CLUSTERING BASED LOCALIZATION FOR WIRELESS SENSOR NETWORKS · CLUSTERING BASED LOCALIZATION FOR...
Transcript of CLUSTERING BASED LOCALIZATION FOR WIRELESS SENSOR NETWORKS · CLUSTERING BASED LOCALIZATION FOR...
CLUSTERING BASED LOCALIZATION FOR
WIRELESS SENSOR NETWORKS
By
ROGER ANTONIUSSEN SLAAEN
A thesis submitted in partial fulfillment ofthe requirements for the degree of
MASTER OF SCIENCE
WASHINGTON STATE UNIVERSITYSchool of Electrical Engineering and Computer Science
MAY 2006
To the Faculty of Washington State University:
The members of the Committee appointed to examine the thesis of ROGER ANTONIUSSEN
SLAAEN find it satisfactory and recommend that it be accepted.
Chair
ii
ACKNOWLEDGEMENT
I would like to express my gratitude toward my advisor, Dr. Murali Medidi. His guidance
during my research kept me on track, focused and helped me get the most out of my studies.
I would like to thank Dr. Sirisha Medidi and Dr. Dave Bakken for serving as committee
members and evaluating my thesis.
I would also like to thank the all the members of Washington State Security and Wireless Ad-
hoc Networking (SWAN) Group and especially Yuanyuan Zhou and Christopher J. Mallery for
their valuable input and help
iii
PUBLICATIONS
Muralidhar Medidi,Roger A Slaaen, Yuanyuan Zhou, Christopher J. Mallery and Sirisha
Medidi, “Cluster-based Localization in Wireless Sensor Networks”, SPIE Defense and Security
Symposium, Orlando, Florida, April 17th-21st, 2006.
Muralidhar Medidi,Roger A Slaaen, Yuanyuan Zhou, Christopher J. Mallery and Sirisha Me-
didi, “Scalable Localization in Wireless Sensor Networks”, In preparation for submission May
2006 to HiPC, International conference On High Performance Computing, Bangalore, India, De-
cember, 2006.
iv
CLUSTERING BASED LOCALIZATION FOR
WIRELESS SENSOR NETWORKS
Abstract
by Roger Antoniussen Slaaen, M.S.Washington State University
May 2006
Chair: Murali Medidi
Localization is an important challenge in wireless sensor networks (WSN). Localization usu-
ally refers to the process of dynamically determining the position(s) of one or more node(s) in a
larger network. The challenge lies in efficiently providing acceptable accuracy while conforming
to the many constraints of WSNs and at the same time handling scalability. Scalability is one of
the majors concerns than must be addressed, both in terms of very dense and very large networks.
We propose a Cluster-based Partial Localization (CPL) to provide efficient localization, where the
focus is on providing scalable partial localization suitable to a large and highly-dense network. By
partial we mean that CPL will provide localization for subsets of a network in different stages.
CPL utilizes both a computationally-intensive localization technique (non-metric MDS) and a less
intensive trilateration to achieve balance between complexity and performance. Both trilateration
and MDS are well known mathematical techniques. Trilateration, similar to triangulation, has pre-
viously been used for localization and similar applications, while variations of MDS have been
used in a variety of fields. MDS is a set of data analysis techniques that display the structure of
distance-like data as a geometrical picture. Clustering is utilized to select a subset of nodes to per-
form the non-metric MDS localization and then extend it to the rest of the network. We show, with
simulation results and analysis, that CPL will provide a considerable reduction in both computation
and communication, while still yielding acceptable accuracy.
v
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
PUBLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
CHAPTER
1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Organization of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2. BACKGROUND AND RELATED WORK . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Sensor networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 MDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 MDS example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Trilateration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Trilateration example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.1 General overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.2 Range aware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.3 Range free . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.4 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
vi
3. CLUSTER-BASED PARTIAL LOCALIZATION . . . . . . . . . . . . . . . . . . . 28
3.0.5 Neighborhood Discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.0.6 Cluster Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.0.7 Cluster-Head Localization . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.0.8 Local Map Merging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.0.9 Cluster-Member Localization . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1.1 Computation Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1.2 Message Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4. PERFORMANCE EVALUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1 Square-shapes network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 C-shaped network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 Irregular node densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 Obstacles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.5 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.6 Scalability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
vii
LIST OF TABLES
Page
2.1 Distance matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.1 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
viii
LIST OF FIGURES
Page
2.1 MDS example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Trilateration example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1 Node neighborhoods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Distance measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Example of random topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Example of clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1 Localization example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2 Topology example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3 Cluster quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.4 Accuracy for square-shaped topologies . . . . . . . . . . . . . . . . . . . . . . . . 45
4.5 Example of a C-shaped topology . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.6 Cluster quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.7 Accuracy for C-shaped topologies . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.8 Illustration of a topology with irregular node-density . . . . . . . . . . . . . . . . 48
4.9 Accuracy for topologies with irregular node densities . . . . . . . . . . . . . . . . 49
4.10 Connectivity in topology with four obstacles . . . . . . . . . . . . . . . . . . . . . 50
4.11 Clustering in topology with four obstacles . . . . . . . . . . . . . . . . . . . . . . 50
4.12 Connectivity in topology with H-shaped obstacle . . . . . . . . . . . . . . . . . . 51
4.13 Clustering in topology with H-shaped obstacle . . . . . . . . . . . . . . . . . . . . 51
4.14 Accuracy for topologies with four obstacles . . . . . . . . . . . . . . . . . . . . . 52
4.15 Accuracy for topologies with one H-shaped obstacle . . . . . . . . . . . . . . . . 52
ix
4.16 Computation and communication overhead . . . . . . . . . . . . . . . . . . . . . 53
4.17 Accuracy in large networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
x
Dedication
This thesis is dedicated to my family,
for without their support I would
never have come this far.
xi
CHAPTER ONE
INTRODUCTION
Wireless sensor networking (WSN), while still in its infancy, has vast potential. A sensor net-
work is usually an ad-hoc network densely populated with small, low cost, resource constrained,
wireless-communication enabled and immobile sensor nodes. Each node, or sensor, will have a
very limited functionality; this will normally consist of some type of short range wireless commu-
nication capabilities and some form of sensing, or actuator, equipment. The sensing or monitoring
of, for example temperature, humidity, etc., constitutes one of the two main tasks of each sensor.
The other main task is packet forwarding using the equipped wireless technology. Whichever way
data is transmitted, the network must provide a way of transporting information from different
sensors to wherever this information is needed. Sensor networks could be deployed in a wide
variety of application domains such as military intelligence, commercial inventory tracking and
agricultural monitoring. Their potential to impact application domains is limitless provided a high
density, low cost, scalable and robust networking is feasible. WSNs can also be employed in haz-
ardous environment or diasters zones, that may present danger to people or simply be unreachable
by other means. A self calibrating sensor network could be placed out covering a large area, and
with very little user input quickly start collecting data, transporting and presenting this data to a
user at a safe distance.
Communication from one point to another in these types of networks will be achieved by uti-
lizing multi-hop transmissions, where the intermediate nodes between source and destination will
provide the forwarding of messages. The associated high cost of transmitting as the transmission-
range is increased is one of the reasons to use multi-hop communication instead of having each
node transmitting directly to one another. The limitations in resource capabilities along with the
fact that network lifetime is a crucial issue and the need for some form of routing, provides many
challenges when considering potential wireless sensor network applications. Sensor networks gets
1
much of their strengths from their inherently distributed nature, the fact that there is no need for
any predetermined structure and the use of effective and most of all low cost nodes. While there
has been much research into different aspects of sensor networks and related problems, there are
still no standards or specifications available.
In many application domains, not to mention internal routing and traffic management, some
knowledge of the topology of a network is not only helpful, but vital. In geographical routing, most
data dissemination techniques and various management techniques, position information about
each node in the network is a necessity. Also, in many applications, data from a sensor should be
correlated with where the data was gathered. For example, knowing the position of a fire-alarm
that has been triggered is just as critical as knowing there has been an alarm. This need drives
assumptions that node location information is available by some means, such as GPS or manual
entry. The problem with assuming GPS-enabled sensor nodes is that the cost of the sensor nodes
increases drastically and limits the applicable environments in which the sensor can be deployed,
not to mention that the energy cost of this would also be prohibitively large. The problem with
manual entry of position information is that it limits the size and scalability of a sensor network,
hence removing much of the strengths of WSNs. Therefore, techniques for self-determination of
position information or network topology, also known as localization protocols, are required for
feasible deployment of large-scale sensor networks.
Localization can usually be described as the process of dynamically determining the position,
or location, of someone or something, relative to someone or something else. For sensor networks
this simply means locating a sensor node in a network. There are however different aspects of
localization that needs to be considered; whether the position is absolute or relative to some other
point in the network, whether the node itself provides the localization or someone else does this
work and what is the required resolution or accuracy, i.e. should the result be a highly accurate
coordinate in 2 or 3 dimensional space or maybe just a direction or a very rough estimate of the
distance to or from some point. All of these are aspects that affect how one should go about
2
producing the position estimate. For a localization technique to be practical it must conform to the
limited recourses of WSNs and their large sizes and densities. Any localization technique must not
only provide accurate position estimates but do so at minimal cost in terms of both communication
and computation.
In this thesis we propose a hop-based localization technique called Cluster-based Partial Lo-
calization (CPL). CPL will provide partial localization for a dense wireless sensor network. Partial
localization means that the algorithm will through several stages localize subsets of the network,
and it also reflects that the algorithm can provide different degrees of accuracy for different needs
and that no localization result for any technique will be100 percent accurate as long as one uti-
lizes inaccurate distance estimates. CPL will localize a subset of a network using an expensive
but accurate technique and with these results efficiently and economically localize the rest of the
network. All position estimate will be relative, each derived position will be relative to all others.
In order to not introduce any new constraints on the network performing the localization CPL will
only depend on connectivity information, but CPL could however potentially utilize additional
information like that from anchor-nodes to orient the relative map and make it absolute or to im-
prove the localization accuracy. CPL works by dividing the network into relatively small, loosely
coupled, independent groups that can maintain local network information and is motivated by the
need for scalability and efficiency. Each of these groups will have one “leader” node. For these
groups to be meaningful and provide a certain level of abstraction, each group should cover a fairly
small area and their chosen representative’s position estimate should represent every member in the
group well. To achieve the desired scalability objective, localization will be first computed for the
smaller subset of representative nodes — one from each group. These nodes will use the connectiv-
ity of the entire group in communication with neighboring groups and in estimating the distances
between it self and its neighboring groups. The remaining nodes will however not be considered
active during this process, they will only be used to forward information between clusters. The
derived position estimates for the chosen subset will be used as references when localizing the rest
3
of the nodes in the network using trilateration.
As opposed to many other proposed localization techniques, CPL will not depend on any type
of anchor nodes or specific node distribution. No information about the network, distributions or
node capabilities will be known or required about the network. CPL will utilize the connectivity
information as the only distance estimate between nodes, but CPL could potentially utilize any
kind of additional information if available to improve the accuracy of position estimates. The use
of clusters will make CPL less sensitive to abnormalities such as obstacles or holes in a network
as they wold cover a larger geographical area and in effect reach around many of these challenges.
CPL’s use of clusters will also reduce the computational and communication complexity signifi-
cantly. With CPL we attempt to provide a technique that can handle the challenges presented when
increasing both network sizes and densities. We will show that we can utilize an existing local-
ization technique and achieve both acceptable localization accuracy and a significant reduction in
complexity.
1.1 Organization of thesis
The remainder of this thesis is organized as follows. Chapter 2 presents the terminology, back-
ground and related work in the area of wireless sensor network localization. Our localization tech-
nique CPL is described in Chapter 3. Chapter 4 contains performance evaluation our technique.
Chapter 5 provides some concluding remarks and potential future work.
