

Boundary sensors estimate the location of the local boundary based on their local ob-

servation and their knowledge of their neighbors’ observations. Considering that a large

continuous object usually spreads in a large area and its boundary has a very large span,

high communication cost is required for the sinks to collect the localized boundary in-

formation distributed in these boundary sensors. In order to implement energy-efficient

tracking in real-time fashion, we propose a partitioned curvilinear belt structure to orga-

nize boundary sensors. Boundary sensors and other adjacent sensors are grouped into a

curvilinear belt structure along the large continuous object’s boundary. The curvilinear

belt structure is separated into several partitions. A head sensor is selected for each par-

tition. The local boundary information is fused within the partition, and the head sensor

in each partition either sends the locally integrated boundary information to the sinks or

80

store it locally. Because the boundary information fusion is driven by events that result

from boundary movements, partitioning boundary sensors reduces the communication

cost by reducing redundant information transmitted when there are only a few sensors

that change their status from boundary sensors to non-boundary sensors and vice versa.

The partitioned curvilinear belt structure is dynamic in that each partition can update

its members when the corresponding portion of the boundary is moving. Therefore, the

dynamic curvilinear belt structure also facilitates boundary tracking in real-time.

6.2 Related Work

There has been some research on detecting and tracking single or multiple in-

dividual targets, such as vehicles, animals, inside a region covered by sensor network.

Mainwaring et al. [66] discuss the application of sensor network for habitat monitoring.

In [56, 60, 85, 100], several techniques for locating targets are proposed. Krishnamachari

et al. discuss the case that three sensors are needed to track a target in a sensor net-

work in [59]. Collaborative signal processing and classification techniques are addressed

in [61]. Zhao et al. propose the collaboration mechanism that utilizes information utility

to decide future sensing actions in [102]. However, neither their algorithms nor their

simulations deals with detecting and tracking large continuous objects, such as wild fire,

bi-chemical materials, with wireless sensor networks.

Recently, some research is proposed for detecting some non-local events or phe-

nomena in [20, 23, 62, 73], which are closely related to the problem we discuss here.

They consider that the non-local phenomena are observable by sensors. Then, they try

to generate its edges. However, they did not consider how to detect the phenomena

81

whose distribution may be random and changing quickly in distributed fashion. Also,

when the phenomena is moving across the area, tracking its edges in distributed and

real-time fashion is not solved. There is no communication protocol proposed to collect

the localized observation of the phenomena by each sensor.

Another related research to our work is on data aggregation in sensor network

[36](LEACH) [22, 55] (Maximum Lifetime Data Aggregation) [60]. The authors proposed

some cluster or tree structure to fuse data as an energy-efficient way to gather data from

a sensor network. However, they barely address how to detect and track a mobile object

in a real-time manner. The large continuous objects detection and tracking tasks that we

address in the dissertation contain issues not only on detection and tracking techniques

but also data aggregation among a large number of sensors with dynamic structure.

Since there is no previous research works for dynamic structure to track and collect

information, we cannot compare the performance of our method with any other method.

However, we discuss the improvement in terms of communication costs by comparing

with some direct message collection schemes.

6.3 Model Assumptions and Challenges

Large continuous objects are different from individual targets in that they are

continuously distributed within a large area. They may be some wild fire or bio-chemical

materials, which are released maliciously from some specific source and then slowly

diffuse. Although they are usually in three dimension space in reality, it is generally

more interesting to know their locations and spread in a two dimension plane of the

earth’s surface.

82

For the detection and tracking problems, we assume that a large number of sensors

are deployed in the given field, and they form a sensor network. Each sensor in the sensor

network knows its physical location. Sensing principles include but are not limited to

mechanical, chemical, thermal, electrical, chromatographic, magnetic, biological, fluidic,

optical, acoustic, ultrasonic, and mass sensing. Sensors usually have a specific sensing

range, ds. If there is any target object existing within the detection range of a sensor,

the sensor can measure the concentration of the object, which ranges between 0 and

1. Sensors can also quantize their detection results by comparing the content of the

object with a threshold, t. If the content of the large continuous object is greater than

the threshold, then the sensor returns sensing result as object existing at the sensor.

Otherwise, the sensor returns that the large continuous object does not exist at the

sensor.

Figure 6.1 illustrates the detection and tracking of three large continuous objects.

Sensors around the objects detect and track their boundaries and send the boundary

information to the sink in a hop-by-hop fashion along the dashed lines. Then the sink

relays the boundary information to external servers or the Internet. An efficient ap-

proach to identify and describe the existence of the target large continuous objects is

to probe their boundaries. The boundary of a large continuous object is consecutive

and enclosing the large continuous object, inside which the concentration of the target

materials per unit region is nearly homogeneous and higher than a threshold. It is also

possible that there are some “holes” inside the continuous objects. As long as a hole is

large enough, it is able to be identified, and the boundary information of the hole should

be extracted. Current signal processing techniques have enabled sensors to precisely

83

��

��

��

��

��

��

Continuous Objects

Hole

Sink

Fig. 6.1. Large continuous objects and their boundaries; The boundary informationmay either be collected by a fixed sink or be scouted/queried by mobile users, such as asoldier

measure the concentration of target material at their nearby region. However, there are

many challenges in detecting and tracking boundaries considering the physical characters

of the large continuous objects.

First, although each sensor is able to detect the existence of the target material at

its nearby region, none of them alone can extract the boundary information of the large

continuous object. Information exchange or communication among sensors is necessary

in order to estimate the boundary in a local area.

Second, individual object(s) usually is able to be efficiently detected and tracked

by several sensors adjacent to it in a collaborative manner [102]. However, even through

many adjacent sensors in the sensor network can cooperatively estimate a portion of the

large continuous object’s boundary within a local area, the global view on the spatial

extent and the boundary of the whole large continuous object is still not available. Such

kind of global information is usually crucial but difficult to obtain, considering that the

84

large continuous object tends to spread across a very large area, and its boundary is

much larger than one or multiple individual targets.

Third, the large continuous objects usually diffuse or drift under the influence of

environment factors, such as winds. This leads to the change in the shape and movement

in the boundary of the objects. In addition, some physical obstacles may also affect the

shape of objects and boundary movement.

Finally, a large continuous object may be split into multiple smaller objects,

or several large continuous objects may merge into a bigger large continuous object.

These topological changes make the boundary detection and tracking task even more

challenging.

6.4 Boundary Localization

Some large continuous objects may have a clear boundary, and the object content

distributes only within the boundary. Inside the boundary, the object concentration

is relatively homogeneous. There also may be some big holes without the continuous

objects. Each sensor makes binary observation of the existing of large continuous objects

(either 1 or 0), or the sensor quantizes sensor reading based on a threshold. We first

select some sensors as boundary sensors, and then estimate the large continuous object’s

boundary with these boundary sensors. In this section, we present the details of our

proposed boundary localization methods.

85

6.4.1 Boundary Sensors Selection

In our boundary estimation framework, sensors either are waked up from sleep

mode or periodically activate and make local observations of the large continuous objects.

When a sensor finds that its observation of the target object’s presence changes at some

time slot, it is very possible that the large continuous object either move in or move

away from the sensing range of the sensor and the sensor is close to the boundary of

the large continuous object. The sensor then exchanges its detection information with

its neighboring sensors within its radio range r. In this way, we reduce the unnecessary

communications between sensors far from the boundary of the large continuous object.

We have introduced the concept of boundary sensor in Section 1. The advantages

of selecting boundary sensors to estimate boundary are that the communication costs for

boundary estimation are reduced and the accuracy of estimated boundary is improved.

The reasons will be explained later. Before we discuss how to select boundary sensors,

we first introduce the concept of compactness distance:

Definition 1: compactness distance dc is the average distance between neighboring

sensors, and is given as

dc =√

S/N,

where S is the size of the area, and N is the total number of sensors deployed in the

area. Small compactness distances mean that the sensors are densely deployed in the

area, while large compactness distances mean that sensors are sparsely deployed in the

given area.

86

Now we are ready to give an more accurate definition of boundary sensors. If

a sensor detects the existence of the target object, and at least one of its neighboring

sensors within the distance of adc (1 ≤ a ≤ r/dc) does not detect the large continuous

object, then the sensor is selected as a boundary sensor. The boundary sensor and each

of its neighboring sensors, which are within the adc range and do not detect the large

continuous object, form a boundary pair. These boundary pairs are used for boundary

location estimation, which will be discussed in the next subsection. Sensors along the

boundary of the object are usually able to estimate the location of the boundary based on

their local observation and their knowledge of their neighbors’ observations. In order to

estimate the boundary information, some sensors are first selected as boundary sensors.

The reason for enforcing the compactness distance for boundary pairs selection is

that when sensors are deployed densely enough, a sensor usually has many neighboring

sensors within its radio range. A non-boundary sensor close to the continuous object

boundary may form several boundary pairs with different boundary sensors within the

radio range. Since each boundary pair estimates a position that the boundary may pass,

there may be several different estimated positions for the boundary in the neighboring

region of the non-boundary sensor. The inconsistency is reduced by eliminating some

error-prone boundary pairs. Figure 6.2 provides several possible cases of error-prone

boundary pairs and illustrates the selection of boundary sensors and boundary pairs.

