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Radio localization techniques using ranked sequences
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Radio localization techniques using ranked sequences
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Content
RADIO LOCALIZATION TECHNIQUES USING RANKED SEQUENCES
by
Suvil Deora
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
May 2016
Copyright 2016 Suvil Deora
Dedication
To my parents.
ii
Acknowledgements
The ancient African proverb, \It takes a village to raise a child" captures my journey
leading up to this moment. This work is the culmination of all the opportunities and
invaluable help that I received from everyone around me. I would like to take this oppor-
tunity to show my gratitude to all of them for their unique contributions.
First, I would like to thank my advisor Professor Bhaskar Krishnamachari, it has
been a privilege to work with him. Having him as a mentor was like having a parent bird
teaching you how to
y, leading by example, giving all the freedom and most importantly
kindling a self-motivation which will help me
y for life. He have been in
uential beyond
my professional life and I am forever indebted to him. This dissertation wouldn't have
been possible without his vision, guidance and help.
I would like to specially thank Professor Alice Parker, who have been my mentor
beyond academics. She have been my go to person anytime I needed an honest opinion
on anything whether it be academics, ideas or personal life. She helped me navigate
through some of the toughest times in my life, without her motivation I would have never
considered the path I chose.
I would like to thank my lab mates Vlad, Antonios, Srikanth, Maheswaran, Ying Chen,
Scott, Parisa, Spencer, Rahul, Amulya, Nachikethas, Pedro, Keywan, Kwame, Jen Stien,
iii
Shangxing, Yi-Hsuan, Quynh, Ranjan, Marcello and Pradipta in no particular order, for
helping me learn, collaborate and enjoy my stay at USC.
My time here at USC went smoothly, thanks to the NSF for supporting part of this
research and the resourceful people who took care of the administrative burdens: Shane
Goodo, Annie Yu, Diane Demetras and Tim Boston.
And nally I would like to thank my parents and my wife for their constant support
throughout this journey.
iv
Table of Contents
Dedication ii
Acknowledgements iii
List Of Tables viii
List Of Figures ix
Abstract xii
Chapter 1: Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Challenges of Indoor Environments . . . . . . . . . . . . . . . . . . 3
1.2 Sequence Based Localization . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Challenges: Sequence Based Localization . . . . . . . . . . . . . . 7
1.3 Proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Contribution and Organization . . . . . . . . . . . . . . . . . . . . 11
Chapter 2: State of the Art 15
2.1 Indoor Localization Applications and Classication . . . . . . . . . . . . . 15
2.2 RF Based Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Time of Arrival Based Systems . . . . . . . . . . . . . . . . . . . . 20
2.2.2 Time Dierence of Arrival Based Systems . . . . . . . . . . . . . . 21
2.2.3 Angle of Arrival Based Systems . . . . . . . . . . . . . . . . . . . . 21
2.2.4 Radio Interferometry Based Systems . . . . . . . . . . . . . . . . . 22
2.2.5 Received Signal Strength Based Systems . . . . . . . . . . . . . . . 22
2.3 Sequence Based Localization . . . . . . . . . . . . . . . . . . . . . . . . . 26
Chapter 3: Non Uniform Sequence Based Localization 30
3.1 Area Partitioning for NU-SBL . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Manifestation of Non-Uniform Power . . . . . . . . . . . . . . . . . . . . . 36
3.3 NU-SBL Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.1 Metric: Area(Largest Face) . . . . . . . . . . . . . . . . . . . . . . 39
3.3.2 Optimization: Simulated Annealing . . . . . . . . . . . . . . . . . 39
3.3.3 NU-SBL with Power Optimization . . . . . . . . . . . . . . . . . . 40
v
3.3.4 NU-SBL: SBL with Power and Location Optimization . . . . . . . 41
3.3.5 NU-SBL with Zoom . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 Simulation: Evaluation Under Fading . . . . . . . . . . . . . . . . . . . . 45
3.4.1 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4.2 Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 Challenges in NU-SBL Implementation . . . . . . . . . . . . . . . . . . . . 51
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Chapter 4: Warped RSS Sequence Based Localization 54
4.1 Warping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1.1 Warp Vector Calculation . . . . . . . . . . . . . . . . . . . . . . . 55
4.2 WR-SBL System Implementation . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.1 Tmote-Sky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.2 Android Smartphone . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.3 Localization Server . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3 WR-SBL Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4 Enhanced WR-SBL Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5 Evaluation and Experimentation . . . . . . . . . . . . . . . . . . . . . . . 62
4.5.1 Sources of Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.5.2 Indoor Experiment Environment and Methodology . . . . . . . . . 62
4.6 Evaluation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.6.1 Estimating : Path Loss Exponent . . . . . . . . . . . . . . . . . . 63
4.6.2 Zigbee Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.6.3 WiFi Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Chapter 5: Sequence of Sequences Based Localization 70
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Modeling of Sequence of Sequences . . . . . . . . . . . . . . . . . . . . . . 71
5.3 Hidden Markov Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.3.1 Viterbi Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.4 Mapping Sequence of Sequences to Hidden Markov Model . . . . . . . . . 77
5.4.1 Transition Probability . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.4.2 Emission Probability . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.4.3 Initial Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.5 Algorithm Implementation and Simulation Results . . . . . . . . . . . . . 88
5.5.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.6 Deployment Details and Experimental Results . . . . . . . . . . . . . . . . 92
5.6.1 Real world Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.6.1.1 Incorporating Floor Plan . . . . . . . . . . . . . . . . . . 96
5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
vi
Chapter 6: Conclusions and Future Work 101
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2.1 Optimum Node Density . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2.2 Antenna Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.2.3 Incorporation of Floor-Plans . . . . . . . . . . . . . . . . . . . . . 104
6.2.4 Dynamic Calibration of Model Parameters . . . . . . . . . . . . . . 105
6.2.5 Using Other Physical Signals with SBL . . . . . . . . . . . . . . . 105
6.2.6 Merging SOSBL with WR-SBL and EW-SBL . . . . . . . . . . . . 106
6.2.7 In-Corporation of Other Sensor Data and Walking Models . . . . . 106
6.2.8 Machine Learning Framework for SOSBL . . . . . . . . . . . . . . 107
6.2.9 Optimization Problem Formulation . . . . . . . . . . . . . . . . . . 107
References 109
vii
List Of Tables
3.1 Maximum number of faces . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Simulation parameters from [76] . . . . . . . . . . . . . . . . . . . . . . . 47
3.3 Run time comparison (n = 16;A = 1600m
2
) . . . . . . . . . . . . . . . . 49
5.1 Error (Mean, Variance) for dierent noise variance values. . . . . . . . . . 90
viii
List Of Figures
1.1 Sequence based localization. Four node topology with faces and corre-
sponding sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Sequence based localization. (a) Two beacon nodes - SBL regions and
equal RSS line. (b) Four beacon nodes - SBL faces and equal RSS lines. . 27
3.1 Area partitioning for sequence based localization under: (a) Equal transmit
power setting, (b) Real transmit power setting, and (c) Optimized transmit
power setting for WiFi access points located in a real oce building. . . 31
3.2 Non-uniform sequence based localization (a) Two beacon nodes un-equal
power: equal RSS lines for dierent values ofP
TA
P
TB
. (b) Four beacon
nodes un-equal transmit power(P
TA
= 34dBm): SBL regions and equal
RSS lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Non-Uniform sequence based localization: Dierence in transmit power vs
equal-RSS circle radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Max-Area improvement by power optimization for 20 randomly picked
topologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.5 Analyzing power and location optimization for 8 beacon node case. Ob-
jective: minimize Max-Area. (a) Grid topology: no optimization. (b)
Grid topology: only power optimization. (c) Equal power: only location
optimization. (d) Joint location and power optimization. . . . . . . . . . . 42
3.6 Analyzing power and location optimization for 16 beacon node case. Ob-
jective: minimize Max-Area. (a) Grid topology: no optimization. (b)
Grid topology: only power optimization. (c) Equal power: only location
optimization. (d) Joint location and power optimization. . . . . . . . . . . 43
ix
3.7 NU-SBL-ZOOM technique (a) NU-SBL with OPT (XYPwr) for N = 16.
(b) Zoom in at (31,35)(2m X 2m Box) for the same topology. (c) Zoom in at
(5,5)(10m X 10m box) for the same topology. (d) Max-Area improvement
with NU-SBL-ZOOM technique at dierent locations(2m X 2m box). . . 46
3.8 Comparison of worse case location error when using LSE, SBL,SBL with
optimized location, NU-SBL, NU-SBL-ZOOM as a function of . (a) =
2:0 (b) = 2:5 (c) = 3:0 . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.1 Network topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 System architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3 Path loss model parameter evaluation for (a) Zigbee. (b) Wi. (c)
variation with location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4 Zigbee results (a) Zigbee stationary target experiments (b) Error Cdf. . . 66
4.5 Wi results (a) Wi stationary target experiments (b) Error Cdf. . . . . 68
5.1 Sequence based localization: Ground truth, estimated path in zero noise
and estimated path in presence of realistic noise . . . . . . . . . . . . . . . 72
5.2 Hidden Markov process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.3 Walking probability distribution function: When direction is uniformly
distributed and distance has a Gaussian distribution with
walk
= 1:6m,
walk
= 0:37m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.4 Walking probability distribution function: When the movement along X
and Y axis is independent and Gaussian with 0 mean. . . . . . . . . . . . 81
5.5 Emission probability: Empirical method of estimation. . . . . . . . . . . . 82
5.6 Emission probability: Theoretical method of estimation. . . . . . . . . . . 85
5.7 Simulation topology with target node's path. The target node starts at
point A goes around and ends its journey at point B . . . . . . . . . . . . 88
5.8 Simulation results: Error in location estimates by SBL and SOSBL as the
target node traverses the path shown in Fig 5.7. . . . . . . . . . . . . . . 91
5.9 Experimental setup: Floor plan with beacon nodes . . . . . . . . . . . . . 92
5.10 Target node's movement as it goes from point A to point B . . . . . . . . 94
x
5.11 Location estimates using SBL and SOSBL as the target node traverses the
path shown in Fig 5.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.12 Error in location estimates for SBL and SOSBL. . . . . . . . . . . . . . . 96
5.13 Location estimates using SOSBL when utilizing building
oor-plan, as the
target node traverses the path shown in Fig 5.10. . . . . . . . . . . . . . . 97
5.14 Error in location estimates for SBL and SOSBL with building
oor-plan. . 98
xi
Abstract
Real-world deployments of indoor localization systems are frequently faced with require-
ments like low stationary beacon node density, calibration, initial learning phase, scala-
bility, non-line of sight deployments, use of crowded frequency channels and many others.
This makes the use of existing localization technology in a real world scenario very costly
and dicult to use. Further, the dynamics of an indoor environment and signal interfer-
ence can adversely eect the accuracy of any such system. Also, localization algorithms
for indoor environment should have a low computational complexity for a real time op-
eration and should be capable of identifying and serving multiple, possibly hundreds of
users simultaneously. Addressing these challenges, we present two key innovations: (1) a
deterministic transformation of the received signal strength vector that can improve the
sequence-based localization accuracy and (2) an orthogonal state estimation of hidden
Markov process based approach that can further improve the accuracy of sequence-based
localization.
Sequence-Based Localization (SBL) is a technique whereby a node is localized based
on the ranked sequence of signal strengths obtained from a set of beacon nodes. SBL
eectively partitions the area into regions corresponding to each of these unique ranked
sequences. Prior work has developed SBL under the assumption that all beacon nodes
xii
have the same transmit power. As the part of the rst innovation, in this work we consider
beacon nodes with unequal transmit power for SBL and present heuristic algorithms for
joint optimization of transmit power and beacon node placement. We show through
comprehensive simulations that a novel enhancement of SBL utilizing optimized non-
uniform transmit powers, coupled with careful beacon node placement, which we refer to
as NU-SBL, can dramatically improve the area partitioning compared to traditional SBL.
However, in evaluating these schemes under stochastic fading, we nd that the original
SBL with optimized location performs nearly as well or slightly better than NU-SBL in
many cases. We introduce another scheme, that we refer to as NU-SBL-ZOOM, which
further allows the power levels to be optimized non-uniformly so as to focus in on a
particular smaller region within the larger localization space. NU-SBL-ZOOM is found
to perform much better in terms of both area partitioning as well as location error in the
presence of fading.
In order to implement the non-uniform versions of SBL in a practical setting where it
is not possible to access and alter the power setting of stationary beacon nodes, we derive
a mathematical transform that essentially achieves the same results as if the transmit
power of beacon nodes was being changed dynamically. Based on these transforms we
present Warped RSS Sequence Based Localization (WR-SBL) and Enhanced WR-SBL
(EW-SBL). We implement these two algorithms on two real-world systems: one a Wi-
based testbed for smart-phones and another a low-power wireless testbed. We show that
the proposed enhancements signicantly reduce average localization error compared to
traditional SBL, with no additional hardware and little additional run-time complexity,
xiii
enabling them to be readily deployed in practice. On the low-density WiFi testbed, we
show a 5-fold reduction in average distance error for EW-SBL compared to LSE.
For the second innovation, we turn our attention to probabilistic model based local-
ization algorithms which generally divide the entire localization area into a ne mesh and
based of sensor readings carefully compute the probability of target node's location at
one of these grid points. We take a little dierent approach: we estimate the path of
the target node and model the problem as a state estimation problem for hidden Markov
process, where the ideal SBL sequences are treated as hidden states, essentially modeling
the location of moving target node in terms of which SBL face it resides on. We treat
the individual SBL sequence estimates of target node's location as mere observations and
then use Viterbi algorithm to deduce the true underlying state transition sequence. We
use a random walking model to calculate transition probabilities and the log-normal fad-
ing modal to compute emission probabilities. We call this scheme Sequence of Sequences
Based Localization (SOSBL). We implement this technique on a 15 node testbed and
show a 40% improvement in the localization accuracy of a moving target. Also, we show
that this technique reduces the error variance by 3 times over SBL.
xiv
Chapter 1
Introduction
1.1 Background
In last two decades there has been a keen interest in location detection and track-
ing [49, 4, 57, 27, 10, 88, 88, 90, 66]. The capability to detect an entity's location can allow
a lot of other technologies to use and to be built on top of it. We have already seen the
rise of utility applications that use Global Positioning System (GPS) in outdoor environ-
ments. They span across every possible aspect of human life including health, navigation,
environment, security, defense, entertainment, agriculture and many more [38]. Absence
of satellite signals inside buildings limit the use of GPS based applications to outdoor
environments only, this opens a new domain called Indoor Localization specically aimed
to come up with better systems and techniques tackling the localization problem for in-
door environments. In last few years a lot of research has been done in this area by both
academia and industry [16, 14, 58, 72]. It is predicted that the market for indoor location
based systems is going to grow with an annual growth rate of 41% and it will be a 2:60
billion dollar market by 2018 [50].
