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INSTITUTO TECNOLÓGICO Y DE ESTUDIOS SUPERIORES DE MONTERREY

PRESENTE.-Por medio de la presente hago constar que soy autor y titular de la obra denominada ".

", en los sucesivo LA OBRA, en virtud de lo

cual autorizo a el Instituto Tecnológico y de Estudios Superiores de Monterrey (EL INSTITUTO) para que efectúe la divulgación, publicación, comunicación pública, distribución, distribución pública y reproducción, así como la digitalización de la misma, con fines académicos o propios al objeto de EL INSTITUTO, dentro del círculo de la comunidad del Tecnológico de Monterrey.

El Instituto se compromete a respetar en todo momento mi autoría y a otorgarme el crédito correspondiente en todas las actividades mencionadas anteriormente de la obra.

De la misma manera, manifiesto que el contenido académico, literario, la edición y en general cualquier parte de LA OBRA son de mi entera responsabilidad, por lo que deslindo a EL INSTITUTO por cualquier violación a los derechos de autor y/o propiedad intelectual y/o cualquier responsabilidad relacionada con la OBRA que cometa el suscrito frente a terceros.

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Position Estimation Using Dead Reckoning and Other Localized

Algorithms in Wireless Networks-Edición Única

Title Position Estimation Using Dead Reckoning and Other

Localized Algorithms in Wireless Networks-Edición Única

Authors Victor Hugo Pérez González

Affiliation ITESM-Campus Monterrey

Issue Date 2008-07-01

Item type Tesis

Rights Open Access

Downloaded 19-Jan-2017 04:26:13

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CAMPUS MONTERREY

DIVISI ´ON DE TECNOLOG´IAS DE INFORMACI ´ON Y ELECTR ´ONICA

PROGRAMA DE GRADUADOS EN INGENIER´IA

Position Estimation Using Dead Reckoning and

Other Localized Algorithms in Wireless Networks

by

Victor Hugo P´

erez Gonz´

alez

Thesis

Presented as a partial fulfillment of the requirements for the degree of

Master of Science in Electronic Engineering

Major in Telecommunications

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CAMPUS MONTERREY

DIVISI ´ON DE TECNOLOG´IAS DE INFORMACI ´ON Y ELECTR ´ONICA

PROGRAMA DE GRADUADOS EN INGENIER´IA

The members of the thesis committee hereby approve the thesis of

Victor Hugo P´erez Gonz´alez as a partial fulfillment of the requirements for the degree

of Master of Science in

Electronic Engineering

Major in Telecommunications

Thesis Committee:

Frantz Bouchereau Lara, Ph.D.

Thesis Advisor

David Mu˜noz Rodr´ıguez, Ph.D.

Synodal

C´esar Vargas Rosales, Ph.D.

Synodal

Joaqu´ın Acevedo Mascar´ua, Ph.D.

Director of the Graduate Program

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To my parents, Martha I. Gonz´alez de Le´on and Oswaldo P´erez C´ardenas, thank you for your love, support and comprehension. To my uncle Luis Rodr´ıguez and my aunt Roc´ıo Gonz´alez, thank you for believing in me, without your help and support none of this would have been possible. To my grandma and my uncle Alejandro Gonz´alez for understanding that it wasn’t possible for me to spend a lot of time with you during these last two years.

To my advisor, Frantz Bouchereau Lara, PhD., for your teachings, friendship, guidance, and help. To my synodals, C´esar Vargas, PhD., and David Mu˜noz, PhD., for the revision and comments of this research work.

Special thanks to Luis Ram´on Peraza Rodriguez, M.S., Jos´e Manuel Rodriguez Delgado, B.S., Ana Laura Calder´on Cardoza, and Diego Vidal Escamilla Coll´ı for all your friendship, help, and support. You are a very important part of this achievement.

To my friends Cecy, Jannett, Roc´ıo, Saracho, Sergio, Carlos, Miguel, Juan, Omar, and Ever, for all your help and for everything we went through during this wonderful time.

To all my students, thanks for working hard on the WiFi Position Estimation project.

Victor Hugo P´

erez Gonz´

alez

INSTITUTO TECNOL ´OGICO Y DE ESTUDIOS SUPERIORES DE MONTERREY

July 2008

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Other Localized Algorithms in Wireless Networks

Victor Hugo P´erez Gonz´alez, M.S.

INSTITUTO TECNOL ´OGICO Y DE ESTUDIOS SUPERIORES DE MONTERREY, 2008

Thesis advisor: Frantz Bouchereau Lara, Ph.D.

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Acknowledgments V

Abstract VI

List of Figures X

List of Tables XXII

Chapter 1. Introduction 1

1.1. Problem Description . . . 2

1.2. Objective . . . 3

1.3. Justification . . . 3

1.4. Contribution . . . 4

1.5. Thesis Organization . . . 4

Chapter 2. Theoretical Background 5 2.1. Free Space Propagation Model . . . 5

2.2. Log Normal Propagation Model . . . 7

2.3. Error Sources . . . 9

2.3.1. Additive Noise . . . 9

2.3.2. Small Scale Fading . . . 9

2.3.3. Shadowing . . . 10

2.3.4. NLOS . . . 10

2.4. Ad-Hoc Networks . . . 11

2.5. Wireless Sensor Networks . . . 11

2.6. Positioning in Ad-Hoc Wireless Sensor Networks . . . 12

2.6.1. Single Hop Localization Scheme . . . 13

2.6.2. Multihop Localization Scheme . . . 13

2.6.3. Localization With Beacons . . . 13

2.6.4. Localization With Moving Beacons . . . 14

2.6.5. Beacon-Free Localization . . . 14

2.7. Classification of Position Location Algorithms . . . 15

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2.7.3. Localized Distributed Algorithms . . . 17

2.8. Measurements . . . 17

2.8.1. RSS . . . 19

2.8.2. AOA . . . 19

2.8.3. TOA . . . 20

Chapter 3. Dead Reckoning 21 3.1. Dead Reckoning Evolution and Applications . . . 21

3.2. Simulated Scenario . . . 22

3.3. Dead Reckoning Path . . . 24

3.4. Linearized Least Squares Algorithm . . . 25

3.5. Simulation Results . . . 28

3.5.1. General MSE performance . . . 29

3.5.2. Vulnerability and Robustness of Dead Reckoning to increments on the channel noise . . . 33

3.5.3. Effects of Low Node Densities in the Estimation Accuracy . . . 44

3.5.4. Dead Reckoning Failure Rate . . . 46

Chapter 4. Dead Reckoning Advantages Over Distance Vector Algo-rithms 49 4.1. DV-based algorithms . . . 49