The definition of compactness distance is based on global knowledge of the sensor

network. It may be pre-computed and then either saved in each sensor as configuration

information or broadcasted to all sensors in the sensor network. Since the sensors are

randomly deployed, an uniform compactness distance is not accurate enough to describe

87

S2

adc

r

A

B

C

S1

(a)

PairSelected Boundar

locationEstimated boundary

ObjectCountinuous

Boundary sensor

Boundary

G

FE

DC

B

A

(b)

Fig. 6.2. (a) Possible cases of boundary estimation by boundary sensors, among whichpair (S1, B) and (S1, C) are error prone. We try to eliminate the two pairs by reducingthe range of neighborhood to adc. (b) Selecting boundary sensors: Only sensors arecovered by the continuous object and marked by the small ellipses are boundary sensors.

88

the sensor density through the network. A set of localized compactness distances can

more accurately describe the sensor distribution in the network. A sensor may initialize

flooding within a limited number of hops to request neighboring sensors locations. Then,

a local compactness distance may be easily calculated as long as neighboring sensors

locations are collected.

��

��

Continuous Object

Boundary sensor

Estimated boundarylccation

E

F

C

D

B

A

G

H

Fig. 6.3. Distributed boundary estimation: E, F , G, and H are boundary sensors;They form five boundary pairs with non-boundary sensors A, B, C, and D, respectively;Five position marked with small circles are estimated as the boundary locations.

6.4.2 Distributed Boundary Localization

In order to estimate the location of the boundary in a boundary sensor’s vicinity,

the boundary sensor collects the location information of its neighboring sensors with

sensor reading equal zero. Since a boundary sensor detects the object while its neigh-

boring sensor does not detect the object, the boundary of the large continuous object,

which may be viewed as a curve, must locate/pass between the boundary sensor and its

89

neighboring sensor. We approximate the position where the boundary curve intersects

with the line between a boundary pair as the middle point of the line connecting the

boundary pair. Algorithm 1 summaries the boundary sensor selection and boundary

detection method.

Figure 6.3 illustrates our distributed boundary estimation algorithm. If sensors

E, F , G, and H do not detect object in the former time slot but they detect the existence

of object in the current time slot, then they are selected as the boundary sensors and

will broadcast messages to their one-hop neighbors. The message of a boundary sensor

contains its location, hop count, and its observation of the object.

The baseline of the communication costs is that each of these boundary sensors

sends its local boundary information to the sink independently. Clearly, the communi-

cation costs are very expensive. In addition, the large continuous object may move or

diffuse, which causes the boundary location to change. In order to track boundary move-

ment and efficiently disseminate boundary information, we propose a dynamic curviliear

belt structure to organize boundary sensors.

6.5 Boundary Movement Tracking

The above distributed boundary estimation method selects boundary sensors and

estimates location information of boundary with boundary sensors. In this section, we

study how to track the movement of boundary.

We propose a dynamic curvilinear belt structure to organize boundary sensors

and non-boundary sensors adjacent to them. The curvilinear belt structure is divided

into several partitions. Each partition has a partition head, which is a boundary sensor.

90

Algorithm 1 Boundary Sensor Selection and Boundary Estimation

while (1) docurrent.reading=Detect(concentration of target object)if current.reading ≥ threshold then

current.reading=1else

current.reading=0end ifif current.reading 6= last.reading then

last.reading=current.readingBroadcast Query to 1-hop neighborsWait(Reponse)if (Reponse 6= current.reading) and (pairdist(my.id, Response.id) ≤ adc) then

if current.reading==1 thencurrent.status=boundary sensor;

elsesend message ⇒ Response.id: You are a boundary sensor

end ifestimated boundary=MiddlePoint(my.id, Response.id)

end ifend ifsleep(Time)

end while

91

The partition head collects boundary information from other boundary sensors in the

partition. Thus, the whole boundary information of the object is divided and stored in a

limited number of partition heads, and they can either relay the boundary information to

sink with existing routing protocols [26, 48, ?] or store the boundary information locally

for future queries.

6.5.1 Curvilinear Belt Structure and Its Partitioning

The boundary sensors are distributed along the boundary of the target large

continuous object. Only those non-boundary sensors that are adjacent to these boundary

sensors are involved in estimating the boundary location and monitoring the movement

of boundary. Thus, an curvilinear belt structure are built to organize these boundary

sensors and non-boundary sensors based on their locations. The selected boundary

sensors are located in the center of the curvilinear belt region. The boundary of the

continuous object is always enclosed by the curvilinear belt structure. The boundary

sensors are linked into a curve to form the backbone of the curvilinear belt structure.

Based on the backbone, some non-boundary sensors within a specific distance to the

backbone are linked to the backbone and form the curvilinear belt structure. Sensors in

the curvilinear belt cooperatively monitor the boundary in a real-time manner. Figure

6.4 shows an example of curvilinear belt structure.

These large continuous objects may move, diffuse, increase in size, change in

shape, split into multiple relatively smaller large continuous objects, or even merge into

a bigger object. With the boundary movement, the sensors in the curvilinear belt struc-

ture need to re-estimate, fuse, and update the boundary information. When boundary

92

moves out of the covered area by the curvilinear belt structure, the membership of sen-

sors in the curvilinear belt structure needs to be changed by adding/removing some

boundary or non-boundary sensors into/from the curvilinear belt. Considering that dif-

ferent portions of the boundary may have different movement speed and direction, the

boundary information updating and curvilinear belt structure updating will perform in

different time and frequency. Globally updating boundary information and curvilinear

belt structure involves some unnecessary operations and costs on sensors within some

portions of the curvilinear belt structure. It is desirable to divide the curvilinear belt

structure into several partitions along the object boundary to locate the updating pro-

cess of boundary information and curvilinear belt structure. Different groups of sensors

monitor different portions of the boundary.

The advantages of partitioning the curvilinear belt structure may be summarized

as following: First, only the partition corresponding to the portion of moved boundary

needs to re-estimate boundary information and update local curvilinear belt structure

when the boundary moved to the margin of the curvilinear belt structure. Second, the

global boundary information is divided into small pieces. Only sensors within the parti-

tion fuse the boundary information. Therefore, the fusion is associated with low commu-

nication costs. Third, we may use some polynomials to describe boundary information,

which reduces the information load of boundary description. The global boundary may

be a very complex curve in real-world, while each small piece of the boundary curve is

relatively simple curve. It is generally easier to perform piecewise interpolation of the

boundary information within a local small area. For example, a line with slope α starting

with the source (x0, y0) is X(t) = x0 + t cos(α), Y (t) = y0 + t sin(α), where t describes

93

travelling distance along the line and 0 ≤ t ≤ MAX. More information about piecewise

curve interpolation is available in [34].

The construction of the curvilinear belt partition structure contains two phases:

discovering the backbone of the curvilinear belt partition and forming the curvilinear

belt partition.

Discovering the Backbone of the curvilinear Belt partition: For sensors

in a partition, a boundary sensor is selected as the head. There are many leader selec-

tion algorithms available for the head selection [90]. A simple solution is to select the

boundary sensor closest to the center of the area covered by the partition structure. To

form the curvilinear belt partition, the head needs to build a backbone of the curvilinear

belt region. The backbone is a route that passes through most boundary sensors in the

partition. In order to do this, the head initializes scoped flooding, which is to broadcast

connection request to its k-hop neighboring sensors. The request contains the maximum

length of the partition in term of hop b, hop count, and partition identification (head

ID). Non-boundary sensors within k hops from the partition head forward the message.

If a boundary sensor receives the request and it is not involved in any partition, it checks

the hop count. If the hop count is less than b, it stores partition identification and the

sender of the connection request. Then, it increases the hop count by one and broad-

casts the request to its k-hop neighboring sensors. Otherwise, it ignores the request.

Other boundary sensors follow the same rule to relay the connection request. A route is

eventually discovered, which connect most of the boundary sensors without loop. Some

boundary sensors of the curvilinear belt partition may not be in the route, and they

then are directly connect to one boundary sensor in the route. Figure 6.4 illustrates the

94

B

��

ContinuousEntity

Boundary Sensor

Entity Boundary

Offset

A Partition

A

C

D

Fig. 6.4. Curvilinear belt structure for object boundary and its partition: The largecontinuous object is on the left side of the object boundary. Black dots are sensors thatdetect the object, and those dark dots along the entity boundary (A, B, C) are boundarysensors. Small circles are sensors that do not detect the object. Most boundary sensorsare connected to the backbone (B, A, D, C). Boundary sensor A is the head of thepartition. A and C are two boundary sensors, and they are out of each others radiorange. An ellipse is formed with A and C as foci, and α is its eccentricity.

95

curvilinear belt structure and its partitions. In the following, we explain why we needs

the k-hop flooding for discovering the backbone and how to decide the k.

