This thesis proposes and evaluates a compressive sensing (CS)-based indoor positioning and tracking system using received signal strength (RSS) from wireless local area network access points. The system is designed and implemented on mobile devices with limited resources. In the offline phase, RSS fingerprints are collected and clustered using affinity propagation. In the online phase, coarse localization is done by matching RSS measurements to precomputed clusters, and fine localization refines the position using CS recovery on the sparse location signal. An indoor tracking system is also presented, which integrates the CS-based positioning with a Kalman filter for sequential location estimates. Experimental results on two testbeds show the system achieves better accuracy than other fingerprinting methods, suitable for implementation

1. RSS-based WLAN Indoor Positioning and Tracking System
Using Compressive Sensing and Its Implementation on
Mobile Devices
by
Anthea Wain Sy Au
A thesis submitted in conformity with the requirements
for the degree of Master of Applied Science
Graduate Department of Electrical and Computer Engineering
University of Toronto
c
Copyright ⃝ 2010 by Anthea Wain Sy Au

2. 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 growing interest in developing an accurate indoor positioning and tracking system on mobile
devices. The core location determination problem can be reformulated as a sparse natured 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

3. 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.
iii

4. 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
2.1
12
Signal Propagation Modeling . . . . . . . . . . . . . . . . . . . .
13
2.1.2
Location Fingerprinting . . . . . . . . . . . . . . . . . . . . . . .
14
Fingerprinting-Based Positioning Methods . . . . . . . . . . . . . . . . .
16
2.2.1
K-Nearest Neighbour Method (KNN) . . . . . . . . . . . . . . . .
16
2.2.2
Probabilistic Approach . . . . . . . . . . . . . . . . . . . . . . . .
17
2.2.3
2.3
12
2.1.1
2.2
Indoor RSS-based WLAN Positioning Techniques . . . . . . . . . . . . .
Region of Interest and Access Points Selections . . . . . . . . . .
19
Indoor Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2.3.1
21
Kalman filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iv

5. 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 during offline phase . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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
3.3
33
Interaction between the database server and the mobile device during online phase . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4
43
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
Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
4.4
v

6. 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
Path Routing Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
5.3.1
Path Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
Tracking Update Analysis Module . . . . . . . . . . . . . . . . . . . . . .
64
5.4.1
Analysis Process . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
5.4.2
Voice Generation . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
5.3
5.4
5.5
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
Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
6.4
7 Experimental Results
7.1
77
77
7.1.1
Experimental Sites . . . . . . . . . . . . . . . . . . . . . . . . . .
77
7.1.2
Performance Benchmarks . . . . . . . . . . . . . . . . . . . . . . .
81
7.1.3
7.2
Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figure of Merit . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
Positioning Results on Bahen Fourth Floor . . . . . . . . . . . . . . . . .
82
7.2.1
82
RSS Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi

7. 7.2.2
Online Phase: Coarse Localization Analysis . . . . . . . . . . . .
87
7.2.4
Online Phase: Fine Localization Analysis . . . . . . . . . . . . . .
90
7.2.5
Performance Comparison . . . . . . . . . . . . . . . . . . . . . . .
92
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
7.4
85
7.2.3
7.3
Offline Phase: Clustering Results by Affinity Propagation . . . . .
Subject Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8 Conclusion
8.1
109
Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Bibliography
113
vii

8. 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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5
Position error statistics for different methods on Bahen fourth floor. (For
validation set) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6
94
A set of optimal parameters for the CS-based position system applied on
CNIB second floor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.8
94
Position error statistics for different methods on Bahen fourth floor. (For
stationary user testing set) . . . . . . . . . . . . . . . . . . . . . . . . . .
7.7
93
99
Positioning error statistics for different positioning methods on CNIB second 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
viii

9. 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
ix

10. 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 offline phase.
3.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
Interaction between the database server and the mobile device during online 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. . . . . . . . . . . . . . .
x
73