1
1.1.1 Requirements
The ideal indoor localization system that researchers seek has some very stringent require-
ments starting from compatibility and going all the way to computational complexity. It
will be easier to understand the trade-os made by system architects if we could outline
these requirements. In this section we iterate some of the key requirements and the logic
behind having them.
A localization system should demonstrate consistent accuracy all across the localiza-
tion space. Although the worst case error values are dictated by the use case, typically if
the worse case error is less then few meter the system can be used for human navigation
and location. The accuracy shouldn't come at any extra hardware cost, meaning the
total number of stationary beacon nodes should be low, ideally using the existing WiFi
infrastructure for doing the localization. Using WiFi infrastructure can make the system
compatible with the smartphones making sure that it can be used by masses with high
acceptance rate. Even if the system is not based on WiFi, the system should be built
using of the shelf available transceivers in order to keep the system cost low. Ease of
use is another important factor to be considered: a long deployment time with a lengthy
calibration and learning phase may pose a serious hurdle. If all the beacon nodes need to
be time synchronized then the system will require additional control on the infrastructure
network, which not only comes at an extra cost but may or may not be possible. The
system should be power ecient and should be capable of being used simultaneously by
several users. Finally, the computational complexity should keep the estimation time low
2
enough to give a real time output. Making a system that meets most of these require-
ments can be tough, all the existing systems make trade-os depending upon intended
use case.
1.1.2 Challenges of Indoor Environments
Finding the location of an entity indoors is a challenging problem because indoor envi-
ronments are much more complex, versatile and unique in themselves. From a Radio
Frequency (RF) localization point of view, the indoor environments come with there own
challenges such as multipath, shadowing, non-uniform attenuation in dierent directions
and dynamics of the environment because of the users themselves. There are three pop-
ular techniques, which are used for RF localization.
First one is to observe the time of the
ight [27] or the angle of arrival [88] of the
RF signal from multiple xed-transmitters and then use trilateration or other geometric
techniques to nd the location of the target. The indoor environment can be brutal to
this technique because of the multipath and lack of line of sight channel due to walls
and other obstacles which can randomly increases the time of
ight. Dynamics of the
environment such as the movement of the occupants can also add signicantly to the error.
To overcome non line of sight channel problem a high density beacon node deployment is
needed, which increases the system cost. But, most importantly these techniques require
specialized hardware which makes these techniques not a good candidate for smartphone
based system. Also, they require a tight time synchronization among the beacon nodes,
which is very dicult to achieve and maintain.
3
The second technique involves measuring one of the electromagnetic wave features,
such as signal strength [92] or envelope phase which changes with the distance traveled by
the wave, then using an empirical or theoretical model that relates the measured quantity
and distance to deduce the distance travelled by the wave. For Received Signal Strength
Indicator (RSSI) this relationship is given by free space path loss model. Fading and
shadowing can add a signicant amount of noise to RSSI or any of the other measured
wave features. The problem specially becomes worse in an indoor environment, causing
such localization techniques to suer in terms of accuracy and repeatability. Another
issue with this technique is the relationship between wave feature and distance, which is
time varying and needs to be updated dynamically.
Fingerprinting [4, 57] is last but the most popular technique of RF localization, it
is a look-up based algorithm where the look-up database consists of signal values from
multiple receivers (RSSI signature) at every grid point of the localization space. This
information is gathered during the learning phase. Learning phase consists of recording
RSSI values at every grid point of the localization space at the time of deployment.
The algorithm estimates the location of a target node by matching the received RSSI
values against the values in the RSSI ngerprint database. The learning phase of this
technique can pose serious usability issues for larger spaces. Another problem in indoor
environments is that they are highly dynamic and because of the time varying nature of
RSSI values at any given point the gathered ngerprints might not paint the true picture.
Evaluating these techniques, it is evident that each one of them has limitations in an
indoor environment and also each one of them is equally capable of achieving the intended
goal.
4
This leaves us with some of the other RSSI based techniques which are very good
candidates when we look at them from the requirements perspective but they suer from
lower accuracy of location estimates. RSSI readings are known to suer with high variance
due to random noise. This raises the question, is it possible to come up with an algorithm
which would take the noisy RSSI readings and still be able to produce results with higher
accuracy? This is something that has been investigated before and there are algorithms
which use only RSSI readings and perform better then simple trilateration or Maximum
Likelihood Estimation (MLE) [81]. One of such algorithm is Sequence-Based Localization
(SBL) [90] which uses ranked RSSI vectors for localization. Other approaches ways such
as combining more readings and mitigating the eect of the random noise or using more
beacon nodes can also be used to improve the accuracy but they might not be applicable
in most of the real world scenarios.
Keeping the above discussion as the backdrop of this thesis we dive deeper in quest of
nding better algorithms for RSSI based indoor localization. In next section we introduce
sequence-based localization which is the basis of the upcoming algorithms.
1.2 Sequence Based Localization
Sequence-Based Localization, rst presented in [90], works on partitioning the entire local-
ization space into regions based on the received signal strength ranked vectors. Consider
two beacon nodes A and B located in a 2D space, the entire space can be divided into
two distinct regions separated by equal-RSS locus: the set of points such that a receiver
located at any of these points will read equal RSS value from both A and B. If the two
5
beacon nodes have equal transmit power then the equal-RSS locus is the perpendicular
line bisector of the line joining the two beacons. Each of the two regions have a unique
rank vector, sequence vector for the region that contains node A is (1; 2) and for the
region that contains nodeB is (2; 1). In a general setting withn beacon nodes Fig 1.1(a)
there will be
n
2
perpendicular bisectors, each of which divides the space. Consider the
faces (polygonal regions) created by the superposition of these lines in 2D space. Each
such face corresponds to a unique set of rank ordering over all beacons. There can be
O(n
n
) possible rank vectors out of which only O(n
4
) are feasible because the total pos-
sible number of faces are O(n
4
) [90]. In an ideal world, a receiver node will generate a
feasible ranked vector by measuring the signal strengths and hence localize its position
to one of these faces. But due to fading, shadowing and other random non-linear eects
the generated vectors may or may not be one of the feasible ones. To overcome this, SBL
utilizes Kendall Tau coecient as a metric to nd the closest feasible vector and localize
the position of the target node to the corresponding face.
As mentioned earlier, the number of geometrically valid sequences is O(n
4
) we call
them feasible sequences, out of O(n
n
) total possible sequences. This gives this algorithm
noise immunity as well as polynomial time complexity. SBL only uses ranked vectors,
hence it doesn't need to learn any of the path loss model parameters. The algorithm
is model-based, hence it doesn't have any learning time associated with it, making the
deployment super quick and ideal for emergency situations. SBL can be used not only for
RSS values but for any other modalities that are dependent on distance such as envelope
phase, time, etc.
6
Figure 1.1: Sequence based localization. Four node topology with faces and corresponding
sequences.
1.2.1 Challenges: Sequence Based Localization
SBL approximates the location of the target node as the centroid of a face. This ap-
proximation inherently adds error to the nal results. Also, the faces are not uniformly
distributed across the localization space, this also manifests in faces with varying sizes
with dierent area. Theoretically the error at any point is proportional to the area of
the corresponding face, hence for SBL the average error at dierent points of localization
space can be drastically dierent. This makes SBL accuracy dicult to quantify in terms
of average error, also the worse case average error is not the right representation of accu-
racy for the entire localization space. It must be noted that the size and distribution of
faces only depends upon the total number of beacon nodes and their topology.
7
1.3 Proposal
In this thesis, we aim to demonstrate two key innovations: rst, a deterministic transfor-
mation of the RSS vector that can improve the sequence-based localization accuracy and
second, an orthogonal technique that utilizes Hidden Markov Model (HMM) to improve
the estimates generated by sequence-based localization.
We substantiate both the innovations presented in this thesis through extensive sim-
ulations and and real world implementation results. Both innovations do not require
any additional hardware or network updates, they can use the same infrastructure and
measurements as used by SBL.
The rst innovation is presented as Enhanced Warped RSS Sequence-Based Localiza-
tion (EW-SBL) algorithm. We rst explain the idea behind the proposed deterministic
transform and then we explain how further improvements to SBL's localization accuracy
can be achieved.
Conceptually, if the faces carved by the perpendicular line bisectors for SBL could
be uniformly distributed across the localization space and were of approximately same
area then the localization accuracy would improve signicantly. The shape, size and
distribution of faces over a a given localization space is aected by the beacon node
topology and number of beacon-nodes hence, there exists an optimum topology which
is better then all the others. But in a real world scenario, for practical reasons such as
previous deployments or because of the building
oor-plan and aesthetics, it might not
be possible to deploy the beacon nodes at these optimum locations.
8
We presents a novel way of achieving the same outcome as achieved by the optimum
placement of the beacon nodes. The key idea is explained as follows: SBL assumes that
all the beacon nodes are transmitting at equal power which results in equal-RSS locus
between two beacon nodes as a perpendicular line bisector, but if the beacon nodes could
transmit at arbitrary power then the equal-RSS locus will be a circle whose radius and
center are only dependent upon the dierence in the transmit power of two nodes. This
extra degree of freedom in terms of transmit power enables the system to distribute the
SBL faces more uniformly across the localization space reducing the worst case average
localization error.
We rst demonstrate that careful selection of the location and transmit power level of
the beacon nodes or either one of them can improve the accuracy of sequence-based local-
ization; we call this technique Non-Uniform Sequence-Based Localization (NU-SBL). We
also show that our zoom technique which dynamically controls the beacon node transmit
power can decrease the localization error even further. The novel insight obtained by
this work helps us to develop Warped RSS Sequence-Based Localization (WR-SBL) and
its enhanced version as Enhanced Warped RSS Sequence-Based Localization (EW-SBL)
scheme, which proposes a mathematical transform that reaps the benets of transmit
power control but without actually going through the trouble of modifying or control-
ling the transmit power of a real deployment. Making it easy to deploy on any existing
network, this also solves the problem of potentially interfering with other aspects of the
network like coverage and quality of service.
9
The second innovation is presented as Sequence of Sequences-Based Localization
(SOSBL) algorithm. We rst explain the reason behind the idea to consider sequence of
sequences. Next we give the mathematical background for implementing the algorithm.
SBL uses the measured RSSI vector at any given time instant in isolation to the
other time instances. This means if there are any outliers, which are many in an indoor
environment, then the algorithm will give a location estimate with very less accuracy for
most of the time. A simple-minded way to mitigate this eect is to combine multiple
measurements made in quick succession so the noise averages out but, this might not
be aordable in practice as it may increase the total number of transmitted beacons by
multiple folds. To overcome the problem without incurring and additional cost in terms
of number of transmitted packets or extra hardware we rethink the problem as follows.
One simple but important observation is that a target node is generally moving when
it is trying to localize itself or even if it is not moving it receives beacons for multiple time
periods. This can be used to improve the accuracy if we look at the indoor localization
problem as a path estimation problem instead of a location estimation problem. What is
suggested here is that we estimate multiple locations of the target node simultaneously,
or at least, in relation to each other, by utilizing data obtained over multiple time slots.
We model the path of the target node as a sequence of states and a state is represented
by one of the feasible SBL sequence. The reason state is represented by a SBL sequence is
because each SBL sequence is associated with a specic region/location in the localization
space which can form a path. Now all we have to do is to nd this sequence of sequences
by looking at the RSS vectors in order to estimate the path. It turns out the problem
can be classied as a hidden Markov process state estimation problem [68]. We employ
10
one of the very well studied technique known as Viterbi Algorithm to estimate the states.
In this thesis we describe our complete model used for SOSBL algorithm and how to
compute the necessary probabilities required by the model. Then we show how to use
the Viterbi algorithm in conjunction with SBL algorithm to obtain path estimates which
are more accurate then the ones given by SBL.
1.3.1 Contribution and Organization
There are two main contributions of this thesis: rst, the concept of having an optimized
non uniform beacon node transmit power vector for a better sequence based localization
accuracy and second, hidden Markov modelling of the path estimation problem using
sequence based localization.
The rst part of this thesis (Chapter 4) explores the implementation and evaluation
of EW-SBL algorithm which is derived from the concept of Non-Uniform Sequence-Based
Localization (NU-SBL) (Chapter 3). We make following contributions:
We prove the locus of of locations that have an equal RSS from two beacon nodes
under deterministic isotropic path loss, which is a line bisector in case of equal
transmit power (SBL), transforms into circle for non uniform transmit power. The
radius and center of the this circle is solely dependent upon the dierence in transmit
power of beacon nodes.
We prove that the number of faces created, or, in other words, number of ranked
RSS sequences, isO(n
4
) in case of non uniform beacon node transmit power. Here
n is number of beacon nodes.
11
We show that Simulated Annealing can be used as a heuristic to optimize the power
vectors for any given topology. These vectors reduce the area of the biggest face
in the localization space and in turn distribute the faces more uniformly across the
localization space.
We show that by using optimal transmit power the maximum theoretical error can
be reduced multiple folds, we call this the NU-SBL technique.
We also present the NU-SBL-ZOOM technique where a separate optimal transmit
power vector is used for smaller sub-sections of the localization space in order to
further improve the localization accuracy.
Next we show extensive simulations, which demonstrate the eectiveness of NU-
SBL-ZOOM. We also outline the diculties to implement the new algorithms in a
real world system.