In some cases, the boundary sensors are sparse so that two adjacent boundary

sensors in the backbone are k or less hops away from each other. For example, A, B, and

C are adjacent three boundary sensors in Figure 6.4. A and C are 2-hop apart because

they are not in each other’s radio range. In order to form the backbone of the partition,

the non-boundary sensor D is included in the backbone. In the following, We adapt the

concept of network compactness in [47] to prove the minimum number of hops, k, for the

scoped flooding in order to guarantee the discovering of the backbone in the following.

We also show that the existence of the shortest path in the local small area to connect

apart boundary sensors in the backbone.

Definition 2: Let d(e) denote the physical distance of a network edge e. If a network

route l contains an edge e, we say e is in l. The length of the route l is d(l) =∑

einl d(e),

which is the sum of the physical distances of all its edges.

Definition 3: Suppose M(i, j) is the set of shortest routes between nodes i and j

in terms of number of hops. The Euclidean network distance of nodes i and j is

d̂(i, j) = minl∈M(i,j) d(l).

Definition 4: α-compactness of a network quantifies the relation between the direct

physical distance and the Euclidean network distance among network nodes. It is de-

fined as the smallest physical distance to Euclidean network distance ratio among the

nodes: α = mini,j∈V d(i, j)/d̂(i, j), where V is the set of nodes in the network.

96

Theorem 1: Let i, j be any two nodes in a α-compact network. Let E(i, j, α) be

an ellipse using i, j as two foci and with eccentricity α. There is at least one shortest

path between i and j inside the ellipse E(i, j, α).

3

j

p

2 i

q

Fig. 6.5. Ellipse

Proof: Assume the theorem is false. Then, there is at least one pair of nodes i and j,

and all of its shortest routes in terms of number of hops have at least one vertex outside

the ellipse E(i, j, α). For all points p on the ellipse,

d(i, p) + d(j, p) = d(i, j)/α.

For any points q out of the ellipse,

d(i, q) + d(j, q) > d(i, j)/α.

97

So,

d̂(i, j) > d(i, p) + d(j, p) = d(i, j)/α.

That is

α >d(i, j)

d̂(i, j), (6.1)

which contradicts the definition of α-compactness of the network. We proof that the

theorem 1 is true. Figure 6.5 shows the shortest path within the ellipse area between

nodes i and j.

Figure 6.6 shows the values of local α along a direction in a randomly and uni-

formly deployed sensor network [47]. The α tends to be constant in the randomly and

uniformly network. Thus, we can take a constant value for α in future computation.

Similarly, the number of hops of the shortest route connecting a pair of sensors may be

specified based on the compactness of the network.

Definition 5: Hop distance of nodes i and j, h(i, j), is the minimum number of network

hops between the pair of nodes.

Definition 6: The β-compactness of a network indicates the relation between the hop

distance and the physical distance among the nodes in a network. It is defined as the

minimum ratio of the physical distance to the hop distance between any two nodes in

the network:

β = mini,j∈V

d(i, j)

h(i, j). (6.2)

98

0 100 200 300 400 500 600 700 800 900 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Location

alph

a

Fig. 6.6. α values for a randomly and uniformly deployed sensor network tend to be aconstant

Theorem 2: For β-compactness network, if any two nodes in the network are at a

physical distance d has a shortest route of no greater than d/β hops.

The Theorem 2 can be proved similarly to that of Theorem 1. Based on the above two

theorems, there is a path which is fewer than the given hops and it is entirely contained

in the ellipse for a pair of adjacent boundary sensors. For a pair of adjacent boundary

sensor, if they are within radio range of each others, a edge is directly established in the

backbone to forward messages. If they are out of each others’ radio range, since their

distance cannot be large in a randomly, uniformly and densely deployed sensor network,

it is guaranteed that there is a shortest route linking them within the small ellipse area,

99

whose foci are the pair of boundary sensors and the eccentricity is α. The length of the

shortest path is less than or equal to k = max(d/β) in terms of hop.

Building the Curvilinear Belt Partition: After establishing a backbone to

connect all boundary sensors that belongs to the partition, we need to find out non-

boundary sensors of the partition in order to establish the curvilinear belt structure.

Each boundary sensors found in the first step broadcasts non-boundary sensor connection

request. The request contains maximum hop distance n, hop count, and the boundary

sensor’s identification. If any other boundary sensor gets the request, it ignores the

request. If a non-boundary sensor gets the request and it is not affiliated to any boundary

sensor, it will check the hop count. If the hop count is less than n, the non-boundary

sensor will affiliate itself with the boundary sensor by storing the boundary sensor ID,

hop count, and the sender of the connection request. Then, it increases the hop count by

one and broadcasts the request. All other non-boundary sensors follow the same rule to

relay the connection request. For a non-boundary sensors that receives multiple requests

from difference boundary sensors, it affiliates itself with the boundary sensor that is

most closest to it in terms of hop count. These selected non-boundary sensors belong

to the partition, and they together with the boundary sensors track the movement of

boundary. In Figure 6.7, non-boundary sensors, which are within two hop distance from

boundary sensors, are assigned to the curvilinear belt. The Algorithm 2 summarizes the

curvilinear belt partition construction procedure.

During probing the boundary sensors and non-boundary sensors of the curvilinear

belt partition, the routes from each sensor in the partition to the partition head is

discovered and saved as well. The boundary information stored in each boundary sensor

100

is sent to the head with time stamp. The head fuses the boundary information in compact

data format, and then either relays it to the sink or store locally for future queries. Since

the curvilinear belt partition is relatively smaller than the whole object boundary and

the head is close to the boundary sensors within the partition, head collecting boundary

information from each boundary sensor in the same partition takes much less messages

than the sink collecting it from each boundary sensor directly. The total communication

costs for boundary information dissemination based on the partitioned curvilinear belt

structure are sensitive to the size of the partition.

6.5.2 Tracking Boundaries

The large continuous object may move, and its boundary changes location. How-

ever, the boundary moves at a natural limited speed, which means the maximum distance

the boundary travels in a certain amount of time is bounded. Boundary’s location is

estimated as long as the boundary is still travelling within the area covered by the par-

tition based on our proposed boundary estimation method. Inside each partition, local

boundary information is fused in the partition head. When local boundary of an object

is going to move out of the area covered by an curvilinear belt partition, the partition

needs to be updated and the membership of sensors in the partition changes. When the

head of a partition finds that it is necessary to re-build the partition, it collects current

estimated boundary location information. The head estimates the midpoint of the local

boundary within the partition covered area, and selects the boundary sensor that has the

shortest distance to the midpoint as a new head. For example, if the boundary moves

toward right in Figure 6.7, it will arrive at the detection range of sensor B after a certain

101

Algorithm 2 A Sensor Process: Constructing curvilinear Belt Partition Structure

TYPEDEFINE sensor: location, isBoundarySensor, isHead, withinObject,partitionID, neighborListTYPEDEFINE message type:Type 1-patitionHeadReq,Type 2-boundarySensorConnectionRequest,Type 3-nonboundarySensorConnectionRequest,Type 4-destroyParitionRequestcreate(”a sensor”)while (1) do

if (I am a boundary sensor) thenset(isBoundarySensor)

end ifif (I have any message) then

if (msgtype==1) thenI am selected as a new head of a paritionBroadcast msgtype 2 to 1-hop neighbors

end ifif (msgtype==2) then

if (I am a boundary sensor) thenSave paititionIDBroadcast msgtype 2 to 1-hop neighbors

elseSave paititionIDBroadcast msgtype 3 to 1-hop neighbors

end ifend ifif (msgtype==3) and (within the width of curvilinear belt) then

Save paititionIDBroadcast msgtype 3 to 1-hop neighbors

end ifif (msgtype==4) then

if (I am head of the partition) thenBroadcast msgtype 4 to 1-hop neighborsFreeFromTheParition()Select a new partition head, and inform it

end ifend if

end ifif (I am a boundary sensor) and (out the width of curvilinear belt) then

Send msgtype 4 to my partition headend ifsleep(Idle Time)

end while

102

amount of time. Then, B will update itself as new boundary sensor. When A realizes the

boundary is close to the border of the curvilinear belt, it selects B as the new head. The

old head sensor will forwards partition size information and other some boundary history

information to the new head. The new head uses the above Algorithm 2 to establish the

new curvilinear belt partition. Some sensors belonging to the old partition are included

in the new partition, and some sensors outside the old partition will be also included in

the new partition.

The maximum size of the partition structure are variable within a large range,

which leads to different message costs even within the same detection and tracking sce-

nario. How to decide the proper size of the partition structure is a non-trivial issue in

constructing the partition structure. The optimal size of the partition depends on the

boundary movement pattern and the density of sensors deployed. In the following, we

provide some constraint conditions to select the proper size of the partition structure.

We also study the time costs for constructing a partition of the curvilinear belt structure.

When a head should assign a new head to reconstruct a new curvilinear belt partition

in order to monitor the boundary in real-time manner is discussed.

Theorem 3: For a network of β-compactness, if th is the average communication la-

tency per hop, then the maximum message delivery speed in the network is β/th.

