au anthea-ws-201011-ma sc-thesis

RSS-based WLAN Indoor Positioning and Tracking SystemUsing Compressive Sensing and Its Implementation on

Mobile Devices

by

Anthea Wain Sy Au

A thesis submitted in conformity with the requirementsfor the degree of Master of Applied Science

Graduate Department of Electrical and Computer EngineeringUniversity of Toronto

Copyright c⃝ 2010 by Anthea Wain Sy Au

Abstract

RSS-based WLAN Indoor Positioning and Tracking System Using Compressive Sensing

and Its Implementation on Mobile Devices

Anthea Wain Sy Au

Master of Applied Science

Graduate Department of Electrical and Computer Engineering

University of Toronto

2010

As the demand of indoor Location-Based Services (LBSs) increases, there is a grow-

ing interest in developing an accurate indoor positioning and tracking system on mobile

devices. The core location determination problem can be reformulated as a sparse na-

tured problem and thus can be solved by applying the Compressive Sensing (CS) theory.

This thesis proposes a compact received signal strength (RSS) based real-time indoor

positioning and tracking systems using CS theory that can be implemented on personal

digital assistants (PDAs) and smartphones, which are both limited in processing power

and memory compared to laptops. The proposed tracking system, together with a simple

navigation module is implemented on Windows Mobile-operated smart devices and their

performance in different experimental sites are evaluated. Experimental results show

that the proposed system is a lightweight real-time algorithm that performs better than

other traditional fingerprinting methods in terms of accuracy under constraints of limited

processing and memory resources.

ii

Acknowledgements

I would like to express my sincere gratitude to my supervisor, Professor Shahrokh Valaee,

whose knowledge, guidance and support have make this work possible. I would also like

to thank Professor Moshe Eizenman, who gives valuable opinions to improve this work.

I owe my special thanks to Chen Feng, whom I have been working with regarding

to this project. In addition, I would like to thank my colleagues at the Wireless and

Internet Research Laboratory (WirLab).

I am grateful for the Natural Sciences and Engineering Research Council of Canada

(NSERC) for its generous financial support.

Finally, I would give my regard to my parents and my sister for their strong moral

supports and encouragement.

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Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 RSS-based WLAN Positioning Systems . . . . . . . . . . . . . . . . . . . 3

1.2.1 Location-Sensing Techniques . . . . . . . . . . . . . . . . . . . . . 3

1.2.2 Existing Positioning Systems . . . . . . . . . . . . . . . . . . . . . 4

1.3 Problem Statement and Objectives . . . . . . . . . . . . . . . . . . . . . 4

1.4 Technical Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.6 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Background and Related Works 12

2.1 Indoor RSS-based WLAN Positioning Techniques . . . . . . . . . . . . . 12

2.1.1 Signal Propagation Modeling . . . . . . . . . . . . . . . . . . . . 13

2.1.2 Location Fingerprinting . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Fingerprinting-Based Positioning Methods . . . . . . . . . . . . . . . . . 16

2.2.1 K-Nearest Neighbour Method (KNN) . . . . . . . . . . . . . . . . 16

2.2.2 Probabilistic Approach . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.3 Region of Interest and Access Points Selections . . . . . . . . . . 19

2.3 Indoor Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.1 Kalman filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

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2.3.2 Particle filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.3 Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.4 Pedestrian Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5 Affinity Propagation Algorithm For Clustering . . . . . . . . . . . . . . . 24

2.6 Compressive Sensing Theory . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3 Compressive Sensing Based Positioning System 28

3.1 Indoor Positioning System Overview . . . . . . . . . . . . . . . . . . . . 28

3.2 Offline Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.1 Fingerprint Collections . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.2 Clusters Generation by Affinity Propagation . . . . . . . . . . . . 31

3.2.3 Interaction between the database server and the mobile device dur-

ing offline phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3 Online Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3.1 Coarse Localization Stage: Cluster Matching . . . . . . . . . . . . 35

3.3.2 Fine Localization Stage: Compressive Sensing Recovery . . . . . . 38

3.3.3 Interaction between the database server and the mobile device dur-

ing online phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4 Indoor Tracking System 46

4.1 General Bayesian Tracking Model . . . . . . . . . . . . . . . . . . . . . . 47

4.2 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.3 Overview of Proposed Indoor Tracking System . . . . . . . . . . . . . . . 49

4.3.1 Modified Coarse Localization Stage . . . . . . . . . . . . . . . . . 50

4.3.2 Map-Adaptive Kalman Filter . . . . . . . . . . . . . . . . . . . . 55

4.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

v

5 Simple Navigation System 59

5.1 Overview of Navigation System . . . . . . . . . . . . . . . . . . . . . . . 59

5.2 Map Database Generation at Initial Setup . . . . . . . . . . . . . . . . . 60

5.2.1 Layout Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.2.2 Map Features Definition . . . . . . . . . . . . . . . . . . . . . . . 61

5.3 Path Routing Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.3.1 Path Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.4 Tracking Update Analysis Module . . . . . . . . . . . . . . . . . . . . . . 64

5.4.1 Analysis Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.4.2 Voice Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6 Software Implementation on Mobile Devices 69

6.1 Software Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.2 Devices in Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.3 Software Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.3.1 Software’s Functionalities . . . . . . . . . . . . . . . . . . . . . . 72

6.3.2 Resources Folder . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.3.3 Libraries’ Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

7 Experimental Results 77

7.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

7.1.1 Experimental Sites . . . . . . . . . . . . . . . . . . . . . . . . . . 77

7.1.2 Performance Benchmarks . . . . . . . . . . . . . . . . . . . . . . . 81

7.1.3 Figure of Merit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.2 Positioning Results on Bahen Fourth Floor . . . . . . . . . . . . . . . . . 82

7.2.1 RSS Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

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7.2.2 Offline Phase: Clustering Results by Affinity Propagation . . . . . 85

7.2.3 Online Phase: Coarse Localization Analysis . . . . . . . . . . . . 87

7.2.4 Online Phase: Fine Localization Analysis . . . . . . . . . . . . . . 90

7.2.5 Performance Comparison . . . . . . . . . . . . . . . . . . . . . . . 92

7.3 Tracking Results on CNIB Second Floor . . . . . . . . . . . . . . . . . . 95

7.3.1 RSS Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

7.3.2 CS-based Positioning Results . . . . . . . . . . . . . . . . . . . . 96

7.3.3 Modified Coarse Localization Analysis . . . . . . . . . . . . . . . 99

7.3.4 Map Adaptive Kalman Filter Analysis . . . . . . . . . . . . . . . 100

7.3.5 Performance Comparison . . . . . . . . . . . . . . . . . . . . . . . 102

7.3.6 Navigation and Real Time Implementations . . . . . . . . . . . . 104

7.3.7 Subject Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

8 Conclusion 109

8.1 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Bibliography 113

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List of Tables

1.1 Existing RSS-based WLAN Position Systems [1] . . . . . . . . . . . . . . 5

1.2 Comparison of a PDA and a laptop . . . . . . . . . . . . . . . . . . . . . 8

6.1 Devices Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

7.1 Comparison of experimental sites . . . . . . . . . . . . . . . . . . . . . . 78

7.2 Traces Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7.3 Actual parameters γ(o) used for experiments on Bahen fourth floor. . . . 87

7.4 A set of optimal parameters for the CS-based position system applied on

Bahen fourth floor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

7.5 Position error statistics for different methods on Bahen fourth floor. (For

validation set) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

7.6 Position error statistics for different methods on Bahen fourth floor. (For

stationary user testing set) . . . . . . . . . . . . . . . . . . . . . . . . . . 94

7.7 A set of optimal parameters for the CS-based position system applied on

CNIB second floor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.8 Positioning error statistics for different positioning methods on CNIB sec-

ond floor. (For mobile user testing set) . . . . . . . . . . . . . . . . . . . 100

7.9 A set of optimal parameters for the proposed tracking system applied on

CNIB second floor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

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7.10 Position error statistics for the CS-based positioning system and the two

tracking systems on CNIB second floor. (For mobile user testing set) . . 104

7.11 Summary of the three traces tested by the subjects . . . . . . . . . . . . 107

7.12 Subjects testing results on CNIB second floor . . . . . . . . . . . . . . . 107

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List of Figures

1.1 The problem setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Kernel-based method [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1 Block diagram of the proposed indoor localization system. . . . . . . . . 29

3.2 Interaction between the database server and the mobile device during of-

fline phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Interaction between the database server and the mobile device during on-

line phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1 Block diagram of the proposed indoor tracking system. . . . . . . . . . . 50

4.2 Coarse localization stage for the proposed tracking system. . . . . . . . . 51

4.3 Map-Adoptive Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . 57

5.1 Navigation System Overview . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.2 Dijkstra Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.3 Tracking update analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.4 A point in close range to a line segment . . . . . . . . . . . . . . . . . . . 65

5.5 Determining the direction of turn based on the two line segments ℓi and ℓi+1 67

6.1 The overview of the software design. Arrows shows the dependency of the

libraries and blue colored boxes are the developed modules for the software. 72

6.2 An example screenshot of Detect AP operation. . . . . . . . . . . . . . . 73

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7.1 Example histograms of RSS distributions of the same access point over

50 time samples for different devices pointing North at the same reference

point on Bahen fourth floor. . . . . . . . . . . . . . . . . . . . . . . . . . 84

7.2 An example of RSS measurements over time and their averages with re-

spect to the number of time samples of the same access point for different

devices at the same reference point on Bahen fourth floor. . . . . . . . . 84

7.3 An example of averaged RSS of the same access point in spatial domain

for different orientations and different devices on Bahen fourth floor. . . . 85

7.4 Number of clusters generated by the affinity propagation algorithm de-

pending on the value of parameter γ(o) for four orientations on Bahen

fourth floor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

7.5 The clustering results on the four fingerprint databases collected by PDA1

on Bahen fourth floor. Each circle is a RP collected in the database and

each color represents one cluster. . . . . . . . . . . . . . . . . . . . . . . 88

7.6 The ARMSE versus number of used APs, when different number of gen-

erated clusters are used for the coarse localization on Bahen fourth floor . 89

7.7 The cumulative error distributions using different number of clusters for

the coarse localization on Bahen fourth floor. (8 APs are used) . . . . . . 89

7.8 The cumulative error distributions using different cluster matching schemes

on Bahen fourth floor. (8 APs are used) . . . . . . . . . . . . . . . . . . 90

7.9 The ARMSE versus number of used APs, using different AP schemes for

fine localization on Bahen fourth floor. . . . . . . . . . . . . . . . . . . . 92

7.10 Effect of the threshold λ1 on ARMSE on Bahen fourth floor. (8 APs are

used) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

7.11 The cumulative error distributions using different positioning systems on

Bahen fourth floor. (8 APs are used) . . . . . . . . . . . . . . . . . . . . 94

xi

7.12 Comparison of mean computation time using different positioning systems

in Bahen fourth floor. (8 APs are used) . . . . . . . . . . . . . . . . . . . 95

7.13 Example histograms of RSS distributions of the same access point over 50

time samples (40 time samples for Smartphone) for different devices at

the same reference point in CNIB second floor. . . . . . . . . . . . . . . . 97

7.14 An example of RSS distributions across time and their averages with re-

spect to the number of time samples of the same access point for different

devices at the same reference point in CNIB second floor. . . . . . . . . . 97

7.15 An example of RSS distributions of the same access point in spatial domain

for different orientations and different devices in CNIB second floor. (only

a part of the fingerprints are shown) . . . . . . . . . . . . . . . . . . . . 98

7.16 The clustering results on the four fingerprint databases collected by PDA2

on CNIB second floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7.17 The cumulative error distributions for different positioning systems on

CNIB second floor. (10 APs are used) . . . . . . . . . . . . . . . . . . . . 99

7.18 Effect of the walking distance β on ARMSE in CNIB second floor. (10

APs are used) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

7.19 The cumulative error distributions using different Kalman filter parame-

ters in CNIB second floor. (10 APs are used) . . . . . . . . . . . . . . . . 101

7.20 The cumulative error distributions for different Kalman filter update schemes

in CNIB second floor. (10 APs are used) . . . . . . . . . . . . . . . . . . 102

7.21 The cumulative error distributions using the CS-based positioning system

and the three tracking systems in CNIB second floor. (10 APs are used) . 103

7.22 Example trace results. The black line is the actual trace, the green dots

are the CS-based positioning results and the purple line is the results of

the proposed tracking system. . . . . . . . . . . . . . . . . . . . . . . . . 104

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7.23 The definition of the connected graph and the map features on CNIB

second floor. The blue lines and blue circles represent the edges and nodes

of the connected graph. The red squares represents the destinations. The

diamonds represents the map features and the pink circles represents the

locations of the 15 deployed access points . . . . . . . . . . . . . . . . . . 105

7.24 Example screenshot of the software that shows the actual track that the

user is walking. The line shows the routed path generated by the nav-

igation module. The squares denote the user’s locations and the circle

denotes the destination. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

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Chapter 1

Introduction

1.1 Motivation

With the wide deployment of the mobile wireless systems and networks, the location-

based services (LBSs) are made possible on mobile devices, such as laptops, smartphones

and personal digital assistants (PDAs). There are a lot of applications that rely on the

locations of these mobile devices, such as navigation, people and assets tracking, location-

based security and coordination of emergency and maintenance responses to accidents,

interruptions of essential services and disasters, etc [3–5].

In order to deliver reliable LBSs, real-time and accurate user’s locations must be ob-

tained. Hence, there is a growing interest in developing effective positioning and tracking

systems. For the outdoor environment, Global Positioning System (GPS) and cellular

network based systems [3,6,7] are commonly used as the techniques to provide navigation

services. However, these techniques cannot be used directly in indoors, as the signals are

usually too weak to be used for localization purposes. Thus, wireless indoor positioning

has become an increasingly popular research topic in recent years.

There are several methods that are built on top of the GPS-capable phones to provide

indoor localization [8]. One example is the Assisted GPS (A-GPS), which requires a

1

Chapter 1. Introduction 2

connection to a network location server in order to obtain the estimated location with

an average of 5-50m accuracy [8]. Another one is the Calibree proposed in [9], which

utilizes the detected signal strength from GSM cell towers to determine relative positions

of mobile phones and their absolute locations can be determined if some of the phones are

equipped with GPS receivers. In addition, indoor localization can also be implemented

on GSM mobile phones [10] and CDMA mobile phones [11] through the use of wide

signal-strength fingerprints. The median errors of these cellular-based system are around

4-5m. Although these methods are able to provide moderately accurate position estimate

in indoors, their accuracies may not be enough to provide reliable LBSs and also they

are only applicable to mobile phones.

Besides the use of GPS and cellular network, different types of wireless technologies

and sensors are also employed for the indoor positioning. In particular, positioning

systems using ultra-wide band (UWB) signals, infrared, radio frequency (RF), proximity

sensors and ultrasound systems [1, 8, 12] are able to localize users with high accuracies.

However, these systems require the installation of additional infrastructures and sensors,

which lead to high budget and labour cost and preventing them from having large-scale

deployments.

Due to the wide deployment of wireless local area network (WLAN), which is specif-

ically referred to as the IEEE 802.11b/g standard in this thesis, there are many indoor

positioning systems that make use of WLAN for estimating user’s position. Time of ar-

rival (TOA) [13] and time difference of arrival (TDOA) [1,14] are two techniques that can

be used for localization, but they require extra configuration and setup to provide valid

measurements. Thus, received signal strength (RSS) is the feature metric used for the

WLAN positioning systems, as it can be obtained directly from existing WLAN access

points (APs) by any device that is equipped with a WLAN network adapter.

This thesis presents an accurate RSS-based WLAN positioning and tracking system

that can be implemented on mobile devices with limited resources. The affinity propa-


gation algorithm for clustering data points [15] and the compressive sensing theory for

recovery of the sparse and incoherently sampled signals [16] are two concepts applied on

the proposed system.

1.2 RSS-based WLAN Positioning Systems

The WLAN IEEE 802.11b/g is a standard used for providing wireless internet access for

indoor areas. It is operated at 2.4 GHz Industrial, Scientific and Medical (ISM) band

within a range of 50-100 m. As mentioned earlier, the RSS can be easily obtained by

using any WLAN-integrated device, thus it is used by most of the WLAN positioning

systems.

1.2.1 Location-Sensing Techniques

There are three major techniques to obtain the location estimate from the RSS [8, 17].

They are listed as follows:

1. Triangulation: The RSS can be translated into distance from the particular AP

according to a theoretical or empirical signal propagation model. Then, with dis-

tance measurements from at least 3 APs with known positions, lateration can be

performed to estimate the locations. This approach does not give accurate esti-

mate, as the indoor radio propagation channel is highly unpredictable and thus the

use of the propagation model is not reliable.

2. Proximity: This method finds the strongest RSS from a specific AP and determines

the location to be the region covered by this AP. This method only gives a very

rough position estimate but it is easy to be implemented.

3. Scene Analysis: This method first collects RSS readings at known positions, which

are referred to as fingerprints, in the area of interest. Then, it estimates the loca-


tions by comparing the online measurements with the fingerprints through pattern

recognition techniques. This method is used by most WLAN positioning systems,

as it is able to compute accurate location estimates. This is the approach used by

the positioning and tracking system proposed in this thesis.

1.2.2 Existing Positioning Systems

Table 1.1 summarizes some of the existing WLAN positioning systems that can be ac-

cessible to the public. It shows that the use of fingerprinting achieves the best accuracy

in indoor areas. Although the Ekahau [18] attains the best accuracy, it uses the the

probabilistic method to compute the estimated positions and thus requires a more com-

prehensive survey of RSS readings in the region of interest. In addition, its position

calculation is computed at the server as the complexity of the probabilistic method is

too high to be performed on the mobile devices. This raises additional issues when using

this systems. First, the devices must be connected to the same network as the server to

obtain position estimates. Second, positions obtained from the server must be encrypted

before it is transmitted to the mobile devices, in order to protect the privacy of the users.

The aim of this thesis is to design an indoor positioning and tracking system that

can provide accurate position estimate with relatively low computational complexity, so

that it can be computed on mobile devices. This solution may have a database server

to keep track of the fingerprints database collected, but once downloaded to the devices,

they are no longer required to be connected to the server to obtain position estimates.

This system is more flexible and has no privacy concerns to the users.

1.3 Problem Statement and Objectives

A typical WLAN indoor tracking scenario as illustrated in Fig. 1.1 consists of 1) a

mobile device equipped with a WLAN adapter, which is carried by a user and collects


Microsoft Research

RADAR [19,20]

Ekahau [18] Inter Place Lab and

Skyhook’s WPS [21]

Range Building/local area Building/local area Metropolitan area

Position

Calculation

Mobile device Server (Ekahau Posi-

tioning Engine)

Mobile device

Position

Method

Fingerprinting +

KNN + Viterbi-like

algorithm

Fingerprinting +

probabilistic

Map-based pinpoint-

ing (obtain APs data

by war driving) and

triangulation

Accuracy 3 - 5 m 1 - 3 m 20+ m

Table 1.1: Existing RSS-based WLAN Position Systems [1]

RSS from detectable access points for localization; 2) access points (APs), which can be

commonly found in most buildings and their exact positions are not necessarily known

to the localization systems, as they may belong to different network groups and possibly

3) a database server, which stores the fingerprints collected by the mobile device. The

WLAN-enabled device can extract information, such as MAC address, SSID and received

signal strength (RSS) about these APs by receiving messages broadcasted from them.

This thesis focuses on the WLAN localization and tracking problem using RSS as the

measurement metric. The mobile device carried by the user collects the RSS from L

different APs whose unique MAC addresses are used for identification. Then, the system

determines the current position based on this RSS measurements and previously collected

fingerprint database.

The goal of this thesis is to propose a real-timeWLAN positioning and tracking system

that can give accurate position estimate and can be implemented on mobile devices, so

that LBSs can be applied. In the context of this thesis, the mobile devices refer to the

handheld devices, such as personal digital assistants (PDAs) and smartphones, which


��

WLAN Access Point

User equipped with mobile device

Database Server

Reference Point

Figure 1.1: The problem setup

have degraded WLAN antennas, limited power, memory and computation capabilities,

thus a light-weight algorithm is required to allow these devices to have real-time and

accurate performance.

