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
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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
3.5 A broadcast initialized by node S collects 24 pairwise distances . . . . . 44
3.6 A broadcast initialized by node S collects 34 pairwise distances . . . . . 44
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
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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
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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.
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����������������������������������������
�����������������������������������
�����������������������������������
������������������
������������������
������������������
������������������
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
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����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������
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
Fig. 3.5. A broadcast initialized by node S collects 24 pairwise distances
B
A
C
GD
F E
rS
Fig. 3.6. A broadcast initialized by node S collects 34 pairwise distances
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
Hop Measurement Error
Err
or R
ates
Localization−along−curveLocalization−with−correctionLocalization−within−region
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
Hop Measurement Error
Err
or R
ates
Localization−along−curveLocalization−with−correctionLocalization−within−region
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
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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
rectangle object without dc rectangle object with dc circle object with dc
(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
rectangle object without dc rectangle object with dc circle object with dc
(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
Boundary travelling distance
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
Boundary travelling distance
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
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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).