Proof: for nodes i and j, the physical distance of them is d(i, j). The shortest route

between i and j is less than or equal d(i, j)/β. If each intermediate node forwards a

message immediately after receiving it, the message travels from one node to another

103

node d(i, j)/β-hop away takes no longer than th∗d(i, j)/β time. Then, the average speed

v of message propagation over distance d(i, j) is greater than or equal to β/th.

In a short time period, we can assume that the large continuous object’s boundary

moves in a constant speed and direction in the local area covered by an curvilinear belt

partition.

Theorem 4: Let l be the length of the object boundary within the area covered by

an curvilinear belt partition. w is the width of curvilinear belt region. The head of the

curvilinear belt partition is located in the center of the area covered by the curvilinear

belt partition. It takes time no longer than th(l+w)/2β to establish the curvilinear belt

partition if we omit the sensors’ local computation time.

Proof: The head of curvilinear belt partition need to propagate connection request

message to all sensors within the area of the curvilinear belt partition. The maximum

distance that the message travels within the area is about (l + w)/2. Since the network

is β-compact, the number of hops the message travelling is no greater than (l + w)/2β.

The total time for message propagation in the curvilinear belt partition is no longer than

th(l + w)/2β.

Based on the above Theorem, it is easily to get the following theorem:

Theorem 5: Let the maximum speed that the boundary moves out of the curvilinear

belt is V in the direction of shortest path from head to the boundary of curvilinear belt

region. When the distance between object boundary and the margin of the curvilinear

104

belt partition is dr = V th(l + w)/2β, the head should select a new head to re-construct

the curvilinear belt partition in order to keep monitoring the boundary. 2dr is also the

minimum width of curvilinear belt partition.

The message delivery speed should be always greater than the object boundary move-

ment speed, otherwise, the curvilinear belt structure will be not able to track the moving

boundary. Considering the relation of message delivery speed and object boundary move-

ment speed, there is following constraints on the size of the curvilinear belt structure.

New Location

AB

drV

Old LocationEntity Boundary

Len

gth

Width

Fig. 6.7. Curvilinear belt partition reconstruction and dr; Boundary moves to left withspeed V . When boundary is close enough to the margin of the current partition, headA will select sensor B as a new head to construct a new partition.

105

Theorem 6: Let the maximum speed that the boundary moves out of the curvi-

linear belt is V in the direction of shortest path from head to the boundary of curvilinear

belt region. Let l and w are the length and width of the curvilinear belt partition. Then,

l ≤ w(β/V th − 1) holds.

Proof: Since in Theorem 5

dr ≤ w/2,

V th(l + w)/2β ≤ w/2.

We can easily get

l ≤ w(β/V th − 1).

Currently, we specify maximum width as w and maximum length as l of an

curvilinear belt partition (as shown in Figure 6.7) in our protocol based on the above

Theorems. The width and length of the curvilinear belt partition may vary within the

range of w/3 ∼ w and l/3 ∼ l, respectively. When the large continuous object moves, the

length of the portion of boundary can either increase or decrease. If the curvilinear belt

partition becomes too large to be covered by the current curvilinear belt partition in the

local area, the partition head will appoint a boundary sensor that is not affiliated with

any curvilinear belt partition as a head to build a new curvilinear belt partition. If two

adjacent curvilinear belt partitions are very small, then their heads may communicate

with each other to merge into an curvilinear belt partition. The merger procedure is

summarized as the Algorithm 3.

106

Algorithm 3 Curvilinear Belt Partition Merger

if (I am a sensor affiliated with an curvilinear belt partition) thenif (I have 1-hop neighbor sensors) then

Exchange my hop count to my partition head with the neighbor sensorsif (neighborSensor.Dist2Head+my.Dist2Head)<(l + w)/3 then

Send Merger.Request to my partition headWait(myPartition.currentLength) from my partition headExchange myPartition.currentLength with the neighbor sensorsif ((myPartition.currentLength+neighSensorPartition.currentLength)<2(l + w)/3) then

Send Merger.Yes to my partition headMy partition head takes over merge procedure, communicate with meigh-borSensor.head to select new partition head

end ifend if

end ifend if

Sensors within curvilinear belt partitions periodically activate to detect and track

the object, while sensors outside curvilinear belt go to sleep status to reduce power

consumption. This will prolong the lifetime of the while sensor network.

6.6 Performance Evaluations

6.6.1 Simulation model

In our simulations, there is a 1000m-by-1000m square area with 1000 ∼ 4000

sensors randomly and uniformly deployed. The radio range of sensors is 30 ∼ 70m and

the number of sensors is varied in order to achieve different deployment density.

Without loss of generality, we simulate two large continuous objects in the square

area: a rectangle and a circle. The reason of using the rectangle and circle as target

continuous objects is that we are able to easily manipulate their boundary movement

and estimate boundary detection accuracy in real-time manner during our simulation.

107

1000 1500 2000 2500 3000 3500 40000.08

0.1

0.12

0.14

0.16

0.18

0.2

Total number of sensors

Err

or r

ates

rectangle object without dc rectangle object with dc circle object with dc

1000 1500 2000 2500 3000 3500 40000

200

400

600

800

1000

1200

1400

1600

1800

Total number sensors

Num

ber

of b

ound

ary

sens

ors


(a) (b)

Fig. 6.8. (a)When the number of sensors deployed in the 1000m-by-1000m field increasesfrom 1000 to 4000, the error rates of estimated boundary decrease. (b)When the numberof sensors deployed in the 1000m-by-1000m field increases from 1000 to 4000, the totalnumber of boundary sensors involved in boundary estimation increases.

The rectangle is initialized with width 500m, height 1000m, and centered in (250, 500).

Its height is fixed, and its right edge move toward right. In order to study the effect of

boundary movement to the curvilinear belt structure, we let the right edge moving right

in three different speeds: 20m, 35, and 50m per 2000 simulation time.

The circle is initialized with radius 250m and centered in (500, 500). In each time

slot, its radius increases by 50m per time slot until 400m. The sink is at (0, 0). We exam

the rectangle and circle boundary detection errors and message costs for detecting and

tracking them.

6.6.2 Evaluation criteria

To examine the effect of our dynamic curvilinear belt structure to the precision

of estimated boundary method, we propose the following evaluation criteria. Based

108

on the true boundaries, we first select boundary sensors, and count estimated points,

n, that the boundary may pass. For each estimated point, we calculate its shortest

physical distance to the true boundary line/curve. Then, we average the shortest physical

distances through all estimated points to get dav. We define the the ratio of dav to the

average hop distance of sensors as the error rate. The smaller the error rate, the better

performance achieved by our boundary estimation method. In order to study the impact

of sensor deployment to the precision of estimated boundary, we vary the number of

sensors deployed in the square area, average hop distance of sensors.

In order to study the efficiency of dynamic curvilinear belt structure in tracking

the continuous object and supporting boundary information fusion and dissemination,

we count the communication costs. The communication costs are the total number

messages sent for constructing, updating the dynamic curvilinear belt structure, and

boundary information dissemination. In a general sensor network model, sensor sends

message through omni-directional radio to its neighboring sensors within hop distance,

and the message sending is the most power-consuming operation of sensors [6, 28]. In

order to prolong the sensor network operating time, we try to minimize the number of

messages sending to save power. Since there is no previous research works for the issue,

we cannot compare the performance of our method with any other method. However,

we discuss the improvement in terms of communication costs by comparing with some

direct message collection schemes.

109

6.6.3 Results

We first study the boundary estimation with our proposed distributed boundary

estimation method. In Figure 6.8, the number of sensors deployed in the 1000m − by −

1000m field increases from 1000 to 4000. The error rates of estimated boundary decrease.

At the same time, the total number of boundary sensors involved in boundary estimation

increases.

The measured continuous objects are a rectangle and a circle. For the rectan-

gle object, its boundary is estimated based on two different boundary sensor selection

strategies: without network compactness distance applied and with network compact-

ness distance applied (1.5dc). The circle object boundary is estimated with compactness

distance applied. With compactness distance applied, the error rates of estimated bound-

ary for the two different objects both drop much faster than the error rates estimated

without compactness distance applied. Without compactness distance applied, the error

rates of estimated boundary for the rectangle object barely decrease even the density

increase significantly. The reasons are indicated by Figure 6.8(b): with the deployed sen-

sor density increasing, a boundary sensor has more neighboring sensors within its radio

range. Some of these neighboring sensors become boundary sensors when compactness

distance is applied for boundary selection. These redundant boundary sensors in the

small area generate inconsistent estimation of local boundary, which eventually increase

the error rates.

In Figure 6.9, the hop distance increases, which means the sensors have larger

radio range. Without compactness distance applied on, the total number of boundary

110

sensors increase sharply, while the error rates of corresponding boundary estimation drop

very little. With compactness distance applied on and the hop distance increases, the

number of selected boundary sensors keeps constant, and the error rates drop certainly

since error rate is equal to the ratio of average boundary distance error to hop distance.