4.2. General MSE performance . . . 50

4.3. Vulnerability of Dead Reckoning and Distance Vector algorithms to in-creases in σRange . . . 58

4.3.1. Dead Reckoning Versus DV-Hop . . . 59

4.3.2. Dead Reckoning Versus DV-Distance . . . 63

4.4. Vulnerability of Dead Reckoning and Distance Vector algorithms to in-creases in σAOA . . . 67

4.4.1. Dead Reckoning Versus DV-Hop . . . 68

4.4.2. Dead Reckoning Versus DV-Distance . . . 72

4.5. Effects of Low Node Densities . . . 76

4.5.1. Failure Rate Comparison . . . 78

4.5.2. Overhead . . . 82

Chapter 5. Conclusions and Future Research 86 5.1. Conclusions . . . 86

5.2. Future Research . . . 86

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A.1. Description of the Main Project Stages . . . 89 A.1.1. AP Hunting . . . 90 A.1.2. Characterization . . . 91 A.2. Estimation of the Communication Channel Parameters n and σ2 . . . 93

A.3. Lognormal Range Estimator . . . 94 A.4. Results . . . 98

Appendix B. Key Concepts and Important Acronyms 103

Vita 110

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3.1. Network with Node Density = 0.1 and 8 APs, APs are located on the edge of the network area . . . 23 3.2. Network with Node Density = 0.1 and 8 APs, APs are randomly located

inside the network area . . . 23 3.3. A single DRP composed by L hops . . . 24 3.4. General tendency on the MSE performance of the Dead Reckoning

al-gorithm. Curves are shown for different values of χ. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node den-sity was fixed to 0.5Nodes/m2, and the measurement noise was defined

as σAOA = 3o and ψ = 1/50. . . 31 3.5. General tendency on the MSE performance of the Dead Reckoning

al-gorithm. Curves are shown for different values of χ. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, and the measurement noise was defined as

σAOA = 3o and ψ = 1/50. . . 31 3.6. General tendency on the MSE performance of the Dead Reckoning

al-gorithm. Curves are shown for different values of χ. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node den-sity was fixed to 0.8Nodes/m2, and the measurement noise was defined

as σAOA = 3o and ψ = 1/50. . . 32 3.7. General tendency on the MSE performance of the Dead Reckoning

al-gorithm. Curves are shown for different values of χ. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.8Nodes/m2, and the measurement noise was defined as

σAOA = 3o and ψ = 1/50. . . 32

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values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2,

the value of χ was set to 4/25, and the angular measurement noise was defined as σAOA = 3o. . . 34 3.9. Vulnerability of the Dead Reckoning algorithm to increasing values of

measurement noise. MSE performance curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value

of χ was set to 4/25, and the angular measurement noise was defined as σAOA = 3o. . . 34 3.10. Vulnerability of the Dead Reckoning algorithm to increasing values of

measurement noise. MSE performance curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2,

the value of χ was set to 6/25, and the angular measurement noise was defined as σAOA = 3o. . . 35 3.11. Vulnerability of the Dead Reckoning algorithm to increasing values of

measurement noise. MSE performance curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value

of χ was set to 6/25, and the angular measurement noise was defined as σAOA = 3o. . . 35 3.12. Vulnerability of the Dead Reckoning algorithm to increasing values of

measurement noise. MSE performance curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2,

the value of χ was set to 8/25, and the angular measurement noise was defined as σAOA = 3o. . . 36

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values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value

of χ was set to 8/25, and the angular measurement noise was defined as σAOA = 3o. . . 36 3.14. Vulnerability of the Dead Reckoning algorithm to increasing values of

measurement noise. MSE performance curves are shown for different values of σAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2,

the value of χ was set to 4/25, and ψ was set to 1/50. . . 37 3.15. Vulnerability of the Dead Reckoning algorithm to increasing values of

measurement noise. MSE performance curves are shown for different values of σAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value

of χwas set to 4/25, andψ was set to 1/50. . . 38 3.16. Vulnerability of the Dead Reckoning algorithm to increasing values of

measurement noise. MSE performance curves are shown for different values of σAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2,

the value of χ was set to 6/25, and ψ was set to 1/50. . . 38 3.17. Vulnerability of the Dead Reckoning algorithm to increasing values of

measurement noise. MSE performance curves are shown for different values of σAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value

of χwas set to 6/25, andψ was set to 1/50. . . 39 3.18. Vulnerability of the Dead Reckoning algorithm to increasing values of

measurement noise. MSE performance curves are shown for different values of σAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2,

the value of χ was set to 8/25, and ψ was set to 1/50. . . 39

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values of σAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value

of χwas set to 8/25, andψ was set to 1/50. . . 40 3.20. Vulnerability of the Dead Reckoning algorithm to increasing values of

ranging measurement noise. MSE performance curves are shown for different values of χ. The setup used to perform this simulation con-sisted of a network with 4 APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, and angular

measurements are assumed to be perfect, σAOA = 0o. . . 41 3.21. Vulnerability of the Dead Reckoning algorithm to increasing values of

ranging measurement noise. MSE performance curves are shown for different values ofχ. The setup used to perform this simulation consisted of a network with 4 APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, and angular measurements

are assumed to be perfect, σAOA = 0o. . . 41 3.22. Vulnerability of the Dead Reckoning algorithm to increasing values of

angular measurement noise. MSE performance curves are shown for different values of χ. The setup used to perform this simulation con-sisted of a network with 4 APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, and ranging

measurements are assumed to be perfect, σRange =0m (ψ=0). . . 43 3.23. Vulnerability of the Dead Reckoning algorithm to increasing values of

angular measurement noise. MSE performance curves are shown for different values ofχ. The setup used to perform this simulation consisted of a network with 4 APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, and ranging measurements

are assumed to be perfect, σRange =0m (ψ=0). . . 43 3.24. Robustness of the Dead Reckoning algorithm to very low network node

densities. MSE performance curves are shown for different values of χ. The setup used to perform this simulation consisted of a network with 4 APs uniformly distributed on the edge of the network area, the node density was variable, and the measurement noise was defined as σAOA = 3o and ψ = 1/50. . . 45

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The setup used to perform this simulation consisted of a network with 4 APs randomly distributed inside of the network area, the node density was variable, and the measurement noise was defined as σAOA = 3o and

ψ = 1/50. . . 45 3.26. Failure rate histograms of the Dead Reckoning algorithm for very low

network node densities. The setup used to perform this simulation con-sisted of a network with 4 APs uniformly distributed on the edge of the network area, the node density was variable, and the measurement noise was defined as σAOA = 3o and ψ = 1/50. . . 47 3.27. Failure rate histograms of the Dead Reckoning algorithm for very low

network node densities. The setup used to perform this simulation con-sisted of a network with 4 APs randomly distributed inside of the net-work area, the node density was variable, and the measurement noise was defined as σAOA = 3o and ψ = 1/50m. . . 47 4.1. General tendency on the MSE performance of the Dead Reckoning and