The localization problem is defined as follow. First, the device collects online RSS

readings from available APs periodically at a time interval ∆t, which is limited by the

device’s network card and hardware performances. These online RSS readings can be

denoted as r(t) = [r1(t), r2(t), . . . , rL(t)], t = 0, 1, 2, ..., where rl(t) refer to the RSS

reading collected from AP l at time t. Then, the proposed positioning and tracking

system uses r(t) to compute the position estimate, denoted as p(t) = [x(t), y(t)]T , where

(x(t), y(t)) are the Cartesian coordinates of the estimated position at time t.

1.4 Technical Challenges

The unpredictable variation of RSS in the indoor environment is the major technical

challenge for the RSS-based WLAN positioning systems. There are four main reasons

that lead to the variation of RSS. First, due to the structures of the indoor environment

and the presence of different obstacles, such as walls and doors, etc, the WLAN signals

experience severe multi-path and fading and the RSS varies over time even at the same

location. Secondly, since the WLAN uses the licensed-free frequency band of 2.4GHz,

the interference on this band can be very large. Example sources of interference are the


cordless phones, BlueTooth devices and microwave. Moreover, the presence of human

bodies also affects the RSS by absorbing the signals [22], as human bodies contain large

amount of water, which has the same resonance frequency as the WLAN. Finally, the

orientation of the measuring devices also affects the RSS, as orientation of antenna affects

the antenna gain and the signal is not isotropic in real indoor environment.

All of the above reasons make it infeasible to find a good radio propagation model

to describe the RSS-position relationship. Thus, a fingerprinting method is often used

instead to characterize the RSS-position relationship. This method computes the position

estimate by matching the online RSS readings to the fingerprints collected during training

phase. This pattern matching process is a non-trivial problem as there are derivations

between the online RSS readings to the fingerprint RSS readings due to the time-varying

characteristics of the indoor radio propagation channel. In addition, the movement of

objects, including the movement of the user who carries the mobile device, also affects

the RSS readings. This type of variation of RSS is needed to be addressed by the

fingerprinting-based positioning systems, in order to provide accurate position estimate.

Another challenge relates to the computational capabilities of the mobile devices.

Table 1.2 compares the processor speed and memory equipped by a PDA, which is used

in this thesis to evaluate the performance of the proposed positioning system and a

labtop with average performance. It shows that the PDA has very limited computation

speed and memory when comparing to the labtop. Thus, some of the positioning systems

that can be implemented on the laptop may not be able to be used by the PDA. The

computational complexity and the use of memory must be taken into consideration when

designing the positioning and tracking systems in this thesis.


Devices Processor Speed RAM

HP iPAQ hx4700 624 MHz 64 MB

Dell Inspiron 15 Laptop 2.2 GHz 4 GB

Table 1.2: Comparison of a PDA and a laptop

1.5 Scope

In this thesis, a two stage indoor RSS-based WLAN positioning and tracking system is

proposed and implemented on two mobile devices. Such system is able to address the

challenges mentioned in the previous section. The structure of this thesis is organized as

follows.

First, Chapter 2 reviews the existing RSS-based WLAN positioning techniques. It

also describes two fingerprinting based methods: K-nearest neighbour (KNN) and kernel-

based probabilistic methods which are used in later chapter as performance benchmarks

to the proposed positioning system. In addition, it presents different ways to improve

these positioning methods, such as the determination of region of interest, selection of

APs and the use of filters with inputs of previous estimate and pedestrian motion models.

Some overview of navigation systems design is also included. Finally, the two concepts

used in this thesis for developing the proposed system are presented. It describes how the

affinity propagation algorithm is operated to generate clusters. Then, the compressive

sensing theory is briefly summarized.

The compressive sensing based positioning system is introduced in Chapter 3. This

chapter presents how such system is operated to estimate the user’s position. It first

describes how the clustering process is done on the collected fingerprint database by ap-

plying the affinity propagation algorithm during offline phase. Then, it discusses the two

stage online phase where the actual positioning is operated. First, the coarse localization

stage reduces the area of interest by choosing a few clusters of RPs, whose RSS readings


from the database are best-matched to the online RSS readings. Then, the fine localiza-

tion stage converts the localization problem into sparse signal recovery problem, so that

CS theory can be applied. The interactions between the mobile device and the server are

also explained in the chapter.

In Chapter 4, the CS-based positioning system is extended into a tracking system. The

proposed tracking system has a modified coarse localization stage, which the previous

estimate is used to select the nearby RPs, in addition to the clusters of RPs selected

according to the online RSS readings. The tracking system uses the Kalman filter to

smooth the estimate update. Since the user is more likely to make turns at intersection

regions and hence may violate the liner motion model, the Kalman filter is reset at these

regions to enhance the performance of such tracking system.

Chapter 5 describes a simple navigation system, which consists of a path routing

module to generate the path that leads the user to the destination and a tracking update

analysis module that checks whether the user follows the path and gives appropriate guid-

ance accordingly. It also explains how the map information is extracted to be used by the

navigation system. This navigation system, together with the proposed positioning and

tracking system are implemented as a software that can be installed on any smartphone

or PDA that uses the Windows Mobile platform. The design of the software is presented

in Chapter 6.

Chapter 7 includes all the experimental results conducted in two experimental sites.

The experiments done on the fourth floor of Bahen Centre focused on the evaluation

of the proposed positioning system, whereas the performance of the proposed tracking

system was evaluated using the data collected on the second floor of Canadian Nation

Institute for the Blind (CNIB).

Finally, Chapter 8 presents the concluding remarks and gives directions for the future

work.


1.6 Contributions

This thesis proposes and implements a two stages indoor RSS-based WLAN position-

ing, tracking and navigation system using compressive sensing, clustering and filtering

techniques. Here are the list of contribution, including the chapters presenting them and

publications referring to them:

1. Compressive sensing based positioning system: This positioning system ap-

plies the affinity propagation algorithm on the collected fingerprint database to

generate clusters of RPs, which have similar RSS values and are geographically

close to each other. Then, such system uses the coarse localization stage to choose

the relevant clusters of RPs, based on the online RSS measurement. Finally, the lo-

calization problem is translated into a sparse signal problem, so that the estimated

position can be computed by solving a ℓ1 norm minimization problem according to

the compressive sensing theory. (Chapter 3 and [23,24])

2. Tracking system: The CS-based positioning system can be easily extended to

include the previous position estimate and the map information to improve its

performance. The tracking system has a modified coarse localization stage. In

addition to the clusters of RPs selected based on the online RSS measurements,

RPs which are physically close to the previous position estimate are also chosen

and the common RPs found in both sets are used in the fine localization stage. The

computed estimate is then post-processed by the Kalman filter. This filter is reset

when the estimate is at the intersection regions, as the user may make turns and

violate the liner motion model used by the Kalman filter. (Chapter 4)

3. Navigation system: A simple navigation system, which uses the map database

to generate path to destination using Dijkstra algorithm and gives guidance, is de-

veloped. It also determines whether the user follows the path and gives appropriate

instructions at proper times. (Chapter 5).


4. Software implementation and performance evaluation: A software is de-

veloped to implement the proposed positioning and tracking system, as well as a

simple navigation system. It is written in C# and can be installed on any smart-

phone or PDA that uses Windows Mobile as its operating system. This software

can give real-time position updates and also navigation guidance to the user. The

performance evaluations of the proposed positioning and tracking system are done

for two different experimental sites: Bahen centre and CNIB. Experimental results

show that these systems are able to provide good position estimate of the user

and can be implemented on the PDAs with limited resources, to give real-time

performance. (Chapter 6 and 7 and [23,24]).

This project is a joint work with Chen Feng, a visiting PhD student from the Bei-

jing Jiaotong University, at the Wireless and Internet Research Laboratory (WirLab),

supervised by Professor Shahrokh Valaee. We work closely together to implement the

indoor tracking and navigation system on the handheld devices. Chen focuses more on

the compressive sensing based positioning system, while I focus more on the tracking and

navigation system, as well as the software implementation.

Chapter 2

Background and Related Works

In this section, a brief overview of RSS-based WLAN positioning and tracking techniques

is given. The two fingerprinting-based methods, namely KNN and Kernel-based are

summarized in Sections 2.2.1 and 2.2.2, as they are implemented in Chapter 7 to compare

the performance of the proposed positioning system. In addition, some works about

pedestrian navigation are summarized.

There are two additional concepts used by this thesis to develop the proposed posi-

tioning and tracking system using the fingerprinting approach. Section 2.5 describes the

operation of the affinity propagation algorithm, which generates clusters of similar data

points. Section 2.6 summarizes the compressive sensing theory which can be applied on

the localization problem to estimate the user’s location.

2.1 Indoor RSS-based WLAN Positioning Techniques

The key problem for the indoor RSS-based positioning systems is to identify the RSS-

position relationship, so that the user’s location can be estimated based on the RSS

collected at that location. There are two approaches in dealing with this relationship [25]:

the uses of signal propagation models [26, 27] and the location fingerprinting methods

[2, 19,28].

12

Chapter 2. Background and Related Works 13

2.1.1 Signal Propagation Modeling

This technique uses the RSS readings collected by the mobile device to estimate the

distances of the device from at least three APs, whose locations are known, based on

a signal radio propagation model. Then triangulation is used to obtain the device’s

position [8].

The accuracy of this technique depends heavily on finding a good model that can

best describe the behavior of the radio propagation channel. However, the indoor radio

propagation channel is highly unpredictable and time-varying, due to severe multipath

in indoor environment; shadowing effect arising from reflection, refraction and scattering

caused by obstacles and walls; and interference with other devices operated at the same

frequency (2.4GHz) as the IEEE 802.11b/g WLAN standard, such as cordless phones,

microwaves and BlueTooth devices. There are two models that are often used for the

indoor radio propagation channel:

• Combined model of path loss and shadowing [29]

This model combines the simplified path-loss model with the effect of shadowing,

which is assumed to be a log-normal random process. The received power pr which

is d meters away from a specific AP is given by:

pr[dBm] = p0[dBm] + 10 log10K − 10γ log10d

d0− ηdB (2.1)

where K is a constant depending on the antenna characteristics and channel atten-

uation, p0 is the signal power at a reference distance d0 for the antenna far field,

γ is the path-loss exponent, which varies for different surrounding environments

(2 ≤ γ ≤ 6 for indoor environment) and ηdB ∼ N (0, σ2η) is a Gaussian random

variable.

• Wall Attenuation Factor model [19]

This model includes the effects of obstacles or walls between the transmitter and


receiver. The received power can be obtained by:

pr[dBm] = p0[dBm]− 10γ log10d

d0−

nW ·WAF nW < C

C ·WAF nW ≥ C(2.2)

where nW is the number of obstacles or walls between the transmitter and receiver,

C is a threshold up to which no significant attenuation can be observed and WAF

is the wall attenuation factor.

The two empirical models require the calibration of the parameters, such as the path

loss exponent, which vary depending on different environments. This often requires a

comprehensive survey of the RSS distributions over the environment, which is a time

consuming process. In addition, the models assume the RSS is distributed isotropically

from the transmitter. This is often not the case for indoor environments due to the

presence of obstacles. The orientation of the antenna of the mobile device also affects

the RSS [22], but it is not reflected in the two models. Finally, the locations of the APs

may not be known in the real scenario, as these APs may be installed and owned by

different vendors. All of these make the models inadequate to describe the RSS-position

relationship in real situation and lead to errors in estimating the user’s location.

2.1.2 Location Fingerprinting

A location fingerprinting method is often used instead of the radio propagation model,

as it can give better estimates of the user’s locations for indoor environments. This

method is divided into two phases: offline and online phases. During the offline phase,

which is also referred to as the training phase, the RSS readings from different APs are

collected by the WLAN-integrated mobile device at known positions, which are referred

to as the reference points (RPs) to create a fingerprint database, also known as the radio

map. Since the orientation of the device’s antenna affects the RSS readings, a more

comprehensive fingerprint database can be built by collecting RSS readings for different


orientations at the same RP. The actual positioning takes place in the online phase. The

mobile device, which is carried by the user collects RSS readings from different APs at an

unknown position. Then, these RSS online measurements are compared to the fingerprint

database to estimate the user’s location by using different methods described in the next

section.

The accuracy of the estimated position of the user depends highly on the number of

RPs collected in the fingerprint database. If there are more RPs, then the radio map

has a finer resolution and thus allows a better estimation [28]. In addition, since the

RSS varies over time, collecting more time samples of RSS readings at the same RP also

improves the position estimation. Thus, this fingerprint database collection is a time

consuming and labour-intensive process. [30] uses the spatial correlation of adjacent RPs

to generate the database by interpolation from a small number of RPs and this method

is able to reduce the labour effort and time required for the offline phase.

Another disadvantage of this fingerprinting approach is the maintenance of such

databases. Since the RSS propagation environment varies with time, the accuracy of

using the database degenerates over time, as the current RSS readings slowly deviate

from the readings in the database. The database may even be rendered useless, if the

environment changes significantly. This requires the fingerprint database to be rebuilt

periodically, in order to ensure the accuracy of the positioning system. [31] presents a

novel method to update the radio map using the online RSS readings, which can effi-

ciently update the fingerprint database without the labour and time overhead cost as

required by rebuilding such database from scratch.

As shown in [32], the RSS readings collected by different network cards are different,

which can vary up to -25dBm. This indicates that the same fingerprint database cannot

be used by different mobile devices, which are equipped with different WLAN network

cards. That means that the fingerprint collection process must be done on each device

and lead to very high labour and time costs. Another method is to use the signal strength


difference (SSD) between APs instead of the RSS as the fingerprint [33].

Although there are limitations to the location fingerprinting, it is a simple and effective

method to be used by indoor positioning systems. This thesis also uses this approach to

estimate the user’s location.

2.2 Fingerprinting-Based Positioning Methods

There are two approaches to estimate the user’s location based on the online RSS mea-

surements and the fingerprint database [34, 35]. The deterministic approach only uses

the average of the RSS time samples from each RP to estimate the location, whereas the

probabilistic approach incorporates all the RSS time samples for the computation.

For the following section, assume the collected fingerprint database is denoted as a

set {(pi,ψi(1), . . . ,ψi(T ))|i = 1, . . . , N}, where pi is the Cartesian coordinates for RP

i, ψi(t) = [ψi,1(t), . . . , ψi,L(t)]T is the RSS readings vector for RP i at time t with ψi,j(t)

denoted as the RSS reading from AP j for RP i at time t. T is the total number of

collected time samples, N is the total number of RPs and L is the total number of APs.

The online RSS measurement vector can be denoted as r = [r1, ...rL]T .

2.2.1 K-Nearest Neighbour Method (KNN)

The K-nearest neighbour (KNN) method is a deterministic approach that uses the average

of the RSS time samples of RPs from the fingerprint database to estimate the user’s

location [19]. It first examines the Euclidean distance of the online RSS measurement

vector to the RPs in the database, namely:

Di = ∥r − ψi∥ (2.3)

where ψi = 1T

∑Tτ=1 ψi,1(τ) is the average RSS vector for RP i. Then, the distances

are sorted in ascending order and the first K RPs that have the smallest distances are


obtained to estimate the location p:

p =1

K

K∑i=1

pi (2.4)

The calculated distances can be used as weights to estimate the location and it is referred

to as the weighted-KNN. The estimated location can be found by

p =

∑Ki=1

1Dipi∑K

i=11Di

(2.5)

2.2.2 Probabilistic Approach

The location estimation problem can be solved by using probabilistic models [2, 36, 37,

37, 38]. The core concept is to find the posterior distribution of the location, which is

the conditional probability p(pi|r) [37]. This conditional probability can be estimated

by using the Maximum A Posteriori (MAP) estimator, which is derived from Bayes rule.

That is:

pMAP = argmaxpi

f(pi|r) = argmaxpi

f(r|pi)f(pi)N∑i=1

f(r|pi)f(pi)(2.6)

where f(pi|r) and f(r|pi) are the conditional probability density functions. Note that

the denominator of (2.6) can be safely ignored as it remains the same regardless of the

choice of pi. In general, there is no prior knowledge of the device’s location and thus

the prior density f(pi) is assumed to be uniform, which transforms this MAP estimation

into a Maximum Likelihood (ML) estimation:

pML = argmaxpi

f(r|pi) (2.7)

The estimation can be further improved by including the likelihood densities as the weight

for the K RPs with the highest likelihood densities, namely:

pML+weight =K∑i=1

wipi (2.8)

wi =f(r|pi)∑Kj=1 f(r|pi)

(2.9)


There are several methods to estimate the likelihood density functions f(r|pi), i =

1, . . . , N from the fingerprint database. Two of the common methods are reviewed here.

Both of them assume that the RSS from different APs are uncorrelated and independent,

so that the density function can be simplified to f(r|pi) =∏L

k=1 f(rk|pi).

Histogram

The likelihood density functions can be estimated by the histogram method. This method

requires two parameters to generate a histogram for the RSS time samples collected for

each of the AP at each of the RP [37]. The first parameter is the number of bins,

which are a set of non-overlapping intervals that cover the whole possible range of the

RSS values. The second is the origin of the bins, which is necessary to determine the

boundaries of the bins. Then, the likelihood density estimate for a particular RSS value

can be obtained as the relative frequency of the bin, which contains that particular RSS

value [37].

There are several drawbacks for this method. First, the likelihood density estimate

depends heavily on the choice of the origin and the bin width and thus careful experi-

mental calibration of these parameters is required [37]. Second, a large amount of RSS

samples for each RP is required to generate a reliable histogram that produces good

location estimate.

Kernel-Based

Instead of using the histogram, the kernel-based method uses the kernel density estimator

to estimate the density functions [2,37]. The density function can be estimated as follows:

f(r|pi) =1

T

T∑t=1

K(r;ψi) (2.10)

where K(r;ψi) denotes the kernel function. A common choice of the kernel function is

the Gaussian kernel. By assuming that the RSS from different APs are uncorrelated and


independent, the Gaussian kernel function is defined as:

K(r;ψi) =1

(√2πσ∗

i )Lexp

(−∥r −ψi(t)∥2

2(σ∗i )

2

)(2.11)

where σ∗i is the kernel bandwidth. The determination of this kernel bandwidth is evalu-

ated in [2]. Since this method takes all the RSS time samples collected at each RP into

account for estimating the likelihood densities, the computation time is much larger than

the KNN method.

In this thesis, the kernel-based method is also implemented to compare its perfor-

mance to the proposed positioning system. The operation of the method using the

Gaussian kernel is summarized in Fig. 2.1 [38].

2.2.3 Region of Interest and Access Points Selections

Before applying the above methods on the whole fingerprint database to estimate the

user’s location, two pre-processing steps can be introduced to confine the localization

problem into a subset of relevant RPs and a subset of APs, which can distinguish the

RPs easily. The region of interest determination step is able to mitigate the effect of the

deviations between the online readings and the radio map due to the time-varying char-

acteristic of the indoor radio channel [39]. In addition, the purpose of AP selection step

is to remove extra APs that may lead to biased estimations and redundant computations,

which is often the case as APs are widely deployed in indoor buildings [38].

Both steps are often carried out together as the reliability of the APs varies for

different RPs [36, 38, 39]. The joint clustering technique proposed in [39] selects the

strongest m APs to generate the probability distribution for each RPs and groups the

RPs, which have the same q strongest APs list, as a cluster during offline phase. The

argument of using strongest APs is that they provide the highest probability of coverage

over time [39]. However, they may not be a good choice, as the variation of the APs may

also lead to error in estimation [28]. [40] presents another AP selection criterion that is


Given:

Radio Map: {(pi,ψi(1), . . . ,ψi(T ))|i = 1, . . . , N}

Number of APs: L

Number of time samples: T

Inputs:

Online RSS measurement vector: r

Outputs:

Position estimate: p

Kernel-based Method:

Optimal bandwidth: σ∗i

σ∗i =

(4

L+2

) 1L+4 σiT

−1L+4

where, σ2i = 1

L

∑Ll=1(σ

li)

2 (σli)

2 = 1T−1

∑Tt=1(ψi,l(t)− ψi,l)

2, ψi,l =1T

∑Tt=1 ψi,j(t)

Weight calculation:

wi =1

T (√2πσ∗

i )L

∑Tt=1 exp

(−∥r−ψi(t)∥2

2(σ∗i )

2

)Estimation:

p =∑N

i=1 wipi∑Ni=1 wi

Figure 2.1: Kernel-based method [2].

based on AP’s discrimination power in terms of entropy calculations. Several more AP

selection schemes and the use of spatial filtering for region of interest determination can

be found in [2].