30 35 40 45 50 55 60 65 700.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Hop distance

Err

or r

ates

rectangel object without dc rectangel object with dc circle object with dc

30 35 40 45 50 55 60 65 700

200

400

600

800

1000

1200

Hop distance

Num

ber

of b

ound

ary

sens

ors


(a) (b)

Fig. 6.9. (a)When hop distance of sensors increases from 30m to 70m, the error ratesof estimated boundary decrease. (b)When hop distance of sensors increases from 30m to70m, the number of selected boundary sensors keeps constant with compactness distanceapplied. The number of boundary sensors increase if they are selected based on hopdistance.

In order to study the performance of our proposed boundary localization methods

during the tracking the continuous object, we collect the error rates and number of

boundary sensors during the rectangle object’s right edge moving right in Figure 6.10

boundary moves from 300 to 600. Although the error rates of estimated boundary vary

a litter at different location, it keeps relatively constant at 0.15 without compactness

111

distance applied and 0.12 with compactness distance applied. Since sensors are randomly

deployed, sensors have different deployment density at different local area within the

square area. It makes error rates changing within a small range along the boundary

moves. The error rates corresponding boundary selection without compactness distance

(based on hop distance only) are always higher than those with compactness distance

applied. Similar phenomena happens to the number of boundary sensors when the

rectangle object’s right boundary moves right. The stability of the error rates and

numbers of boundary sensors indicates that our proposed boundary detection method is

effective and robust.

We also collect the error rates and number of boundary sensors during the circle

object’s radius increasing in Figure and the it radius increases, which means the object

expands and the length of its boundary increases as well. During the simulation, the

radius increases from 250 to 400. Although the error rates of estimated boundary vary a

litter at different location, it keeps relatively constant at 0.10 with compactness distance

applied Figure 6.11(a). Figure 6.11(b) shows the number of boundary sensors changes

when the circle object’s radius increases. The dot-line in Figure 6.11(b) has slop of 1.

The number of boundary sensors involved in boundary estimation deviates a lot while

roughly centered in the dot-line. That means that the number of boundary sensors

increases approximately linearly with the length of the boundary.

The above simulation results indicate that the application of network compact-

ness distance is an important step to achieve stable and effective boundary estimation.

In order to select the the a for best performance, we study the relation between error

rates and a and relation between the number of boundary sensors and a. 2000 sensors

112

300 350 400 450 500 550 6000

0.05

0.1

0.15

0.2

0.25

Location of rectange object boundary

Err

or r

ates

rectangle object without dc rectangle object with dc

300 350 400 450 500 550 6000

100

200

300

400

500

600

Location of rectangle object boundary

Num

ber

of b

ound

ary

sens

ors

rectangle object without dc rectangle object with dc

(a) (b)

Fig. 6.10. (a)When the rectangle object’s right boundary moves from 300 to 600,the error rates of estimated boundary are stable. (b)When the rectangle object’s rightboundary moves from 300 to 600, the numbers of boundary sensors of estimated boundaryare stable.

250 300 350 4000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Radius of circle object

Err

or r

ate

150 200 250 300 350 400

150

200

250

300

350

400

Radius of circle object

Num

ber

of b

ound

ary

sens

ors

(a) (b)

Fig. 6.11. (a)The error rates of the estimated boundary for a circle object are relativelyconstant when its radius increase. (b)The number of boundary sensors involved in acircle object boundary estimation are increasing approximately linearly with the lengthof the boundary.

113

are deployed in a 1000-by-1000 square area with hop distance 50. So, the compactness

distance is:

dc =

√

1000 × 1000

2000= 22.3606,

and

1 ≤ a ≤hopdistance

dc≈ 2.

When a increases from 1 to 2, both the number of boundary sensors and the error rates

increase in Figure 6.12. The number of boundary sensor increases even faster than the

error rates. This indicates a small a is preferable for boundary estimation. However, a

very small a generates very few boundary sensors or estimated points for a boundary,

which may not be sufficient to describe the target object’s spatial extents.

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

a

Err

or r

ate

circle object with dc rectangle object with dc

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 20

50

100

150

200

250

300

350

400

a

Num

ber

of b

ound

ary

sens

ors

circle object with dc rectangle object with dc

(a) (b)

Fig. 6.12. (a)When a increases from 1 to 2, error rates of estimated boundary increase.(b) When a increases from 1 to 2, the number of boundary sensors involved in boundaryestimation increases.

114

In order to study the procedure of our continuous object boundary tracking, we

do simulation with CSIM to exam the total message costs of tracking with our proposed

curvilinear belt structure. A separate process is created in our simulation to simulate

the movement of a boundary. The boundary moves forward a given distance at the end

of each time slot. Related results are shown in Figure 6.14.

There are 1000 sensors deployed in a 1000-by-1000 square area. The hop distance

of sensors is 50m. We first calculate the baseline of total communication costs based on

the following analysis. If there is no curvilinear belt structure or any other infrastructure

to help local boundary information fusion, the sink needs to collect all sensors reading of

the continuous object in each time slots in order to get the boundary information of the

object. Suppose the sink floods the network to discover shortest routes to each sensor,

and each sensors knows its shortest route in terms of hops to the sink, each sensor needs

to forward its reading through the shortest route at the end of each time slot. Without

lose of generality, the Figure 6.13 illustrates the shortest routes from each sensors to the

sink, which is the root of the flooding tree. The average length of the shortest route

from a sensor to the sink in our sensor network is about 17 hops. If each sensor sends

its reading to the sink separately through the shortest path, the total message costs are

1000 × 17 = 17000 messages sending for information fusion once. Of course, the total

costs may be partially reduced with some optimization protocols such as integrating a

sensor’s message content with messages of intermediate sensors along its shortest route

to the sink. But, the reduction for total number of message sent will be counteracted

by the increase of each message size. So, we use 17000 as baseline of message costs per

information fusion, and total message costs are 17000t, where t is the total time slots.

115

0

1

2

3

4

5

6

7

8

9

100 1 2 3 4 5 6 7 8 9 10

Fig. 6.13. Shortest path from sensors to the sink in the baseline case.

Clearly, the totally message costs for constructing, updating, and tracking the boundary

with our proposed curvilinear belt structure is much smaller than the 17000t as shown

in Figure 6.14.

Figure 6.14(a) shows totally message costs for monitoring the boundary travelling

from 0 to 300 at different speeds. Please notice that the time it takes for travelling at

different speeds are different. In Figure 6.14(b), for the same boundary, different numbers

of curvilinear belt partition will cause different total message costs. The total number of

message keep constant in some time period, while it increases a lot in next time period.

The reason is that the boundary may be within the coverage of current curvilinear belt

structure. When it moves out of the current curvilinear belt structure, the curvilinear

belt needs be re-constructed, which will cause many message costs. Since the width of

the curvilinear belt structure is defined by the number of hops, increase of hop distance

will generate a wider coverage area by the curvilinear belt structure. So, a large hop

116

distance cause less total message costs during boundary moving, as shown in Figure

6.14(c). Similarly, for a fixed hop distance, width in terms of hop count increases will

also make the coverage area larger. Thus, less message costs for curvilinear belt structure

update in Figure 6.14(d).

6.7 Summary

In summary, our contributions in the research include: (1) We identify the impor-

tant application of detection and tracking large-scale continuous objects or phenomena,

which is barely investigated in existing research. The large continuous objects detec-

tion and tracking represents a new class of object detection and tracking tasks in sensor

networks. We also present the challenges in performing energy-efficient and real-time de-

tection and tracking these objects. (2) We propose a robust and energy-efficient method

for accurate large continuous object location. The method selects the “most relevant”

sensors, boundary sensors, to perform the objects’ location and boundary estimation

in distributed manner. The mechanism enables most sensors in the network in sleep

mode to reduce power consumption. (3) In order to perform energy-efficient boundary

tracking, we propose a curvilinear belt structure along the objects’ boundary to organize

sensors close to the boundary to perform real-time tracking of the movement of objects’

boundaries. With the structure, only sensors that are within a given number of hops

to the objects’ boundary active and perform boundary information fusion, while other

sensors keep sleep. The structure is further divided into many partitions so that each

partition is able to adaptively self-update according to the different mobility of different

portions of the boundary. For example, when boundaries move, the structure partition

117

0 50 100 150 200 250 3001000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

Boudary travelling distance

Tot

al m

essa

ge c

osts

20m/200s 35m/200s 50m/200s

0 20 40 60 80 100 120 140 160 1801000

1500

2000

2500

3000

3500

4000

4500

Boundary travelling distance

Tot

al m

essa

ge c

osts

3 parititions 4 parititions 5 partitions

(a) (b)

0 20 40 60 80 100 120 140 160 1801500

2000

2500

3000

3500

4000

4500

5000

5500


Tot

al m

essa

ge c

osts

hop distance=30 hop distance=50 hop distance=70

0 20 40 60 80 100 120 140 160 1801000

1500

2000

2500

3000

3500

4000

4500

5000

5500


Tot

al m

essa

ge c

osts

width=3 hops width=4 hops width=5 hops

(c) (d)

Fig. 6.14. (a)Total message costs during boundary travelling from 0 to 300 with differentspeeds. (b)Total message costs during boundary travelling from 0 to 180 with differentnumber of partitions of the curvilinear belt structure. (c)Total message costs duringboundary travelling from 0 to 180 with different hop distances. (d)Total message costsduring boundary travelling from 0 to 180 with curvilinear belt structure in differentwidth.