DV-Hop algorithms. Comparison curves are shown for different values of χ. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, and the

measurement noise was defined as σAOA = 3o and ψ= 1/50. . . 51 4.2. General tendency on the MSE performance of the Dead Reckoning and

DV-Hop algorithms. Comparison curves are shown for different values of χ. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, and the measurement

noise was defined as σAOA = 3o and ψ = 1/50. . . 52 4.3. General tendency on the MSE performance of the Dead Reckoning and

DV-Distance algorithms. Comparison curves are shown for different val-ues of χ. The setup used to perform this simulation consisted of a net-work with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, and the

measurement noise was defined as σAOA = 3o and ψ= 1/50. . . 53

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ues of χ. The setup used to perform this simulation consisted of a net-work with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, and the

mea-surement noise was defined as σAOA = 3o and ψ = 1/50. . . 53 4.5. General tendency on the MSE performance of the Dead Reckoning and

DV-Hop algorithms. Comparison curves are shown for different values of χ. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.8Nodes/m2, and the

measurement noise was defined as σAOA = 3o and ψ= 1/50. . . 55 4.6. General tendency on the MSE performance of the Dead Reckoning and

DV-Hop algorithms. Comparison curves are shown for different values of χ. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.8Nodes/m2, and the measurement

noise was defined as σAOA = 3o and ψ = 1/50. . . 55 4.7. General tendency on the MSE performance of the Dead Reckoning and

DV-Distance algorithms. Comparison curves are shown for different val-ues of χ. The setup used to perform this simulation consisted of a net-work with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.8Nodes/m2, and the

measurement noise was defined as σAOA = 3o and ψ= 1/50. . . 56 4.8. General tendency on the MSE performance of the Dead Reckoning and

DV-Distance algorithms. Comparison curves are shown for different val-ues of χ. The setup used to perform this simulation consisted of a net-work with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.8Nodes/m2, and the

mea-surement noise was defined as σAOA = 3o and ψ = 1/50. . . 57 4.9. General tendency on the MSE performance of the Dead Reckoning and

DV-based algorithms. One curve is displayed for each algorithm. The setup used to perform this simulation consisted of a network with 4 APs randomly distributed inside of the network area, the node density was fixed to 0.6Nodes/m2, and the measurement noise was defined as

σAOA = 3o and ψ = 1/50. . . 58

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are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs uni-formly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 4/25, and the angular

measurement noise was defined as σAOA = 3o. . . 59 4.11. Vulnerability of the Dead Reckoning and DV-Hop algorithms to

increas-ing values of measurement noise. MSE performance comparison curves are shown for different values of ψ. The setup used to perform this sim-ulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 4/25, and the angular

measure-ment noise was defined as σAOA= 3o. . . 60 4.12. Vulnerability of the Dead Reckoning and DV-Hop algorithms to

increas-ing values of measurement noise. MSE performance comparison curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs uni-formly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 6/25, and the angular

measurement noise was defined as σAOA = 3o. . . 61 4.13. Vulnerability of the Dead Reckoning and DV-Hop algorithms to

increas-ing values of measurement noise. MSE performance comparison curves are shown for different values of ψ. The setup used to perform this sim-ulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 6/25, and the angular

measure-ment noise was defined as σAOA= 3o. . . 61 4.14. Vulnerability of the Dead Reckoning and DV-Hop algorithms to

increas-ing values of measurement noise. MSE performance comparison curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs uni-formly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 8/25, and the angular

measurement noise was defined as σAOA = 3o. . . 62

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are shown for different values of ψ. The setup used to perform this sim-ulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 8/25, and the angular

measure-ment noise was defined as σAOA= 3o. . . 62 4.16. Vulnerability of the Dead Reckoning and DV-Distance algorithms to

increasing values of measurement noise. MSE performance comparison curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value ofχwas set to 4/25, and the angular

measurement noise was defined as σAOA = 3o. . . 64 4.17. Vulnerability of the Dead Reckoning and DV-Distance algorithms to

increasing values of measurement noise. MSE performance comparison curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 4/25, and the angular

measurement noise was defined as σAOA = 3o. . . 64 4.18. Vulnerability of the Dead Reckoning and DV-Distance algorithms to

increasing values of measurement noise. MSE performance comparison curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value ofχwas set to 6/25, and the angular

measurement noise was defined as σAOA = 3o. . . 65 4.19. Vulnerability of the Dead Reckoning and DV-Distance algorithms to

increasing values of measurement noise. MSE performance comparison curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 6/25, and the angular

measurement noise was defined as σAOA = 3o. . . 66

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curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value ofχwas set to 8/25, and the angular

measurement noise was defined as σAOA = 3o. . . 66 4.21. Vulnerability of the Dead Reckoning and DV-Distance algorithms to

increasing values of measurement noise. MSE performance comparison curves are shown for different values of ψ. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 8/25, and the angular

measurement noise was defined as σAOA = 3o. . . 67 4.22. Vulnerability of the Dead Reckoning and DV-Hop algorithms to

increas-ing values of measurement noise. MSE performance comparison curves are shown for different values of σAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs uni-formly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 4/25, and ψ was set to

1/50. . . 68 4.23. Vulnerability of the Dead Reckoning and DV-Hop algorithms to

increas-ing values of measurement noise. MSE performance comparison curves are shown for different values of σAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs ran-domly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 4/25, and ψ was set to 1/50. 69

4.24. Vulnerability of the Dead Reckoning and DV-Hop algorithms to increas-ing values of measurement noise. MSE performance comparison curves are shown for different values of σAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs uni-formly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 6/25, and ψ was set to

1/50. . . 70 4.25. Vulnerability of the Dead Reckoning and DV-Hop algorithms to

increas-ing values of measurement noise. MSE performance curves are shown for different values of σAOA. The setup used to perform this simulation con-sisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2,

the value of χ was set to 6/25, and ψ was set to 1/50. . . 70

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parison curves are shown for different values ofσAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value ofχ was set to 8/25, andψ

was set to 1/50. . . 71 4.27. Vulnerability of the Dead Reckoning and DV-Hop algorithms to

increas-ing values of measurement noise. MSE performance comparison curves are shown for different values of σAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs ran-domly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 8/25, and ψ was set to 1/50. 71

4.28. Vulnerability of the Dead Reckoning and DV-Distance algorithms to increasing values of measurement noise. MSE performance comparison curves are shown for different values ofσAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value ofχ was set to 4/25, and ψ was set

to 1/50. . . 72 4.29. Vulnerability of the Dead Reckoning and DV-Distance algorithms to

increasing values of measurement noise. MSE performance comparison curves are shown for different values ofσAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 4/25, and ψ was set to