4
CHAPTER TWO
BACKGROUND AND RELATED WORK
2.1 Sensor networks
To provide a feasible and cost effective implementation of the types of large networks that WSNs
will be, with as many as100, 000 nodes and a density of10 nodes perm2, both the size and
production cost of each sensor must be kept to a minimum. Many of the proposed uses for sensor
networks considers non-reusable nodes, where when either a battery is depleted or an error in a
node occurs, the failed node will be not recycled. In any case the requirements to cost and size
ensures that each sensor will have very limited capabilities both in terms of computation, storage
and communication capabilities. As each sensor usually will be battery-powered and recharging
or replacing power source is not a viable option, energy efficiency and network lifetime are two
very important issues. Energy efficiency considers how to perform the assigned task with the least
possible energy used, while network lifetime is related to when a network can no longer perform
its duties. Energy efficiency is very much an issue when considering any communication task, as
this will usually be the most expensive operation. Data dissemination, routing and general network
management are all tasks that should consider energy efficiency when performing their tasks. The
lifetime of one network will be specified by the application, and while one network might be
considered ”dead“ or useless when only a few sensors fail, another might be usefully until the
network becomes disconnected. Because of the importance of network lifetime balancing the load
on a network must be considered as part of the requirements to energy efficiency. Because of the
stringent requirement to preserving energy one can simply not justify spending a large amount of
the available energy on a process like localization. In addition to the energy concerns comes the
time needed for localization. A network can not afford to devote much of its lifetime, in terms of
energy or time, to management tasks like localization, so tasks like this must be both fairly quick
5
and very efficient.
2.2 MDS
Multidimensional scaling (MDS) [14] refers to a family of models with which one can represent
information contained in a data-set as points in a space. MDS has its origins in psychometrics.
where it was proposed to help understand people’s judgments of the similarity of members of a
set of objects. MDS has now become a general data analysis technique used in a wide variety
of fields. MDS techniques have been successfully applied in fields like marketing, sociology,
physics, political science, and biology. MDS can be used to produce a picture which is much
easier understood than say a large matrix, and correlations in the data can be represented spatially
by portraying each variable as a point and placing the points in such a way that the inter-point
distances represent reproduce the correlation coefficients.
There exists several different variations of MDS, where the major difference between each lies
in the assumptions made about the input data and whether the data is complete, i.e. the data con-
tains the relation between all pairs of variables. The input data, a representation of the differences
between variables of some other data, to any MDS techniques is referred to as similarities, dis-
similarities, inequalities, distances, or proximities. Through MDS each object or event in the data
is represented by a point in a multidimensional space. The points are arranged in this space so
that the distances between pairs of points have the strongest possible relation to the similarities
among the pairs of objects. That is, two similar objects are represented by two points that are close
together, and two dissimilar objects are represented by two points that are far apart. The space
is usually a two- or three-dimensional Euclidean space, but may be non-Euclidean and may have
more dimensions. An example of how MDS can be used can be found below.
2.2.1 MDS example
In this example we will show how one can estimate the locations of cities in the US by using
MDS and the estimated distances between the cities. In table 2.1 the metric distances between
6
four objects can be seen. The original positions of the objects can be viewed in figure 2.1(a), and
estimates for the positions of the same objects are shown in figure 2.1(b) along with the deviation
from the true position. As Figure 2.1(b) shows the result of an MDS algorithm will deviate from
the “correct” output, but the goal of any MDS techniques is to best fit the dissimilarities between
pairs of estimates with the corresponding dissimilarities in the input data.
A B C D E FA 0 7.21 9.48 15.81 13.45 17.46B 0 3.60 9.89 8.54 14.03C 0 6.40 6.00 12.16D 0 4.12 9.21E 0 7.81F 0
Table 2.1: Distance matrix
(a)
-8
-6
-4
-2
0
2
4
6
-6 -4 -2 0 2 4 6 8 10
(b)
Figure 2.1: MDS example
As previously mentioned different variations of MDS exists, and specifically when MDS is
used for localization in sensor network and each variable is a node in the network the difference
between classical and non-metric MDS is easily illustrated. Classical, or metric, MDS assumes
there is a linear equation that relates the path distance between pair of nodes, and the Euclidean
7
distance between each pair of nodes. The non-metric MDS only assumes a monotonicity con-
straint, which puts less requirements on the input data. This assumption also seems to fit better
with the problem of localization in sensor networks, as the distances estimates, whether they are
range free or range aware, will in many situations not be a precise indicator of the Euclidean inter-
node distances. Non-metric MDS is the first example of using quantitative models to describe
qualitative data.
The goal of non-metric MDS is to minimize the sum of squares of the errors between actual
measured distancesd′ij (input data) and the calculated distanceddij between the position estimates
δi andδj. The distances between estimated positions is modelled using the Euclidean distance 2.1.
In Equation 2.1xi is the estimated position ofa. Non-metric MDS is an iterative algorithm, where
in each iteration the “goodness”β of the derived estimate is tested.β is a indication of how well the
distanced between the estimated positions fit with the corresponding input data. There exist several
standardized “goodness” tests, Kruskal’s Stress-tests#1 and#2, respectively in Equations 2.2 and
2.3 are two commonly used tests. In Equation 2.3,djk andd′jk are the measured distances (input
data) and the distances between the estimated positions respectively.d is the average of the distance
between the estimates. The monotonicity (order preserving) constraint of non-metric MDS can be
either weak or strong; weak monotonicity means that wheneverδij < δkl then it should never be the
case thatdij > dkl, while strong monotonicity means that wheneverδij < δkl holds thendij < dkl
should also hold. For our implementation we use weak monotonicity. The monotonicity constraint
is used in every iteration to determine how to change the position estimates.
dij =√
(xi − xj)2 (2.1)
S1 =
√√√√∑
(djk − d′jk)
2
∑d2
jk
(2.2)
S2 =
√√√√∑
(djk − d′jk)
2
∑(djk − d)2
(2.3)
8
2.3 Trilateration
Trilateration is a method of determining the relative positions of objects using the geometry of
triangles in a similar fashion as triangulation. Unlike triangulation, which uses angle measurements
to calculate a position, trilateration uses the known locations of two or more reference points, and
the measured distance between the subject and each reference point. To accurately and uniquely
determine the relative location of a point on a 2D plane using trilateration alone, generally at least
3 reference points are needed.
2.3.1 Trilateration example
Figure 2.2 illustrates the trilateration process. Starting at pointB, we want to determine our posi-
tion relative to the reference pointsP1, P2, andP3. The distance fromB to P1, r1, narrows the
position down to a circle. Next, The distance fromB to P2, r2, narrows it down to two points,A
andB. A third measurement,r3, gives your coordinates atB. A fourth measurement could also
be made to reduce the potential error.
Figure 2.2: Trilateration example
9
2.4 Related work
2.4.1 General overview
Localization in wireless sensor networks has recently become an active area of research. This re-
search can be dividend into two categories; range-aware and range-free localization. This thesis is
focused on, but not limited to, range-free localization. Both range-aware and range-free approaches
often employ traditional mathematical 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 distribution and simplified transmission ranges in order to reduce
the problem so that traditional mathematical techniques can be used.
Range-aware localization techniques are typically dependent on some form of distance esti-
mates, where these estimates generally are inter-node distances. There are several ways of ob-
taining an estimate for the distance between two nodes; received signal strength, time of arrival,
angle of arrival, etc. The accuracy of the estimate will be highly dependent on the environment and
quality of the transmission equipment, errors caused by multipath fading, echoes from obstacles,
interference, etc. can produce highly inaccurate estimates. Some range-aware localization tech-
niques also depend on a number of specialized nodes; these can be anchor nodes, beacon nodes or
mobile robots. An anchor node is usually a GPS enabled sensor node, but can also be more capable
than a “normal” sensor node. Beacon nodes are nodes that normally have no “sensing” functions,
and the tasks of theses nodes are just used to help the localization progress. A mobile robot can
combine tasks of anchor nodes, beacon nodes and mobility, and these robots often also function as
data collectors.
Range-free localization, often also referred to as hop-based or connectivity-based localization,
aim to overcome the inherent difficulty of accurately determining exact inter-node distances in sen-
sor networks. While hop-based techniques do not require inter-node distance information, many
10
hop-based techniques have the ability to take advantage of such information, if available, to pro-
vide more accurate results. The connectivity of a sensor node is used as an indication of how close
this nodes is to other nodes, and all nodes within its transmission range are said to be one hop
away. The measure of hops is simply a very crude approximation of distance.
In [21], Hightower and Borriello presents a survey and taxonomy of location systems for mo-
bile computing applications. Comparing different techniques and their performance can be very
difficult because many different applications solves many different problems, and each technique
can differ from others in many ways. The physical media used for the location, the context where
the position is needed, power requirements, infrastructure and resolution of results will all change
from application to application. Hightower and Borriello attempts to provide the means to make
an easier comparison of implementations and applications. Another survey is presented in [53],
where Guolin et al. provide a survey of positioning designs for wireless communications tech-
nology, Guolin et al. look at localization both in cellular technology and in wireless networks
like WSN. The survey provides a categorization of the different technologies ranging from GPS to
sensor network techniques.
Practical results concerning two key issues in the deployment of localization service in wire-
less sensor networks are presented in [3], where Anlauff and Sunbul discusses both the selection
of appropriate sensors for acquiring the data needed to preform localization and the actual local-
ization algorithm. The authors looks at the use of Motes or motes-like technologies and points out
that for most applications there will not be any map of the monitored area. Motes are tiny devices
equipped with a sensor, an onboard computer and wireless communication technology. Motes with
both long and short distance antennas were tested to determine the ranges of the transmissions. The
authors claim that not only signal strength and distance determines how much of the information
is received, but also the angle between the sender and receiver and the environment in which the
11
signal is sent. Already at distances of only40cm, the percentage of information received is un-
predictable. Both trilateration and bivariate Gaussian distribution based algorithm is presented as
localization algorithms. Trilateration is shown to work well when the sensor reading are accurate,
but the accuracy of the localization drops when the accuracy of the readings drop. The Gaussian
distribution based algorithm is more robust and almost insensitive to deviation in the accuracy
of the sensor readings, but is also much more complex in terms of space and time requirements.
Theoretical foundation for network localization in wireless sensor networks are also presented in
[18]. Eren et al. point out that the problem of localization shares a number of features with other
active fields of study; rigidity and global rigidity in frameworks; the coordination formations of au-
tomonous agents; and geometric constraints in CAD. The authors uses techniques and results from
other techniques to lay a coherent solid foundation for the underlying problem of when a network
is uniquely localizable. The computational complexity of localization is also studied. In [11] the
Chang and Sahai presents studies of the the Cramer-Rao lower bound (CRB) of localization. The
authors looks at two kinds of sensor network localization based on noisy range measurements, both
with and without anchor nodes. CRB is used to evaluate the hardness of an estimation problem and
a CRB-like bound for the estimation variance is presented. In [54] a Bayesian method to analyst
the lower bounds of localization uncertainty in sensor networks is presented and compared it to
the Cramer-Rao bound. The authors attempts to analyze the dependency of localization on sensor
network topologies.
2.4.2 Range aware
In [44] a technique that uses range measurements between pairs of nodes and the known coordi-
nates of the anchor nodes in wireless ad hoc networks, to estimate the position of every node is
proposed. The method will first establish the position of the nodes close to one of the anchor nodes,
and then use this information to estimate positions of nodes further away from the anchor nodes.
As in most range aware techniques, inaccuracies in the range measurements will severely affect
12
this algorithm, and errors may propagate fast throughout the network; the distribution and number
of anchor nodes in a network will also affect the performance of the algorithm. Another similar
distributed algorithm for localization in wireless sensor network is described in [45]. This algo-
rithm is based on the iterative propagation of information through the network, and measurements,
with limited accuracy, of the distances between pairs of nodes used to derive position estimates.
Savarese et al. mention the standard methods for acquiring these measurements, but the technique
described is independent of the method used for distance measurement. The authors also mention
that different techniques offer different tradeoffs between accuracy, complexity cost, etc. Errors
in the measurements can come from multipath interference, line-of-sight obstructions and more.