11. 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. . . . . . . . . . . . . . . . . . . . . . . . . .
7.2
84
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. . . . . . . . .
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. . . .
7.4
84
85
Number of clusters generated by the affinity propagation algorithm depending on the value of parameter γ (o) for four orientations on Bahen
fourth floor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5
86
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. . . . . . . . . . . . . . . . . . . . . . .
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 .
7.7
89
The cumulative error distributions using different cluster matching schemes
on Bahen fourth floor. (8 APs are used) . . . . . . . . . . . . . . . . . .
7.9
89
The cumulative error distributions using different number of clusters for
the coarse localization on Bahen fourth floor. (8 APs are used) . . . . . .
7.8
88
90
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) . . . . . . . . . . . . . . . . . . . .
xi
94

12. 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 respect 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 parameters 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
xii

13. 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 navigation module. The squares denote the user’s locations and the circle
denotes the destination. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
xiii

14. Chapter 1
Introduction
1.1
Motivation
With the wide deployment of the mobile wireless systems and networks, the locationbased 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, locationbased 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 obtained. 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

15. 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 specifically 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 arrival (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-

16. Chapter 1. Introduction
3
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 distance measurements from at least 3 APs with known positions, lateration can be
performed to estimate the locations. This approach does not give accurate estimate, 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-

17. Chapter 1. Introduction
4
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 accessible 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 comprehensive 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

18. 5
Chapter 1. Introduction
Microsoft
Research Ekahau [18]
RADAR [19, 20]
Inter Place Lab and
Skyhook’s WPS [21]
Range
Building/local area
Building/local area
Position
Mobile device
Server (Ekahau Posi- Mobile device
Calculation
Metropolitan area
tioning Engine)
Position
Fingerprinting
+ Fingerprinting
+ Map-based pinpoint-
Method
KNN + Viterbi-like probabilistic
ing (obtain APs data
algorithm
by war driving) and
triangulation
Accuracy
3-5m
1-3m
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-time WLAN 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

19. 6
Chapter 1. Introduction
Reference Point
WLAN
Access Point
User equipped with
mobile device
Database Server
000
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) = [ˆ(t), y (t)]T , where
ˆ
x
ˆ
(ˆ(t), y (t)) are the Cartesian coordinates of the estimated position at time t.
x
ˆ
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

20. Chapter 1. Introduction
7
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.

21. 8
Chapter 1. Introduction
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 kernelbased 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 applying 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

22. Chapter 1. Introduction
9
from the database are best-matched to the online RSS readings. Then, the fine localization 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 guidance 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.

23. Chapter 1. Introduction
1.6
10
Contributions
This thesis proposes and implements a two stages indoor RSS-based WLAN positioning, 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 applies 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 localization 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 developed. It also determines whether the user follows the path and gives appropriate
instructions at proper times. (Chapter 5).

24. Chapter 1. Introduction
11
4. Software implementation and performance evaluation: A software is developed 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 smartphone 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 Beijing 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.

25. 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 positioning 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 RSSposition 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

26. 13
Chapter 2. Background and Related Works
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 log10 K − 10γ log10
d
− ηdB
d0
(2.1)
where K is a constant depending on the antenna characteristics and channel attenuation, 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
(2 ≤ γ ≤ 6 for indoor environment) and ηdB ∼ N (0, ση ) is a Gaussian random
variable.
• Wall Attenuation Factor model [19]
This model includes the effects of obstacles or walls between the transmitter and

27. Chapter 2. Background and Related Works
receiver. The received power can be obtained by:


 nW · W AF nW < C
d
pr [dBm] = p0 [dBm] − 10γ log10
−
d0  C · W AF

nW ≥ C
14
(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 W AF
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

28. Chapter 2. Background and Related Works
15
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 efficiently 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

29. Chapter 2. Background and Related Works
16
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 measurements 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 , ψ i (1), . . . , ψ i (T ))|i = 1, . . . , N }, where pi is the Cartesian coordinates for RP
i, ψ i (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 − ψ i ∥
¯
where ψ i =
1
T
∑T
τ =1
(2.3)
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

