indoor localization techniques using wireless...
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INDOOR LOCALIZATION TECHNIQUES USING WIRELESS NETWORK AND
ARTIFICIAL NEURAL NETWORK
AIMAN BIN IBRAHIM
UNIVERSITI TEKNOLOGI MALAYSIA
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INDOOR LOCALIZATION TECHNIQUES USING WIRELESS NETWORK AND
ARTIFICIAL NEURAL NETWORK
AIMAN BIN IBRAHIM
A thesis submitted in fulfilment of the
requirements for the award of the degree of
Master of Philosophy
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
OCTOBER 2017
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ACKNOWLEDGEMENT
Preparing this thesis involves cumulative efforts from many kind-hearted
individuals providing vast contributions in terms of constructive inputs, tips, advices,
knowledge and thoughts essential for completing the research works presented. I
would like to address my gratitude to my main supervisor, Assoc. Prof. Ir. Dr. Sharul
Kamal Abdul Rahim for the excellent supervision, encouragement, support and
guidance. I also wish to express my sincere appreciation to my co-supervisor, Dr.
Leow Chee Yen for being the superhero in my heart, whom always been there to help
and assist especially at times when I was lost in the dark. My research work would
have never been able to shed some daylight without their repeated support and interest.
My gratitude extends to the lecturers whom allow me to attend their classes to get some
insight on knowledge relating to my research, namely Dr. Norhudah Seman, Prof. Dr.
Zuhaimy Ismail, Prof. Dr. Martin Haardt and Prof. Dr. Matthias Hein. I am also
thankful to librarians of UTM library and TU Ilmenau library for their assistance in
providing relevant literatures supplies throughout my study. I would like to highlight
my recognition the Ministry of Higher Education Malaysia for providing scholarship
for my study through the MyBrain15 scheme. Additionally, I feel indebted to the
Research Management Centre UTM for providing allowances through the research
student grant. Furthermore, sincere acknowledgement goes to UTM International
Office for organizing plus providing the funds for the student exchange program I
attended in Germany. Finally, many thanks to my parents, family members and friends
for their love friendship and support which with no doubt helped propelled my research
work into smooth sailing towards the end of completion.
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ABSTRACT
This research focuses on improving indoor localization using wireless network
and artificial neural network (ANN). This involves strategic study on wireless signal
behavior and propagation inside buildings, suitable propagation model to simulate
indoor propagation and evaluations on different localization methods such as distance
based, direction based, time based and signature based. It has been identified that
indoor signal propagation impairments are severe, non-linear and custom to a specific
indoor location. To accommodate these impairments, an ANN is proposed to provide
a viable solution for indoor location prediction as it learns the location specific
parameters during training, and then performs positioning based on the trained data,
while being robust to severe and non-linear propagation effects. The versatility of
ANN allows different setup and optimization possibilities to affect location prediction
capabilities. This research identified the best feedforward backpropagation neural
network configuration for the generated simulation data and introduced a new
optimization method. Indoor-specific received signal strength data were developed
with the Lee’s in-building model according to a custom indoor layout. Simulation
work was done to test localization performance with different feedforward
backpropagation neural network setups with the generated received signal strength
data as input. A data preparation method that converts the received signal strength raw
data into average, median, min and max values prior to be fed into the neural network
process was carried out. The method managed to increase location prediction
performance using feedforward neural network with two hidden layers trained with
Bayesian Regularization algorithm producing root mean squared error of 0.0821m,
which is 50% better in comparison to existing research work. Additional tests
conducted with six different relevant scenarios verified the scheme for localization
performance robustness. In conclusion, the research has improved the performance of
indoor localization using wireless network and ANN.
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ABSTRAK
Kajian ini memberi tumpuan kepada menambah baik penyetempatan lokasi
tertutup menggunakan rangkaian isyarat tanpa wayar dan rangkaian neural tiruan
(ANN). Ini merangkumi kajian tentang kelakuan isyarat tanpa wayar dan perambatan
dalam bangunan, model perambatan yang sesuai untuk simulasi perambatan dalam
kawasan tertutup dan penilaian ke atas kaedah penyetempatan berbeza seperti kaedah
berdasarkan jarak, kaedah berdasarkan arah, kaedah berdasarkan masa dan kaedah
berdasarkan corak. Telah dikenal pasti bahawa ketaksempurnaan perambatan isyarat
di lokasi tertutup adalah teruk, tidak sekata dan unik untuk lokasi tertutup tertentu.
Bagi mengatasi ketaksempurnaan ini, satu ANN dicadangkan untuk memberikan
penyelesaian baik kepada penyetempatan lokasi tertutup kerana ianya dapat
mempelajari maklumat khusus lokasi semasa latihan dan melakukan jangkaan lokasi
tertutup berdasarkan data latihan, sambil kekal teguh kepada kesan perambatan teruk
dan tidak sekata. Kepelbagaian ANN membolehkan persediaan berbeza dan
kemungkinan pengoptimuman bagi mempengaruhi kemampuan ramalan lokasi. Oleh
itu, kajian ini mengenal pasti konfigurasi rangkaian neural suap depan rambatan balik
terbaik untuk data simulasi yang dibangunkan sambil memperkenalkan kaedah
penambahbaikan yang baharu. Data kekuatan isyarat penerima khusus untuk lokasi
tertutup telah dibangunkan menggunakan model dalam bangunan Lee berdasarkan
susun atur lokasi tertutup unik. Simulasi dijalankan untuk menguji prestasi
penyetempatan menggunakan rangkaian neural suap depan rambatan balik berbeza
menggunakan data kekuatan isyarat yang telah dibangunkan sebagai input. Satu
kaedah penyediaan data yang menukarkan data kekuatan isyarat yang diterima kepada
nilai purata, nilai tengah, nilai minimum dan nilai maksimum sebelum dimasukkan ke
dalam proses rangkaian neural telah dilaksanakan. Penggunaan kaedah ini berjaya
meningkatkan prestasi jangkaan lokasi menggunakan rangkaian neural suap depan
rambatan balik dengan dua lapisan tersembunyi yang dilatih dengan algoritma
pengaturan Bayesian, menghasilkan ralat min punca kuasa dua pada 0.08210 meter,
iaitu 50% lebih baik berbanding kajian terkini. Ujian-ujian tambahan yang dijalankan
dengan enam senario berbeza membuktikan keteguhan prestasi jangkaan lokasi
menggunakan kaedah yang diperkenalkan dalam kajian ini. Kesimpulannya, kajian ini
berjaya menambah baik prestasi penyetempatan lokasi tertutup menggunakan
rangkaian isyarat tanpa wayar dan ANN.