To overcome the real world implementation diculties for non uniform transmit
power algorithms, we propose and derive a mathematical transform to be applied
to measured RSS vectors. This not only reaps all the benets of optimal non-
uniform transmit power but enables the zoom technique to be used simultaneously
for multiple target nodes and is called EW-SBL.
We present the system architecture, algorithm and details of two real world im-
plementations of EW-SBL. The evaluations substantiate the simulation results and
shows localization error go down over SBL.
12
The next part of the thesis (Chapter 5) describes the design of an orthogonal tech-
nique where a sequence of sequences is used to estimate the path of the target node.
Thesis presents the implementation and evaluation of SOSBL algorithm and show the
improvement in localization accuracy. This part of the thesis makes following contribu-
tions:
We provide an introduction to the idea of Sequence of Sequences-Based Localization
(SOSBL) for path estimation and combining measurements made in dierent time
slots to get better localization accuracy.
Next, we map the problem of sequence of sequences based localization to the state
estimation problem for a Markov process with hidden states.
We identify a suitable walking model to derive the state transition probabilities to
be used for solving the above problem using Viterbi algorithm.
We address another piece of the puzzle: the calculation of the emission probabilities
to be used by Viterbi algorithm. A novel way to rapidly approximate emission
probabilities using log-normal model of noise is presented.
We present details of the SOSBL implementation. Using detailed simulations we
show for realistic noise variance the SOSBL can reduce the localization error to
almost half when compared to simple SBL. SOSBL also reduces the variance in
error values which shows its capability to lter out the outliers.
We elaborate the details of a real world experiment. The evaluation results from
this experiment are presented. The results show an improvement of more than
13
40% in localization accuracy over SBL. The error variance in this case also drops
signicantly.
Finally, we show how the building
oor-plan can be used to further improve the
path estimation and overall accuracy.
The rest of this thesis is divided into ve chapters. Chapter 2 gives a detailed overview
of the existing indoor localization techniques and explores the state of the art work done
in this area. In chapter 3, we give a detailed description of NU-SBL and NU-SBL-ZOOM
techniques. Chapter 4 is about WR-SBL and EW-SBL, where we introduce the concept
and give details of its implementation. The evaluation results obtained using Zigbee and
WiFi infrastructure are also presented in this chapter. Chapter 5 presents the SOSBL
algorithm, which combines SBL with a hidden Markov model and redene the localization
problem when using ranked sequences as a hidden state estimation problem. The last
chapter outlines the future research work possibilities based on the work presented in this
thesis.
14
Chapter 2
State of the Art
Indoor Localization has attracted much interest from both the industry [16, 14, 58, 72]
and the research community because of its utility in every day use of smartphones and
multitude of other areas such as asset tracking, interactive media, robotics etc. It has
become the \next big thing" in mobile computing, human-computer interaction and busi-
ness analytics [87, 96, 24]; this has given rise to development of many advanced indoor
localization systems.
2.1 Indoor Localization Applications and Classication
There are numerous real-world indoor localization applications starting from navigation,
nding things indoors, games, building safety, asset tracking in commercial buildings
like hospitals and warehouses, advertisement, keeping a track of personal space, reducing
energy footprint of buildings, personal safety, interactive media, personal robots, theft
protection, inventory control and many more. This vast applicability has pushed the
advancement of the technology. The forecast studies predict a 41% cumulative annual
growth rate for global indoor location, positioning and navigation [87, 96, 24] market.
15
Prior work has shown that there is a need for a better localization algorithm which
can utilize inexpensive hardware or can run on smartphones and have a very limited
infrastructure requirements. This gave rise to the radio frequency based localization
techniques as most of the applications either use a smartphone or a device which already
has an RF front-end. It is also important that these techniques work in non-line of sight
settings making them easier and cheaper to deploy.
There are other physical entities that can be measured and be utilized for the purpose
of indoor localization the simplest one being distance and direction as used in case of dead
reckoning [84, 85, 5, 73, 74, 67, 42, 26, 6]. Sound [43, 77, 33, 34, 53, 65, 25], magnetic
eld [82, 32, 46, 7, 13, 75, 63, 51, 3], thermal infrared [79, 9, 40, 83] and vibration [54,
59] are some of the other entities that have been used for the purpose of localization.
With the advent of better computer vision techniques and high computational power,
cameras [39, 17, 41] and lasers [79] are also being used for doing indoor localization in
highly dynamic environments.
Dead reckoning is probably the simplest and the oldest technique for localization,
it has been around for hundreds of years [84] as a marine navigation tool, the estimated
position is a function of the previous position distance travelled and direction. This tech-
nique was used by Charles Lindbergh in 1927 to nd his way on the rst
ight across
Atlantic to Paris from United States [85]. Cumulative error is the main drawback of dead
reckoning and there is a need for continuous tracking for this technique to work. In recent
years dead reckoning for indoor localization has been explored in depth [67, 42, 26, 6];
coupled with particle lters and other sensors, it can provide good estimate of target's
16
location [5]. The key issue with this technique is walking speed and direction measure-
ment, with specialized hardware on user's shoes and body [73, 74]. Dead reckoning can
be used for situations where no infrastructure is available.
Sound waves have been long used for ranging applications, indoor localization
systems that use sound, measure time taken by the sound pulses to reach the tar-
get [43, 33, 34, 53, 65, 25]. These systems use either an optical or RF pulse as a reference
pulse. Sound based localization on smartphones [43, 34] have been perfected to give an
accuracy of 0:3m. But there are two major drawbacks, rst the target should be in direct
line of sight of at least three speakers, second this scheme requires new infrastructure
installation. Another ambient sound ngerprinting approach [77] can give room level
accuracy but the error rate is too high for any real world application.
Magnetic eld based localization most commonly utilizes the fact that each point
inside or outside a building has a unique magnetic signature or a magnetic ngerprint due
to either earth's magnetic eld or because of building material [82, 32, 7, 13, 75]. Once the
entire localization space is surveyed for this information, it can be used to estimate the
location of the target. This technique doesn't require infrastructure but due to dynamic
nature of indoor environment where movement of dierent things can alter the magnetic
signature of a point signicantly. Studies have also shown that only magnetic eld is
not adequate for indoor localization [46] because it only has two components and the
magnetic elds need to be surveyed with a very high resolution because they can be
very dierent at points just a few centimeters apart. Techniques that use low frequency
oscillating magnetic elds [63, 51, 3] have also been proposed and have shown localization
accuracy of few meters.
17
Structural vibrations caused by walking can be sensed and used for localization [54,
59]. The technique uses time dierence of arrival readings at dierent sensor locations
and uses this information to solve the multilateration localization problem. The work
done in [59] has demonstrated that it is possible to identify people using foot vibrations.
The drawbacks are large errors and additional infrastructure requirements.
Thermal infrared sensors or lasers have been used extensively in robotics for ranging
and localization. The system works on time of
ight measurement and location estima-
tion [9, 40, 83]. The infrared sensors are cheap and easy to use with accurate measurement
capabilities. Infrared laser based LiDAR systems similar to the ones manufactured by
Velodyne [79] are highly accurate and expensive. They are widely deployed in robotics,
self driving cars and in defense industry.
Computer vision has emerged as one of the most versatile and useful elds in
computer science. Using multiple cameras that detects naturally occurring features and
utilizes simultaneous learning and mapping technique for localization [39, 17, 41]. The
work is very useful in the eld of robotics and manufacturing.
2.2 RF Based Localization
RADAR [4] was one of the earliest demonstration of indoor localization using received
signal strength values, the system showcased the use of WiFi transceiver chips for esti-
mating target node's location inside a building. But it was also clear that fading and
shadowing eects in an indoor environments can adversely aect the accuracy of such
18
estimates. Since then researchers have demonstrated that use of other sensors such as ac-
celerometer and magnetometers can improve the localization accuracy signicantly. But
the question still stands: is it possible to achieve better indoor localization accuracy only
by measuring RSS values? With this question in mind, we dive deeper into the realm of
indoor localization using radio frequency (RF).
RF signal based indoor localization systems can be broadly categorized in the following
categories based on what property of RF signal they utilize for generating the location
estimate:
Time of Arrival (TOA)
Time Dierence of Arrival (TDOA)
Angle of Arrival (AOA)
Radio Interferometry
Received Signal Strength (RSS)
Indoor RF environment is very dynamic due to stochastic eects like fading and
shadowing, where RF signal at a location
uctuates over time; this happens due to
multipath propagation and dynamics of the physical environment. One other drawback
of indoor environment is lack of line of sight channels from target node to xed RF
transmitters, even if the density of deployed RF transmitters is substantial, this is due
to the walls and other physical objects. Movement of the occupants adds another layer
of complexity when it comes to signal stability. Due to these random factors, each of
the mentioned RF localization system faces a lot of challenges in this environment. For
19
example, propagation time and angle of arrival based systems suer because of lack of line
of sight and multipath channel, which may seriously alter the time and angle of arrival
of the signal, hence adversely aecting the accuracy, whereas RSS based systems suer
because of the fading and shadowing. The next few sections present a brief introduction
to each of these systems and state of the art work done in those niche areas.
2.2.1 Time of Arrival Based Systems
Time of arrival (TOA) based localization techniques measure travel time between the
target and beacon nodes. If the nodes are synchronized in time, then the target node
(receiver) can determine the time of arrival of the incoming signal, this incoming signal
arrives with a time stamp at which the signal left the reference node. This gives the
signal travel time between the nodes and hence the distance. For line of sight additive
Gaussian white noise channel the error is inversely proportional to bandwidth and signal
to nose ratio [64, 15]. For a non line of sight channel this technique cannot come up with
any good estimate of receiver location. This issue is mitigated in UWB systems [27],
however these schemes typically require more sophisticated transceivers and also require
ne-grained global time synchronization, and consequently the hardware complexity and
cost is higher, preventing them from being deployed easily in commodity radio platforms
such as mobile phones and low power wireless sensors. A very detailed survey of time of
arrival based techniques for line of sight and non line of sight scenarios is presented in
[31], the paper also provides a comparison based on simulations results.
There have been an clear eort by the industry to bring UWB systems to the market,
there are systems such as Ubisense [78] and Time Domain [22] which have been around
20
since 2009, none of them stood out the way DecaWave ScenSor DW1000 [18] an UWB
tranciver IC that can can provide researchers with all the information needed for TOA
based localization systems.
2.2.2 Time Dierence of Arrival Based Systems
Time dierence of arrival technique can be used in situations where the reference beacon
nodes are time synchronized but there is no synchronization between the beacon node
and the target nodes. [10, 44, 1] For each target node the the beacon nodes measure the
round trip time hence the distance, the distance from two beacon nodes gives the location
of the target node on a hyperbola. A third beacon node is required for localization of the
target node. This technique also suer the same way as TOA technique in non line of
sight scenarios, it also has another major
aw and that is scalability in terms of number
of target nodes that can be localized in a given area. The beacon nodes cannot broadcast
time stamped signals they need to be addressed to specic target nodes.
Similar to TOA systems, the TDOA systems using UWB can perform better in terms
of accuracy and are able to mitigate the errors caused due to non line of sight channel
scenarios [27]. Time measurement based systems lack the wide acceptance due to addi-
tional infrastructure and hardware requirements, this may change in the future but for
now it is not easy to deploy such systems for daily use by smartphone users.
2.2.3 Angle of Arrival Based Systems
Angle of arrival based systems can provide highly accurate localization in line of sight
scenarios [27]. The technique involves measuring angles of the target node seen by beacon
21
nodes, this is done by using antenna arrays. For estimating the location of the target
node it is sucient to measure only one angle in a 2D space at multiple beacon nodes.
The angle of arrival based systems are not suited for ultra wide band because the number
of paths can be quite large due to high bandwidth [27].
Recently there has been a huge push by researchers using AOA technique to come
up with systems that uses next generation WiFi routers, some of the state of the art
systems are Spinloc [70], Arraytrack [88], PinPoint [37] and Phaser [28]. These systems
are capable of achieving sub-meter localization accuracy and are being seen as a very
good candidate for real world use.
2.2.4 Radio Interferometry Based Systems
Radio interferometry based localization works best with specialized tone-emitting ra-
dios [52] (though recent work has implemented them in other radios at the cost of reduced
accuracy [21]) and works best in line of sight settings. It also requires tight synchroniza-
tion and calibration and is computationally quite demanding due to the complexity of
signal processing associated with it.
2.2.5 Received Signal Strength Based Systems
Almost every commercially available transceiver chip is capable of measuring the received
signal strength. This makes using RSS values for localization easy and without a need
of any sophisticated additional hardware. The RSS based localization systems can be
further categorized based on the underlying reference model or technique to generate a
reference plane for estimation:
22
Fingerprinting
Log-Normal Shadowing Model
Free Space Model of Signal Propagation
Geometric Model
Fingerprinting is a technique where the entire localization space is mapped empir-
ically by measuring signal strength from all the transmitters at every grid point in the
localization space. These readings are stored and then used as a reference when esti-
mating the location of a target node. The way the stored information is used has given
rise to multitude of dierent
avors of ngerprinting. RADAR [4] and LANDMARC [57]
both examples of nger-printing based techniques that select k known locations from
a database which are closest to the one obtained by the receiver. Receiver location is
obtained by averaging over the k co-ordinates. Maximum likelihood estimation with n-
gerprinting has been demonstrated by Youssef et al. [94, 93]. Horus [94] improves its
performance by using a probability distribution of the observed RSS values at all grid
locations instead of single values as used in RADAR. Seshadri et al. [71] use a Bayesian
sampling approach for indoor localization with ngerprinting. Fingerprinting mainly suf-
fers from the fact that there is a learning phase involved and a lot of ground work needs to
be done when deploying a system, this issue is overcome by using techniques like SLAM
along with ngerprinting [35, 89].
Log-Normal Shadowing in path loss model of signal propagation [29] is another way
to generate a reference model which can be used to compare the RSS vales and estimate
the location of the target node. However it requires an online, accurate, estimation of the
23
fading variance and other channel parameters, and incurs a higher algorithmic complexity.