30. 17
Chapter 2. Background and Related Works
obtained to estimate the location p:
ˆ
K
1 ∑
p
p=
ˆ
K i=1 i
(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
∑K 1
pi
i=1
p = ∑K Di1
ˆ
(2.5)
i=1 Di
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:
pM AP = arg max f (pi |r) = arg max
ˆ
pi
pi
f (r|pi )f (pi )
N
∑
(2.6)
f (r|pi )f (pi )
i=1
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:
pM L = arg max f (r|pi )
ˆ
(2.7)
pi
The estimation can be further improved by including the likelihood densities as the weight
for the K RPs with the highest likelihood densities, namely:
pM L+weight =
ˆ
K
∑
wi p i
(2.8)
i=1
f (r|pi )
wi = ∑K
j=1 f (r|pi )
(2.9)

31. Chapter 2. Background and Related Works
18
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 f (rk |pi ).
k=1
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 experimental 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:
T
∑
ˆ(r|p ) = 1
f
K(r; ψ i )
i
T t=1
(2.10)
where K(r; ψ i ) 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

32. Chapter 2. Background and Related Works
19
independent, the Gaussian kernel function is defined as:
)
(
1
∥r − ψ i (t)∥2
K(r; ψ i ) = √
exp −
∗
∗
2(σi )2
( 2πσi )L
(2.11)
∗
where σi 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 performance 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 characteristic 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

33. 20
Chapter 2. Background and Related Works
Given:
Radio Map: {(pi , ψ i (1), . . . , ψ i (T ))|i = 1, . . . , N }
Number of APs: L
Number of time samples: T
Inputs:
Online RSS measurement vector: r
Outputs:
Position estimate: p
ˆ
Kernel-based Method:
∗
Optimal bandwidth: σi
( 4 ) 1
−1
∗
σi = L+2 L+4 σi T L+4
ˆ
∑
1
l
where, σi = L L (ˆi )2
ˆ2
l=1 σ
(ˆi )2 =
σl
1
T −1
∑T
t=1 (ψi,l (t)
¯
− ψi,l )2 ,
¯
ψi,l =
1
T
∑T
t=1
ψi,j (t)
Weight calculation:
)
(
∑
2
1
i
wi = T (√2πσ∗ )L T exp − ∥r−ψ∗(t)∥
t=1
2(σ )2
i
i
Estimation:
p=
ˆ
∑N
i=1 wi pi
∑N
i=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,

34. Chapter 2. Background and Related Works
21
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

35. Chapter 2. Background and Related Works
22
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 estimator. 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 computed 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 nonparametric 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.

36. Chapter 2. Background and Related Works
2.4
23
Pedestrian Navigation
Indoor navigation for pedestrian is different from the vehicular navigation using GPS,
which becomes an essential tool to the driver. Gilli`ron and Merminod [56] describes
e
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 information 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 visually 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 commonly 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 software 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.

37. Chapter 2. Background and Related Works
2.5
24
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. Another 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 preferences 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 responsibility 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 considerations the other potential exemplars. It is updated according to
r(i, j) = s(i, j) − ′ max {a(i, j ′ ) + s(i, j ′ )}
′
j s.t.j ̸=j
(2.12)

38. 25
Chapter 2. Background and Related Works
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) +

∑
max{0, r(i′ , j)}
i′ s.t.i′ ̸={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) − ′ max {a(i, j ′ ) + s(i, j ′ )}
′
a(j, j) =
∑
j s.t.j ̸=j
max{0, r(i′ , j)}
(2.14)
(2.15)
i′ s.t.i′ ̸=j
The exemplars can then be identified by combining the two messages. For data point
i, find
j ′ = arg max{a(i, j) + r(i, j)}
(2.16)
j
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 samples than traditional methods, which according to the Nyquist sampling theory requires

39. Chapter 2. Background and Related Works
26
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 {ψ i }N . Constructing a N × N basis
i=1
matrix Ψ = [ψ 1 , ψ 2 , ...ψ N ], the signal x can be expressed as
x=
N
∑
si ψi = Ψs
(2.17)
i=1
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 | < ϕi , ψ j > | is small.
1≤i,j≤N
Compressive sensing theory requires both the sparsity and incoherent sampling, so
that the signal can be recovered exactly with high probability. If M ≥ cKlog(N/K) ≪ N ,
where c is a small constant, the signal can be reconstructed by solving the following l1
norm minimization problem:
s = arg min ∥s∥1 such that Θs = y
ˆ
(2.19)
s∈RN
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

40. Chapter 2. Background and Related Works
27
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 Cand`s [65].
e
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 positioning 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 compressive sensing theory for sparse and incoherent sampled signals are discussed, these
concepts are used by the proposed positioning and tracking systems.