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TABLE OF CONTENTS
CHAPTER TITLE PAGE
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES xi
LIST OF FIGURES xii
LIST OF ABBREVIATIONS xvi
LIST OF SYMBOLS xviii
LIST OF APPENDICES xx
1 INTRODUCTION 1
1.1 Background 1
1.2 Problem Statement and Research Motivation 3
1.3 Objectives of Research 4
1.4 Scope of Research 5
1.5 Research Contributions 6
1.6 Thesis Organization 7
2 LITERATURE REVIEW 8
2.1 Introduction 8
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2.2 Radio Signal Propagation 9
2.2.1 Signal Fading 9
2.2.1.1 Large-scale fading 11
2.2.1.2 Small-scale fading 12
2.2.2 Basic Propagation Mechanisms 13
2.2.2.1 Reflection 14
2.2.2.2 Diffraction 17
2.2.2.3 Scattering 18
2.2.3 Critical review on Radio Signal Propagation literature 19
2.3 Localization Methods 20
2.3.1 Closeness to a point of association 21
2.3.2 Distance based techniques 22
2.3.2.1 Time of Arrival/Time Difference of Arrival 27
2.3.2.2 Received Signal Strength 28
2.3.2.3 Received Signal Phase 30
2.3.3 Direction based techniques 31
2.3.4 Signature based techniques 31
2.3.5 Hybrid positioning schemes 34
2.3.6 Critical review on Localization Methods literature 35
2.4 Artificial Neural Network 36
2.4.1 Multiple-layered Perceptrons 36
2.4.2 Transfer functions 37
2.4.3 Training algorithms 39
2.4.4 Research work on neural network based localization 40
2.4.5 Critical review on Artificial Neural Network literature 44
2.5 Summary 44
3 METHODOLOGY 46
3.1 Introduction 46
3.2 Research Organizational Structure 48
3.3 Simulation Data Development 49
3.3.1 The Lee’s in-building model 51
3.3.2 LOS condition 52
3.3.3 NLOS condition 53
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3.3.3.1 Receiver in close-in region 55
3.3.3.2 Receiver beyond close-in region 57
3.3.4 Application of Lee’s in-building model to custom indoor
layout 60
3.4 Applying neural network for location prediction 71
3.4.1 Preprocessing and post-processing of data 73
3.4.2 Location prediction process with neural network 74
3.4.2.1 Training 75
3.4.2.2 Testing 75
3.4.2.3 Validation 76
3.4.2.4 Number of exemplar sets 76
3.4.3.5 Number of hidden layers and neurodes per
hidden layer 78
3.5 Simulation process 80
3.5.1 Location prediction with feedforward backpropagation
neural network 80
3.5.2 Data preparation method to optimize neural network
based localization 84
3.6 Summary 88
4 NEURAL NETWORK LOCATION PREDICTION WITH
DATA PREPARATION METHOD 90
4.1 Introduction 90
4.2 Matlab neural network toolbox plots 91
4.3 Location prediction with feedforward backpropagation neural
network 92
4.3.1 Single hidden layer feedforward backpropagation neural
network 92
4.3.2 2 hidden layer feedforward backpropagation neural
network 94
4.4 Applying data preparation method on neural network based
localization 95
4.5 Location prediction comparison with the weighted mean filter
method 97
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4.6 Overall analysis and discussion 100
4.7 Summary 101
5 PERFORMANCE EVALUATION OF NEURAL NETWORK
LOCATION PREDICTION WITH DATA PREPARATION
METHOD 102
5.1 Introduction 102
5.2 Scenario 1: 2 receivers; 1m x 1m transmitter resolution 103
5.21 Scenario 1 neural network location prediction 108
5.3 Scenario 2: 4 receivers; 1m x 1m transmitter resolution 110
5.31 Scenario 2 neural network location prediction 117
5.4 Scenario 3: 5 receivers; 1m x 1m transmitter resolution 117
5.41 Scenario 3 neural network location prediction 126
5.5 Scenario 4: 0.5m x 0.5m transmitter resolution; 3 receivers 127
5.51 Scenario 4 neural network location prediction 133
5.6 Scenario 5: 2m x 2m transmitter resolution; 3 receivers 134
5.61 Scenario 5 neural network location prediction 141
5.7 Scenario 6: Untrained transmitter points; 3 receivers 141
5.71 Scenario 6 neural network location prediction 143
5.8 Overall analysis and discussion 144
5.9 Summary 145
6 CONCLUSION AND FUTURE WORKS 146
6.1 Conclusion 146
6.2 Recommendations for Future Works 147
REFERENCES 149
Appendices A - Q 158-235
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LIST OF TABLES
TABLE NO. TITLE PAGE
2.1 Permittivity and conductivity values of different material 15
2.2 Triangulation application scenarios 22
2.3 List of transfer functions for neural network 38
2.4 Neural network training algorithm references 40
2.5 Comparison of research works on neural network based
localization 43
3.1 Symbol definitions for custom indoor layout 61
3.2 Lee’s in-building model constant variables 68
3.3 Neural network training algorithms 75
4.1 Location prediction with 1 hidden layer FFBNN 93
4.2 Location prediction with 2 hidden layer FFBNN 94
4.3 Location prediction with 2 hidden layer FFBNN and DPM 96
4.4 Location prediction with 2 hidden layer FFBNN and WMF 98
5.1 Scenario 1 results with 2 hidden layer FFBNN, BR and DPM 108
5.2 Scenario 2 results with 2 hidden layer FFBNN, BR and DPM 117
5.3 Scenario 3 results with 2 hidden layer FFBNN, BR and DPM 126
5.4 Scenario 4 results with 2 hidden layer FFBNN, BR and DPM 134
5.5 Scenario 5 results with 2 hidden layer FFBNN, BR and DPM 141
5.6 Scenario 6 results with 2 hidden layer FFBNN, BR and DPM 143
5.7 Location prediction performance evaluation analysis for
different scenario setups 144
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LIST OF FIGURES
FIGURE NO. TITLE PAGE
2.1 Classification of signal fading 10
2.2 Graphical representation of large-scale fading versus
small-scale fading 10
2.3 Classification of small-scale fading 13
2.4 Smooth surface reflections 14
2.5 Comparison of reflection between horizontally and
vertically polarized radio waves: (a) horizontal polarization
(b) vertical polarization 16
2.6 Illustration of diffraction 18
2.7 Classification of localization methods 21
2.8 (a) An illustration of the three-circle Venn diagram
(b) The geometry of a circular triangle displaying involved
chords and radii 24
2.9 A method of addressing the specifications of a circular triangle
in ordinance of a main coordinate system (x,y) relative to
complimentary sub coordinate systems (x’, y’) and (x”, y”) 25
2.10 Classification of fingerprinting algorithms 32
2.11 The multilayered perceptrons 36
3.1 General blueprint of the research 49
3.2 Process of simulation data development 50
3.3 Application of Lee’s in-building model in LOS situation 52
3.4 Fresnel zone between the reactive near-field and far-field zones 54