1/50. . . 73 4.30. Vulnerability of the Dead Reckoning and DV-Distance algorithms to

increasing values of measurement noise. MSE performance comparison curves are shown for different values ofσAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value ofχ was set to 6/25, and ψ was set

to 1/50. . . 74

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curves are shown for different values ofσAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 6/25, and ψ was set to

1/50. . . 74 4.32. Vulnerability of the Dead Reckoning and DV-Distance algorithms to

increasing values of measurement noise. MSE performance comparison curves are shown for different values ofσAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs uniformly distributed on the edge of the network area, the node density was fixed to 0.5Nodes/m2, the value ofχ was set to 8/25, and ψ was set

to 1/50. . . 75 4.33. Vulnerability of the Dead Reckoning and DV-Distance algorithms to

increasing values of measurement noise. MSE performance comparison curves are shown for different values ofσAOA. The setup used to perform this simulation consisted of a network with a variable amount of APs randomly distributed inside of the network area, the node density was fixed to 0.5Nodes/m2, the value of χ was set to 8/25, and ψ was set to

1/50. . . 75 4.34. Robustness of the Dead Reckoning and DV-Hop algorithms to very low

network node densities. MSE performance comparison curves are shown for different values of χ. The setup used to perform this simulation consisted of a network with 4 APs uniformly distributed on the edge of the network area, the node density was variable, and the measurement noise was defined as σAOA = 3o and ψ = 1/50. . . 76 4.35. Robustness of the Dead Reckoning and DV-Hop algorithms to very low

network node densities. MSE performance comparison curves are shown for different values of χ. The setup used to perform this simulation consisted of a network with 4 APs randomly distributed inside of the network area, the node density was variable, and the measurement noise was defined as σAOA = 3o and ψ = 1/50. . . 77 4.36. Robustness of the Dead Reckoning and DV-Distance algorithms to very

low network node densities. MSE performance comparison curves are shown for different values ofχ. The setup used to perform this simulation consisted of a network with 4 APs uniformly distributed on the edge of the network area, the node density was variable, and the measurement noise was defined as σAOA = 3o and ψ = 1/50. . . 77

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shown for different values ofχ. The setup used to perform this simulation consisted of a network with 4 APs randomly distributed inside of the network area, the node density was variable, and the measurement noise was defined as σAOA = 3o and ψ = 1/50. . . 78 4.38. Failure rate histograms of the Dead Reckoning and DV-based algorithms

for very low network node densities. The setup used to perform this simulation consisted of a network with 4 APs uniformly distributed on the edge of the network area, the node density was variable, and the measurement noise was defined as σAOA = 3o and ψ= 1/50. . . 80 4.39. Failure rate histograms of the Dead Reckoning and DV-based algorithms

for very low network node densities. The setup used to perform this simulation consisted of a network with 4 APs randomly distributed inside of the network area, the node density was variable, and the measurement noise was defined as σAOA = 3o and ψ = 1/50. . . 81 4.40. Overhead histograms of the Dead Reckoning and DV-based algorithms

for a general network scenario. The setup used to perform this simu-lation consisted of a network with 4 APs uniformly distributed on the edge of the network area, the coverage range of the nodes was a vari-able parameter, the node density was fixed to 0.5Nodes/m2, and the

measurement noise was defined as σAOA = 3o and ψ= 1/50. . . 83 4.41. Overhead histograms of the Dead Reckoning and DV-based algorithms

for a general network scenario. The setup used to perform this simulation consisted of a network with 4 APs randomly distributed inside of the network area, the coverage range of the nodes was a variable parameter, the node density was variable, and the measurement noise was defined as σAOA = 3o and ψ = 1/50. . . 84 A.1. Map of ITESM campus Monterrey, red box indicates the area of interest 89 A.2. APviewer screen . . . 90 A.3. Software developed in LabWindows to characterize APs . . . 92 A.4. Characterization arcs for the AP 00:12:7f:3f:ca:a0 . . . 93

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A.1. Main APs physical localization . . . 91 A.2. AP Hunting Results . . . 99 A.3. Characterization of AP 00:12:7f:3f:ca:a0 . . . 100 A.4. Characterization of AP 00:12:7f:3a:74:60 . . . 101 A.5. Characterization of AP 00:12:7f:3a:74:61 . . . 102 A.6. Channel Parameters . . . 102

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Introduction

Classical localization systems assume direct connectivity between a Node of In-terest (NOI) and the available land reference devices. This assumption leads to the concept of single hop routing [1], where any node in the network is located within the coverage radius of any Land Reference (LR), beacon, or anchor node. To localize a NOI in this type of networks, range estimates are obtained throughout channel obser-vations; different measurements can be utilized to accomplish this goal. Received signal strength (RSS), time of arrival (TOA), or time difference of arrival (TDOA) are three measurements widely used to obtain range estimates. Range measurements from mul-tiple anchors may be combined using a multilateration technique to obtain an estimate of the real position of the NOI.

This conventional approach to the localization problem is, in many instances, not applicable in Ad-Hoc Wireless Sensor Networks (WSNs) [2]. In this type of networks, several low power nodes whose transmission range is limited are randomly deployed in a given area, few of them are aware of their physical location coordinates and serve as an-chors, this implies that even the available anchor nodes may have limited transmission range, hence, it turns into an almost impossible event to find a NOI within the coverage area of more than three LRs. For this reason, single hop algorithms will be difficult to apply to solve the localization problem in Ad-Hoc WSNs. Another category of al-gorithms called multihop alal-gorithms [1] have been developed to overcome this difficulty.

An important number of multihop algorithms exist [3], [4], in this research work, iterative algorithms are our focus of interest. These algorithms rely on the distribution of information among certain sections of the network to obtain resultant range esti-mates of the complete path from one LR to the NOI. This information may consist of range estimates between intermediate links, or angle of arrival (AOA) measurements

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between the nodes involved in a specific route. There are other categories like the centralized algorithms [5]. In this type of algorithms a central node with high compu-tational capabilities, gathers information about the network and computes the position of the nodes with unknown coordinates. Although the problem this work aims to solve will be described in the following section, the reader should be aware that iterative algorithms represent the best solution to the localization problem for the particular case we envision in this work. The reasons that allow us to say this will be explained in the following chapters of this thesis.

