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LOCATION AND TOPOLOGY DISCOVERY IN WIRELESS SENSOR NETWORKS
By
CHRISTOPHER JERRY MALLERY
A dissertation submitted in partial fulfillment ofthe requirements for the degree of
DOCTOR OF PHILOSOPHY
WASHINGTON STATE UNIVERSITYSchool of Electrical Engineering and Computer Science
MAY 2009
c© Copyright by CHRISTOPHER JERRY MALLERY, 2009All rights reserved
c© Copyright by CHRISTOPHER JERRY MALLERY, 2009All rights reserved
To the Faculty of Washington State University The members of the Committee appointed to examine the dissertation of CHRISTOPHER JERRY MALLERY find it satisfactory and recommend that it be accepted. ______________________________ Muralidhar Medidi, Chair ______________________________ Sirisha Medidi ______________________________ Carl H. Hauser
ii
ACKNOWLEDGEMENT
Foremost, I would like to thank my advisor Dr. Murali Medidi. He has been a mentor to me
in all things, both professionally and personally, and most importantly, he has been a valuable
friend. In addition, I would also like to thank the rest of my committee, Dr. Sirisha Medidi and
Dr. Carl Hauser, for their valuable input and advice throughout my research and program of study.
The School of Electrical Engineering and Computer Science also deserves acknowledgement for
funding my graduate studies, without which this dissertation would likely not be possible. I would
also like to acknowledge Dirk Robinson and Rob Rydberg for their infinite patience reviewing the
mathematic content that was crucial to my research. Last, but certainly not least, I would like
to give great thanks to Jack Hagemeister and my wife, Janette Mallery, for having a seemingly
endless supply of faith in me and never doubting that I would finish my Ph.D.
iii
LOCATION AND TOPOLOGY DISCOVERY IN WIRELESS SENSOR NETWORKS
Abstract
by Christopher Jerry Mallery, Ph.D.Washington State University
May 2009
Chair: Muralidhar Medidi
Although the specifics of sensor network deployment scenarios are entirely application domain
specific, it is envisioned that wireless sensor networks are densely deployed over large monitoring
areas. The post-deployment discovery of location and topological information in arbitrarily de-
ployed wireless sensor network is critical to the effective use of a wireless sensor network. Funda-
mental to wireless sensor networks is the problem of developing a low-cost GPS-free localization
technique. Therefore, we first present ANIML, a straightforward, iterative, anchor-free, range-
aware, relative localization technique for wireless sensor networks. Through simulation, despite
using a non-idealized MAC, we show that ANIML provides good relative localization in uniform,
C-shaped and non-uniform topologies. However, while knowing the physical positions of every
node in the network provides information about the deployed topology of a wireless sensor net-
work, it does not provide a complete view of a network’s topology, such as the shape of the network
deployment. The boundaries of the network have a physical correspondence to the environment
in which the sensors are deployed. Therefore, we next present a robust, distributed technique that
addresses the problem of boundary recognition in wireless sensor networks. We show that our
boundary recognition technique constructs accurate perimeters (i.e. correctly bounding all nodes)
in randomly deployed topologies of varying densities, perturbed grid topologies of varying den-
sities and in sparsely populated/low-density topologies, in addition to highly irregularly shaped
iv
connectivity holes and networks. Lastly, we address the problem of edge detection in wireless sen-
sor networks. Edge detection is the idea of reducing data analysis overhead through the geometric
identification of sensed phenomena within a sensor network. We adapt our boundary recognition
technique to address the more general problem of edge detection in wireless sensor networks. Our
edge detection technique keeps inter-group communication to a minimum, while still constructing
correct outer perimeters in the presence of anomalous perimeter crossings and phenomena wholly
surrounded by other phenomena. We show that our technique constructs accurate perimeters in
randomly deployed topologies of varying densities, perturbed grid topologies of varying densities
and in sparsely populated/low-density topologies, in addition to highly irregularly shaped phenom-
ena and networks.
v
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
CHAPTER
1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Geographic Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Simple Distance Estimation using RSSI . . . . . . . . . . . . . . . . . . . . . . . 7
3. LOCALIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2.1 Range-Aware Localization . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2.2 Hop-Based Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2.3 Iterative Multilateration . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2.4 Underwater Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3.1 ANIML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
vi
3.3.2 Improving ANIML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.3 ANIML-Abs & ANIML-Hop . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.1 Comparison of Basic ANIML using 1-Hop vs. 2-Hop Information . . . . . 27
3.4.2 Basic ANIML vs. Improved ANIML . . . . . . . . . . . . . . . . . . . . 28
3.4.3 Uniform Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4.4 C-shaped Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.5 Non-Uniform Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.6 In the Presence of Obstacles . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.4.7 Using RSSI to Estimate Distance . . . . . . . . . . . . . . . . . . . . . . 37
3.5 Sea-ANIML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.1 Sea-ANIML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5.2 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4. BOUNDARY RECOGNITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3.1 Outer perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.2 Inner perimeter(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.4 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4.1 Effect of node distribution and density . . . . . . . . . . . . . . . . . . . . 67
4.4.2 Further examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
vii
5. EDGE DETECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.3.1 Outer perimeter(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3.2 Identifying the relationships between sensed phenomena . . . . . . . . . . 87
5.3.3 Inner perimeter(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3.4 Mitigate unresolved relationships between outer perimeters . . . . . . . . . 95
5.4 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4.1 Effect of node distribution and density . . . . . . . . . . . . . . . . . . . . 97
5.4.2 Further examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
viii
LIST OF TABLES
Page
3.1 Reported Results of ILS, MDS-MAP(P) and SDP . . . . . . . . . . . . . . . . . . 33
5.1 Sensed Phenomena Outer Perimeter Relationship Identification Criteria . . . . . . 92
ix
LIST OF FIGURES
Page
3.1 Basic Iterative ANIML Technique . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Least-squares Multilateration (k = 4) . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Comparison of ANIML using 1-hop and 2-hop Information . . . . . . . . . . . . . 23
3.4 1-Hop ANIML vs. 2-Hop ANIML . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5 Enhanced ANIML vs. the Basic ANIML Technique . . . . . . . . . . . . . . . . . 30
3.6 ANIML Convergence Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.7 Localization Effectiveness of ANIML in Uniform Topologies . . . . . . . . . . . . 33
3.8 Localization in C-shaped Networks . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.9 Localization in Irregular Densities . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.10 Localization with Obstacles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.11 Distance Estimates from TwoRayGround Propagation Model . . . . . . . . . . . . 38
3.12 Localization accuracy of Sea-ANIML . . . . . . . . . . . . . . . . . . . . . . . . 40
3.13 Localization accuracy of Zhou et al.’s technique, taken from [95, 96] . . . . . . . . 41
3.14 Localization coverage of Zhou et al.’s technique, taken from [95, 96] . . . . . . . . 41
4.1 Our technique executed on an example topology with one concave hole. . . . . . . 53
4.2 The self-identified boundary nodes (black squares) for (a) a single hole topology
(4050 nodes with an average degree of 10) and (b) a multi-hole topology (4050
nodes with an average degree of 10). . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3 The initial group for (a) a single hole topology and (b) a multi-hole topology. . . . 55
4.4 Graham’s Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5 The identified convex hull nodes (black squares) for (a) a single hole topology and
(b) a multi-hole topology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
x
4.6 The initial external perimeter for a (a) single hole topology and (b) multi-hole
topology, in addition to the groups of remaining uncaptured nodes. . . . . . . . . . 58
4.7 An example of capturing a small set of nodes left uncaptured by the construction
of the initial rough outer perimeter. . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.8 The identified perimeters after all nodes are captured for (a) a single hole topology
and (b) a multi-hole topology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.9 An example of merging on the of the perimeters identified in Figure 4.7. . . . . . . 60
4.10 The final rough outer perimeter after all perimeters are merged for (a) a single hole
topology and (b) a multi-hole topology. . . . . . . . . . . . . . . . . . . . . . . . 61
4.11 The final external perimeter after refinement for (a) a single hole topology and (b)
a multi-hole topology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.12 The first perimeter split for (a) a single hole topology and (b) a multi-hole topology. 65
4.13 The final internal and external perimeters for (a) a single hole topology and (b) a
multi-hole topology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.14 Randomly distributed sensor field. . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.15 Wang et al.’s technique, taken directly from [85], in a uniformly distributed sensor
field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.16 Results for randomly perturbed grids. . . . . . . . . . . . . . . . . . . . . . . . . 70
4.17 Wang et al.’s technique, taken directly from [85], in a randomly perturbed grid. . . 70
4.18 Results when the density of the graph decreases. . . . . . . . . . . . . . . . . . . . 71
4.19 Wang et al.’s technique, taken directly from [85], as the density of the graph de-
creases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.20 Results for more interesting examples, adapted from [85]. . . . . . . . . . . . . . . 73
4.21 Wang et al.’s technique, taken directly from [85], for more interesting examples. . . 73
5.1 Our technique executed on an example topology with one sensed phenomena. . . . 85
xi
5.2 The self-identified boundary nodes (black squares) for (a) a single phenomenon
topology (4050 nodes with an average degree of 10) and (b) a multi-phenomena
topology (4050 nodes with an average degree of 10). . . . . . . . . . . . . . . . . 86
5.3 The initial groups for (a) a single phenomenon topology and (b) a multi-phenomena
topology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.4 The identified convex hull nodes for (a) a single phenomenon topology and (b) a
multi-phenomena topology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.5 The initial connected perimeters for a (a) single phenomenon topology and (b)
multi-phenomenon topology, in addition to the groups of remaining uncaptured
nodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.6 The identified perimeters after all nodes are captured for (a) a single phenomenon
topology and (b) a multi-phenomena topology. . . . . . . . . . . . . . . . . . . . . 89
5.7 The final rough perimeters after all perimeters are merged for (a) a single phe-
nomenon topology and (b) a multi-phenomena topology. . . . . . . . . . . . . . . 89
5.8 The final outer perimeters after refinement for (a) a single phenomenon topology
and (b) a multi-phenomena topology. . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.9 Possible relationships between constructed outer perimeters. From left to right: (a)
true overlap; (b) surrounding; (c) surrounded; (d) crossing; (e) crossed. . . . . . . . 92
5.10 The first round of perimeter splits for (a) a single phenomenon topology and (b) a
multi-phenomena topology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.11 The final internal and external perimeters for (a) a single phenomenon topology
and (b) a multi-phenomena topology. . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.12 An example of our technique mitigating crossings perimeters. . . . . . . . . . . . . 96
5.13 Randomly distributed sensor field. . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.14 Results for randomly perturbed grids. . . . . . . . . . . . . . . . . . . . . . . . . 99
5.15 Results when the density of the graph decreases. . . . . . . . . . . . . . . . . . . . 100
xii
5.16 Results for more interesting shaped phenomena. . . . . . . . . . . . . . . . . . . . 101
xiii
Dedication
I dedicate this dissertation to my daughter Kalie,
the greatest gift I have ever known.
xiv
CHAPTER 1
INTRODUCTION
Wireless sensor networks are application-specific, wireless ad-hoc networks populated with small,
low-cost, resource-constrained immobile nodes equipped with one, or more, external sensors [77].
Wireless sensor networks also contain one or more base stations, which are less resource-constrained
devices that are responsible for connecting the wireless sensor network to the users of the network.
Initially military applications, such as target acquisition/tracking and battlefield surveillance, drove
the development of wireless sensor networking technology [4]. However sensor networks are now
commonplace in civilian monitoring applications, such as environment and habitat monitoring,
healthcare applications, home automation, traffic control and fire detection/control [15]. In many
sensor network applications, such as battlefield surveillance or hostile environment monitoring,
there is no viable node recovery plan making each sensor node a disposable asset [64]. Addition-
ally, some sensor network applications require that the sensor nodes do not influence the deployed
environment, such as habitat monitoring. Therefore, for the practical deployment of many sensor
network applications the cost and physical size of each sensor node is critical, which makes hard-
ware selection crucial. In general, the sensor nodes that compose a typical wireless sensor network
contain five key components: microcontroller, wireless transceiver, external memory, power source
and sensor(s) [84]. While the microcontroller and external memory components of a sensor node
dictate the processing power and storage capacity of a sensor node, these two components are not
key indicators of the suitability of a sensor node to a particular sensor network application. Ad-
ditionally, most sensor node hardware currently in production have a modular sensor interface, so
the choice of sensor node hardware is independent of specific sensor needs. This makes the power
source and wireless transceiver the key indicators of the suitability of a sensor node to a sensor
network application. Since there is no way to replace sensor batteries for many sensor network
applications the correct choice of power supply is critical to the longevity of the wireless sensor
1
network, coupled to the fact that the most energy consuming task on a sensor node is the wireless
transmission of data. Therefore, the selection of the least powerful wireless transceiver, in terms
of data speed and transmission range, to meet the needs of the sensor network application is ideal.
For example, The Mica2 Mote, developed by U.C. Berkeley, has a Atmel ATmega128L microcon-
troller with 128k of program flash memory and 512k of external memory, typically operates on 2
AA batteries, is built upon a 51 pin modular sensor system and capable of wireless transmissions
of 38.4 kbits/sec with an outdoor line-of-sight range of about 500 feet [1].
Although the specifics of sensor network deployment scenarios are entirely application domain
specific, it is envisioned that wireless sensor networks are densely deployed over large monitoring
areas. Deployment scenarios range between manual deployment to completely random scatter-
ing over a specific region, such as aerial or artillery-based deployment. Regardless of deployment
mechanism or application, most general purpose sensor networking services, such as sensor identi-
fication, routing, data fusion and data analysis, require some knowledge of a network’s topology in
order to operate effectively [87]. For example, one or more sensor nodes detecting a fire are useless
if the location of the sensors is unknown. Identifying the positions of each node in a sensor deploy-
ment is considered a fundamental operation in wireless sensor network and almost every wireless
sensor network has some knowledge of node positions, or localization technique in place [85].
There remain many unsolved problems in the field of wireless sensor network research. One
fundamental wireless sensor network problem that remains unsolved is the development of a low-
cost GPS-free localization technique. Localization is the process by which the nodes of a sensor
network self-determine the network’s topology, by identifying the physical coordinates of every
node in the network. The most straightforward methods of localization are GPS and manual entry.
Manually entering the positions of every node in large, dense sensor deployment is not a scalable or
realistic option in most situations [16]. On the other hand, equipping every sensor node with GPS
technology, while obviating the need for localization, increases the cost of each individual node
and greatly increases the deployment costs of deploying a sensor network. Greatly increasing the
2
cost of each sensor node directly conflicts with the overall goal of sensor network nodes becoming
low enough in cost that they are considered disposable [64]. Additionally, depending on GPS
for localization limits the applicability of sensor networks to outdoor environments [61]. The
prohibitive cost of equipping sensors with GPS is the reason many localization techniques restrict
GPS ability to only a small subset of the total network nodes, called anchors [77]. Deploying even
a small set of anchors into a sensor network provides the ability for the network to be localized
absolutely (i.e. estimated positions are directly related to GPS positions), whereas a network with
no deployed anchors can only be localized relatively (i.e. estimated positions are only meaningful
relative to other positions in the same network). However, in most sensor network applications,
absolute localization is not strictly necessary; instead it is overall topology identification, or relative
localization, that is critical for sensor identification, routing, data fusion and data analysis [87].
Considering the cost increase of equipping just a single node with GPS technology, localization
techniques that minimizes the use of anchors become critical [89]. However, an ideal relative
localization technique should take advantage of the additional information provided by anchors in
the event of their availability; just not strictly depend on them.
While knowing the physical positions of every node in the network provides a large amount
of information about the deployed topology of a wireless sensor network, it does not provide a
complete view of a network’s topology. Knowing the coordinates of each node in the network only
allows for the gathering of sensor data values associated with discrete locations. While obtaining
location/value pairs is the purpose of a sensor deployment, it may not provide everything about the
deployed environment of a sensor network. Specifically, the shape of the network deployment can
provide important information about the region under observation. The boundaries of the network,
both the inner (i.e. internal connectivity holes) and the outer (i.e. the network’s external perime-
ter), almost always have a physical correspondence to the environment in which the sensors are
deployed [85]. For example, consider an internal connectivity hole caused by a previously uniden-
tified body of water in the middle of the sensor deployment. Knowing the shape of the connectivity
3
hole provides previously unknown information about the body of water, or other entity, that caused
the hole. The same also goes for the shape of the entire network deployment, for example if the
monitored region is the bottom of a large ravine. Additionally, not being aware of the boundaries
within a sensor network can lead to degradation in performance over time. For example, in shortest
path routing, nodes along the boundary of a hole tend to receive more intermediate route requests,
increasing their overall load and ultimately reducing their power sources faster than other nodes
in the network [27]. This can cause a small hole to grow over the lifetime of the network due to
failing boundary nodes.
Another key aspect of topology discovery is the geometric identification of sensed phenomena
currently within a wireless sensor network. Obtaining how the sensed data relates to the physical
topology is fundamentally the goal of deploying a sensor network. Again, while knowing the co-
ordinates of each node in the network does allow for the gathering of sensor data values associated
with discrete locations, it does not directly provide any relationships between obtained data. For
example, it is difficult to identify whether or not two relatively close nodes in a sensor network
with the same or reasonably similar sensed data are identifying the same sensed phenomena or are
identifying different phenomena that just happen to have the same sensed data value. Traditionally,
each individual sensor node forwards its data to a single less resource-constrained location for cen-
tralized analysis. However, this approach hides or removes any relationships between the gathered
sensed data from the network, can cause high network overhead and even reduce the lifetime of the
network. The potential drawbacks of the centralized collect and analyze paradigm for sensor data
analysis makes the development of more advanced data analysis techniques for sensor networks
important, which has led to several distinct approaches to solve the problem. The most recent
of which is broadly referenced in the literature as edge detection. Edge detection aims to reduce
data analysis overhead by providing a more concise view of sensed data through the geometric
identification of sensed phenomena within a sensor network.
4
Our research efforts target the discovery of location and topological information in arbitrar-
ily deployed wireless sensor network in the absence of any accessible global information about
the deployed topology. The first topic addressed in this dissertation is the design of an anchor-
free relative localization for wireless sensor networks. The creation of a distributed boundary
recognition requiring only a relative coordinate system is address next. Lastly, we generalize our
boundary recognition technique into a general edge detection technique. The organization of this
dissertation follows. Chapter 2 provides some background information specific to our localiza-
tion, boundary recognition and edge detection techniques in WSN. The contents of Chapters 3–5
provided presents our anchor-free relative localization technique, distributed boundary recogni-
tion technique and unified technique for both edge detection and boundary detection, respectively.
Chapter 6 presents conclusions and discusses possible future work.
5
CHAPTER 2
BACKGROUND
2.1 Overview
In this chapter, we provide a brief required background on wireless sensor networks. These topics
are discussed as they directly relate to the research presented later in this dissertation. They are
included for the purpose of completeness and are not intended as exhaustive discussions on the
topics. This chapter is organized as follows. Section 2.2 presents a brief introduction to geographic
forwarding in wireless ad-hoc networks. Section 2.3 discusses the basic technique behind distance
estimation using received signal strength in a wireless network.
2.2 Geographic Routing
Traditional routing techniques in wireless sensor networks depend heavily on network flooding to
determine suitable paths between two non-neighboring nodes. Unfortunately, floods are a source
of high communication overhead, which in turn increases the energy expenditure of the entire net-
work deployment. Flooding in of itself is not necessarily a bad thing and in some cases it is the
most effective and efficient way to disseminate information throughout a sensor network, however
requiring a flood for every route request, considered a fundamental operation in ad-hoc sensor net-
works, can be incredibly detrimental to the health of a network consisting of resource-constrained
sensor nodes. The newest class of ad hoc routing protocols are geographical, or location aware,
routing protocols. The general principles of geographical routing have been widely applied in other
types of networks, such as cellular networks [45]. Geographic routing protocols take advantage of
knowing the physical location of hosts in order to facilitate efficient, effective and scalable routing
in ad hoc networking environments. This is accomplished through various approaches from simply
using location information to reduce the overhead of traditional ad hoc routing protocols to the de-
sign of completely coordinate-dependent routing protocols. The limitation of geographic routing
6
protocols is their complete dependence on every host in the network having the ability to ascertain
its own physical location. However, unlike mobile ad-hoc networks, most sensor networks have
some form of localization in place [85]. This allows them to take advantage of geographic routing
protocols.
The most basic geographic routing technique is simple geographic forwarding. In simple geo-
graphic forwarding there is no route identification process, instead nodes simply forward packets
to their neighboring host that is located closer to the intended receivers than they are. In uniformly
dense ad hoc networks, simple geographic forwarding works extremely well. However, in net-
works that contain large voids, simple geographic forwarding does a terrible job routing packets
around the void [70]. GPSR [43], or greedy perimeter stateless routing, is a routing protocol that
consists of two packet forwarding methods: greedy and perimeter forwarding. GPSR’s greedy for-
warding technique is just simple geographic routing and the protocol tries to take advantage of this
form of forwarding as much as possible. GPSR switches to perimeter forwarding when it deter-
mines that greedy forwarding is unable to get a packet to its destination. Perimeter forwarding uses
the graph traversal concept of the right-hand rule. The right hand rule states that when arriving at
a vertex x from a vertex y the next edge that is traversed is the edge that is next counterclockwise
edge from yx leaving x. Using the right-hand rule the traversal of the outside of a polygon, or
face, is possible. The idea is that a void in an ad hoc network is simply a face that to be routed
around. GPSR then forwards a packet along faces trying to keep on a line from the last host where
perimeter forwarding was required and the known position of the destination.