It is assumed that there is a large error in the distance measurements used, and mentions that this
should be representative of realistic measurements. The algorithm described is divided into two
phases; start-up and refinement. The authors describes a Hop-TERRAIN algorithm that is used
in the start-up phase and the result from this phase is iteratively improved during the refinement
phase. The HOP-TERRAIN algorithm is similar to the DV-Hop algorithm [34]. All tests were
implemented in C++ using OMNeT++ discrete event simulator. All nodes were either randomly
placed with a uniform distribution or placed according to a grid, but the refinement algorithm does
not show any better results in the later case. As the average connectivity in the network decreases
both algorithms tested fail to derive positions for parts of the network. The Hop-TERRAIN al-
gorithm is shown to be insensitive to ranger errors, while the refinement algorithm needs a range
error below40% to show average performance.
In [28], Partial Range Information (PRI) and a partial-range-aware localization technique is de-
scribed. Partial range information (PRI) is defined as any type of measurement which is monoton-
ically increasing or decreasing and has an unknown or environment-dependent one-to-one rela-
tionship with the range measurement. The described technique is distributed and uses received
signal strength measurements in the localization process. The algorithm is developed as a module
13
that can be plugged in to any range free hop-based localization algorithm to improve the result.
The technique described is called RangeQ. It is a distributed range quantization technique that will
associate range values with all1-hop connections with unknown distances. The quantization is
similar to quantization in image processing. Li et al. considers three different models, simple lin-
ear, min-max neighbor linear and area proportional model, for use in the quantization to obtain the
cluster sizes and range values of each node. The technique presented is shown to reduce position
errors with up to 50% from previous range-free-algorithms and it preforms better than both range
free and range aware methods when the range errors is between15% and35%.
In [4] the Approximate Maximum-likelihood (AML) method for source localization and Di-
rection of Arrival (DOA) estimation [12] is reviewed, and the authors also considers a least squares
method applied to the DOA bearing crossings to preform the source localization. A virtual array
model applicable for the AML-DOA method for use in reverberant scenarios is proposed. The
work illustrates that the proper usage of novel array and signal processing algorithms implemented
on very low-cost Commercial-Off-The-Shelf (COTS) platforms is capable of achieving quite so-
phisticated real-time acoustical beamforming operation for source localization.
In [50] localization based on a the use of a single mobile beacon is presented. The technique
uses received signal strength to estimate the distances between nodes and the beacon. This gives
the method an accuracy of a few meters. The beacon will broadcast its own position and any node
receiving this messages can infer that it is positioned in a certain area with a certain probability.
The received signal strength is measured for every received beacon message and will place a con-
straint on the possible position of a node. Each node will used Bayesian inference to compute the
position estimate. This technique can be implemented both centralized and distributed, and scales
well, both in terms of number of nodes and density of nodes. The trajectory of the mobile beacon
will affect the results and must be considered. A localization technique that uses the signal strength
from two static beacons is presented in [5]. Interference and fading in the signals are handled by
using the average over several measurements within a certain time-frame. The two beacons are
14
placed in two non-opposite corners of a rectangle that encloses all devices. Problems occurring
both with static and mobile nodes are considered and the best performance in both scenarios is
obtained in a fast fading environment. The minimum error is in both cases where the variance in
error as a function of the size of the time-frame is said to be very small. Beacons are also used
in [37], where an efficient localization algorithm using four mobile beacons is described. The
rectangle, formed by the four beacon nodes, will have the sensor node in the center, and localiza-
tion is performed by moving the beacon nodes towards the node. The node can then estimate its
own position by position information from the four beacons. Received signal strength is used to
estimate the distance between a sensor and a beacon. In this method the beacon nodes will pre-
form the distance measurements in several iterations and provide the node with this information.
All nodes will be assigned an unique ID to separate the localized and non-localized nodes. In
[52] several distributed scalable and probabilistic localization algorithms and one mobile beacon
driven communication protocol are proposed. In the proposed method every unknown node will
localize itself based on received beacon packets. The position is estimated using both parametric
and non-parametric probabilistic estimation techniques. This technique will make use of a beacon
node in a network, and Time of Arrival (TOA) measurements are used to estimate the positions of
other nodes. The mobile beacon will traverse the network after initialization and broadcast packets
containing the position of the beacon. When an node picks up a packet from the beacon it can
infer with a certain probability that it is in a certain proximity to the beacon. The trajectory of
the beacon in the simulations is a helix, but this might not be optimal and determining thecorrect
trajectory is a difficult problem that is not discussed in this paper. Sun and Guo presents simulation
results for different distributed localization algorithms. The Non-parametric probabilistic method
is shown to be more robust and more accurate that other methods. The authors also argue that
the proposed technique presents a good tradeoff between scalability, robustness, energy saving and
accuracy. In [9] motivations for the need for empirical adaptive beacon placement is presented.
Bulusu et al. describe the design and evaluate three adaptive beacon placement algorithms based
15
on RF-proximity. The authors claim the the density of beacon nodes has greater impact on the
performance of placement algorithms than noise levels. In [55] a formulation to determine optimal
beacon placement in wireless sensor networks is described. The authors note that any placements
algorithm must consider both beacon coverage area and network lifetime. The authors formulate
an optimization problem which is solved by Integer Linear Programming.
The work described in [16] is motivated by the Smart Dust project that is aimed at scaling
sensing communication platforms down to cubic milliliter. Doherty et al. proposes a technique for
estimating node positions in wireless sensor networks based on connectivity-induced constraints.
Known peer-to-peer communications are modelled as a set of geometric constraints on the node
positions. The algorithm proposed, provides results close to the actual positions of node, given
tight enough constraints. The paper also provides an additional method for placing rectangular
bounds around the possible positions of all unknown nodes in the network. The methodology for
formulating the position estimation problem as a linear or semidefinite programming is presented.
Results from simulations with on average194 nodes, with average connectivity5.7 are presented.
The performance metric is defined as the mean error between the actual position and the estimated
position. With a low number of anchor nodes, the algorithm will produce very inaccurate results,
and only when the number of anchor nodes is very high is the accuracy acceptable. When using
angular constraints,26 anchor nodes gives a mean square error of23R in a10R×10R network. The
results can be improved by running the algorithm several times and used the intersection between
the different results. Additional improvements can be achieved by placing the anchor nodes at the
perimeter of the network. In [19] a distributed localization technique where geometric constraints,
placed by both connectivity and sensing, is used to increase the accuracy of position estimates
is proposed. Sensing constraints are caused by mobile objects that are sensed by several nodes.
These constraints are said to usually be tighter than connectivity induced constraints. The authors
assume a fraction of the nodes will know their own position and the paper also assumes that the
transmission range of each sensor is modelled as a disk with radiusr and the node in the center
16
and that all nodes will have the same transmission range. The authors argue that it makes sense to
integrate the localization process with the application and exploit additional information gathered
over the course of running the application. The technique described suggests that instead of using
triangulation, abounding boxfor each node can be established. Negative information, i.e. when
a target is not sensed, can also be used as constraint on a position. The efficiency of proposed
technique is compared to the efficiency of a centralized solution. Using the distance bound sensing
model and negative constraints the proposed algorithm outperforms the centralized one. The paper
shows that the technique described can be used to increase the accuracy in localization. Simulations
is done using TinyOS-Nido platform.
In [24] a distributed localization algorithm is proposed. The algorithm is based on the estimation-
comparison-correction paradigm. Multidimensional scaling (MDS) [14] is used to merge maps
from neighboring sensors. This is done along a path between a sensor and an anchor node to es-
timate the sensor position. Errors in the estimates caused by anisotropic network topologies is re-
duced by iterative estimation, comparison and correction. Received signal strength measurements
are used to estimate the distances between the sensors. In [2] much of the same ideas as our own
is adopted. The technique presented is Simple Hybrid Absolute Relative Positioning (SHARP).
SHARP will attempt to preform localization on a subset of the nodes in a network using ranging
measurements. The subset will be localized using the MDS-MAP algorithm [41], and this subset
will then be used as anchor-nodes when the remaining nodes are localized using APS [34]. The
test are, as in [41], done using MATLAB, but their metric for performance is different in that it
also considerers the work needed to achieve the accuracy. Ahmed et al. present a new metric for
localization performance calledPerformance-Cost Metric(PCM). PCM reflects both localization
accuracy and localization cost in terms of delay and/or energy consumption.
17
2.4.3 Range free
In [34] APS, a distributed, hop by hop positioning algorithm, is proposed. The algorithm works
as an extension of both distance vector routing and GPS positioning, and will provide a position
estimate for all unlocalized nodes in a sensor network. The technique assumes a limited fraction
of the nodes have the ability to determine their own actual position, this can be done with for
example GPS. The algorithm will derive the absolute position because this will incur lower sig-
naling cost if the topology changes, and it enables the use of a unique namespace. One aim of the
proposed technique is to enhance the accuracy of the position estimates as the fraction of anchor
nodes increases. The paper describes three different hop-by-hop distance propagation techniques.
The DV-Hop propagation method uses classical distance vector exchange. The anchor nodes will
estimate the average hop size based on the number of hops between different anchor nodes. This
average is distributed to the network by controlled flooding, and used to correct the estimates in
the network. In large networks a “Time To Live” would be used in the propagation messages to
limit the number of anchor nodes that each node acquires. This methods does not depend on mea-
surement error, but will not work well in anisotropic networks. The authors present simulations
done in ns-2. Test are done on two different topologies, nodes placed in random uniform manner,
and the shape of the letter “C”. The DV-based algorithms are shown to perform better when the
ratio of anchor nodes is low. The message complexity is also shown to be better in DV-hop in the
uniform topology. The errors in position estimates range from around2% to almost200% of the
hop distance depending on the topology and ratio of anchor nodes.
In [43] an algorithm for estimating the positions of nodes in wireless sensor networks using
connectivity information is presented. The information concerning one node is assumed very likely
to already be available to that node. This technique can also use additional information such as
estimated distances between neighbors or known positions of nodes in a network. The position es-
timates are derived using Multidimensional Scaling (MDS) [14]. This technique shows especially
18
good performance when the nodes are distributed relatively uniformly, and improves over other
techniques when the network has fewer anchor nodes. The accuracy results from MDS method is
dependent on the accuracy of the distance estimates, so MDS can potentially yield a perfect map.
Test are done in MATLAB with randomly with uniform distribution, and in both a square and
hexagonal grids with different placement errors. The experiments show that the algorithm works
much better where the nodes are placed on one of the grids.
In [41] an improvement to the techniques presented in [43] is proposed. Sang and Ruml de-
scribes a distributed algorithm MDS-MAP(P), that usespatchesof relative maps. These maps
can be computed in parallel at different nodes, to generate estimate for the positions of subsets of
nodes. The algorithm is shown to improve over previous when networks are irregularly shaped,
and performs as well as others on uniformly shaped networks. This technique is best applied to net-
works where the shortest distance between two nodes does not correspond well to their Euclidian
distance. The main idea for this method is to compute the local map for each node using MDS, as
described in [43]. These local maps can then be merged to form the complete map. This approach
can reduce the affect that, when estimating the position of one node, a far away node will have
on this estimate. An additional refinement step is also employed to improve the accuracy of each
local map. The technique describe uses least square minimization, but different techniques, like
collaborative multilateration, can also be used. The method is said to often find the right general
layout of a network, but not necessarily the precise location of the nodes. The test are done using
two different scenarios; when only connectivity information is available and when both connec-
tivity information and distance estimates are available. The authors present simulation results for
four types of topologies, a uniform random placement, uniform grid placement, and random and
grid placement in a “C” shape. When using connectivity information only the proposed algorithm
performs better than earlier methods. The average error when using only connectivity information
on uniform networks is shown to be27%. Results from tests using distance measurements are also
19
shown, but as earlier, the error used is only5%. The algorithm is shown to always derive an esti-
mate for all nodes in the network. The proposed algorithm is also shown to perform better the “C”
shaped networks. The authors also present comparisons between the MDS based algorithms and
both DV-hop and DV-distance algorithms. In general the proposed algorithm is shown to perform
better. Another distributed variation of the before mentioned MDS-MAP technique is presented
in [42]. In this technique estimates the relative positions of nodes in wireless sensor network are
derived. The algorithm utilizes a given communication path between a starting and a remote node.