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3.5 Application of Lee’s in-building model in NLOS situation
within the close-in region 55
3.6 Application of Lee’s in-building model in NLOS situation
beyond the close-in region 57
3.7 Custom indoor layout with 3 receivers 60
3.8 Distance calculations between the transmitter at grid point {3,4}
and receiver 1, receiver 2 and receiver 3 62
3.9 Depiction if distances d1 up to d5 along transmission path
between the mobile transmitter at point {1,9} and the receiver 2 64
3.10 Set 1 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 69
3.11 Set 2 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 70
3.12 Set 3 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 71
3.13 Neural network process flow 73
3.14 Flowchart of neural network location prediction process 81
3.15 Neural network structure for first stage simulation process 82
3.16 Neural network structure for first stage simulation process in
matlab 82
3.17 2 hidden layer neural network structure for first stage simulation
process 83
3.18 2 hidden layer neural network structure for first stage simulation
process in matlab 83
3.19 Path loss data generated by the log-normal shadowing model 85
3.20 Data preparation applied to data generated by the log-normal
shadowing model 85
3.21 2 hidden layer neural network structure for simulation process
with DPM 87
3.22 2 hidden layer neural network structure for simulation process
with DPM in matlab 88
4.1 Location prediction performance comparison with 1 hidden layer
FBNN with different training algorithms 93
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4.2 Location prediction performance comparison between 1 hidden
layer FBNN and 2 hidden layer FBNN 95
4.3 Location prediction performance comparison between 2 hidden
layer FBNN with and without data preparation method applied 96
4.4 Location prediction performance comparison between 2 hidden
layer FBNN with WMF and with DPM 99
5.1 Location prediction performance evaluation in different
scenarios 102
5.2 Custom indoor layout with two receivers 104
5.3 Set 1 of simulated RSS values: (a) at receiver 1 (b) at receiver 2 105
5.4 Set 2 of simulated RSS values: (a) at receiver 1 (b) at receiver 2 105
5.5 Set 3 of simulated RSS values: (a) at receiver 1 (b) at receiver 2 106
5.6 2 hidden layer neural network structure for third stage scenario 1
simulation process 107
5.7 2 hidden layer neural network structure for third stage scenario 1
simulation process in matlab 108
5.8 Symmetrical problem between 2 receivers 109
5.9 Custom indoor layout with 4 receivers 110
5.10 Set 1 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 (d) at receiver 4 112
5.11 Set 2 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 (d) at receiver 4 113
5.12 Set 3 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 (d) at receiver 4 114
5.13 2 hidden layer neural network structure for third stage scenario 2
simulation process 115
5.14 2 hidden layer neural network structure for third stage scenario 2
simulation process in matlab 116
5.15 Custom indoor layout with 5 receivers 118
5.16 Set 1 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 (d) at receiver 4 (e) at receiver 5 120
5.17 Set 2 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 (d) at receiver 4 (e) at receiver 5 122
5.18 Set 3 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
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(c) at receiver 3 (d) at receiver 4 (e) at receiver 5 123
5.19 2 hidden layer neural network structure for third stage scenario
3 simulation process 124
5.20 2 hidden layer neural network structure for third stage scenario
3 simulation process in matlab 126
5.21 Custom indoor layout with 0.5m transmitter grid 127
5.22 Set 1 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 128
5.23 Set 2 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 129
5.24 Set 3 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 130
5.25 2 hidden layer neural network structure for third stage scenario
4 simulation process 132
5.26 2 hidden layer neural network structure for third stage scenario
4 simulation process with matlab 133
5.27 Custom indoor layout with 2m transmitter grid 135
5.28 Set 1 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 136
5.29 Set 2 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 137
5.30 Set 3 of simulated RSS values: (a) at receiver 1 (b) at receiver 2
(c) at receiver 3 138
5.31 2 hidden layer neural network structure for third stage scenario
5 simulation process 140
5.32 2 hidden layer neural network structure for third stage scenario
5 simulation process in matlab 141
5.33 Untrained transmitter locations: (a) between 2m grids (b)
between 1m grids (c) between 0.5m grids 142
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LIST OF ABBREVIATIONS
WSN - Wireless Signal Networks
GNSS - Global Navigation Satellite Systems
GPS - Global Positioning System
GLONASS - Global Navigation Satellite Systems
CNSS - Chinese Navigation Satellite System
QZSS - Quasi-Zenith Satellite System
IRNISS - Indian Regional Navigational Satellite System
LOS - Line of sight
NLOS - Non line of sight
RSS - Received signal strength
ISI - Intersymbol interference
TOA - Time of arrival
TDOA - Time difference of arrival
DGPS - Differential global positioning system
AOA - Angle of arrival
DOA - Direction of arrival
SMP - Smallest M-vertex polygon
SOM - Self organizational map
PCA - Principle component analysis
BP - Backpropagation
MLP - Multiple layered perceptrons
ART - Adaptive resonance theory
BAM - Bidirectional associative memory
RBF - Radial Basis Function
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SVM - Support vector machine
FANN - Feedforward artificial neural network
LQI - Link Quality Indicator
CIR - Channel impulse response
PSO - Particle swarm optimization
FFBNN - Feedforward backpropagation neural network
RBFNN - Radial basis function neural network
BFGS - Broyden-Fletcher-Goldfarb-Shanno
LM - Levenberg-Marquardt
BR - Bayesian regularization
OSS - One step secant
RP - Resilient backpropagation
CG - Conjugate gradient
GD - Gradient descent
RAM - Random access memory
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LIST OF SYMBOLS
𝑃𝑡 - Transmitted power
𝑃𝑟 - Received power
𝐺𝑡 - Transmitting antenna gain
𝐺𝑟 - Receiving antenna gain