The main purpose of this thesis work is to prove that by taking more sophisticated measurements in the intermediate links of the routes to the NOI, the resultant range estimation will be more accurate, to do this we will analyze and compare two multihop solutions for Ad-Hoc WSNs via simulations, these solutions are the Ad-Hoc Positioning System (APS) [6], and Dead Reckoning [4], [7]. APS is a well known and widely used positioning system that has two variants, DV-Hop and DV-Distance (where DV stands for Distance Vector), they have two operation stages, a calibration stage where the av-erage hop size is obtained in the case of DV-Hop, or where a distance correction factor is calculated in DV-Distance, and an estimation stage where mere connectivity is used to calculate the resultant range estimates using the data obtained in the calibration stage. On the other hand, Dead Reckoning is a well known navigational technique whose operation consists of measuring distance and AOA from the last known position or fix.

1.1.

Problem Description

The problem analyzed in this research work is the position estimation of a node upon request from a network manager, or upon request from the node itself. Several algorithms have been developed to solve the localization problem. Some of them are simpler than others and are usually preferred to estimate the position of the NOI. This work aims to justify the use of algorithms that use more sophisticated measurements to obtain their resultant ranging estimations from the available anchor nodes to the NOI. This justification will be provided by comparing the performance of Dead Reckoning with that of DV-based algorithms. This comparison will show that more sophisticated measurements will result in more accurate resultant ranging estimates.

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estab-lish the advantages and disadvantages offered by each one of them. This will be done by calculating the Mean Squared Error (MSE) of the position estimations obtained by the algorithms, the failure rate under different network scenarios, and the traffic overhead in the network.

1.2.

Objective

Our main purpose is to show the advantages of using Dead Reckoning based lo-cation algorithms and justify the increase in necessary measurement complexity when compared to simpler positioning techniques such as DV-Hop and DV-Distance, to do this, several simulations will be presented where the environmental factors of the net-work are varied to cover several scenarios. Performance will be analyzed with respect to node density, amount of available anchor nodes in the network, node coverage or reachability radius, and measurement noise.

Another objective is to observe if hybrid schemes improve the performance of al-gorithms such as Dead Reckoning by combining more than one type of measurement in the solution of the multilateration problem.

A side objective is to develop a position estimation project at ITESM campus Monterrey based on ranging measurements between WiFi Access Points and wireless PCMCIA cards. This project required to characterize the propagation model of the channel and to define statistical estimators for the path loss exponentn, and the noise standard deviation σ.

1.3.

Justification

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1.4.

Contribution

In this thesis work, an exhaustive statistical comparison between different multi-hop position estimation schemes such as Dead Reckoning and Distance Vector (DV-Hop and DV-Distance) algorithms will be presented. It will be shown that Dead Reckoning based methods improve performance considerably justifying the increase in measure-ment complexity that arises in these techniques.

1.5.

Thesis Organization

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Theoretical Background

This chapter provides background information that will be used in later chapters of this thesis. In this chapter we describe important concepts that relate to the multi-hop localization problem such as: propagation models, types of error sources, wireless sensor networks, different types of measurements used to estimate range and AOA, and the classification of the different position estimation algorithms.

2.1.

Free Space Propagation Model

The free space propagation model [8] is used to predict received signal strength when the transmitter and receiver have a clear, unobstructed line-of-sight (LOS) path between them. Satellite communication systems and microwave LOS radio links typi-cally undergo free space propagation. As with most large-scale radio wave propagation models, the free space model predicts that received power decays as a function of the transmission-reception (T-R) separation distance raised to some power (i.e. a power law function). The free space power received by an antenna which is separated from a radiating transmitter by a distance ofdmeters, is given by the Friis free space equation,

Pr(d) =

PtGtGrλ2

(4π)2d2L (2.1)

wherePtis the transmitted power,Pr(d) is the received power which is a function of the T-R separation; Gt is the transmitter antenna gain, Gr is the receiver antenna gain, L is the system loss factor not related to propagation (L 1), and λ is the wavelength in meters. The gain of an antenna is related to its effective aperture, Ae, by

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G= 4πAe

λ2 (2.2)

The effective aperture Ae is related to the physical size of the antenna, and λ is related to the carrier frequency by

λ = c f =

2πc ωc

(2.3)

where f is the carrier frequency in Hertz, ωc is the carrier frequency in radians per second, and c is the speed of light given in meters/s. The values for Pt and Pr must be expressed in the same units, andGt and Gr are dimensionless quantities. The miscellaneous losses L (L 1) are usually due to transmission line attenuation, filter losses, and antenna losses in the communication system. A value ofL= 1 indicates no loss in the system hardware.

The Friis free space equation of Eq. 2.1 shows that the received power falls off as the square of the T-R separation distance. This implies that the received power decays with distance at a rate of 20 dB/decade.

As explained in [8], the path loss, which represents signal attenuation as a positive quantity measured in dB, is defined as the difference (in dB) between the effective transmitted power and the received power. The path loss for the free space model is given by

P LdB = 10 log10

Pt

Pr

=10 log10GtGrλ

2

(4π)2d2 (2.4)

The Friis free space model is only a valid predictor for Pr for values of d which are in the far-field of the transmitting antenna. The far-field, or Fraunhofer region, of a transmitting antenna is defined as the region beyond the far-field distance df, which is related to the largest linear dimension of the transmitter antenna aperture and the carrier wavelength. The Fraunhofer distance is given by

df = 2D2

λ (2.5)

where D is the largest physical dimension of the antenna. Additionally, to be in the far-field region, df must satisfy

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and

df ≫λ (2.7)

Furthermore, it is clear that Eq. 2.1 does not hold for d = 0. For this reason, large-scale propagation models use a close-in distance, d0, as a known received power

reference point. The received power, Pr(d), at any distance d > d0, may be related to

Pr atd0. The value Pr(d0) may be predicted from Eq. 2.1, or may be measured in the

radio environment by taking the average received power at many points located at a close-in radial distanced0 from the transmitter. The reference distance must be chosen

such that it lies in the far-field region, that is, d0 ≥ df, and d0 is chosen to be smaller

than any practical distance used in the mobile communication system. Thus, using Eq. 2.1, the received power in free space at a distance greater than d0 is given by

Pr(d) =Pr(d0)

d0

d

!2

dd0 ≥df (2.8)

Where Pr(d0) is in units of watts.

Eq. 2.8 may be expressed in units of dBm or dBW by simply taking the logarithm of both sides and multiplying by 10.

Pr(d)dBm= 10 log10

Pr(d0)

0.001W + 20 log10

d0

d d≥d0 ≥df (2.9)

or

Pr(d)dBW = 10 log10Pr(d0) + 20 log10

d0

d d≥d0 ≥df (2.10)

2.2.

Log Normal Propagation Model

Both theoretical and measurement-based propagation models indicate that aver-age received signal power decreases logarithmically with distance, whether in outdoor or indoor radio channels. Such models have been used extensively in the literature [8]. The average large-scale path loss for an arbitrary T-R separation d is expressed as a function of distance by using a path loss exponent, n

P L(d) d d0

!n

(2.11)

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P LdB =P L(d0) + 10nlog10

d d0

!