Maximum likelihood estimation based localization based systems are the most common
when using log-normal shadowing model, [81, 95] evaluate maximum likelihood estimation
in real word setting, Patwari et al. [60] have derived Cramer-Rao bound and maximum
likelihood estimators for RSS and TOA measurements. Chitte [12] shows maximum
likelihood estimation under log-normal shadowing is inecient and mean square error in
this case grows exponentially with noise power, this work then proposes linear minimum
mean square error estimate that has bounded mean square error in the noise power.
Minimum mean square error estimation is investigated in [36] and the authors show
using simulations that the mean square error increases with the distance variance. Linear
least squares method [48] is shown to be better in terms of computational complexity.
Free Space Model of Signal Propagation doesn't require estimation of RSS value
variance; it only uses path loss exponent for estimating the location of the target node.
The most basic technique in the literature that uses RSS in free space is the proximity [61]
based scheme. Where RSS value is quantized in 1 or 0 and the location of receiver is
approximated as the nearest transmitter's location. Another similar technique that uses
weighted centroids [8] for localization uses expected distance error for evaluation and is
only good for very high density deployments. The classical approach of least squares
estimation (LSE) [69] which also uses free space model gives its best performance in low
RSS value variance environments, the performance suers a lot in real world variance
scenarios. EZ [11] localization algorithm demonstrates the benets of a model based
localization approach by presenting a calibration free localization algorithm. SpinLoc [70]
24
uses angle and RSS value to eliminate the attenuation caused due to user's body, but it
does require the user to spin whenever she wants to know his location.
Geometric Model is very unique to the class of algorithms which are based on the
ranked vector of RSS values called sequences. Each sequence corresponds to a region in
the two dimensional space. The algorithms in this category are equally applicable to Time
of Arrival and other physical entity measurements that directly translate to distance.
Sequence Based Localization (SBL), rst introduced as ecolocation in [91] and rened
in [90], oers a low-complexity alternative to these approaches that requires no prior train-
ing or model estimation. It has therefore been found particularly well suited for emergency
response operations where the localization system needs to be deployed rapidly [47]. One
third party study [20] compared nger-printing, MLE and sequence based localization em-
pirically under dierent antenna orientation and calibration settings. It showed that SBL
can outperform the other approaches in an uncalibrated, dynamically-varying realistic
environment, where poor estimation of model parameters or the underlying environment
hurt the performance of MLE and ngerprinting approaches. Authors of [98] use series
of sequences for improved tracking; they construct a graph with sequences as nodes and
edge weight as extended Kendall tau distance between the neighbouring sequences. For
the given input sequences they nd shortest path through this graph for improving the
tracking accuracy. In [97] authors show how sequences can be used to nd distance be-
tween neighbours. The next section explains sequence based localization in a greater
detail.
25
2.3 Sequence Based Localization
In this section we launch into an introductory description of sequence based localization
and give a summary of the core idea behind this algorithm, then we provide a simple
description of how the algorithm is implemented and some of the practical limitations.
Sequence Based Localization, rst presented in [90], uses stationary transmitters called
the beacon nodes and works on partitioning the entire localization space into regions
based on the ranked transmitter distance vectors. Each ranked distance vector called
the sequence uniquely corresponds to a specic region called "facet" in the 2-dimensional
localization space. SBL exploits this unique relationship between the sequences and faces
for accurate localization. This sequence-facet one-to-one relationship can be stored in a
table as sequence centroid of the facet pair. This table is called the sequence-centroid
table.
Receivers approximate the distance to a transmitter with corresponding RSS values
and because it works on the ranked vectors it doesn't need to calculate the distance using
path loss propagation model.
At each time instant t the receiver (target node) receives a RSS vector which can
be ranked easily with rank 1 for the transmitter with highest RSS value. This observed
RSS sequence is compared with every sequence in the sequence-centroid table, the location
estimate of the target node is given as the centroid corresponding to the matched sequence
in the table. It must be noted that SBL doesn't need path loss exponent or the RSS
variance to generate reference model (sequence-centroid table) which as explained above
is only based on the distances from the transmitter, a simple geometric model.
26
The size, shape and the total number of faces is dependent on the number of beacon
nodes and their placement. To understand SBL better consider two beacon nodes A
and B located in a 2D space as shown in Fig 2.1(a), the entire space can be divided
into two distinct regions separated by the perpendicular line bisector joining the two
beacon nodes: the set of points such that a receiver located at any of these points will be
equidistant from bothA andB. It is assumed that the two beacon nodes are transmitting
at equal transmit power, if this was not true then the equal-distance locus as shown in the
Fig 2.1(a) will not be same as equal-RSS locus. At any point in the region that includes
node A, RSS (P
RA
) from node A is greater then RSS (P
RB
) from node B. Therefore
the sequence for this region will be (1; 2), similarly for the second region it will be (2; 1).
Knowing this the target node can localize itself in one of these regions. It does it by
comparing the observed sequence against the ones generated by the geometric model.
(a) (b)
Figure 2.1: Sequence based localization. (a) Two beacon nodes - SBL regions and equal
RSS line. (b) Four beacon nodes - SBL faces and equal RSS lines.
27
In a general setting with n beacons there will be
n
2
perpendicular bisectors, each
of which will divide the space into two regions. Consider the faces (polygonal regions)
created by the superposition of these lines in 2D space, Fig 2.1(b). Each such face
corresponds to a unique set of rank ordering over all beacons. There can be O(n
n
)
possible rank vectors out of which only O(n
4
) are feasible because the total number of
possible faces can only be O(n
4
) [90].
In an ideal world a receiver node will generate a feasible ranked vector by measuring
the signal strengths and hence localize its position to one of these faces. But due to fading,
shadowing and other random, non-linear eects the generated vectors may or may not
be one of the feasible ones. To overcome this SBL utilizes Kendall's Tau as a distance
metric to nd the closest feasible vector and localize the position of the target node to the
corresponding face. Kendall's Tau calculates the correlation between the relative ordering
in the two sequences under consideration. Its value ranges between [1; 1].
Once a received sequence is associated with a face then the location of the target
node is given by the centroid of that face. Which means bigger the face higher is the
localization error. Making the worse case error directly proportional to the largest region
formed which in turn depends on the beacon node topology. As seen from the Fig 2.1(b)
there is a lot of variation in face sizes and some can be signicantly bigger than the others
giving rise to areas more prone to error. Another requirement for SBL is to make all the
beacon nodes transmit at equal power. This is mostly not true when using the already
existing WiFi Access point network.
28
Techniques that add to the accuracy of the sequence based localization and overcome
its shortcomings are the focus of this thesis. The next few chapters present these tech-
niques, some of them applicable to other localization as well. It is important to note that
SBL's use is not limited to RSS based systems only.
29
Chapter 3
Non Uniform Sequence Based Localization
This work
1
is motivated by our experience with implementing a real-world indoor lo-
calization system at the USC Cinema School to enable personalized interactive media.
While developing a system based on sequence based localization [90], with pre-deployed
WiFi access points acting as beacon nodes and users carrying mobile devices in the space
being located. The mobile devices collected RSS readings from each AP, and sent them
to a central server where the SBL computations were performed. In traditional SBL, it
is assumed that all beacon nodes transmit at the same power, and the area is partitioned
into regions based on linear perpendicular bisectors between pairs of beacon nodes that
represent equal RSS from both beacon nodes. Each region then corresponds to a unique
RSS sequence, which is used to identify the location of the unknown nodes. For the
building where the system was deployed, this partition of the area via equal-RSS lines
is shown in Fig 3.1(a). However, it was found that in practice AP's are deployed with
signicantly dierent transmit powers. This was the motive to determine the correct area
partitioning with unequal powers for sequence based localization, as shown in Fig 3.1(b).
1
The work in this chapter appears in the following work: S. Deora and B. Krishnamachari, Harnessing
Non-Uniform Transmit Power Levels for Improved Sequence Based Localization (Distributed Computing
in Sensor Systems (DCOSS), 2014).
30
Figure 3.1: Area partitioning for sequence based localization under: (a) Equal transmit
power setting, (b) Real transmit power setting, and (c) Optimized transmit power setting
for WiFi access points located in a real oce building.
31
As can be seen, when the transmit powers are unequal, the curves separating dierent
sequences, which we refer to as equal-RSS curves, are no longer straight lines, but rather
circles (proved later). This was the point where we decided to treat transmit power as a
design variable and the possibility of using it to try and create more equitable partitions
with the aim of reducing the localization error seemed promising. Fig 3.1(c) shows that
for this particular deployment of access points, optimizing the transmit power can result
in a conguration of equal-RSS curves such that the area of the largest region is reduced
all the way to 92.82m
2
(from 487.4 m
2
obtained in the case of equal power-based area
partition, and 316.6 m
2
obtained in case of the observed unequal powers).
Moving on from here, the key question is to nd the optimal value of transmit power
for each beacon node with an objective to decrease the localization error. To understand
this we rst look into the shape of the equal RSS curves and what are the factors that
can aect it.
3.1 Area Partitioning for NU-SBL
It is easy to visualize that for SBL with equal transmit powers, the equal RSS locus
between two beacon nodes is the perpendicular bisector of the line segment joining them.
Now if the transmit powers of the two beacon nodes are un-equal it is not easy to see
what shape the equal RSS locus will take. Here is a small derivation for this case.
Let Q(x;y) be a point such that it is located at a distance d
1
from beacon node
A(x
1
;y
1
) and at a distance d
2
from beacon node B(x
2
;y
2
).
32
d
1
=
p
(xx
1
)
2
+ (yy
1
)
2
(3.1)
d
2
=
p
(xx
2
)
2
+ (yy
2
)
2
(3.2)
If beacon nodeA andB are transmitting at un-equal powerP
TA
andP
TB
respectively.
Using the path-loss model for signal propagation, we can say that the RSS values at point
Q due to node A and B are given by:
P
RA
=P
TA
P
d
0
10 log
d
1
d
0
(3.3)
P
RB
=P
TB
P
d
0
10 log
d
2
d
0
(3.4)
Where is the path loss exponent and P
d
0
is the power received at the reference
distance ofd
0
whenP
T
= 0dBm. By equatingP
RA
andP
RB
we can nd the set of points
where the two received powers are equal.
P
TA
10 log (d
1
) =P
TB
10 log (d
2
) (3.5)
without loss of generality we can assume d
2
> 0
P
TA
P
TB
= 10 log
d
1
d
2
(3.6)
Let
33
10
P
TA
P
TB
10
=k (3.7)
Where k is a positive constant. Substituting d
1
, d
2
based on equations (3.1) and (3.2)
and solving, we get
(1k
2
)x
2
+ (1k
2
)y
2
2x(x
1
k
2
x
2
) 2y(y
1
k
2
y
2
) +x
2
1
+k
4
x
2
2
+y
2
1
+k
4
y
2
2
= 0
(3.8)
Comparing with the standard non-degenerate conic section equation
Ax
2
+Bxy +Cy
2
+Dx +Ey +F = 0 (3.9)
we get
A = (1k
2
);B = 0;C = (1k
2
)
hence B
2
4AC =4(1k
2
)
2
< 0 and A =C which makes this curve a Circle.
The center of this circle is always on the line which passes through beacon nodes A
and B. As the dierence in transmit power P
TA
P
TB
increases, the center moves from
1 towards beacon node B never crossing it. Also the radius of this circle shrinks to
zero as the P
TA
P
TB
becomes larger and larger. This gives enough control to re-shape
and rearrange the SBL faces in the localization space, all just by carefully selecting the
transmit power of the beacon nodes and not even moving them. This is really useful
34
(a) (b)
Figure 3.2: Non-uniform sequence based localization (a) Two beacon nodes un-equal
power: equal RSS lines for dierent values of P
TA
P
TB
. (b) Four beacon nodes un-
equal transmit power(P
TA
= 34dBm): SBL regions and equal RSS lines.
in those scenarios where there is very small or no possibility to change the beacon node
topology.
The radius and the center of an equal RSS circle is also dependent on the value. It
is interesting to see how the radius of this circle changes with P
TA
P
TB
for dierent
values Fig 3.3(a). The key observations are as follows:
Circle with radius equal to1, in other words a straight line can be obtained by
using equal transmit power for both the beacon nodes for any value of .
The equal RSS circles are aected by the dierence in transmit powers P
TA
P
TB
and not the absolute value itself. Also the circle radius is inversely proportional to
P
TA
P
TB
.
Another observation is that for the same radius and a higher we would need a
higher P
TA
P
TB
.
35
(a)
Figure 3.3: Non-Uniform sequence based localization: Dierence in transmit power vs
equal-RSS circle radius
3.2 Manifestation of Non-Uniform Power
The equal RSS circle formed due to unequal transmit power can change the shape and
number of faces formed. For a two beacon node system the equal-RSS circle for dierent
values ofP
TB
P
TA
are shown in Fig 3.2(a), as we increase the transmit power of one of
the beacon nodes the equal-RSS line turns into a circle and shrinks around the beacon
node with smaller transmit power. The entire 2D space is still divided into two faces, but
the one of these faces is closed. Even with the modied shape of the equal-RSS locus it is
still possible to use the same principles for sequence based localization. Fig 3.2(b) shows
how for a four node (A, B, C, D) topology the faces modify as we increase the transmit
power P
TA
of beacon node A keeping the others same.
36
The number of faces also change when unequal transmit powers are used, if the number
of faces increases then it is benecial from the localization perspective. In this section
we derive an upper bound on the maximum number of faces with unequal power and we
also show that it is greater than the equal transmit power case.
Forn beacon nodes in the localization space, the maximum number of faces is O(n
4
)
each one of which corresponds to unique ranked RSS vector. One of the properties of the
ranked vectors for faces is that all the elements are unique. Therefore out of n! possible
vectors only O(n
4
) are feasible face vectors. The upper bound on number of faces for
equal power case is given by
n
4
8
5n
3
12
+
7n
2
8
7n
12
+ 1 [90].
We hereby derive similar upper bound for the unequal power case. Let f
m
be the
maximum number of faces generated by intersection of m circles. For m = 1, f
m
= 2.