This path can be discovered using techniques like constraint-based routing or limited broadcasting.
The nodes on the path will compute their local map, as in [43], based on local distance estimates.
As in the previously mentioned technique, [41], the number of hops may be changed, and varying
this may give different accuracies in different network topologies. The computation of the local
maps will, as long as the network stays static, only have to be done once at each node. The relative
maps of nodes along the path will then be aligned according to common nodes in the map before
the optimal linear transform between the two is computed. The maps of two nodes will be aligned
two at a time as long as the two maps have three or more common nodes. These common nodes can
not be placed on one line as this would not provide enough information for accurate alignment. The
optimal linear transformcan be computed in the least-squares sense. The relative position of the
remote node in the coordinate-system of the starting node, is computed by applying the sequence
of linear transformations. The authors document tests done on proposed algorithm with changes in
the chosen hop size in building the local maps and how many common nodes exists when aligning
the local maps of neighbors. The test shows that the accuracy of the algorithm depends on the
network connectivity, the errors in local distance measurements, the length of the chosen path and
the number of common nodes between two adjacent nodes along the path. The technique performs
well on both regular and irregular networks, as long as the network has sufficient connectivity and
small enough errors in the distance measurements. Tests done on both randomly uniform and grid
based topologies are presented. As before [41] the assumed average range error is5%. The test
20
show that the method does not perform well when only one-hop neighbors is considered when es-
tablishing the local maps. With the connectivity above10 and 2-hop neighbors being considered,
the algorithm performs well, but has a higher message complexity. The paper also describes tests
done using different sized local maps and with different range errors.
In [47], Multilateration based localization like APS [34] and MDS-MAP [41] are compared.
Key issues that affect their performance are studied. The authors studied the affect changing the
number of anchor nodes and their distribution has on the performance of the localization algo-
rithms.
In [30] a range free localization (ROCRSSI) is described. In ROCRSSI each node uses a series
of overlapping rings to narrow down the possible area in which it resides. The technique has a low
overhead and is said to perform well and be robust when employed in irregularly shaped networks.
In [38], a differential Ad-Hoc Positioning System is described. A differential error correction
method designed to reduce the cumulative distances and positioning error over multiple hops is
used. A HopCount algorithm and a HopDistance algorithm are presented and both algorithms use
beacon nodes to estimate other nodes positions. The authors present simulations where70% of the
nodes are estimated with error less than50% of the transmission range.
In [29] a localization algorithm based on growing local map is presented. The algorithm starts
with a local map computed from three non-collinear neighboring nodes, and will continue until
all localizable nodes are covered in the map. When the first local map is computed the position
of these nodes are broadcast to neighboring nodes, and these nodes will, when they have received
the position of two or three different nodes, start to localize themselves and then broadcast their
own position. Simulations show that compared to APS DV-distance [34] the proposed technique
is about two times more accurate for C-shaped grid or hexagon networks with the same coverage
as the APS DV-distance algorithm, when the range error is less than10%.
[10] is one of several recent papers that attempts to provide more scalable and feasible localiza-
tion techniques. Chan et al. proposes a localization technique that employs clustering information
21
and a small number of “anchor nodes”. The clustering is used to provide a regular pattern in the
network and helps reduce the communication overhead since only cluster heads will be involved in
the initial phase of the localization process. Anchor nodes are assumed to be able to derive the po-
sition of all adjacent cluster-heads, this set of localized nodes will be used by other cluster-heads
to localize themselves. All cluster-heads will recompute their estimate as more information be-
comes available. The hop-distance to localized cluster-heads and the regularity in the edge-length
between clusters is used to produce the position estimates. In [56] a technique for energy efficient
distributed clustering in wireless sensor networks is proposed. The technique is shown to have low
overhead and in simulations the method outperforms weight-based clustering.
2.4.4 Miscellaneous
In [26] a very low power dedicated hardware implementation for localization is proposed. The
paper describes the design of the localization hardware, the algorithm used, the power consump-
tion and power dissipation of the hardware. A sensor network is assumed to be distributed and
to have a set of anchor nodes that know their own position while none of the other sensor nodes
will have any specialized capabilities. The positions is computed using least squares method and
the Hop-TERRAIN algorithm [45]. The least squares method is used for triangulation, but other
non-triangulation techniques can also be used. In Hop-TERRAIN the number of hops between an-
chor nodes and sensor nodes are used instead of the actual Euclidian distance. The method will be
repeated every1-10 minutes to track potential changes in a network. Another hardware implemen-
tation is presented in [32]. The authors describe the implementation and analysis of PAVENET, a
software and hardware system, and ANTH (ANtenna Things), an application using PAVENET, are
described. A battery-less sensor network implementation (Solar Biscuit) is also described. In Solar
Biscuit each device draws its power from a super-capacitor with small solar cells. This system is
developed to illustrate possible devices that do not need to be replaced or recharged. A commu-
nication strategy for robust use of the Solar Biscuit system is presented. A simple and distributed
22
localization system called DOLPHIN (Distributed Object Localization System for Physical Space
Internetworking) is also described. This technique can determine the position of devices using a
few manually configured references. The method determines the positions of sensors by evaluat-
ing a time of arrival measurement and uses both RF-communication and ultrasonic pulses. Both
error accumulation and non-line-of-sight propagation are factors that leads to errors in position es-
timates. The accuracy of the localization is over2 meters. The paper argues that both simulations
and practical test-beds are needed to thoroughly evaluate these systems. In [31] Speckled Com-
puting is described. A Speck is intended to integrate sensing, the needed processing and wireless
communication on a minute semiconductor grain. Specknets can simply be thought of as one type
of sensor networks where each arenot assumed to be static. The authors describe an algorithm for
distributed localization. The algorithm will utilize 2-hop neighborhood connectivity information.
Results from simulations using a Java-based simulator is presented. In [20] a system capable of
both localization and time synchronization using only commercial off-the-shelf components is dis-
cussed. The localization is done using a ranging system that times the flight of a wideband acoustic
pulse. The proposed system is said to be accurate to within10 centimeters and10 µseconds.
A localization technique bases on uncontrolled environmental sounds observed by each sensor
is described in [7]. All sounds that have a clear onset can be used. The technique is said to expend
less power, require no known infrastructure and to make the network less detectable than networks
using active techniques like beacons. However, the clocks in the sensors needs to be synchronized,
and done using the Reference Broadcasts protocol (RBS) [17]. Good synchronization is needed to
record accurate times of sounds at each node. The relationship between variables is encapsulated
as a Bayesian network and the localization problem is reduced to the problem of maximum likeli-
hood estimation using gradient decent in the Bayesian network. A probabilistic generative model
is presented and it is shown that the sensor localization problem is equivalent to the maximum
likelihood estimation in the model. Four additional algorithms for sound localization are analyzed
23
in [25]. Signals recorded in a natural environment with an array of commercial off-the-shelf mi-
croelectromechanical systems, microphones and a specially designed compact acoustic enclosure
are used. The techniques analyzed coherent approaches at the node level, so no synchronization is
needed.
In [8] a localization technique based on nodes uncertain observations of other nodes in a net-
work is presented. Both Monte Carlo and Kalman filtering are used and the goal presented by the
authors is that a sensor node quickly can localize it self and setup and startworkingautomatically
without any assistance or extra information. The approach taken by the authors is to use a network
of nodes where at least one is well-localized, to localize another node. A well-localized node is
used as the features of a dynamic map. Upon initialization only information of the size of the map
in which a sensor must lie is known. Results from experiments done using stationary nodes that
in real-time self-localized by observing Pioneer robots moving in their field of view, is presented.
The robots take observations of surveyed beacons in the environment and provide estimates of their
positions to the rest of the network.
In [36] a technique for localization in DTN (Delay Tolerant Sensor Networks) is described.
Devices in a DTN are often organized in mutually disconnected clusters so a mobile robot can
be used to collect data from the different clusters. Pathirana et al. proposes a method where the
mobile robot preforms localization based on received signal strength. The localization is solved
using Robust Extended Kalman Filter (REKF)-based state estimator. In DTN is assumed that
nodes need not be localized in realtime nor all at once. Test of the method was done using a hybrid
sensor network test bed. The tests show that the method can achieve accuracy within1m in a
large indoor setting. In [51] Walking GPS for localization in real, manual deployments of sensor
network is proposed. The technique is shown to localize all nodes with average errors between1
and2 meters. The system proposed is divided into two software components; the GPS Mote and the
sensor Mote. Only one node in a network will contain the GPS component, and this node will be
24
mobile and will broadcast its current position periodically as it moves through a network. Nodes
may also use the positions of neighbors to triangulate its own position if it can not be inferred
otherwise after the initial phase.
[15] describes a parameterized algorithm for Sensor Topology Retrieval at Multiple Resolu-
tions (STREAM). The technique makes tradeoffs between the resolution in retrieved topology and
bandwidth. Deb et al. illustrate how different resolutions are sufficient to determine certain net-
work properties. The STREAM algorithm will create a Minimal Virtual Dominating Set. The sets
will be based on a virtual range. The range in effect determines the resolution of the result.
A technique for estimating and tracking multiple target locations is presented in [49]. The
method is compared to Maximum Likelihood source localization [48], and is shown to out pre-
form this technique both in terms of robustness and computational efficiency. A particle filter is
employed to determine the source locations. Target detection is also described in [57]. Here Zou
and Chakrabarty propose an energy-aware target detection and localization strategy for cluster-
based wireless sensor networks is proposed. The method is based on an a posteriori algorithm
with a two-step communication protocol between the cluster head and the sensors within the clus-
ter. In [22] Howard et al. describe how localization of a robot in an unknown environment and
calibrating an embedded sensor network are combined and solved as ageneral localization prob-
lems. A physically inspired mesh based formalism for solving suchgeneral localization problems
is presented.
In [39], an approximate maximum likelihood strategy and the received strength of signals from
nodes with well-known positions is used to estimate the position of the receiving node. Beacons are
used as the nodes with known positions. A parameter called normalized collinearity is described.
This new parameter is used as a metric for the nodes to evaluate how the different beacon nodes
are aligned relative to the nodes. Based on the metric, the best aligned beacon nodes can be
chosen by the nodes. In [35] a refined approach to localization that uses a combination of mobile
anchor node scenarios for anchor information distribution and a statistical localization technique
25
is presented. This is done to improve estimate accuracy and to better handle inaccurate ranging
data and non-uniform anchor node distribution. Static anchor nodes are used in [33], where a
localization method using triangulation and received signal strength measurements is presented.
Mondinelli and Kovacs-Vajna assumes that sensor nodes might move and presents methods using
both one and three anchor nodes. In both methods estimate accuracy and energy efficiency is
considered.
In [6], a semidefinite programming (SDP) relaxation based method for localization is presented.
The basic idea behind the technique is to convert the nonconvex quadratic distance constraints into
linear constraints. This is done by introducing a relaxation to remove the quadratic term in the
formulation. Biswas and Yinyu claim that the approach can be extended to more complex and
more realistic connectivity models.
