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