Now let us assume that there are m 1 circles and we add one more. The new circle
will intersect each of the existing circles at maximum 2 points. Hence the m
th
circle can
have 2(m1) intersection points with rest of them1 circles. The 2(m1) intersection
points dividem
th
circle into 2(m1) curve segments. Each of which can potentially split
an existing face in two, adding 2(m 1) more faces to the existing face count. This can
be written as a recursion.
f
m
=f
m1
+ 2(m 1) (3.10)
)f
m
= (m 1)m + 2 (3.11)
37
Table 3.1: Maximum number of faces
Number of Nodes Equal Transmit Power Unequal Transmit Power
8 351 757
16 6701 14281
32 118297 245521
The above proof holds true for any set of convex closed curves. Now we know that
n beacon nodes will have
n(n1)
2
equal-RSS circles. Therefore maximum number of faces
F
m
will be given by
F
n
=fn(n1)
2
=
n
4
4
n
3
2
n
2
4
+
n
2
+ 2;n> 1 (3.12)
Comparing theF
n
upper bounds for equal and unequal power we see that for that for
the same number of beacon nodes operating at unequal power can potentially generate
more number of faces. As discussed earlier higher number of faces correspond to higher
accuracy.
F
n;unequal
F
n;equal
=
n
4
8
n
3
12
9n
2
8
+
13n
12
+ 1 (3.13)
This is positive for n = 2 and higher. From Table: 3.1 it can be seen the maximum
number of regions for unequal power case are more than double the ones for the equal
power case.
38
3.3 NU-SBL Optimization
To nd an optimum transmit power vector
!
P
T
for a given topologyS of beacon nodes is
important from the pre-existing static beacon node deployment point of view. Second,
optimization over power as well as location can potentially be more benecial for a new
deployment of beacon nodes. The Objective of both of these optimizations is to improve
the localization accuracy.
3.3.1 Metric: Area(Largest Face)
Improving the localization accuracy doesn't necessarily translates into reducing the aver-
age face area. For this reason we purpose area of the largest face for the given localization
space as the optimization metric, let us call it Max-Area. Area of the largest face corre-
sponds to the worse case error and minimizing it inherently tries to make all the faces of
equal size. Hence keeping the error across the entire space uniform.
3.3.2 Optimization: Simulated Annealing
The exhaustive search over all the possible power vectors for even a small network with 10
beacon nodes with 10 dierent power levels is computationally very intense. We analyzed
this optimization problem to see if it ts any know optimization frameworks but it so
happens that the problem is not convex or sub-modular so we resorted to use Simulated
Annealing to nd a near optimal solution.
39
Figure 3.4: Max-Area improvement by power optimization for 20 randomly picked topolo-
gies.
3.3.3 NU-SBL with Power Optimization
Here we present simulation results which show how for any given topology of beacon
nodes, we can improve the localization error by transmit power vector
!
P
T
optimization.
For this we picked 20 randomly chosen 8 beacon node topologies in a 40mX40m = 1600m
2
area. We run several instances of simulated annealing for a given topology and pick
optimum
!
P
T
for the minimum Max-Area. These results are shown in Fig 3.4. The three
plots represent Max-Area for equal transmit power
!
P
T
, randomly chosen
!
P
T
and optimum
!
P
T
. We observe that it is possible to signicantly improve the localization accuracy for
any given topology just by nding the right transmit power for each node. Also not all
unequal transmit power vectors
!
P
T
are necessarily better. To get this improvement we
need to know the value of path loss exponent. For the above experiment we used = 2,
but the observation holds true for any value of .
40
3.3.4 NU-SBL: SBL with Power and Location Optimization
Learning from the power optimization work we decided to take it a step further and
optimize over both location and power of a beacon node jointly. Even for a 4 beacon
node topology this problem becomes computationally intractable. It must be reminded
that these calculations are only needed once at the time of deployment and with simulated
annealing it is possible to obtain a good approximation of the optimal result in a very
reasonable time.
For this section only the number of beacon nodes N, total area A = 40mX40m =
1600m
2
and = 2:0 are xed. Fig 3.6, shows faces created by equal-RSS circles for
regular SBL (radius =1) and all the other dierent
avors of optimization. For each
sub-g the corresponding value of Max-Area is also shown. Fig 3.5(a),3.5(b),3.5(c),3.6(d)
are for N = 8 and g 3.6(a),3.6(b),3.6(c),3.6(d) are for N = 16.
Fig 3.5(b), 3.6(b) show improvement by optimization over transmit power, while
keeping the same grid topology used for regular SBL. It is a signicant improvement
obtained by simply changing the each beacon node's transmit power. Fig 3.5(c), 3.6(c)
explores the possibility of improvement by optimizing over the node locations while keep-
ing equal transmit power for all beacon nodes. The improvement is of the same order
as Fig 3.5(b),3.6(b). Next in Fig 3.5(d),3.6(d) we show how the joint optimization over
location and power of beacon nodes can signicantly improve the theoretical accuracy
of SBL. It can also be seen from the Fig 3.6(d),3.5(d) how the faces are uniformly dis-
tributed over the entire area and are of similar size. The Max-Area for n = 16 plunges
41
(a) Regular SBL Grid: 57:6m
2
(b) Opt(Pwr): 33:15m
2
(c) Opt(X,Y): 26:55m
2
(d) Opt(X,Y,Pwr): 15:4m
2
Figure 3.5: Analyzing power and location optimization for 8 beacon node case. Objective:
minimize Max-Area. (a) Grid topology: no optimization. (b) Grid topology: only power
optimization. (c) Equal power: only location optimization. (d) Joint location and power
optimization.
42
(a) Regular SBL Grid: 16:9m
2
(b) Opt(Pwr): 3:9m
2
(c) Opt(X,Y): 3:6m
2
(d) Opt(X,Y,Pwr): 1:9m
2
Figure 3.6: Analyzing power and location optimization for 16 beacon node case. Objec-
tive: minimize Max-Area. (a) Grid topology: no optimization. (b) Grid topology: only
power optimization. (c) Equal power: only location optimization. (d) Joint location and
power optimization.
43
from 16:9m
2
to 1:9m
2
for the shown total area. Following are the key observations from
these simulations:
Beacon node locations and power are symmetric with respect to the center of the
plane in case of OPT(XY) and OPT(XYPwr). Where OPT(XY) means optimized
for location only and OPT(XYpwr) means jointly optimized for both transmit power
and location.
Optimized beacon node locations tend to be on X = Y and X =Y if center of
the plane is considered the origin.
Our simulations suggest rst optimizing for location assuming equal powers, and
then optimizing for power doesn't yield any further improvement.
3.3.5 NU-SBL with Zoom
In real world scenarios people are not uniformly spread out inside a building. They tend
to gather in certain areas. For example if there is a conference going on inside a building
then relatively there well be a lot more people inside the conference room then anywhere
else. So the question arises that can we selectively improve the localization accuracy in
certain areas. The answer is yes and the solution is the proposed zoom technique.
Zoom technique improves the localization accuracy by moving the equal RSS circles
to a specic area of the localization space (building) hence creating much more and
much smaller face regions in that area. This zoom area can be moved to any location
in the localization space, which is done by changing the beacon nodes transmit powers.
44
The transmit power vector value is dependent on the topology of beacon nodes and the
location and size of the zoom area.
Say we already have the optimized the location and power for all the beacon nodes,
this setting is represented in Fig 3.7(a) and now we want to improve localization accuracy
in the 10m X 10m box around the point (5; 5), we can do this by optimizing only the
transmit power of the beacon nodes for the same topology. For this optimization our
metric should be the Max-Area for that specic 10m X 10m box. This scenario is shown
in Fig 3.7(c). By doing this optimization we improve the accuracy in any part of the
building just by changing the beacon node transmit power vector
!
P
T
. These vectors can
be precomputed for dierent parts of the building.
Fig 3.7(b) shows another interesting scenario. Say we want to track an individual
inside a building, we can use the same zoom technique just by decreasing the size of the
box and moving it along with the individual by changing
!
P
T
every second. The results in
Fig 3.7(d) show that Max-Area value drops to almost zero if we use this technique with
a smaller area to focus. But even if the area is as large as 100m
2
the Max-Area values
(which represent the worst case area size) are, remarkably, less then 0:5m
2
.
3.4 Simulation: Evaluation Under Fading
In a real world setting, localization error for any RSS based scheme is highly dependent
upon the RF-channel parameters. In this section we evaluate SBL (i.e., equal powers, with
and without location optimization), NU-SBL, and NU-SBL-ZOOM localization schemes
in a real world like scenario, using extensive simulations. In these simulations we consider
45
(a) Max-Area: 1:9m
2
(b) Max-Area: 0:025m
2
(c) Max-Area: 0:45m
2
(d) Max-Area: 0:05m
2
Figure 3.7: NU-SBL-ZOOM technique (a) NU-SBL with OPT (XYPwr) for N = 16.
(b) Zoom in at (31,35)(2m X 2m Box) for the same topology. (c) Zoom in at (5,5)(10m
X 10m box) for the same topology. (d) Max-Area improvement with NU-SBL-ZOOM
technique at dierent locations(2m X 2m box).
46
RSS variations caused due to fading and shadowing. To incorporate them in simulation
we use the combined path loss and shadowing model[30]. Here we show a comparision
between SBL, NU-SBL and NU-SBL-ZOOM techniques with Least Square Estimator
(LSE) scheme.
3.4.1 Simulation Model
One of the most widely used model for generating RSS values at a distance d is the
combined path loss and shadowing model [30]:
P
R
=P
T
P
d
0
10 log
d
1
d
0
(3.14)
WhereP
R
,P
T
,P
d
0
,
are indB andd,d
0
are inm. This model is the superimposed
version of path loss and non-linear eects due to fading and shadowing. Where
is a
Gaussian-distributed random variable with zero mean and variance
2
. Typical values
of the equation parameters for an in-door WiFi environment are tabulated in Table: 3.2.
Our simulations evaluate the performance of dierent localization schemes for dierent
values of path loss exponent and standard deviation .
Table 3.2: Simulation parameters from [76]
Parameter Typical Value Typical Range
P
d0
37dB(d
0
= 1m) NA
2:2 1:5 3:5
6 4 10
47
3.4.2 Simulation Procedure
All the simulations were done for 16 eacons placed in a 40m X 40m area. For regular
SBL and LSE schemes a grid topology and equal transmit power was used as shown in
Fig 3.6(a), note that there is no other more reasonable setting for LSE since at 0 variance
it can provide an exactly correct solution regardless of beacon node placement and none
of the schemes are optimized for particular higher variances. For SBL, results with the
optimized location are also presented, this scheme is independent of . For NU-SBL we
optimize for location and power for the given assuming zero fading and then use the
resulting topology and transmit power settings for simulation at dierent fading levels.
The NU-SBL-ZOOM10 scheme uses the same topology as NU-SBL but has a dierent
transmit power setting so as to focus on the 10m X 10m area around (5; 5). The NU-
SBL-ZOOM2 scheme has a dierent transmit power setting so as to focus on the 2m X
2m area around (1; 1).
Running the simulation involves generating the RSS vector using the above described
simulation model for given (;) and then using the localization scheme to come up with
the location estimate. We assume that noise aects RSS
i
value from the i
th
beacon
node independently of the other RSS values. For every grid point under consideration we
randomly generate 150 RSS vectors and compute the location estimate for each one of
them to get the expected location error for that grid point with a 96% condence interval.
To generate the result graphs we pick a grid point with highest expected location error
and plot its expected location error. This means that we are considering the worse case
error over the entire space.
48
To be fair to the NU-SBL-ZOOM techniques we only consider as the possible locations
of the user being localized the grid points which are in the zoom region.
Table 3.3: Run time comparison (n = 16;A = 1600m
2
)
SBL NU-SBL LSE
Worst case complexity (Kn
6
) (Kn
6
) (nA)
Empirical Computation Time 2 3ms 5 6ms 16 18ms
3.4.3 Simulation Results
The results from the simulations are shown in Fig 3.8. The three cases presented are
for dierent values of the path loss exponent . (As a reference, note that the literature
reports typical indoor path loss exponents of about 2.18 [76]).
SBL with optimized location is singicantly better than SBL on a grid placement.
surprisingly, NU-SBL with optimized location (with respect to area partitions) is
only slightly better than SBL with optimized location for the no-fading case. But
with fading, it turns out that optimized-location-SBL is more robust.
NU-SBL-ZOOM technique improves NU-SBL signicantly, and the NU-SBL-ZOOM
technique gives better results if the zoom area is smaller.
SBL with optimized location, NU-SBL, NU-SBL-ZOOM all perform better then
LSE at reasonable values of . The crosover point is between 2 and 5. This is
an important comparison point for these schemes as LSE also requires the same
information as NU-SBL (the path loss exponent) and performs arbitrarily well at
low variances, limited only by the granularity at which space is sampled.
49
(a) (b)
(c)
Figure 3.8: Comparison of worse case location error when using LSE, SBL,SBL with
optimized location, NU-SBL, NU-SBL-ZOOM as a function of . (a) = 2:0 (b) = 2:5
(c) = 3:0
50
Table: 3.3 compares the worst-case computational complexity and the empirically
measured computational run-times for our implementations of the three techniques. It
can be seen that NU-SBL takes about twice as long as SBL, but both are quite a bit faster
than LSE for the simulated scenario. This is essentially because the compute time for
LSE is directly tied to the size of the entire region, while the complexity of SBL schemes
is a function of the number of beacon nodes, and for typical densities of dozens of nodes
is likely to be lower.
3.5 Challenges in NU-SBL Implementation
Any implementation of NU-SBL algorithm would need to have a control over the transmit
power of all beacon nodes, infact NU-SBL-ZOOM technique would require a dynamic
control. This would add extra complexity in form of a new layer of network control.
When using an existing WiFi access point infrastructure doing this might not be possible.
Even if we had the access to the WiFi access points, transmit power setting required for
the localization algorithm can interfere with the existing setup of access points which are
optimized to provide maximum coverage or certain quality of service to the users.