This thesis uses the affinity propagation algorithm to generate cluster of RPs with

similar RSS readings during offline phase. Then, a coarse localization stage is introduced

in online phase to identify in which cluster of RPs should the user be located. In addition,


different AP selection schemes are also explored for the proposed positioning system.

2.3 Indoor Tracking

Most of the indoor tracking methods use past position estimates and pedestrian motion

dynamics to refine the current position estimate determined by the above positioning

methods. In addition, the dynamic motion model can also be used in conjunction with

the current position estimate to predict the future possible locations. The pedestrian

motion dynamics can be modeled by a general Bayesian tracking model and a filter

is then derived to refine the position estimates [41]. There are two filters that are used

commonly to improve the accuracy of positioning systems [41]: Kalman filter and Particle

filter.

2.3.1 Kalman filter

By assuming the Gaussian tracking noise model and linear motion dynamics, the general

filter becomes a Kalman filter, whose optimal solution is a minimum mean square error

(MMSE) estimate. Although the assumption of Gaussian RSS-position relationship is

not often the case [22], the application of the Kalman filter as the post-processing step

is able to improve the accuracy of the positioning systems [41–44]. The parameters of

the Kalman filter are needed to be found experimentally. [45] provides some guidelines

on how to set the parameters for each update steps based on the map information.

2.3.2 Particle filter

The particle filter is a sequential Monte Carlo method that generates random samples,

known as particles, according to a motion models and estimates their probability densities

[46,47]. Unlike the Kalman filter, the particle filter can be applied on non-Gaussian and

non-linear models. In addition, map information can be used to further improve the


performance of the particle filter by assigning zero weights to the invalid particles, such as

those across the wall [48,49]. Backtracking based on the map information is also proposed

in [50]. Moreover, information obtained from accelerometers and inertial measurement

units (IMU) can also be used to refine the motion models and let the filter to generate

particles that are more relevant and hence improve the tracking accuracy [51,52].

However, the major drawback of the particle filter is its high computation complexity.

For example, 1600 particles are needed for each filter update for a 40m×40m experimental

area to achieve the best performance [49]. This large computation workload can not be

handled by the mobile devices to give real-time updates to the user. Hence, this thesis

chooses the Kalman filter to post-process the estimates instead of the particle filter, which

may severely hinder the operations of the mobile devices.

2.3.3 Other Methods

Besides the use of the above filters, several other methods are also used for the indoor

tracking. The Horus positioning system [36] smooths out the resulting location estimate

by simply averaging the last W location estimates obtained by the discrete-space esti-

mator. Liao et al. proposed a method to predict the user’s orientation, which is then

used for the next position estimate to improve the accuracy, from the previously com-

puted location estimates [53]. A Viterbi-like algorithm, which is developed to enhance

the RADAR system [20] and is also implemented by [54], makes use of historical data

based on the KNN method to determine the location estimates. Finally, a nonparamet-

ric information filter based on the kernel-based probabilistic method is proposed in [55].

This filter, whose computational complexity is lower than particle filter, is able to deal

with tracking scenarios where Kalman filter is inapplicable.


2.4 Pedestrian Navigation

Indoor navigation for pedestrian is different from the vehicular navigation using GPS,

which becomes an essential tool to the driver. Gillieron and Merminod [56] describes

how to implement the personal navigation system for indoor applications. It is crucial to

extract information from the indoor maps as topological models and node/link models,

so that they can be used for implementation of route guidance. They also implement

map matching algorithms, so that the system can self-correct the user’s locations due

to bad estimates based on the topological elements from the map databases, traveled

distances and direction changes. [48] also describes how the map information can be used

for indoor location-aware systems. There are different ways to present the guidance infor-

mation graphically to the users based on different output devices and they are explored

in [57]. The experience of using the indoor navigation systems can be enhanced in a

smart environment, which is equipped with different kinds of sensors that can convey

additional information to users [58].

There are more restrictions for the navigation systems when they are targeted to visu-

ally impaired users. [59] describes the path planning and following algorithms specifically

designed for visually impaired. In summary, such systems generate obstacle-free paths;

provide more detailed information about the surrounding area and give the guidance in

relation to special objects, such as walls, doors and rails, etc. In addition to the com-

monly used Dijkstra algorithm to generate the routes [56], a cactus tree-based algorithm

is also used to generate a high-level guidance. A more detailed development of an indoor

routing algorithm for the blind and its comparison to the one for the sighted can be found

in [60].

This thesis develops a simple navigation system, which uses the proposed tracking

system to provide updates of user’s locations. Such system is implemented as a soft-

ware on PDAs and smartphones and is given to the visually impaired people to test its

usefulness in helping them to get familiar with the indoor environment.


2.5 Affinity Propagation Algorithm For Clustering

In this thesis, the affinity propagation algorithm described in [15] is used to cluster the

RPs with similar RSS readings, so that the proposed positioning and tracking system is

able to confine the localization problem into a smaller region.

Unlike the traditional K-means clustering method, which may lead to bad clustering

results due to bad choice of randomly selected K initial exemplars [61], the affinity

propagation algorithm is able to generate good clustering results without predetermining

the initial exemplars. This algorithm allows all the data points to have equal chance

to become exemplars and is easy to be implemented, thus it is chosen in this thesis to

cluster the RPs.

The affinity propagation algorithm generates a set of exemplars and corresponding

clusters by recursively transmitting real-valued messages between data points with an

input measure of similarity between pairs of data points [15]. The pairwise similarity

s(i, j) indicates the suitability of data point j to be the exemplar of data point i. An-

other input measure is the preference, which is also the self similarity for data point k,

p(k) = s(k, k). This value defines the a priori possibility that data point k to become an

exemplar. If all the data points are equally possible to be exemplars, then their prefer-

ences can be set to a common value. High preference values will lead to large number

of clusters generated by the algorithm. In practice, the preference values are commonly

assigned as the minimum or median similarity to generate moderate number of clusters.

The core operations of the algorithm is the transmission of two kinds of real-valued

messages: responsibility message, r(i, j) and availability message, a(i, j). The responsi-

bility message, r(i, j), is sent from data point i to candidate exemplar j to reflect the

suitability of data point j to serve as the exemplar for data point i taking into consider-

ations the other potential exemplars. It is updated according to

r(i, j) = s(i, j)− maxj′s.t.j′ =j

{a(i, j ′) + s(i, j′)} (2.12)


The availability message, a(i, j) is sent from candidate exemplar j to data point i

to reflect how appropriate that data point i should choose data point j as its exemplar,

taking into account the responsibility messages from other data points that data point j

should be an exemplar. Its update rule is:

a(i, j) = min

0, r(j, j) +∑

i′s.t.i′ ={i,j}

max{0, r(i′, j)}

(2.13)

Two additional messages: self-responsibility, r(i, i) and self-availability, a(i, i) are also

calculated for each data point i. These messages reflect accumulated evidence that i is

an exemplar. The formulas to update these two messages are stated below:

r(i, i) = p(i)− maxj′s.t.j′ =j

{a(i, j′) + s(i, j ′)} (2.14)

a(j, j) =∑

i′s.t.i′ =j

max{0, r(i′, j)} (2.15)

The exemplars can then be identified by combining the two messages. For data point

i, find

j′ = argmaxj

{a(i, j) + r(i, j)} (2.16)

If j′ = i, then data point i is an exemplar; otherwise, data point j′ is the exemplar

for data point i. The messages are passed recursively between pairs of data points by

following the above updating rules (2.12) to (2.15) until a good set of exemplars and

corresponding clusters gradually emerges.

2.6 Compressive Sensing Theory

This thesis describes how the localization problem can be re-formulated into a sparse

signal recovery problem, so that the compressive sensing theory discussed in [16, 62, 63]

can be applied to estimate the user’s location.

Compressive sensing theory allows compressible signals to be recovered by fewer sam-

ples than traditional methods, which according to the Nyquist sampling theory requires


the sampling rate to be at least twice the maximum bandwidth. This is possible when

signals of interest are sparse and are sampled incoherently. The compressive sensing

problem can be formulated as follow [16,63]:

Consider a discrete-time signal x as a N × 1 vector in RN . Such signal can be

represented as a linear combination of a set of basis {ψi}Ni=1. Constructing a N×N basis

matrix Ψ = [ψ1,ψ2, ...ψN ], the signal x can be expressed as

x =N∑i=1

siψi = Ψs (2.17)

where s is a N × 1 vector and is an equivalent representation of x in the different basis

Ψ. A signal is K-sparse when it can be represented as a linear combination of K ≪ N

basis vectors. This means that there is only K nonzero entries for vector s.

The overall compressive sensing problem can be expressed as

y = Φx = ΦΨs = Θs (2.18)

where Φ is a M × N , M < N measurement sensing matrix for sensing the signal x,

Θ = ΦΨ is an M × N matrix, and y is a M × 1 observation vector collected as a

result of this sensing process. This problem can be referred to as incoherent sampling

if the largest correlation between the sensing matrix Φ and the representation basis Ψ,

µ(Φ,Ψ) =√N · max

1≤i,j≤N| < ϕi,ψj > | is small.

Compressive sensing theory requires both the sparsity and incoherent sampling, so

that the signal can be recovered exactly with high probability. IfM ≥ cKlog(N/K) ≪ N ,

where c is a small constant, the signal can be reconstructed by solving the following l1

norm minimization problem:

s = argmins∈RN

∥s∥1 such that Θs = y (2.19)

This is a convex optimization problem that can be easily converted into a linear program,

known as basis pursuit, through primal-dual method [62, 64]. Additional algorithms


to solve this optimization problem can also be found in [64]. In this thesis, the ℓ1-

minimization problem is solved by using the basis pursuit linear program provided in the

matlab toolbox, ℓ1-MAGIC, developed by Candes [65].

2.7 Chapter Summary

This chapter gives a brief overview of different methods developed for the RSS-based

WLAN indoor positioning systems. It also discusses how the reduction of the region of

interest and selection of access points can enhance the accuracy of these systems. Two

fingerprinting methods, KNN and kernel-based probabilistic techniques are described in

details, as they are served as the performance benchmarks for the proposed position-

ing system. Moreover, several indoor tracking techniques that are able to improve the

accuracy through the use of previous estimates and pedestrian motion models are also

discussed. The developments of indoor navigation systems are also included to provide

some insight on how the location information produced by the positioning and tracking

systems can be used.

Finally, the affinity propagation algorithm for clustering data points and the com-

pressive sensing theory for sparse and incoherent sampled signals are discussed, these

concepts are used by the proposed positioning and tracking systems.

Chapter 3

Compressive Sensing Based

Positioning System

Due to the unpredictable nature of the RSS distribution at indoor environment, most

of the indoor RSS-based WLAN positioning systems use the fingerprinting approach to

acquire the explicit RSS and position relationship, in order to compute a more accurate

estimation of user’s position. The compressive sensing based positioning system proposed

in this chapter is also a fingerprinting method. Unlike the traditional fingerprinting

systems, the proposed system reformulates the localization problem into a sparse-natured

problem and thus the compressive sensing concept can be applied to find the estimated

positions. A coarse localization stage is also introduced to constraint the region of interest

into smaller relevant area, which effectively reduces the computation time and minimizes

the maximum errors attained.

3.1 Indoor Positioning System Overview

As depicted in Fig. 3.1, the compressive sensing based positioning system consists of

two phases: offline phase where the training is done to generate the fingerprint database

and the affinity propagation algorithm is applied to generate clusters; online phase where

28

Chapter 3. Compressive Sensing Based Positioning System 29

RSS readings are obtained for the actual localization to take place. The online phase

consists of two stages. First, the coarse localization stage is carried out to reduce the

area of interest into a smaller region by choosing clusters of RPs based on online RSS

readings. Then, in fine localization stage, the localization problem is reformulated into

a sparse signal recovery problem, which allows the application of compressive sensing

theory to estimate the device’s position. The following sections describe the individual

blocks as shown in Fig. 3.1 in details.

Online Phase

Offline PhaseFingerprinting

RSS Collections in 4 orientations

Coarse Localizationcluster matching

Fine LocalizationCompressive Sensing

online RSS readings

Estimated Location

Orthogonalization

L1-norm minimization

AP selection

ClusteringAffinity Propagation

Figure 3.1: Block diagram of the proposed indoor localization system.

3.2 Offline Phase

Offline phase is the training period that allows the positioning system to collect RSS

data at the area of interest and preprocess them to enable the system to estimate the

mobile device’s position in the online phase. This training must be done wherever the

positioning system is first deployed. The time required for the training depends on the


size of the survey site. Moreover, the database may need to be rebuilt if the surrounding

environment of the area of interest changes significantly.

According to Fig. 3.1, two operations are performed in the offline phase for the

proposed system and they are described in the following subsections.

3.2.1 Fingerprint Collections

The first operation of the offline phase is the fingerprinting. During fingerprinting, RSS

readings from different APs are collected by a WLAN-enabled mobile device at desired

known positions, referred to as the reference points (RPs), which are often the grid points

pre-defined on the map. RSS readings are sampled at a regular time interval, in order to

obtain their distributions over time. Since the orientation of the antenna inside the device

affects the RSS readings, the device is pointed to a specific orientation when collecting

RSS readings at each RP. In this thesis, RSS readings are collected at four common

directions, namely North, East, South and West as represented mathematically by the

set O = {0◦, 90◦, 180◦, 270◦}.

The raw set of RSS time samples collected from AP i at RP j and orientation o is

denoted as {ψ(o)i,j (τ), τ = 1, ..., q, q > 1}, where q is the total number of time samples

collected. Then, the average of these raw time samples are computed and stored in a

database, known as the radio map on the server. Such radio map database gives the

spatial and RSS relationship in the given environment and can be represented as Ψ(o):

Ψ(o) =

ψ(o)1,1 ψ

(o)1,2 · · · ψ

(o)1,N

ψ(o)2,1 ψ

(o)2,2 · · · ψ

(o)2,N

......

. . ....

ψ(o)L,1 ψ

(o)L,2 · · · ψ

(o)L,N

(3.1)

where o ∈ O = {0◦, 90◦, 180◦, 270◦} and ψ(o)i,j = 1

q

∑qτ=1 ψ

(o)i,j (τ) is the average of RSS

readings over time from AP i at RP j at a specific orientation o, for i = 1, 2, . . . , L and

j = 1, 2, . . . , N . L is the total number of APs detected throughout the whole region of


interest and N is the total number of RPs. The columns of Ψ(o) represent the average

RSS readings at each RP, which can be referred to as the radio map vector and is denoted

as

ψ(o)j = [ψ

(o)1,j ψ

(o)2,j · · · ψ

(o)L,j]

T , j = 1, 2, . . . , N (3.2)

Besides the average RSS reading matrix Ψ(o), the database server also stores the

variance of these time samples, which are useful in determining which APs should be

selected for localization. The variance vector for each RP is defined as

∆(o)j = [∆

(o)1,j ∆

(o)2,j · · · ∆

(o)L,j]

T , j = 1, 2, . . . , N (3.3)

where ∆(o)i,j = 1

q−1

∑qτ=1(ψ

(o)i,j (τ) − ψ

(o)i,j )

2 is the unbiased variance of RSS readings from

AP i at RP j for orientation o.

For each RP j, its position represented as Cartesian coordinates (xj, yj), together with

its average and variance of the RSS readings from different APs at different orientations

form a set of (xj, yj;ψ(o)j ;∆

(o)j ), o ∈ O, which is stored in the fingerprint database. The

database is then preprocessed as described in the next subsection before being used for

the computation of position estimation during online phase. Note that if there is no RSS

readings collected from an AP at a RP and an orientation, the corresponding value in

the fingerprint database is set to a small value to imply its invalidity.

3.2.2 Clusters Generation by Affinity Propagation

Due to the time varying characteristics of the indoor propagation channel, RSS readings

collected during online phase may deviate from those stored in the radio map database.

As a result, these deviation may lead to error estimation of position. In addition, the

computation time for finding position updates increases proportionally to the number of

RPs. Therefore, a coarse localization stage is introduced at the online phase to confine

the localization problem into a smaller region, namely a subset of RPs that have similar

RSS readings to the online measurement, before the fine localization is performed. This


stage can effectively reduce the computation time due to the reduction of number of

relevant RPs, as well as the errors introduced by the potential outliers.

The RPs collected in the offline phase are required to be divided into subsets, so that

a coarse localization stage can take place during the online phase. The RPs whose RSS

readings are similar and physically close to each other should belong to the same group.

This group division process, which is referred to as the clustering process in the proposed

system is done during the offline phase after the fingerprints collection is finished. Since

the RSS readings for the same RP vary for the four orientations, the clustering process

is performed on each of the four radio map databases separately.

The affinity propagation algorithm described in Section 2.5 is used to generate the

desirable clusters, as this algorithm allows all the RPs to have equal chances to be

exemplars and is easily to be implemented. It requires two input parameters, namely the

similarity between pairs of RPs and the preference values. At orientation o, the similarity

between RP i and RP j is defined as

s(i, j)(o) = −∥ψ(o)i −ψ(o)

j ∥2, ∀i, j = i ∈ {1, 2, ..., N}, o ∈ O (3.4)

Since all of the RPs are equally desirable to be exemplars, their preferences are set

to a common value. In order to generate a moderate number of clusters, the common

preference for orientation o is defined as

p(o) = γ(o) ·median{s(i, j)(o),∀i, j = i ∈ {1, 2, ..., N}}, o ∈ O (3.5)

where γ(o) is a real number which is experimentally determined, such that a desired

number of clusters is generated.

For each orientation, o ∈ O, the affinity propagation algorithm takes the above defi-

nitions of similarity (3.4) and preference (3.5) as inputs and then it recursively updates

the responsibility messages and availability messages according to (2.12) to (2.15) until

a good set of exemplars and the corresponding clusters emerges [15]. This set of gener-

ated exemplars is denoted as H(o) and the corresponding cluster member set with RP


j as the exemplar is represented as C(o)j , j ∈ H(o). In general, the RPs that are within

the same cluster should be physically in close proximity, as the neighboring RPs should

attain similar RSS readings. However, due to the varying characteristics of RSS readings

(such as the shadowing effects), there exist RPs that are physically far away from their

assigned clusters. These RPs, referred to as outliers, are manually assigned back to the

clusters that are physically closeby to reduce the potential errors in position estimations.

3.2.3 Interaction between the database server and the mobile

device during offline phase

Fig. 3.2 illustrates how the proposed positioning system is set up on the mobile device

and the server during offline phase to obtain and process the training data required for the

localization. The mobile device collects RSS time samples from detectable APs at specific

positions (RPs) and transmits these data to the server. After the fingerprint collection is

done by the device, the server creates the radio map database and generates clusters for

each orientation by applying the affinity propagation algorithm. This algorithm is run

on the server as it is an iterative process that consumes a large amount of memory and

processing power that may not be supported by the mobile device. At the end of the

offline phase, the server obtains the coordinates of the RPs, radio map matrices, variance

of RSS readings and also clusters information for each orientation. These data are then

used in the online phase for the computation of position estimations.