118

dynamically updates its sensors’ membership so that the boundary is within the region

covered by the structure.

119

Chapter 7

Conclusions and Future Work

7.1 Summary

The primary functions of sensor networks include localization, tracking, naviga-

tion, and sensing. Sensor localization in sensor networks is fundamental and crucial

because sensor position information is prerequisite for positioning objects, tracking ob-

jects, targeting, routing in network, and many other tasks. However, in most cases,

sensors are randomly deployed or are deployed in inaccessible terrains. It is desirable to

develop robust and efficient algorithms that enable sensors to perform self-localization.

As one of the most important functions of sensor networks, object localization

and their tracking have attracted many research efforts. Large continuous objects, such

as spreading wild fires and bio-chemical spills inside buildings, usually have a coverage

far larger than the sensor’s sensing range. Identifying the distribution and spatial extent

of the large continuous objects and tracking their movement require the collaboration of

a large number of sensors. This collaboration involves high communication and complex

information processing. Therefore, detection and tracking of the objects represents a

class of important research issues in sensor networks.

In the dissertation, we studied the issues of sensor localization, objects localization

and their movement tracking in wireless sensor networks. We identified challenges of

120

these problems, proposed algorithms, and quantified their superior performance with

simulations.

We surveyed state-of-the-art of research relevant to localization, and identified

challenges to robust and accurate localization. These challenges are caused by sensor’s

irregular radio pattern, anisotropic sensor network topology, and complex and heteroge-

nous terrains. We discovered the inherent connections between the issues of sensor local-

ization and the techniques of data dimensionality manipulation. We therefore developed

a centralized sensor localization algorithm, a distributed sensor localization algorithm

and a robust sensor localization algorithm are developed to overcome these challenges

[52, 49, 50]. They have the advantages of tolerating sensors’ distance measurement

errors, reducing errors caused by anisotropic network topology, and eliminating the ac-

cumulation of measurement errors. In addition, three differentiated sensor localization

methods were proposed to provide scalable and energy-efficient sensor localization [52].

This is the first research effort on scalable and energy-efficient sensor localization, to our

knowledge.

We proposed distributed algorithms to locating the boundary of continuous ob-

jects in the coverage of a sensor network. Since the continuous objects usually span a

large area, the fusion and dissemination of local boundary information is very challeng-

ing. We also proposed a dynamic cluster structure and an belt structure that represent

the boundary information and also facilitate the fusion and dissemination of boundary

information in a sensor network. Mobility behaviors of continuous objects, such as dif-

fusion, change in size, merging, and splitting into multiple relatively smaller continuous

121

objects, cause many difficulties in tracking objects and their determining boundary infor-

mation. Our proposed structures overcome these difficulties and enable efficient tracking

in real-time fashion [51, 53]. The research fills the critical void in object detection and

tracking research.

7.2 Future Research

The importance of the sensor network is well-accepted by the research community.

There are many open issues to be addressed. Along the way of the dissertation research,

we have identified several interesting research problems in the area.

We envision a Bionic Sensor Network framework. In this framework, sensor net-

works not only passively sense and collect information but also actively adjust themselves

to respond to the dynamic environment and internal conditions. Most sensor network

applications are developed upon one or several elementary service components includ-

ing localization, target detection, target tracking, coverage, and communication. In the

framework of Bionic Sensor Network, each elementary service component is capable of

self-adaptation, active response, and differentiated reaction. Currently, the localization

service component was developed in the framework based on my previous research. The

localization service component is able to provide scalable and differentiated localization

for the sensor network.

Many sensor networks are deployed in unattended or adversarial environments.

This opens many challenges in the security field since these sensor networks are more

prone to various intrusions and denial-of-service attacks. It is critical to design certain

security mechanisms that provide confidentiality and authentication for sensor network

122

operation. Due to resource limitation in sensor nodes, it is particularly challenging to

secure sensor networks.

Sensor networks will collect large amount of data. Efficient storage, organization,

retrieval and mining of these information are very challenging and important research

tasks. Traditional techniques need to be tailored or broadened to address the unique

challenges.

123

References

[1] Alert systems. http://www.alertsystems.org/.

[2] Matlab. http://www.mathworks.com/.

[3] Wireless intergated network systems(wins). http://wins.rsc.rockwell.com/.

[4] G.H. Ahn, A. T. Campbell, A. Veres, and L. H. Sun. Swan: Service differentiation

in stateless wireless ad hoc networks. In IEEE INFOCOM, New York, June 2002.

[5] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cyirci. A survey on sensor

networks. IEEE Communications Magazine, 40(8):102–114, 2002.

[6] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cyirci. Wireless sensor

networks: A survey. Computer Networks, 38(4):393–422, 2002.

[7] J. Aspnes, D. Goldenberg, and Y. R. Yang. On the computational complexity

of sensor network localization. In Proceedings of First International Workshop on

Algorithmic Aspects of Wireless Sensor Networks (ALGOSENSORS 2004), Turku,

Finland, July 2004.

[8] B. R. Badrinath, M. Srivastava, K. Mills, J. Scholtz, and K. Sollins. Special issue on

smart spaces and environments. IEEE Personal Communications, October 2000.

[9] J. Beutel. Geolocation in a picoradio environment. Master’s thesis, ETH Zurich,

1999.

124

[10] S. Bhatnagar, B. Deb, and B. Nath. Service differentiation in sensor networks.

In Fourth International Symposium on Wireless Personal Multimedia Communi-

cations, Aalborg, Denmark, September 2001.

[11] I. Borg and P. Groenen. Modern multidimensional scaling theroy and applications.

Series in Statistics. Springer-Verlag, New York, 1997.

[12] M. Braukus, J. Bluck, and M. Goodkind. Developing computerized breast cancer

diagnostic tool. National Aeronautics and Space Administration, (1):98–184, 1998.

[13] Bulusu. Self-Configuring Localization Systems. PhD thesis, University of Califor-

nia, Los Angeles, 2002.

[14] N. Bulusu, J. Heidemann, V. Bychkovskiy, and D. Estrin. Density-adaptive beacon

placement algorithms for localization in ad hoc wireless networks. In Proceedings

of the 21st Annual Joint Conference of the IEEE Computer and Communications

Societies (INFOCOM-21), New York, NY, June 2002.

[15] N. Bulusu, J. Heidemann, and D. Estrin. Gps-less lowcost outdoor localization for

very small devices. IEEE Personal Communications, 7(5):28–34, October 2000.

[16] N. Bulusu, J. Heidemann, and D. Estrin. Adaptive beacon placement. In Pro-

ceedings of the 21st International Conference on Distributed Computing Systems

(ICDCS-21), pages 489–498, Phoenix, Arizona, USA, April 2001.

125

[17] S. Capkun, M. Hamdi, and J.-P. Hubaux. Gps-free positioning in mobile ad-hoc

networks. In Proceedings of Hawaii Int. Conf. on System Sciences (HICSS-34),

pages 3481–3490, Maui, Hawaii, January 2001.

[18] J. Chen, K. Yao, and R. E. Hudson. Source localization and beamforming. IEEE

Signal Processing Magazine, 19(2), March 2002.

[19] X. Cheng, A. Thaeler, G. Xue, and D. chen. Tps: A time-based positioning scheme

for outdoor wireless sensor networks. In Proceedings of the 23rd Conference of

the IEEE Communications Society (IEEE INFOCOM), Hongkong, China, March

2004.

[20] K. Chintalapudi and R. Govindan. Localized edge detection in sensor fields. In

Proceedings of the IEEE ICC Workshop on Sensor Network Protocols and Appli-

cations, April 2003.

[21] K. Chintalapudi, R. Govindan, G. Sukhatme, and A. Dhariwal. Ad-hoc localization

using ranging and sectoring. In Proceedings of the 23rd Conference of the IEEE

Communications Society (IEEE INFOCOM), Hongkong, China, March 2004.

[22] K. Dasgupta, K. Kalpakis, and P. Namjoshi. An efficient clustering-based heuristic

for data gathering and aggregation in sensor networks. In Proceedings of the IEEE

Wireless Communications and Networking Conference (WCNC), March 2003.

126

[23] D. Devaguptapu and B. Krishnamachari. Applications of localized image process-

ing techniques in wireless sensor networks. In SPIE’s 17th Annual International

Symposium on Aerospace/Defense Sensing, Simulation, and Controls, (Aerosense

’03), Orlando, Florida, April 2003.

[24] L. Doherty, K. Pister, and L. El Ghaoui. Convex position estimation in wireless

sensor networks. In Proceedings of the 20th Annual Joint Conference of the IEEE

Computer and Communications Societies (INFOCOM-20), pages 1655–1663, An-

chorage, AK, April 2001.