2.3 Simple Distance Estimation using RSSI
There are many methods by which wireless receivers are capable of estimating their distance from
a transmitter. The simplest of which is using the received signal strength (RSSI) of a transmission
to infer the distance the transmission traveled between the receiver and the sender. In order to
accurately determine the distance between a transmitter and receiver using RSSI requires that the
7
original transmission power used by the transmitter to send the transmission is known [47]. In
traditional wireless networks assuming to know the transmission power of a received transmission
is not safe due to differing transmission power settings, however in wireless sensor networks where
it is usually assumed that all nodes use the same wireless transmitters, or at the very least, that any
differing hardware is known prior to deployment. Since it is nearly impossible to completely
quantify the propagation characteristics of any uncontrolled environments due to unknown sources
of interference, in order to get an estimated distance between the sender and receiver, freespace
propagation of radio signals is often assumed. In freespace only distance traveled causes a loss
to signal strength, therefore easily allowing for the calculation of distance from RSSI. Obviously,
using the distance traveled in freespace only provides an estimate in real environments. In order to
calculate distance traveled, in freespace, of a transmission, assuming we know the received signal
strength and the original transmission strength, we use Friis Equation [47]:
PRx = PTx
GTxGRxλ2
16π2d2L, (2.1)
where GTx is transmitter antenna gain, GRx is receiver antenna gain, λ is wavelength, d is distance
separating Tx and Rx antennas and L is the system loss factor (≥ 1). Solving for d we get:
d =
√PTxGTxGRxλ
2
16π2LPRx
. (2.2)
Simplifying, we assume perfect antennas, GRx = GTx = 1, and no external signal loss, L = 1,
leaving us with:
d =
√PTxλ
2
16π2PRx
. (2.3)
Despite being error-prone, this equation is usable as a means to estimate the distance between a
sender and a receiver knowing only minimum required information.
8
CHAPTER 3
LOCALIZATION
3.1 Overview
Localization is the process by which the nodes of a sensor network self-determine the network’s
topology. This typically involves identifying the physical coordinates of every node in the network.
Equipping every node in a wireless sensor deployment with GPS or manually placing every node
in predetermined locations does technically solve the problem of localization. However, a well-
designed localization technique should minimize the cost of localizing a network. Unfortunately,
equipping every node with GPS is financially costly and manual placement is labor intensive. A
significant challenge faced in the design of a cost effective localization techniques is the depen-
dence on globally available information (i.e. network-wide flooded information). While using
globally available information provides a technique with more information on which to base its
solution, it also introduces the problem of cascading errors. Cascading errors are the result of
compounding estimation errors propagating through the network. Since many localization tech-
nique depend on estimated inter-node distances in order to localize the network, cascading ranging
errors significantly affect the accuracy of many localization techniques [90]. A common approach
to reduce the effects of cascading ranging errors is to restrict information propagation to only lo-
cal neighborhoods. ILS [55] implements this strategy to control the effects of cascading ranging
errors. However, the restriction of information propagation to handle cascading ranging errors
creates another problem. Information propagation restrictions introduce the problem of nodes in a
single neighborhood getting stuck at a local optimum. That is, there is not enough external infor-
mation to keep a single neighborhood from choosing wildly inaccurate final positions in a global
sense, while the positions are accurate in a local sense. This tends to happen in neighborhoods that
not well surrounded by other neighborhoods, such as corner and edge neighborhoods. ILS [55] is
9
the only localization technique in the literature to address this phenomenon. It deals with it using
an error control mechanism that prevents “bad seeds” from contaminating the position estimation
of other nodes. Championed as not requiring additional message overhead to implement, control
mechanisms are not without cost. The computational overhead of error control mechanisms can
be significant depending on the underlying filtering technique used.
While wireless sensor networks have become commonplace in many different areas of monitor-
ing, current wireless sensor networking technology is not necessarily suitable for all environments.
In recent years, there has been increasing interest in the extensive monitoring of large-scale un-
derwater environments. The ideal solution to extensive monitoring of large-scale environments is
the deployment of wireless sensor networks. However, terrestrial sensor networking technology
is not readily deployable in aquatic environments. The need for large-scale monitoring in aquatic
locations has given rise to the research field of underwater sensor networks [96]. Many different
fields of research benefit from the use and continued improvement of underwater sensor network-
ing technology. Archeology, seismic research and ocean life observations are just a few of the fields
that directly benefit from the use of underwater sensor networks [22]. While the overall goal and
basic operation of underwater sensor networks is the same as terrestrial wireless sensor networks,
there are several important differences. Foremost, underwater sensor nodes are deployable into
true three-dimensional topologies, capable of controlling and measuring their own depth. Also,
communications between underwater sensor nodes is done using acoustic communication, which
has much lower bandwidth, higher propagation delay and higher bit error rates than traditional RF
wireless communication [60]. Most research topics of importance to the development of terres-
trial wireless sensor networks remain important in the development underwater sensor networks,
with some even being more important to the development of underwater sensor networks due to
the adverse nature of underwater environments. Localization is a critical challenge in underwater
sensor networks, even more so than in terrestrial networks, because GPS is not readily available
due to GPS signals not propagating correctly through water [22]. Additionally, the differences
10
between acoustic and RF communication channels render many terrestrial localization techniques
impractical or infeasible [82].
In this chapter, we present a straightforward, iterative, anchor-free, range-aware relative lo-
calization technique for wireless sensor networks, called Anchor-free, local Neighborhood-based,
Iterative MultiLateration (ANIML). ANIML is capable of providing accurate relative localization
without making assumptions about a deployed topology. ANIML does not depend on globally
flooded information, reducing the effects of cascading ranging errors by restricting its derived
distance estimates to a node’s 1- and 2-hop neighbors. While least-squares minimization is a
mathematically simple constraint optimization technique, by utilizing 1- and 2-hop neighbor in-
formation as constraints, ANIML provides accurate relative localization without the need for an-
chors, sophisticated error control and/or global information. In addition to presenting ANIML, we
also introduce three ANIML variants: ANIML-Abs, ANIML-Hop and Sea-ANIML. While AN-
IML does not require anchors in order to provide accurate relative localization, ANIML-Abs takes
advantage of any deployed anchor nodes to allow for absolute localization. ANIML-Hop is capa-
ble of localizing a network using only hop counts, in the absence of ranging equipment. Neither
ANIML-Abs nor ANIML-Hop requires changes to the underlying ANIML technique. Extensive
performance analysis shows that ANIML, ANIML-Abs and ANIML-Hop provide accurate local-
ization and scale well. Lastly, we adapted ANIML into a range-aware localization technique for use
in underwater wireless sensor networks, called Sea-ANIML. Simulations show that Sea-ANIML is
able to provide accurate localization in three-dimensional deployments where each sensor directly
measures its own depth.
The rest of this chapter’s organization follows. Section 3.2 presents related work on localization
in wireless sensor network and underwater sensor networks. Section 3.3 introduces our ANIML
technique as well as ANIML-Abs and ANIML-Hop. Section 3.4 contains performance analysis.
Section 3.5 presents Sea-ANIML and Section 3.6 presents a summary of the chapter.
11
3.2 Related Work
Previous attempts at solving the problem of localization in sensor networks can be categorized into
two groups: range-aware and hop-based. In range-aware techniques a distance metric is somehow
derived and used to estimate node positions. In hop-based localization no ranging hardware is
needed, and in many ways the distance estimates between nodes are simplified to the number of
hops in the shortest path. Both range-aware and hop-based approaches often employ traditional
methods, such as triangulation or optimization techniques, in order to calculate node positions.
However, localization techniques are often overburdened by constraints, such as specific node dis-
tribution and approximated transmission ranges in order to reduce the problem so that traditional
mathematical techniques can be applied. Additionally, most localization techniques for WSN pro-
vide absolute localization, however there are some techniques that do provide relative localization
for use when absolute localization is not strictly necessary, such as MDS-MAP [78], SPA [83], Rao
et al.’s localization technique for mobile ad-hoc networks [70], the convex optimization technique
in [21], the distributed Kalman filter approach [74], VCap [13], CBL [58] and nQUAD [87].
The rest of this section’s organization follows. Sections 3.2.1 and Section 3.2.2 present brief
related work on range-aware and hop-based localization techniques, respectively. Section 3.2.3
provides a more detailed survey of iterative multilateration localization techniques, which is the
class of localization approaches that are the most closely related to ANIML. Section 3.2.4 presents
related work on localization in underwater sensor networks.
3.2.1 Range-Aware Localization
Range-aware localization techniques typically derive inter-node distances based on received signal
strength measurements from another transmitting node [3, 6–8, 10, 16, 21, 23, 31, 33, 41, 50, 53,
55, 61, 65, 68, 71–74, 79–81, 83]. Most techniques calculate the distances that transmissions have
supposedly traveled between two nodes in the network directly from signal strength [3, 7, 10, 16,
33, 41, 50, 55, 65, 68, 71–74, 79, 83]. However, inter-node distances may also be estimated by other
12
means, such as the time required for a packet to travel from a node at a known network location [6,
81], the angle of arrival of a packet from a known network location [12] or interferometric ranging
[39]. The problem with directly calculating distances by means of signal strength observations is
that since all possible sources of signal interference cannot be accurately anticipated, prior to sensor
deployment, the estimated distances can become wildly inaccurate due to multi-path interference,
line-of-sight obstructions, etc. A common assumption, which can provide more accurate location
estimations, is an estimation of the distance between a normal sensor node and one, or more,
beacons or three, or more, anchor nodes [3, 7, 16, 33, 41, 53, 55, 65, 72, 74, 79, 80]. The exact duties
of an anchor node vary, but often it is assumed that anchors are less resource-constrained than
ordinary sensor nodes, deployed at known specific locations, deployed in a specific density within
the network, have different radio characteristics and/or are capable of determining their absolute
positions. Anchor nodes are also often assumed to provide some absolute positions within a sensor
network in order to improve the general performance of a localization technique. MAL [68] and
ADO [88] even involves a mobile rover, a sort of anchor node, that helps localize a network in the
event that terrain or deployment prevent stationary nodes from communicating distance estimates
to each other.
3.2.2 Hop-Based Localization
Hop-based localization techniques aim to overcome the inherent difficulties of accurately deter-
mining exact inter-node distances in sensor networks. While hop-based techniques do not require
inter-node distance information, many hop-based techniques have the ability to take advantage of
such information, if available, to provide more accurate results. One of the primary hop-based
methods is APS [61], a distributed, hop-by-hop positioning algorithm. The algorithm works as an
extension of both distance vector routing and GPS positioning, providing position estimates for all
unknown nodes in a sensor network, assuming a subset of nodes in the network have the ability
to determine their own positions. The accuracy of the position estimates in APS will be improved
13
as the number of anchor nodes increase. Notable extensions of APS are Hop-TERRAIN [42] and
differential APS [66]. Another approach of hop-based localization is the use of multi-dimensional
scaling (MDS). Sang et al. proposed MDS-MAP which uses mere network connectivity and MDS
in order to localize a sensor network [78]. The extensions of MDS-MAP, MDS-MAP(P) [77]
and MDS-MAP(R) [76] are distributed versions of MDS-MAP. Wong et al. [86] and Medidi et
al. [58] also depend on MDS as the mathematical basis in their proposed hop-based localization
techniques. Another hop-based localization technique, but for ad-hoc networks, has been proposed
by Rao et al. which dynamically determines a network’s perimeter nodes, using only hops, as the
initial step in using neighborhood coordinate averaging to localize internal network nodes [70].
Caruso et al. propose VCap which is a hop-based, GPS-free localization method that first local-
izes three sensor nodes to act as pseudo-anchors for the rest of the localization [13]. Yang et al.
have proposed HCRL [89] which uses single flooding and Apollonius Circles to localize a sensor
network, while providing a significant reduction in power consumption. Yi et al. [90] propose
using Monte Carlo methods to reduce the overestimation that they observe in many hop-based lo-
calization schemes. nQUAD [87] uses a hop-based cooperative quadrant prediction technique to
improve upon hop-based lateration techniques for relative positioning.
3.2.3 Iterative Multilateration
The class of localization techniques that iteratively converge on a network topology using only
ranging estimates are known as “iterative multilateration” techniques [2]. Capkun et al. [83] have
shown that MANETs with no anchor nodes can be localized by means of iteration, using their
range-aware Self-Positioning Algorithm (SPA), using only local neighborhood information. In
SPA each node first constructs a local coordinate system containing just its 1- and 2-hop neighbor-
hoods and then each node’s local coordinate space is mapped into a larger global coordinate space,
by aligning overlapping nodes between nodes’ local coordinate spaces. Similar to our technique,
SPA is designed to provide relative positioning, however SPA does not attempt to provide position
14
estimates that necessarily correlate with the true physical network topology, since the goal of SPA
is to only provide non-GPS equipped ad hoc networks the ability to take advantage of geographical
routing. Additionally, SPA is not designed for use on resource-constrained sensor nodes.
Robinson and Marshall [71] present a distributed iterative multilateration approach for MANETs
in which nodes guess and re-guess their position estimates with a constantly improving perceived
error metric. This series of guesses and re-guesses, by means of linear regressions, will eventually
converge to a topology that satisfies all distance estimates measured within the network. Robinson
and Marshall’s approach assumes that a small subset of nodes are GPS-enabled. This approach
uses iterations to perfect the localization of the network, even in the event of zero mobility. Unlike
ANIML, the accuracy of Robinson and Marshall’s approach is heavily dependent on the accuracy
of the distance estimates it makes and can require as many as 100,000 iterations to ensure an accu-
rate solution even with perfect distance estimates, which are rarely available in practice. Another
approach towards iterative multilateration, although computationally expensive, is Savvides’ et
al. [74] approach of using a distributed Kalman filter and having a subset of anchor nodes handle
localization in both the static and mobile cases. Doherty et al. [21] explain how localization can be
done through convex optimization on the definition of local neighborhood geometric constraints.
The algorithm provides accurate node positioning, given tight enough constraints. However, this
method requires centralized computation and a significant density of anchors is needed, in order to
provide the tight constraints needed for an accurate localization result.
Liu et al. have recently proposed ILS which is a neighborhood-based, iterative least-squares
localization technique, which controls cascading ranging errors by scoring distance estimates [55].
This allows only known good estimates to be used for localization and the “bad seeds” to be filtered
out. ILS strictly requires anchors in order to perform its localization and the localization proceeds
out, in a synchronized fashion, from the anchors to the non-localized nodes in the network. Also
recently proposed is Sweeps [33] which is similar to ILS with the exception that it is designed to be
used in sparse networks and uses graph theoretical methods instead of least-squares calculations.
15
3.2.4 Underwater Sensor Networks
As with terrestrial wireless sensor networks localization techniques, localization techniques for un-
derwater sensor networks can be categorized as either range-aware or hop-based. However, with-
out a readily available accurate localization infrastructure, such as GPS, for use in the case that
accuracy is more important than deployment costs, hop-based localization techniques designed
specifically for underwater sensor networks are not widely researched. The fundamental aspect of
range-aware localization techniques in UWSN require identifying inter-node distances, however
the number of ranging options are more limited than in terrestrial wireless sensor networks, due to
the unique properties of acoustic communication channels. The most common approach to deter-
mine inter-node distance in terrestrial wireless sensor networks is measuring the Received Signal
Strength Indicator (RSSI) of a transmission. Other common ranging techniques are measuring the
Angle of Arrival (AoA), Time of Arrival (ToA) or Time Difference of Arrival (TDoA) of a received
transmission. Distance estimation using RSSI is much more unreliable in aquatic environments us-
ing acoustic communication than in traditional wireless sensor networks. Both the surface of the
water and the seafloor act as reflectors, causing significant interference to acoustic signals. Addi-
tionally, air bubbles and noise, such as shrimp noises, cause significant and unpredictable signal
loss in acoustic signals. Due to the larger number of unpredictable source of signal interference and
loss that are present in aquatic environments distance estimation using RSSI is not the preferred
distance estimation technique in underwater sensor networks. Distance estimation using AoA typ-
ically require special antenna configurations that are suited for aquatic deployment. The drawback
of distance estimation using ToA or TDoA is that all nodes must be tightly time synchronized. Un-
fortunately, common time synchronization techniques used in terrestrial wireless networks are not
feasible in underwater sensor networks since they often assume low latency RF communication.
Despite the need for tight time synchronization, the preferred methods of distance estimation in
underwater sensor networks is ToA or TDoA [17].
16
Othman et al. propose an anchor-free relative localization technique for underwater sensor
networks [63]. Othman et al.’s technique begins with a single seed node, which becomes the ori-
gin of the relative coordinate system, and expands outwards until all nodes are localized. This
technique requires an initial node discovery phase, which can require a high number of message
exchanges [22]. Zhou et al.’s localization technique for underwater sensor networks [95, 96], sim-
ilar to ILS [55], is a hierarchical range-aware technique and requires three types of nodes: surface
buoys, anchor nodes and ordinary nodes. The technique then proceeds in two phases. In the
first phase, the surface buoys accurately localize the anchor nodes. Anchor nodes are uniformly
distributed throughout the entire topology, in order to enable scalable localization. Then the or-
dinary nodes use the anchor nodes to localize themselves. Clearly, the accurate localization of
anchors from the surface buoys is the most difficult part of the technique and it is not discussed
in detail [22]. Teymorian et al. propose USP, a localization technique for underwater sensor net-
works which non-degeneratively projects reference nodes onto the plane containing non-localized
nodes [82]. However, Mirza and Schurgers show that the localization accuracy of reducing the
problem of three-dimensional localization in underwater sensor networks to two-dimensions, when
the depth is known, is still greatly affected by the topology’s three-dimensional geometry [60].
Some localization techniques for underwater sensor networks aim to provide ongoing accu-
rate localization in the case where currents cause nodes to drift from their initial deployed posi-
tions. Erol et al. have proposed Dive’N’Rise (DNR) positioning, a novel range-aware localization
technique using Dive’n’Rise (DNR) beacons and takes into account node mobility due to ocean
currents [22]. DNR beacons are buoys that rise to the surface to obtain GPS coordinate and then
slowly sink relaying the new position information to the sensor deployment. Zhou et al. adapted
their localization technique previously discussed hierarchical localization technique [95, 96] into
SLMP, a localization technique that takes advantage of past location information in order to predict
future mobility, aiming to allow nodes to estimate their future positions [93,94]. Mirza and Schurg-
ers take motion-aware localization to the next step by proposing a technique that keeps fields of
17
underwater drifters localized while they travel freely with ocean currents [59, 60].
3.3 Approach
This section presents ANIML, our anchor-free localization technique. Section 3.3.1 presents the
basic ANIML technique. While Section 3.3.2 discusses limitations of the basic ANIML tech-
niques. Section 3.3.2 also presents our improvements to the basic ANIML technique to address
the discussed limitations. Lastly, Section 3.3.3 discusses the ANIML variants: ANIML-Abs and
ANIML-Hop, that extend ANIML’s applicability to WSN with anchors and without ranging capa-
bility, respectively.
3.3.1 ANIML
The basic idea behind ANIML is for nodes to expand their positions outward, from their starting
positions at the origin, closer towards their actual relative positions in the network, with each itera-
tion. Since there are no anchors to provide known absolute positions in the network, the localizing
sensor nodes have no predefined coordinate system available on which they can converge. ANIML
handles this by choosing a single node, the reference node, to remain “stationary” at the origin
through all iterations. This gives nodes a common “absolute” position from which to expand out-
wards. Other than remaining at the origin, the reference node is identical in capability to all other
sensor nodes in the network. ANIML assumes the use of sensors equipped with ranging hardware
that is capable of making distance estimates from received transmissions.
Figure 3.1 outlines ANIML’s iterative localization process, run independently on each node.
Note that these ANIML iterations across the nodes do not require any tight synchronization. The
underlying mathematical technique in ANIML is least-squares multilateration. Given that a node
recalculates its position estimate x knowing only the estimated positions xi and distances di of n
1- and 2-hop neighbors, we can formulate n constraints of the form:
||x− xi|| = di. (3.1)
18
Node k:while termination condition not met do
BroadcastMessage()collect messages from neighborsfor each message rcvd from a node i do
dk,i ← measured distance estimate from node iupdate stored information for node ifor each node j in rcvd list of i’s neighbors do
dk,j ← dk,i+ rcvd dist of node j from iupdate stored information for node j
end forend forRecalculateCoordinates()
end while
Figure 3.1: Basic Iterative ANIML Technique
From these n non-linear constraints, we can approximate n linear constraints. Assuming x ≈x0, where x0 is the current estimated position of the recalculating node, we get ∆x = x − x0.