𝐿 - Loss factor
𝜆 - Wavelength
𝑓 - frequency
d - Distance
𝑋𝜎 - Gaussian random variable
𝜎 - Standard deviation
v - Speed
𝐵𝑠 - Bandwidth of transmitted signal
𝑇0 - Time of arrival
𝑇𝑠 - Reciprocal bandwidth
𝜎𝜏 - RMS delay spread
𝐵𝐻 - Coherence bandwidth
𝑅𝑆 - Signal data rate
𝑓𝑑 - Doppler frequency
𝑛 - Refraction index
𝜃1 - Incident angle
𝜃2 - Reflected angle
𝑎ℎ - Horizontal reflection coefficient
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𝑎𝑣 - Verticle reflection coefficient
휀𝑐 - dielectric constant
휀𝑟 - permittivity
𝛽 - Brewster angle
ℎ𝑐 - Critical height of surface protuberance
Γ - Reflection coefficient of smooth surface
Γ𝑟𝑜𝑢𝑔ℎ - Reflection coefficient of rough surface
𝜌𝑠 - Scattering loss factor
c - speed of light
𝜏 - transmission time
α - Decay rate
b - Bias
𝐷𝑐 - close-in distance
ℎ𝑡 - height of transmitter
ℎ𝑟 - height of receiver
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LIST OF APPENDICES
APPENDIX TITLE PAGE
A List of Author’s Publications 158
B Simulation Data Development with Microsoft Excel 159
C MATLAB ANN Toolbox Settings 161
D Complete Location Prediction Results with 1 Hidden
Layer FBNN 166
E Complete Location Prediction Results with 2 Hidden
Layer FBNN 176
F Complete Location Prediction Results with 1 Hidden
Layer FBNN and DPM 186
G Complete Location Prediction Results with 2 Hidden
Layer FBNN and DPM 196
H Complete Location Prediction Results with 2 Hidden
Layer FBNN and WMF 206
I Simulation Data Development for Performance
Evaluation Scenario 1 216
J Complete Location Prediction Results for Performance
Evaluation Scenario 1 218
K Simulation Data Development for Performance
Evaluation Scenario 2 220
L Complete Location Prediction Results for Performance
Evaluation Scenario 2 218
M Complete Location Prediction Results for Performance
Evaluation Scenario 3 218
N Simulation Data Development for Performance
Evaluation Scenario 4 226
xxi
O Complete Location Prediction Results for Performance
Evaluation Scenario 4 231
P Simulation Data Development for Performance
Evaluation Scenario 5 233
Q Complete Location Prediction Results for Performance
Evaluation Scenario 5 234
1
CHAPTER 1
INTRODUCTION
1.1 Indoor Localization
Localization is a process of determining the position of devices within a
specific area. It is also recognized as geolocation, radiolocation, parameter sensing or
positioning [1]–[5]. Normally localization determines the coordinates of a target node
in two or three dimensions, specifying the latitude and longitude of where the node is
located. Localization leads to many pioneering application potentials which can be
developed by utilizing this technology especially when the targeted device’s
coordinates can be identified wirelessly or even better, involving capability to engage
mobile or non-static devices. Consequently, over the past decades a lot of research
work have been done due to the interest of improving current systems in terms of
accuracy performance, computational cost, complexity and production cost [6]. While
resolving and finding solutions for many issues, research work also contribute in
identifying new problems and limitations. This therefore introduces opportunities for
further research work to be done.
In reference to Elliot D. Kaplan et. al [7], a popular method for localization
would be through the implementation of the Global Navigation Satellite Systems
(GNSS), which estimates the target node positions by calculating the transmitted data
from multiple satellites to the receiver. The most well-known among currently
available GNSSs is the Global Positioning System (GPS) which is managed by the
United States government. Other options of GNSSs include the Global Navigation
2
Satellite System (GLONASS), Galileo, Chinese Navigation Satellite System (CNSS)
named Compass/Beidou, Japanese Quasi-Zenith Satellite System (QZSS) and the
Indian Regional Navigational Satellite System (IRNSS). In total more than 100
satellites are involved to operate GNSSs around the globe. These satellites transmit
their time and position data continuously while the receivers on the ground monitor
and process these data with equations that estimate location via calculations involving
measurements of deviation with the true time relative to the satellites position. In order
to achieve acceptable coordinating performance, a minimum of 4 satellites must be in
view of the receiver for sufficient data computation [8].
As a result, particular limitations are introduced upon urban areas where
satellite signals are most likely to be blocked by the high density of buildings and
infrastructures. Therefore, an alternative method is required to apply localization
especially in indoor situations where GNSSs do not work [9]. Many researchers are
going through the route of using Wireless Signal Networks to achieve this as it is
already widely used inside buildings for telecommunication and data transmissions
[1]. However, various errors on location prediction are occurring due to non-linear
propagation effects, which are more severe in indoor areas and are sensitive to the
performance of the localization system [10].
Having an accurate and reliable GPS like system indoors would open up
towards many possibilities of useful applications [11]. For example, during an
emergency situation in a busy hospital, where a patient must be attended as soon as
possible, having a system that would know the positions of every doctor or medical
officer and call the closest one available may contribute to having an efficient
personnel management in complicated environments while increasing the chances of
being a life saver. This may also apply similarly to other situations where people can
be quickly allocated and assembled for immediate meetings in business, government,
educational or law enforcement organizations. On the other hand, asset or equipment
management can be improved through parameter fencing system where attached nodes
can be monitored on real-time basis preventing misplacement and also making sure
the security is optimized by applying triggering mechanisms when the asset or
equipment is taken out from a certain set of parameters. Additionally, an indoor
3
navigation system would benefit users on finding desirable destinations more
effectively and conveniently within a large building such as shopping malls, faculty
buildings, stadiums or expo halls.