In [46] a micro-level behavioral analysis to identify the possible protocol error scenarios and
their conditions and bounds are presented. Results from a simulation study of GPSR [27] and
GHT [40] to quantify the performance degradation due to location errors is also presented. Last
the paper presents small changes to face routing that eliminates probable errors and lead to very
good performance. The assumptions in the paper are highly idealized but even then the result show
that small localization errors lead to incorrect geographical routing with considerable performance
degradation. Simulations is shown for what the paper consider to be state of the art localization
systems. How the density of anchor nodes and errors in range measures affect the performance
of localization systems is investigated in [13]. Chintalapudi et al. makes the argument that the
class of ad-hoc localization methods considered in the literature so far fundamentally require high
node densities in order to get acceptable performance. By contrast, new methods that can use
range and bearing estimates, or even range and sector estimates, can give good performance even
at densities that ensure node connectivity. In [23] it is demonstrated that the information used for
sensor localization is fundamentally local with regard to the network topology. This observation is
used to reformulate the problem within a graphical model framework. A generalization of particle
26
filtering called nonparametric belief propagation (NBP) is also presented. In NBP each sensor
will use noisy distance measurements to a subset of other sensors in a network where three sensors
know their respective position prior to initialization. The paper suggest that the Cramer-Rao bound
may be an overly optimistic characterization of the actual sensor localization uncertainty, and that
Gaussian noise models are often inadequate for real world noise.
27
CHAPTER THREE
CLUSTER-BASED PARTIAL LOCALIZATION
The goals for the proposed technique are to provide feasible, robust, scalable and highly-efficient
topology-discovery and partial localization for wireless sensor networks. In addition to address-
ing on low energy consumption and low overhead and it is also very important that the process is
distributed and although some centralized computation and management might be needed, a net-
work should not be overstrained by a single point of failure, bottlenecks or high communication
overhead. The proposed method will perform partial localization, where partial refers to the lo-
calization of smaller subsets of the network, these subsets will be several nodes grouped together
with one chosen representative node for each group. This use of subsets is motivated by the need
for scalability and efficiency. One can not expect to achieve good localization without spending a
considerable amount of both communication and computation, but by utilizing the groups we can
limit the message and computation complexity and hence provide for a better scalability. However
for the use of groups to be meaningful each group should represent a fairly small geographical
area, and the chosen representative should be able to provide a position estimate that will represent
every member in the group. The nodes in one group will all be in close proximity to each other
and preserve some level of abstraction. The defining characteristics of a group will be its size,
range, shape and group to group relationship. Controlling the potential shape of a group will be
very difficult, and although possible to some degree it might become too expensive. Each groupA
will consist of some number of nodes in astar topology, a groupB will be a neighboring group
where two-way communication can be achieved between some node fromA and some other node
from B. A node providing communication with a neighboring group will be considered agateway
to that group. The density of nodes at any place will define much of the characteristics of the group
and although a very small group does not provide a good abstraction there will be no minimum
size. This is simply because multi-hop groups does not provide a good solution for localization,
28
and the work needed to form and maintain these types of larger and more complex groups will be
much more than the single-hop group.
In our localization algorithm, we apply clustering techniques to group nodes into clusters and
select representatives (cluster-heads) for each cluster. We differentiate between the localizations
of cluster-heads and the remaining nodes, or cluster-members, so as to improve scalability as well
as reduce computation overhead. In particular, we divide our algorithm into five phases described
below.
• Neighborhood Discovery
• Cluster Construction
• Cluster-head Localization
• Local Map Merging
• Cluster-member Localization
In the cluster construction phase, nodes are quickly grouped into clusters and a cluster-head
is selected for each cluster. In the cluster-head localization phase, we apply non-metric MDS
[14], a visualization technique that derives a relative map of nodes, to calculate coordinates for
each cluster-head, which is expected to obtain a decent localization precision; Cluster-members,
on the other hand, will be localized in the cluster-member localization phase by using trilatera-
tion technique and cluster-heads as reference nodes. Since trilateration typically incurs much less
computation overhead than MDS and the number of cluster-heads is much smaller than that of
cluster-members, the entire localization process should yield relatively low computation overhead.
3.0.5 Neighborhood Discovery
In this first phase all nodes will, for a set time, periodically broadcast their own unique ID in what
is called HELLO messages. These messages will be picked up by any receiving node to build a
29
list of adjacent nodes and their respective ID. None of the broadcasts will be forwarded so that
when this phase is over all nodes will know only their 1-hop neighborhood. For this phase to work
all nodes must initiate at roughly the same time, if some node arrives late it must be handled in a
different manner and will not be part of the described localization process. Two nodes are called
neighbors if they are adjacent, i.e. within each others transmission range. In Figure 3.1 we show an
example of node neighborhoods, where the dotted circle represents the transmission ranger and in
effect the 1-hop neighborhood of the node in the center(node a). We call the number of adjacent
nodes to a node itsdegree, and we will usedensityas a term for the number of nodes within one
transmission range. In figure 3.1 nodea has degree8 and the node-density in area enclosed by the
range ofa is 9.
Figure 3.1: Node neighborhoods
3.0.6 Cluster Construction
The objective of this phase is to form clusters and select cluster-heads. Although we perform no
form of time-synchronization the transitions between phases will ensure that all participating nodes
have some simple form of synchronization. A cluster head can for example not move to localization
30
before it has collected the data from all neighboring clusters, and a neighboring cluster must finish
the clustering phase before this information can be sent out.
Based on the available neighborhood information acquired in the previous phase, a node will
either wait to be contacted if any of its neighbors have a bigger ID than itself, or assumes the role of
cluster-head if it has the largest ID among its neighbors. A node that is creating a cluster is called
an INITIATOR, while other nodes are called WAITING. An INITIATOR will start to contact one
random node among its neighbors to build its own cluster whose size is bounded by a thresholdθ.
Each cluster is identified by the unique ID of the cluster-head. Each INITIATOR will send out a
request to join the cluster to a WAITING node; any WAITING node, upon this request, will send
a positive reply back and join this cluster. Such a node will then no longer be WAITING, but has
become a MEMBER of a cluster and any other requests received will be rejected. When a node
becomes a MEMBER it will announce to all its lower ID members that is it no longer waiting. An
INITIATOR will in a similar fashion announce that it is done building its cluster to all neighboring
nodes not in its cluster. An INITIATOR is finished building the cluster when either there are no
more WAITING nodes in its neighborhood or the cluster size has reached the thresholdθ. Since
the chosen cluster-heads essentially become the representatives of the clusters and will be taken as
reference nodes for localizing cluster-members, they should be carefully chosen so as to provide a
good abstraction of the whole network. As we will pick the cluster-head based on the node’s ID we
attempt to form clusters in which cluster-member are evenly distributed around the cluster-head.
In particular, each cluster-head will maintain the setS of all the neighboring nodes of the cluster,
i.e. all nodes that are adjacent to one or more nodes in the cluster. The cluster-head will chose
a new member from its own neighborhoodN that are not inS. If N = S the cluster head will
resetS and start the process again, only including the neighbors ofnewmembers intoS. This
process will ideally form cluster with a star shape and with the cluster head is in the center. We
will call two clustersneighborsif two nodes, one from each cluster, are neighbors. We will also
discern between the distance between nodes and the distance between clusters, we call the distance
31
between neighboring clusters for1-step, this is similar to hop distance between nodes, so if two
clusters are not neighbors but have one common neighboring cluster they will be2-stepneighbors.
In Figure 3.2, we illustrate the difference between hops and steps. In Figure 3.2 the dotted lines
encloses each cluster and a line between two clusters means that they are neighbors. The grey lines
between nodes indicate a shortest path between cluster-heads. The distance betweenA andB is
1-stepor 3 hops, while the distance betweenA andC is 2-stepsor 4 hops.
Figure 3.2: Distance measurements
In Figure 3.3, we provide the illustration of one random topology and the connectivity between
each node, a line is drawn between two nodes if they are within each-others transmission range. In
Figure 3.4, we show the result after performing clustering on the topology in Figure 3.3. In Figure
3.4(a) a cluster-head is shown as a small circle and a cluster-member is represented as a line from
its cluster-head to itself. In Figure 3.4(b) the connectivity between the clusters is shown, as with the
nodes in Figure 3.3 a line is drawn between two cluster-heads if the clusters are neighbors. It can
be observed from the figures that the cluster-members of each cluster are well distributed around
the cluster-heads, and the cluster-heads do provide a good abstraction for the initial topology.
32
Figure 3.3: Example of random topology
3.0.7 Cluster-Head Localization
The localization algorithm used to localize the cluster-heads is motivated by the technique pro-
posed by MDS-MAP(P) [41]. In MDS-MAP(P) each node will first use classical-MDS to con-
struct a local map that reflects the location of the nodes in its nearby area. The nodes will merge
their local maps recursively to form a global map that indicates unique coordinates for each node
in the network. Our work differs from MDS-MAP(P) in that only the cluster-heads are required
to perform the computationally-intensive MDS operations. This will greatly reduces the compu-
tation overhead since only a small portion of nodes are cluster-heads. Furthermore, to improve
the practicality of our algorithm, we do not use any pre-installed anchor nodes that are used by
MDS-MAP(P), and we deploy the non-metric MDS technique that has a weaker assumption on
the input data, rather than classical MDS. We should note that the localization algorithm used in
this phase can be swapped with other techniques; for example, a more lightweight technique like
DV-hop [34] could potentially replace our non-metric MDS.
In this phase the needed input data must be collected before localization can be performed. The
cluster-members are in this phase not regarded as active, they will only forward messages to and
33
(a) (b)
Figure 3.4: Example of clustering
from its own cluster-head and respond to requests from other cluster-heads. The data collection
is initiated by the cluster-heads and each cluster-head will ask each of the nodes adjacent to one
or more of its cluster-members, which cluster it belongs to and count the number of hops to the
cluster-heads. Because we utilize the star-shapes clusters two adjacent clusters can be separated
by at most three hops, i.e. two intermediate cluster-members. The first step of the data collection
will establish which clusters are adjacent and the number of hops between each adjacent cluster;
the set of adjacent clusters are called1-stepneighborhood. The next step in this phase consists
of all cluster-heads informing its adjacent clusters of its own1-stepneighborhood. This way all
cluster-heads will be aware of their own2-stepneighborhood. Although we choose to us the2-step
neighborhood for the localization CPL is not limited to this. We chose the2-stepas this gives us a
decent sized data-set while still limiting the message complexity.
MDS is, as mentioned before, a set of well-known data analysis techniques for geometrical
position estimation and information visualization. In our algorithm, we deploy the non-metric
MDS. The algorithm works by iteratively improving how well the position estimates fit with the
input data. The main steps of the non-metric algorithm are outlined below and we will describe
each step in detail.
34
Non-metric MDS
1. Create initial estimates
2. Calculate the Euclidean distances
3. Use monotonic regression to improve the estimates
4. Use Kruskal’s stress test 1 (Equation 2.2 on page 8) to find “goodness”
5. If “goodness”> α goto2, if not quit
The first step of the algorithm is to create the initial estimatesδi. These will be random num-
bers, but the numbers will be scaled according to the squared of the average pairwise distance in
the input data. This adjustment will improve the performance slightly and make the algorithm con-
verge faster. The second step is to compute the Euclidean distancesdij between the estimates. Next
we use monotonic regression to find how the distances will be changed. The monotonic regression
will check whether pairwise the valuesdij anddkl and the corresponding values in the input dataeij
andekl adhere to the monotonicity constraint (Equation 3.1). We used the Pool-Adjacent Violators
(PAV) algorithm for the monotonic regression. In PAV all pairs are ranked and checked through
several iterations. If two values do not adhere to the constraint the new value is computed using
Equation 3.2. If the values do adhere to the monotonicity constraint we use Equation 3.3. Once the
monotonic regression has calculated the new distancesd′ij we will find the new estimatesδNEW
i
based on these distances.δNEWi is calculated using Equation 3.4. We will then use Equation 2.2
to find the stress valueS. If S is less than a predetermined constant the algorithm will exit and the
localization is finished, but if not, the algorithm will run another iteration from step 2.
if dij < dkl thend′ij < d
′kl (3.1)
d′ij = d
′kl =
eij + ekl
2(3.2)
35
d′ij = eij andd
′kl = ekl (3.3)
δNEWi = δi +
α
n− 1
∑
j 6=i
(1− d
′ij
dij
)(δj − δi) (3.4)
3.0.8 Local Map Merging
After obtaining a local map through MDS calculation, CPL must grow a global map. From the
previous phase each cluster-head has a relative local map of its neighborhood, all these local maps
must then be combined in the best possible way to form the global map. To merge two maps we
utilize the common nodes, i.e. the nodes present in both maps. The process of merging two maps
is outlined below.