Substituting ∆x into (3.1) and expanding, we get:
√||x0 − xi||2 + 2(x0 − xi)T ∆x + ||∆x||2 = di. (3.2)
Taking the first order Taylor series expansion of (3.2) with respect to ∆x, in order to approximate
the square root, ignoring the ||∆x||2 term (∆x is assumed to be small), re-substituting for ∆x and
simplifying we obtain:(x0 − xi)
T (x− xi)
||x0 − xi|| = di. (3.3)
With the equation of the unit vector from xi to x0 being ri = (x0 − xi)/ ||x0 − xi||, (3.3) can be
simplified to:
riTx = ri
Txi + di. (3.4)
Here riT is a 2× 1 vector and ri
Txi + di is a single scalar.
19
Thus, we have obtained n linear constraints, expressed in matrix form:
Ax = b, (3.5)
where A = (r1T , r2
T , · · · , rnT )T and b = (r1
Tx1 + d1, r2Tx2 + d2, · · · , rn
Txn + dn)T . The least-
squares solution to the linear system (3.5) is x = (ATA)−1ATb. Note that if A is collinear we
simply perturb x a small amount, which usually makes it noncollinear in the next iteration. This
process is shown graphically, for the case of n = 4, in Figure 3.2.
=2
22 y
xn
=1
11 y
xn
3d
=
3
33 y
xn
1d
2d
=4
44 y
xn
5d 524 ddd +=
in
in'
Figure 3.2: Least-squares Multilateration (k = 4)
Initially every node will only be aware of its own estimated position, making it unable to re-
calculate a new estimated position, in which case it will broadcast its current estimated position
to its 1-hop neighbors. In the next iteration, every node will be aware of their estimated position,
those of its 1-hop neighbors and the estimated distances of its 1-hop neighbors made through direct
ranging. This information allows a node to begin recalculating its own position estimate. Since
each node’s initial position is the origin, this first recalculation will place a node roughly the av-
erage estimated distance it is from all of its 1-hop neighbors away from the origin in an arbitrary
20
direction. Every node then broadcasts its new position estimate, in addition to the position esti-
mates it has received from its 1-hop neighbors and the distance estimates it has made for its 1-hop
neighbors. The size of an ANIML packet depends on the node’s 1-hop neighborhood. ANIML’s
total message complexity is the product of the number of nodes and iterations. In most randomly
deployed topologies ANIML usually requires only 10 to 15 iterations.
In the third, and subsequent iterations, every node is aware of their own estimated position,
those of its 1- and 2-hop neighbors, the estimated distance of its 1-hop neighbors made through
direct ranging and the estimated distances of its 2-hop neighbors. ANIML infers a node’s distance
from a 2-hop neighbor by adding the received distance estimate between the intermediate 1-hop
neighbor and the 2-hop neighbor to the directly calculated distance estimate of the intermediate
1-hop neighbor. While there are possibly other ways to obtain a more accurate distance to a node’s
2-hop neighbors, since the sum of distances provides a gross overestimate due to triangular in-
equalities, we chose the straightforward sum of distances in ANIML. In addition, since a node can
receive duplicate information about any 1- or 2-hop neighbor, ANIML always utilizes the smallest
inferred distance it has estimated to any node. Now every node is fully able to take advantage of
least-squares multilateration to recalculate a more accurate position estimate, at least relative to
its immediate neighbors, because its immediate neighbors’ estimated positions have spread apart
and not all located at in the same spot. Additionally, the availability of 2-hop neighbor infor-
mation allows the nodes of a neighborhood to begin moving closer towards their actual distance
away from the reference node and any adjoining 1-hop neighborhoods. This is possible because
ANIML explicitly provides nodes with a sense of how they should line up globally with adjacent
neighborhoods, while remaining consistent with their 1-hop neighbors.
In a network where every distance estimate was perfect and the only unknowns in the net-
work were positions, ANIML would not require an explicit termination condition. Each node will
converge to a single location. However, having only estimated knowledge of distance requires an
explicit termination condition. With only estimated distance estimates, there is no single solution
21
to the localization, so any one slight position estimate change can cause an unending cascade of
changes in the position estimate of every node in the network. This makes determining the correct-
ness of ANIML difficult. The termination condition we have most used is a node keeps its current
position estimate when it has not moved more than 5% of its transmission range in 5 successive
iterations. Once a node stops, it simply acts as a forwarder for the messages it receives from still
actively localizing nodes. Unfortunately, it is possible, although rare, for some nodes to never settle
near a single position. These nodes flip back and forth between two relatively far apart positions
estimates. In these cases, we employ a cap on the maximum number of iterations to insure that a
node does not attempt to localize itself indefinitely.
3.3.2 Improving ANIML
By restricting distance estimates to only 1- and 2-hop neighbors, instead of globally propagated
information, such as the positions of anchors, we reduce the effects of cascading ranging errors;
such cascading errors significantly affect the accuracy of many range-aware localization techniques
[90]. Naturally, to control the message and computation complexity, we would have preferred to
restrict ANIML to use only 1-hop neighbor information. However, we found that while this can
provide accurate localization in some cases, in many cases individual neighborhoods localize too
rapidly based on only their own 1-hop neighborhood’s information, fold onto themselves, and get
stuck at a local optimum. This problem is also encountered in ILS [55] and other techniques
[61, 74]. Such folding of neighborhoods cannot be either detected or rectified with only 1-hop
neighbor information. Fig. 3.3(a) shows the localization of a network by ANIML using only 1-
hop neighbor information (estimated positions are denoted by circles with the arrows pointing to
the true positions). The accuracy of the localization is poor with an average positioning error
of 90 meters; however the average pair wise distance error is only 21 meters. Several different
ways to address local optima are presented in the literature. For instance, DV-Hop [61] favors
positioning information from physically closer nodes. ILS [55] by spreading the localization out
22
in successive stages, scoring the error estimates, and controlling the error propagation. On the
other hand, Savvides et al. [74] presented Kalman filtering-based localization technique that uses
weighting. However, by simply basing nodes’ position calculations on 1- and 2-hop information
ANIML can prevent the folding of neighborhoods and from getting stuck at a local optimum. Two-
hop neighbor information acts as a natural dampener to the localization process, slowing down the
changes of nodes in each iteration which allows neighborhoods that would otherwise rapidly reach
a local optimum extra time to receive additional information that could prevent it from getting
stuck. Fig. 3.3(b) shows the same topology as Fig. 3.3(a) localized by ANIML using 1- and 2-hop
neighbor information. The localization has an average localization error of only 8 meters with an
average pairwise distance error of 3 meters.
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Figure 3.3: Comparison of ANIML using 1-hop and 2-hop Information
One issue with ANIML’s iterative localization approach is that it can be slow to complete. In
the initial ANIML iterations, nodes’ positions are in a state of flux; ANIML’s iterative behavior
causes the nodes to settle down, but slowly. However by having nodes include its number of
hops from the network’s reference node in its broadcasts, it is possible to increase the speed of
convergence. From the hop-distance, h, to the reference node at the origin, a node can check if its
position is within the distance range of [r × h, r × (h− 1)] to the origin, where r is the maximum
23
transmission range. Otherwise, the node is able to either push or pull its position to the closer of
the two bounds in the above range, along the same angle from the reference node as before. This
push-pull refinement, done prior to broadcasting its new position estimate, allows a node to place
itself closer to its final position much faster, allowing the localization to converge more rapidly.
The basic ANIML technique requires no explicit error control mechanisms, since error control
mechanisms are implicitly built into each step of the technique. Using a node’s 1- and 2-hop
neighborhood allows for some prevention against neighborhoods getting stuck at local optima,
without needing to resort to scoring or weighting of received information. Also, restricting to 2-
hop neighborhood information prevents cascading of ranging errors over multiple hops. Iteratively
refining a node’s position naturally provides error control by allowing any transient errors to be
smoothed away over several iterations. Using least-squares multilateration, on a node’s entire 2-
hop neighborhood, to recalculate a node’s position smoothes out the affects of error prone distance
estimates. This is even more critical considering that using triangle inequalities for the 2-hop
distance estimates are gross overestimates. Even after introducing significant ranging error in the
2-hop neighbor distances, due to triangular inequality, least-square multilateration is still able to
smooth over these affects and provide good position estimates. The push-pull technique used to
speed convergence also provides further error control, since it keeps nodes from drifting too far or
remaining too close to the reference node. This is important not only for the accuracy of a node’s
own position estimate, but also for the nodes located around it.
The iterative nature of ANIML naturally places a node into its correct position when it neigh-
borhood is well distributed around it, the problem occurs when a node’s neighbors are biased in one
direction from the node (i.e. corner and edge nodes). Corner and edge nodes can end up estimating
their position on the “wrong” side of their 1-hop neighborhood. Since least-squares multilateration
depends on unit vectors from a node’s neighbors to the current estimate, a node will continue es-
timating its position to be on the “wrong” side of its 1-hop neighborhood. These corner and edge
nodes that have been placed on the “wrong” side of their 1-hop neighborhood appear “flipped” into
24
their 2-hop neighbors, towards the center of the network. Additionally our push-pull refinement
cannot help push these flip nodes closer to their proper position on the boundary of the network
since it is a conservative push. ANIML is naturally capable of preventing flipped nodes, however
as the network diameter increases the propagation of information from within the network gets
progressively slower to the edges of the network allowing some neighborhoods to still move too
rapidly into a local optimum, which is the underlying cause of flipped nodes.
In order to combat the problem of anomalous flipped nodes we extended ANIML with a simple
sanity check technique to detect a flip and correct it if necessary. We could have used known tech-
niques to detect nodes on the periphery of the network and then treated them differently in ANIML
than internal nodes, however only a small number of boundary nodes flip and our simple flipped
node sanity check provides effective correction. A node cannot be sure whether it has flipped or
one, or more, of its 2-hop neighbors being flipped. Without access to global knowledge of the sen-
sor network it is impossible for a node to be absolutely positive that it has flipped. However, based
on two observations: corner nodes have much smaller 1-hop neighborhoods than other nodes and
nodes closer to the reference node are more likely to be well represented by their neighbors than
nodes farther away from the reference node, this simplistic sanity check is able to identify most of
the flipped nodes. If a node detecting a flip has a smaller 1-hop neighborhood than its identified
inconsistent 1-hop neighbors then it is most likely a flipped corner node and needs to have its own
position corrected. Correction for this case is flipping the node’s position 180◦ around the centroid
of its “inconsistent” 1-hop neighbors. Unfortunately, neighborhood size does not sufficiently iden-
tify flipped edge nodes. Instead, if a majority of a detecting node’s inconsistent 1-hop neighbors
are closer to the reference node then the node assumes it is the offending flipped node. Correction
is done by placing the node in the center of its inconsistent 1-hop neighbors that are closer to the
reference node. In both correction cases, subsequent iterations would let the previously flipped
node identify better position estimates on the correct side of its biased neighborhood. This san-
ity check is independently executed at a much lower frequency than the basic ANIML iterations,
25
roughly once for every 10 iterations of ANIML. In most cases, the sanity check is able to identify
and correct flipped nodes within two such executions.
3.3.3 ANIML-Abs & ANIML-Hop
There are two obvious variants of ANIML: ANIML-Abs and ANIML-Hop. While ANIML is a
range-aware, anchor-free relative localization technique, the ability to use anchors to provide ab-
solute localization (ANIML-Abs) and to provide localization in the absence of ranging equipment
(ANIML-Hop) are both attractive options. Neither variant requires any changes to the underlying
ANIML technique. For ANIML-Abs there must be at least three anchor nodes, one of which is
selected to be the network’s reference node. Other anchors act no differently than the location-
unaware nodes in the network, they just do not need to update or refine their own coordinates.
Note that ANIML could have taken advantage of the other anchors as additional reference nodes
to improve ANIML-Abs further. ANIML-Hop, applicable when no ranging equipment is available,
simply selects the estimated distance for each hop to be 3r/4, where r is the maximum transmis-
sion range. This value is slightly higher than the expected inter-node distance in random uniform
distributions of r/√
(2). ANIML-Hop provides also provides absolute localization, but does not
require ranging equipment.
3.4 Performance Evaluation
We implemented ANIML (with and without our flipped node sanity check), ANIML-Abs and
ANIML-Hop in ns-2. We compared ANIML’s effectiveness to APS (DV-Hop) [61], a popular
technique for baseline comparisons. Since the authors’ own results show that DV-Hop outper-
forms DV-Distance, we compare against DV-Hop instead of the range-aware DV-Distance. The
simulation environment for ANIML uses 802.11 MAC. We obtained all DV-Hop data by replicat-
ing the experiments using the DV-Hop authors’ CAML implementation of APS. We used both 5%
and 10% anchor distributions in the DV-Hop, ANIML-Abs and ANIML-Hop experiments. We
generated topologies in four different sizes (250 by 250, 500 by 500, 750 by 750 and 1000 by 1000
26
m2) and two different node densities (400 and 800 nodes/km2) in order to investigate ANIML’s
scalability. The maximum transmission range of each sensor is 250 meters, although our presented
results scale to smaller transmission ranges. This makes the hop distance used in ANIML-Hop ex-
periments 187.5m (3/4 of 250m). Distance estimates for ANIML and ANIML-Abs are obtained
by adding a uniformly distributed error (0-90%) to the true distance between two neighboring
nodes to mimic experiments reported in [61]. Each data point presented in our plots is the average
of ten runs with differing random seeds, with no discarding of outliers.
The metric for localization effectiveness, used in the literature, is the average distance away
their estimated positions are from the nodes’ actual positions in the network. We give the measure-
ment of effectiveness as a percentage of the transmission range of the sensor nodes in the network.
Since ANIML produces relative localization, the determined network coordinates may have un-
dergone a global flip, rotation and/or shift making direct comparisons to the actual coordinates
difficult. Therefore, comparisons are done post localization by (i) shifting the real coordinates by
the difference between the origin and the reference node’s true position, (ii) globally rotating both
the real and relative coordinates to place node 1 on the y-axis and (iii) then, if needed, flipping the
relative set of coordinates to place them in the same coordinate space. Please note that no scaling
of position estimates is involved in this transformation.
3.4.1 Comparison of Basic ANIML using 1-Hop vs. 2-Hop Information
Providing only 1-hop neighbor information to ANIML for localization can lead to poor overall
localization due to neighbors getting stuck at local optima. Figure 3.4 shows the localization effec-
tiveness of ANIML using 1-hop information compared to ANIML using 1- and 2-hop information.
Please note that data points are shifted slightly left and right of the real values (0.0625, .25, .5625,
1) on the x-axis to allow for clear presentation of the error bars. Figure 3.4 shows that ANIML
using 1- and 2-hop information provides better overall localization accuracy than ANIML using
27
only 1-hop information. However, using only 1-hop information does not necessarily prevent AN-
IML from accurately localizing a network, as can be seen by the best case (i.e. lower error bars)
inaccuracy for ANIML (1hop/400) and ANIML (1hop/800). In fact, the best case using only 1-hop
information is comparable to the best case using 1- and 2-hop information. The problem with using
only 1-hop information compared to using both 1- and 2-hop information, since potential accuracy
is not the issue, is the potential inaccuracy of the resulting localization. In the 1-hop ANIML cases
the difference between the best case results and the worst case results (i.e. upper error bars) are
at least two times larger than the 2-hop ANIML cases. A large difference between the best and
worst case localization of 1-hop ANIML alone does not necessarily imply inaccurate localization
results, since the worst case results could be isolated outliers (e.g. the end localization contains
one or more neighborhoods that got stuck at a local optima). However, if the worst case results
of 1-hop ANIML were outliers the overall mean inaccuracy would be located closer to the best
case result in all 1-hop ANIML cases, not near the middle of the error bars, as is the case with the
mean inaccuracy of the 2-hop ANIML cases. Therefore, while 1-hop ANIML has the potential to
provide as accurate localization as 2-hop ANIML, there is much larger potential for 1-hop ANIML
to produce wildly inaccurate localization.
3.4.2 Basic ANIML vs. Improved ANIML
Figure 3.5 shows the localization effectiveness of the basic ANIML technique compared to the
basic ANIML technique extended with our flipped node sanity check. Again note that data points
are shifted slightly left and right of the real values on the x-axis to allow for clear presentation
of the error bars. The data shows that ANIML augmented with our flipped node sanity check
provides better overall localization than the basic ANIML technique. The worst case localizations
(i.e. upper error bars) of the non-enhanced ANIML cases are caused directly by end localizations
in which 2-hop information was not completely sufficient to prevent one or more neighborhoods
from getting stuck at local optima. These outliers cause a larger difference between the best case
28
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Figure 3.4: 1-Hop ANIML vs. 2-Hop ANIML
localizations (i.e. lower error bars) and the worst case localizations, which demonstrates increased
potential inaccuracy. The introduction of our flipped node sanity check allows ANIML to identify
and repair neighborhoods stuck at local optima that adding 2-hop information could not prevent,
therefore decreasing the potential of ANIML producing an inaccurate localization. This prevention
of anomalous localization due to unresolved local optima can be seen by the enhanced ANIML
cases having much tighter error bars than the non-enhanced ANIML cases. Therefore, ANIML
augmented with our flipped node sanity check greatly reduces the potential inaccuracy of ANIML
by resolving any remaining local optima that using 2-hop information did not prevent. The data
also demonstrates that ANIML is robust in the presence of less information on which to base its
localization, since 400 nodes/km2 (the number of nodes ranges from 25-400) provides comparable
localization to 800 nodes/km2 (the number of nodes range from 50 to 800). By comparison, if
ANIML had three perfectly accurate distances from three nodes knowing their true positions then
it would be able to localize a node perfectly. Since ANIML does not have the benefit of anchors
or perfect distance estimates, it requires more information than three nodes, but after a certain
threshold of available information, adding more information provides only a small increase in
29
accuracy.
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Figure 3.5: Enhanced ANIML vs. the Basic ANIML Technique
Figure 3.6 shows the number of iterations ANIML, with and without our push-pull mechanism,
performed to localize a network. The results show, as expected, that ANIML with push-pull con-
verges faster than ANIML without push-pull, particularly as the diameter of the network increases.
The data also shows that the convergence time of ANIML is not directly dependent on the number
of nodes in the network and, as expected, increases with the diameter of the network. The conver-
gence does not depend on the total number of nodes in the network because ANIML is distributed
and uses only local information. For the localization results to be globally consistent any node’s
position estimate should be influenced by all other nodes; the farther apart they are, the longer
ANIML should need before converging. The network diameter, a measure of this farthest number
of hops, should contribute to convergence linearly.
3.4.3 Uniform Networks
Figure 3.7 shows the localization effectiveness of ANIML, ANIML-Abs and ANIML-Hop com-
pared to DV-Hop in uniform topologies. The results show that ANIML provides accurate relative
localization in uniform topologies, since it only incurs very low single digit inaccuracies in both
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Figure 3.6: ANIML Convergence Time
the 400 and 800 nodes/km2 results. Additionally, the results show as expected, higher node density
allows ANIML to provide slightly better localization accuracy since there is more data to provide
more constraints for the underlying least-squares calculation. However, the lower density cases
still provide exceptionally high accuracy demonstrating that ANIML, while being able to use high
node densities to its advantage, does not need highly dense topologies to provide effective local-
ization. Additionally, the inaccuracies incurred by ANIML increase nearly linearly as the network
area increases. The reason being that as the network area increases so does the diameter of the
network, which leads to an increase in small positioning errors due to the implicit cascading of
position estimates.
Figure 3.7 also shows that ANIML-Abs provides accurate absolute localization in uniform
topologies, since it also only incurs very low single digit inaccuracies in both the 400 and 800nodes/km2
and 5% and 10% anchor density results. ANIML-Abs shows similar properties as ANIML, such
as increases in node density directly increase localization accuracy, but it does not require high-
density deployments in order to provide accurate localization. As expected, ANIML-Abs also
shows the same linear increase in localization inaccuracy as the network area increases as ANIML.
31
While adding a small percentage of anchor nodes will result in the propagation of less position es-
timates, 5 and 10 percent is not a large enough percentage of anchor nodes to eradicate cascading
positioning errors. The results also show, the addition of anchors into ANIML serves only to pro-
vide absolute localization and does not significantly improve the accuracy of ANIML, since the
accuracy of ANIML and both ANIML-Abs cases are nearly the same. Therefore, it is to be ex-
pected that increasing the anchor density does not increase the accuracy of ANIML-Abs, since
ANIML-Abs with 5% anchors and ANIML-Abs with 10% anchors provide the same localization
inaccuracies.