3.3 Online Phase

During the online phase, the device, carried by a mobile user and pointed to an unknown

orientation, collects online RSS readings from detectable APs, which are then used to-

gether with the fingerprint database to estimate the device’s location. The online RSS


Mobile Device Server

Collect RSS time samples from APs at RP j for 4 orientations

Compute the average and variance of RSS readings over time, ψ_j (o), ∆_j(o)

Send RP j’ s information:ψ_j (o),∆_j (o) & coordinates (x_j, y_j)Collect fingerprint for RP j

in 4 orientations

Create overall radio map matrix: Ψ(o) = [ψ_1(o),ψ_2(o),…,ψ_N(o)]

SEND

Apply affinity propagation on each radio map to generate sets of

exemplars H(o) and their corresponding members C_j(o)

Use the device to collect N RPs

Outlier adjustment for each radio map

Figure 3.2: Interaction between the database server and the mobile device during offline

phase.

measurement vector at time t is denoted as

r(t) = [r1(t), r2(t), · · · , rL(t)]T (3.6)

where {rk(t), k = 1, ..., L} is the online RSS readings from AP k at time t. Since the

positioning system does not take into account the previous estimate, the time dependency

notation (t) is dropped in this chapter for simplicity purpose, i.e. the online RSS reading

is denoted as r instead of r(t).

As shown in Fig. 3.1, the collected measurement vector is the input to the proposed

positioning system. First, it is used in the coarse localization stage to reduce the area of

interest. Then it is also used in the fine localization stage to obtain the final estimated

position. The details of these two stages are described in the following sections.


3.3.1 Coarse Localization Stage: Cluster Matching

As mentioned earlier, the goal of the coarse localization stage is to reduce the region of

interest from the whole fingerprint database to a subset of it. Thus, it can reduce the

computation time for the fine localization stage, as fewer RPs are considered. It can also

confine the maximum localization error to be the size of this subset, whereas this error can

be much larger when no coarse localization stage is implemented. The coarse localization

is done by selecting the clusters, as defined in the offline phase, whose RSS radio map

vectors best-match with the online RSS measurement vector r. Since the target device

can be physically located at the boundaries of the defined clusters, a few best-matched

clusters, instead of only one cluster, are selected to eliminate the inaccuracy due to the

edge problem.

The cluster matching process can be interpreted as finding a set of best-matched

exemplars SRSS with their corresponding cluster members set CRSS, such that they have

the highest similarities with the online reading. It is crucial to have a good similarity

function between the online reading r and an exemplar j ∈ H(o),∀o ∈ O, denoted

as SMatch(r, j)(o), so that the clusters for which the online measurement vector r should

belong to can be correctly identified. The worst case scenario, where wrong sets of clusters

are chosen for the online measurement vector r, should be avoided, as this results in a

wrong localization region and thus introduces large localization error. This may happen,

as the online RSS readings may deviate from the fingerprint database due to the time

varying indoor radio propagation channel. In order to reduce the occurrences of such

scenarios, several matching schemes are considered in this thesis. These schemes provide

different ways to define the appropriate similarity function SMatch(r, j)(o).

1. Exemplar based cluster matching

This is the most basic scheme, which uses the same definition as (3.4) for the

clustering in offline phase. The similarity computes the Euclidean distance of the


online measurement vector r to the individual exemplar’s RSS radio map vector

from each cluster:

SMatch(r, j)(o) = −∥r −ψ(o)

j ∥2, ∀j ∈ H(o), ∀o ∈ O (3.7)

2. Average based cluster matching

Instead of using the exemplar RSS radio map vector, the average of the RSS radio

map vectors of all the cluster members, which gives a more comprehensive and

representative readings of the whole cluster, is used to compute the Euclidean

distance against the online measurement vector r:

SMatch(r, j)(o) = −∥r − 1

|C(o)j |

∑k∈C(o)

j

ψ(o)k ∥2, ∀j ∈ H(o),∀o ∈ O (3.8)

3. Weighted Average cluster matching

This scheme takes into account the stability of the RSS readings from a specific

AP at different RPs. Different weights are added to the similarity function for each

AP of each cluster at each orientation, so that it gives more weight to the stable

RSS readings. The stability of an AP at a RP can be determined as the inverse of

the variance of the RSS readings collected from that AP at that RP calculated in

the offline phase, thus APs with smaller variances are more reliable and have larger

weights. The similarity function is defined as:

SMatch(r, j)(o) = −∥W(o)

j · (r − 1

|C(o)j |

∑k∈C(o)

j

ψ(o)k )∥2, ∀j ∈ H(o), ∀o ∈ O (3.9)

W(o)j =

√w

(o)1,j 0 · · · 0

0√w

(o)2,j 0 0

... 0. . . 0

0 · · · 0√w

(o)L,j

(3.10)


where W(o)j is the diagonal weight matrix and w

(o)l,j , l = 1, 2, . . . , L is the weight of

AP l for cluster j at orientation o. This weight is proportional to the inverse of the

variance of the AP for the specific cluster, namely

w(o)l,j ∝ 1

∆(o)l,j

(3.11)

∆(o)l,j =

1

|C(o)j |

∑k∈C(o)

j

∆(o)l,k (3.12)

Then these weights are normalized, so that∑L

k=1w(o)l,j = 1.

4. Strongest APs matching

In this scheme, the online measurement vector is first pre-filtered to determine L′

APs that have the strongest RSS readings. Then, the similarity can be calculated

using any of the above schemes by only considering the RSS readings from these

selected APs. Since the APs that have stronger RSS readings tend to be more

stable as the device is with high probability within their coverage area, whereas the

APs with weaker signals tend to vary in time, the scheme is able to provide good

matching similarity definition by only considering the reliable APs.

All the above cluster matching schemes attempt to reduce the possibility of choosing

the wrong clusters used by the fine localization and thus improving the system’s stability

and accuracy. The performances of these schemes are evaluated in details in Chapter 7.

By evaluating the similarity function described above, the set of best matched exem-

plars SRSS with their corresponding cluster members set CRSS can be found as:

SRSS = {(j, o)| SMatch(r, j)(o) > α, j ∈ H(o), o ∈ O} (3.13)

CRSS = {(k, o)| k ∈ C(o)j , (j, o) ∈ SRSS} (3.14)

where α is a predefined threshold value to determine whether a cluster should be included

into SRSS. Since only a few set of clusters are desired to be included in SRSS, α is set to


be a high percentage, α1, of the maximum similarity difference, that is

α = α1 · maxj∈H(o),o∈O

{SMatch(r, j)

(o)}+ (1− α1) · min

j∈H(o),o∈O

{SMatch(r, j)

(o)}

(3.15)

Finally, the region of interest of the localization problem can be reduced to the set of

CRSS. The modified radio map matrix ΨL×N , N = |CRSS| can be obtained as

Ψ = [ψ(o)j , ∀(k, o) ∈ CRSS]. (3.16)

This matrix will then be used by the following fine localization stage. Note it is

possible that this matrix may contain the radio map vectors from the same RP but at

different orientations, as all clusters from different orientations are considered for cluster

matching.

3.3.2 Fine Localization Stage: Compressive Sensing Recovery

The fingerprint-based localization problem can be reformulated as a sparse signal recovery

problem, as the position of the mobile user is unique in the discrete spatial domain. By

assuming that the mobile user is located exactly at RP j and facing at orientation o, such

that (j, o) ∈ CRSS, the user’s location can be represented relative to these RPs instead

of the actual location. The mathematical representation is a 1-sparse vector, denoted as

θN×1, whose elements are all equal to zero except the n-th element, so that θ(n) = 1,

where n is the corresponding index of the RP at which the mobile user is located, that is

θ = [0, ..., 0, 1︸︷︷︸nth element

, 0, ..., 0]T (3.17)

Then, the online RSS measurement r obtained by the mobile device can be expressed

as:

y = Φr = ΦΨθ + ε (3.18)

where Ψ is the modified radio map matrix as defined in (3.16) and ϵ is an unknown

measurement noise. The matrix ΦM×L is an AP selection operator applied on the online


RSS measurement vector r to obtain vector y, where M < L is the desired number of

APs to be selected.

Based on this sparse signal recovery formulation, the following parts explain how the

location of the mobile user can be recovered by using the compressive sensing theory.

A. Access Points Selection

Since most modern buildings are equipped with a large number of APs to ensure good

quality of wireless services, the total number of detectable APs in these buildings, L is

often much greater than that required for positioning. These extra APs lead to excessive

computations and possibly biased estimations if some of the APs are not reliable. Inclu-

sion of RSS readings from unstable APs may introduce error to the estimations, as online

RSS values may deviate from the readings in the offline database. Therefore, an access

point selection step is introduced to select a subset of reliable and stable APs from the

available ones to be used for the actual positioning, in order to eliminate the errors due

to large number of APs. Denote the set of all available APs found within all the RPs by

L with |L| = L. Then the AP selection step is to determine a subset of APs, M ⊆ L,

such that |M| =M ≤ L.

The AP selection process is carried out by applying the AP selection operator Φ on

the online measurement vector r as defined in (3.18). Each row of Φ, is a 1 × L vector

that selects the desired lthm AP, where lm ∈ M, by assigning ϕ(lm) = 1 and zero to the

rest of the elements, namely:

ϕm = [0, ..., 0, 1︸︷︷︸lm−th element

, 0, ..., 0], lm ∈ M,∀m = 1, 2, . . . ,M (3.19)

In this thesis, three AP selection schemes are used based on APs stabilities and

differentiability in spatial domain. Their performances are evaluated in a later chapter.

1. Strongest APs [39]


This scheme selects the set of M APs with the strongest RSS readings from the

online RSS measurement vector. These APs with strong RSS readings are more

reliable than the ones with weak RSS readings, as they provide a high probability

of coverage over time. The set of APs can be obtained by sorting the elements

of the online measurement vector r in descending order and selecting indices of

the first M values that correspond to the APs with highest RSS readings. Since

the online RSS readings are different for each run, the AP selection operator Φ is

created dynamically on the device for each update during the online phase.

2. Fisher Criterion [38, 66]

This scheme selects the APs which discriminate themselves the best within RPs.

The discrimination ability for each AP i, i ∈ {1, 2, . . . , L} can be quantified through

the Fisher criterion. The metric for AP i, denoted as ξi is defined as

ξi =

∑(j,o)∈CRSS

(ψ(o)i,j − ψi)

2∑(j,o)∈CRSS

∆(o)i,j

(3.20)

where ψi =1N

∑(j,o)∈CRSS

ψ(o)i,j . The APs with highest ξi are chosen to construct

the AP selection operator Φ for the actual localization. This metric accounts

for two factors: the denominator ensures that RSS values should not vary too

much over time, thus implies that the offline and online values are similar and

the numerator evaluates the discrimination ability of each AP by considering the

strength of variations of mean RSS across RPs. Since this metric calculations are

done across the RPs j at orientation o chosen in the coarse localization stage,

(j, o) ∈ CRSS, the AP selection operator Φ is created dynamically on the device for

each update during the online phase.

3. Random Combination

Unlike the above two schemes, which select the appropriate APs based on different

criteria and create the AP selection operator Φ dynamically for each update, the


random combination scheme does not take into account the performance of the

APs and thus have less computation complexity during online phase and also does

not require large number of RSS time samples for the variance calculation in the

offline phase as required by the Fisher criterion. The AP selection operator Φ is

defined as a randomly generated i.i.d. Gaussian M ×L matrix. Thus, according to

(3.18), y = Φr, y is a set of M linear combinations of online RSS values from L

APs. Since the same matrix can be reused for each update, it can be generated and

stored first during the training period and retrieved for use directly in the online

phase, saving the time to dynamically generate the matrix as required by the other

two schemes.

B. Orthogonalization and Signal Recovery using ℓ1-minimization

Compressive sensing theory requires both sparsity and incoherence of the signal, so that

it can be recovered accurately. Although the localization problem as defined in (3.18)

satisfies the sparsity requirement, Φ and Ψ are in general coherent in the spatial domain.

Thus, an orthogonalization procedure is applied to induce the incoherence property as

required by the CS theory [67,68].

The orthogonalization process is done by applying an orthogonalization operator, T,

on the vector y, such that z = Ty. The operator is defined as

T = QR† (3.21)

where R = ΦΨ, and Q = orth(RT )T , where R† is a pseudo-inverse of matrix R and

orth(R) is an orthogonal basis for the range of R. By applying this operator on y, (3.18)

becomes:

z = Ty = QR†y

= QR†Rθ +QR†ε

= Qθ + ε′

(3.22)


where ε′ = Tε. If M is in the order of log N , the minimum bound required by the

CS theory, θ can be well-recovered from z with very high probability, by solving the

following ℓ1-minimization problem [67,68].

θ = argminθ∈RN

∥θ∥1, s.t. z = Qθ + ε′. (3.23)

The computation complexity of the ℓ1-minimization algorithm grows proportional to

the dimension of vector θ, which is the number of potential RPs. Therefore, the coarse

localization stage, which reduces the area of interest from all the N RPs into a subset

of N < N RPs, reduces the computational time and resources required for solving the

ℓ1-minimization problem, and thus allows this procedure to be carried out by resource-

limited mobile devices.

C. Interpretation of Actual Position

The above procedure is able to recover the exact position, if the mobile user is located at

one of the RPs facing one of the orientations in the set ofO, which is the assumption made

earlier in order to formulate the localization problem into a 1-sparse natured problem.

However, in real situation, the mobile user may not be located at an RP facing a certain

orientation. Thus, in actual implementation, the recovered position vector θ is not a

1-sparse vector, rather a vector with a few non-zero coefficients. A post-processing step

is conducted to interpret this recovered location vector θ into an actual location and

compensate the error induced by the grid assumption. The procedure chooses the set of

all indices of the dominant elements in θ, which are above a certain threshold λ, denoted

as R

R = {n|θ(n) > λ} (3.24)

λ = λ1 max(θ) (3.25)

where λ1 is a parameter within a range (0, 1) and is adjusted experimentally. Then, the

estimated location of the mobile user can be calculated as a weighted average of these


potential candidate points, using the normalized value in θ as the corresponding weight

for each potential RP, that is

p = (x, y) =∑n∈R

ηn · (xn, yn) (3.26)

where ηn = θ(n)/∑

n∈R θ(i) and (xn, yn) is the cartesian coordinates of RP n.

3.3.3 Interaction between the database server and the mobile

device during online phase

The roles of the mobile device and the server during the online phase are illustrated in

Fig. 3.2. First, the device collects the online RSS readings from all the detectable APs,

namely r. Then the device requests the map and the representative RSS readings for each

cluster from the server, in order to perform coarse localization. After the best-matched

clusters are found, the device communicates with the server to obtain the relevant radio

map matrix Ψ for the following fine localization. The device carries out steps of AP

selection, orthogonalization and ℓ1-minimization to obtain the recovered location vector

θ. Finally, the device asks the server for the potential candidate RP’s coordinates and

computes the estimated position according to θ.

3.4 Chapter Summary

In this chapter, the proposed compressive sensing based positioning system is described

in details. The system involves two phases. The offline phase is the training period

that collects RSS values from detectable access points at reference points to create the

fingerprint database. It also runs the affinity propagation algorithm to create different

clusters of RPs with similar RSS reading patterns and within physical proximity. The

actual localization takes place in the online phase, which consists of two stages. First,

the mobile device collects the online RSS readings, which are used to find the subset of


Mobile Device Server

Collect online RSS readings, r

Request and obtain map and RSS values of exemplars.

Find best matched cluster exemplars, S

AP selection

Retrieve map and RSS readings of exemplars

Use the received matched cluster exemplars S to obtain the matched cluster members C and generate a

smaller radio map matrix Ψ Coarse

Localization(cluster

matching)

Fine Localization(CS-theory)

It contains: Ψ(o), ∆_j(o), H(o), C_j(o)

- list of RPs coordinates - map

REQUEST

SEND

SEND S

Orthogonalization

l1-norm minimization

Interpret device’s location using relevant RPs coordinates.

Retrieve relevant RPs’ coordinates

REQUESTRPs’ coordinates

SEND RPs’ coordinates

Send Ψ , ∆_j(o)Obtain Ψ , ∆_j(o) SEND

Figure 3.3: Interaction between the database server and the mobile device during online

phase.

relevant RPs by the coarse localization stage through cluster matching process. Several

cluster matching schemes are discussed in an attempt to reduce the effect of outliers and

derivations in RSS readings between offline and online phases. This stage reduces the area

of interest from the whole database into a smaller region, thus reducing the computation

time for the latter stage, and also minimizes the effect of outliers and RSS time varying

derivations. Then, a fine localization stage is applied on this reduced area to find the

estimated position. It is done by formulating the localization problem into a sparse-

natured signal recovery problem, such that the compressive sensing theory can be applied

to recover the desired signal. There are several steps to compute the estimated position:

access point selection, orthogonalization, ℓ1-minimization problem and interpretation of

recovered location vector into actual location, which are described in the chapter.

The chapter also explains different roles of the mobile device and the server in the


proposed system. The server is mainly served as a database storage, which when re-

quested by the device, sends required information, such as map and RSS readings to

the device. It is also responsible for running the affinity propagation algorithm to form

clusters during offline phase, as the device does not have enough computation resources

to run such clustering scheme. The mobile device collects the RSS readings and obtains

information from the server, in order to estimate its location locally.

Chapter 4

Indoor Tracking System

The previous chapter describes a positioning system that can accurately estimate a sta-

tionary user’s position. This positioning system is modified in this chapter in order to

track the dynamic mobile user. The proposed indoor tracking system uses the Kalman

filter with map information to smooth out the location estimate and also uses previous

position estimate to choose the relevant region of interest in the coarse localization stage.

This chapter first describes the Kalman filter and then the proposed indoor tracking

system.

In this chapter, the tracking problem is defined as follows. The device carried by

the mobile user periodically collects the online RSS readings from each APs at a time

interval ∆t, which is limited by the device’s network card and hardware performances.

The online RSS readings vector is denoted as r(t) = [r1(t), r2(t), . . . , rL(t)], t = 0, 1, 2, ...,

where rl(t) corresponds to the RSS from AP l at time t. Then, the indoor tracking system

uses these RSS readings to estimate the user’s location at time t, which is denoted as

p(t) = [x(t), y(t)]T .

46

Chapter 4. Indoor Tracking System 47

4.1 General Bayesian Tracking Model

The tracking problem of a mobile user can be modeled by a general Bayesian tracking

model as follows [41] and [47]:

x(t) = ft(x(t− 1),w(t)) (4.1)

z(t) = ht(x(t),v(t)) (4.2)

where x(t) = [x(t), y(t), vx(t), vy(t)] is the state of the user at time t with (x(t), y(t))

as the Cartesian coordinates of the user’s location and vx(t) and vy(t) as the velocities

in x and y directions, respectively. Assuming the tracking is a Markov process of order

one, the state evolves as a function ft of previous state and w(t), i.i.d. process noise

vector only. In addition, the measurement z(t) depends on the current state and the

i.i.d. measurement noise vector v(t) through the function ht.

The current location of the mobile user, x(t) can then be estimated recursively from

the set of measurements up to time t, i.e. z(1 : t) = {z(i), i = 1, ..., t}, in terms of the

probability distributive function (pdf), denoted as p(x(t)|z(1 : t)). Assuming that the

initial pdf p(x0|z0) ≡ p(z0) and p(x(t−1)|z(1 : t−1)) are known, the pdf p(x(t)|z(1 : t))

can be obtained by the following prediction and update stages:

1. Prediction Stage:

The prior pdf p(x(t)|z(1 : t−1)) can be predicted based on p((x(t)|x(t−1)), which

is defined by the state process equation (4.1) and the previous state pdf.

p(x(t)|z(1 : t− 1)) =

∫p((x(t)|x(t− 1))p(x(t− 1)|z(1 : t− 1))dx(t− 1) (4.3)

2. Update Stage:

Then, the prior pdf can be updated by the measurement z(t) obtained at time t


using the Bayes’ rule,

p(x(t)|z(1 : t)) =p(z(t)|x(t))p(x(t)|z(1 : t− 1))

p(z(t)|z(1 : t− 1))(4.4)

p(z(t)|z(1 : t− 1)) =

∫p(x(t)|z(1 : t− 1))dx(t) (4.5)

where p(z(t)|x(t)) is defined by the measurement model (4.2).