To acknowledge all the above mentioned issues and to make NU-SBL easily compatible
with the existing Wi infrastructure we looked at a few approaches mentioned below along
with there drawbacks.
Using additional hardware just to send out beacons: Cost, intrusive to the building.
Still doesn't solves the issue of dynamic control for Zoom. Would need a dynamic
control of the additional hardware making the algorithm very complex to implement.
51
Transmission of beacon packets at every power level using the existing hardware:
Needs at-least one time reprogramming of the access points (beacon nodes). Would
require a bigger time window to capture beacons from each node. The radio chips
on access points might not even allow such a reprogramming.
Additional hardware with beacon packets being transmitted at every power level:
There can only be nite power levels that are allowed by the radio chip, hence no
ne grain control of power is possible.
In pursuit of solving the above issues we came up with an algorithm which still can
rearrange and reshape the SBL faces and is easy enough to be implemented using the
existing hardware. This is described in the next chapter.
3.6 Conclusions
We have carefully studied enhancements to sequence-based localization, one of the state
of the art techniques for pure RF-based localization. The main contributions of this chap-
ter have been to show that sequence based localization can be substantially improved by
carefully optimized placement of beacon nodes. We found that while the further opti-
mization of power levels (in NU-SBL) brings improvements in area partitioning (ignoring
fading), this improvement does not hold when considering stochastic fading. However,
the novel NU-SBL-ZOOM technique utilizing non-uniform powers in order to help lo-
calize a node known to be within a sub-region dramatically improves performance even
with fading. We also compared these techniques with the more traditional least squares
estimation approach and found that they oer benets beyond certain thresholds of the
52
fading standard deviation, ranging from 2 to 5, and are also computationally faster by
3x-6x.
While this work has made a head-start on understanding how non-uniform power
levels can be used to improve localization accuracy, it does not oer insights on how
knowledge of obstructions or real environment maps could be taken into account.
53
Chapter 4
Warped RSS Sequence Based Localization
We
1
now present a novel algorithm called Warped RSS sequence based localization or
simply WR-SBL. WR-SBL doesn't requires any kind of control over the beacon nodes
therefore it is well suited for existing WiFi access point networks. The network side
implementation of WR-SBL is very straightforward and same as the basic SBL. The
server side code has a few extra steps to be carried out. The transformation applied to
the RSS values is linear and computationally trivial at run time.
WR-RSS is based on the linear relationship between the received powerP
R
and trans-
mit powerP
T
, if bothP
R
andP
T
are known then it is easy to estimate the value of received
power for a dierent value of transmit power. In sections to follow we explain this concept
in more detail.
4.1 Warping
Considern beacon nodes with a given topology and transmit powers
!
P
T
in a localization
space of areaA. Target node q generates an observed RSS vector
!
P
R
, instead of using
1
The work in this chapter appears in part in the following work: S. Deora and B. Krishnamachari,
Received Signal Strength Transformation to Achieve Better Indoor RF Localization (unpublished).
54
RSS vector
!
P
R
directly for ranked sequence vector calculation, WR-SBL transforms the
!
P
R
into a warped RSS vector
!
W
R
which is then used to generate the warper RSS sequence
vector. This new sequence vector becomes the starting point for the rest of the algorithm.
Warping of
!
P
R
to
!
W
R
is done by adding a warp vector
!
w as shown by the following
equation.
!
W
R
=
!
P
R
+
!
w
4.1.1 Warp Vector Calculation
Calculation of the warp vector is based on two simple observations, rst: there is a linear
relationship between transmit power and received power given by the path loss model and
second: the noise due to multipath fading is independent of the transmit power value.
So at any instant of time t if
p;q;t
is the noise power added by the environment to the
signal on its way from beacon node p to target q then for any value of transmit power
P
Tp
we can say that
P
Rpqt
=P
Tp
P
d
0
10 log (d=d
0
) +
p;q;t
Where P
Rpqt
is the the signal strength received by q from p at time t. To calculate
the RSS at q if the beacon node p was transmitting at a dierent P
0
Tp
instead of P
Tp
we
can do a simple transformation as shown
P
0
Rpqt
=P
Rpqt
+ (P
0
Tp
P
Tp
)
55
This gives us the capability to observe RSS values for a pre-dened transmit power
and transform them into RSS values for any other transmit power. Thus, its possible
to apply power optimization techniques without actually changing the transmit power of
the beacon nodes.
Optimized transmit power vector
!
P
T
for a given topology and localization space can
be found using simulated annealing in the same way as for NU-SBL. The warp vector is
given by the dierence of the optimal power vector and the actual transmit power vector.
!
w =
!
P
T
!
P
T
Warp vector only needs to be computed once, at the beginning, during initialization
and then can be used for every received RSS vector. Warp factor is only applied for the
beacon nodes whose beacon packets are received.
(a)
Figure 4.1: Network topology
56
(a)
Figure 4.2: System architecture.
4.2 WR-SBL System Implementation
The implementation of WR-SBL was done on two platforms: Tmote-Sky devices which
use IEEE 802.15.4 (Zigbee) and Android Smartphones which use IEEE 802.11 (WiFi).
This is done to demonstrate the ease of implementation of this protocol. The two imple-
mentations are completely separate stand alone systems. The back end server for both
of them runs the same algorithm but for two dierent network topologies.
4.2.1 Tmote-Sky
The Tmote-Sky based system consists of target nodes and 18 beacon nodes Fig 4.1(a).
The 18 Zigbee beacon nodes are part of a permanent testbed (TutorNet) [2] installation
at University of Southern California. Tmote-Sky motes use CC2420 radio chip [55] with
maximum transmit power of 0dBm. TinyOS [45] was used to program these Tmotes.
Each beacon node is programmed to broadcast beacons every second. On receiving these
beacons, target node Tmote-Sky device which is connected to a laptop forwards the RSS
57
vector to the localization server for further processing and localization. For this setup,
even if the roles of transmitter and receiver were to be interchanged, WR-SBL algorithm
would still work.
4.2.2 Android Smartphone
An android app which can periodically gather WiFi RSS information from all the neigh-
boring WiFi access points and send the RSS vector to the server is installed on a smart-
phone to make it act as a target node. WiFi access point infrastructure show in Fig 4.1(a)
is used for the purpose of beacon nodes. No modications of any sort were made on the
WiFi network. The smartphones communicate with the server over the Internet. After
the server processes the received RSS vectors it sends out the localized co-ordinates to
the phone as a reply.
4.2.3 Localization Server
Localization server implementation is done in Java. It is responsible for (a) receiving
the RSS vectors from the target nodes, (b) running the WR-SBL algorithm, (c) logging
the results along with the RSS vector and (d) returning the results back to the target
node. The localization server consists of two main modules: Initialization module and
Localization Engine as shown in the Fig 4.2(a). For the evaluation and experimentation
purpose it is also capable of running Maximum Likelihood Estimation (MLE) and Se-
quence Based Localization (SBL) algorithms. Initialization Module only executes once
when the system starts up. It requires three inputs: beacon node network topology, lo-
calization space dimensions and path loss exponent. Once it has populated the database
58
it hands over the control to the localization engine which is then responsible for running
the algorithm. The connection handler module uses TCP/IP ports to communicate with
the target nodes.
4.3 WR-SBL Algorithm
The implementation of WR-SBL algorithm is simple, its pseudocode is described be-
low. As described in the earlier sections WR-SBL computes warp vector
!
w during the
initialization phase. On reception of RSS vector, localization module performs a warp
transformation to obtain warped RSS vector
!
wrss which is used to derive a sequence
vector
!
seq. During the initialization phase, a Sequence Centroid tableT is generated
using
!
P
T
and beacon node topologyS. TableT contains all the valid sequences and
corresponding centroids based on path loss model. Every received RSS ranked sequence
!
seq is compared against every entry ofT using Kendal Tau correlation coecient as a
metric. The centroid corresponding to the best matched sequence is given out as the
localized co-ordinates.
4.4 Enhanced WR-SBL Algorithm
After implementing WR-SBL algorithm we decided to take it a step further by making a
few modications and called it Enhanced-WR-SBL (EW-SBL). The idea is simple instead
of nding just one (
!
P
T
,
!
w ) for the entire localization space, an optimum power vector,
warp vector (
!
P
Tij
,
!
w
ij
) is calculated for every zoneZ
ij
dened by its centroid (i;j). Each
59
Algorithm 1: WR-SBL Server Side Algorithm
Input: Number of Nodes: n
Input: Topology: SetS of (i;X
i
;Y
i
)8i = 1n
Input: Tx Pwr:
!
P
T
=fP
T1
P
Ti
P
Tn
g
Input: Building Dimensions: (l;b) and Origin
Input: Path loss model Parameters: (;K
dB
)
/* INITIALIZATION */
begin
Read Inputs
if
!
P
T
forS doesn't exists then
/* Using Simulated Annealing */
!
P
T
( SimAnneal(S)
else
Fetch
!
P
T
forS
!
w =
!
P
T
!
P
T
T ( GenSeqCentTbl(
!
P
T
;S)
/* LOCALIZATION ENGINE */
while 1 do
!
rss( LISTEN()
!
wrss =
!
rss +
!
w
!
seq( SeqGenrtr(
!
wrss)
(x;y;k
d
)( KendalTauSearch (
!
seq;T )
LogData(x;y;k
d
;
!
rss)
REPLY(x;y)
zone is a square of side d and the entire localization space is divided in multiple zones
forming a grid as shown in Fig 4.1(a). The localization is performed in two steps.
First, if the location from the previous time slot is not known then it runs WR-SBL as
before and nds out the estimated (x;y), so as to nd the zone which contains (x;y) else
if the location from the previous time slot is known it nds zone which contains (x
old
;y
old
)
. The second step involves running WR-SBL for that particular zone. For more details
refer to the pseudocode.
60
Algorithm 2: Enhanced WR-SBL Server Side Algorithm
Input: Number of Nodes: n
Input: Topology: SetS of (i;X
i
;Y
i
)8i = 1n
Input: Tx Pwr:
!
P
T
=fP
T1
P
Ti
P
Tn
g
Input: Building Dimensions: (l;b) and Origin
Input: Path loss model Parameters: (;K
dB
)
/* INITIALIZATION */
begin
Read Inputs
if
!
P
T
forS doesn't exists then
/* Using Simulated Annealing */
!
P
T
( SimAnneal(S)
else
Fetch
!
P
T
forS
!
w =
!
P
T
!
P
T
T
( GenSeqCentTbl (
!
P
T
;S)
for Z
ij
8 i;j do
if
!
P
Tij
forS doesn't exists then
/* Use Simulated Annealing */
!
P
Tij
( SimAnneal(S;Z
ij
)
else
Fetch
!
P
Tij
for Z
ij
,S
!
w
ij
=
!
P
Tij
!
P
T
T
ij
( GenSeqCentTbl(
!
P
Tij
;S)
/* LOCALIZATION ENGINE */
while 1 do
!
rss( LISTEN()
if previous location from time slot t 1 is not known then
!
wrss =
!
rss +
!
w
!
seq( SeqGenrtr(
!
wrss)
(x;y;k
d
)( KendalTauSearch (
!
seq;T )
(p;q)( FindZone(x;y)
else
(p;q)( FindZone(x
old
;y
old
)
!
wrss
pq
=
!
rss +
!
w
pq
!
seq
pq
( SeqGenrtr(
!
wrss
pq
)
(x;y;k
d
)( KendalTauSearch (
!
seq
pq
;T
pq
)
LogData(x;y;k
d
;
!
rss)
REPLY(x;y) 61
4.5 Evaluation and Experimentation
This section presents the evaluation procedure and details about the real world experi-
ments. First, we discuss the some inherent sources of error for a real world deployment.
Then we describe key features of the indoor environment where the experiments were
conducted. Finally, we discuss the results.
4.5.1 Sources of Error
Sequence based localization estimates the location by mapping a sequence to a face (re-
gion). The co-ordinates of this face's centroid are returned as the result. Even in ideal
conditions this approximation can signicantly add to the error. Hence, it is important
to have every region of approximately the same size. This is where the optimized power
vector helps reduce the error and makes a dierence.
The path loss model considered to generate the sequence centroid table doesn't take
walls and other obstacles into account. In indoor environments, it is very common to
loose the signal from a beacon node which is a couple of walls away. At this point, no
special treatment is given to the walls and other obstacles, and is going to be handled in
future work.
Finally, the major source of error is due to the random errors in RSS measurements
which can be contributed to multipath fading and shadowing eects of the RF channel.
4.5.2 Indoor Experiment Environment and Methodology
All the Experiments were conducted on the fourth
oor of an oce building at the
University of Southern California. The
oor is mainly occupied by robotics, network
62
research labs and oce space for professors. Majority of the labs have cubical-like setting.
Fig 4.1(a) shows the
oor plan of the entire localization space, which is 55m X 30m in
area. During the regular oce hours, there are an average of 40 to 50 people present in
this area.
The experiments were carried out between 10:00 AM to 11:00 AM on a regular oce
day. Experiments were carried out to evaluate the performance of the algorithm in
localizing a user. 18 dierent locations were randomly selected. The ground truth about
the user's position was precisely measured for every location. At every location, a reading
was taken every second for approximately 60 seconds. Experiments for Zigbee and WiFi
were done separately. The Zigbee beacon nodes are a part of a permanently deployed
testbed and are located above the false ceiling along with the ventilation ducts and other
cables where as, the Wi access points are openly deployed in the hallways. Experiments
were conducted on both Zigbee and WiFi platforms separately.
4.6 Evaluation Results
4.6.1 Estimating : Path Loss Exponent
Path Loss exponent estimation is one of the key building blocks in the implementation of
WR-SBL and EW-SBL algorithms. Estimation of value was done using the same set
of data which was collected for the stationary user experiments. We performed a linear
regression on this set of data in order to nd the value of . This was done while keeping
K
dB
ford
0
= 1m xed to the value evaluated experimentally. Fig: 4.3(a) and Fig: 4.3(b)
63
shows the linear regression done on Zigbee and WiFi data. The values of found are
typical for indoor environments as reported by [76].