[25] T. Eren, D. Goldenberg, W. Whiteley, Y. Yang, A. Morse, B. Anderson, and

P. Belhumeur. Rigidity, computation, and randomization in network localization.

In Proceedings of the 23rd Conference of the IEEE Communications Society (IEEE

INFOCOM), Hong Kong, China, March 2004.

[26] D. Estrin, R. Govindan, J. Heidemann, and S. Kumar. Next century challenges:

Scalable coordination in sensor networks. In Proceeding of 5th ACM International

Conference on Mobile Computing and Networking (MOBICOM), pages 263–270,

1999.

[27] D. Fox, W. Burgard, H. Kruppa, and S. Thrun. A probabilistic approach to

collaborative multi-robot localization. Autonomous Robots, 8(3):325–344, 2000.

[28] S. R. Gandham, R. Musunuri, P. Rentala, and U. Saxena. A survey on self-

organizing wireless sensor networks. In Industrial Information Technology Hand

Book. CRC Press, March 2004.

127

[29] G. Golub. Matrix Computations. The Johns Hopkins University Press, 1996.

[30] P. E. Green, F. J. Caromone, and S. M. Smith. Multidimensional scaling: concepts

and applications. Allyn and Bacon, Boston, MA, 1989.

[31] L. Guibas. Sensing, tracking and reasoning with relations. IEEE Signal Processing

Magazine, 19(2), March 2002.

[32] A. Harter, A. Hopper, P. Steggles, A. Ward, and P. Webster. The anatomy of a

context-aware application. In Proceedings of the Fifth Annual ACM/IEEE Inter-

national Conference on Mobile Computing and Networking (MobiCom 99), pages

59–68, Seattle, WA, August 1999.

[33] T. He, C. Huang, B. Blum, J. Stankovic, and T. Abdelzaher. Range-free local-

ization schemes for large scale sensor networks. In Proceedings of the 9th annual

international conference on Mobile computing and networking, pages 81–95, 2003.

[34] M. T. Heath. Scientific Computing: An Introductory Survey. McGraw-Hill. New

York, 1997.

[35] W. Heinzelman, A. P. Chandrakasan, and H. Balakrishnan. An Application-

Specific Protocol Architecture for Wireless Microsensor Networks. IEEE Transac-

tions on Wireless Communications, 1(4):660, 2002.

[36] W. Heinzelman, A.P. Chandrakasan, and H. Balakrishnan. Energy-efficient com-

munication protocols for wireless microsensor networks. In Proceedings of Hawaiian

International Conference on Systems Science, 2000.

128

[37] J. Hightower and G. Borriello. Location Systems for Ubiquitous Computing. IEEE

Computer, 34(8):57, 2001.

[38] J. Hightower and G. Borriello. A survey and taxonomy of location systems for

ubiquitous computing. Technical Report UW-CSE 01-08-03, U. of Washington,

Computer Science and Engineering, Seattle, WA, August 2001.

[39] J. Hill and D. Culler. A wireless embedded sensor architecture for system-level

optimization. Technical report, Computer Science Department, University of Cal-

ifornia at Berkeley, 2002.

[40] J. Hill, R. Szewczyk, S. Holar A. Woo, D. Culler, and K. S. J.Pister. System

architecture directions for networked sensors. Operating Systems Review, 34:93–

104, 2000.

[41] J. Hill, R. Szewczyk, and A. Woo. Tinyos: Operating system for sensor networks.

Technical report, Electronics Research Laboratory of the University of California,

Berkeley, 2001.

[42] J. Hill, R. Szewczyk, A. Woo, S. Hollar, and D.C.K. Pister. System architecture

directions for networked sensors. In ACM SIGMOD international conference on

on Management of data, San Diego, CA, June 2000.

[43] C. Hofner and G. Schmidt. Path planning and guidance techniques for an au-

tonomous mobile cleaning robot. Robotics and Autonomous Systems, 14:199–212,

May 1998.

129

[44] A. Howard, M. Mataric, and G. S. Sukhatme. Localization for mobile robot teams

using maximum likelihood estimation. In Proceedings of the IEEE/RSJ Interna-

tional Conference on Intelligent Robots and Systems, pages 434–459, Lausanne,

Switzerland, October 2002.

[45] A. Howard, M. J. Mataric, and G. S. Sukhatme. An incremental self-deployment

algorithm for mobile sensor networks. J. of Autonomous Robots (Special Issue on

Intelligent Embedded Systems), 13(2):113–126, 2002.

[46] A. Howard, M. J Mataric, and G. S. Sukhatme. Mobile sensor network deployment

using potential fields: A distributed, scalable solution to the area coverage problem.

In Distributed Autonomous Robotic Systems 5: Proceedings of the 6th International

Conference on Distributed Autonomous Robotic Systems (DARS02), pages 299–

308, Fukuoka, Japan, June 2002.

[47] Q. Huang, C. Lu, and G. Roman. Spatiotemporal multicast in sensor networks. In

Proceedings of the 1th Annual ACM Conference on Embedded Networked Sensor

Systems (ACM SenSys), pages 205–217, 2003.

[48] C. Intanagonwiwat, R. Govindan, and D. Estrin. Directed diffusion: a scalable and

robust communication paradigm for sensor networks. In Proceedings of the Sixth

Annual International Conference on Mobile Computing and Networks (MobiCom),

pages 56–67, 2000.

130

[49] X. Ji and H. Zha. Multidimensional scaling based sensor positioning algorithms

in wireless sensor networks. In Proceedings of 1th Annual ACM Conference on

Embedded Networked Sensor Systems (ACM SenSys), Los Angeles, Ca, November

2003.

[50] X. Ji and H. Zha. A robust sensor localization algorithm in wireless ad hoc sensor

networks. In 12th International Conference on Computer Communications and

Networks. (ICCCN 03), Dallas, Tx, October 2003.

[51] X. Ji and H. Zha. Large continuous objects detection and tracking in wireless

ad-hoc sensor network. Submitted to Journal, 2004.

[52] X. Ji and H. Zha. Sensor positioning in wireless ad-hoc sensor networks with mul-

tidimensional scaling. In Proceedings of the 23rd Conference of the IEEE Commu-

nications Society (IEEE INFOCOM), Hongkong, China, March 2004.

[53] X. Ji, H. Zha, and J. Metzner. Dynamic cluster structure for entity detection and

tracking in wireless ad-hoc sensor network. In Proceedings of the 2004 International

Conference on Communications (ICC 2004), Paris, France, June 2004.

[54] J. M. Kahn, Randy H. Katz, and K. S. J. Pister. Next century challenges: Mobile

networking for “smart dust”. In Proc. ACM/IEEE International Conference on

Mobile Computing and Networking(MobiCom 99), Seattle, WA, August 1999.

[55] K. Kalpakis, K. Dasgupta, and P. Namjoshi. Maximum lifetime data gathering

and aggregation in wireless sensor networks. In Proceedings of IEEE Networks’02

Conference, 2002.

131

[56] L.M. Kaplan, Q. Le, and P. Molnar. Maximum likelihood methods for bearings-

only target localization. In Proceedings of IEEE ICASSP, pages 554–557, Salt Lake

City, UT, May 2001.

[57] B. Karp and H. T. Kung. GPSR: Greedy perimeter stateless routing for wireless

networks. In Proc. 6th Intl. Conf. on Mobile Computing and Networking (ACM

Mobicom), 2000.

[58] C. D. Kidd, R. J. Orr, G. D. Abowrd, C. G. Atkeson, I. A. Essa, B. MacIntyre,

E. Mynatt, T. E. Starner, and W. Newstetter. The aware home: A living laboratory

for ubiquitous computing research. In Proc. 2nd Intl. Workshop on Cooperative

Buildings, 1999.

[59] B. Krishnamachari, S.B. Wicker, and R. Bejar. Phase transition phenomena in

wireless ad-hoc networks. In Proceedings of IEEE GLOBECOM, San Antonio,

TX, November 2001.

[60] H. T. Kung and D. Vlah. Efficient location tracking using sensor networks. In IEEE

Wireless Communications and Networking Conference (WCNC), March 2003.

[61] D. Li, K. Wong, Y. Hu, and A. Sayeed. Detection, classification and tracking of

targets in distributed sensor network. IEEE Signal Processing Magazine, 19(2):17–

29, March 2002.

132

[62] J. Liu, P. Cheung, L. Guibas, and F. Zhao. A dual-space approach to tracking

and sensor management in wireless sensor networks. In ACM International Work-

shop on Wireless Sensor Networks and Applications Workshop, Atlanta, September

2002.

[63] J. Liu, J. Reich, P. Cheung, and F. Zhao. Distributed group management for track

initiation and maintenance in target localization applications. In Proceedings of 2nd

International Workshop on Information Processing in Sensor Networks (IPSN),

April 2003.

[64] C. Lu, B. M. Blum, T. F. Abdelzaher, J. A. Stankovic, and T. He. Rap: A real-time

communication architecture for large-scale wireless sensor networks. In Proceedings

of the 8th IEEE Real-Time and Embedded Technology and Applications Symposium

(RTAS 2002), pages 55–66, San Jose, CA, September 2002.