4.2 Kalman Filter

If the process and measurement noises are assumed to be Gaussian and the motion

dynamic model is linear, i.e. the process and measurement functions ft and ht are linear

in equations (4.1) and (4.2), then the general Bayesian tracking model is reduced to

a Kalman filter. The optimal solution can be obtained for this Kalman filter as the

minimum mean square estimates (MMSE). The process and measurement equations of

the Kalman tracking model can be formulated as

x(t) = Fx(t− 1) +w(t) (4.6)

z(t) = Hx(t) + v(t) (4.7)

where x(t) = [x(t), y(t), vx(t), vy(t)]T is the state vector and z(t) is the measurement

vector. The process noise w(t) ∼ N (0,S) and the measurement noise v(t) ∼ N (0,U)

are assumed to be independent with the corresponding covariance matrices S and U.

The matrices F and H in (4.6) define the linear motion model. For the tracking

problem, they are assigned as follows:

F =

1 0 ∆t 0

0 1 0 ∆t

0 0 1 0

0 0 0 1

H =

1 0 0 0

0 1 0 0

(4.8)

That means the current location of the mobile user is assumed to be the previous location

of the user plus distance traveled, which is computed as the time interval ∆t times the


current velocity, and is corrupted with Gaussian noise. The current measurement should

be the current location subject to Gaussian noise.

By assigning the initial conditions of x(0) and P(0), the steps to obtain the final

estimates of state vector x(t) and the error covariance P(t) are computed as follows:

1. Prediction Stage

x−(t) = Fx(t− 1) (4.9)

P−(t) = FP(t− 1)FT + S (4.10)

2. Update Stage

K(t) = P−(t)HT (HP−(t)HT +U)−1 (4.11)

x(t) = x−(t) +K(t)(z(t)−Hx−(t)) (4.12)

P(t) = (I−K(t)H)P−(t) (4.13)

For each time step t, the measurement vector z(t) in (4.12) is the current user’s esti-

mated location computed by the positioning system. After the state vector is estimated,

the final filtered estimate of the user’s location can be found as:

p(t) = Hx(t) (4.14)

4.3 Overview of Proposed Indoor Tracking System

The Kalman filter can be applied on the CS-based positioning system described in the

previous chapter to improve the accuracy in estimating the dynamic user’s trajectory.

Fig. 4.1 shows the proposed indoor tracking system that is built on top of the CS-based

positioning system. As compared to Fig. 3.1, there are two major modifications for the

tracking system. Besides the introduction of the Kalman filter stage after the end of

the fine localization stage, the tracking system also has a different coarse localization


stage that uses the previous user’s position estimate in aiding the selection of relevant

area of interest. The offline phase and the fine localization stage in the online phase

remain unchanged for the tracking system. The following subsections describe these two

modifications of the tracking system.

Online Phase

Offline PhaseFingerprinting

RSS Collections in 4 orientations

Coarse Localizationcluster matchingbased on

1) RSS readings2) Physical proximity

within previous position

Fine LocalizationCompressive Sensing

online RSS readings

Computed Location

Orthogonalization

L1-norm minimization

AP selection

ClusteringAffinity Propagation

TrackingKalman Filter with Map Information

Final Estimated Location

r(t)

Delay

Navigation1) Location analysis with routed path

2) Generation of voice commands

Voice Command

ˆ ( 1)p t −

ˆ ( )p t

( )p t�

Figure 4.1: Block diagram of the proposed indoor tracking system.

4.3.1 Modified Coarse Localization Stage

During the online phase, the device periodically collects the online RSS readings. The

online measurement vector collected at time t, denoted as r(t) is first evaluated at coarse


localization stage to reduce the area of interest by selecting the relevant RPs in the

database for the fine localization stage. In addition to using the online RSS readings to

find the relevant RPs, the tracking system also uses the previous user’s position estimate

to select the appropriate RPs. Fig. 4.2 depicts the coarse localization stage employed

by the tracking system. The modified coarse localization stage chooses the relevant RPs

based on two criteria: Group I) online RSS readings, and Group II) physical proximity

of previous estimate.

Group IChoose clusters of RPs

with similar RSS

Group IIChoose RPs within physical proximity

Fingerprint Database

r(t)

Find Common RPs

CRSS

CDist

C

O

ˆ ( 1)p t −

Figure 4.2: Coarse localization stage for the proposed tracking system.

Group I: RPs with similar online RSS readings

The system first selects the clusters of RPs defined in the offline stage that have similar

RSS reading patterns to the online RSS vector r(t). This cluster matching process is the

same as that described in Section 3.3.1. In summary, the system uses one of the cluster

matching schemes to evaluate the cluster matching similarities to the online RSS vector,

i.e. {SMatch(r(t), j)(o),∀j ∈ H(o),∀o ∈ O} and then selects the best-matched clusters

CRSS according to (3.13).


Group II: RPs within physical proximity

Besides the use of the online RSS readings to choose the relevant RPs, they can be

chosen by finding the possible range of the device’s current location based on the previous

estimated location, p(t− 1) = (x(t− 1), y(t− 1)). Since a person cannot walk far away

within a short period of time, it is reasonable that the system can limit the region of

interest into the possible walking range based on the previous estimated position, if it is

known and reliable. There are two schemes to choose this possible walking range and are

discussed as follows.

1. Unpredicted - Based only on previous estimation

This scheme selects a set of RPs that are within walking distance during the spec-

ified update time interval to the previous estimated location, that is

CDist = {j|√

(xj − x(t− 1))2 + (yj − y(t− 1))2 < β, j ∈ {1, . . . , N}} (4.15)

where (xj, yj) is the location of RP j and β is the walking distance within the

specified update time interval ∆t.

2. Predicted - Based on previous estimation and prediction using linear motion model

This scheme uses the previous estimated location to predict the current possible

location based on a linear motion model and then chooses the RPs which are within

the walking range of this predicted position. The same linear model used by the

Kalman filter defined in (4.8) and (4.6) without the addition of Gaussian noise can

be used to predict the user’s current locations, denoted as p(t):

p(t) = HFx(t− 1) (4.16)

where x(t − 1) = [x(t − 1), y(t − 1), vx(t − 1), vy(t − 1)]T is the state vector with

(x(t−1), y(t−1)) = p(t−1) as the previous user’s estimated position computed by

the tracking system. The velocities in x and y directions, represented as vx(t− 1)


and vy(t − 1), respectively, can be defined in several ways. First, if both of them

are set to zeros, then the predicted location is the same as the previous estimate,

p(t) = p(t − 1). This is equivalent to the previous described scheme. Second, if

the user is known to be walking at a constant speed, these values can be assigned

accordingly. However, for real applications, a user may walk to a random direction

at a random speed. Thus, it is necessary to find a way to predict the user’s velocity

at each time interval, in order to have a good estimation for the current location.

The estimation of these velocities can be obtained from the output of the Kalman

filter, which is implemented after the fine localization stage and will be described

in Section 4.3.2. Then, the state vector for (4.16) can be assigned directly as the

final estimate of the state vector for the Kalman filter, i.e. x(t− 1) = x(t− 1).

The system then selects a set of RPs which are in close proximity to this predicted

current location p(t) = [p1(t), p2(t)]T , that is:

CDist = {j|√

(xj − p1(t))2 + (yj − p2(t))2 < β, j ∈ 1, . . . , N} (4.17)

After the selection of these two groups of relevant RPs based on RSS readings simi-

larities and physical proximities, the system then includes the common RPs that appear

in both groups as the set of reduced region, where the final localization stage is applied.

The common RPs is obtained as a set C,

C = CRSS

∪{(j, o)|j ∈ CDist and o ∈ O} (4.18)

This set contains RPs that satisfy both conditions of similar RSS readings to the

online RSS measurement and within close range to the user’s previous location. Thus,

they are very likely to be the possible locations that the current user is located. By

introducing the constraint of physical range, the system is able to identify the instants

when the online RSS readings collected is not useful to find the user’s position. In normal

operation, the user must be within a range around his previous location. If the selected


clusters of RPs in CRSS are far away from the previous location, then the online RSS

readings can be regarded as invalid, as there are large deviations between the online

readings and offline database, so that the cluster matching based on similarities of RSS

readings fails to find the correct clusters of RPs. This scenario leads to an empty set of C

and halts the fine localization stage. If such thing occurs, the system discards this online

RSS measurement vector and obtains a new one to restart the localization process.

There may be a possibility that all the consecutive online RSS measurement vectors

lead to empty sets of C. This makes the system continuously collect a new online RSS

measurement, which is then discarded, preventing it from computing the true estimate of

the user’s location. This happens as the previous position estimate is not accurate and

hence the selection of RPs based on such estimate does not match with the RPs selected

based on the online RSS measurement vector. Thus, the system is reset to use only the

online RSS measurement vector to select the RPs, when Nempty consecutive online RSS

measurement vectors are discarded, arguing that the previous position estimate is no

longer valid to reduce the localization problem into a smaller relevant region.

After a successful computation of finding the non-empty set of C, the modified radio

map matrix ΨL×N , N = |C| can be obtained as

Ψ = [ψ(o)j ,∀(j, o) ∈ C]. (4.19)

This matrix will then be used by the fine localization stage. The fine localization

stage for the tracking system remains the same as the one in the CS-based positioning

system, which is already described in Section 3.3.2. Since the estimated user’s position

computed by the fine localization stage is then fed into the Kalman filter to obtain the

final estimate in the tracking system, such temporal solution is referred to as p(t) in this

chapter, which indicates that it is not the final solution.


4.3.2 Map-Adaptive Kalman Filter

After the computation of the location estimate, p(t) at the end of the fine localization

stage, the Kalman filter described in Section 4.2 is applied to enhance the tracking

performance. By substituting z(t) = p(t) into the Kalman filter updating equations

(4.9) to (4.14), the final estimated position p(t) can be obtained from the estimated

state x(t) according to (4.14).

In real situation, the Kalman filter is able to enhance the tracking performance when

the user is walking along a corridor inside a building, as the linear motion assumed by

the filter is sufficient to model the user’s trajectory. However, when the user is making a

turn at an intersection, the linear model does not apply on this behavior which involves

abrupt change in direction and hence the Kalman filter requires several more updates to

reflect the user’s true trajectory and thus leads to more errors in position estimate.

This issue can be addressed by updating the Kalman filter according to the map

information. Since the Kalman filter behaves the best when the user is walking straight

along a corridor but performs poorly around the intersections, the Kalman filter is reset

when the user is in the region of intersection. Prior to the actual tracking, the map of

region of interest is studied to extract a list of intersections which are represented as non-

rotated bounding boxes, denoted as a set Rintersection = {(ximin, yimin), (x

imax, y

imax)| i =

1, ..., B}, where (ximin, yimin) and (ximax, y

imax) are the lower-left and upper-right corners

respectively of intersection i and B is the number of intersections found on the map.

Thus, the user is within the intersection region i at time tturn if the below two conditions

are satisfied:

ximin ≤ x(tturn) ≤ ximax

yimin ≤ y(tturn) ≤ yimax

(4.20)

When the user is within any of the intersection regions, the Kalman filter is reset

by reassigning the state vector and covariance matrix at time tturn, which are the initial


conditions for this new Kalman filter. Namely,

x(tturn) = [p(tturn), 0, 0]T

P(tturn) = P(0)

(4.21)

Then, the Kalman filter is updated as normal according to (4.9) to (4.13) for the next

estimate at time (tturn+1) using z(tturn+1) = p(tturn+1). This removes the inaccurate

estimation by the Kalman filter when the user is making a turn. Fig. 4.3 summarizes

how the Kalman filter is applied on the proposed tracking system.

4.4 Chapter Summary

This chapter modifies the CS-based positioning system described in the previous chapter

into a tracking system, which is able to improve the accuracy in estimating the mobile

user’s locations. By using the user’s previous estimated locations, the tracking system

is able to refine the current estimate in two ways: 1) to select appropriate RPs in the

coarse localization stage and 2) to apply Kalman filter for better location estimate.

First, during the coarse localization stage, a set of RPs that are within walking range

to the i) previous estimated location p(t − 1) or ii) the predicted current location p(t)

based on the previous estimated location, are selected as the potential region of interest,

arguing that a user cannot be physically far away within a short period of time in the

indoor environment. The RPs appeared in both set of CDist, found based on previous

estimated location and the set of CRSS, determined by the original cluster matching

scheme for the CS-based positioning system, are then used to generate a modified radio

map matrix Ψ that is required for the fine localization stage. This modified coarse

localization stage ensures that the reduced region of interest are within the walking

range of the user and provides a way to reject the invalid online RSS readings when no

common RPs are found in both sets.

The tracking system also introduces the Kalman filter stage, which uses the temporal


Given:

Intersections Set: Rintersection = {(ximin, yimin), (x

imax, y

imax)| i = 1, ..., B}

Inputs:

Computed estimate from fine localization stage: p(t)

Final estimate of previous update: p(t− 1) = (x(t− 1), y(t− 1))

Outputs:

Final estimate of current update: p(t) = (x(t), y(t))

Kalman Filter:

Initial conditions

x(0) = [p(0), 0, 0]T ,P(0)

Check if user is already at intersection

for i = 1, . . . B

if (ximin ≤ x(t− 1) ≤ ximax and yimin ≤ y(t− 1) ≤ yimax) then

At intersection, reset Kalman filter

x(t− 1) = [p(t− 1), 0, 0]T

P(t− 1) = P(0)

break for loop

endif

endif

Update

set z(t) = p(t) to update the Kalman filter through (4.9) to (4.13)

compute for p(t) according to (4.14)

Figure 4.3: Map-Adoptive Kalman Filter


position estimation, p(t), computed at the end of the fine localization stage as the input

to update the previous estimated location p(t− 1) into the current final estimation p(t).

Since the Kalman filter performs poorly when the user makes turns and thus does not

follow the linear model, the proposed tracking system is designed to reset the Kalman

filter whenever the user is in an region of intersection, which is a possible place for the

user to make turns.

Chapter 5

Simple Navigation System

The proposed indoor tracking system can be implemented on mobile devices to provide

reliable and accurate real-time location estimates of the mobile user and thus is adequate

to provide location based services to the user. As an illustration and a way to evaluate

the performance of the tracking system, a simple navigation system is designed and

implemented on top of the tracking system to provide real-time guidance to the user to

reach the desired destination. The design and the implementation of such navigation

system is described in details in this chapter.

5.1 Overview of Navigation System

The goal of the navigation system is to decide a path between the user’s current location

and his desired destination and then provide guidance, which can be in the form of voice

instructions to let the user follow this planned path. In addition, the location updates,

{p(t), t = 1, ...}, generated periodically by the tracking system are fed into the navigation

system to generate adequate instructions that are helpful to the user to get familiar with

the surrounding area. All of these operations require a detail map database that stores all

the map-related data for path routing and guidance. Fig. 5.1 illustrates the navigation

system. It consists of a map database, which is generated at the initial set up to provide

59

Chapter 5. Simple Navigation System 60

the required map information for the navigation system; a path routing module, which

generates the path that leads the user to reach the destination and a tracking update

analysis module, which generates appropriate voice instructions according to the user’s

locations.

During Real-TimeNavigation

Initial SetupMap Database Generation

- represent the layout as a connected graph- define coordinates of special map features- create audio files for all possible voice commands

Path Routing ModuleTracking Update Analysis Module

User-defined destination

Indoor Tracking System

Require reroute?

Yes

No

Voice Instructions

Routed path

ˆ (0)p ˆ ( )p t

ˆ ( )p t

Figure 5.1: Navigation System Overview

5.2 Map Database Generation at Initial Setup

The navigation system relies heavily on the map of the region of interest, which illustrates

the layout of different features such as rooms, corridors, elevators, etc. For the initial

setup, different map features are extracted from the map, which allow the system to

generate a feasible path and descriptive instructions about the surrounding to the user

during the actual navigation process. The map database generation can be divided into

two operations: i) to represent the map layout as a connected path and ii) to define

locations of the map features.


5.2.1 Layout Definition

The layout of the map is interpreted as a connected graph, so that the path routing

problem can be transformed into a graph problem [56], which is solved by the path

routing module described in the later section. The nodes of this graph are a set of

Cartesian coordinates of the possible passage points along the corridors or destinations.

Two nodes are connected together with an edge, if both nodes can reach each other

physically without obstacles in their ways. A non-negative weight is assigned to each

edge and is defined as the Euclidean distance between the connected nodes. In order to

ensure that at least one feasible path can be generated for all the destinations defined on

the map, the graph must be connected meaning that there must be a path, which is a

set of edges that connect any pairs of nodes defined in this graph. This connected graph

can be represented as G = (E, V ), where E is a set of edges and V is a set of nodes. The

weight of the edges can be represented as a matrix DG = [dGij]|V |×|V |, where dGij

th entry

corresponds to the Euclidean distance between node i and node j if they are connected

by an edge, otherwise the value is set to infinity which implies the two nodes are not

connected to each other.

5.2.2 Map Features Definition

In order to provide more information about the surrounding environment, which will be

useful to help user to get familiar with the area, a list of map features can be extracted

from the map to generate a more comprehensive map database for the navigation sys-

tem. This list of the map features can include general facilities and accesses and can be

expanded as needed depending on user’s preferences. Washrooms, elevators and stairs

are some examples of map features that are of interest to users. The list of the features

can be stored as a set Fmap = {(pjf ,Featurej), j = 1, ..., nF}, where pjf = (xjf , yjf ) is the

location of feature j and Featurej is the feature’s name and nF is the total number of


map features defined on the map.

5.3 Path Routing Module

At the beginning of the actual navigation, the device first obtains the user’s input of

the desired destination and user’s current location, which can be either specified by the

user or estimated by the device using the proposed tracking system. Then, the system

identifies the source node, vsource and the target node, vtarget on the connected graph

predefined in the setup stage, that are closest to the user’s current location and the

destination, respectively. The path routing problem is interpreted as finding the shortest

path between these two nodes on the connected graph [56]. This problem can be easily

solved by applying the Dijkstra algorithm, which is described in [69] and is summarized

in Fig. 5.2.

5.3.1 Path Analysis

After a set of nodes sequence, P , which constitutes the shortest path from the user’s

current position to the destination, is generated, the path is then analyzed to produce

necessary navigation information to the user.

The generated path is first divided into series of line segments, such that consecutive

line segments are pointing at different directions and the connected point between the

two segments becomes the turning point. This set of line segments extracted for the path

P can be denoted as Pl = {ℓ1, ℓ2, ...ℓS}, where S is the total number of line segments

and each segment is denoted as ℓi = {pis,pie}, where pis = (xis, yis) and pie = (xie, y

ie)

are the starting and ending points of the ith line segment, respectively. The turning

points are identified as the ending points between line segments, that is T = {pie|i =

1, . . . , S − 1}. Based on these generated line segments, the system is able to determine

the turning points, the direction of turns and the distance traveled at each line segment


Given:

Connected graph of the map layout with weight: G(E, V ), DG = [dGij]|V |×|V |

Inputs:

User’s current location: p(t) → Source node: vsource

Destination location → Target node: vtarget

Outputs:

A list of nodes of the shortest path from target node to source node: P

Dijkstra:

Initializations:

d = [d(1), ..., d(|V |)]; {d(vi) = ∞, ∀vi = vsource ∈ V }, d(vSource) = 0

e = [e(1), ..., e(|V |)]; {e(vi) = −1,∀vi ∈ V }

Vunvisited := V

Actual operations:

while Vunvisited is not empty

u = argminVunvisisted

d, remove u from Vunvisited

exit while loop if d(u) = ∞ or u == vtarget

for each v in Vunvisited

exit foreach loop ifdGuv == ∞

a = d(u) + dGuv ; if a < d(v) then d(v) = a; e(v) = u

Determine path sequence:

u := vtarget, P = {}

insert u at beginning of P and u := e(u) while e(u) = −1

Figure 5.2: Dijkstra Algorithm


which facilitate the analysis of the user’s current locations in the tracking update analysis

module.

In addition, the system also finds out a list of relevant map features that appeared

along this generated path. For each line segment i, the system chooses the map features

from the set Fmap that are within βf meters from the line segment i and form a set

F ipath ⊆ Fmap. These sets {F i

path, i = 1, . . . , S} are useful for the system to effectively

determine if the user is close to these map features when he is following the path correctly,

and thus save the system from searching the full map feature set Fmap for each tracking

update.