(2.12)

where n is the path loss exponent which indicates the rate at which the path loss increases with distance, d0 is the close-in reference distance which is determined from

measurements close to the transmitter, anddis the T-R separation distance. The bars in Eq. 2.11 and in Eq. 2.12 denote the ensemble average of all possible path loss values for a given value of d. When plotted on a log-log scale, the modeled path loss is a straight line with a slope equal to 10n dB per decade. The value ofn depends on the specific propagation environment [8].

The model in Eq. 2.12 does not consider the fact that the surrounding environ-mental clutter may be vastly different at two different locations having the same T-R separation. This leads to measured signals which are vastly different than the average value predicted by Eq. 2.12 [9]. Measurements have shown that at any value of d, the path loss P L(d) at a particular location is random and distributed log-normally (normal in dB) about the mean distance-dependent value [10], [11]. That is

P L(d)dB =P L(d) +Xσ =P L(d0) + 10nlog10

d d0

+Xσ (2.13)

and

Pr(d)dBm=Pt(d)dBm−P L(d)dB (2.14) whereXσ is a zero-mean Gaussian distributed random variable (in dB) with stan-dard deviationσ (also in dB).

The log-normal distribution describes the random shadowing effects which occur over a large number of measurement locations which have the same T-R separation, but have different levels of clutter on the propagation path. This phenomenon is referred to as log-normal shadowing.

The close-in reference distance d0, the path loss exponent n, and the standard

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2.3.

Error Sources

To obtain a position estimate of a NOI, what we basically do is measuring phenom-ena and turning this measurement into useful data such as range and AOA estimates. This data will then be used to tell how accurate the positioning system is in the envi-ronment it has been deployed on. Even thought measurement techniques have evolved in recent years, it is still impossible to obtain clear readings of the phenomena that is being measured. Measurements are noisy signals that have negative effects on the accuracy of the positioning system (i.e. noisy ranging measurements will result in an inaccurate position estimate of the NOI). There exist several categories of measure-ment error sources and it is indispensable to understand each one of them in order to mitigate the effects they have on any positioning system. In Chapter 4 it will be seen that some algorithms are more robust than others to measurement noise.

2.3.1.

Additive Noise

Even in the absence of multipath signals, the estimation accuracy of the arrival time and arrival angle is limited by additive noise [12]. Additive noise affects the per-formance of the estimators by altering the statistical behavior of the estimates, it can produce bias by incrementing the variance of the estimators. Some techniques used to mitigate the effects of additive noise are the simple cross-correlator (SCC) and the generalized cross-correlator (GCC). Typically, TOA estimates are those values that maximize the cross-correlation between the received signals and the known transmit-ted signal. This estimator is known as the (SCC). The generalized cross-correlator (GCC) [13] extends the SCC by applying prefilters to amplify spectral components of the signal that have little noise and attenuate components with large noise. As such, the GCC requires knowledge (or estimates) of the signal and noise power spectra [1].

2.3.2.

Small Scale Fading

Small scale fading refers to multiple signals with different amplitudes and phases arriving at the receiver, and these signals adding constructively or destructively as a function of frequency causing frequency-selective fading [1].

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order to estimate the first time of arrival for ranging purposes (i.e. for estimation of distance between a transmitter and a receiver), the receiver must find the first-arriving peak because there is no guarantee that the LOS signal will be the strongest of the arriving signals. This can be done by measuring the time at which the cross-correlation first crosses a threshold. Alternatively, in template-matching, the leading edge of the cross-correlation is matched in a least-squares (LS) sense to the leading edge of the auto-correlation (the auto-correlation of the transmitted signal with itself) to achieve subsampling time resolutions [14]. Generally, errors in estimation are caused by two problems:

1. Early-arriving multipath. Many multipath signals arrive very soon after the LOS signal, and their contributions to the cross-correlation obscure the location of the peak of the LOS signal.

2. Attenuated LOS. The LOS signal can be severely attenuated compared to the late-arriving multipath components, causing it to be “lost in the noise” and missed completely; this leads to large positive errors in the estimation.

2.3.3.

Shadowing

Shadowing is an environment dependent RSS error, is defined as the attenuation of a signal due to obstructions (furniture, walls, trees, buildings, and more) that a signal must pass through or diffract around on the path between the transmitter and receiver. Shadowing effects are modeled as random (as a function of the environment in which the network is deployed). An RSS model considers the randomness across an ensemble of many deployment environments [1].

2.3.4.

NLOS

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TDOA measurements that are in error by the extra path length [16].

2.4.

Ad-Hoc Networks

An Ad-Hoc wireless network is a collection of two or more devices equipped with wireless communications and networking capability. Such devices can communicate with another node that is immediately within their radio range or one that is outside their radio range. For the latter scenario, an intermediate node is used to relay or forward the packet from the source toward the destination [2].

An Ad-Hoc wireless network is self-organizing and adaptive. This means that a formed network can be de-formed on the fly without the need for any system admin-istration. The term “ad-hoc” tends to imply “can take different forms” and “can be mobile, standalone, or networked”. Ad-Hoc nodes or devices should be able to detect the presence of other such devices and to perform the necessary handshaking to allow communications and the sharing of information and services.

Since Ad-Hoc wireless devices can take different forms, the computation, stor-age, and communications capabilities of such devices will vary tremendously. Ad-Hoc devices should not only detect the presence of connectivity with neighboring de-vices/nodes, but also identify the devices type and their corresponding attributes. Since an Ad-Hoc wireless network does not rely on any fixed network entities, the network itself is essentially infrastructureless. There is no need for any fixed radio base stations, no wires or fixed routers. However, due to the presence of mobility, routing information will have to change to reflect changes in link connectivity.

The diversity of Ad-Hoc mobile devices also implies that the battery capacity of such devices will vary. Since Ad-Hoc networks rely on forwarding data packets sent by other nodes, power consumption becomes a critical issue.

2.5.

Wireless Sensor Networks

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different areas. In the health-care industry, sensors allow continuous monitoring of life-critical information. In the food industry, biosensor technology applied to quality control can help prevent rejected products from being shipped out, thus enhancing con-sumer satisfaction levels. In agriculture, sensors can help to determine the quality of soil and moisture level; they can also detect other bio-related compounds. Sensors are also widely used for environmental and weather information gathering. They enable us to make preparations in times of bad weather and natural disaster.

A wireless sensor network is one form of an ad hoc wireless network [17], [18]. Sensors are wirelessly connected and they, at appropriate times, relay information back to some selected nodes. These selected nodes then perform some computation based on the collected data (a process commonly known as data fusion) to derive an ultimate statistic (that reflects an assessment of the environment and tactical conditions) to allow critical decisions to be made [2].