Lastly, Figure 3.7 shows that ANIML-Hop also provides accurate absolute localization in uni-
form topologies, in all simulations, once the network diameter is greater than one. While the 15%
to 10% inaccuracy of ANIML-Hop is clearly higher than ANIML and ANIML-Abs measured
inaccuracies, it shows that even without ranging equipment, on which ANIML and ANIML-Abs
highly depend upon, the basic ANIML technique is still able to provide good localization. The rea-
son that ANIML-Hop and DV-Hop incur a large decrease in localization in accuracy between the
first two network areas is because without a multiple hop network, neither technique has any avail-
able information upon which to localize the network. In other words, in a one-hop network both
ANIML-Hop and DV-Hop place every node in a random position. Overall, Figure 3.7 shows AN-
IML, ANIML-Abs and ANIML-Hop all outperform DV-Hop in all simulations. However, while
its excepted that ANIML and ANIML-Abs would provide higher accuracy than DV-Hop, since
they depend on ranging equipment, the data more importantly shows that ANIML-Hop, despite its
simple static hop distance estimation, is able to provide better overall accuracy than DV-Hop and
its dynamic hop distance technique.
For qualitative assessment only, since others do not have a readily available implementation for
direct experimentation, ANIML’s localization effectiveness is compared against the localization
effectiveness of MDS-MAP(P), ILS and SDP in uniform topologies using the data provided in
32
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Figure 3.7: Localization Effectiveness of ANIML in Uniform Topologies
[77], [55] and [10]. This data is summarized in Table 3.1. ANIML, ANIML-Abs and ANIML-
Hop incur less inaccuracy than SDP, ILS and hop-based MDS-MAP(P). ANIML and ANIML-Abs
provide comparable localization to range-aware MDS-MAP(P). However, while range-aware and
computationally expensive MDS-MAP(P)’s accuracy is comparable to ANIML and ANIML-Abs,
the distance measurements used were the true distance plus 5% error whereas our simulations used
true distance plus a uniformly distributed error between 0 and 90%. Also, although ANIML-Hop
provides slightly less accuracy than range-aware MDS-MAP(P), ANIML-Hop requires no ranging
equipment.
Table 3.1: Reported Results of ILS, MDS-MAP(P) and SDPReported
Method Range Error InaccuracyILS 20m 4m 20%MDS-MAP(P)Range-aware N/A N/A 5%Hop-based N/A N/A 15− 20%SDP 0.2− 0.3m <= .08m <= 40%
33
3.4.4 C-shaped Networks
Figure 3.8 shows the localization effectiveness of ANIML, ANIML-Abs, ANIML-Hop and DV-
Hop in C-shaped networks. We created our C-shaped topologies by first creating a random uni-
form deployment over the desired network size of n × n and then removing all nodes located in
the square (n/2, n/4), (n, 3n/4). ANIML-Abs and ANIML-Hop having the benefit of anchors do
as well in C-shape topologies as they did in uniform topologies, while DV-Hop’s accuracy incurs a
small decrease in accuracy compared to uniform networks. Additionally, most of the relationships
between ANIML, ANIML-Abs, ANIML-Hop and DV-Hop identified from the results shown in
Figure 3.7 remain true, such as increased anchor density not significantly increasing the accuracy
of ANIML-Abs and increased node density slightly increasing localization accuracy. However,
ANIML’s accuracy decreases significantly as the network area increases. This happens because
in relative localization schemes C-shaped topologies are isomorphic to S-shaped topologies. Any
application that needs only relative localization, such as geographic routing, will find the resulting
S-shaped topology to be identical to a C-shaped topology and will benefit equally in either topol-
ogy. However, the inaccuracy metric used does not accurately capture this isomorphism and only
sees that the coordinates in one arm of the C, in a global sense, are in the wrong place. The reason
that this S-shaped localization result could occur in ANIML, and not in DV-Hop, ANIML-Abs
and ANIML-Hop, is that there are no anchors to keep the two arms of the C “in place.” However,
the results of ANIML-Abs and ANIML-Hop in C-shape topologies show that adding anchors to
ANIML completely avoids this C-to-S transformation.
3.4.5 Non-Uniform Networks
Figure 3.9 shows the localization effectiveness of ANIML and DV-Hop in networks with irregu-
lar node densities. We generated our topologies with non-uniform node densities by first creating
a random uniform deployment over the desired network area and then moving half of the nodes
from a random quadrant to another random quadrant of the network. ANIML and ANIML-Abs
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Figure 3.8: Localization in C-shaped Networks
in networks with irregular node densities provides comparable accuracy to that of ANIML and
ANIML-Abs in uniform topologies, while DV-Hop and ANIML-Hop as expected incur a slight
reduction in accuracy. ANIML-Hop’s decrease in accuracy is due to the simplistic selection of a
static hop distance. A hop distance estimate of 187.5m was selected based on a node’s neighbors
likely being about 3/4 the maximum transmission range away from the node in uniformly dis-
tributed networks, but with irregular node densities this likelihood is no longer the same. However,
despite not dynamically adjusting its hop distance estimate (as done in DV-Hop), ANIML-Hop
still performs at least as well as DV-Hop in networks with irregular node densities.
3.4.6 In the Presence of Obstacles
Overall, our experimentation shows ANIML provides effective localization in the presence of
error-prone range estimates, irregular shapes and densities. However, in realistic environments,
any localization method must be effective even in the presence of obstacles. In our simulation ex-
periments, obstacles are incorporated by randomly placing RF opaque “walls” of length between
25 and 50 meters within uniform network topologies at a density of 16 obstacles per square kilo-
meter (translates to 4 obstacles in the smallest test scenario). Nodes obstructed by such obstacles
cannot receive each other’s communications.
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Figure 3.9: Localization in Irregular Densities
Figure 3.10 shows the results of localization inaccuracy of ANIML in networks containing
“RF”-opaque obstacles. There is no comparisons to DV-Hop since the DV-Hop simulator did not
allow for the simulation of obstacles. The results show that obstacles do not affect the accuracy of
ANIML and ANIML-Abs. While ANIML-Hop does incur the effects of obstacles in the network
the results are only slightly worse than ANIML-Hop’s performance in uniform topologies. The
increase in inaccuracy in ANIML-Hop not seen in ANIML or ANIML-Abs can be again attributed
to the static selection of a hop distance estimate. In ANIML and ANIML-Abs if two nodes are
placed close to each other with an obstacle between them preventing line-of-sight communication
having ranging equipment allows them to use a close intermediate neighbor to estimate their dis-
tance between each other while incurring only a small error to the distance estimate. However in
ANIML-Hop, given the same situation, having to go through an intermediate node, if at all pos-
sible, enlarges the distance estimate significantly, even though they may be much closer to each
other. Despite being affected by obstacles, ANIML-Hop still provides comparable accuracy to
that of DV-Hop in uniform networks, even in the presence of obstacles and without dynamically
adjusting the hop distance estimate.
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ANIML (400)ANIML-Abs (5/400)
ANIML-Abs (10/400)ANIML-Hop (5/400)
ANIML-Hop (10/400)
(a) 400 nodes/km2
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ANIML (800)ANIML-Abs (5/800)
ANIML-Abs (10/800)ANIML-Hop (5/800)
ANIML-Hop (10/800)
(b) 800 nodes/km2
Figure 3.10: Localization with Obstacles
3.4.7 Using RSSI to Estimate Distance
Using artificially introduced ranging errors is useful for determining how a range-aware localiza-
tion technique handles ranging errors. However, in real sensor network deployments nodes must
handle ranging errors introduced due to outside interference. The difference being that ANIML
prefers smaller distance estimates to larger distance estimates and in all previous simulations, we
introduced a new random ranging error on every transmission, so the likelihood of improving
an extremely incorrect distance estimate was good. However, when using true RSSI, since out-
side influences causing signal losses are likely to continue to cause signal losses on successive
transmission, the likelihood of improving significantly inaccurate distance estimations is small.
Figure 3.11 shows the localization effectiveness of ANIML and ANIML-Abs in uniform networks
using RSSI to determine distance estimates, simulated using ns-2’s TwoRayGround propagation
model. Obviously, using RSSI to determine distance estimates has no effect on ANIML-Hop. The
data demonstrates while suffering a small 5-10% decrease in localization accuracy as compared to
Figure 3.7, ANIML still provides good accuracy even when using much less predictable RSS to
estimate distances. Qualitatively even though the results of ANIML using RSS are naturally less
ideal than using a simplified freespace model, ANIML using RSS still provides better localization
37
than DV-Hop, and still remains comparable to SDP, ILS and MDS-MAP(P).
0
2
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Network Area (square kilometers)
ANIML w/ RSS (0/400)ANIML-Abs w/ RSS (5/400)
ANIML-Abs w/ RSS (10/400)ANIML (0/400)
ANIML-Abs (5/400)ANIML-Abs (5/400)
(a) 400 nodes/km2
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Network Area (square kilometers)
ANIML w/ RSS (0/800)ANIML-Abs w/ RSS (5/800)
ANIML-Abs w/ RSS (10/800)ANIML (0/800)
ANIML-Abs (10/800)ANIML-Abs (10/800)
(b) 800 nodes/km2
Figure 3.11: Distance Estimates from TwoRayGround Propagation Model
3.5 Sea-ANIML
The ideal solution to extensive monitoring of large-scale environments is the deployment of wire-
less sensor networks, however most sensor networking technology is not readily designed for the
deployment in aquatic environments. Localization is a critical challenge in underwater sensor
networks, even more so than in terrestrial networks, because GPS is not readily available due to
GPS signals not propagating correctly through water [22]. In this section, we present an adapta-
tion of ANIML specifically for use as an underwater sensor network localization technique, called
Sea-ANIML. We implemented Sea-ANIML and Sea-ANIML in order measure their localization
effectiveness. We found that Sea-ANIML retains all the advantages of ANIML, while requiring no
additional computation and incurring only a small increase in message complexity.
This section is organized as follows. Section 3.5.1 introduces our Sea-ANIML technique as an
adaptation of ANIML and Section 3.5.2 contains performance analysis of Sea-ANIML.
38
3.5.1 Sea-ANIML
Operationally, Sea-ANIML functions the same as ANIML, the only exception being that each node
now has an additional piece of information to broadcast and collect. Formally, the only difference
mathematical difference between ANIML and Sea-ANIML is all position vectors (i.e. x, xi and
x0) are 1× 3 vectors, instead of 1× 2 vectors, which changes the A of Equation 3.5 into a 3 × n
matrix. This alone implies for Sea-ANIML requires more computation in order to localize in the
three-dimensions of an underwater sensor network. However, in underwater sensor networks the
depth, or z component of x, is a known quantity for all nodes in the network. Therefore, since z is
constant, the z component of riTx moves to the other side of the equation, leaving us with a set of
equations of the form:[
rix riy
]
x
y
= ri
Txi + di − rizz, (3.6)
where rix, riy and riz are the x, y and z components of ri and x, y and z are the x, y and z
components of x. This allows our A of Equation 3.5 to remain a 2× n matrix, which allows Sea-
ANIML to localize a three-dimensional underwater sensor network with no additional computation
over that of ANIML.
3.5.2 Performance Evaluation
Zhou et al. provide a comprehensive evaluation of their localization technique for large-scale un-
derwater sensor networks [95,96]. Their evaluation also provided sufficient experimentation detail
to allow us to mimic their performance evaluation in order to evaluate the localization accuracy
of our own approach with respect to anchor density and average node degree. We executed Sea-
ANIML with 0%, 5%, 10% and 20% anchor density and average node degrees of 8 through 16.
All simulations operate in a 100m3 region containing 500 randomly placed nodes. We varied the
average degree of the nodes by adjusting the communication radius of the nodes. All distance es-
timates are obtained by adding a uniformly distributed error (0-90%) to the true distance between
39
two neighboring nodes, in order to replicate range measurement errors. Each data point presented
in our plots is the average of ten runs with differing random seeds, with no discarding of outliers.
Results show that our approach provides complete and accurate localization, independent of anchor
node density, in underwater sensor networks of varying densities.
Figure 3.12 shows the localization accuracy of Sea-ANIML, while Figure 3.13 shows the lo-
calization accuracy of Zhou et al.’s localization scheme, as well as their baseline recursive and Eu-
clidean localization schemes. The results show the accuracy of Zhou et al.’s is heavily dependent
on the anchor density within the network, whereas the anchor density also does not significantly
impact the accuracy of Sea-ANIML, since Sea-ANIML provides the same localization accuracy
independent of anchor density. This allows Sea-ANIML to provide accurate localization at less
cost than Zhou et al.’s technique, since fewer anchors are required to ensure a high level of abso-
lute localization accuracy and no anchors are required to ensure a high level of relative localization
accuracy.
0
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(d) Anchor percentage=20%
Figure 3.12: Localization accuracy of Sea-ANIML
40
(a) Anchor percentage=5% (b) Anchor percentage=10% (c) Anchor percentage=20%
Figure 3.13: Localization accuracy of Zhou et al.’s technique, taken from [95, 96]
While the localization accuracy of Zhou et al.’s technique is better than Sea-ANIML when the
average degree is low in a low anchor density, Sea-ANIML will localize any node in the network
that can communicate with three or more other nodes, which is almost always 100% of nodes when
the average node degree is above 5. In all simulations present here, the localization coverage of
Sea-ANIML was 100%. However, Figure 4 shows that the localization coverage of Zhou et al.’s
technique ranges from as low as 5% to a maximum of only about 60% when the average degree is
low.
(a) Anchor percentage=5% (b) Anchor percentage=10% (c) Anchor percentage=20%
Figure 3.14: Localization coverage of Zhou et al.’s technique, taken from [95, 96]
41
3.6 Summary
In this chapter, we have presented ANIML, an iterative, anchor-free, range-aware relative localiza-
tion technique for wireless sensor networks. The key advantages of ANIML are that requires no
explicit error control or global information. By using only iterative least-squares off of a node’s
1- and 2-hop neighborhood ANIML is capable of providing accurate relative localization. We also
showed that ANIML is easily adaptable into other types of network deployments, such as net-
works with deployed anchors (ANIML-Abs), networks with no ranging equipment (ANIML-Hop)
and underwater sensor networks (Sea-ANIML). We implemented ANIML and its terrestrial vari-
ants in ns-2 and performed extensive performance evaluation. The performance evaluation showed
that ANIML, ANIML-Abs and ANIML-Hop provide accurate localization in uniform topologies
and scales well in large sensor deployments. Additionally, they provide better overall localization
than DV-Hop [61] in uniform topologies. Further results showed that ANIML, ANIML-Abs and
ANIML-Hop also provides better overall localization than DV-Hop and are robust in the presence
of non-uniform deployment scenarios, such as C-shaped and non-uniformly dense networks. We
also showed that ANIML continues to provide accurate localization in the presence of RF-opaque
obstacles and when depending on the inaccurate distance measurements encountered from RSSI.
Lastly, we showed that Sea-ANIML provides better absolute localization in underwater sensor
networks than Zhou et al.’s technique [95, 96] and is also capable of providing accurate relative
localization in underwater sensor networks.
42
CHAPTER 4
BOUNDARY RECOGNITION
4.1 Overview
Most large-scale sensor deployment scenarios do not assume placing node in predetermined posi-
tions. This leads to a WSN in which the topology is completely unknown. Localizing the network
provides some information about a network’s topology, such as, total area covered, whether or not
one or more node are located at a specified location and, in the case of having absolute localiza-
tion, where on a map the sensors are located. However, there are significant pieces of information
that localizing a network does not provide. Specifically, the shape of the network deployment
can provide important information about the region under observation. The boundaries of the net-
work, both the inner (i.e. internal connectivity holes) and the outer (i.e. the network’s external
perimeter), almost always have a physical correspondence to the environment in which the sen-
sors are deployed [85]. One key aspect of identifying the deployed topology of a wireless sensor
network is that of boundary recognition, which entails the identification of all connectivity holes,
including the external perimeter, within a wireless sensor network. The basis for the development
of many boundary recognition techniques is that the techniques will be topological, which means
they do not depend on a localized network. In fact, the intention of many topological boundary
recognition techniques is to replace the need to localize network. The commonly accepted no-
tion is that localizing a network provides everything there is to know about a deployed network
topology, but at a significantly high cost. So, many propose boundary recognition techniques as a
lesser cost alternative to localization that provides a courser granularity of data. However, localiz-
ing a network does not necessarily provide the same type information as a boundary recognition
technique. Localization techniques, like ANIML, usually do not directly provide any associations
between nodes, such as the boundaries of holes located in the network and boundary recognition
43
techniques do not match sensor data readings to topological information. So instead, the argument
goes that if you have physical coordinates of all nodes you can use a geometric approach, such
as [24,25], to identify the topology of the sensor deployment. However there is no straightforward
geometric technique for hole detection that does not assume connectivity is simply a function of
node distance. Determining holes based only on physical coordinates does not consider the case
of two nodes whose coordinates are within communication range of each other not being able
to communicate directly (e.g. in the presence of obstacles or non-unit-disk transmission ranges).
Additionally, without location information the accuracy of any identified boundary cannot be eval-
uated, or improved, because it is not possible to determine if there are any nodes located on the
inside of a boundary.
While boundary recognition may not seem critical to the operation of a wireless sensor net-
work, not being aware of the boundaries within a wireless sensor network can lead to degradation
in performance over time. For example, in shortest path routing, nodes along the boundary of a
hole tend to receive more intermediate route requests, increasing their overall load and ultimately
reducing their power sources faster than other nodes in the network [27]. This can cause a small
hole to grow over the lifetime of the network due to failing boundary nodes. Also knowing infor-
mation about connectivity holes in a wireless sensor network can indirectly provide information
about unknown geographic features that caused the holes. Further, relationships between connec-
tivity holes and known geographical features could allow mapping from relative coordinates to
absolute coordinates without any deployed anchors.
A significant challenge in the problem of boundary recognition is identifying holes without
making assumptions that do not necessarily hold true in general wireless sensor network deploy-
ments. Commonly made assumptions can involve network density, the minimum size of a hole
and the communication properties of nodes. The problem with assumptions about network density
is not necessarily the making of unreasonable assumptions about what it means to be dense or
sparse, but that techniques too often only work in networks of certain densities. For example, the
44
techniques presented in [28] and [27] assume an average node degree of at least 100, whereas the
technique presented in [85] assumes an average node degree of at most 10. In both situations, the
performance of the techniques suffers when the actual density does not meet the assumed ideal
density. Related to density, another commonly made assumption is that density will be uniform
over the entire wireless sensor network. Without controlled node deployment, no guarantee about
uniformity or uniform degree is possible. The most common assumption about the communication
properties of the nodes is strictly assuming that transmission range is a perfect circle, or near per-
fect circle, and that the ability for two nodes to communicate is determined only by the distance
between the two nodes. However, making these assumptions is not necessarily wrong, they just
need to be restricted to use as approximations and not assumptions (i.e. techniques making these
assumptions still require the exchange of HELLO messages in order to determine actual connec-
tivity). The final common assumption in boundary recognition is making an assumption about
the minimum size of a hole. While there actually is a minimum size to a connectivity hole in a
wireless sensor network, it is not defined on the scale of multiple hops as assumed by the tech-
nique in [85]. Fang et al. more generally define the boundary of an connectivity void in a sensor
network’s communication graph as “a closed cycle with no self-intersections that bounds a closed
region” [25]. By this definition, the smallest possible hole in a wireless sensor network is bound
by a quadrilateral of four nodes that can only communicate along the outside of the square and not
across the diagonals.
In this chapter, we present a distributed boundary recognition technique that accurately identi-
fies connected perimeters for not only the outer boundary of the entire network, but also any inter-
nal connectivity holes within a wireless sensor network, or inner boundaries. Our technique makes
no assumptions about the network deployment or shape of holes within a network. The technique is
geometric in that nodes are aware of their own relative coordinates in the network deployment, but
is topological in that it uses actual connectivity rather than simplifying connectivity to a function
of node positions and maximum transmission range (i.e. unit disk graph communication). This
45
combination of node positions and actual connectivity information allows our technique to provide
accurate connected perimeters with no assumptions about the network deployment. While having
location-aware nodes makes some tasks easier, the identification of global geometric structures,
like connectivity hole boundaries, remains a challenge, and hence, several different techniques for
boundary recognition were proposed. In reference to the usefulness of node positions in identi-
fying boundary nodes in wireless sensor networks, Fekete et al. state “Computing coordinates is
not an end in itself. Instead, some structural location aspects do not depend on coordinates” [28].
Chintalapudi and Govindan show that “. . . irregular node placement makes it hard to even define
precisely whether a node is at an edge or not” [18]. Our technique provides three significant
benefits, overcoming the difficulties other boundary recognition techniques encounter. First, our
boundary recognition technique uses only connectivity when determining neighboring nodes and
does not assume unit disk graph communication; due to radio irregularity, the actual transmission
ranges of sensor nodes are not perfect circles [92]. Second, our approach identifies connected
outer and inner perimeters of the network and not just the nodes that are located on or near the
boundaries. The identification of connected perimeters implicitly identifies boundary nodes within
a network deployment in addition to how the nodes relate. Due to the complexity required to
identify the relationships between boundary nodes needed to connect them, identifying connected
perimeters is the harder of the two approaches [85]. Last and most significant, our technique pro-
duces accurate boundary recognition, leaving no connected nodes outside the constructed outer
perimeter or inside any of the constructed inner perimeters.