5.4 Tracking Update Analysis Module

Tracking Module(periodic update )

Reach destination?

Match to one of line segments in path?

Near end of the line segment?

Determine if user turn left or right

Is walking in wrong direction ?

Routing Module

Voice Generation Engine

(1) “Please wait for rerouting” (2) “Go straight” (3) “Prepare to turn left /right” (4) “Turn left/right” (5) “Wrong direction” (6) “<map feature> is on your left/right” (7) “You have arrived at <destination>”

Are there any nearby map

feature?

Yes

Yes

No

Yes

No

For Noffpath

consecutive updates

For Nwrong direction

consecutive updates

No

NoNo

Yes

Yes

(1)

(3), (4)

(2)

(5)

(6)

(7)

ˆ ( )p t

Figure 5.3: Tracking update analysis

After the generation of the path that can lead the user to his targets, the device


starts the tracking system to keep track of user’s position. For each tracking update,

the analysis module compares the location estimate to the routed path to check if the

user follows the path properly and then generate voice instructions when necessary. The

analysis process is illustrated in Fig. 5.3.

5.4.1 Analysis Process

The analysis module first determines if the user already reaches the destination by check-

ing the Euclidean distance between the user’s current position and the target being within

a range of βdestination. If the user is at the destination, the module generates the voice in-

struction stating that the destination is reached and stops tracking system and navigation

module automatically.

pis = (xi

s, yis )

p ie = (xi

e, yie )

pi

ˆ ˆ ˆ( ) ( ( ), ( ))t x t y t=p

Figure 5.4: A point in close range to a line segment

Otherwise, the module attempts to match the user’s current position p(t) to one of

the line segments in the generated path set Pl. If this tracking update is close to line

segment ℓi as illustrated in Fig. 5.4, then we can find the projection and the minimum

distance of the tracking update point p(t) to the line segment ℓi by solving the two

equations [70]:

pi = pis + µi(pie − pis) (5.1)

(p(t)− pi) · (pie − pis) = 0 (5.2)

where pi is the projected point which is collinear with pis and pie, and µ is the ratio in

terms of the distance between pis and pie indicating how far the point pi is away from pis.


By substituting (5.1) into (5.2), the solution to µi is

µi =(p(t)− pis) · (pie − pis)

∥pis − pie∥2(5.3)

If the computed µi is within the range [0, 1], then the projected point falls onto the line

segment, which implies that the update estimate is within the range of this line segment.

By substituting (5.3) back into (5.1), the projected point pi can be computed and the

shortest distance of the tracking update point to the line segment can be obtained as

dimin = ∥p(t)− pi∥.

The system determines that the tracking estimate p(t) follows the line segment ℓi if

i) µi ∈ [0, 1] and ii) dimin < βpath. If there are consecutively Noffpath tracking estimates

failing to match with any of the line segments in Pl, the analysis module assumes that

the user does not follow the path properly. Thus, the analysis module will ask the user

to stop walking and inputs the user’s current position as the starting point to the path

routing module to reroute an alternate path for the user to reach the destination.

The value of µi is also a good indicator to tell if the user is walking along the path

properly. In normal situation, where the user follows the path correctly, the value of µi

should increase from zero to one along the same line segment ℓi for consecutive tracking

updates and then eventually move to the next segment ℓi+1, where the value of µi is no

longer valid and the value of µi+1 is then computed. Thus, when µi, i < S is close to

one, this indicates that the user is close to the end of the line segment ℓi, where a turn is

required for the user to move to the next line segment ℓi+1. The direction of turn can be

determined by finding the positive angle difference, ∆ρi between the two vectors that are

formed by joining the starting and ending points of the current and next line segments

as illustrated in Fig. 5.5. For simplicity, the module only identifies either a left or right

turn.

The module assumes a very simple scheme to determine the orientation of the mobile

user. For each tracking update, a direction vector is computed between the current update

and the previous one and then is compared with the currently matched line segment


pis = (xi

s, yis )

pie = (xi

e, yie ) = Pi+1

s = (xi+1s, y

i+1s )

Pi+1e = (xi+1

e, yi+1

e )

iρ�

1iρ +�

11) i i iρ ρ ρ+∆ = −� �

2) if 0 , then 360i i iρ ρ ρ∆ < ° ∆ = ∆ + °3) if 90 , then it is a right turn

else if 180 , then it is a left turn

i

i

ρρ

∆ ≈ °∆ ≈ °

Figure 5.5: Determining the direction of turn based on the two line segments ℓi and ℓi+1

direction. If consecutive Nwrong direction tracking updates are in opposite direction of the

line segment, then a voice command of wrong direction is issued to the user.

Finally, the analysis module computes the Euclidean distance between the user’s

current estimate p(t) to the map features in F ipath, where i corresponds to the line segment

i that the user is currently following. If the distance is smaller than βf , then the module

will generate the corresponding voice command regarding this specific map features to

the user.

5.4.2 Voice Generation

The voice instructions of the analysis module can be generated on-the-fly by using text-

to-speech (TTS) engine. However, TTS engines are not readily available for free to be

used on smart devices and render delays in giving real-time instructions to the user. Thus,

the navigation system uses an alternate method to obtain the voice commands. Since the

navigation system only has a small library of instructions, all of these commands are first

created and saved as audio files during initial setup. The audio can be generated from

text by using the online AT&T Natural VoicesR⃝ Text-to-Speech Demo [71]. Then, the

analysis module determines which instructions are needed and plays the corresponding

audio files. Although these audio files occupy extra amount of memory spaces on the

smart devices, the system is able to generate reliable voice instructions in real time, which


may not be achievable by using the TTS engines.

5.5 Chapter Summary

This chapter describes the navigation system that is built on top of the tracking system

to provide guidance to the user. The navigation system requires an initial setup to

extract information from the map and generates pre-determined voice instructions that

are used by the actual navigation process. The navigation system is then divided into two

modules. One is the path routing module, which takes in the user’s current location and

desired destination as inputs to generate a feasible path based on the connected path

defined according to the layout of the map and identifies the turning points and map

features found along this path. Then, the tracking update analysis module uses the path

information along with the current user’s estimated position to determine the appropriate

voice instructions to be given to the users. This navigation system is implemented on

the smartphone and its details are found in the next chapter.

Chapter 6

Software Implementation on Mobile

Devices

This chapter describes how the indoor CS-based positioning and tracking system, along

with the navigation application described in Chapters 3 to 5 are implemented as a soft-

ware on the PDAs and smartphones.

6.1 Software Platform

The software is developed on PDAs and smartphone that are installed with Windows Mo-

bile operating systems to implement the proposed indoor tracking and navigation system.

Unlike Android platform [72], which has become popular just recently and only avail-

able on android-powered smartphones, the Windows Mobile platform has been developed

maturely and in addition to Window Mobile-powered smartphones, such platforms have

also been used on PDAs. The development of software application for the iPhone is also

ruled out as the wifi scanning functionality, which is the core requirement for the indoor

tracking system, is not provided by the Apple’s official software development kit (SDK).

Although there are private libraries available online to provide that function, they require

the jailbreaking of the iphone and thus violate the Apple’s development license [73], [74].

69

Chapter 6. Software Implementation on Mobile Devices 70

The software is written in C# using Microsoft .Net Compact Framework version 3.5 in

Visual Studio 2008. It utilizes two open source libraries available on the internet to relieve

the burden on developing the application on this platform. They are the OpenNetCF

library [75] and the DotNetMatrix library [76], which provide the WiFi RSS scanning

functions and basic matrix operations respectively.

6.2 Devices in Testing

The developed software has been deployed onto three different devices and their speci-

fications in comparison to a standard laptop of the same price level (around $ 600) are

shown in Table 6.1 [77–80].

Devices Processor

Speed

RAM Window Mobile

Version

WLAN WiFi Scan-

ning Rate

PDA1: HP iPAQ

hx4700

624 MHz 64 MB Pocket PC 2003

2nd

802.11b 1 sam-

ple/second

PDA2: HP iPAQ

hx2750

624 MHz 128 MB Pocket PC 2003

2nd

802.11b 1 sam-

ple/second

Smartphone:

Samsung Omnia II

800 MHz 256 MB Professional 802.11b/g 0.67 sam-

ple/second

Dell Inspiron 15

Laptop

2.2 GHz 4 GB Windows 7 802.11g

Table 6.1: Devices Specifications

It is obvious that the PDAs and smartphone have much more restricted resources in

processing power and memory than a standard laptop. Thus, indoor tracking systems

that use probabilistic approach [38] and particle filters [47, 51, 81] that require large

computation power may not be realizable on these devices. The proposed indoor tracking


system is implemented on these devices to illustrate that such system is a compact

algorithm that is able to provide real-time and accurate estimate of user’s location. The

performances of these devices are evaluated in Chapter 7.

Note that the Samsung smartphone is equipped with an accelerometer and a digital

compass. By using the Samsung Mobile SDK [82], the software is able to access these two

sensors. The maximum sampling interval that can be set by the SDK for these sensors

is 200 milliseconds. Attempts have been made to let the system utilize both sensors in

aiding to determine the user’s travel distances and orientations. However, the phone is

incompetent to handle both sampling of the sensors’ data and scanning the WiFi RSS

from APs at the same time and thus the program becomes unstable and often crashes

unexpectedly. Besides, the sampling rate and the response are too slow for both sensors

to let the system obtain useful real-time data within a short time interval for the tracking

updates. Thus, these sensors are not incorporated into the proposed tracking system in

this thesis.

Both of the PDAs use the WiFi network adaptor as the basic wireless connection

method, unlike the smartphone, which cellular reception precedes the WiFi reception.

Thus, the signal strength level and the refresh rate of the WiFi antenna of the smart-

phone are inferior to the ones in PDAs. By using the OpenNetCF library, the software

is able to detect the WiFi adaptor on the devices and then scan the detectable APs

with their unique media access control (MAC) address as their identifications and their

RSS readings. All the three devices require a duration of one second to accomplish this

operation. However, tests have shown that the smartphone is required to wait for 500

milliseconds between each scanning operations, rather than 100 milliseconds for both

PDAs, in order to detect valid RSS readings, thus proved that the refresh rate for smart-

phone is slower. Since the PDAs have a faster refresh rate, the performance evaluations

in the next chapter are focused on these PDAs.


6.3 Software Design

IndoorLocalizerProg

OpenNetCFOpenNetCF.Net

DotNetMatrixCF

Samsung Mobile SDK

MathAlgorithm

LocalizerBasicLibrary

Localization

Tracking

Navigation

IndoorLocResources

• Config.txt• Fingerprint Database with

clustered information• Map Database • Log files

Figure 6.1: The overview of the software design. Arrows shows the dependency of the

libraries and blue colored boxes are the developed modules for the software.

The overall design of the software is illustrated in Fig. 6.1. The screenshot of the

PDA shows the menu of the software, which has five major operations. The flowchart on

the left of the screenshot shows the dependencies of the libraries of the software design

structure. The resources, such as the fingerprint and map databases, which are needed

by the software are stored in a folder on the PDA and represented as the cylindrical

shape on this figure.

6.3.1 Software’s Functionalities

As depicted in Fig. 6.1, the software has five major operations. They are:

1. Detect APs, which run the WiFi scanning function provided by the OpenNetCF

library and displays the MAC address and RSS for each detectable APs in table

format as depicted in Fig. 6.2


Figure 6.2: An example screenshot of Detect AP operation.

2. Collect Fingerprints, which let the user to properly setup the tracking system by

collecting fingerprints and defining the map features on the screen;

3. Localize Yourself, which runs the CS-based position system described in Chapter

3 and displays the user’s position on the screen;

4. Tracking, which periodically collects RSS readings and runs the tracking system

described in Chapter 4 and displays the user’s position on the screen;

5. Navigation, which asks the user’s input of destination and implements the naviga-

tion system described in Chapter 5.

6.3.2 Resources Folder

There is a folder on the device that contains all the required resources to run the tracking

and navigation system properly and is accessible by the software. This folder, Indoor-

LocResources, also contains a configuration setting file, namely Config.txt, which defines

the device in test, the map scale ratios and also all the parameters that can be adjusted

for the tracking and navigation system. In addition, an image file, which displays the


map of the region of interest, is included to allow the software to use it to collect fin-

gerprints and displays user’s location properly on the screen. This image map is stored

as a bitmap format and is scaled, so that it can be showed properly on the screen of

smart devices. The same image map file is used by all the three devices and their image

pixel to actual distance meter scale is included in the Config.txt to allow the system to

estimate the actual distance according to the map. During the initial setup, the user

uses the Collect Fingerprint functions to collect fingerprint database and map features

which are all stored in this folder. The raw fingerprint database is then transferred to a

computer to generate clusters based on Section 3.2.2 using affinity propagation algorithm

and put this cluster information back to the PDA’s resources folder. Then, the online

operations: localization, tracking and navigation obtain the fingerprint database and the

map database from this folder to achieve their purposes.

6.3.3 Libraries’ Definitions

Fig. 6.1 shows that the software is divided into six blocks of libraries. These libraries

are organized so that each individual block deals with one specific task and allows the

developer to modify these codes easily. These libraries are:

• MathAlgorithm This library contains the math algorithms that are required by

the proposed system. It uses the open source library DotNetMatrix to perform

the standard matrix operations. The four algorithms defined in this library are i)

affinity propagation algorithm, which is converted from matlab code found in [15];

ii) ℓ1-minimization by using primal-dual interior point method, known as basis

pursit, which is also converted from matlab code found in CS-solver ℓ1-Magic [65];

iii) Dijkstra algorithm as depicted in Fig. 5.2 and iv) the Kalman Filter as defined

in Section 4.2. Although the affinity propagation algorithm is implemented, the

software can only handle the computation for a small number of collected RPs.

It complains for the lack of memory and crashes when the number of collected


fingerprints exceeds 15. Thus, the clustering process is done by a computer instead.

• LocalizerBasicLibrary This library provides the basic functions that are used by

the rest of the program. It uses the open source libraries OpenNetCF to obtain

the WiFi scanning function and the Samsung Mobile SDK to control the sensors

of the Samsung smartphone. In addition, the config file is read by this library to

set up the software to run properly with user’s defined parameters. The behavior

of the software during its launch is recorded in log files produced by this library

for later observation. Moreover, it contains the functions to collect and write the

fingerprint and map database into the IndoorLocResources folder.

• Localization This library implements the CS-based positioning system described

in Chapter 3. It refers to MathAlgorithm to solve the ℓ1-minimization problem.

• Tracking This library implements the CS-based tracking system described in

Chapter 4. It is built based on the Localization and MathAlgorithm libraries.

• Navigation This library implements the navigation system described in Chapter

5. It refers to the MathAlgorithm library to run the Dijkstra algorithm for the

path routing module. In addition, it also includes functions to load and play the

voice instructions audio properly.

• IndoorLocalizerProg This is the main program of the software which defines the

user interface and connects all the libraries together to the desirable functionalities.

6.4 Chapter Summary

This chapter describes the software developed on the PDAs and smartphones for the

proposed indoor tracking and navigation system. The software is developed in C# using

Microsoft .Net Compact Framework version 3.5 for Windows Mobile-powered smartde-

vices. Besides the online operations that localize, track or navigate the user, the software


also includes the functions to collect offline fingerprint and map databases. In this thesis,

the software is deployed on three devices: two HP PDAs and one Samsung smartphone

to evaluate the performance of the proposed tracking and navigation system.

Chapter 7

Experimental Results

In this chapter, the proposed CS-based positioning and tracking system is evaluated in

different experimental sites using the devices mentioned in the previous chapter. Due to

the dynamic and unpredictable nature of the radio channel in indoor environment, the

RSS varies over time and cannot be modeled accurately by a propagation model. Thus,

RSS readings are collected in real indoor environments to evaluate the performance of

the proposed system. The results obtained by using different parameters for proposed

systems are also examined to illustrate the effect of these parameters. In addition, the

proposed systems are also compared with other positioning and tracking algorithms.

Finally, the implementation of the navigation system for the actual sites is also included.

7.1 Experimental Setup

7.1.1 Experimental Sites

The experiments took place at two different sites: i) Bahen Centre for Information Tech-

nology of the University of Toronto and ii) Canadian National Institute for the Blind

(CNIB). Their general information is summarized in Table 7.1.

The proposed positioning and tracking system can be directly used in the buildings

77

Chapter 7. Experimental Results 78

Sites in Study Dimensions # of additional

deployed APs

Total #

of APs

Device

in Test

# of

RPs

Bahen 4th Floor 30 m× 31 m 8 26 PDA1 72

CNIB 2nd Floor 35 m× 71 m 15 23 PDA2 128

Table 7.1: Comparison of experimental sites

that are already equipped with access points (APs), whose settings and positions are

unknown. Besides the original access points, several additional access points are deployed

in the experimental sites to ensure that the sites have enough reliable RSS readings to

estimate the locations accurately. The additional deployed APs denoted in Table 7.1 are

the off-the-shelf access points, Cisco Linksys Wireless-G Router WRT54G2, which are

set to have maximum transmission power 18dBm and set to transmit signals at channel

1. Note that all RSS readings collected by the devices are in dBm scale.

Bahen Center: Positioning Analysis

The first experimental site is a part of the fourth floor of the eight storey building, Bahen

centre at the University of Toronto [83]. The main focus of this site is to analyze the

performance of the CS-based positioning system as described in Chapter 3. The region

of interest is a office area with a L-shaped corridor with a dimension of 30 m × 31 m,

which is comparable to those experimented in [19, 28, 38, 49]. Including the 8 additional

deployed access points, which are spread across the whole area, a total of 26 access points

can be detected. Both the PDA1 and Smartphone as defined in Table 6.1 are used

for the fingerprint collection, but the analysis of the positioning system is mainly based

on the PDA1 device, as it can obtain a better RSS fingerprint database due to better

antenna and faster WiFi scanning rate than the Smartphone.


Fingerprint Collections For this experimental site, the PDA1 and Smartphone,

each carried by an individual, are used to collect the fingerprints during the offline phase.

At each RP, 50 RSS time samples from 26 APs were collected for each of the four orien-

tations: North, East, South and West, by PDA1 and Smartphone with the sampling

rates of 1 sample/second and 0.67 sample/second respectively. If the devices cannot de-

tect the RSS from a particular AP, a small default value of -110dBm is assigned to that

particular reading. A total of 72 RPs, which were evenly distributed along the corridors

of the site with an average grid spacing of 1.5m were collected on both devices over a

period of 5 days and 8 days for PDA1 and Smartphone respectively. These raw sets

of RSS readings are then processed to generate the required fingerprint database for the

positioning systems. Note that, the samples of default readings (-110dBm) are excluded

when calculating the average and variance of the RSS readings. The positioning system

is then evaluated by the following two RSS sets as the online RSS measurement vectors.

Validation Data The positioning system is first tested by a validation set, which is

extracted from the raw RSS readings of the fingerprint database. That is, at each of the

RPs, choose one of the 50 RSS time samples at one of the four orientations collected

by the device as the online RSS measurement vector to estimate the desired location,

which should be the location of the corresponding RP. This set is used to evaluate the

performance of the system under zero noise interference situation.

Stationary User Testing Data Another set of online RSS readings were collected

by the PDA1 on a different day to evaluate the performance of the system under time-

varying environment. In order to obtain the actual locations of the user, the device let

the stationary user orientated at an arbitrary orientation to click on the map, which was

shown on the device’s touchscreen, where he was standing and then the device started the

WiFi scanning process. Each online observation was an average of 2 RSS time samples

which was taken over a period of 2 seconds. In total, 3 online observations of 48 locations


spread across the area of interest were collected as the stationary user set.