[65] A. Mainwaring, J. Polastre, R. Szewczyk, D. Culler, and J. Anderson. Wireless sen-

sor networks for habitat monitoring. In ACM International Workshop on Wireless

Sensor Networks and Applications, Atlanta, GA, September 2002.

[66] A. Mainwaring, J. Polastre, R. Szewczyk, D. Culler, and J. Anderson. Wireless

sensor networks for habitat monitoring. In In proceeding of ACM International

Workshop on Wireless Sensor Networks and Applications, September 2002.

[67] C. Meesookho, S. Narayanan, and C. Raghavendra. Collaborative clasification

applications in sensor networks. In Proceedings of the Second IEEE Multichannel

and Sensor array signal processing workshop, Arlington, VA, 2002.

133

[68] R. Min, M. Bhardwaj, S. Cho, Nathan Ickes, E. Shih, A. Sinha, A. Wang, and A. P.

Chandrakasan. Energy-centric enabling technologies for wireless sensor networks.

IEEE Transactions on Wireless Communications, 9(4):28, 2002.

[69] A Morrison, G. Ross, and M. Chalmers. Combining and comparing clustering and

layout algorithms. Technical report, Computing Science Department, University

of Glasgow, 2003.

[70] D. Niculescu and B. Nath. Ad-hoc positioning system. In Proceeding of IEEE

Global Communications Conference (GLOBECOM), pages 2926–2931, November

2001.

[71] D. Niculescu and B. Nath. Ad hoc positioning system (aps) using aoa. In Proceed-

ings of the 20th Annual Joint Conference of the IEEE Computer and Communi-

cations Societies (INFOCOM-20), April 2003.

[72] D. Niculescu and B. Nath. Error characteristics of ad hoc positioning systems. In

Proceedings of Fifth International Symposium on Mobile Ad Hoc Networking and

Computing (Mobihoc 2004), Tokyo, Japan, May 2004.

[73] R. Nowak and U. Mitra. Boundary estimation in sensor networks: Theory and

methods. In Proceedings of the Second International Workshop on Information

Processing in Sensor Networks, Palo Alto, CA, April 2003.

[74] N. B. Priyantha, A. Chakraborty, and H. Balakrishnan. The cricket location-

support system. In Proc. 6th Intl. Conf. on Mobile Computing and Networking

(ACM Mobicom), 2000.

134

[75] N. B. Priyantha, A. Miu, and H. Balakrishnan. The cricket compass for context-

aware applications. In Proceeding of 7th ACM International Conference on Mobile

Computing and Networking (MOBICOM), pages 1–14, Rome, Italy, July 2001.

[76] T. S. Rappaport. Wireless Communications: Principles and Practice. Prentice

Hall PTR, 1996.

[77] S. Ratnasamy, M. Handley, R. Karp, and S. Shenker. Topologically-aware overlay

construction and server selection. In Proc. IEEE Infocom, pages 1190–1199, New

York, NY, 2002.

[78] S. Ratnasamy, B. Karp, L. Yin, F. Yu, D. Estrin, R. Govindan, and S. Shenker.

Ght: A geographic hash table for data-centric storage. In Proc. First ACM Intl.

Workshop on Wireless Sensor Networks and Applications (WSNA’02), Atlanta,

GA, 2002.

[79] S. Roumeliotis and G. Bekey. Collective localization: a distributed kalman fil-

ter approach. In Proceedings of IEEE International Conference on Robotics and

Automation (ICRA), pages 2958–2965, San Francisco, May 1999.

[80] C. Savarese. Robust positioning algorithms for distributed ad hoc wireless sensor

networks. Master’s thesis, University of California at Berkeley, 2002.

[81] C. Savarese, J. Rabaey, and J. Beutel. Locationing in distributed ad-hoc wireless

sensor networks. In IEEE Int. Conf. on Acoustics, Speech, and Signal Processing

(ICASSP), pages 2037–2040, Salt Lake City, UT, May 2001.

135

[82] A. Savvides, W. Garber, S. Adlakha, R. Moses, and M. Srivastava. On the error

characteristics of multihop node localization in wireless sensor networks. In Pro-

ceedings of Second International Workshop on Information Processing in Sensor

Networks (IPSN 2003), pages 317–332, Palo Alto, CA, April 2003.

[83] A. Savvides, C.-C. Han, and M. Srivastava. Dynamic fine-grained localization in

ad-hoc networks of sensors. In The 7th ACM Int. Conf. on Mobile Computing and

Networking (Mobicom), pages 166–179, Rome, Italy, July 2001.

[84] S. S. Schiffman, M. L. Reynolods, and F. W. Young. Introduction to multidimen-

sional scaling. Academic Press, New York, 1981.

[85] J.S. Scholl, L.P. Clare, and J.R. Agre. Wavelet packet-based target classification

schemes. In Meetings of IRIS Specialty Group on Acoustic and Seismic Sensing,

Laurel, MD, September 1998.

[86] L. Schwiebert, S. K. S. Gupta, P. Siy, and G. Auner. A biomedical smart sensor

for the visually impaired.

[87] L. Schwiebert, S. K. S. Gupta, and J. Weinmann. Research challenges in wireless

networks of biomedical sensors. In Mobile Computing and Networking, pages 151–

165, 2001.

[88] G. T. Sibley, M. H. Rahimi, and G. S. Sukhatme. Robomote: A tiny mobile robot

platform for large-scale sensor networks. In Proceedings of the IEEE International

Conference on Robotics and Automation (ICRA2002), 2002.

136

[89] S. Tabbane. Location management methods for third-generation mobile systems.

IEEE Communications, 35:72–85, 1997.

[90] G. Tel. Introduction to Distributed Algorithms. Cambridge University Press, 2000.

[91] S. Thrun, D. Fox, W. Burgard, and F. Dellaert. Robust monte carlo localization

for mobile robots. Artificial Intelligence, 128(1):99–141, Summer 2001.

[92] A. Ward, A. Jones, and A. Hopper. A new location technique for the Active Office.

IEEE Personal Communications Magazine, 4(5):42, 1997.

[93] B. Warneke, M. Last, B. Liebowitz, and K.S.J. Pister. Smart dust: Communicating

with a cubic-millimeter computer. IEEE Computer, 34(1):44–51, 2001.

[94] M. Weiser. The computer for the 21st century. Scientific American, 43(3):66–75,

September 1991.

[95] M. Weiser. Ubiquitous computing. IEEE Computer, October 1993.

[96] G. Welch, G. Bishop, L. Vicci, S. Brumback, K. Keller, and D. Colucci. The hiball

tracker: High-performance wide-area tracking for virtual and augmented environ-

ments. In Proceedings of Symposium on Virtual Reality Software and Technology,

pages 1–10, December 1999.

[97] B. H. Wellenhoff, H. Lichtenegger, and J. Collins. Global positions system: theory

and practice. Springer-Verlag, 1997.

137

[98] E. Welsh, W. Fish, and P. Frantz. GNOMES: A Testbed for Low-Power Hetero-

geneous Wireless Sensor Networks. In IEEE International Symposium on Circuits

and Systems (ISCAS), Bangkok, Thailand, May 2003.

[99] T. Yan, T. He, and J. A. Stankovic. Differentiated surveillance for sensor networks.

In Proc. First ACM SenSys 2003, Los Angeles, CA, November 2002.

[100] K. Yao, R.E. Hudson, C.W. Reed, T.L. Tung, D. Chen, and J. Chen. Estima-

tion and tracking of an acoustic/seismic source using a beamforming array based

on residual minimizing methods. In Proceedings of IRIA-IRIA, pages 152–163,

January 2001.

[101] F. Ye, H. Luo, J. Cheng, S. Lu, and L. Zhang. A two-tier data dissemination

model for large-scale wireless sensor networks. In Proceedings of Eighth Annual

International Conference on Mobile Computing and Networking (Mobicom), pages

148–159, Atlanta, GA, September 2002.

[102] F. Zhao, J. Shin, and J. Reich. Inforamtion-driven dynamic sensor collaboration

for target tracking. IEEE Signal Processing Magazine, 19(2):61–72, March 2002.

Vita

Xiang Ji received the B.S. degree from the Department of Computer Science and

Technology, University of Science and Technology of China, Hefei, China in 1999 and

the M.S. degree in Computer Science from The University of Western Ontario, Canada

in 2000. Since August 2000, he has been a Ph.D student in the Department of Computer

Science and Engineering, The Pennsylvania State University, University Park, PA. He

spent the summer of 2001 and 2002 working at the NEC USA Computer and Com-

munications Research Laboratory and Lawrence Berkeley National Laboratory, respec-

tively. His current research interests include information processing in sensor networks,

data mining, and information retrieval. He is a student member of the Association for

Computing Machinery (ACM) and the Institute of Electrical and Electronics Engineers

(IEEE).

LOCALIZATION ALGORITHMS FOR WIRELESS SENSOR …

Documents

Transcript of LOCALIZATION ALGORITHMS FOR WIRELESS SENSOR …