For excellent tutorial papers on the state of the art of position estimation in WSNs refer to [19] and [20].

2.6.

Positioning in Ad-Hoc Wireless Sensor

Net-works

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2.6.1.

Single Hop Localization Scheme

This localization scheme assumes that direct connectivity between a NOI and sev-eral anchors can be established, it is primarily used by technologies such as GPS where the transmitter node does not have to establish intermediate links to reach its desti-nation. Localization in Sensor Networks cannot rely on single hop solutions because the nodes are not capable of high power transmission and usually can only reach their closer neighbors.

2.6.2.

Multihop Localization Scheme

This is the most appropriate scheme for localization in sensor networks. Low transmission power nodes establish intermediate links along the route from a transmit-ting node to a NOI and estimate parameters such as RSS, TOA or AOA to calculate resultant range and angular estimates, their disadvantage is that most of them carry errors caused by channel noise throughout the routes, and the total effect of the errors is a cumulative function of the amount of intermediate links of the route.

Several multihop algorithms have been developed, among them we can find Dead Reckoning, DV-Hop, and DV-Distance algorithms. Assuming that a routing algorithm exists that establishes the shortest path between a given anchor node and the NOI, multihop routes are formed by concatenating multiple nodes whose coordinates are also unknown. When the NOI is reached, it may have enough information to compute a resultant range or angular estimate. Each one of these algorithms has its own metric, for example, DV-Hop counts the number of hops needed to reach the NOI and then multiply this number by the estimated average hop size (in Chapter 4, DV-Hop and DV-Distance algorithms will be explained in detail).

2.6.3.

Localization With Beacons

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an unknown has estimated its position, it may act as a beacon and other unknowns can use it in their position estimations. The major challenge in localization with beacons is to make localization algorithms as robust as possible using as few beacons as possible. The resulting design should then consume little energy and few radio resources [21].

2.6.4.

Localization With Moving Beacons

Using moving beacons in a system design can significantly reduce power consump-tion and cost. In this type of system, nodes determine their own locaconsump-tions by estimating their distance from moving beacons (also referred to as mobile observers) in a coor-dinated fashion by applying a transform to the range estimations to determine each node’s position within a global coordinate system. The impact of predictable observer mobility upon power consumption in a sensor network is discussed in [24]. A local-ization system design for processing information using a single mobile beacon aware of its position is proposed in [25]. Sensor nodes receiving beacon packets infer their distance from a mobile beacon and use these measurements as constraints to construct and maintain position estimates. However, optimizing mobility is not feasible for full coverage in some areas. The relationship between mobility, navigation, and localiza-tion in the context of wireless sensor networks with mobile beacons or targets has been studied in [26]. Also, once localized, network nodes can localize and track a mobile object and guide its navigation [21].

2.6.5.

Beacon-Free Localization

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[27], [21].

2.7.

Classification of Position Location Algorithms

When a large number of beacons is distributed on the network, it is most likely that almost every node will be in range of multiple beacons and will be able to per-form multilateration in order to get its position estimates, just as in the case of GPS. However, in reality this is not a probable scenario, a large number of landmarks will increase installation expenses, and because of this, landmarks will be sparse, and sensor nodes, being low-power devices, will generally not be in range of any or some anchor nodes.

Cooperative localization or multihop routing algorithms can be classified as cen-tralized, non-localized distributed, or localized distributed algorithms [7], [28]. This category division has direct impact on the applicability of the algorithm and on the efficiency of the positioning system. Centralized algorithms collect measurements of the entire network at a central node that optimizes for the position estimation of the NOI, non-localized distributed algorithms require no specialized central node because nodes share information with their neighbors in an iterative fashion, this algorithms rely on the distribution of anchor nodes among the network until the NOI is surrounded by them. Finally, localized algorithms, besides being distributed, do not need to create anchor nodes among the network, the only requirement is that a NOI can be reached via multihop routes starting at the LRs. This implies that only nodes on delimited areas of the network will participate in the localization of the NOI.

2.7.1.

Centralized Algorithms

Centralized solutions besides gathering measurements of the entire network in a single main powerful central node that must deal with large and complex data struc-tures, may face the problem of communication bottleneck and higher energy drain at and near the central node caused by the high traffic associated with large networks.

Some centralized methods are mentioned next:

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If a Maximum Likelihood Estimator (MLE) is going to be used to obtain posi-tion estimates, convex optimizaposi-tion methods [5] are a viable soluposi-tion to avoid the problem of finding a local maxima instead of a global maxima in our maximiza-tion search. Besides modeling the localizamaximiza-tion problem as a convex optimizamaximiza-tion problem provides optimal solutions, it has the advantages of simplicity in the modeling of sensor nodes and the availability of computational methods for this kind of problems.

MDS-MAP

Multi-Dimensional Scaling (MDS) [29] algorithms are eigen-decomposition based algorithms that solve a LS problem to obtain position estimates. MDS-MAP can provide absolute positioning (its coordinate system is based on GPS coordinates provided by LRs) or relative positioning (Network coherent system whose coordi-nates are not aligned to popular coordinate systems) depending on the availability of anchors. It’s a method that operates in two or three stages depending again on the availability of anchors, in the first stage a distance matrix is initialized through the obtention of pairwise range measurements, in the second stage MDS is applied to the distance matrix and Singular Value Decomposition (SVD) is used to generate a map based on the two largest eigenvalues and eigenvectors, finally, the third stage is optional, if there are LRs in the network, the map can be converted to an absolute coordinates map.

2.7.2.

Non-Localized Distributed Algorithms

These algorithms enjoy the advantage of load balancing because they don’t de-pend on a single central node that represents a single failure point, if this node fails, the entire chain breaks down and no localization can be performed. As they iteratively share information among themselves, nodes may be capable of computing data and handle the needed calculations.

A non-localized distributed method is briefly explained below:

Ad-Hoc Localization System (AhLOS)

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available on the network. In atomic localization each node with unknown coor-dinates is in range of at least three landmarks and therefore is able to compute its own position estimate, in iterative localization some nodes are not in range of the necessary amount of LRs to perform multilateration but nodes surround-ing them may be able to get position estimates, so the amount of landmarks on the network is iteratively increasing until every node has estimated its coordi-nates, finally, cooperative localization is used when there are still some nodes with unknown coordinates after using iterative localization, this scheme divides the network in groups and the groups obtain the estimations in a collaborative fashion by solving a set of non-linear equations.

2.7.3.

Localized Distributed Algorithms

Localized methods base their estimations on multihop connectivity between at least three anchor nodes and the NOI. They are not landmarks dependent algorithms because they don’t need to estimate the coordinates of intermediate nodes or the NOI to be in the range of three or more anchors to obtain its position estimate. It has the advantage of reducing traffic overhead, computational complexity, and power require-ments if shortest path multihop routing is used [31].