CNIB: Tracking and Navigation Analysis

The evaluation of the performance of the proposed tracking and navigation systems

described in Chapter 4 and 5 took place on the second floor of CNIB, located in mid-

town Toronto. Subject testings were also conducted at this site to evaluate the usefulness

of the navigation system to the visually impaired people. This building is designed to

provide easy accessibility to anyone, especially the visually impaired people [84]. The area

of dimensions 35 m× 71 m, which is larger than the experimental site at Bahen Centre,

consists of a main straight central hallway connected to a C-shaped small corridor that

leads to different conference rooms. Unlike the campus areas, such as the Bahen centre,

which are densely populated with access points, there are only a few APs detectable in

the CNIB. Thus, 15 additional APs are deployed throughout the whole area, creating a

total of 23 APs that can be used in the experiments. All the three devices described in

Table 6.1 are used to collect the fingerprint database, but the analysis of the tracking and

navigation systems is mainly focused on the PDA2 device, as it has the best fingerprint

database in terms of the number of real RSS readings from detectable APs, whereas the

other two devices often cannot obtain the RSS readings from APs during the sampling

periods.

Fingerprint Collections Similar to the fingerprint collection process at the Bahen

Centre, 50 RSS time samples were collected for each orientation at each RP by all the

devices, except the Smartphone, which only 40 RSS time samples were collected instead.

A total of 128 RPs, which were evenly distributed along the hallway and corridors with an

average grid spacing of 1.5m were collected by PDA2. The number of RPs collected by

the PDA1 (120 RPs) and Smartphone (126 RPs) varied slightly as they were operated

by different individuals. It took about 10 days to finish this offline phase.


Mobile User Testing Data In order to evaluate the performance of the tracking

system, several traces were collected on a different day by PDA2. The user carried the

PDA2 device, which obtained RSS samples at every second, and walked at a constant

speed along 4 different traces, as summarized in Table 7.2. The actual locations of the

user for each step can be deduced based on the user’s speed and elapsed time.

Trace # # of turns # Repetitions Distance Average Duration

1 2 4 53.63m 156.3s

2 2 4 29.43m 89.2s

3 0 4 30.80m 84.6s

4 4 2 91.84m 279.5s

Table 7.2: Traces Summary

7.1.2 Performance Benchmarks

The performance of the proposed positioning system is compared to two methods. The

first one is the KNN method [19], described in Section 2.2.1, which is a simple technique

that can be easily implemented on the mobile devices. In the following experiments, three

neighbors (k = 3) are used to estimate the user’s location. Another one is the kernel-

based method [38], which is summarized in Fig. 2.1. The computation of this probabilistic

approach technique involves all the RSS time samples collected during the offline phase

and thus requires more processing time and resources. It may not be realizable by the

mobile devices, as they have limited processing power and memory.

As for the proposed tracking system, two performance benchmarks are used for com-

parison. They are the original proposed positioning system and the direct application of

the Kalman filter on the original proposed positioning system.


7.1.3 Figure of Merit

The performance of the positioning and tracking systems can be evaluated in terms of

the position error, which is defined as the Euclidean distance between the actual location

and its estimation. The average root mean square error (ARMSE) is used as a metric

for the performance evaluations and it is defined below:

Average Root Mean Square Error (ARMSE)

The ARMSE for the stationary user is defined as:

ARMSE , 1

Np

Np∑i=1

√√√√ 1

Ti

Ti∑t=1

∥pi − pi(t)∥2 (7.1)

where pi is the actual location for test point i and pi(t) is the estimated location for test

point i using test sample t. Np and Ti are the number of test points and number of test

samples for test point i respectively.

Similarly, the ARMSE for the mobile user is defined as:

ARMSE , 1

Ntrace

Ntrace∑i=1

√√√√ 1

Ni

Ni∑t=1

∥pi(t)− pi(t)∥2 (7.2)

where pi(t) and pi(t) are the actual and estimated locations for a particular trace i at

step t. Ntrace is the number of traces and Ni is the number of steps of trace i.

7.2 Positioning Results on Bahen Fourth Floor

This section focuses on the evaluation of the implementation of proposed CS-based po-

sitioning system using the PDA1 device on the fourth floor of Bahen Centre.

7.2.1 RSS Distributions

RSS readings in an indoor environment vary due to several factors. The radio channel

impediments such as shadowing and multi-path propagation due to walls and obstacles,


the orientation of the antennas of the wireless devices, the movements of human bodies

are some of the causes that induce the time varying characteristics of the RSS, which

cannot be easily predicted by a radio propagation model. In this section, the RSS distri-

butions collected by PDA1 and Smartphone on the Bahen fourth floor are examined

to illustrate these variations of RSS in indoor environment.

RSS Distribution Over Time

Fig. 7.1 depicts the histograms of RSS time samples from the same access points collected

by both devices at the same reference point. Both histograms show that the RSS varies

around the average values with certain variances. In this example, the mean and variance

of the RSS collected by PDA1 are -48dBm and 23dBm, whereas for Smartphone

(excluding the invalid -110dBm instances) are -68dBm and 18dBm respectively. The

RSS readings collected by Smartphone are much lower than the ones collected by

PDA1. This illustrates that the antenna gain for Smartphone is smaller than the one

for PDA1. In addition, there are several instances that Smartphone is not able to

detect any RSS (which is then assigned to a default value of -110dBm). This may be due

to the hardware limitation of the antenna of the Smartphone. The low quality antenna

of Smartphone makes it not as reliable as the PDA1 to be a WiFi-scanning device.

The actual RSS readings across time are shown in Fig. 7.2a. This figure further

illustrates that the RSS collected by PDA1 is much more stable and higher than the one

collected by Smartphone, thus the RSS data collected by the PDA1 is used for the

analysis of the CS-based positioning system applied on the Bahen fourth floor. Since the

average RSS values are used by the proposed positioning and tracking system to estimate

the user’s location, it is important to obtain a reliable average value. Fig. 7.2b depicts

the average RSS values against the number of RSS samples used. The average RSS for

PDA1 converges to -48dBm after 30 samples are used, thus the fingerprint database

that is generated from 50 time samples should be enough for the system.


−55 −50 −45 −40 −35 −300

1

2

3

4

5

6

7

RSS Readings [dBm]

Fre

quen

cy

(a) RSS collected by PDA1

−120 −110 −100 −90 −80 −70 −60 −500

1

2

3

4

5

6

7

RSS Readings [dBm]

Fre

quen

cy

(b) RSS collected by Smartphone

Figure 7.1: Example histograms of RSS distributions of the same access point over 50

time samples for different devices pointing North at the same reference point on Bahen

fourth floor.

0 5 10 15 20 25 30 35 40 45 50−110

−100

−90

−80

−70

−60

−50

−40

−30

RS

S r

eadi

ngs

[dB

m]

Time [s]

PDA1 − NorthSmartphone − North

(a) RSS measurements over time

0 5 10 15 20 25 30 35 40 45 50−80

−75

−70

−65

−60

−55

−50

−45

Number of RSS time samples

RS

S A

vera

ge [d

Bm

]


(b) RSS averages across time samples

Figure 7.2: An example of RSS measurements over time and their averages with respect

to the number of time samples of the same access point for different devices at the same

reference point on Bahen fourth floor.

RSS Distribution Across Reference Points

The RSS distributions in spatial domain are shown in Fig. 7.3. Several observations are

made from these figures. First, the orientation of the antenna of the same device affects

the RSS variations slightly as illustrated in Fig. 7.3a. Second, the variations of RSS are

much larger when different devices are used as shown in Fig. 7.3b. However, the trends


of the RSS distributions across the spatial domain are similar for all these cases. This

particular access point is located close to the 20th RP, thus the RSS at this RP is the

strongest and decreases as the RPs are moving away from the access point. Note that

there is a second peak of the RSS value at the 6th RP, as this RP is in the same corridor

where the AP is located.

0 10 20 30 40 50 60 70 80−80

−70

−60

−50

−40

−30

−20

Reference Points Indices

RS

S R

eadi

ngs

[dB

m]

PDA1 − NorthPDA1 − South

(a) Different Orientations

0 10 20 30 40 50 60 70 80−80

−70

−60

−50

−40

−30

−20

Reference Points IndicesR

SS

Rea

ding

s [d

Bm

]


(b) Different Devices

Figure 7.3: An example of averaged RSS of the same access point in spatial domain for

different orientations and different devices on Bahen fourth floor.

7.2.2 Offline Phase: Clustering Results by Affinity Propagation

The fingerprint database collected by the PDA1 are used for the analysis of the CS-based

positioning system. As described in Chapter 3, the fingerprints are first pre-processed

during the offline phase to generate clusters that are required for the later coarse location

stage.

Effect of Preferences on the Number of Clusters Generated

According to (3.5), γ(o) is determined experimentally to obtain desirable number of clus-

ters for the fingerprints. The number of clusters generated by affinity propagation using

different values of γ(o) is shown in Fig. 7.4. Since the medians of the similarities defined

in (3.4) are negative, smaller values of γ(o) result in larger values of preferences and hence


more clusters; this is a property for the affinity propagation algorithm [15]. The number

of clusters generated for different orientations are very similar for the same value of γ(o)

as RSS only varies slightly for different orientations.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

5

10

15

20

25

30

35

40

γ(o)

Num

ber

of C

lust

ers

North − γ(0°)

East − γ(90°)

South − γ(180°)

West − γ(270°)

Figure 7.4: Number of clusters generated by the affinity propagation algorithm depending

on the value of parameter γ(o) for four orientations on Bahen fourth floor.

Generated Clusters Result

The number of desirable clusters required by the CS-based positioning system is deter-

mined based on two criteria. First, most of the RPs from the same generated cluster

should be geographically close to each other to minimize the number of distant outliers.

This can be done by observing the clustering results generated in the above section us-

ing different values of γ(o). Second, the number of clusters should reasonably divide the

fingerprints into smaller regions. If there are too few clusters, it leads to more RPs to be

included for the fine localization stage and thus increases the computation cost in solving

the ℓ1 minimization problem, whereas too many clusters are undesirable as well, as the

fine localization stage within a small set of RPs becomes insignificant.

The clustering results used by the CS-based positioning system for the following

experiments are obtained by first setting the parameters γ(o) for the affinity propagation

algorithm as in Table 7.3 and then reassigning the outliers that are physically far away

from their own clusters to their geographically surrounding clusters. A total of 56 clusters


are generated in four orientations and the clustering results on the map are illustrated

in Fig 7.5.

North East South West

γ(o) 0.25 0.26 0.25 0.30

Number of clusters 14 14 16 14

Table 7.3: Actual parameters γ(o) used for experiments on Bahen fourth floor.

7.2.3 Online Phase: Coarse Localization Analysis

By using the validation set and the stationary user testing set collected by the PDA1,

the performance of the CS-based positioning system is evaluated. This section examines

the different settings and schemes used by the coarse localization stage as described in

Section 3.3.1. In order to ensure that only a few set of best-matched clusters are selected

for the fine localization stage, the value of α1 defined in (3.15) is set to 0.99. In addition,

the settings for the fine localization stage remain the same in this section, which are i)

the random combination is used for the AP selection scheme and ii) the threshold defined

in (3.24) is set to λ1 = 0.4.

Effect of the Number of Generated Clusters

As shown in Fig. 7.6, the number of generated clusters affects the ARMSE of the posi-

tioning system when the same cluster matching scheme, namely the average-based plus

strongest APs matching scheme as described in Section 3.3.1 is applied. The same trend

is observed for both the validation and stationary user testing data. When the system

skips the coarse localization stage, which corresponds to the ‘No clustering’ curve in the

figure, the system has the highest ARMSE. This proves that the coarse localization stage

is able to reduce the errors in estimating the user’s position by reducing the area of


(a) North (b) East

(c) South (d) West

Figure 7.5: The clustering results on the four fingerprint databases collected by PDA1

on Bahen fourth floor. Each circle is a RP collected in the database and each color

represents one cluster.

interest into a smaller region and hence minimizing the effect of outliers. Furthermore,

increasing the number of clusters also reduces the ARMSE, as the system is able to

confine the problem into a much smaller region in the coarse localization stage.

The ARMSE remains fairly the same when eight or higher number of APs are used.

Fig. 7.7 depicts the cumulative error distributions of the system using different number

of generated clusters when eight APs are selected. The figure shows that the 58 clusters


used by the system achieve the best performance and attain the smallest maximum error.

Note that the error obtained from the stationary user testing set is slightly higher. This

is justified, as this set of data is collected on a different day and thus their RSS readings

are varied from the fingerprint database, introducing errors in estimations.

5 10 15 20 250

1

2

3

4

5

6

7

8

9

10

Number of APs Used

AR

MS

E [m

]

No clustering

29 clusters; γ(o)=1

43 clusters; γ(o)=0.558 clusters; actual clusters used by system

(a) Validation Data

5 10 15 20 250

1

2

3

4

5

6

7

8

9

10

Number of APs Used

AR

MS

E [m

]

No clustering



(b) Stationary User Testing Data

Figure 7.6: The ARMSE versus number of used APs, when different number of generated

clusters are used for the coarse localization on Bahen fourth floor

0 2 4 6 8 10 12 14 160.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Error [m]

Cum

ulat

ive

Err

or P

roba

bilit

y

No clustering



(a) Validation Data

0 2 4 6 8 10 12 14 160.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Error [m]

Cum

ulat

ive

Err

or P

roba

bilit

y

No clustering




Figure 7.7: The cumulative error distributions using different number of clusters for the

coarse localization on Bahen fourth floor. (8 APs are used)


Different Matching Schemes

Section 3.3.1 describes several cluster matching schemes that can be used to select the

clusters, which best matched to the online RSS measurement vector r. Fig. 7.8 shows

the comparison of using different matching schemes. It is obvious that in the validation

set, the schemes that are applied on the strongest APs set have better accuracies and

they have similar performances, except that the exemplar-based scheme has a higher

maximum error. However, this trend is not as obvious as in the stationary user testing

set, as the gap between the schemes with and without the use of strongest APs set is very

small. In fact, the weighted average applied on the strongest APs set attains the highest

maximum error. According to both sets of data, the average based strongest APs cluster

matching scheme is a good choice for the system and is selected as the default operation

for the coarse localization stage as it gives reliable results in both sets.

0 2 4 6 8 10 12

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Error [m]

Cum

ulat

ive

Err

or P

roba

bilit

y

Exemplar−basedAverage−basedWeighted AverageExemplar−based + Strongest APsAverage−based + Strongest APsWeighted Average + Strongest APs

(a) Validation Data

0 2 4 6 8 10 12

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Error [m]

Cum

ulat

ive

Err

or P

roba

bilit

y

Exemplar−basedAverage−basedWeighted AverageExemplar−based + Strongest APsAverage−based + Strongest APsWeighted Average + Strongest APs


Figure 7.8: The cumulative error distributions using different cluster matching schemes

on Bahen fourth floor. (8 APs are used)

7.2.4 Online Phase: Fine Localization Analysis

This section focuses on the evaluation of using different settings for the fine localization

stage.


AP Selection Schemes

There are three access point selection schemes for the fine localization stage as described

in Section 3.3.2. The performances of using these schemes are compared in Fig. 7.9. For

the random combination AP selection scheme, the x-axis refers to the number of linear

random combinations of online RSS values from L APs according to (3.18). When the

number of used APs is less than 14, both the Fisher criterion and the random combination

AP selection schemes have similar results and achieve slightly better than the strongest

APs scheme. However, when the number used APs is higher than 14, the strongest APs

and Fisher criterion schemes achieve the same ARMSE in both sets of data, whereas,

the random combination results in a slightly higher ARMSE. Although the random com-

bination may sometime leads to slightly higher ARMSE than the other two schemes,

it is chosen to be the default operation of the CS-based position system, as i) it does

not require large samples of RSS data for the calculations of variance as required by the

Fisher criterion; ii) it achieves better results when a small number of APs is used and iii)

the same random matrix Φ can be reused, unlike the other two online RSS schemes that

require on-the-fly generation of the AP selection matrix Φ and thus reduce the online

update time.

Sensitivity to Threshold λ1

Another parameter that is required to be determined experimentally is the threshold λ1

defined in (3.24), as it determines how many non-zero entries of the θ should be used

to interpret the actual location of the user. Fig. 7.10 illustrates the effect of λ1 on

the ARMSE results. It shows that the ARMSE can vary for a range of 0.4m, which is

not very significant when comparing to the magnitude of the ARMSE, just by setting

a different value of λ1. Although the value of λ1 does not have a linear relationship

to the ARMSE, the figures show that the λ1 should not be set to a high value, which

implies that the system only obtains a few entries with highest value for the location


5 10 15 20 251.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

Number of APs Used

AR

MS

E [m

]

Strongs APsFisher CriterionRandom Combination

(a) Validation Data

5 10 15 20 251.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

Number of APs Used

AR

MS

E [m

]

Strongs APsFisher CriterionRandom Combination


Figure 7.9: The ARMSE versus number of used APs, using different AP schemes for fine

localization on Bahen fourth floor.

interpretation. According to this experiments, this threshold should be set to λ1 = 0.4

to let the system have the best performance.

0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

λ1

AR

MS

E [m

]

(a) Validation Data

0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

λ1

AR

MS

E [m

]


Figure 7.10: Effect of the threshold λ1 on ARMSE on Bahen fourth floor. (8 APs are

used)

7.2.5 Performance Comparison

Throughout the above experimentations, a set of optimal parameters that gives the best

performance of the CS-based positioning system can be determined and is given in Table


7.4. The performance of this positioning system is then compared to the KNN and

kernel-based techniques in terms of the position error and computation time.

Total number of generated clusters 58

Coarse Localization - cluster matching scheme Average-based + Strongest APs

Coarse Localization - α1 0.99

Fine Localization - AP selection scheme Random combination

Fine Localization - λ1 0.4

Number of APs used 8

Table 7.4: A set of optimal parameters for the CS-based position system applied on

Bahen fourth floor.

Position Error

The position errors of the three methods are compared in Fig. 7.11 in terms of their

cumulative error distributions. Table 7.5 and 7.6 summarize the statistics of their position

errors.

For validation set, the performance of the CS-based positioning system outperforms

the other two methods. It reduces the ARMSE by 0.45m (22%) and 0.30m (16%) over

the KNN and Kernel-based methods. In addition, the system also improves significantly

in terms of maximum error (46%) and variance (62%).

The position error is slightly higher for the stationary user testing set, as these RSSs

are collected on a different day. Although the improvement of the CS-based positioning

system is not significant in terms of ARMSE (4% for KNN and 12% for Kernel-based),

the system still outperforms the other two methods in terms of maximum errors and

variances.


0 2 4 6 8 10 12 14 160.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Error [m]

Cum

ulat

ive

Err

or P

roba

bilit

y

KNNKernel−basedCS−based Positioning

(a) Validation Data

0 2 4 6 8 10 12 14 160.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Error [m]

Cum

ulat

ive

Err

or P

roba

bilit

y



Figure 7.11: The cumulative error distributions using different positioning systems on

Bahen fourth floor. (8 APs are used)

Method ARMSE [m] Mean [m] 90th Percentile [m] Max[m] Variance [m2]

KNN 2.02 1.78 3.15 17.3 5.74

Kernel-based 1.87 1.56 3.78 13.39 3.99

CS-based 1.57 1.29 2.84 7.19 1.51

Table 7.5: Position error statistics for different methods on Bahen fourth floor. (For

validation set)


KNN 2.00 1.76 3.39 8.35 2.51

Kernel-based 2.19 1.86 3.81 10.54 3.81

CS-based 1.92 1.67 3.38 7.16 1.76

Table 7.6: Position error statistics for different methods on Bahen fourth floor. (For

stationary user testing set)

Computation Time

Fig. 7.12 shows the computation time required for each step on a 2.50GHz IntelR⃝ CoreTM

2 Quad processor with 4GB RAM using the three different localization techniques. Since


the Kernel-based method is a probabilistic approach that incorporates all RSS time

samples from the fingerprint database for computation, it requires much more time to

obtain the estimated position than the other two methods. Its computation time also

increases as the number of used APs increases. Due to its high-volume computation cost,

it is not desirable to implement on the resource-limited mobile devices as a real-time

positioning system. Although the CS-based system requires a little more computation

time than the KNN method, its simplicity and accuracy makes it a good method to be

implemented on any mobile device.