The two setsA andB contains the nodes in the two local maps,A′ contains the nodes fromA
that are present inB, and similar forB′, soA andB will contain the same nodes but potentially
in a different order. We will find the best linear transformation of the position of the nodes inA′
to the positions of the corresponding nodes inB. We will then apply this transformation to all
nodes inA. The resulting position of all common nodes will be the average of their position inB′
and in the transformedA. All nodes inB not in A will retain their position, while all nodes inA
not in B will used their transformed position. The best linear transformation is calculated by first
computing thesingular value decompositionof the position of the nodes inB′, then we can use
the resulting component to find the best linear transform of the position of the nodes inA′.
The map growing process is completely distributed, but we will use the unique node ID to break
ties in a similar fashion to what is done in the clustering phase. The local maps of neighboring
clusters from the cluster-head localization will be overlapping, so neighboring maps should have
at least a few common nodes. We will give neighboring maps with a high number of common nodes
a higher priority to merge as this will improve the resulting accuracy. The merging phase will have
several “iterations” in which one or more maps will be merged. When two maps are merged one of
the cluster-heads will assume the position of leader, while the rest are merge-members. The leader
will perform the merge and distribute the resulting map to all merge-members. The leader will
36
also inform any neighbors of the merge-members about the new bigger cluster. When this phase is
finished all cluster-head will know the same global map.
3.0.9 Cluster-Member Localization
After determining the relative position of all cluster-heads in the network we will localize the
remaining nodes. This will be done in a similar fashion to the algorithms in [34]. Each cluster-head
will first calculate the average hop distance based on its own position and its neighboring cluster-
heads’ positions and the hop distance between them (Equation 3.5). In Equation 3.5eij means
the Euclidean distance between cluster-headsi and j, andhij means the hop distance between
the respective cluster-heads. The average hop distance will therefore be a reflection of how long
the average transmission distance is in that particular part of the network. Each cluster-head will
then broadcast a message containing its own position, the computed average hop distance, and
a hop-counter. We use selective forwarding to limit the number of duplicate messages and the
overall message complexity. Each node will forward the message if the hop-counter is below a
certain thresholdκ and if it has either not received this message before, or if the hop-counter is
lower then in any previously received messages. Each node will store the received cluster-head
positions, the average hop distance and their own distance away from the cluster-heads. When the
nodes receive the position of at least three cluster-heads, it can compute its own position. If only
three cluster-head position are available, trilateration will be used. Here the distances away from
the cluster-heads are estimated based on the hop-counter and the received average hop distance. If
more than three cluster-head positions are available, we will use least squares trilateration, where
the result which yield the lowest error will be used.
∑(eij)∑(hij)
(3.5)
37
3.1 Analysis
In this section, we will compare the computation complexity and message complexity between
MDS-MAP(P) and CPL.
3.1.1 Computation Complexity
MDS-MAP(P)
Similar to parts of CPL, MDS-MAP(P) includes two major phases: local map construction and
map merging. For the local map construction phase, each node needs to calculate the local map
involving all the neighboring nodes within two hops. Assume the average number of neighboring
nodes isk, then we haven
k=
R2
π(2r)2⇒ k =
4nπr2
R2
, whereR andr denote the network edge length and transmission range, respectively, wheren is
the total number of nodes in the network. Therefore, the computation complexity of local map
construction phase isO(nk3) = O(n(4nπr2
R2 )3) = O(n4). Similarly, the computation complexity
of map merging phase isO(nk3) = O(n4). Therefore, MDS-MAP(P)’s computation complexity is
O(n4).
CPL
For simplicity we divide CPL into three phases: clustering, cluster-head localization and cluster-
member localization. Both the first and last phase haveO(n) complexity since each node has a
constant computation complexity (we assume that in the cluster-member localization phase the
number of reference nodes each cluster-member would use is bounded by a constant).
There are two sub-phases included in the cluster-head localization phase: local map construc-
tion and map merging, which is similar to that in MDS-MAP. However, CPL only requires cluster-
head to perform this phase. For the local map construction, each cluster-head needs to collect its
two-step neighboring cluster-heads’ information (i.e., the neighboring cluster-heads’ neighboring
38
cluster-heads, which are at most 6 hops away) for MDS computation. Assume the average cluster
size ism, we haven/m
kcluster−head
=R2
π(6r)2⇒ kcluster−head =
36nπr2
mR2,
wherekcluster−head denotes the number of neighboring cluster-heads within two “steps”. Therefore,
the computation complexity of local map construction isO( nm
k3cluster−head) = O( n
m(36nπr2
mR2 )3) =
O(( nm
)4). Similarly, the computation complexity of map merging phase isO( nm
k3cluster−head) =
O(( nm
)4). Therefore, CPL’s computation complexity isO(( nm
)4). For simplicity we assume thatm
is n1/2. We will later show through simulations that the average cluster-sizem will stay very close
to the upper boundθ, so if θ = 10 and the network size is100, m will be very close ton1/2. So if
m is n1/2, CPL’s computation complexity becomesO(n2).
3.1.2 Message Complexity
MDS-MAP(P)
The local map construction phase of MDS-MAP(P) requires each node to broadcast messages to all
its neighbors within two hops, which leads to the message complexity ofO(kn) = O(n2). Its map
merging phase createsO(n) messages, since each node needs to merge with one of its neighbors,
during which a node exchange constant messages with its immediate neighbors. Therefore, MDS-
MAP(P)’s message complexity isO(n2).
CPL
The clustering phase hasO(n) message complexity since each node needs to broadcast constant
messages to immediate neighbors. In the cluster-head localization phase, CPL hasO( nm
)2 mes-
sages for local map construction andO( nm
) messages for map merging, so cluster-head local-
ization hasO( nm
)2 message complexity. In the cluster-member localization phase, each cluster-
head floods its position messages within certain number of hops, so the message complexity is
O( nm
n) = O(n2
m). Therefore, CPL’s message complexity isO(n2
m). If we setm to ben1/2, CPL’s
39
message complexity becomesO(n3/2).
40
CHAPTER FOUR
PERFORMANCE EVALUATION
The proposed technique was implemented in ns-2 [1] as arouting-agent. Although CPL does
not offer any form of routing, a routing-agent was used so that no additional information will
be exchanged and the communication and computation at each node will be kept to a minimum.
The implementation of CPL utilizes the MAC and physical layers from 802.11, as there are no
specific WSN implementations available. All simulation results are based on averages from2 to
10 different runs. While most tests have been run at lest5 times some of the large tests with cluster
sizes of one were too time-consuming to run this many times.
Simulations were performed on several different topologies. We used two main categories;
square and C-shaped. In addition to these two cases we augment the square-shaped topologies
with obstacles and varying node-densities to further test our algorithm. We fixed the number of
nodes and their radio range and varied the enclosing network area, by doing this we can effectively
control the average number of nodes within aπr2 area, wherer is the radio range of the nodes. We
will refer to this number as thenode density. In Table 4.1 we summarize the simulation parameters.
We utilize no special metric for distances, but will simply count the number of units. For example,
the radio range is set to 15 units and the enclosing area can be 100x 100 units. The topologies
used for the simulations are randomly generated for every experiment, so no two tests will be
performed on the same topology. Our main metric for the simulations isaccuracy. Similar to what
is done in [41] the localization accuracy is best represented by the difference between the estimated
positions and the corresponding actual positions compared to the radio ranger. Equations 4.1
and 4.2 shows how the accuracya is calculated. In 4.2n is the number of nodes, andd′i is the
Euclidean desistance between the actual position and the estimated position ofi. The actual and
estimates positions are compared by finding the best linear transformation of the estimates onto
the actual coordinates, this is done the same way as is done in the merging phase of CPL. We then
41
calculate the average Euclidean distanceτ between corresponding points in the actual map and the
transformed estimated map. In Figure 4.1 we show an example localization results. In both Figure
4.1 (a) and(b) a circle denotes the estimated position and the lines indicates the deviation from
the correct position. Figure 4.1(a) shows the deviation for the chosen cluster-heads, while Figure
4.1(b) shows for the result all nodes.
ns-2 version 2.29area 100x100, 90x90, 80x80. . . 50x50nodes 100, 110transmission range 15cluster size (θ) 1 to 10,∞
Table 4.1: Simulation parameters
dij =
√∑(xia − xja)2 (4.1)
a =
∑d′i
n
r∗ 100 (4.2)
(a) (b)
Figure 4.1: Localization example
In our data collection step of the cluster-head localization, all hop values used are perturbed
by adding noiseσ to each entry in theinput-databefore the non-metric MDS is employed. This
42
is done to eliminate ties and help the non-metric MDS converge, because the non-metric MDS
technique is dependent on the differences in the distance estimations. The values used forσ are
random values from 0 to10−5 and will be insignificant compared to the entries in the input-data.
4.1 Square-shapes network
For theses topologies we use random node placement, which will yield a fairly uniform topology.
A typical example of the topologies used here can be seen in Figure 4.2. As a key step to provide
a good abstraction of the network, the cluster technique we deployed directly affects the quality
of localization as well as the computation overhead. To evaluate the clustering quality, we present
the cluster size and cluster degree as a function of the network density in Figure 4.3. By cluster
degree we mean the average number of different cluster-neighbors. It can be observed from Figure
4.3(a) that the average group size stays close to the current upper-bound, which reflects clusters’
high quality as observed in Figure 3.4 (page 34) in the previous chapter. From Figure 4.3(b), we
can observe the density drops significantly, as expected, for the larger clusters, and the density
will also grow slower than when using single-node clusters. This means that additionally the
computationally intensive non-metric MDS algorithm will only be run on a subset of the nodes, the
size of the input data to the MDS algorithm will be significantly smaller when using larger sized
clusters. This is a good indication of the scalability of CPL, and that the complexity reduction
increases as a network or the density increases.
Figure 4.4 shows the resulting accuracy for square-shaped topologies. Since we build upon
the cluster-heads localization to obtain the cluster-members position, we present cluster-heads’ ac-
curacy results in Figure 4.4(a) and all nodes’, both cluster-heads and cluster-members, accuracy
results in Figure 4.4(b). We also include two reference lines; one which is based on the perfor-
mance of MDS-MAP(P) [41] at the same densities as our experiments and another which is based
on the performance of DV-hop [34], in both accuracy figures. It should however be noted that
both MDS-MAP(P) and DV-hop rely on several anchor nodes to achieve the presented results,
43
(a)
Figure 4.2: Topology example
and MDS-MAP also utilizes an extra refinement step to improve the accuracy of the local maps.
The figures show that changing the cluster size does not lead to significant performance degrada-
tion: compared to the single-node clusters the performance-reduction when increasing the cluster
size bound to 10 is at most around20 percent. MDS-MAP(P) achieves better accuracy than CPL,
which, however, still obtains an acceptable localization accuracy considering that it does not uti-
lize any anchor nodes or extra refinement of the estimates as MDS-MAP(P) does. Furthermore,
it can be observed that the difference between the accuracy of all nodes and the accuracy of only
the cluster-heads is very small, which reflects the effectiveness of the clustering techniques we
applied. It should also be noted that the performance of CPL when using single-node clusters
(θ = 1) is also worse than MDS-MAP(P), but follows the same trend. This would indicate that
using an algorithms closer to MDS-MAP(P) in the cluster-head might improve the performance of
CPL. We also include results from running CPL with unbounded clusters. The accuracy for these
are very close to the accuracy of the size bounded cases. This low deviation is mostly because of
the fairly uniform distribution of nodes and that the node-densities naturally limit the size of the
44
0
5
10
15
20
5 10 15 20 25 30 35
Clu
ster
Siz
e
Node Density
θ=4θ=6
θ=10θ=∞
(a)
0
5
10
15
20
25
30
5 10 15 20 25 30 35
Clu
ster
Deg
ree
Node Density
θ=4θ=6
θ=10θ=1θ=∞
(b)
Figure 4.3: Cluster quality
0
5
10
15
20
25
5 10 15 20 25 30 35
Acc
urac
y
Node Density
θ=4θ=10
θ=1θ=∞
MDS-MAP(P)DV-hop
(a)
0
5
10
15
20
25
5 10 15 20 25 30 35
Acc
urac
y
Node Density
θ=4θ=10
θ=1θ=∞
MDS-MAP(P)DV-hop
(b)
Figure 4.4: Accuracy for square-shaped topologies
clusters. In more irregular networks one might expect the unbounded case to deviate more from
the size-bounded cases.