P
R
=P
T
K
dB
10 log (d=d
0
)
Here in Fig: 4.3(c) it is demonstrated how values vary in dierent parts of the
oor.
It can be seen that the variation in estimated eta values at dierent locations is less than
10% of the mean value. Hence from a practical point of view permanently xed one or
two stationary nodes on a
oor can be used for a periodic estimation of .
4.6.2 Zigbee Results
Evaluation of WR-SBL and EW-SBL algorithms on Tmote-sky, Zigbee system is pre-
sented here. Data collected by the Tmote-Sky motes is send to the server where it is
logged rst and then used by WR-SBL, EW-SBL, Sequence based localization and Maxi-
mum Likelihood Estimation localization algorithms to give out the results. Which means
the only dierence is the algorithm and not the data acquisition part. All the algorithms
use the same data in its entirety but the results are drastically dierent as shown in gure
Fig 4.4(a).
The bar graph shows how each algorithm compares for each set of experiment and the
horizontal lines show the average error for all the experiments combined. As expected SBL
performs better then MLE [90], WR-SBL shows a little improvement over SBL but not
a lot. The real gain is achieved by EW-SBL algorithm it reduces the error dramatically
across all experiments. Fig 4.4(b) presents the cumulative distribution of the error, it
64
(a) (b)
(c)
Figure 4.3: Path loss model parameter evaluation for (a) Zigbee. (b) Wi. (c) variation
with location.
65
(a)
(b)
Figure 4.4: Zigbee results (a) Zigbee stationary target experiments (b) Error Cdf.
66
shows the median is lower then the mean meaning more than 50% of the time the error
is less than the average error.
4.6.3 WiFi Results
Evaluation of WR-SBL and EW-SBL algorithms on Android smartphones, WiFi system
is presented here. Data collected by the smartphone motes is send to the server where
it is logged rst and then used by WR-SBL, EW-SBL, Sequence based localization and
Maximum Likelihood Estimation localization algorithms to give out the results. Which
means the only dierence is the algorithm and not the data acquisition part. All the
algorithms use the same data in its entirety but the results are drastically dierent as
shown in gure Fig 4.5(a).
The bar graph shows how each algorithm compares for each set of experiment and the
horizontal lines show the average error for all the experiments combined. As expected SBL
performs better then MLE [90], WR-SBL shows a little improvement over SBL but not
a lot. The real gain is achieved by EW-SBL algorithm it reduces the error dramatically
across all experiments. Fig 4.5(b) presents the cumulative distribution of the error, it
shows the median is lower then the mean meaning more than 50% of the time the error
is less than the average error.
4.7 Conclusions
We have considered in this chapter the problem of implementing the non-uniform trans-
mit power based localization technique in a sparse to moderately-dense (realistic) deploy-
ment of beacon nodes. We found through simulations and experiments that the widely
67
(a)
(b)
Figure 4.5: Wi results (a) Wi stationary target experiments (b) Error Cdf.
68
used MLE algorithm for RSS localization performs poorly in such settings compared to
sequence-based localization. We introduced a new technique for SBL called WR-SBL, in
which received signal strength vectors from the dierent beacons are modied by adding
to them a warp vector (carefully designed using an optimization formulation solved by
simulated annealing to minimize the area of the largest face corresponding to a location
sequence.) We further improved it to obtain the EW-SBL by generating dierent warp
vectors for dierent regions of the localization space. Our experiments on a real WifI
and WSN testbed show that for moderate density ( 8 nodes in a 55m 30m space)
this technique signicantly outperforms previous known algorithms including the origi-
nal SBL, MLE, and LSE. On a much more dense deployment (18 nodes in 55m 30m
space), MLE is indeed still better, but the proposed novel algorithm still oers signicant
improvements over traditional SBL.
69
Chapter 5
Sequence of Sequences Based Localization
5.1 Introduction
Sequence based localization
1
estimates the location of a target node every time it receives
a new sequence; this means for every time instant the location estimation is performed
in isolation from the other time instants. Most of the localization applications running
on smartphones are used by people while they are walking, in scenarios like this, it is
benecial to estimate the path of the target node instead of its instantaneous location,
this concept has been demonstrated by Rai et al. in [66] and many others. Using
data gathered over multiple time instants for estimating a path can naturally lter the
outliers and can improve the estimation accuracy. Use of multiple observed sequences for
estimating the path of the target node is presented in form of Sequence of Sequences-Based
Localization (SOSBL) algorithm. In this chapter we formulate the problem of estimating
path as a state estimation problem for a Markov process with unobserved (hidden) states.
We present a technique using Viterbi algorithm to solve this problem. Every feasible SBL
1
Someofthecontentinthischapteriscontainedinthefollowing: S.Deora,S.Congero,P.Mansourifard
and B. Krishnamachari, Sequence of Sequences Based Localization (Manuscript in preparation).
70
sequence constitutes a state of this Markov process. The same formulation can be applied
to other
avors of sequence based localization.
Rest of the chapter is divided into three more sections, in the next section we for-
mulate the hidden Markov state estimation problem, third section describes the details
of the algorithm and simulation results. Finally, we present the details of a real world
deployment of the system and the evaluation of SOSBL and its comparison with simple
SBL.
5.2 Modeling of Sequence of Sequences
At every time instant, t target nodes receive beacon packets from stationary beacon
nodes: using the RSS measurement for each of these received packets a RSS vector is
constructed. SBL uses the ranked version of this RSS vector to nd the closest feasible
sequence from the sequence-centroid database. Location of the target node is estimated
as the corresponding centroid value from the database. As described in previous chapters,
in an ideal world where there is no noise, the ranked RSS vectors gives a very accurate
estimate of the target node's location, but in a realistic scenario there could be large
errors present in some of these estimates.
Consider the movement of a target node as shown in the Fig 5.1: the target moves
along the dashed green line starting from the left hand side top corner. This path repre-
sents the ground truth of the target's location from time 0 toT (in this exampleT = 17).
As the target moves across the localization space it moves through dierent SBL faces
one after the another, the sequence corresponding to face traversed by the target node
71
Figure 5.1: Sequence based localization: Ground truth, estimated path in zero noise and
estimated path in presence of realistic noise
72
at timet is represented by Q
t
and the entire sequence of sequences from time 0 to T can
be written as Q
0
;Q
1
;Q
2
;:::Q
T
. This also represents the sequence of sequences that SBL
would detect if there was no noise and estimated path would be given by the blue line as
shown in the Fig 5.1. Let's call Q
t
as the true sequence at time t.
As mentioned earlier in reality things are very dierent due to noise, most of the
time the sequence estimated by SBL is not going to match the true sequence. Let's
represent this estimated sequence at time t by O
t
and call it the observed sequence. It
must be noted that theO
t
is not the ranked RSS vector but the sequence pulled from the
sequence-centroid database after using Kendall Tau coecient to nd the closest ideal
sequence to the ranked RSS vector. Therefore, the red line in Fig 5.1 represents an actual
path estimate given by SBL in a realistic scenario. It is clear that the in a real world
scenario the SBL estimate of the SBL region given O
t
has a huge discrepancy from the
true sequence Q
t
.
Another important property to notice is that if we model the target node's movement
as random walk then the location (x
t+1
;y
t+1
) of the target node at time t + 1 is only
dependent on target node's location (x
t
;y
t
) at time t. This in turn means that the Q
t+1
is only dependent on Q
t
: this can be mathematically represented as follows. Let the set
Q =fq
0
;q
1
;q
2
;q
3
;:::;q
N1
g be the set of all the possible valid SBL sequences for the
given topology and localization space. The probability that the target node will move to
a face with SBL sequence q
t+1
at time t + 1 given the entire movement history of target
node is only dependent on target node's location in terms of its true sequence at time t.
73
P
Q
t
=q
t
jQ
t1
=q
t1
;Q
t2
=q
t2
;:::;Q
0
=q
o
= P
Q
t
=q
i
jQ
t1
=q
t1
(5.1)
This property also known as Markov property [68], it gives a better insight and raises
the question: is it possible to do better then SBL by looking at the problem of localization
as a problem of path estimation rather as location estimation? SBL treats every local-
ization estimate O
t
independently but we can also look at the series O
0
;O
1
;O
2
;:::;O
T
of SBL location estimates together as a set of observations for estimating the the true
sequence Q
0
;Q
1
;Q
2
;:::;Q
T
. This is essentially treating the Q
0
;Q
1
;Q
2
;:::;Q
T
as the
hidden states of a Markov process and the SBL estimates O
t
as the observations. The
problem of estimating hidden states of a Markov process is very well studied in the lit-
erature and we are going to leverage some of these state estimation methods to improve
the path estimation using SBL.
We call this technique Sequence Of Sequences Based Localization (SOSBL), it takes
the SBL location estimates as observations and attempts to estimate the true sequence
for every time instant for which the observations are known. In the next section we give a
brief introduction to Hidden Markov Models (HMM) also known as Markov process with
hidden states.
5.3 Hidden Markov Process
A discrete-time stochastic process that has the Markov property is considered as a Markov
process. For a system that is modeled using Markov process, the Markov property dictates
74
that system state transition only depends on the system's current state. In a simple
Markov process, the states are directly observable and hence the description of the model
only requires the state transition probabilities.
Figure 5.2: Hidden Markov process
There is another class of systems which can be modeled using a Markov process but
the state of these systems is not directly observable; instead only an output dependent
on the current system state can be observed. This calls for a new kind of model which
can truly represent these dierences. Hence to describe such a system, we rst dene set
of all distinct N states of this Markov process as X =fx
0
;x
1
;x
2
;:::;x
N1
g and set of
all the possible values taken by the output asV =fv
0
;v
1
;v
2
;:::;v
M1
g. Each state inX
emits an output value fromV , this output value can be dierent for dierent observation
times even for the same state, the observations made follow a probability density function
over all possible outputs. Consider the Fig 5.2 that illustrates a generic hidden Markov
process for observation time T . Here X
t
2 X represent the system state at time t. As
mentioned above X
t
's are not directly observable; instead, only the output value O
t
2V
is observable. The probability of observing an output O when in state X is given by
a NM emission probability matrix E and the state transitions are governed by the
transition probability matrix S of sizeNN. The initial probability distribution size
N 1 is dened as the probability of system being in one of the state at time t = 0.
75
Given the model = (S;E; ) and the sequence of observations O the problem of
estimating the hidden state sequenceX
0
;X
1
;:::;X
T
is what we need to do for estimating
the path of moving target using SBL. For any given system modeled as an HMM, once
all the model parameters are determined either theoretically or experimentally, we can
use the Viterbi Algorithm [80] for hidden state estimation.
Viterbi algorithm, a dynamic program at the core, was rst proposed by Andrew
Viterbi [80] in 1967 for decoding the convolution code used in wireless communications.
Since then it has been extensively applied in dierent areas where nding the most likely
sequence of the hidden states of a HMM is the primary objective [23]. Some of the ap-
plications include speech recognition, speech synthesis, keyword spotting, computational
linguistics, and bio-informatics.
5.3.1 Viterbi Algorithm
For a HMM described by = (S;E; ) for a state space X and given an observation se-
quenceO
0
;O
1
;O
2
;:::O
T
. The most likely sequence of statesX
0
;X
2
;:::;X
T
that produces
the given observations is estimated by the recurrence relations.
Z
0;k
= P
O
0
jk
:
k
(5.2)
Z
t;k
=max
x2X
(P
O
t
jk
:s
x;k
:Z
t1;k
) (5.3)
For observations from 0 to t that have k as the nal state, Z
t;k
is dened as the
probability of the most probable state sequence given by P
X
0
:::;X
t
;O
0
;:::;O
t
. The
back pointers which point to the state X
t1
used in the previous time step are used to
76
retrieve the Viterbi path. Let Ptr(k;t) be the function that returns the value of X
t1
used to compute Z
t;k
if t> 0, or k if t = 0. Then:
X
T
=argmax
x2X
Z
T;x
(5.4)
X
t1
= Ptr(X
t
;t) (5.5)
The complexity of this algorithm is O(TjSj
2
). Next we show how the SBL based
localization technique can be mapped to a hidden Markov process.
5.4 Mapping Sequence of Sequences to Hidden Markov Model
There are ve entities that need to be clearly dened for a hidden Markov model and in
this section we dene them for the problem under investigation. The state spaceX in case
of sequence of sequence based localization is the set of all the feasible sequences Q for a
given node topology and localization space. The size of the state space isO(n
4
), wheren is
the total number of stationary beacon nodes in the topology. As explained in section 5.2,
the set of all the possible output valuesV is the same as the state space because the SBL
gives result in form of one of the possible sequence. This is also benecial from a practical
point of view because if we consider raw ranked RSS vectors as observations then the size
of the setV is ofO(n
n
); this can make it computationally intractable. Hence we rst run
SBL to get an observation that is from a set same as Q and then use it further.
The three probability matrices: transition probability, emission probability and the
initial probabilities can be calculated using empirical and theoretical ways. The next
77
three subsections go into the details of how they are computed based on the underlying
assumptions.
5.4.1 Transition Probability
The transition probability dictates how the system transitions from one state to the next.
In case of HMMs it is not possible to observe these transitions directly, hence the way
to calculate this probability matrix has to be theoretical and based on the underlying
assumptions. Two such methods were evaluated and theoretical analysis of both of these
methods is presented.
In case of SBL localization, the probability that the target node goes from one SBL
face to the other is dependent on how does the target node moves. If we consider a person
walking with the target node, then we can use one of the many existing walking models.
The walking model gives a probability distribution function over the two dimensional
localization space for node's location in the next time step.
The rst model presented is based on two simple assumptions: rst, the node can
move in any direction with an equal probability, hence probability of choosing a direction
is uniform. Second, the probability density function over traveled distance in one time
slot is given by a normal function with mean equal to average distance
walk
travelled
in a single time slot and standard deviation
walk
given by equation 3
walk
=D
walk
whereD is the upper limit on walking speed. If we consider polar co-ordinates (;r) then
the probability distribution function for the next location in the polar 2D space can be
derived as follows. Here we consider that the target is at the orign.