4 6 8 10 12 14 16 18 20 22 24 260

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Number of APs Used

Mea

n C

ompu

tatio

n T

ime

[s]


(a) Validation Data

4 6 8 10 12 14 16 18 20 22 24 260

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Number of APs Used

Mea

n C

ompu

tatio

n T

ime

[s]



Figure 7.12: Comparison of mean computation time using different positioning systems

in Bahen fourth floor. (8 APs are used)

7.3 Tracking Results on CNIB Second Floor

In this section, the performance of the proposed tracking system described in Chapter 4

is evaluated based on the RSS data collected by the PDA2 device on the second floor of

CNIB.


7.3.1 RSS Distributions

The RSS distributions based on the three sets of fingerprint databases collected by

PDA1, PDA2 and Smartphone are examined briefly in this section. Fig. 7.13, 7.14

and 7.15 show the RSS distributions in terms of different parameters for all the three

devices. Several observations can be made from these figures:

• There are some instances during the RSS sampling period that PDA1 and Smart-

phone are not able to detect the RSS from certain APs, thus their fingerprint

databases are degraded.

• Although the RSS collected by PDA1 is the strongest, its RSS distribution in

spatial domain fluctuates significantly when comparing to the other two devices as

shown in Fig. 7.15b. This large fluctuation is undesirable as it introduces error to

the positioning system.

• The RSS collected by Smartphone is significantly lower than the other two meth-

ods, as the device’s antenna is of poor quality.

• The fingerprint database collected by PDA2 is the most stable over all the three

devices and thus is used by the proposed tracking analysis for the following sections.

7.3.2 CS-based Positioning Results

Before the analysis of the tracking system, the original CS-based positioning system is

first compared to the KNN and Kernel-based methods. The generated cluster results

after the modification of outliers are shown in 7.16 and the optimal set of parameters

used by the system is summarized in Table 7.7.

Fig. 7.17 and Table 7.8 compare the performances of the three localization methods

on the mobile user testing set. The CS-based method behaves slightly worse than the

KNN method unlike the results obtained for the Bahen fourth floor. This happens as a


−120 −110 −100 −90 −80 −70 −60 −50 −400

1

2

3

4

5

6

7

8

9

10

RSS Readings [dBm]

Fre

quen

cy

(a) RSS collected by PDA1

−66 −65 −64 −63 −62 −61 −60 −59 −58 −57 −560

2

4

6

8

10

12

RSS Readings [dBm]

Fre

quen

cy

(b) RSS collected by PDA2

−120 −110 −100 −90 −80 −70 −600

1

2

3

4

5

6

RSS Readings [dBm]

Fre

quen

cy

(c) RSS collected by Smart-

phone

Figure 7.13: Example histograms of RSS distributions of the same access point over

50 time samples (40 time samples for Smartphone) for different devices at the same

reference point in CNIB second floor.

0 5 10 15 20 25 30 35 40 45 50−110

−100

−90

−80

−70

−60

−50

−40

RS

S r

eadi

ngs

[dB

m]

Time [s]

PDA1 − NorthPDA2 − NorthSmartphone − North

(a) RSS distributions across time

0 5 10 15 20 25 30 35 40 45 50−85

−80

−75

−70

−65

−60

−55

−50

−45

Number of RSS time samples

RS

S A

vera

ge [d

Bm

]


(b) RSS averages across time samples

Figure 7.14: An example of RSS distributions across time and their averages with respect

to the number of time samples of the same access point for different devices at the same

reference point in CNIB second floor.

part of the CNIB second floor does not have a good coverage of the APs, which leads

to poor clustering results around that region and makes the system hard to identify the

correct clusters during the coarse localization stage. This also explains why the system

attains very high maximum error, as it selects the wrong regions for localization. This

effect is less prominent for the KNN method, as it compares the online RSS measurement


0 5 10 15 20 25 30−110

−100

−90

−80

−70

−60

−50

−40


RS

S R

eadi

ngs

[dB

m]

PDA2 − NorthPDA2 − South

(a) Different Orientations

0 5 10 15 20 25 30−110

−100

−90

−80

−70

−60

−50

−40


RS

S R

eadi

ngs

[dB

m]


(b) Different Devices

Figure 7.15: An example of RSS distributions of the same access point in spatial domain

for different orientations and different devices in CNIB second floor. (only a part of the

fingerprints are shown)

(a) North (11 Generated Clusters) (b) East (17 Generated Clusters)

(c) South (15 Generated Clusters) (d) West (16 Generated Clusters)

Figure 7.16: The clustering results on the four fingerprint databases collected by PDA2

on CNIB second floor

readings to each of the RP’s RSS values instead of a subset of them.

The proposed tracking system described in Chapter 4 is able to improve the CS-


Total number of generated clusters 59

Coarse Localization - cluster matching scheme Average-based + Strongest APs

Coarse Localization - α1 0.99

Fine Localization - AP selection scheme Random combination

Fine Localization - λ1 0.4

Number of APs used 10

Table 7.7: A set of optimal parameters for the CS-based position system applied on

CNIB second floor.

based positioning system by using previous history to ensure it chooses the correct rel-

evant region during the coarse localization stage and smooths out the trajectory by the

application of the Kalman filter. Their analysis are in the following sections.

0 2 4 6 8 10 12 14 16 180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Error [m]

Cum

ulat

ive

Err

or P

roba

bilit

y

KNNKernel−basedCS−based

Figure 7.17: The cumulative error distributions for different positioning systems on CNIB

second floor. (10 APs are used)

7.3.3 Modified Coarse Localization Analysis

In this section, the use of different schemes to choose the RPs which are in physical prox-

imity to the previous estimate, described in Section 4.3.1, are examined. The covariances



KNN 3.02 2.56 4.84 16.55 3.49

Kernel-based 3.73 3.06 6.24 15.30 6.31

CS-based 3.28 2.68 5.26 26.64 4.79

Table 7.8: Positioning error statistics for different positioning methods on CNIB second

floor. (For mobile user testing set)

of the process and measurement noises of the Kalman filter are set to S = diag(1) and

U = diag(80), where diag(d) refers to a diagonal matrix with the diagonal entries set to

the scalar value d.

According to Section 4.3.1, there are two parameters to be set for choosing the relevant

RPs depending on their geographical locations to the previous user’s location. The first

parameter is to decide whether the previous estimated location (Unpredicted) should be

used for the distance calculations to the RPs or the predicted location using the Kalman

filter estimated state vector (Predicted) should be used. The second parameter is the

walking distance range β defined in (4.15) and (4.17).

Fig. 7.18 shows the ARMSE versus the walking distance range β when different

schemes are used. Both schemes work the best when β = 4. In addition, the Unpredicted

one works better than the Predicted one. This happens as the Predicted scheme may

not be able to predict the correct user’s current location and thus introduce errors when

including non-relevant RPs for the fine localization stage.

7.3.4 Map Adaptive Kalman Filter Analysis

In this section, the unpredicted user’s location and β = 0.4 are used for the coarse

localization stage and different parameters for the Kalman filter are examined.


3 3.5 4 4.5 5 5.5 62

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

β [m]

AR

MS

E [m

]

UnpredictedPredicted

Figure 7.18: Effect of the walking distance β on ARMSE in CNIB second floor. (10 APs

are used)

Sensitivity to the Covariances of Process and Measurement Noises.

Fig. 7.19 illustrates the performances of the proposed tracking system using different

combinations of covariances of process and measurement noises, S = diag(ds) and U =

diag(du), respectively. The performances are very similar for most of the combinations,

except for the case when ds = 10 and du = 80. It shows that the performance of the

proposed tracking system is not affected significantly by changing the parameters of the

Kalman filter.

0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Error [m]

Cum

ulat

ive

Err

or P

roba

bilit

y

ds = 1, du = 80ds = 1, du = 100ds = 1, du = 50ds = 10, du = 80ds = 0.5, du = 80

Figure 7.19: The cumulative error distributions using different Kalman filter parameters

in CNIB second floor. (10 APs are used)


Resetting Kalman Filter at Intersections

Section 4.3.2 mentions that the Kalman filter should be reset at the intersections, where

there are a higher chance for the user to make turns and thus violate the linear motion

model assumed by the Kalman filter. Fig. 7.19 compares the performance with and

without resetting the Kalman filter at the intersections. Resetting the Kalman filter

at intersections improves the system’s accuracy. For the ARMSE, the resetting scheme

improves from 2.20m to 2.07m (6%) and at the 90th percentile, it improves from 3.76m

to 3.33m (11%).

0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Error [m]

Cum

ulat

ive

Err

or P

roba

bilit

y

No reset Kalman filter at cornerReset Kalman filter at corner

Figure 7.20: The cumulative error distributions for different Kalman filter update schemes

in CNIB second floor. (10 APs are used)

7.3.5 Performance Comparison

From the above analysis, a set of optimal parameters that gives the best performance for

the proposed tracking system is shown in Table 7.9. This tracking system is compared

with the original CS-based positioning system and the direct applications of the Kalman

filter on both the KNN method and the CS-based positioning system. Fig. 7.21 shows the

comparison results in terms of cumulative error distributions and Table 7.10 shows the

position error statistics for these four systems. The proposed tracking system outperforms


the other three methods. It reduces the ARMSE by 1.27m (39%), 0.64m (27%) and 0.53m

(21%) over the CS-based positioning system, the KNN method with the Kalman filter

and the CS-based position system with the Kalman filter, respectively. In addition, the

proposed tracking system also has the smallest 90th percentile error and variance when

compared to the other systems.

Modified Coarse Localization - Comparison schemes Non-Prediction scheme

Modified Coarse Localization - β 4m

Kalman Filter Covariances S = diag(1) U = diag(80)

Table 7.9: A set of optimal parameters for the proposed tracking system applied on CNIB

second floor.

0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance Error [m]

Cum

ulat

ive

Err

or P

roba

bilit

y

CS−basedKNN + Kalman FilterCS−based + Kalman FilterProposed Tracking

Figure 7.21: The cumulative error distributions using the CS-based positioning system

and the three tracking systems in CNIB second floor. (10 APs are used)

Some of the example trace results are shown in Fig. 7.22. The estimated traces by the

proposed tracking system are able to follow the actual traces walked by the user. These

traces certainly improve the locations estimated by the CS-based positioning system

shown as green dots on the figures.


Method ARMSE [m] Mean [m] 90th Percentile [m] Max [m] Var [m2]

CS-based Positioning 3.28 2.68 5.26 26.64 4.79

KNN + 2.75 2.41 4.41 10.95 2.42

Kalman Filter

CS-based + 2.54 2.17 4.15 24.10 2.69

Kalman Filter

Proposed Tracking 2.01 1.74 3.36 17.93 1.91

Table 7.10: Position error statistics for the CS-based positioning system and the two

tracking systems on CNIB second floor. (For mobile user testing set)

(a) Trace #1 (b) Trace #2

(c) Trace #3 (d) Trace #4

Figure 7.22: Example trace results. The black line is the actual trace, the green dots

are the CS-based positioning results and the purple line is the results of the proposed

tracking system.

7.3.6 Navigation and Real Time Implementations

Using the PDA2, which is installed with the developed software that implemented the

proposed positioning and tracking system as described in Chapter 6, the user is able to


obtain the real-time estimated position updates periodically from the device. In addition,

the user is able to use the navigation function provided by the software.

The navigation module of the software requires the input of the map database, which

helps the module to generate useful guidance to the user according to his locations. Fig.

7.23 depicts the definition of the connected graph and the map features on CNIB second

floor, which are obtained according to Section 5.2.

Figure 7.23: The definition of the connected graph and the map features on CNIB second

floor. The blue lines and blue circles represent the edges and nodes of the connected

graph. The red squares represents the destinations. The diamonds represents the map

features and the pink circles represents the locations of the 15 deployed access points

At the beginning of the navigation, the device asks the user to enter the desired target

and then the module will route the path and play appropriate audio files to ask the user

to follow the path. The actual operations of the navigation can be found in Chapter 5.

Fig. 7.24 shows an example screenshot that is obtained from the device at the end of the

real experiment carried on the CNIB second floor. The device is able to track the user’s

trajectory and give appropriate commands accordingly. Several video files can be found

online in [85] to show the actual experiments conducted on CNIB second floor.


Figure 7.24: Example screenshot of the software that shows the actual track that the

user is walking. The line shows the routed path generated by the navigation module.

The squares denote the user’s locations and the circle denotes the destination.

7.3.7 Subject Testing

A preliminary research study was conducted over two months (in July and August 2010)

at this site in collaboration with the CNIB research unit to evaluate if such navigation

software developed on the smart device is useful in providing guidance to people with low

vision, as defined according to [86]. Before the actual testing, the subject’s visual acuity

was first examined by a doctor for low vision. A total of 16 visually impaired subjects

with an average age of 55 took part in this study and they were randomly assigned

into two groups, each group contains 8 subjects: i) subjects in the Control group were

only given instructions at the beginning of the test to reach the target by themselves;

whereas ii) subjects in the Testing group were given the PDA2, which provided real-time

navigation to guide them to the target. Each subject carried either a mobility cane or a

guide dog and was required to walk three pre-determined paths, which are the same as

the first three testing traces in the mobile user testing data. Table 7.11 gives a summary

about these traces. The results of this study are summarized in Table 7.12. Successful

trial means that the subject is able to reach the destination at the end of the test.

Several observations can be made according to the results in Table 7.12:

• The Testing group has a higher successful rate than the Control group. Since the


Trace Start Position Destination # of Turns Distance

1 (Fig. 7.22a) Rm 207 Rm 218E 2 53.63m

2 (Fig. 7.22b) Rm 218E Spring Water Fountain 2 29.43m

3 (Fig. 7.22c) Spring Water Fountain Elevator 0 30.80m

Table 7.11: Summary of the three traces tested by the subjects

Trace Group Number of successful Average Elapsed Time

trials (out of 8) (for successful trials)

1 Control 4 180.3 s

1 Testing 6 252.4 s

2 Control 3 83.3 s

2 Testing 8 130.5 s

3 Control 7 76.4 s

3 Testing 8 97.5 s

Table 7.12: Subjects testing results on CNIB second floor

device is able to identify the user’s location and informs that the subject has reached

the destination, the users are able to stop accordingly. However, the users from the

Control group have no extra assistance in identifying the destinations except the

instructions given at the beginning, thus they have to rely on their limited visions

to identify the targets and have difficulties to stop at the correct destinations. This

is especially obvious for the second trace, as the target is a spring water fountain,

which is small and is easy to be missed by the subjects.

• The time required for the subjects from the Testing group to reach the destinations

is longer than the one required for the Control group. This happens because of

two reasons. First, since the device generates additional descriptive instructions


about the surrounding area, the users spend extra time to get familiar with the

building. Second reason is due to hardware limitations of the PDA2. The slow

response of the WiFi network adaptor of the PDA2 and the duration time to play

the instructions lead to the slow actual update rate of the tracking system. Hence,

the subjects are required to walk slowly to accommodate these limitations.

This study shows positive results that the navigation software is useful to give real-

time guidance to the visually impaired people. However, further research is required to

improve the actual tracking rate of the system. This may be done by using a different

device that has a better processor, memory or WiFi network adaptor than PDA2.

7.4 Chapter Summary

This chapter evaluates the performances of the proposed CS-based positioning and track-

ing system. There are two experimental sites. The experiments carried on the fourth

floor of Bahen Centre focus on the analysis of the CS-based positioning system, whereas

the analysis of the proposed tracking system is done on second floor of the CNIB. The

CS-based positioning system outperforms the KNN and kernel-based methods on the Ba-

hen fourth floor and the proposed tracking system is able to further improve the accuracy

in estimating the user’s locations on the CNIB second floor. This lightweight algorithm

can be implemented as a software on the resource-limited mobile devices, such as PDAs

and smartphones. Furthermore, a simple navigation module is included and the real-time

performance can be found in [85].

Chapter 8

Conclusion

In this thesis, a RSS-based WLAN indoor positioning system, which can be implemented

on resource-limited mobile devices, is proposed. It is a fingerprint-based localization

system, which an offline phase, also known as a training phase, is required to collect the

RSS readings from access points (APs) at known positions, referred to as the reference

points (RPs). Unlike the probabilistic methods, which incorporate each individual RSS

time samples collected in the database for computation of the position estimate, the

proposed system uses only the averages of those RSS samples and perhaps their variances

depending on the choice of AP selection scheme. Thus, its computation complexity is

much less than the probabilistic methods and can be implemented on the mobile devices

without exhausting their computation powers. After the fingerprint database collection is

done, a clustering process is carried on to group the RPs with similar RSS values together

by applying the affinity propagation algorithm. The cluster members in the same cluster

should also be geographically close to each other and the outliers are manually assigned

back to the clusters that are physically close to them. The proposed positioning system

contains two stages for the actual positioning that happens in the online phase. First, the

coarse localization stage confines the localization problem into a smaller relevant region

by choosing the clusters of RPs, which are most similar to the online RSS measurement

109

Chapter 8. Conclusion 110

values. Then, the fine localization stage translates the fingerprint-based localization

problem into a sparse-signal recovery problem, so that the compressive sensing (CS)

theory can be applied and the user’s location can be estimated by solving a ℓ1 norm

minimization problem.

This CS-based positioning system can be easily extended to improve the accuracy by

using the previous estimate to refine the position estimates. First, the tracking system

uses the previous position estimate, in addition to the online RSS values to select the

subset of relevant RPs in the coarse localization stage. Second, the Kalman filter is used

to post-process the estimate computed at the end of fine localization stage to obtain

the final estimate. Resetting the Kalman filter when the location estimate is within a

intersection region helps to improve the accuracy, as the user is more likely to make

turns at intersections and thus violates the linear motion model assumed by the Kalman

filter. The tracking system is able to provide real-time estimates on the resource limited

devices, as the computation cost for the Kalman filter is very low when comparing to the

particle filter.

The proposed position and tracking system is implemented as a software which can

be installed on any Windows Mobile based handheld devices. The performance of the

proposed positioning and tracking system is evaluated in two different experimental sites:

fourth floor of Bahen centre and second floor of CNIB, where the RSS readings are

collected by two different PDAs. Experimental results show that the CS-based positioning

system performs better than the KNN and kernel-based methods on the Bahen fourth

floor in terms of average, maximum and 90th percentile errors, whereas on the CNIB

second floor, the proposed tracking system is able to further improve the accuracy in

estimating the user’s locations.

Finally, the simple navigation system is also implemented on top of the proposed

tracking system on the software. This software installed on the PDA was tested by

several visually impaired subjects on the second floor of CNIB. Results from this study


show that the system is able to track the users’ trajectories properly and give useful

guidance.

8.1 Future Works

There are several problems that can be explored to further enhance the performance of

the proposed WLAN positioning and tracking system. They are listed as follow:

• Besides the WiFi adapter, most of the smartphones and PDAs are now equipped

with extra sensors, such as accelerometer and digital compass. The information

generated from these sensors can be interpreted as user’s walking distances and

orientations. Although the samsung smartphone evaluated in this thesis is incom-

petent to handle the WiFi scanning and the operations of the sensors together,

recent smartphones are equipped with higher performance processor [87] and may

allow the sensors to be used in conjunction to the WLAN positioning system.

Thus, the proposed positioning system should be extended to use the information

obtained from these sensors to improve the accuracy of the estimated position.

• One of the disadvantages of using a fingerprinting based methods is the high labour

and time cost for collecting the required fingerprint database during the offline

phase. Since the fingerprints can be considered sparse in terms of the spatial

domain for the whole region of interest, the compressive sensing theory may be

applied on a smaller set of RPs to produce a larger radio map to reduce the time

to collect the fingerprints.

• In addition to using the CS theory to reduce the number of fingerprints, empirical

indoor radio propagation models may be used in conjunction to the fingerprinting

process to interpolate the RSS of extra RPs based on a small set of fingerprints, as

Fig. 7.3 and Fig. 7.15 show that the signal strength varies smoothly over spatial


domain.

• The proposed positioning system is device-dependent, thus the fingerprinting pro-

cess must be done for each different mobile devices. Recent studies show that using

signal strength differences (SSD) between pairs of APs instead of RSS can improve

the accuracy of the position estimate when different devices are used in a small

region [33]. Thus, research and analysis can be done to evaluate if the proposed

positioning system can use the SSD as the measurement metric.

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