The rest of this chapters’s organization follows. Section 4.2 presents related work on boundary
recognition. Section 4.3 introduces our approach. Section 4.4 contains performance evaluation
and Section 4.5 a summary of the chapter.
46
4.2 Related Work
Previous work in boundary recognition techniques is closely related to the geographical routing
technique known as geographic face [46] or perimeter [11,43] routing, which allows geographical
routing strategies to successfully navigate around holes in the connectivity of a network. Boundary
recognition techniques can be classified into one of three categories: geometric, statistical and
topological [85].
Closely related to the field of computational geometry, geometric-based techniques use geo-
graphical location information to detect holes in connectivity. However, it is not simply the avail-
ability of node coordinates that makes a boundary recognition technique a geometric technique;
instead, it is the simplification that connectivity is just a function of node coordinates and trans-
mission range, which is never the case in practice [92]. Martincic and Schwiebert have proposed
a geometric-based technique for identifying nodes on the outer perimeter of a wireless sensor net-
work using valid enclosing cycles to differentiate internal nodes from nodes on the perimeter [57].
This approach assumes transmission ranges are perfect disks and it does not associate identified
nodes together into an identified perimeter. Fang et. al propose two face routing strategies, one
that pre-builds routes around holes in a wireless sensor network using Delaunay triangulation and a
second simple greedy method for determining boundary cycles in the event that a transmission gets
stuck at a node [24,25]. The single biggest disadvantage of both of Fang et. al’s approaches is that
a hole is identified as a hole if and only if a geographically forwarded transmission can get stuck at
a node on the edge of the hole. In addition, the techniques only consider routing around holes and
do not guarantee the actual perimeter of any holes will be identified. Another disadvantage is both
approaches also depend on the assumption that transmission ranges are perfect disks. In general,
the problem with pure geometric-based techniques is that small connectivity holes introduced by
the placement of obstacles cannot be identified using only location information.
Statistical methods for boundary detection make assumptions about the statistical properties
47
of a wireless sensor deployment in order to detect holes, in addition to other common assump-
tions about wireless sensor networks (e.g. unit disk graph communication and hence symmetric
communication links). Fekete et. al present a boundary recognition technique that makes a sta-
tistical assumption regarding the degree of nodes on boundaries versus those in the interior of the
network [28]. In order to handle different possible boundary shapes, the technique dynamically
selects an appropriate threshold for the degree of a node in order to differentiate between a bound-
ary node and an interior node. However, making assumptions about the degree of boundary nodes
could lead to the non-identification of smaller connectivity holes. An additional disadvantage is the
technique strictly requires an extremely dense uniform deployment of sensor nodes, which cannot
be guaranteed in practice. Another statistical approach towards boundary recognition, also pro-
posed by Fekete et. al, computes the “restricted stress centrality” of a vertex, which is the measure
of the number of shortest paths of bounded length that go through a vertex [27]. Similar to the
first technique, nodes in the interior tend to have a greater centrality than nodes on the boundary.
This approach suffers similar disadvantages as the previous approach. Bi et al. [9] present another
statistical method that identifies boundary nodes because boundary nodes typically have smaller
degrees than their 2-hop neighbors do. However, this technique suffers from a high false positive
rate.
Topological methods for boundary detection use only network connectivity information to de-
termine boundaries. Ghrist et al. propose a centralized algorithm that uses homology to detect
holes in a wireless sensor network for the purpose of determining insufficient coverage area, but
it requires that transmission ranges are carefully tuned disks [32]. Additionally, this algorithm
only identifies whether or not there is hole and does not determine the properties of the hole. An
algorithm for boundary detection that searches for combinatorial structures called flowers and aug-
mented cycles has been proposed by Kroller et. al [48]. This algorithm, unlike many mathematical
approaches for boundary detection, lessens the restriction that transmission ranges must be per-
fect disks, instead requiring that the communication graph be a quasi-unit disk graph. Funke and
48
Klein have developed a practical and simple heuristic for boundary detection using only connec-
tivity information [29, 30]. The approach is to construct hop-based isocontours from a single root
node and simply identify where the contours are broken. Although the authors’ proof of correct-
ness assumes uniform transmission ranges, the presented distributed technique does not require
the assumption to hold true, since connectivity is determined through HELLO messages. Given
sufficient density, this technique successfully identifies nodes on the boundary of a hole as well
as the external perimeter of the network. However, this technique in no way relates the identified
boundary nodes together into perimeters. Therefore, while the technique can identify boundary
nodes it is not able to associate them together into specific holes or perimeters within the network,
which does not provide much information about the holes or even how many of them exist. Wang
et al. have developed another practical approach for boundary recognition using only connectivity
information [85]. The basic idea is to first build a shortest path tree from a root node and then iden-
tify adjacent nodes whose least common ancestor in the shortest path tree is too far away. These
identified adjacent nodes with a far away least common ancestor are labeled as cut nodes and are
used to identify whether the shortest path tree was built around a connectivity hole. By grouping
together adjacent cut node pairs and favoring the cut node pair closest to the root of the shortest
path tree, the technique forms a perimeter around internal holes by connecting the two paths in
the tree from the cut nodes to their least common ancestor. This technique also allows for the
identification of the external perimeter by broadcasting hop counts from the determined internal
perimeter(s). The first disadvantage of this technique is that it uses a diameter-based threshold to
define “far away,” which has to be carefully chosen in order to not ignore small holes, in the case of
a large threshold, or misidentify non-holes as holes, in the case of a small threshold. Additionally,
this approach requires a rather low density sensor deployment in order to build an ideal shortest
path three for the technique (i.e. one in which two adjacent nodes which share a common neighbor
closer to the root of the tree will most likely have that node be their least common ancestor in the
tree). However, in the general case, especially in high-density deployments, the shortest path tree
49
can build long adjacent parallel paths, which to this technique appear as traversing non-existent
connectivity holes. This technique suffers from a limitation that all topological boundary recogni-
tion methods encounter, which is without any location information it is difficult to determine if any
node exists on the wrong side of a perimeter. More recently Fayed and Mouftah developed lcv, a
convex hull-based technique to accurately identify the nodes on the outer perimeter of a wireless
sensor network [26]. This technique also does not associate nodes into perimeters and it can incur
high false positives in the presence of internal connectivity holes.
4.3 Approach
We assume every node knows its own position. While the need for nodes to know their own
positions within the network could increase the cost of deploying the network if every node was
required to be GPS-equipped, our technique only requires a relative coordinate system. A relative
coordinate system for a wireless sensor network can be determined dynamically after deployment,
with no need for any GPS equipment, by taking advantage of ANIML’s relative localization. On the
other hand, we do not assume that the communication graph of the wireless sensor network follows
the unit disk graph assumption, instead relying only on actual node connectivity to determine which
nodes can communicate directly. An additional benefit of executing in a localized network is that
our technique can take advantage of geographic forwarding, instead of traditional flood-based ad-
hoc routing techniques, in order to reduce its overall communication cost.
Without loss of generality we assume operation in a connected network (i.e. there exists a
path from any node to any other node in the network). Obviously, in the case of a partitioned
network deployment, the technique treats each network partition as its own independent network
deployment; instead of a single outer boundary, our technique identifies an outer perimeter for each
partition. In addition, for ease of presentation, we assume symmetric connectivity.
We now provide an outline of our boundary recognition technique and then elaborate on these
steps.
50
1. Identify the outer perimeter of the network (Figures 4.1a–4.1g).
(a) Identify the boundary nodes of the network (Figure 4.1a).
(b) Construct a single group of all connected nodes (Figure 4.1b).
(c) Identify the convex hull of the network (Figure 4.1c).
(d) Connect the convex hull nodes of the network together into a rough outer perimeter
(Figure 4.1d).
(e) While there are uncaptured nodes remaining (i.e. nodes not bound by some constructed
perimeter), repeat steps 1b–1d on increasingly smaller connected subsets of uncaptured
nodes (Figure 4.1e).
(f) While there is more than one identified perimeter, merge the perimeters together to
form the final outer perimeter (Figure 4.1f).
(g) Refine the final external perimeter (Figure 4.1g).
2. Identify the inner perimeter(s) of the network (Figures 4.1h–4.1i).
(a) For each perimeter, starting with the outer perimeter, find a path between two points on
the perimeter, entirely contained within the perimeter.
(b) Split the perimeter along the identified path (Figure 4.1h).
(c) Repeat until no more splits are possible (Figure 4.1i).
The single most costly process, in terms of communication, required for our boundary recog-
nition technique is in Step 1b, constructing a single group of all connected nodes. Our technique
employs a leader election process, in order to construct a single group of all connected nodes.
Additionally, with the exception of the simple one-to-many flood required to notify all nodes in
the group about the initial outer perimeter constructed in Step 1d, all other communication in our
51
boundary recognition technique either are local neighborhood broadcasts or point-to-point com-
munications.
4.3.1 Outer perimeter
The first step, consisting of seven substeps, of our technique is to determine a connected outer
perimeter for the network. This constructed outer perimeter is the starting point for the identifica-
tion of any inner perimeters in Step 2.
Identifying the Boundary Nodes of the Network
While this step is an optional, it drastically decreases the processing and communication cost of
computing the convex hull in Step 1c. Fayed and Mouftah’s lcv is an effective way for a sensor
node to self-determine if it is likely on the outer edge of a wireless sensor network [26]. The
technique simply collects the coordinates of its 1-hop neighbors than identifies whether it is on the
convex hull of its 1-hop neighborhood. If it is not on the convex hull it is not on the outer perimeter
of the network because it is an internal node in its 1-hop neighborhood and therefore an internal
node of the entire network. Fig. 4.2 shows the identified outer perimeter nodes for both a single
hole and a multi-hole topology. The reason that performing this pre-processing step decreases the
processing and computation cost of the computing the convex hull of the entire network is that
reduces the number of nodes that must be eliminated when determining the convex hull. Any
node on the network’s convex hull must also be the on the convex hull of its local neighborhood.
This makes the convex hull of the entire network is the same as the convex hull of all nodes that
identify themselves on the convex hull of their 1-hop neighbors, which, as shown in Figure 4.2, is
a small fraction of the total nodes in the network. Additionally, the fact that lcv is error-prone in
the presence of internal connectivity holes, also shown in Figure 4.2, is irrelevant since accuracy
is not key, only reducing the search space for the the Graham scan algorithm in Step 1c.
52
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 4.1: Our technique executed on an example topology with one concave hole. The averagedegree is 20. (a) The self-identified perimeter nodes (black squares); (b) The initial group and self-identified perimeter nodes (black squares); (c) The identified convex hull nodes (black squares);(d) The initial external perimeter, in addition to the groups of remaining uncaptured nodes (blacksquares identify uncaptured groups with only a single uncaptured node); (e) The identified perime-ters after all nodes are captured (black squares identify perimeters composed of only a single node);(f) The final rough external perimeter after all perimeters are merged; (g) The final external perime-ter after refinement; (h) The first perimeter split; (i) The final internal and external perimeters.
53
(a) (b)
Figure 4.2: The self-identified boundary nodes (black squares) for (a) a single hole topology (4050nodes with an average degree of 10) and (b) a multi-hole topology (4050 nodes with an averagedegree of 10).
Building the initial group
The second substep of identifying the outer perimeter of the network is to collect the entire network
into a single group. Initially every node attempts to start its own group, through a network flood,
with each node abandoning its own group and joining a group created by a node with a smaller
unique identifier, if discovered. This will eventually leave a single group of all nodes within the
network, the node which started the last remaining group is known as the group leader of the
network. Fig. 4.3 shows the initial groups for both a single hole and a multi-hole topology.
Identifying the convex hull
The computation of the convex hull of a finite set of points is considered fundamental to the field
of computational geometry. In a Euclidean space, an object is convex if for any pair of points
within the object, any point on the straight line segment that joins them is also within the object.
The definition of the convex hull for a finite set of points is defined as the smallest convex set that
contains the entire set of points. Intuitively, if the points of a set where protruding pegs on a board
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(a) (b)
Figure 4.3: The initial group for (a) a single hole topology and (b) a multi-hole topology.
and a rubber band was stretched around all of the pegs, the convex hull would be the pegs that the
rubber band touches when released. A simple and well-known algorithm for finding the convex
hull is known as Graham’s scan, shown in Figure 4.4. Graham’s scan can identify the convex hull
of a set of points, S, in O(NlogN) time, where N is the number of points in the set. Additional
detail on this algorithm, including a proof of correctness, is available in [67].
Once the initial group is built in the previous step, the initial group’s leader identifies the
network’s convex hull. The identification of the network’s convex hull is easily accomplished using
Graham’s scan algorithm, on the perimeter nodes identified in Step 1a. The coordinates of all the
self-identified perimeter nodes from Step 1a piggyback themselves to the initial group’s leader
on the messages sent in the previous step. If Step 1a was not done, our technique still operates
properly, however the group leader will have to calculate the convex hull on the entire set of
network coordinates. This will greatly increase the amount of data the group leader must gather and
that the network must propagate, in addition to the increased computation time required to compute
the convex hull. Following the identification of the convex hull, the nodes composing the convex
hull receive notification of their status as well as the identity of the convex hull node immediately
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1. Choose an internal point q.
2. Using q as the origin, sort the points of S by polar angle and distance from q and insert theminto a doubly-linked list l.
3. Scan.START ← l[0]v ← STARTwhile v.Next 6= START do
if the three points v, v.Next and v.Next.Next form a left turn thenv ← v.Next
elseDelete v.Next from lv ← v.Prev
end ifend while
Figure 4.4: Graham’s Scan
following them in an angular ordering of all the convex hull nodes. Since the identification of the
convex hull requires node positions, this step is geometric in nature and not topological. Fig. 4.5
shows identified convex hull nodes for a single hole and multi-hole topology.
At first, it seems that identifying the convex hull of the network provides less information than
simply identifying an angular ordering of all the external perimeter nodes, with something like
lcv [26]. However, identifying the convex hull provides several advantages. First, identifying the
convex hull ensures robustness in the presence of connectivity holes. In the presence of connec-
tivity holes, an external perimeter detection technique can identify one or more nodes on the edge
of a connectivity hole as an outer boundary node and with no straightforward way to identify false
positives can lead to anomalies in the connected outer perimeter. The second, and most impor-
tant, ability gained through the identification the convex hull is the ability to operate on arbitrarily
shaped networks. In the case of convex networks, and even some concave networks, an angular
ordering of all external nodes will provide the same, if not more, information as the convex hull.
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However, in the case of arbitrarily shaped networks it is possible that a traversal of the external
boundary nodes actually changes directions. In this case, connecting the identified external nodes
in angular order will connect the perimeter together incorrectly, whereas connecting the convex
hull nodes will correctly navigate the irregularity of the outer perimeter.
(a) (b)
Figure 4.5: The identified convex hull nodes (black squares) for (a) a single hole topology and (b)a multi-hole topology.
Constructing the rough outer perimeter
The convex hull nodes are likely not within communication range, therefore, in parallel, each con-
vex hull node determines a route to the next convex hull node. Routes are determined using a
geometric routing technique, in order to reduce communication cost. The individual routes are
concatenated together to form the rough outer perimeter. This perimeter is very close to the true
outer perimeter of the network. The intuitive notion is that the connection of the convex hull
nodes should result in a final outer perimeter. However, due to the possibility of multiple paths
and/or irregularities existing between the convex hull nodes, it is possible that one or more nodes
are left uncaptured, remaining outside of the constructed rough perimeter. Typically only a very
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small number of nodes remain outside the constructed perimeter. Once the rough perimeter is con-
structed, the leader informs the entire network with a broadcast and each node uses this information
locally to determine if it remains uncaptured and in turn notifies the leader node of its status. Fig.
4.6 shows the constructed rough outer perimeter for a single and multi-hole topology, in addition
to the nodes that remain uncaptured. For clarity, large outlined squares identify uncaptured nodes.
Now any of the remaining uncaptured nodes need to be assimilated into the rough outer perimeter,
which is the sole purpose of the next two steps.
(a) (b)
Figure 4.6: The initial external perimeter for a (a) single hole topology and (b) multi-hole topology,in addition to the groups of remaining uncaptured nodes. Black squares identify uncaptured nodes.
Capturing the remaining uncaptured nodes
If no nodes remain uncaptured after the previous step, this and the following step are not necessary.
However, if uncaptured nodes remain, Steps 1b, 1c and 1d execute, in parallel on each set of
connected uncaptured nodes. This repeats on increasingly smaller sets of connected uncaptured
nodes until there are no nodes that remain uncaptured. Figure 4.7 shows an example of capturing a
small set of nodes left uncaptured by the construction of an initial rough outer perimeter. Since, the
remaining uncaptured nodes tend to be single isolated nodes or very small groups of nodes; we find
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that only two additional repetitions are required in order to capture all nodes in most topologies.
Fig. 4.8 shows the single multi-hole topologies after the capturing of all nodes.
(a) (b) (c) (d)
Figure 4.7: An example of capturing a small set of nodes left uncaptured by the construction ofthe initial rough outer perimeter. From left to right: (a) The connecting of the network’s convexhull nodes has left a small group of nodes uncaptured by the rough initial perimeter; (b) The nodesgroup themselves together and identify their own convex hull nodes (white circles); (c) The convexhull nodes connect themselves together, but one node is left uncaptured; (d) The uncaptured nodefinds no other nodes to group with, so it is its own group and therefore its own perimeter.
(a) (b)
Figure 4.8: The identified perimeters after all nodes are captured for (a) a single hole topology and(b) a multi-hole topology.
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Merging constructed perimeters
Once no uncaptured nodes remain, we are left with the task of assimilating a set of small perimeters
or single nodes into the rough outer perimeter. The assimilation of perimeters and nodes outside
the rough perimeter into the rough outer perimeter is a localized decision making process requiring
the use of only local node coordination and exchanges of information. By taking advantage both
geometric and topological knowledge of the network, the merging of uncaptured nodes into a single
outer perimeter allows our technique to provide an accurate outer boundary while not making
unrealistic assumptions about the connectivity of the deployed sensor nodes. Figure 4.9 shows an
example of merging on the of the perimeters identified in Figure 4.7.
(a) (b) (c) (d)
Figure 4.9: An example of merging on the of the perimeters identified in Figure 4.7. From leftto right: (a) The perimeters identified in Figure 4.7; (b) The last perimeter to be identified is thesingle node, therefore it merges into the six-node perimeter from which it was left uncaptured; (c)The new seven-node perimeter and its attempt to merge into the initial rough outer perimeter, fromwhich its original six-nodes were left uncaptured; (d) The outer perimeter once the seven-nodeperimeter is merged.
In general, there are three types of perimeters, which we call outer perimeters, that need merg-
ing: single nodes, lines and polygons. Outer perimeters merge into what we call inner perimeters.
The terms inner and outer perimeters in relation to this subsection should not be confused with the
more general terms inner and outer perimeters/boundaries used throughout this chapter to denote
the perimeters of any connectivity holes and the external perimeter of the network. Since nodes
can only be left uncaptured by a polygon perimeter (i.e. at least three other nodes had to form
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the perimeter that left them uncaptured), inner perimeters are always polygons. Therefore, outer
perimeters only ever need to merge into a polygon inner perimeter. The ideal merging case is
that the outer perimeter can communicate directly with at least two nodes on the inner perimeter,
without the two newly created edges crossing each other. This ideal case makes merging trivial;
however, a specific non-ideal case can arise. Making the assumption that a network is connected,
but not assuming that communication follows a unit-disk graph, leads to the possibility that an
outer perimeter can only communicate with nodes inside the inner perimeter and cannot commu-
nicate with nodes on the inner perimeter itself. In this case, one or more nodes inside the inner
perimeter need placed onto the inner perimeter before merging the outer perimeter. Fortunately,
it is typical that these nodes are very close to the inner perimeter itself and added easily through
short route requests. Once added to the inner perimeter, merging proceeds in the same fashion as
the trivial case. Figure 4.10 shows the single hole and multi-hole topologies after the merging of
all the perimeters into a single outer perimeter.
(a) (b)
Figure 4.10: The final rough outer perimeter after all perimeters are merged for (a) a single holetopology and (b) a multi-hole topology.
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Refining the identified external perimeter
The identified outer perimeter after Step 1b or Step 1d, depending on whether or not Step 1b
left one or more nodes uncaptured, is a correct perimeter. However, it is desirable to generate
a more compact representation of the perimeter (i.e. a perimeter with fewer nodes) in order to
reduce the cost of transmitting the perimeter throughout the network and beyond. The refinement
phase consists of identifying non-adjacent nodes on the perimeter that are connectable in one hop
without uncapturing any bypassed perimeter nodes, in order to reduce the number of nodes on
the perimeter. For example, given a portion of the perimeter a → b → c → d, where a and d
can communicate directly, a → b → c → d would be replaced with a → d if the nodes b and
c where still captured inside of the new perimeter. Fig. 4.11 shows the final outer perimeter for
the single hole and multi-hole topologies. Since the identified perimeter is much more irregular
than the actual shape of the network deployment, a naive interpretation is that our technique has
produced an inaccurate outer perimeter. However, there are no nodes outside the identified external
perimeter, meaning the identified perimeter is the closest possible perimeter to the true shape of
the network that these topologies will allow.