1.2 Problem Statement and Research Motivation
In order to understand the relationship between radio signal propagation and
radio signal transmission distance, it is essential to know behavior of electromagnetic
radiation relative to the space between the transmitter and receiver. According to
David M. Pozar [12], research on the nature of electromagnetic radiation has started
since the 18th century where James Clerk Maxwell developed his theory stating that
radio waves move through free space at finite velocity with an order of magnitude
similar to the of speed of light while involving instantaneous propagation effects which
were not consistent with ‘action at a distance’ theories. Maxwell’s theory was then
verified by Heinrich Hertz whom undertook controlled experiments to confirm that the
electromagnetic behavior predictions by Maxwell were indeed true.
Fundamental theories provide a basis of the understanding radio propagation
with the assumption of radio signal transfer in free space or in a uniform dielectric
medium. However, real live implementation requires further considerations as it
involves contact with large variety of transfer medium which are different in
properties, shapes, sizes and distribution. This results to radio signal impairments and
distortion as it goes through the transmission process from the transmitter to the
receiver. Subsequently, the impairments of radio signal transfer also contribute to error
in location measurements based on radio propagation. The effects of radio propagation
include reflection, diffraction, scattering and fading.
Indoor localization introduces a very tough environment for signal
propagation. The signal distortion and impairments are more severe inside buildings
due to the existence of multiple objects of different materials affecting the transmission
of signal between the transmitting antenna and the receiving antenna. Different surface
4
shapes and roughness, object sizes and composition and object location and
distribution all lead to different propagation effects. Furthermore, the higher density
of these objects indoors increases the complexity of signal propagation as non-line of
sight (NLOS) situations are more likely. Indoor environments are very different at
different locations. This means signal distortion and impairments are also different
depending on the location. Therefore, in general, a parameter adaptive method of
location estimation is necessary to solve non-linear propagation effects for indoor
localization scheme.
The main motivation of this research is the profound ability of artificial neural
networks to classify non-linear problems for pattern recognition. Artificial neural
network mimics the brain function of learning and solving problems based on the
information learnt. This concept can be applied directly for indoor localization which
needs an adaptive mechanism to estimate position based on the parameters of a certain
location. The signal propagation will provide a specific pattern for each location and
these data will be taught and trained into the artificial neural network. Then during the
online phase, the neural network will predict the location based on the training data.
There are many ways to configure the neural network plus there are numerous
optimization possibilities within the application of neural network process.
As severe indoor propagation causes non-linear and location specific signal
patterns relative to the distance of signal transmission, this creates challenging input
data for the neural network to process and utilize to predict the mobile node location.
Therefore, there is a need of an effective optimization technique to allow the neural
network to receive a more distinguishable pattern which would lead to better
performance in mobile location prediction.
1.3 Objectives of Research
The paramount objective of this research is to provide a valid location
prediction solution for the problems occurring during indoor parameter sensing using
5
wireless networks, following the path of our research motivations, with the end goal
of producing a better performance for indoor localization system by utilizing suitable
artificial neural network processes. Specifically, the objectives of this research are
stated in the list below:
i. To investigate for a feedforward backpropagation neural network
configuration suitable for indoor localization using the developed simulation
data.
ii. To optimize neural network based indoor localization with proposed data
preparation strategy for improved location prediction accuracy.
iii. To conduct comprehensive performance evaluation on the proposed method of
indoor localization.
1.4 Scope of research
The research focuses on WSN localization for indoor parameter sensing.
Centralized localization method is used where the computation takes place at the
receivers which are interconnected while mobile nodes only act as transmitters. The
study is based on 5.8GHz radio frequency suitable for short range femtocell
applications. The basic triangulation technique is adopted where the received signal
strengths (RSS) from three different receiver base station locations provide input
parameters for the neural network to process and conduct location prediction
accordingly. The primary simulation tool is the Matlab software. The neural network
toolbox is utilized to process the obtained simulation data with different types of
Artificial Neural Network algorithm configurations for location prediction. With
exemption to the max epoch and max validation error, all training parameters are
according to default values of the neural network toolbox. Data preparation provides
strategic input pattern to the Artificial Neural Network. The prepared data is limited to
100 values generated from 100 raw data. The research is based on static receivers and
ignores the effect movements of the mobile transmitter nodes as indoor localization
applications normally involve static or low velocity movements of the mobile
6
transmitter nodes. The received signal strength data is developed using the Lee’s in-
building model according to a custom indoor layout. The indoor layout design is
limited to an empty building structure.
1.5 Research Contributions
The research work done provide contributions by introducing methodologies
which are compliant to improving indoor localization approach and application as
listed below.
i. The research provides an indoor specific development of simulation data by
utilizing the Lee’s in-building model to provide received signal strength data
in locations according to a custom indoor layout. In contrary to the log-normal
shadowing model used by many research works related to indoor localization
[13]–[17], the Lee’s in-building model takes into consideration of additional
indoor-specific parameters including wall thickness, wall material, floor
material, height of the transmitter and the receiver, Fresnel zone distance
between the transmitter and receiver, LOS and NLOS properties of the signal
path and the number of rooms within the signal path to model the received
signal strength accordingly. Therefore, a more relevant simulation data is
produced which better simulates severe radio signal propagation in indoor
environments.
ii. The research also proposes the application of a novel data preparation method
on the RSS data to optimize location prediction with 2 hidden layer
feedforward backpropagation neural network trained with Bayesian
Regularization training algorithm. The proposed data preparation method
involves manipulating the raw RSS data into min, max, median and average
values which provide a more strategic input to be processed by the neural
network for location prediction. This method is contrary to traditional filtering
methods where portions of valuable RSS information is eliminated to create a
desirable range of RSS data. The proposed data preparation method enables
7
respectable location prediction accuracy with RMSE of 0.08210m which better
than the most recent related research work [18]. This research also provides
comprehensive analysis on indoor localization with the proposed data
preparation method by evaluating several different scenario applications.
1.6 Thesis Organization
This thesis is organized into 6 chapters respectively. The first chapter provides
introductory insight into the research by laying out the fundamental background of the
research topic, the problem statements, the research objectives, the scope which limits
the research and the contributions yielded by the completion of the research. The
second chapter provides elaborate discussion on the theories and previous research
work related to the research topic. By conducting critical review of relevant literatures,
the research problem is magnified which consequently reveals existing research gaps
providing reference for the direction of research. The third chapter establishes the
general blueprint of the research. This is where the methodology framework is
presented in detail, presenting actions taken to achieve the objectives of the research.