4.2 C-shaped network
Similar to what is done in both [41] and [34], we also evaluate the performance of the algorithm
in C-shaped network. The C-shape network provides a good test for how the techniques handles
an irregular topology, where the hop distances between nodes can be very different from the actual
Euclidean distances. This generally is a problem for any technique using any form of distance
45
estimates based on connectivity, whether its range-free or not. In irregular topologies distance
estimates might be severely overestimated compared to the actual Euclidean distance and it is
important to overcome this problem. In Figure 4.5 we show an example of a C-shaped topology.
To create this topology we start with the same topologies as in the previous section and remove a
small set of the nodes to create a network with the shape of a “C” and roughly90% of the nodes.
By doing this we maintain roughly the same node-densities as in the previous section, and as can be
seen from Figure 4.6, both the cluster-sizes and cluster-degree are very similar to the square-shaped
networks.
Figure 4.5: Example of a C-shaped topology
In Figure 4.7 (a) and (b), we show the resulting accuracy for both the cluster-heads and all nodes
respectively. As in the case of random topologies, the resulting accuracy when using large cluster
sizes is not significantly reduced. Furthermore, compared to MDS-MAP(P), CPL’s accuracy is
only slightly reduced, while providing the same lowered computation as in the random networks.
CPL can also provide a better accuracy than DV-hop for these irregular topologies, this is the result
of that, the overestimation of distance affects the trilateration used in DV-hop more than our local
MDS based localization.
46
0
5
10
15
5 10 15 20 25 30
Clu
ster
Siz
e
Node Density
θ=4θ=6
θ=10θ=∞
(a)
0
5
10
15
5 10 15 20 25 30
Clu
ster
Deg
ree
Node Density
θ=4θ=6
θ=10θ=∞
(b)
Figure 4.6: Cluster quality
0
5
10
15
20
25
30
5 10 15 20 25 30 35
Acc
urac
y
Node Density
θ=4θ=10
θ=1θ=∞
MDS-MAP(P)DV-Hop
(a)
0
5
10
15
20
25
30
5 10 15 20 25 30 35
Acc
urac
y
Node Density
θ=4θ=10
θ=1θ=∞
MDS-MAP(P)DV-hop
(b)
Figure 4.7: Accuracy for C-shaped topologies
4.3 Irregular node densities
It is highly likely that in any realistic scenario node densities will vary in different parts on a
network. To test this we created an irregular topology. We use a random topology enclosed in
an area of sizes x s with n nodes, we then includen10
new nodes in ans5
x s5
area. An example
topology is shown in Figure 4.8, where the area indicate in the lower left corner has a significantly
higher degree than the rest of the network. We can see from Figure 4.9 that CPL is not greatly
affected by the irregularity in node density. The accuracy of cluster-head localization (Figure
47
4.9(a)) is not affected, while the accuracy for all node is reduce by at most20% from the case with
regular densities, this verifies that because in CPL the estimated position of a node does not have
much effect on estimates of nodes far away, and the overall accuracy will not be adversely affected
by changing densities. One might however expect that the achieved accuracy in different part of
a network might differ, as the high-density area is likely to achieve a better accuracy. The use of
clusters does not have any significant impact on the performance in these topologies, it will simply
obtain an abstraction of the network, retaining the same changes in density in the clusters as in the
underlying network, although the changes is somewhat smoothed over.
Figure 4.8: Illustration of a topology with irregular node-density
4.4 Obstacles
Obstacles is also an important issue to handle, as this, just as irregular node-densities and irregular
topologies, will be present in realistic scenarios. However, obstacles usually create great difficulty
for any localization technique as one can no longer make the assumption that if two nodes are
not adjacent or connected they will not be positioned close to each-other. To test the performance
48
5
10
15
20
25
5 10 15 20 25 30 35
Acc
urac
y
Node Density
θ=4θ=10θ=∞
Uniform desity, θ=10
(a)
5
10
15
20
25
5 10 15 20 25 30 35
Acc
urac
y
Node Density
θ=4θ=10θ=∞
Uniform desity, θ=10
(b)
Figure 4.9: Accuracy for topologies with irregular node densities
of CPL under these difficult conditions we preformed simulations on square-shaped topologies
with two different types of obstacles; four line-shaped obstacles or one H-shaped obstacle. The
topologies used are the same as in Section 4.1. In the case with four line-shaped obstacles, shown
in Figure 4.10, we use four statically placed lines, that each will hinder two nodes from connecting
if the line between the two intersect with the obstacle. The obstacles has an average length of1r,
wherer is the radio range. In Figure 4.11(a) we show the resulting clusters, with cluster-heads as
circles with a line to each of its members. In Figure 4.11(b) we show the inter-cluster connectivity,
from this figure one can see that the clusters are not significantly affected by the obstacles. The
H-shaped obstacle, shown in Figure 4.12, is placed in roughly the center of the random topology,
and provides for a worse node-connectivity than the previous case. As can be seen in Figure 4.12
the nodes that are most affected by the H-shaped obstacle is the nodes close to the horizontal
line of the obstacle. These nodes will derive severely overestimated inter-node distances between
them-selves and nodes on the other side of the horizontal line. By using the H-shade obstacle
we are effectively creating an artificial perimeter and dividing the network into two parts with a
fairly low connectivity between them. In Figure 4.13 (a) and (b) we show the resulting clusters and
cluster-connectivity, here we can clearly see that this obstacle will lead to distance overestimation.
49
(a) (b)
Figure 4.10: Connectivity in topology with four obstacles
(a) (b)
Figure 4.11: Clustering in topology with four obstacles
As with the irregular density case, obstacles does not significantly affect CPL. The use of clus-
ters produces an algorithm that is less sensitive to obstacles and by covering a larger geographical
area the clusters can in effect reach around many of the obstacles. Although the inter-cluster dis-
tances at times might be overestimated the overall accuracy is not significantly affected. As can
be seen from Figures 4.14 and 4.15 the resulting accuracy for both cluster-heads and the the entire
network shows very little change from the networks without obstacles.
50
(a) (b)
Figure 4.12: Connectivity in topology with H-shaped obstacle
(a) (b)
Figure 4.13: Clustering in topology with H-shaped obstacle
4.5 Complexity
As we mentioned before, CPL is deliberately designed to improve scalability and reduce computa-
tion overhead. We show the time and message overhead of CPL, which are two important metrics
that reflect its scalability, in Figure 4.16.
In the case of single-node clusters, effectively no clustering is used and every node will be a
cluster-head, which is similar to what is done in MDS-MAP(P). Clearly, CPL significantly reduces
the running time if clustering is applied, as it spends less than 6% of the time if the cluster size
51
5
10
15
20
25
5 10 15 20 25 30 35
Acc
urac
y
Node Density
θ=4θ=10θ=∞
No obstacles, θ=10
(a)
5
10
15
20
25
5 10 15 20 25 30 35
Acc
urac
y
Node Density
θ=4θ=10θ=∞
No obstacles, θ=10
(b)
Figure 4.14: Accuracy for topologies with four obstacles
5
10
15
20
25
5 10 15 20 25 30 35
Acc
urac
y
Node Density
θ=4θ=10θ=∞
No obstacles, θ=10
(a)
5
10
15
20
25
5 10 15 20 25 30 35
Acc
urac
y
Node Density
θ=4θ=10θ=∞
No obstacles, θ=10
(b)
Figure 4.15: Accuracy for topologies with one H-shaped obstacle
is more than5. This reduction is because the computation overhead of MDS techniques greatly
depend on the network density, which is relieved by the clustering. The clustering also reduces
the number of nodes that need to perform MDS computation. As shown in Figure 4.16(b), we
see a significant decrease in the messages needed to perform the localization as the cluster size is
increased from1. This is mainly because the messages exchanged when merging local maps are
greatly reduced, and the complexity of each merge is also lowered as each local map is smaller as
the cluster sizes increases.
52
10-1
100
101
102
103
8 10 12 14 16 18
Run
ning
Tim
e
Node Density
θ=5θ=10
θ=1
(a)
0
5000
10000
15000
20000
25000
30000
35000
5 10 15 20 25 30
Mes
sage
s
Node Density
θ=5θ=10
θ=1
(b)
Figure 4.16: Computation and communication overhead
4.6 Scalability
The scalability of any localization technique is interesting not only because of the large number
of nodes and area covered, but because we rely on a very crude estimate of inter nodes distances,
the inaccuracies in these will affects the performance increasingly as the scale is increased. The
scalability of CPL is illustrated by Figure 4.17. We maintain the same densities and increase
coverage area and the number of nodes. The densities are set to around11, and the number of
nodes is increased from100 to 1000. We have included a curve for DV-hop as a reference. For all
DV-hop simulations we used4 anchor nodes. For both CPL and DV-hop we see degradation in the
accuracy as the node numbers and network sizes increases, but as opposed to DV-hop, CPL is not
dependent on the anchor-nodes.
53
0
20
40
60
80
100
120
140
160
180
60 80 100 120 140 160 180 200 220 240
Acc
urac
y
Network area
θ=11θ=∞
DV-hop
Figure 4.17: Accuracy in large networks
54
CHAPTER FIVE
CONCLUSIONS
As many wireless sensor network applications require nodes to be aware of their locations, we
proposed CPL, a distributed sensor node localization technique. In CPL, we exploited clustering
to obtain an abstraction of the network, differentiating between the localization of cluster-heads and
of cluster-members. This greatly reduces the computation and communication overhead, as well as,
providing decent localization accuracy. CPL will also perform well in irregular-shaped networks
(e.g. C-shaped networks), networks with irregular node-densities and the use of clustering makes
the algorithm more resilient to irregularities like obstacles. We have shown that the technique of
localizing only a small subset of the nodes and using this to quickly and efficiently localize the
remaining nodes is feasible and produces good results. As previously stated our goal was to create
a scalable and more feasible localization algorithm, and with CPL we achieved this scalability, even
when using a high cost technique such as non-metric MDS. CPL can fairly easily be changed to
facilitate other localization techniques in the cluster-head localization. If one wanted a more light-
weight technique one might use something like DV-hop instead of MDS, this modularity is one
of the main strengths of CPL. The algorithm can provide a parameterized abstraction of networks
for many kinds of localization techniques. Feasible localization is achieved by not introducing any
new constrains on a network, CPL does not rely on any kind of specialized, extra capable nodes,
or predetermined information about distributions, size, etc. In addition to the localization CPL will
provide a simple structure to a network. The work put into establishing the clusters can be very
helpful in other scenarios besides in our localization process. Both security and traffic management
applications can potentially utilize the already available structure further.
CPL does however produce a slight reduction in the accuracy compared to that of MDS-
MAP(P) in most cases, and the actual difference between MDS-MAP(P) and CPL using the very
same localization should be investigated, as well as how well CPL would perform when trading
55
non-metric MDS for a more light-weight localization technique. In all our simulations we assumed
a highly simplified transmission model with no irregularities, this model will most likely not be
representative of any realistic scenario. Including some form of irregular transmission ranges will
probably create more complex topologies and this might reduce the accuracy of CPL.
56
BIBLIOGRAPHY
[1] ns-2, discrete event simulator.http://www.isi.edu/nsnam/ns/ .