4.3.2 Inner perimeter(s)
An intuitive approach to the challenging problem of identifying inner perimeters of wireless sensor
network, given an identified outer perimeter, is to shrink the given outer boundary until it tightly
surrounds the connectivity hole(s) of the network. However, this approach does not easily translate
into an effective programmatic solution. Shrinking of the outer perimeter cannot happen in the
typical continuous sense (i.e. the length of the perimeter decreases while maintaining the same in-
ternal center point); the perimeter must shrink through the addition and removal of sensor nodes on
the perimeter. Compounding the problem is the fact that the choice of which nodes to add/remove
and how to add/remove them is non-trivial, due to the spatial irregularity of the nodes in wireless
sensor network. Additionally, this adding and removing of nodes happens on the same perimeter,
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(a) (b)
Figure 4.11: The final external perimeter after refinement for (a) a single hole topology and (b) amulti-hole topology.
which makes it more difficult to distribute the work, since the choices are not independent. Based
on the principle of tightening perimeters around connectivity holes, our technique’s approach to
identifying any inner perimeters conceptually provides the same results as shrinking the outer
perimeter, but allows for natural work distribution and requires no tricky addition or removal of
nodes, using only point-to-point communications.
The simple definition of a connectivity hole in a wireless sensor network is a region of the
network over which no communication is possible. Therefore, given an arbitrary path through
a sensor network, if a connectivity hole exists, the path must pass to one side of the hole. This
principle is the foundation of our technique’s ability to identify inner perimeters in a wireless
sensor network. If split a perimeter in a sensor network into two new perimeters, along some path
contained entirely within the original, any existing connectivity holes bound by the original will
remain bound by one of the new perimeters. Our technique determines the inner perimeters of the
network by repeatedly splitting a set of potential inner perimeters, into two until no more splits
are possible, using the constructed outer perimeter as the initial potential inner perimeter. A single
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split is determined by geographically forwarding a request message from one node, the source,
on a potential inner perimeter to another node on the same potential perimeter, the destination,
where any node outside the potential inner perimeter immediately drops the message. Immediately
handled locally are trivial single hop splits between nodes non-adjacent on the perimeter, without
the need for a split request message. A split request message requires the inclusion of the splitting
potential inner perimeter in the geographically forwarded split request message. Since a localized
node can locally determine if it is inside or outside a given perimeter, upon receiving a route
request a node can locally determine whether to drop or forward the request. While the source and
destination nodes of a split can be arbitrary, the ideal choice of a perimeter’s source and destination
nodes is two nodes likely connected by a path that splits the perimeter into two roughly equal parts,
such as the two nodes farthest apart on the perimeter.
The following procedure illustrates the splitting of a perimeter into two new perimeters using
our technique. If a path a0 → b0 → · · · → bm → an/2, where a0 is the source and an/2 is the
destination, is found within a potential inner perimeter A = a0 → a1 → a2 → · · · → an/2 →· · · → an−2 → an−1 → a0, where the nodes b0, · · · , bm are bound by A, the perimeter is split into
the two new potential inner perimeters a0 → b0 → · · · → bm → an/2 → · · · → a2 → a1 → a0
and a0 → b0 → · · · → bm → an/2 → · · · → an−2 → an−1 → a0. Fig. 4.12 shows the first split of
the outer perimeter for the single hole and multi-hole topologies.
When a selected source and destination node fail to provide a split, another split is attempted
using a different combination of source and destination nodes. An exhaustive search of every
combination of source and destinations nodes on a perimeter for a split could potentially require
a large amount of work. However, an exhaustive search typically only occurs after the perimeter
is almost tightly identifying an inner connectivity hole or the perimeter is very small. In both
cases the cost of failed split request messages are very low. If a perimeter only consists of three
nodes, the perimeter eliminates itself as an inner perimeter, since a perimeter of three nodes cannot
be surrounding a connectivity hole. For example, the left hand perimeter in Fig. 4.12(a) will
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(a) (b)
Figure 4.12: The first perimeter split for (a) a single hole topology and (b) a multi-hole topology.
eventually reduce into many small perimeters of only three nodes, since there is no connectivity
hole within it. When no more splits are possible within a single potential inner perimeter, the
perimeter tightly surrounds an internal connectivity hole and is a true inner perimeter. The rest
of the candidate perimeters in Fig. 4.12 will each eventually split into a perimeter around the
connectivity holes contained within them. Fig. 4.13 shows the final inner and outer perimeters for
the single hole and multi-hole topologies.
4.4 Performance Evaluation
We duplicated the experiments presented by Wang et al. [85] in order to evaluate the performance
of our approach with respect to node density, average neighborhood size and network and hole
shapes. Also, we compared our techniques effectiveness directly against the results presented by
Wang et al. However, since the exact topologies used in Wang et al.’s experiments were not readily
available for us to execute our technique on, we instead ran our technique on topologies generated
using the exact simulation parameters given by Wang et al. All of our experiments assuming non-
unit disk communication, unlike [85]. In order to obtain a non-unit disk communication graph and
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(a) (b)
Figure 4.13: The final internal and external perimeters for (a) a single hole topology and (b) amulti-hole topology.
better emulate the irregularities of wireless communication, we did not determine the connectivity
of our experimental topologies based on only position and transmission range. Instead, we obtained
the connectivity of all topologies by using the shadowing propagation model. The shadowing
propagation model assumes that the signal strength of a transmission decreases logarithmically
with distance and includes a Gaussian random variable to account for environmental influences
[75].
There is no generally accepted metric for measuring the accuracy of a boundary recognition
technique, so the evaluation of a boundary recognition techniques results usually requires visual
inspection. Unfortunately, visual inspection does not allow for easy quantitative assessment of
a boundary recognition technique. This is especially problematic when trying to compare the
accuracy of two different boundary recognition techniques. One simple, often used and easy to
understand metric for measuring the accuracy of a boundary recognition technique is the number
of nodes not correctly bound by the constructed boundaries. Although, for comparing techniques
executing on topologies with different number of nodes, the percentage of nodes not correctly
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bound by the constructed boundaries is more useful. However, there is no clear definition of this
metric for techniques that only identify boundary nodes and do not construct connected perimeters.
In addition, it is difficult to determine by visually inspecting the provided results of techniques that
do not provide readily available implementations.
4.4.1 Effect of node distribution and density
For each figure in this section the circle in the upper left hand corner of the figure represents the
idealized maximum possible transmission range of the sensors in the experiment.
Random distribution of sensors
For this group of simulation experiments, we randomly placed 3500 nodes in a square region with
a single circular hole. We varied the maximum communication radius of the nodes in order to
achieve the desired average node degree. Figure 4.14 shows the results of our approach on ran-
domly distributed nodes with varying average node degrees. In all four simulations, zero nodes
remain outside the outside perimeter constructed by our technique or inside any inner perime-
ters constructed by our technique. Clearly, this shows our technique provides accurate bound-
ary recognition in randomly deployed networks with a single, large regularly shaped connectivity
hole. Additionally, as expected, our technique provides slightly smoother perimeters, more closely
emulating the true boundary of the hole and network, as the degree increases, since fewer inter-
mediate nodes are required to construct the perimeters, due to the nodes having larger maximum
transmission ranges. More interesting, but as expected, Figures 4.14(b)–4.14(d) show that as the
transmission range of the nodes increases some of the irregularities on the constructed inner and
outer boundaries of Figure 4.14(a) become additional internal connectivity holes. Our technique is
naturally able to identify these holes and construct additional inner perimeters around them, even
though there creation was unintentional. The results also show that our technique is able to identify
accurate perimeters even in the event of highly irregular node placement along the edge of the hole,
as is shown when the degree decreases. Lastly and most importantly, Figure 4.14 show that our
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approach is robust in wireless sensor networks with low average degree.
Further, we compare our results, shown in Figure 4.14, to those of Wang et al.’s technique,
shown in Figure 4.15, in a similar, but not identical, network topology with the same number of
nodes and the same average degrees resulting from similar transmission ranges. The results in Fig-
ure 4.15 show that the accuracy of Wang et al.’s technique is highly affected by network density,
since the number of nodes incorrectly bound nodes visibly decreases as the network density in-
creases, whereas our technique’s ability to provide accurate boundaries is independent of network
density. While Wang et al.’s technique constructs close to accurate perimeters when the average
node density is 16, many incorrectly bound nodes remain clearly visible. Overall, our technique
is capable of better boundary recognition than Wang et al.’s technique in randomly deployed net-
works, since our technique provides accurate boundary recognition independent of node density.
(a) (b) (c) (d)
Figure 4.14: Uniformly distributed sensor field. (a) the average degree is 7; (b) the average degreeis 10; (c) the average degree is 13; (d) the average degree is 16.
Grid with random perturbation
In this group of simulations, we again placed 3500 nodes on a grid and then perturbed each point
by a small random amount. The goal of this distribution method is to approximate the manual
deployment of sensors [85]. Again, we varied the maximum communication radius of the nodes
in order to achieve the desired average node degree. Figure 4.16 shows the results of our approach
on a perturbed grid topology with varying average degrees. In all three simulations, as expected,
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(a) (b) (c) (d)
Figure 4.15: Wang et al.’s technique, taken directly from [85], in a uniformly distributed sensorfield. (a) the average degree is 7; (b) the average degree is 10; (c) the average degree is 13; (d) theaverage degree is 16.
zero nodes remain outside the outside perimeter constructed by our technique or inside any inner
perimeters constructed by our technique. In addition, as expected, our approach more closely
captures the true outer and inner boundary in a perturbed grid topology than in a randomly deployed
topology, due to the regularity of node placement provided by the underlying grid. Figure 4.16(b)
again shows that our technique is able to naturally identify small, unintended connectivity holes and
construct additional inner perimeters around them. This is seen as some of the irregularities on the
constructed inner and outer boundaries of Figure 4.16(a) becoming additional internal connectivity
holes in Figure 4.16(b).
Again, we compare our results, shown in Figure 4.16, to those of Wang et al.’s technique,
shown in Figure 4.17, in a similar, but not identical, network topology with the same number of
nodes and the same average degrees resulting from similar transmission ranges. The results in
Figure 4.17 show that Wang et al.’s technique provides more accurate boundary recognition in
perturbed grid deployments than random deployments. In addition, the results show that Wang
et al.’s technique handles much lower node densities with much more accuracy in perturbed grid
deployments than in random deployments. However, despite the much more accurate boundary
recognition of Wang et al.’s technique in perturbed grid deployments, there are still many, clearly
visible, incorrectly bound nodes in Figures 4.17(a)–4.17(c). Overall, our technique is capable of
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better boundary recognition than Wang et al.’s technique in perturbed grid topologies, since our
technique even more closely captures the true outer and inner boundary in perturbed grid topolo-
gies than in a randomly deployed topologies and Wang et al.’s technique continues to produce
perimeters that leave nodes incorrectly bound.
(a) (b) (c)
Figure 4.16: Results for randomly perturbed grids. (a) the average degree is 6; (b) the averagedegree is 8; (c) the average degree is 12.
(a) (b) (c)
Figure 4.17: Wang et al.’s technique, taken directly from [85], in a randomly perturbed grid. (a)the average degree is 6; (b) the average degree is 8; (c) the average degree is 12.
Low density, sparse graphs
In this group of simulations, we again use a perturbed grid but instead of varying the communi-
cation range to vary the average degree of the network we fixed the communication range of each
node and adjusted the average degree by directly decreasing the density of the topology. Figure
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4.18 shows the results of our approach on topologies with varying node densities. In all four sim-
ulations, again as expected, zero nodes remain outside the outside perimeter constructed by our
technique or inside any inner perimeters constructed by our technique. Again, as expected, our
approach more closely captures the true outer and inner boundary in a perturbed grid topology
than in a randomly deployed topology, due to the regularity of node placement provided by the
underlying grid. However, as was the case before, as the average degree decreases our technique
provides slightly rougher perimeters, less closely emulating the true inner and outer boundaries,
since more nodes are required to construct the perimeters.
Again, we compare our results, shown in Figure 4.18, to those of Wang et al.’s technique,
shown in Figure 4.19, in a similar, but not identical, network topology with the same number of
nodes and the same average degrees. The results in Figure 4.19 again show that Wang et al.’s tech-
nique provides more accurate boundary recognition in perturbed grid deployments than random
deployments. Again, the results also show that Wang et al.’s technique handles much lower node
densities with much more accuracy in perturbed grid deployments than in random deployments.
However, the overall results remain the same as previous experiments; our technique provides more
accurate boundary recognition that Wang et al. technique, even in low-density sparse topologies.
(a) (b) (c) (d)
Figure 4.18: Results when the density of the graph decreases. (a) 842 nodes and the average degreeis 7; (b) 1742 nodes and the average degree is 16; (c) 2628 nodes and the average degree is 25; (d)3443 nodes and the average degree is 35.
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(a) (b) (c) (d)
Figure 4.19: Wang et al.’s technique, taken directly from [85], as the density of the graph decreases.(a) 842 nodes and the average degree is 7; (b) 1742 nodes and the average degree is 16; (c) 2628nodes and the average degree is 25; (d) 3443 nodes and the average degree is 35.
4.4.2 Further examples
In Figure 4.20 we duplicated the more challenging experiments from Wang et al. [85] in order
to show that our technique is robust in the presence of irregularly shaped networks and holes. In
all four simulations, even in the presence of significantly irregularly shaped holes and networks,
zero nodes remain outside the outside perimeter constructed by our technique or inside any inner
perimeters constructed by our technique. These results show that, in addition to our technique
being able to produce accurate perimeters in the presence of regularly shaped holes and networks;
our technique is capable of producing accurate perimeters in the presence of highly irregularly
shaped holes and networks.
Again for comparison, the results of Wang et al.’s technique are shown in Figure 4.15 for
similarly shaped network topologies. Since Wang et al.’s technique still produces perimeters that
leave node incorrectly bound, our technique is better at providing accurate boundary recognition
in the presence of irregularly shaped holes and/or networks.
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(a) (b) (c) (d)
Figure 4.20: Results for more interesting examples, adapted from [85]. (a) A spiral shape with5040 nodes and the average degree is 21; (b) A building floor shape with 3420 nodes and theaverage degree is 20; (c) A cubicle shape in an office with 6833 nodes and the average degree is17; (d) A double star shape with 2350 nodes and the average degree is 17.
(a) (b) (c) (d)
Figure 4.21: Wang et al.’s technique, taken directly from [85], for more interesting examples. (a)A spiral shape with 5040 nodes and the average degree is 21; (b) A building floor shape with3420 nodes and the average degree is 20; (c) A cubicle shape in an office with 6833 nodes and theaverage degree is 17; (d) A double star shape with 2350 nodes and the average degree is 17.
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4.5 Summary
In this chapter, we have presented a robust distributed technique that addresses the problem of
boundary recognition in wireless sensor networks. Our technique overcomes the three significant
challenges encountered in current boundary recognition techniques, which are unrealistic assump-
tions about the communication model of the deployed sensor nodes, not connecting identified
boundary nodes into perimeters and high false positive rate in identifying boundary nodes and/or
the construction of inaccurate perimeters. First, our boundary recognition technique uses only
connectivity when determining neighboring nodes and does not assume unit disk graph commu-
nication; due to radio irregularity, the actual transmission ranges of sensor nodes are not perfect
circles [92]. Second, our approach identifies connected outer and inner perimeters of the network
and not just the nodes that are located on or near the boundaries. The identification of connected
perimeters implicitly identifies boundary nodes within a network deployment in addition to how
the nodes relate. Last and most significant, our technique produces accurate boundary recognition,
leaving no connected nodes outside the constructed outer perimeter or inside any of the constructed
inner perimeters We implemented our technique in order to evaluate its performance. Our perfor-
mance evaluation showed that our boundary recognition technique constructs accurate perimeters
(i.e. correctly bounding all nodes) in randomly deployed topologies of varying densities, perturbed
grid topologies of varying densities and in sparsely populated/low-density topologies. Addition-
ally, we showed that our technique is capable of not only being able to produce accurate perimeters
in the presence of regularly shaped connectivity holes and networks, but also capable of producing
accurate perimeters in the presence of highly irregularly shaped connectivity holes and networks.
Lastly, we showed that our technique outperforms Wang et al.’s [85] current boundary recognition
technique.
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CHAPTER 5
EDGE DETECTION
5.1 Overview
Spanning large monitoring areas where the need for efficient and effective collection and analysis
of sensor data is critical in wireless sensor networks. Traditionally, each individual sensor node
forwards its data to a single less resource-constrained location for centralized analysis. However,
this approach can cause high network overhead and reduce the lifetime of the network. The poten-
tial drawbacks of the centralized collect and analyze paradigm for sensor data analysis makes the
development of more advanced data analysis techniques for sensor networks important, which has
led to several distinct approaches to solve the problem. The simplest approach for decreasing the
overhead of data analysis in sensor network are data aggregation techniques, such as SPIN [37]
and LEACH [36]. Data aggregation techniques reduce the overhead of data analysis through basic
packet operations, such as duplicate packet elimination. A more advanced approach for decreasing
data analysis overhead is data fusion. The purpose of data fusion is to reduce overhead by having
the sensors of the network make intelligent choices about the data itself in order to reduce the ob-
tained dataset quickly, thus minimizing the consumption of valuable resources [34]. Last, and more
recent, is edge detection. Edge detection is the idea of reducing data analysis overhead through the
geometric identification of sensed phenomena within a sensor network. A key advantage of iden-
tifying geometric representations of a sensed phenomenon is it provides a more concise view than
enumeration of all nodes identifying a phenomenon, especially if the phenomenon is large [18]. A
more concise view of sensed data can reduce the communication and energy costs of data analysis
and extend the lifetime of the network. Geometrically identifying sensed phenomena also provides
additional benefits such as the ability to map sensed phenomena onto known geographical features
in the deployed region based on geometric shape and to coordinate sleep/wakeup cycles of nodes
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contained within a sensed phenomena’s identified perimeter.
A significant difficulty in edge detection is that sensed data is not normally static or slow chang-
ing, as is the case with node locations. A technique that constructs geometric representations of
sensed phenomena in WSN must have the ability to maintain these geometric representations in
the face of changing sensor values. Not only does this imply that it must construct new geometric
representations as sensed values change, but the technique must also quickly restructure existing
boundaries around these new boundaries. However, this dynamic behavior is not obtainable with-
out a technique for initially constructing static geometric representations of sensed phenomena.
Currently, there are no a static edge detection techniques that do not make significantly restrictive
assumptions about the sensed phenomena they are trying to identify geometrically. Neither of the
techniques presented in [18] and [62] address edge detection in the dynamic case and they both
make assumptions about the number and/or size of sensed phenomena in the static case.
Ideally, we could simply modify our boundary recognition technique, presented in the previous
chapter, into an edge detection technique by adapting it to construct connected groups out of nodes
with the same sensed value and then have each group execute the technique independently allowing
each sensed phenomena to identify its own a geometric representation itself. However, there are
additional challenges in edge detection, even in the static case, not found in boundary recognition.
Foremost, in edge detection, sensed data is completely independent of network connectivity. This
leads to a fact in boundary recognition that does not hold for edge detection: if two nodes can
communicate with each other there is no connectivity hole between them. This is not necessarily
the case in edge detection because one or more nodes belonging to one or more different sensed
phenomena could be between them. Therefore, a more sophisticated adaptation is required in
order to handle this challenge. Edge detection techniques in the literature avoid the difficulty
of delineating small sensed phenomena by assuming that sensed phenomena in the network are
large in scale and cover uninterrupted continuous regions within the network. While in some
environments this may be a sound assumption, in general this does not hold true. In the general
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case, sensed phenomena can be arbitrarily small and even fully contained within other sensed
phenomena.
In this chapter, we extend our boundary detection technique to handle the more generic prob-
lem of distributed edge detection, treating boundary detection as a case of edge detection with only
one sensed data value within the network. Current edge detection techniques do not attempt to
connect identified edge nodes into perimeters, which is the more difficult problem [85]. The basis
for our edge detection technique is the simple idea, mentioned above, that instead of just grouping
nodes together based on connectivity, as is the case in our boundary detection technique, nodes are
grouped together based on sensor reading and connectivity. Therefore, each group of connected
nodes having the same sensed value cooperatively identifies its own inner and outer perimeters,
nearly independently of any other group of connected nodes with the same sensed value in the net-
work. Ideally, the groups of nodes would be able to identify their own inner and outer boundaries
completely independently of all other groups, however the technique must address the problem of
a small sensed phenomenon being partially or wholly surrounded by a another sensed phenom-
ena. Not even the assumption that all sensed phenomena are large in scale prevents the need for
some cooperation between groups of nodes. It is possible that a sensed phenomenon partially
surrounds a small portion of another large sensed phenomenon. So unless all sensed phenomena
are large and assumed incredibly regularly shaped, the problem small sensed phenomena pose to
distributed edge detection techniques is not mitigated without some cross group communication.