The fourth chapter provides analysis discussions on the indoor localization
performance of different feedforward backpropagation neural network configurations,
the effects of the data preparation method to location prediction and comparison
analysis between the proposed data preparation method and the weighted mean filter
method. The obtained results are analyzed to verify that the fulfillment of objectives 1
and 2 of the research. Chapter 5 proceeds with location prediction performance
evaluation analysis of the proposed method in different controlled scenarios to satisfy
the third objective of the research. The last chapter synthesizes the overall research
work into a complimentary conclusion and recommends future research works to
further improve indoor location prediction.
149
REFERENCES
[1] H. Liu, H. Darabi, P. Banerjee, and J. Liu, “Survey of wireless indoor
positioning techniques and systems,” IEEE Trans. Syst. Man Cybern. Part C
Appl. Rev., vol. 37, no. 6, pp. 1067–1080, 2007.
[2] N. Patwari, J. N. Ash, S. Kyperountas, A. O. Hero, R. L. Moses, and N. S.
Correal, “Locating the nodes: cooperative localization in wireless sensor
networks,” IEEE Signal Process. Mag., vol. 22, no. 4, pp. 54–69, 2005.
[3] K. Pahlavan, X. Li, and J. P. Makela, “Indoor geolocation science and
technology,” IEEE Communications Magazine, vol. 40, no. 2. pp. 112–118,
2002.
[4] J. J. Caffery and G. L. Stuber, “Overview of radiolocation in CDMA cellular
systems,” IEEE Communications Magazine, vol. 36, no. 4. pp. 38–45, 1998.
[5] A. P. S. Thengal, N. Rastogi, A. Medhi, R. Srivastava, and K. Datta,
“Parameter sensing and object tracking using global positioning system,” 2016
Sixth International Symposium on Embedded Computing and System Design
(ISED). pp. 289–293, 2016.
[6] K. Pahlavan and P. Krishnamurthy, Principles of wireless access and
localization. John Wiley & Sons, 2013.
[7] E. Kaplan and C. Hegarty, Understanding GPS: principles and applications.
Artech house, 2005.
[8] P. Banerjee, “GPS : A powerfull tool for time transfer,” URSI Radio Science
Bulletin, vol. 81, no. 2. pp. 56–73, 2008.
[9] K. Pahlavan, P. Krishnamurthy, and A. Beneat, “Wideband radio propagation
modeling for indoor geolocation applications,” IEEE Communications
Magazine, vol. 36, no. 4. pp. 60–65, 1998.
[10] K. Pahlavan, F. O. Akgul, M. Heidari, A. Hatami, J. M. Elwell, and R. D.
Tingley, “Indoor geolocation in the absence of direct path,” IEEE Wireless
Communications, vol. 13, no. 6. pp. 50–58, 2006.
150
[11] Y. Gu, A. Lo, and I. Niemegeers, “A survey of indoor positioning systems for
wireless personal networks,” IEEE Communications Surveys & Tutorials, vol.
11, no. 1. pp. 13–32, 2009.
[12] D. M. Pozar, Microwave engineering. John Wiley & Sons, 2009.
[13] A. Payal, C. S. Rai, and B. V. R. Reddy, “Artificial Neural Networks for
developing localization framework in Wireless Sensor Networks,” Data Min.
Intell. Comput. (ICDMIC), 2014 Int. Conf., pp. 1–6, 2014.
[14] M. S. Rahman, Y. Park, and K.-D. Kim, “RSS-Based Indoor Localization
Algorithm for Wireless Sensor Network Using Generalized Regression Neural
Network,” Arab. J. Sci. Eng., vol. 37, no. 4, pp. 1043–1053, 2012.
[15] L. Gui, M. Yang, P. Fang, and S. Yang, “RSS-based indoor localisation using
MDCF,” IET Wireless Sensor Systems, vol. 7, no. 4. pp. 98–104, 2017.
[16] A. Alhammadi, Fazirulhiysam, M. Fadlee, and S. Alraih, “Effects of different
types of RSS data on the system accuracy of indoor localization system,” 2016
IEEE Region 10 Symposium (TENSYMP). pp. 311–314, 2016.
[17] P. Pivato, L. Palopoli, and D. Petri, “Accuracy of RSS-Based Centroid
Localization Algorithms in an Indoor Environment,” IEEE Transactions on
Instrumentation and Measurement, vol. 60, no. 10. pp. 3451–3460, 2011.
[18] S. K. Gharghan, R. Nordin, M. Ismail, and J. A. Ali, “Accurate Wireless
Sensor Localization Technique Based on Hybrid PSO-ANN Algorithm for
Indoor and Outdoor Track Cycling,” IEEE Sens. J., vol. 16, no. 2, pp. 529–
541, 2016.
[19] W. C. Jakes and D. C. Cox, Microwave mobile communications. Wiley-IEEE
Press, 1994.
[20] A. Goldsmith, Wireless communications. Cambridge university press, 2005.
[21] Y. S. Cho, J. Kim, W. Y. Yang, and C. G. Kang, MIMO-OFDM wireless
communications with MATLAB. John Wiley & Sons, 2010.
[22] T. S. Rappaport and others, Wireless communications: principles and practice,
vol. 2. Prentice Hall PTR New Jersey, 1996.
151
[23] W. Lee, Integrated Wireless Propagation Models. McGraw Hill Professional,
2014.
[24] M. P. Fewell, M. Operations Division, and M. Operations Division Chief,
Area of common overlap of three circles. 2006.
[25] B. Denis, J. B. Pierrot, and C. Abou-Rjeily, “Joint distributed synchronization
and positioning in UWB Ad Hoc networks using TOA,” IEEE Trans. Microw.
Theory Tech., vol. 54, no. 4, pp. 1896–1910, 2006.
[26] E. Xu, Z. Ding, and S. Dasgupta, “Source localization in wireless sensor
networks from signal time-of-arrival measurements,” IEEE Trans. Signal
Process., vol. 59, no. 6, pp. 2887–2897, 2011.
[27] G. Wang, S. Cai, Y. Li, and M. Jin, “Second-order cone relaxation for TOA-
based source localization with unknown start transmission time,” IEEE Trans.
Veh. Technol., vol. 63, no. 6, pp. 2973–2977, 2014.