41. 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

42. 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.
Offline Phase
Fingerprinting
RSS Collections in 4
orientations
Clustering
Affinity Propagation
Online Phase
online RSS
readings
Fine Localization
Compressive Sensing
Coarse Localization
cluster matching
AP selection
Orthogonalization
L1-norm
minimization
Estimated
Location
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

43. Chapter 3. Compressive Sensing Based Positioning System
30
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
(o)
denoted as {ψi,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

(o)
ψ
 1,1
 (o)
ψ
 2,1
Ψ(o) =  .
 .
 .

(o)
ψL,1
environment and can be represented as Ψ(o) :

(o)
(o)
ψ1,2 · · · ψ1,N


(o)
(o) 
ψ2,2 · · · ψ2,N 
(3.1)
.
. 
..
.
. 
.
.
. 

(o)
(o)
ψL,2 · · · ψL,N
where o ∈ O = {0◦ , 90◦ , 180◦ , 270◦ } and ψi,j =
(o)
1
q
∑q
τ =1
(o)
ψi,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

44. Chapter 3. Compressive Sensing Based Positioning System
31
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
(o)
(o)
ψ j = [ψ1,j
(o)
ψ2,j
···
(o)
ψL,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)
(o)
∆j = [∆1,j
(o)
where ∆i,j =
1
q−1
∑q
(o)
τ =1 (ψi,j (τ )
(o)
∆2,j
···
(o)
∆L,j ]T ,
j = 1, 2, . . . , N
(3.3)
(o)
− ψi,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
(o)
(o)
form a set of (xj , yj ; ψ j ; ∆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

45. Chapter 3. Compressive Sensing Based Positioning System
32
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
(o)
(o)
s(i, j)(o) = −∥ψ i − ψ 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 definitions 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 generated exemplars is denoted as H(o) and the corresponding cluster member set with RP

46. Chapter 3. Compressive Sensing Based Positioning System
33
(o)
j as the exemplar is represented as Cj , 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 together with the fingerprint database to estimate the device’s location. The online RSS

47. Chapter 3. Compressive Sensing Based Positioning System
Mobile Device
34
Server
Collect RSS time samples from APs
at RP j for 4 orientations
Compute the average and variance of
RSS readings over time, _j (o), _ j(o)
∆
ψ
Send RP j’ s information:
_j (o), _j (o) & coordinates (x_j, y_j)
SEND
Collect fingerprint for RP j
in 4 orientations
∆
Use the device to
collect N RPs
ψ
Create overall radio map matrix:
(o)
= [ _ 1(o), _ 2(o),…, _N (o)]
ψ
ψ
ψ
Ψ
Apply affinity propagation on each
radio map to generate sets of
exemplars H(o) and their
corresponding members C_j (o)
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.

48. Chapter 3. Compressive Sensing Based Positioning System
3.3.1
35
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 SM atch (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 SM atch (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

49. Chapter 3. Compressive Sensing Based Positioning System
36
online measurement vector r to the individual exemplar’s RSS radio map vector
from each cluster:
(o)
SM atch (r, j)(o) = −∥r − ψ 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:
SM atch (r, j)(o) = −∥r −
∑
1
(o)
|Cj |
(o)
k∈Cj
(o)
ψ 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:
(o)
SM atch (r, j)(o) = −∥Wj · (r −
(o)
Wj
1
∑
(o)
|Cj |
(o)
k∈Cj
(o)
ψ k )∥2 , ∀j ∈ H(o) , ∀o ∈ O
√

(o)
w1,j
0
···
0


√


(o)
 0
w2,j 0
0 


= .

..
 .

.
0
0 
 .