Our technique is robust in that it operates in the general case under no assumptions about network
deployment or shape of phenomena within a network. Additionally, our technique attempts to
simplify and minimize all cross group cooperation. We implemented our technique and conducted
extensive experiments; results show that our technique provides accurate perimeters for all sensed
phenomena within a wireless sensor network even in the presence of phenomena surrounded by
larger phenomena.
The rest of this chapters’s organization follows. Section 5.2 briefly presents related work on
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edge detection. Section 5.3 introduces our approach. Section 5.4 contains performance evaluation
and Section 5.5 summarizes the chapter.
5.2 Related Work
Chintalapudi and Govindan proposed three different approaches to identify the nodes within the
edge of a sensed phenomenon inside a WSN [18]. The authors define an edge as a region that inter-
sects both the interior and exterior areas of an observed phenomenon. The first of the techniques is
a statistical approach in which nodes build a local decision function based on information gathered
from neighboring nodes. This local decision function is then used by node to determine if it is an
edge node. The second method is an image-processing based technique, in which a high-pass filter
removes all uniformities from the deployment leaving only abrupt changes such as edges. How-
ever, since sensors are irregularly placed, unlike pixels, sensor values are weighted to compensate.
The final approach is a classifier-based technique that separates sensed values into a bipartite data
set with the edge identified at the intersection of the two sets. The limitation of these approaches
are the assumption that there is only one large-scale continuous phenomenon within the network
at a time. The authors also assume it is easy to connect related edge nodes into a perimeter, but do
acknowledge that the spatial irregularity of the nodes in WSN makes any sort of edge or boundary
detection difficult.
Nowak and Mitra discuss a technique for detecting an estimated boundary between two re-
gions of relatively homogeneous sensed data [62]. The technique takes advantage of hierarchical
quad-trees in order to identify small clusters that estimate the regions in which the boundary be-
tween two sets of sensors with differing sensor readings passes. While this technique does not
suffer from the assumption that there is only one phenomenon within a WSN at a time, the tech-
nique still assumes the phenomena are large and continuous. Neither technique provides an actual
boundary to any sensed phenomena, only an identification, or estimation, of the regions in which
the boundaries pass. Liao et al. have proposed a technique, similar to one of Chintalapudi and
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Govindan approaches, that not only identifies the nodes on the edge of phenomena, but also the
nodes outside the phenomena that border the phenomena’s edge [52]. All three of these approaches
accurately identify the edge of sensed phenomena within a WSN, however none of them provides
connected boundaries for the sensed phenomena. This poses a problem because the underlying
shapes of sensed phenomena are a critical component to the analysis of the underlying sensed en-
vironment [85]. Of course connecting the edge nodes into a boundary after the fact is possible,
however it is incredibly difficult to accomplish in the presence of irregularly shaped phenomena.
Additionally, even in the presence regularly shaped phenomena the distribution of nodes on the
edges is usually going to present itself irregularly, requiring the creation of irregularly shaped
perimeters [18].
While there is little direct related research in the area of edge detection in WSN, the primary
purpose of edge detection is for data fusion, for which there is a large body of related research.
Fusion techniques can be classified into three different categories: data-level, feature-level and
decision-level fusion [51]. These are roughly equivalent with Hall and Llinas’ concept of Central-
ized, Hybrid and Autonomous fusion system architectures, respectively [34]. Each type of fusion
encounters trade-offs among energy consumption, communication cost and data preservation. The
decision of what type of fusion is used for a specific sensor network application is dependent on
the overall goals of the application. Data-level fusion, where all fusion is done in a centralized
manner, provides the most data preservation, but encounters the highest communication cost and
energy consumption. Feature-level fusion, where some fusion is decentralized and the final fusion
is centralized, provides a good moderate balance between energy consumption, communication
cost and data preservation. Finally, decision level fusion, where all fusion is decentralized, while
having the lowest energy consumption and communication cost, incurs the worst data preservation.
Data-level fusion techniques present the most straightforward approach to data gathering in
wireless sensor networks, since no distributed processing is required and all data gathered is pre-
served. However, since data-level fusion is essentially the process of forwarding all data packets
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towards the network’s sink, or base station, data-level fusion is the bar which other techniques
must surpass. Cron and Dubuisson propose using fuzzy logic to combine several opinions on a
given question into a more precise answer than any given single opinion can provide by weighting
of the opinions expressed in terms of data reliability [20]. Intanagonwiwat et. al introduced the
data transport paradigm of directed diffusion, which is the fundamental principle behind almost
all modern fusion techniques [40]. The idea of directed diffusion is that when a request is made
for data the source pushes the data through carefully set up paths (via the interest request) towards
the requesting node, but not in an end-to-end fashion. The intermediate nodes can potentially
transform the data to better answer the request for data, although this is not strictly required. This
paradigm only depends on local interactions, not global interactions. Simulation results show di-
rected diffusion, as a data transport mechanism, performs much better than flooding and not much
worse than optimal omniscient data transport.
The most discussed data gathering techniques for wireless sensor networks are feature-level
fusion techniques, often referred to as data aggregation techniques. The reason being that feature-
level fusion provides a good balance between energy consumption, communication costs and data
preservation, without necessarily needing complex distributed processing. LEACH (Low-Energy
Adaptive Clustering Hierarchy) is a cluster-based routing protocol for wireless sensor networks
that uses aggregation to minimize data transmissions [36]. The clusterheads, which rotate to re-
duce energy demands on the clusterheads, act as aggregation points for the data gathered in the
cluster. PEGASIS (Power-Efficient GAthering in Sensor Information Systems) was proposed as
an improvement over LEACH, since the overhead of building clusters is not needed [54]. Again
PEGASIS is primarily concerned with energy-efficient routing, but the current round of “cluster-
heads” aggregate the received data from neighboring nodes for transmission to the base station, in
order to reduce transmission costs. Coleri and Varaiya present a fusion technique in which a short-
est path tree rooted at the network’s base station is formed and each node in the tree encodes the
data of is descendants into its own data packet before transmission [19]. The Data Aggregation and
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Dilution by Modulus Addressing (DADMA) protocol is a protocol in which all sensing is initiated
by means of a SQL-like relational algebra query from a sink or some external entity [14]. Zhu
et. al discuss the idea of correlation unaware routing in wireless sensor networks as opposed to
correlation aware routing in wireless sensor networks [97]. The authors’ goal is to create a routing
structure that approximates the efficiency of a Steiner tree without the high overhead of construct-
ing a Steiner tree. They therefore propose creating a ring and sector infrastructure, surrounding
the sink node, within the sensor network. Kulakov et. al show that neural networks and wavelets
can be applied to the problem of data aggregation in wireless sensor networks with distributed
cluster heads [49]. He et. al propose VigilNet [35], which is a four-tiered feature-level data fusion
technique designed specifically for ground-based real-time military target tracking. Luo et. al em-
ploy an extremely general aggregation model where data aggregation can occur anywhere in the
network [56]. They then add to the minimum energy routing problem the consideration of fusion
cost, which they assume is not necessarily trivial compared to the transmission cost unlike many
other papers.
The most difficult fusion technique to implement effectively is decision-level fusion. This is
due to the difficulty of data preservation and the potential for greatly increased computation at
each sensor node. Although, due to the potential for greatly reduced energy consumption and
communication cost, it is often viewed as the ideal fusion technique. Honarbacht et. al propose
using Kalman filtering and Taylor approximation as a simple way of performing data fusion [38].
The simulations results of this method show that only 1.6% of the original sensed data needs to be
obtained at the sink in order to sufficiently reconstruct the original sensed signal. On the downside,
Kalman filtering is not a computationally lightweight filtering technique, especially considering the
use of lightweight sensor nodes. Banerjee et. al present a local tree-based aggregation scheme,
called FORM QT, in which a regression function is applied to the data from a node’s children
and only the set of approximation coefficients from the function are sent up to the next level
[5]. A promising side effect of this approach is that it allows for queries of the type f(x, y),
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even accepting coordinates for which there is no discrete data. On the other hand, this technique
provides no guarantees for the preservation of the discrete data in the network. Zhang et. al [91]
argue that fusion techniques based on functional link artificial neural networks are able to reduce
the computational and time complexity, as well as reducing the level of measurement uncertainty
at each sensor node, of decision-level fusion systems. While the authors argument may hold, the
computation cost at each node is significant.
Another approach for data fusion, independent of the three types of fusion techniques, is that
of providing flexible frameworks or APIs that allow a sensor application developer control over
the level of fusion without the need for them to implement a fusion technique explicitly. One
such framework is DFuse [69]. DFuse is an overlay system for distributed data fusion that aims
to provide a fusion API, a distributed role assignment algorithm and a abstraction migration facil-
ity that aids in dynamic role assignment. Experimentation on an iPAQ-based test bed shows that
DFuse has very low overhead and is able to reduce the development of complex fusion applica-
tions in wireless sensor networks. Simulations also show that DFuse is able to extend the lifetime
of sensor networks due to its power-aware assignment of roles and scalability in large networks.
Another attempt at framework is I-Sense [44]. I-Sense, unlike DFuse, aims for a multi-level fu-
sion framework allowing for data-level, feature-level and decision-level fusion within the sensor
network. The idea behind the system is to allow each individual sensor node to determine, but not
necessarily exclude entirely, which data is important for the application at hand. The sensors then
transmit their own reduced data to fusion nodes, which are sensors with slightly more capability
and better suited to further reducing the acquired data by aligning and combining data together
from multiple sensor nodes. The fusion nodes then forward this combined data to a central base
station where a final determination is made about the data gathered. The amount of work done at
each level is customizable allowing I-Sense to be used in a wide variety of sensor applications.
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5.3 Approach
As with our boundary recognition technique, in addition to Chintalapudi and Govindan’s approach
[18], a requirement for the correct operation of our technique is that every node knows its own
position. On the other hand, we still do not assume that the communication graph of the WSN
follows the unit disk graph assumption, again relying only on actual node connectivity to determine
which nodes can communicate directly. We again, without loss of generality, assume operation in
a connected WSN (i.e. there exists a path from any node to any other node in the network). Some
implementation details differ between the steps of our edge detection technique and our boundary
recognition technique, in order to handle the more general case of edge detection. However, the
general idea of the approach remains the same. In fact, if all nodes have the same sensed value
our edge detection technique produces the same result as our boundary recognition technique.
Additionally, the message complexity of our edge detection technique is similar to that of our
previously presented boundary recognition technique. We now provide an outline of our edge
detection technique and then elaborate on these steps.
1. Identify the outer perimeter of each sensed phenomenon (Figures 5.1a–5.1g).
(a) Identify the boundary nodes of each sensed phenomenon. (Figure 5.1a).
(b) Collect all nodes with the same sensed value together into connected groups. (Figure
5.1b).
(c) Identify the convex hull of the each identified group. (Figure 5.1c).
(d) Connect each group’s convex hull nodes together using routes consisting only of nodes
and edges within the group. (Figure 5.1d).
(e) While there are uncaptured nodes remaining (i.e. nodes not bound by some constructed
perimeter), repeat steps 1b–1d on increasingly smaller connected subsets of uncaptured
nodes (Figure 5.1e).
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(f) While there is more than one identified perimeter per sensed phenomenon, merge the
perimeters together to form one perimeter per sensed phenomenon (Figure 5.1f).
(g) Refine the sensed phenomena’s final external perimeters (Figure 5.1g).
2. Identify any relationships that exist between all outer perimeters identified in the network
(i.e. crossings or inclusions).
3. Identify the inner perimeter(s) of each sensed phenomena (Figures 5.1h–5.1i).
(a) For each perimeter, starting with the each sensed phenomenon’s final outer perimeter,
find a path between two points on the perimeter, entirely contained within the perimeter.
(b) Split the perimeter along the identified path (Figure 5.1h).
(c) Repeat until no more splits are possible (Figure 5.1i).
4. Mitigate any unresolved crossings, identified in Step 2, between outer perimeters.
5.3.1 Outer perimeter(s)
As with our boundary recognition technique, the first step of our edge detection technique is to
identify the outer boundaries of all sensed phenomena in the network. The key difference between
Steps 1a–1g of our boundary recognition technique and Steps 1a–1g of our edge detection tech-
nique is that nodes do not act on received information from nodes without the same sensed value
as themselves. This leads to the formation of one group per sensed phenomena in the network,
instead of one group per connected set of nodes within the entire network. Each group then con-
structs its own outer perimeter independently of the other formed groups. Since Steps 1c–1g are all
group-aware steps they remain completely unchanged from our boundary recognition technique.
Therefore, the only required implementation details are in the non-group-aware steps (i.e. Steps
1a and 1b).
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(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 5.1: Our technique executed on an example topology with one sensed phenomena. Theaverage degree is 20. (a) The sensed phenomena’s true shapes and their self-identified perimeternodes (squares); (b) The initial groups for the sensed phenomena; (c) The identified convex hullnodes of the phenomena (squares); (d) The initial external perimeters of the phenomena, in additionto the groups of remaining uncaptured nodes (squares identify uncaptured groups with only asingle uncaptured node); (e) The identified perimeters after all nodes sensing either phenomenaare captured (squares identify perimeters composed of only a single node); (f) The final roughexternal perimeters of the phenomena after all perimeters are merged; (g) The phenomena’s finalexternal perimeters after refinement; (h) The phenomena’s first perimeter split; (i) The final outerand inner perimeters of the phenomena.
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Step 1a of our edge detection technique, similar to Step 1a of our boundary recognition tech-
nique, identifies the boundary nodes of each sensed phenomena using lcv in order to drastically
decrease the processing and communication cost of computing the convex hull in Step 1c. How-
ever, since a node’s neighbors may have different sensed values and actually belong to different
sensed phenomena, a slight modification is required. Since our edge detection technique identifies
the outer boundaries of sensed phenomena instead of the entire network, lcv should not consider
any nodes that do not have the same sensed value in its processing. Procedurally, lcv simply
needs to be modified to ignore any nodes that do not have the same sensed value, which would
be obtained via the initial HELLO messages used for neighbor discovery along with the nodes’
coordinates. Figure 5.2 shows the true boundaries of the sensed phenomena and identified outer
perimeter nodes for both a single phenomenon and a multi-phenomena topology.
(a) (b)
Figure 5.2: The self-identified boundary nodes (black squares) for (a) a single phenomenon topol-ogy (4050 nodes with an average degree of 10) and (b) a multi-phenomena topology (4050 nodeswith an average degree of 10). The surrounding boundaries are the true boundaries of the sensedphenomena.
Step 1b of constructing the outer boundary in our edge detection technique, building the initial
group(s), is also similar to Step 1b of our boundary recognition technique. However, groups should
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only contain nodes sensing the same sensed phenomenon. Similar to the modification of Step 1a,
nodes simply do not acknowledge the group construction messages from neighbors that do share
the same sensed data value. This allows for parallel group construction resulting in one group
representing each sensed phenomena, instead of one group for each set of connected nodes in the
network deployment. Obviously, the discretization of real-valued sensor data is required in order
to have a meaningful definition of “the same.” Figure 5.3 shows the initial groups for both a single
phenomenon and a multi-phenomena topology.
(a) (b)
Figure 5.3: The initial groups for (a) a single phenomenon topology and (b) a multi-phenomenatopology.
Since Steps 1c through 1g of our boundary recognition technique are already operate only
within predefined groups of nodes, Steps 1c through 1g of our edge detection technique operate
the same as they do in our boundary recognition technique. Figures 5.4–5.8 show the outcome of
Steps 1c–1g for both a single phenomenon and a multi-phenomena topology.
5.3.2 Identifying the relationships between sensed phenomena
If we make the assumption all sensed phenomena are large and incredibly regular this step is not
necessary. However, in a practical sensor network deployment this assumption does not hold true.
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(a) (b)
Figure 5.4: The identified convex hull nodes for (a) a single phenomenon topology and (b) a multi-phenomena topology.
(a) (b)
Figure 5.5: The initial connected perimeters for a (a) single phenomenon topology and (b) multi-phenomenon topology, in addition to the groups of remaining uncaptured nodes. Black squaresidentify uncaptured groups with only a single uncaptured node.
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(a) (b)
Figure 5.6: The identified perimeters after all nodes are captured for (a) a single phenomenontopology and (b) a multi-phenomena topology. Black squares identify perimeters composed ofonly a single node.
(a) (b)
Figure 5.7: The final rough perimeters after all perimeters are merged for (a) a single phenomenontopology and (b) a multi-phenomena topology.
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(a) (b)
Figure 5.8: The final outer perimeters after refinement for (a) a single phenomenon topology and(b) a multi-phenomena topology.
Prior to proceeding to construct the inner perimeters located within the group of nodes, each group
leader first notifies the group leaders of any neighboring groups of its constructed outer perime-
ter. By neighboring, we mean the neighboring group has nodes within the local neighborhood
of at least one node in the group. While group leaders are not explicitly aware of other groups
of nodes, the nodes at the edge of a group know information about likely other groups of nodes.
The nodes at the edge of groups obtained knowledge about nodes with differing sensed values,
indicating the construction of other groups of nodes, during the initial HELLO messages of the
neighbor discovery phase in Step 1a. The edge nodes mark themselves as knowing about nodes
with differing sensed value in Step 1a and propagate this mark to their group leader in Step 1b,
which allows each group leader to query these edge nodes, which in turn query their foreign neigh-
bors, for information regarding the neighboring group(s). Once other groups are identified, each
group leader communicates with the other group leaders through point-to-point communication to
reliably transmit their and receive other groups’ outer perimeters. Once these communications are
complete, the groups resume independent operation and no cross-group communication is required
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for the remainder of the technique.
With each group leader knowing the outer perimeters of its neighboring groups, it must decide
its outer perimeter’s relationship to each of its neighboring groups’ outer perimeters. There are
five potential relationships, in addition to their being no relationship at all, between neighboring
groups’ perimeters. These relationships are true overlap, surrounding, surrounded, crossing and
crossed. Each of these relationships is shown graphically from the point of view of a group A
in Figure 5.9. True overlap between two perimeters, shown in Figure 5.9(a), is when one, or
more, perimeter nodes from both groups are located within the constructed outer perimeter of the
other group. Conceptually, this situation happens when two phenomena overlap, but do not “mix”
to form a new sensed phenomena (i.e. oil and water). Surrounding and surrounded, shown in
Figures 5.9(b) and 5.9(c), is when one sensed phenomena completely surrounds another sensed
phenomena. Crossing and crossed, shown in Figure 5.9(d) and 5.9(e), is when one, or more,
perimeter nodes of one sensed phenomena are located within the constructed outer perimeter of
another sensed phenomena. The crossing and crossed by relationships are actually an error in the
constructed outer perimeter of one sensed phenomena caused by the fact that communication was
possible over a region of the network containing another sensed phenomenon. This possibility
is the key difficulty of an edge detection technique over a boundary recognition technique. In
boundary recognition, if two nodes can communicate with each other there is no connectivity
hole between them. This is not necessarily the case in edge detection because one or more nodes
belonging to one or more different sensed phenomena could be between them.
In order to identify the relationships a group’s perimeter has with a neighboring group’s perime-
ter, the group leader first iterates over each node in the neighboring groups perimeter and deter-
mines if any of the nodes are internal to the group’s own perimeter. Next, it then iterates over
each node in its own perimeter and determines if any of the nodes are internal to the neighboring
group’s perimeter. With this information, the group leader can determine its own outer perimeter’s
relationship with neighboring groups’ perimeters. It does this for each group, then, if necessary,
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(a) (b) (c) (d) (e)
Figure 5.9: Possible relationships between constructed outer perimeters. From left to right: (a)true overlap; (b) surrounding; (c) surrounded; (d) crossing; (e) crossed.
handles the relationships prior to proceeding to Step 3 of our edge detection technique. Table
5.1 shows the relationship identification criteria. The first match found in Table 5.1 identifies the
relationship.