[28] H. Xiong, Z. Chen, B. Yang, and R. Ni, “TDOA localization algorithm with
compensation of clock offset for wireless sensor networks,” China Commun.,
vol. 12, no. 10, pp. 193–201, 2015.
[29] M. Liu, H. Leung, and A. Maddumabandara, “Experimental Evaluation of
Indoor Localization Using Wireless Sensor Networks,” IEEE Sens. J., vol. PP,
no. 99, pp. 1–1, 2015.
[30] S. Gezici et al., “Localization via ultra-wideband radios: A look at positioning
aspects of future sensor networks,” IEEE Signal Process. Mag., vol. 22, no. 4,
pp. 70–84, 2005.
[31] N. Patwari et al., “Relative location estimation in wireless sensor networks,”
Signal Process. …, vol. 51, no. 8, pp. 2137–2148, 2003.
[32] W. D. Wang and Q. X. Zhu, “RSS-based Monte Carlo localisation for mobile
sensor networks,” IET Commun., vol. 2, no. 5, pp. 673–681, 2008.
[33] Y. Kong, Y. Kwon, and G. Park, “Robust localization over obstructed
interferences for inbuilding wireless applications,” IEEE Trans. Consum.
Electron., vol. 55, no. 1, pp. 105–111, 2009.
152
[34] R. W. Ouyang, A. K. S. Wong, and C. T. Lea, “Received signal strength-based
wireless localization via semidefinite programming: Noncooperative and
cooperative schemes,” IEEE Trans. Veh. Technol., vol. 59, no. 3, pp. 1307–
1318, 2010.
[35] H. R. H. Ren and M. Q.-H. Meng, “Power Adaptive Localization Algorithm
for Wireless Sensor Networks Using Particle Filter,” IEEE Trans. Veh.
Technol., vol. 58, no. 5, pp. 2498–2508, 2009.
[36] R. K. Martin, “Based Positioning Performance,” vol. 18, no. 12, pp. 741–744,
2011.
[37] Q. Wang, I. Balasingham, M. Zhang, and X. Huang, “Improving RSS-based
ranging in LOS-NLOS scenario using GMMs,” IEEE Commun. Lett., vol. 15,
no. 10, pp. 1065–1067, 2011.
[38] H. C. So and L. Lin, “Linear least squares approach for accurate received
signal strength based source localization,” IEEE Trans. Signal Process., vol.
59, no. 8, pp. 4035–4040, 2011.
[39] G. Wang and K. Yang, “A new approach to sensor node localization using rss
measurements in wireless sensor networks,” IEEE Trans. Wirel. Commun.,
vol. 10, no. 5, pp. 1389–1395, 2011.
[40] P. Pivato, L. Palopoli, and D. Petri, “Accuracy of RSS-based centroid
localization algorithms in an indoor environment,” IEEE Trans. Instrum.
Meas., vol. 60, no. 10, pp. 3451–3460, 2011.
[41] C. Feng, W. S. A. Au, S. Valaee, and Z. Tan, “Received-signal-strength-based
indoor positioning using compressive sensing,” IEEE Trans. Mob. Comput.,
vol. 11, no. 12, pp. 1983–1993, 2012.
[42] N. Salman, M. Ghogho, and A. H. Kemp, “Optimized low complexity sensor
node positioning in wireless sensor networks,” IEEE Sens. J., vol. 14, no. 1,
pp. 39–46, 2014.
[43] I. T. Haque and C. Assi, “Profiling-based indoor localization schemes,” IEEE
Syst. J., vol. 9, no. 1, pp. 76–85, 2015.
[44] S. H. Fang and T. N. Lin, “Indoor location system based on discriminant-
153
adaptive neural network in IEEE 802.11 environments,” IEEE Trans. Neural
Networks, vol. 19, no. 11, pp. 1973–1978, 2008.
[45] E. D. Kaplan and S. Lewis, “Understanding GPS: Principles and applications,”
J. Electron. Def., vol. 20, pp. 81–84, 1997.
[46] K. Li, J. Bigham, and L. Tokarchuk, “Validation of a Probabilistic Approach
to Outdoor Localization,” IEEE Wirel. Commun. Lett., vol. 2, no. 2, pp. 167–
170, 2013.
[47] D. Li, B. Zhang, and C. Li, “A Feature-Scaling-Based k -Nearest Neighbor
Algorithm for Indoor Positioning Systems,” IEEE Internet Things J., vol. 3,
no. 4, pp. 590–597, 2016.
[48] C. Nerguizian, S. Belkhous, A. Azzouz, V. Nerguizian, and M. Saad, “Mobile
robot geolocation with received signal strength (RSS) fingerprinting technique
and neural networks,” Industrial Technology, 2004. IEEE ICIT ’04. 2004
IEEE International Conference on, vol. 3. p. 1183–1185 Vol. 3, 2004.
[49] M. Stella, M. Russo, and D. Begusic, “Location Determination in Indoor
Environment based on RSS Fingerprinting and Artificial Neural Network,”
2007 9th International Conference on Telecommunications. pp. 301–306,
2007.
[50] G. Sun and W. Guo, “Robust mobile geo-location algorithm based on LS-
SVM,” IEEE Trans. Veh. Technol., vol. 54, no. 3, pp. 1037–1041, 2005.
[51] D. a. Tran and T. Nguyen, “Localization In Wireless Sensor Networks Based
on Support Vector Machines,” IEEE Trans. Parallel Distrib. Syst., vol. 19, no.
7, pp. 1–13, 2008.
[52] W. Kim, J. Park, J. Yoo, H. J. Kim, and C. G. Park, “Target localization using
ensemble support vector regression in wireless sensor networks,” IEEE Trans.
Cybern., vol. 43, no. 4, pp. 1189–1198, 2013.
[53] Z. Wu, K. Fu, E. Jedari, S. R. Shuvra, R. Rashidzadeh, and M. Saif,
“Positioning Using Received Signal Strength,” vol. 65, no. 12, pp. 9747–9758,
2016.
[54] W. H. Wong, J. K. Ng, and W. M. Yeung, “Wireless LAN Positioning with
154
Mobile Devices in a Library Environment,” 25th IEEE Int. Conf. Distrib.
Comput. Syst. Work., pp. 633–636, 2005.
[55] Y. Qi, H. Kobayashi, and H. Suda, “Analysis of wireless geolocation in a non-
line-of-sight environment,” IEEE Trans. Wirel. Commun., vol. 5, no. 2, pp.