[2] A. Ahmed, Hongchi Shi, and Yi Shang. Sharp: A new approach to relative localization in
wireless sensor network. In25th IEEE International Conference on Distributed Computing
Systems Workshop, ICDCSW, pages 892–898, 2005.
[3] M. Anlauff and A. Sunbul. Deploying localization services in wireless sensor networks. In
24th International Conference on Distributed Computing Systems Workshops, pages 782–
787, 2004.
[4] P. Bergamo, S. Asgari, Hanbiao Wang, D. Maniezzo, L. Yip, R.E. Hudson, Kung Yao, and
D. Estrin. Collaborative sensor networking towards real-time acoustical beamforming in free-
space and limited reverberance.IEEE Transactions on Mobile Computing, 3(3):211–224,
2004.
[5] P. Bergamo and G. Mazzini. Localization in sensor networks with fading and mobility. InThe
13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications,
volume 2, pages 750–754, 2002.
[6] P. Biswas and Yinyu Ye. Semidefinite programming for ad hoc wireless sensor network lo-
calization. InThird International Symposium on Information Processing in Sensor Networks,
pages 46–54, 2004.
[7] R. Biswas and S. Thrun. A passive approach to sensor network localization. InIEEE/RSJ
International Conference on Intelligent Robots and Systems, volume 2, pages 1544–1549,
2004.
[8] A. Brooks, S. Williams, and A. Makarenko. automatic online localization of nodes in an
57
active sensor network. InIEEE International Conference on Robotics and Automation, vol-
ume 5, pages 4821–4826, 2004.
[9] N. Bulusu, J. Heidemann, and D. Estrin. Adaptive beacon placement. In21st International
Conference on Distributed Computing Systems, pages 480–498, 2001.
[10] Haowen Chan, Mark Luk, and Adrian Perrig. Using clustering information for sensor net-
works localization. InInternational Conference on Distributed Computing in Sensor Systems,
DCOSS, 2005.
[11] C. Chang and A. Sahai. Estimation bounds for localization. InFirst Annual IEEE Commu-
nications Society Conference on Sensor and Ad Hoc Communications and Networks, pages
415–424, 2004.
[12] J. Chen, R. Hudson, and K. Yao. Maximum-likelihood source localization and unknown
sensor location estimation for wideband signals in the near-field.IEEE Transactions on
Signal Processing, 50(8):1843–1854, 2002.
[13] K.K. Chintalapudi, A. Dhariwal, R. Govindan, and G. Sukhatme. Ad-hoc localization using
ranging and sectoring. InTwenty-third AnnualJoint Conference of the IEEE Computer and
Communications Societies INFOCOM, volume 4, pages 2662–2672, 2005.
[14] A.P.M Coxon. The Users Guide to Multi Dimensional Scaling. Heinemann Educational
Books, 1982.
[15] B. Deb, S. Bhatnagar, and B. Nath. Multi-resolution state retrieval in sensor networks.First
IEEE Workshop on Sensor Network Protocols And Applications, 2003.
[16] L. Doherty, K.S.J. Pister, and L. El Ghaoui. Convex position estimation in wireless sensor
networks. InIEEE INFOCOM, volume 3, pages 1655–1663, 2001.
58
[17] J. Elson, L. Girod, and D. Estrin. Fine-grained network time syncronization using referece
broadcasts. InOSDI, 2000.
[18] T. Eren, O.K. Goldenberg, W. Whiteley, Y.R. Yang, A.S. Morse, B.D.O. Anderson, and P.N.
Belhumeur. Rigidity, computation, and randomization in network localization. InINFOCOM
Twenty-third AnnualJoint Conference of the IEEE Computer and Communications Societies,
volume 4, pages 2673–2684, 2004.
[19] A. Galstyan, B. Krishnamachari, K. Lerman, and S. Pattem. Distributed online localization
in wireless sensor networks using a moving target. InThird International Symposium on
Information Processing in Sensor Networks, pages 61–70, 2004.
[20] L. Girod, V. Bychkovskiy, J. Elson, and D. Estrin. Locating tiny sensors in time and space a
case study. InIEEE International Conference on Computer Design: VLSI in Computers and
Processors, pages 214–219, 2002.
[21] J. Hightower and G. Borriello. Location systems for ubiquitous computing.IEEE Computer,
34(8):57–66, 2001.
[22] A. Howard, M.J. Mataric, and G. Sukhatme. Relaxation on a mesh a formalism for general-
ized localization. InIEEE/RSJ International Conference on Intelligent Robots and Systems,
2001, volume 2, pages 1055–1060, 2001.
[23] A.T. Ihler, III Fisher, J.W., R.L. Moses, and A.S. Willsky. Nonparametric belief propagation
for self localization of sensor networks.IEEE Journal on Selected Areas in Communications,
23(4):809–819, 2005.
[24] X. Ji and H. Zha. Robust sensor localization algorithm in wireless ad hoc sensor networks.
In The 12th International Conference on Computer Communications and Networks, pages
527–532, 2003.
59
[25] P. Julian, A.G. Andreou, L. Riddle, S. Shamma, D.H. Goldberg, and G. Cauwenberghs. A
comparative study of sound localization algorithms for energy aware sensor network nodes.
IEEE Transactions on Circuits and Systems I: Regular Papers, 51(4):640–648, 2004.
[26] T.C. Karalar, S. Yamashita, M. Sheets, and J. Rabaey. A low power localization architecture
and system for wireless sensor networks. InIEEE Workshop on Signal Processing Systems,
pages 89–94, 2004.
[27] B. Karp and H.T. Kung. Gpsr: Greedy perimeter stateless routing for wireless networks. In
AMC MOBICOM, 2000.
[28] X. Li, H. Shi, and Y. Shang. A partial-range-aware localization algorithm for ad hoc wire-
less sensor networks. In29th Annual IEEE International Conference on Local Computer
Networks, pages 77–83, 2004.
[29] Xiaoli Li, Hongchi Shi, and Yi Shang. A map-growing localization algorithm for ad-hoc
wireless sensor networks. InTenth International Conference on Parallel and Distributed
Systems, pages 395–402, 2004.
[30] Chong Liu, Kui Wu, and Tian He. Sensor localization with ring overlapping based on com-
parison of received signal strength indicator. InIEEE International Conference on Mobile
Ad-hoc and Sensor Systems, pages 516–518, 2004.
[31] R. McNally, K.J. Wong, and D.K. Arvind. A distributed algorithm for logical location estima-
tion in speckled computing. InIEEE Wireless Communications and Networking Conference,
volume 3, pages 1854–1859, 2005.
[32] M. Minami, S. Saruwatari, T. Kashima, T. Morito, H. Morikawa, and T. Aoyama.
Implementation-based approach for designing practical sensor network systems. In11th
Asia-Pacific Software Engineering Conference, pages 703–710, 2004.
60
[33] F. Mondinelli and Z.M. Kovacs-Vajna. Self localizing sensor network architectures.IEEE
Transactions on Instrumentation and Measurement, 53(2):277–283, 2004.
[34] D. Niculescu and B. Nath. Ad hoc positioning system (APS). In GLOBECOM’01. IEEE
Global Telecommunications Conference, volume 5, pages 2926–2931, 2001.
[35] T. Parker and K. Langendoen. Refined statistic-based localisation for ad-hoc sensor networks.
In Global Telecommunications Conference Workshops, pages 90–95, 2004.
[36] P.N. Pathirana, N. Bulusu, A.V. Savkin, and S. Jha. Node localization using mobile robots
in delay tolerant sensor networks.IEEE Transactions on Mobile Computing, 4(3):285–296,
2005.
[37] R.K. Patro. Localization in wireless sensor network with mobile beacons. In23rd IEEE
Convention of Electrical and Electronics Engineers in Israel, pages 22–24, 2004.
[38] D. Perkins and R. Tumati. Reducing localization errors in sensor ad hoc networks. InIEEE
International Conference on Performance, Computing, and Communications, pages 723–
729, 2004.
[39] C. Poggi and G. Mazzini. Collinearity for sensor network localization. InIEEE 58th Vehicu-
lar Technology Conference, volume 5, pages 3040–3044, 2003.
[40] S. Retnasamy, B. Karp, L. Yin, F. Yu, D. Estrin, R. Govindan, and S. Shenker. Ght: A
geographic hash table for data-centric storage. InAMC WSNA, 2002.
[41] Y. Sang and W Ruml. Improved MDS-based localization. InINFOCOM, volume 4, pages
2640–2651, March 2004.
[42] Yi Sang, Jing Meng, and Hongchi Shi. A new algortihm for relative localization in wireless
sensor networks. InIPDPS, April 2004.
61
[43] Yi Sang, Wheeler Ruml, Ying Zang, and Markus P. J. Fromhertz. Localization from mere
connectivity. InACM MobiHoc, pages 202–212, Annapolis, MD, June 2003.
[44] C. Savarese, J.M. Rabaey, and J. Beutel. Locationing in distributed ad-hoc wireless sen-
sor networks. InICASSP, IEEE International Conference on Acoustics, Speech and Signal
Processing, volume 4, pages 2037–2040, 2001.
[45] C. Savarese, J.M. Rabaey, and K. Langendoen. Robust positioning algorithms for distributed
ad-hoc wireless sensor networks. In2002 USENIX Annual Technical Conference, pages 317–
327, June 2002.
[46] K. Seada, A. Helmy, and R. Govindan. On the effect of localization errors on geographical
face routing in sensor networks. InThird International Symposium on Information Processing
in Sensor Networks, pages 71–80, 2004.
[47] Yi Shang, Hongchi Shi, and A.A. Ahmed. Performance study of localization methods for
ad hoc sensor networks. InIEEE International Conference on Mobile Ad-hoc and Sensor
Systems, pages 184–193, 2004.
[48] X. Sheng and Y.H. Hu. Energy based source localization. InIPSN, pages 285–300, 2003.
[49] Xiaohong Sheng and Yu Hen Hu. Sequential acoustic energy based source localization in
a distributed sensor network. InIEEE International Conference on Acoustics, Speech, and
Signal Processing, volume 3, pages 972–975, 2004.
[50] M.L. Sichitiu and V. Ramadurai. Localization of wireless sensor networks with a mobile
beacon. InIEEE International Conference on Mobile Ad-hoc and Sensor Systems, pages
174–183, 2004.
[51] R. Stoleru, Tian He, and J.A. Stankovic. Walking gps a practical solution for localization in
62
manually deployed wireless sensor networks. In29th Annual IEEE International Conference
on Local Computer Networks, pages 480–489, 2004.
[52] G. Sun and W. Guo. Comparison of distributed localization algorithms for sensor networks
with a mobile beacon. InIEEE International Conference on Networking, Sensing and Con-
trol, volume 1, pages 536–540, 2004.
[53] Guolin Sun, Jie Chen, Wei Guo, and K.J.R. Liu. Signal processing techniques in network-
aided positioning a survey of state-of-the-art positioning designs.IEEE Signal Processing
Magazine, 22(4):73–100, 2005.
[54] Hanbiao Wang, Len Yip, Kung Yao, and D. Estrin. Lower bounds of localization uncertainty
in sensor networks. InIEEE International Conference on Acoustics, Speech, and Signal
Processing, volume 3, pages 917–920, 2004.
[55] J. Yick, A. Bharathidasan, G. Pasternack, B. Mukherjee, and D. Ghosal. Optimizing place-
ment of beacons and data loggers in a sensor network - a case study. InIEEE Wireless
Communications and Networking Conference, volume 4, pages 2486–2491, 2004.
[56] O. Younis and S. Fahmy. Distributed clustering in ad-hoc sensor networks a hybrid, energy-
efficient approach. InTwenty-third Annual Joint Conference of the IEEE Computer and
Communications Societies INFOCOM, volume 1, pages 629–640, 2004.
[57] Y. Zou and K. Chakrabarty. Energy-aware target localization in wireless sensor networks. In
First IEEE International Conference on Pervasive Computing and Communications, pages
60–67, 2003.
63