Table 5.1: Sensed Phenomena Outer Perimeter Relationship Identification CriteriaRelationship ‖B in A‖ ‖A in B‖True Overlap > 0 > 0
A is surrounding B ‖B‖ 0A is surrounded by B 0 ‖A‖
A is crossing B 0 > 0A is crossed by B > 0 0
No Relationship 0 0
Once identified the group leader must takes action based on the type(s) of relationships it iden-
tified with neighboring groups’ perimeters. Obviously, a perimeter takes no action if there is no
relationship between two perimeters. In addition, since both perimeters involved in a true overlap
are correct there is also no action taken. An action is necessary if a group leader identifies it is in a
crossing or surrounded relationship with another group’s outer perimeter. However, the associated
group identifying the opposite crossed or surrounding relationship actually takes the action. In or-
der to the reduce the computation necessary to identify the relationship between two groups, if at
least one node, but not all nodes, of the neighboring group’s perimeter are determined to be within
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its own perimeter in the first iteration then the second iteration is not necessary, since no action is
taken anyways. Therefore, the first actual action taken is due to the identification of a surrounded
relationship, or that another group’s outer perimeter surrounds a group’s outer perimeter. In the
event that all sensed phenomena are large and regular, no action is necessary. However, in practical
deployments, neither of these things always holds true. This leads to the possibility of nodes in
the surrounding perimeter communicating over a small surrounded perimeter which would prevent
an inner perimeter of the surrounding perimeter from correctly forming around the surrounded
perimeter because no “hole” would form in the place of the surrounded perimeter. The mitigation
for this problem, at this stage, is to inform the entire group of the surrounded phenomena’s perime-
ter. The purpose of this announcement is to prevent our splitting technique’s underlying routing
algorithm from using communication paths that cross the surrounded phenomena’s outer perimeter
in Step 3. A crossed relationship requires the same action, however full mitigation of a crossed
relationship is not complete until after the identification of all inner perimeters within the crossed
into perimeter. The reason mitigation is not complete is that the crossed edge on the outer perime-
ter of the crossed group requires replacement with a path that correctly navigates the crossing outer
perimeter and the easiest way to accomplish this is to patch the inner perimeter surrounding the
crossing outer perimeter into the crossed group’s outer perimeter.
5.3.3 Inner perimeter(s)
Once the outer perimeters for the sensed phenomena are constructed, we use them as the starting
point for identifying any inner perimeters (i.e. connectivity holes or other sensed phenomena)
within the sensed phenomena. Our basic approach of continually reducing a set of potential inner
perimeters, through repeated splitting, into inner perimeters remains the same. However, there is
one small implementation change in the routing algorithm used to find paths to use as perimeter
splits. While a valid split in our boundary recognition is any route wholly included by the outer
perimeter, the same does not hold true in our edge detection technique. In our edge detection
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technique, a valid split must also consist of only of nodes belonging to the same group of nodes
as the outer perimeter being split and must not use any path that crosses the outer perimeter of
any crossing or surrounding perimeter identified in Step 2. Therefore, routing technique requires
a small additional amount of computation overhead, but remains conceptually the same. Figure
5.10 shows the first split of the outer perimeter for the single phenomenon and multi-phenomena
topologies.
(a) (b)
Figure 5.10: The first round of perimeter splits for (a) a single phenomenon topology and (b) amulti-phenomena topology.
Other than the new requirements for valid splits, our inner perimeter construction technique
continues the same as in our boundary recognition technique. Eventually, every perimeter will
reduce to a true inner perimeter to a perimeter of only three nodes. In our boundary recognition
technique, we remove perimeters of three nodes, as there is no connectivity hole within a triangle
perimeter. However, in edge detection it is possible that a very small sensed phenomena exists
within the bounds of a triangle perimeter. Therefore, before the removal of a triangle perimeter as
a potential inner perimeter the nodes on the perimeter must first ensure there are no nodes sensing
a different sensed phenomenon within their perimeter. If there are nodes sensing a different sensed
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phenomenon within their perimeter, the perimeter remains a potential inner perimeter. Figure
5.11 shows the final inner and outer perimeters for the single phenomenon and multi-phenomena
topologies.
(a) (b)
Figure 5.11: The final internal and external perimeters for (a) a single phenomenon topology and(b) a multi-phenomena topology.
5.3.4 Mitigate unresolved relationships between outer perimeters
In the event that no crossed relationships exist between outer perimeters, this step will never exe-
cute and our edge detection technique is complete after the previous step. However in the presence
of one or more crossed relationships between outer perimeters, those perimeter crossings have still
not been fixed and there remains one or more perimeters that incorrectly cross. Unlike in Step 2,
we know have identified an inner perimeter that surrounds the crossing outer perimeter and it can
be patched into the crossed outer perimeter in place of the crossed edge of the crossed perimeter.
After all inner perimeters have been identified, each unfixed crossed by relationship consists of a
crossing perimeter A = a1 → · · · → i1 → j1 → · · · → m1 → n1 → · · · z1 → a1, a crossed
perimeter B = a2 → · · · → i2 → j2 → · · · → · · · z2 → a2 and an inner perimeter surrounding
the part of A in B, C = a3 → · · · → i2 → j2 → · · · → · · · z3 → a3, where the edges i1 → j1 and
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m1 → n1 cross the edge i2 → j2. In order to fix the crossed perimeter i2 → j2 in B is replaced
with i2 → · · · → a3 → z3 → · · · → j2. Figure 5.12 shows our technique handling perimeter
crossings from start to finish. The result shown in Figure 5.12(d) and the intermediate steps shown
in Figures 5.12(b) and 5.12(c) are the actual result of executing our edge detection technique on the
topology shown in Figure 5.12(a). This shows that our edge detection technique is able to produce
accurate perimeters in topologies containing a large phenomenon that has edges that incorrectly
cross much smaller phenomena.
(a) (b) (c) (d)
Figure 5.12: An example of our technique mitigating crossings perimeters. (a) The sensed phe-nomena’s true shapes (the small phenomena are all smaller than the maximum transmission rangein at least one direction); (b) The constructed outer perimeters of the sensed phenomena after Step1; (c) The constructed inner and outer perimeters of the sensed phenomena after Step 2; (d) Thefinal inner and outer perimeters of the sensed phenomena after the mitigation of unresolved outerperimeter relationships in Step 4.
5.4 Performance Evaluation
We adapted the experiments presented by Wang et al. [85] in order to evaluate the performance of
our approach with respect to node density, average neighborhood size and network and hole shapes.
In order to obtain a non-unit disk communication graph and better emulate the irregularities of
wireless communication, we did not determine the connectivity of our experimental topologies
based on only position and transmission range. Instead, we again obtained the connectivity of
all topologies by using the shadowing propagation model. As mentioned prior, the shadowing
propagation model assumes that the signal strength of a transmission decreases logarithmically
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with distance and includes a Gaussian random variable to account for environmental influences
[75].
Same as boundary recognition, there is no generally accepted metric for measuring the accuracy
of a edge detection technique. This makes the evaluation of an edge detection technique difficult, as
the evaluation usually requires visual inspection. This is even more problematic for edge detection
techniques than boundary recognition techniques, since there is typically more to inspect with the
results of an edge detection technique. Our already proposed metric for measuring the accuracy of
a boundary recognition technique of the number of nodes not correctly bound by the constructed
boundaries still works well for measuring the accuracy of an edge detection technique. Although,
“correctly bound by the constructed boundaries” also implies that all nodes are correctly grouped
together according to sensed data value when used to measure the accuracy of edge detection. This
makes visual inspection much harder if no visual representation of sensed data value is present.
Unfortunately, our simple metric does not completely capture all aspects of accuracy in an edge
detection technique. Even if all constructed perimeters properly bound all nodes, the edge detection
may still not be accurate, since constructed perimeters could still incorrectly intersect. So, in
addition to the number of nodes incorrectly bound we must also consider the number of incorrect
perimeter intersections in any analysis of the accuracy of an edge detection technique. None of
the simulation topologies in this chapter contains any true overlap relationships between sensed
phenomena and therefore the results should not contain any perimeter intersections.
5.4.1 Effect of node distribution and density
Random distribution of sensors
For this group of simulation experiments, we randomly placed 3500 nodes in a square region with
a single circular phenomenon. We varied the maximum communication radius of the nodes in
order to achieve the desired average node degree. Figure 5.13 shows the results of our approach
on randomly distributed nodes with varying average node degrees. In all four simulations, our
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technique left no nodes incorrectly grouped or bound by the constructed perimeters. In addition,
as there are no true overlap relationships, there are no perimeter intersections in any of these sim-
ulation results. Clearly, this shows our technique provides accurate edge detection in randomly
deployed networks with a single, large regularly shaped phenomenon. Additionally, as expected,
our technique provides slightly smoother perimeters, more closely emulating the true boundary
of the phenomenon and network, as the degree increases, since fewer intermediate nodes are re-
quired to construct the perimeters, due to the nodes having larger maximum transmission ranges.
More interesting, but similar to our boundary recognition technique, Figures 5.13(b)–5.13(d) show
that as the transmission range of the nodes increases some of the irregularities on the constructed
inner and outer boundaries of Figure 5.13(a) become internal connectivity holes to the network,
or internal connectivity holes to the baseline phenomenon within the network. Our technique is
still naturally able to identify these holes and construct additional inner perimeters around them,
even though there creation was unintentional. The results also show that our technique is able to
identify accurate perimeters even in the event of highly irregular node placement along the edge
of the phenomenon, as is shown when the degree decreases. Lastly and most importantly, Figure
5.13 show that our approach is robust in wireless sensor networks with low average degree.
(a) (b) (c) (d)
Figure 5.13: Uniformly distributed sensor field. (a) the average degree is 7; (b) the average degreeis 10; (c) the average degree is 13; (d) the average degree is 16.
98
Grid with random perturbation
In this group of simulations, we again placed 3500 nodes on a grid and then perturbed each point
by a small random amount. The goal of this distribution method is to approximate the manual
deployment of sensors [85]. Again, we varied the maximum communication radius of the nodes in
order to achieve the desired average node degree. Figure 5.14 shows the results of our edge detec-
tion approach on a perturbed grid topology with varying average degrees. In all three simulations,
our technique left no nodes incorrectly grouped or bound by the constructed perimeters. In addi-
tion, as there are no true overlap relationships, there are no perimeter intersections in any of these
simulation results. Again same as our boundary recognition technique, our approach more closely
captures the true boundaries of the phenomenon and network in a perturbed grid topology than in
a randomly deployed topology, due to the regularity of node placement provided by the underlying
grid. Figure 5.14(b) again shows that our technique is able to naturally identify small, unintended
connectivity holes within phenomena and construct inner perimeters around them. This is seen as
some of the irregularities on the constructed inner and outer boundaries of Figure 5.14(a) becoming
additional internal connectivity holes in Figure 5.14(b).
(a) (b) (c)
Figure 5.14: Results for randomly perturbed grids. (a) the average degree is 6; (b) the averagedegree is 8; (c) the average degree is 12.
Low density, sparse graphs
In this group of simulations, we again use a perturbed grid but instead of varying the communi-
cation range to vary the average degree of the network we fixed the communication range of each
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node and adjusted the average degree by directly decreasing the density of the topology. Figure
5.15 shows the results of our approach on topologies with varying node densities. In all four sim-
ulations, our technique left no nodes incorrectly grouped or bound by the constructed perimeters.
In addition, as there are no true overlap relationships, there are no perimeter intersections in any
of these simulation results. Clearly, this shows our technique provides accurate edge detection in
randomly deployed networks with a single, large regularly shaped phenomenon. Again same as
our boundary recognition technique, our approach more closely captures the true boundaries of the
phenomenon and network in a perturbed grid topology than in a randomly deployed topology, due
to the regularity of node placement provided by the underlying grid. However, as was the case
before, as the average degree decreases our technique provides slightly rougher perimeters, less
closely emulating the true boundaries, since more nodes are required to construct the perimeters.
(a) (b) (c) (d)
Figure 5.15: Results when the density of the graph decreases. (a) 842 nodes and the average degreeis 7; (b) 1742 nodes and the average degree is 16; (c) 2628 nodes and the average degree is 25; (d)3443 nodes and the average degree is 35.
5.4.2 Further examples
In Figure 5.16 we adapted some of the more challenging experiments from Wang et al. [85] in
order to show that our technique is robust in the presence of irregularly shaped phenomena. Fig-
ures 5.16(a)–5.16(d) shows the topologies and true boundaries of all the phenomena, while Figures
5.16(e)–5.16(h) show there result of our technique’s edge detection on the topologies In all four
100
simulations, our technique left no nodes incorrectly grouped or bound by the constructed perime-
ters. In addition, as there are no true overlap relationships, there are no perimeter intersections
in any of these simulation results. These results show that, in addition to our technique being
able to produce accurate perimeters in the presence of regularly shaped phenomena and networks;
our technique is capable of producing accurate perimeters in the presence of highly irregularly
phenomena and networks.
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 5.16: Topologies (a–d) and results (e–h) for more challenging shaped phenomena. (a & e )A spiral shape with 5040 nodes and the average degree is 21; (b & f) A building floor shape with3420 nodes and the average degree is 20; (c & g) A cubicle shape in an office with 6833 nodes andthe average degree is 17; (d & h) A star shape with 2350 nodes and the average degree is 17.
5.5 Summary
In this chapter, we adapted our boundary recognition technique, presented in Chapter 4, to address
the more general problem of edge detection in wireless sensor networks. Our edge detection tech-
nique keeps inter-group communication to a minimum. However, it is still capable of construct-
ing correct outer perimeters for sensed phenomena even in the presence of anomalous perimeter
101
crossings, caused by wireless communication traveling over another sensed phenomenon, and phe-
nomena wholly surrounded by other phenomena. Our technique allows for the more concise view
of sensed data within a sensor network, by reducing the identification of a sensed phenomenon
to its constructed perimeters, both inner and outer. This allows for a potential reduction of trans-
mitted sensor data to an offsite location. We implemented our technique in order to evaluate its
performance. Our performance evaluation showed that our edge detection technique constructs ac-
curate perimeters in randomly deployed topologies of varying densities, perturbed grid topologies
of varying densities and in sparsely populated/low-density topologies. Additionally, we showed
that our technique is capable of not only being able to produce accurate perimeters in the presence
of regularly shaped phenomena and networks, but also capable of producing accurate perimeters
in the presence of highly irregularly shaped phenomena and networks.
102
CHAPTER 6
CONCLUSIONS
In this dissertation, we presented several techniques that allow wireless sensor networks to self-
determine location and topological information. The cost of trying to tightly control the deploy-
ment of a large-scale sensor network is in more cases too high. So, the typical assumption is that
the deployed topology of a new sensor network is completely unknown. However, the more in-
formation known about the resulting topology of a deployed sensor network, the more useful the
wireless sensor network is to its deployers. Therefore, the focus of this dissertation is the proposal
of techniques that allow for the self-identification of location and topological information in arbi-
trarily deployed wireless sensor network in the absence of any accessible global information about
the deployed topology.
First, we have proposed ANIML, an iterative, anchor-free, range-aware relative localization
technique for wireless sensor networks that requires no explicit error control or global information.
Localization is the process by which the nodes of a sensor network self-determine the network’s
topology, by identifying the physical coordinates of every node in the network. By explicitly basing
a nodes positioning off its 1- and 2-hop neighborhood, to reduce the effects of cascading ranging er-
rors, instead of just its 1-hop neighborhood, ANIML is capable of providing accurate localization,
even in the presence of packet losses, using nothing more than simple iterative least-squares. While
adding 2-hop information does slightly increase the computational complexity of ANIML’s least-
squares multilateration by a constant factor, using 1- and 2-hop information allows ANIML the
ability to provide resilient localization. Through simulation, despite using a non-idealized MAC,
we showed that ANIML provides good relative localization and better accuracy than DV-Hop in
uniform, C-shaped and non-uniform topologies. ANIML is also capable of accurate localization
in the presence of RF-opaque obstacles and when using actual RSSI to make inter-node distance
estimates. Simulations also showed that ANIML localization convergence time is independent of
103
the total number of nodes in the network. We also showed that ANIML is able to provide absolute
localization, instead of relative localization, without any changes to the basic ANIML technique,
only the deployment of anchors (i.e. ANIML-Abs). Additionally, even though ANIML is a range
aware technique, we adapted ANIML to use hop-counts instead of distance estimates in the event
that ranging equipment is unavailable (i.e. ANIML-Hop). We also proposed an adaptation of AN-
IML, called Sea-ANIML, for use in underwater sensor networks that and is capable of providing
accurate relative localization in underwater sensor networks.
There is no doubt that knowing the physical positions of every node in the network provides a
large amount of information about the deployed topology of a wireless sensor network. However,
it does not provide a complete view of a network’s topology, so we next proposed a robust dis-
tributed technique that addresses the problem of boundary recognition in wireless sensor networks.
Boundary recognition in wireless sensor networks is a crucial process because the boundaries of
the network, both the inner (i.e. internal connectivity holes) and the outer (i.e. the network’s ex-
ternal perimeter), almost always have a physical correspondence to the environment in which the
sensors are deployed [85]. Our technique overcomes the three significant challenges encountered
in current boundary recognition techniques, which are unrealistic assumptions about the commu-
nication model of the deployed sensor nodes, high false positive rate in identifying boundary nodes
and/or the construction of inaccurate perimeters and not connecting identified boundary nodes into
perimeters. Our technique uses actual connectivity to determine directly communicating nodes and
does not make assumptions about the communication model of the deployed sensor nodes. It con-
structs connected perimeters of both convex and irregularly shaped networks and holes and does
not just identify the nodes bordering the outer perimeter and/or inner connectivity holes. Lastly,
it provides accurate perimeters, leaving no connected nodes outside the outer perimeter or inside
any inner perimeters. Additionally, we showed that our technique provides accurate perimeters in
topologies of varying densities, average degree and communication range and outperforms current
boundary recognition techniques.
104
Obtaining how the sensed data relates to the physical topology is fundamentally the goal of
deploying a sensor network. Again, while knowing the coordinates of each node in the network
does allow for the gathering of sensor data values associated with discrete locations, it does not
directly provide any relationships between obtained data. However, geometrically identifying the
boundaries of sensed phenomena allows for the association of nodes identifying the same sensed
phenomena in a wireless sensor network. Therefore, we lastly proposed an edge detection tech-
nique that geometrically identifies the boundaries of sensed phenomena within a wireless sensor
network. Our presented edge detection technique extends our boundary detection technique to
handle the more generic problem of distributed edge detection, treating boundary detection as a
case of edge detection with only one sensed data value within the network. It is robust, distributed,
implementable and capable of accurately identifying connected perimeters for sensed phenom-
ena within wireless sensor network, without any unit disk communication graph assumptions. In
addition, our approach correctly identifies connected perimeters of convex shaped phenomena, ir-
regularly shaped phenomena and phenomena containing one or more internal connectivity holes.
We also showed that our technique is robust in topologies of varying densities, average degree and
communication range.
There are several possible directions for future work. The first is reducing the message com-
plexity of ANIML without affecting overall accuracy. The simulation results presented in 3.4 show
that ANIML is robust in the presence of less information on which to base its localization. This
makes intuitive sense, since if ANIML had three perfectly accurate distances from three nodes
knowing their true positions then it would be able to localize a node perfectly. However, ANIML
does not have the benefit of perfectly accurate distance estimates, so it requires more information
than three nodes. However, we showed that doubling the node density did not cause a significant
decrease in localization accuracy. Therefore, if we somehow could selectively limit the amount
of information used, and therefore propagated, by each node to a level that provided some pre-
determined level of accuracy, we could greatly decrease the amount of data each node needed
105
to broadcast per iteration without significantly affecting accuracy. Reducing the amount of data
broadcast per iteration would directly decrease the needed convergence time of ANIML and there-
fore reduce the amount of energy required to localize the network. While we could However,
how to filter the available information to a node without increasing computation with explicit error
control, while ensuring localization accuracy, is one open and challenging research direction.
Another possible direction for future work is to extend our edge detection technique to maintain
identified perimeters as sensed values change within the network. Unlike sensor node locations,
sensed data is neither static nor slow changing. Since sensed data is not slow changing, it is infea-
sible to rerun our edge detection technique every time one or more identified sensed phenomena
changes. Therefore, an edge detection technique that maintains identified perimeters as the under-
lying sensed phenomena change must quickly restructure existing boundaries around these new
boundaries. A possible solution is to maintain the constructed groups of nodes for each sensed
phenomena and take advantage of the pseudo-infrastructure they provide to allow for new group
construction and node transfers between existing groups. Unfortunately, solely depending on group
leaders to make restructuring decisions could create a lot of unnecessary traffic. The nodes on or
near the edge of sensed phenomena should be more capable of locally and rapidly restructuring the
perimeters identifying sensed phenomena than group leaders. However, building new perimeters
internal to existing perimeters is a difficult local decisions and likely more easily done in a “cen-
tralized” fashion by one or more group leaders. Therefore, a hybrid solution is the likely answer.
Besides, the challenging question of how this hybrid solution would function, another challenging
question is how to efficiently maintain consistency between changes local perimeter nodes make
and changes the group leader makes.
A third direction for future research is further work on Sea-ANIML. Foremost, while having
anchor nodes uniformly positioned throughout the sensor network deployment is acceptable for
the purposes of performance analysis, it is not practical for real underwater sensor deployments.
Since GPS does not propagate correctly through water, the only way to deploy anchors uniformly
106
through an underwater sensor network is to place them in pre-determined locations. This is even
a less practical in underwater sensor networks, than in terrestrial wireless sensor networks. The
typical scenario in underwater sensor networks is all anchor nodes are GPS-enabled surface buoys
with acoustic transceivers for communicating with the submerged portion of the network. In order
to understand the effects of this type of topology on Sea-ANIML we need to perform simulations
on topologies where the anchors are located on the surface. Another possible area of future work
on Sea-ANIML is the ability to handle the non-trivial mobility that ocean currents can cause.
107
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