672–681, 2006.
[56] C. Li and Z. Weihua, “Hybrid TDOA/AOA mobile user location for wideband
CDMA cellular systems,” IEEE Trans. Wirel. Commun., vol. 1, no. 3, pp.
439–447, 2002.
[57] Y. Fu and Z. Tian, “Cramer-Rao bounds for hybrid TOA/DOA-based location
estimation in sensor networks,” IEEE Signal Process. Lett., vol. 16, no. 8, pp.
655–658, 2009.
[58] L. Taponecco, A. A. D’Amico, and U. Mengali, “Joint TOA and AOA
estimation for UWB localization applications,” IEEE Trans. Wirel. Commun.,
vol. 10, no. 7, pp. 2207–2217, 2011.
[59] D. Kriesel, “A brief Introduction on Neural Networks,” 2007.
[60] C. G. Looney, Pattern recognition using neural networks: theory and
algorithms for engineers and scientists. Oxford University Press, Inc., 1997.
[61] K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks
are universal approximators,” Neural networks, vol. 2, no. 5, pp. 359–366,
1989.
[62] H. B. Demuth, M. H. Beale, O. De Jess, and M. T. Hagan, Neural network
design. Martin Hagan, 2014.
[63] J. Dennis and R. Schnabel, Numerical Methods for Unconstrained
Optimization and Nonlinear Equations. Society for Industrial and Applied
Mathematics, 1996.
[64] M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the
Marquardt algorithm,” IEEE Transactions on Neural Networks, vol. 5, no. 6.
pp. 989–993, 1994.
[65] F. D. Foresee and M. T. Hagan, “Gauss-Newton approximation to Bayesian
155
learning,” Neural Networks,1997., International Conference on, vol. 3. pp.
1930–1935 vol.3, 1997.
[66] M. Riedmiller and H. Braun, “A direct adaptive method for faster
backpropagation learning: the RPROP algorithm,” IEEE International
Conference on Neural Networks. pp. 586–591 vol.1, 1993.
[67] M. F. Moller, “A scaled conjugate gradient algorithm for fast supervised
learning,” NEURAL NETWORKS, vol. 6, no. 4, pp. 525–533, 1993.
[68] P.-J. Chuang and Y.-J. Jiang, “Effective neural network-based node
localisation scheme for wireless sensor networks,” IET Wirel. Sens. Syst., vol.
4, no. 2014, pp. 97–103, 2014.
[69] L. Luoh, “ZigBee-based intelligent indoor positioning system soft
computing,” Soft Comput., vol. 18, no. 3, pp. 443–456, 2014.
[70] N. Irfan, M. Bolic, M. C. E. Yagoub, and V. Narasimhan, “Neural-based
approach for localization of sensors in indoor environment,” Telecommun.
Syst., vol. 44, no. 1–2, pp. 149–158, 2010.
[71] A. Azenha, L. Peneda, and A. Carvalho, “A neural network approach for
Radio Frequency based indoors localization,” IECON 2012-38th Annu. …, pp.
5990–5995, 2012.
[72] C. Nerguizian and V. Nerguizian, “Indoor fingerprinting geolocation using
wavelet-based features extracted from the channel impulse response in
conjunction with an artificial neural network,” IEEE Int. Symp. Ind. Electron.,
pp. 2028–2032, 2007.
[73] A. Payal, C. S. Rai, and B. V. R. Reddy, “Analysis of Some Feedforward
Artificial Neural Network Training Algorithms for Developing Localization
Framework in Wireless Sensor Networks,” Wirel. Pers. Commun., vol. 82, no.
4, pp. 2519–2536, 2015.
[74] K. Thongpull, N. Jindapetch, and W. Teerapakajorndet, “A Neural Network
based Optimization for Wireless Sensor Node Position Estimation in Industrial
Environments.”
[75] S. Yun, J. Lee, W. Chung, E. Kim, and S. Kim, “A soft computing approach to
156
localization in wireless sensor networks,” Expert Syst. Appl., vol. 36, no. 4, pp.
7552–7561, 2009.
[76] A. Payal, C. S. Rai, and B. V. R. Reddy, “Comparative Analysis of Bayesian
Regularization and Levenberg-Marquardt Training Algorithm for Localization
in Wireless Sensor Network,” pp. 191–194, 2013.
[77] L. Gogolak, S. Pletl, and D. Kukolj, “Indoor fingerprint localization in WSN
environment based on neural network,” SISY 2011 - 9th Int. Symp. Intell. Syst.
Informatics, Proc., pp. 293–296, 2011.
[78] D. J. Y. Lee and W. C. Y. Lee, “Propagation prediction in and through
buildings,” IEEE Trans. Veh. Technol., vol. 49, no. 5, pp. 1529–1533, 2000.
[79] C. A. Balanis, Antenna theory: analysis and design. John Wiley & Sons, 2016.
[80] M. H. Beale, M. T. Hagan, and H. B. Demuth, “Neural Network ToolboxTM
User’s Guide,” MathWorks Inc, 1992.
[81] A. Wieland and R. Leighton, “Geometric analysis of neural network
capabilities,” in Proceedings of the Second IEEE International Conference on
Nerual Networks, 1987, vol. 3, pp. 385–392.
[82] J. Makhoul, A. El-Jaroudi, and R. Schwartz, “Formation of disconnected
decision regions with a single hidden layer,” in Proceedings of the
International Joint Conference on Neural Networks I, 1989, vol. 455, p. 460.
[83] N. K. Bose and A. K. Garga, “Neural network design using Voronoi
diagrams,” IEEE Trans. Neural Networks, vol. 4, no. 5, pp. 778–787, 1993.
[84] M. Hagiwara, “Removal of hidden units and weights for back propagation
networks,” in Neural Networks, 1993. IJCNN’93-Nagoya. Proceedings of
1993 International Joint Conference on, 1993, vol. 1, pp. 351–354.
[85] J. De Villiers and E. Barnard, “Backpropagation neural nets with one and two
hidden layers,” IEEE Trans. Neural Networks, vol. 4, no. 1, pp. 136–141,
1993.
[86] J. K. Kruschke, “Improving generalization in back-propagation networks with
distributed bottlenecks,” in Proceedings of the IEEE/INNS International Joint