√
(o)
0
···
0
wL,j
(3.9)
(3.10)

50. Chapter 3. Compressive Sensing Based Positioning System
(o)
where Wj
37
(o)
is the diagonal weight matrix and wl,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
(o)
wl,j ∝
1
¯ (o)
∆
l,j
¯ (o)
∆l,j =
1
(3.11)
∑
(o)
|Cj |
(o)
k∈Cj
Then these weights are normalized, so that
(o)
∆l,k
∑L
k=1
(3.12)
(o)
wl,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 exemplars SRSS with their corresponding cluster members set CRSS can be found as:
SRSS = {(j, o)| SM atch (r, j)(o) > α, j ∈ H(o) , o ∈ O}
(o)
CRSS = {(k, o)| k ∈ Cj , (j, o) ∈ SRSS }
(3.13)
(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

51. 38
Chapter 3. Compressive Sensing Based Positioning System
be a high percentage, α1 , of the maximum similarity difference, that is
α = α1 ·
max
j∈H(o) ,o∈O
{
}
SM atch (r, j)(o) + (1 − α1 ) ·
min
j∈H(o) ,o∈O
{
SM atch (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
(o)
˜
Ψ = [ψ 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
θ N ×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
, 0, ..., 0]T
(3.17)
nth element
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

52. 39
Chapter 3. Compressive Sensing Based Positioning System
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. Inclusion 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
th
that selects the desired lm AP, where lm ∈ M, by assigning ϕ(lm ) = 1 and zero to the
rest of the elements, namely:
ϕm = [0, ..., 0,
1
, 0, ..., 0],
lm ∈ M, ∀m = 1, 2, . . . , M
(3.19)
lm −th element
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]

53. Chapter 3. Compressive Sensing Based Positioning System
40
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 =
(o)
(j,o)∈CRSS (ψi,j
∑
(j,o)∈CRSS
¯
where ψi =
1
˜
N
∑
(j,o)∈CRSS
¯
− ψi )2
(o)
(3.20)
∆i,j
(o)
ψi,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

54. Chapter 3. Compressive Sensing Based Positioning System
41
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)

55. Chapter 3. Compressive Sensing Based Positioning System
42
˜
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].
ˆ
θ = arg min ∥θ∥1 ,
s.t. z = Qθ + ε′ .
(3.23)
˜
θ∈RN
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 resourcelimited 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 of O, 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
ˆ
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
ˆ
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
ˆ
all indices of the dominant elements in θ, which are above a certain threshold λ, denoted
as R
ˆ
R = {n|θ(n) > λ}
(3.24)
ˆ
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

56. Chapter 3. Compressive Sensing Based Positioning System
43
ˆ
potential candidate points, using the normalized value in θ as the corresponding weight
for each potential RP, that is
p = (ˆ, y ) =
ˆ
x ˆ
∑
ηn · (xn , yn )
(3.26)
n∈R
∑
ˆ
ˆ
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
ˆ
θ. Finally, the device asks the server for the potential candidate RP’s coordinates and
ˆ
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

57. Chapter 3. Compressive Sensing Based Positioning System
Mobile Device
Coarse
Localization
(cluster
matching)
Server
Collect online RSS readings r
,
44
It contains: Ψ (o), ∆_j (o), H(o), C_j(o)
- list of RPs coordinates
- map
REQUEST
Request and obtain map and RSS
values of exemplars.
SEND
Retrieve map and RSS readings of
exemplars
Find best matched
cluster exemplars, S
SEND S
Use the received matched cluster
exemplars S to obtain the matched
cluster members C and generate a
smaller radio map matrix Ψ
Obtain Ψ ͂ , ∆_j(o)
SEND
Send Ψ ͂ , ∆_j(o)
͂
AP selection
Orthogonalization
Fine
Localization
(CS-theory)
l1-norm minimization
Interpret device’s location
using relevant RPs coordinates.
REQUEST
RPs’ coordinates
Retrieve relevant RPs’ coordinates
SEND
RPs’ coordinates
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 sparsenatured 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

58. Chapter 3. Compressive Sensing Based Positioning System
45
proposed system. The server is mainly served as a database storage, which when requested 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.

59. Chapter 4
Indoor Tracking System
The previous chapter describes a positioning system that can accurately estimate a stationary 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) = [ˆ(t), y (t)]T .
ˆ
x
ˆ
46

60. Chapter 4. Indoor Tracking System
4.1
47
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 |z 0 ) ≡ p(z 0 ) 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