Some localized distributed methods will be mentioned next:

Ad-Hoc Positioning System (APS)

APS is a well known localized iterative position estimation scheme based on mere connectivity. Performance curves of APS algorithm will be provided in Chapter 4.

Dead Reckoning (DR)

DR is a navigational technique that estimates both range and AOA at each hop. Being the main topic of this work, an exhaustive explanation of the algorithm will be provided in Chapter 3.

2.8.

Measurements

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(TSOA), Direction Of Arrival (DOA), and AOA [32]. In this section we will describe the three more common measurements, RSS, TOA, and AOA; and consider the ways in which they are affected by environment-dependent errors that may be statistically characterized in order to improve the accuracy of our positioning system.

Two important assumptions about the statistical behavior of the measurement errors are made; these assumptions are listed below.

1. Measurements in the network are independent [33]. This means that knowledge about an error that has occurred in one link, provides no knowledge about the occurrence of errors in other links.

2. The measurement errors are from the same family of distributions (Gaussian, Exponential, etc). This is a simplifying assumption, because we can easily char-acterize the errors calculating the distribution parameters, such as the mean and variance, from our set of measurements.

If none of these assumptions are considered, then it will be necessary to character-ize the behavior of the measurements in order to obtain their most important statistics, (i.e. the ranging error variance). The procedure that may be followed to characterize any given measurement is explained next.

1. Deployκ identical Ad-Hoc WSNs, everyone of them must have the same amount of nodes identically positioned based on a fixed geometry and must be deployed in the same type of environment, but not in the same place. As an example consider testing an Ad-Hoc WSN in κ different classrooms.

2. In each network, depending on the positioning system used, measurements must be realized with the method associated with the corresponding classification of the system.

3. The last point should be repeated over a short period of time in order to get data to compute the time average of the measurements.

4. Obtain the joint conditional distribution of the time-averaged measurements.

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2.8.1.

RSS

RSS is defined as the voltage measured by a receiver’s received signal strength indicator (RSSI) circuit. Often, RSS is equivalently reported as measured power, i.e., the squared magnitude of the signal strength. We can consider the RSS of acoustic, RF, or other signals. Wireless sensors communicate with neighboring sensors, so the RSS of RF signals can be measured by each receiver during normal data communication without presenting additional bandwidth or energy requirements. RSS measurements are relatively inexpensive and simple to implement in hardware. They are an important and popular topic of localization research. Yet, RSS measurements are notoriously unpredictable [1].

2.8.2.

AOA

By providing information about the direction to neighboring sensors rather than the distance to neighboring sensors. AOA measurements provide localization informa-tion complementary to the TOA and RSS measurements [1].

There are two common ways that sensors measure AOA. The most common method is to use a sensor array and employ so-called array signal processing tech-niques at the sensor nodes. In this case, each sensor node is comprised of two or more individual sensors (microphones for acoustic signals or antennas for RF signals) whose locations with respect to the node center are known. The AOA is estimated from the differences in arrival times for a transmitted signal at each of the sensor array elements. See [34], [35], [36] for more detailed information on AOA estimation.

A second approach to AOA estimation uses the RSS ratio between two (or more) directional antennas located on the sensor. Two directional antennas pointed in differ-ent directions, such that their main beams overlap, can be used to estimate the AOA from the ratio of their individual RSS values.

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2.8.3.

TOA

TOA is the measured time at which a signal (RF, acoustic, or other) first arrives at a receiver. The measured TOA is the time of transmission plus a propagation-induced time delay. This time delay, Ti,j, between transmission at sensor i and reception at sensor j, is equal to the transmitter-receiver separation distance, di,j, divided by the propagation velocity, νp. This speed for RF is approximately 106 times as fast as the speed of sound; as a rule of thumb, for acoustic propagation, 1ms translates to 1ft (0.3m), while for RF, 1ns translates to 1ft [1].

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Dead Reckoning

In this chapter the Dead Reckoning algorithm will be explained, we will briefly talk about its history and principally describe its application in the position estima-tion field, some graphs will also be presented here in order to show the behavior of this algorithm, the results shown were obtained through computer simulations where several environmental parameters were taken into account in order for the results to represent, as accurately as possible, the performance this algorithm can achieve in real applications.

3.1.

Dead Reckoning Evolution and Applications

The history of this algorithm goes back in time to the thirteenth century, when the first meaningful but yet tenuous advancement on the state of the art of ocean nav-igation occurred, the magnetic compass evolved from being just a magnetized needle floating on a straw to the 32 point compass that was used during the Columbian period, Dead Reckoning [39], [40], [4], was then designed as a navigational technique based on the concept of computing the direction and distance of travel from a known starting position.

Dead Reckoning has been implemented to solve several different problems in di-verse areas of engineering, for example: unicast routing problems in Ad-Hoc networks, and tracking motion of vehicles, robots, and pedestrians.

Although Dead Reckoning was designed to track the actual position of a single mobile based on speed, acceleration and direction of traveling measurements, it can be

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adapted to fit our requirements in Ad-Hoc WSNs. We can compare both scenarios, in navigation, the mobile follows a route to its destination, and several intermediate points on this route serve to find the location of the mobile itself on a specific given time. On the other hand, when we work on the position estimation of a NOI in multihop wireless networks, a route must be followed in order to reach that NOI, of course, the anchor node which is our starting point will not travel the entire route to the NOI, instead, several intermediate nodes will serve as communication links in order for the anchor to be able to establish a wireless connection with the NOI.

It can now be seen that both scenarios are quite similar, thus, it will now be ex-plained how Dead Reckoning is implemented in our case. In Ad-Hoc WSNs, received power measurements are used to obtain range estimates, in Appendix A, a lognormal range estimator will be presented and statistically analyzed. For now, it will suffice to take into account that because the communication channel is considered to be log-normal [8], the range estimates will be affected by noise that may be modeled as a Gaussian random variable with zero mean and variance σ2

Range. To obtain AOA mea-surements, antenna arrays are used, literature shows that the angle estimation error is also modeled as a zero mean Gaussian random variable with varianceσ2

AOA.

3.2.

Simulated Scenario

MATLAB was used to obtain every result shown in this work, a very important part of the experimentation stage is the simulation of Ad-Hoc WSNs, so, a description of the procedure followed in the simulations will be provided next.

Figure

Figure 3.1: Network with Node Density = 0.1 and 8 APs, APs are located on the edge of the network area
Figure 3.3: A single DRP composed by L hops
Figure 3.5: General tendency on the MSE performance of the Dead Reckoning algo- algo-rithm
Figure 3.9: Vulnerability of the Dead Reckoning algorithm to increasing values of measurement noise
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