78
P
=
1
2
(5.6)
P
R
=
1
q
2
2
walk
exp
(r
walk
)
2
2
2
walk
(5.7)
P
;R
= P(R):P() =
1
q
(2)
3
2
walk
exp
(r
walk
)
2
2
2
walk
(5.8)
The joint distribution for andR is simply the product of two individual distributions
because the two are independent. The same joint distribution in Cartesian co-ordinate
system can be evaluated using change of variable technique [62]. The distribution is
shown Fig 5.3
Figure 5.3: Walking probability distribution function: When direction is uniformly dis-
tributed and distance has a Gaussian distribution with
walk
= 1:6m,
walk
= 0:37m
P
X;Y
=
1
q
(2)
3
2
walk
(x
2
+y
2
)
exp
(
p
x
2
+y
2
walk
)
2
2
2
walk
(5.9)
=tan
1
y
x
;r =
p
x
2
+y
2
(5.10)
79
The state transition probabilities in case of SBL is the probability to go from one SBL se-
quence face to the other. This can be evaluated by considering the starting SBL sequence
face centroid (starting state) at origin and nding the volume under the probability dis-
tribution curve given by Equation 5.9 at the face of the landing SBL sequence (nish
state). For the above described joint distribution, the value is not dened at the origin,
and needs a very good estimate of the walking speed which makes it dicult to use. Even
with an approximate estimate of the walking speed, the distribution did not give a good
estimate of the transition probabilities and the SOSBL algorithm fails to work. The main
aw of the distribution is that it cannot model if the target node is stationary for some
time; also, it fails to stay in the same state if the next observation is an outlier.
This brings us to our second model. As explained above, the insight behind this model
is that some times the target node is not moving and sometimes due to outliers there are no
probable transitions and the state needs to jump back to feasible state. This distribution
considers, that target node movement follows normal distribution along X-axis as well
as Y-axis with zero mean and high standard deviation such that =
x
=
y
= 2D
where D is the upper limit on walking speed. This distribution can be represented by
the following equations and is shown in Fig 5.4:
P
X
=
1
p
2
2
x
exp
x
2
2
2
x
(5.11)
P
Y
=
1
q
2
2
y
exp
y
2
2
2
y
(5.12)
P
X;Y
=
1
2
x
y
exp
x
2
2
2
x
exp
y
2
2
2
y
(5.13)
80
P
X;Y
=
1
2
2
exp
r
2
2
2
(5.14)
r =
p
x
2
+y
2
Figure 5.4: Walking probability distribution function: When the movement along X and
Y axis is independent and Gaussian with 0 mean.
Here r is the shortest distance between the starting and landing point of the target
node. For the evaluation we use this distribution and the state transition probabilities are
calculated by nding the volume under the distribution as mentioned earlier for the rst
model. This model doesn't require an estimation of the exact walking speed, it also works
if the target node's motion consists of movement and brief pauses and can successfully
leave out the outliers. The value is selected such that, it is between average walking
speed and the maximum possible human speed. For our system we chose it to be 3:0.
5.4.2 Emission Probability
Emission probability dictates the chances to observe an output from a given state. In
this case as explained in Section 5.2 the set of output values is given by all the feasible
81
sequences. The set of states is also given by the set of all the possible feasible sequences.
Emission probability e
ij
is the probability that the SBL algorithm estimates the target
node's location on the face with sequence q
j
when in reality the target node is actually
located on a face with sequence q
i
. This behaviour occurs due to the noise added to
the signal. Mathematically the RSS values with noise can be modeled using a path loss
model of signal propagation with a log-normal noise. This model can be described by the
following equations:
P
R
= P
T
P
d
0
10 log
d
1
d
0
(5.15)
=
1
p
2
2
exp
2
2
2
(5.16)
Figure 5.5: Emission probability: Empirical method of estimation.
82
Here, P
R
, P
T
, P
d
0
,
are in dB andd, d
0
are in m. This model is the superimposed
version of path loss and non-linear eects due to fading and shadowing. We model
as
a Gaussian-distributed random variable with zero mean and variance
2
.
Our aim is to estimate the emission probabilities based of this model. The rst way
is to simulate a target node on a face with sequence q
i
, then using the above model
randomly generate a RSS vector (RSS values from each beacon node) and running SBL
for this vector and nd q
j
. Repeating this a suciently large (say 100) number of times
will give a very good estimate of e
ij
for all j values. This will have to be done for all q
i
sequences for us to get the complete E matrix of size NN where N is the number of
feasible sequences which can be of O(n
4
) where n is number of beacon nodes, hence N
can run into thousands even for a small topology of 15 nodes. This makes this technique
of nding emission probability computationally very expensive.
The second technique to evaluate emission probability also uses the path loss model of
signal propagation with log-normal noise but in a completely dierent way. Consider the
event I that the target node is on a face with sequence q
i
and another event J that the
SBL estimates the target node's location on the face with sequence q
j
then the emission
probability e
ij
by denition is the probability of J given I:
P
J
I
=
P(I;J)
P(I)
(5.17)
The probability of target node being on the face with sequence q
i
is equal to the
normalized area of the face, P(I) =a
i
=A. This can be explained by considering that the
target node can be present anywhere in the localization space.
83
Now the tricky part is to evaluate P(I;J) for which we use the path loss model with
log-normal noise and we do some approximations explained later. At any point in the
localization space the mean received power from a stationary beacon node k is given by
the path loss model without the noise component. Let
P
ik
represent the RSS from beacon
node k at the centroid of the face with sequence q
i
where the target node is located.
P
ik
= P
Tk
P
d
0
10 log
d
ik
d
0
(5.18)
Due to the noise component
, the SBL algorithm estimates the target node's loca-
tion on a face with sequence q
j
. Hence, if we can come up with a technique which can
map the added noise to the estimated sequence by the SBL then we can evaluate the
probability of observing q
j
instead of q
i
.
In absence of noise, on the face with sequenceq
j
every point receives a dierent power
from a xed beacon node k. The value of received power is solely dependent upon the
distance between the point and the transmitting beacon node. Therefore, for a given
beacon node there is a minimum and maximum value of the RSS associated with every
face, let these values be Pmin
jk
and Pmax
jk
, this is shown in the Fig 5.6(a).
Pmin
jk
= P
Tk
P
d
0
10 log
dmin
jk
d
0
(5.19)
Pmax
jk
= P
Tk
P
d
0
10 log
dmax
jk
d
0
(5.20)
Wheredmin
jk
anddmax
jk
are the distances to the closest and the farthest boundary
points of face with sequenceq
j
from the beacon nodek. This can be generalized for every
84
(a) Visualization in 2D
(b) Visualization in power domain
Figure 5.6: Emission probability: Theoretical method of estimation.
85
beacon node for the given face which means that if the received power was between the
corresponding minimum and maximum received power from all the n beacon nodes then
SBL would estimate the location of the target node to be on face with sequence q
j
. It
wouldn't matter if the received power was due to the noise component or the path loss
component of the Equation 5.15.
Next question is if the mean RSS value is
P
ik
then what is the probability that receiver
will receive an RSS value between Pmin
jk
and Pmax
jk
? This can be calculated using
the log normal probability distribution Fig 5.6(b) as shown by the Equation 5.21.
P
k
(i;j) =
Z
Pmax
jk
Pmin
jk
1
p
2
2
exp
(p
P
ik
)
2
2
2
dp (5.21)
The mean RSS value from beacon node k at every point on face with sequence q
i
is not
P
ik
. In fact, it is dierent for every point on the face, but to make calculations
simpler we approximate it by the value at the centroid that is
P
ik
, this approximation is
justied because at the end, for the entire face the values average out.
Therefore, the probability that the two events I andJ happen simultaneously, target
node is located on face with sequence q
i
and SBL estimates its location on face with
sequence q
j
, can be calculated by the multiplying P
k
(i;j) for all values of k basically for
all beacon nodes and to consider all points with sequence q
i
we multiply it with the area
of the face. This is given by Equation 5.22 and the logic behind is simple, for SBL to
estimate the target node's location on face with sequence q
j
the RSS values will have to
be between Pmin
jk
and Pmax
jk
for all values of k and because we assume that noise
86
adds independently to each signal path the overall probability P(I;J) is the product of
all the individually calculated P
k
(i;j):
P(I;J)a
i
n
Y
k=1
P
k
(i;j) (5.22)
Hence,
P
J
I
= e
ij
A
a
i
a
i
n
Y
k=1
P
k
(i;j)
(5.23)
P
J
I
= e
ij
A
n
Y
k=1
P
k
(i;j) (5.24)
5.4.3 Initial Probability
The starting probability represents the state of the system at timet = 0. Initially, we can
consider that the target node can be in at any point in the localization space, which means
that the probability that the target node is located on one of the faces is proportional to
its area. Therefore the normalized area a
i
=A of a face gives the initial probability where
a node can be. We also tried the initial probability to be uniform across all the states
but determined empirically that it doesn't work as well as normalized area.
i
=
a
i
A
a
i
8i2Q (5.25)
With this we have all the three probability matrices required by the Viterbi algorithm;
in the next section we give a detailed overview of the system, experimental setup and the
core algorithm.
87
5.5 Algorithm Implementation and Simulation Results
Before we dive into the real world experiments, we rst present simulation results for a
15 node topology in a 55m30m area as shown in the Fig 5.7. The small triangles in the
gure represent the beacon nodes. The gure also shows the simulated path traversed by
the target node representing ground truth. The RSS vectors are generated every second
considering that the target node moves at a speed of 1:6m=s. We use path loss model
( = 2:2;P
d0
= 54dBm) with log-normal noise (variance =
2
) for generating the RSS
values.
Figure 5.7: Simulation topology with target node's path. The target node starts at point
A goes around and ends its journey at point B
This RSS vector is then given to a SBL algorithm module which generates an estimated
sequenceq
j
corresponding to the target node's location. The sequenceq
j
goes as an input
observation to the Viterbi algorithm. The complete
ow is given by Algorithm 3.
88
The complexity of the localization engine can be broken down in two parts: rst, the
complexity of SBL part which generates the observation sequences which isO(n
4
) for each
incoming RSS vector, where n is the number of beacon nodes and second, complexity of
Viterbi algorithm which isO(Tn
8
) whereT is the length of the horizon. In practice, it is
observed that due to outliers the probabilities in the Viterbi trellis goes below a very small
threshold for all the states and in such scenarios the responsible outlier is skipped, this
is implemented by carrying forward the state probabilities from the previous time slot.
The horizon T value is set as a constant making the complexity of the overall algorithm
to beO(n
8
). Just to give an idea, once the observations starts to come in, it takes less
then 200msec (on a mac book air) for the system to calculate a location estimate. This
execution time is good enough for a real time operation.
5.5.1 Simulation Results
The simulation results are presented in Fig 5.8 for dierent values of signal noise variance
2
. As the target node moves around the localization space, the plots show the error
vs time as reported by the SBL and the new algorithm SOSBL. The error increases
as the noise increases which is very natural, what is interesting to see is the SOSBL
algorithm not only improves the localization accuracy by more then 40% over SBL but
also reduces the error variance dramatically. Reduction of variance in error signies that
the algorithm lters out the outlier input vectors. The mean and variance values of error
are summarized in the Table 5.1 for dierent values of noise variance. From the shown
table we observe that SOSBL is better over SBL even in high noise environments, which
89
Algorithm 3: Sequence of Sequences Based Localization Algorithm
Input: Number of Nodes: n
Input: Topology: SetL of (i;X
i
;Y
i
)8i = 1n
Input: Tx Pwr:
!
P
T
=fP
T1
P
Ti
P
Tn
g
Input: Building Dimensions: (l;b) and Origin
Input: Path loss & Log-Normal model Parameters: (;K
dB
;)
Input: Walking Model:
walk
;
walk
/* INITIALIZATION */
begin
Read Inputs
T ( GenSeqCentTbl(
!
P
T
;L)
E( EmissionProb(T;;K
dB
;)
S( TransitionProb(
walk
;l;b)
( InitialProb(L)
/* LOCALIZATION ENGINE */
while 1 do
!
rss( LISTEN()
!
seq( SeqGenrtr(
!
rss)
!
q
j
( KendalTauSearch(
!
seq;T)
(x;y)( Viterbi(E;S;;
!
q
j
)
LogData(x;y;
!
rss)
REPLY(x;y)
Table 5.1: Error (Mean, Variance) for dierent noise variance values.
Noise Var.
2
= 9:0
2
= 25:0
2
= 49:0
2
= 81:0
SBL (3:7; 8:4) (5:3; 15:4) (6:3; 14:9) (7:1; 27:4)
SOSBL (2:8; 2:3) (3:1; 2:2) (3:7; 6:0) (4:1; 5:0)
% Gain (29:7%; 72:6%) (41:5%; 85:71%) (41:2%; 59:7%) (42:2%; 81:75%)
90
Figure 5.8: Simulation results: Error in location estimates by SBL and SOSBL as the
target node traverses the path shown in Fig 5.7.
91
makes it more signicant in real world environments where the noise variance can be in
the 64 to 81 dBm range.
5.6 Deployment Details and Experimental Results
The system described in this section was installed in a building that houses research labs
and oce spaces for students and professors at University of Southern California. The
total
oor plan area that was monitored by the system was 1650m
2
with dimensions of
55m 30m. There were 15 beacon nodes that were positioned as shown in the Fig 5.9.
Figure 5.9: Experimental setup: Floor plan with beacon nodes
The hardware used for the beacon nodes is a very common platform commercially
available Tmote Sky device [55]. The device is battery powered and small in size with a
footprint approximately the size of two AA batteries. Tmote Sky has a 802.15.4 complaint
CC2420 radio front end, a TI MSP430 microprocessor, 10kB RAM and 48kB of Flash
memory. The radio consumes approximately 18mA at 3V when receiving or transmitting,
92
and has a maximum transfer rate of 250kbps. The MSP430 is a 16-bit micro- processor
operates at 8MHz clock.
The beacon nodes are set in a mode where they transmit a beacon packet periodically
every 1 second. The beacon nodes only have the responsibility to transmit beacon packets
and do not act as a mesh network for transporting data from the target nodes. The beacon
nodes don't need to be synchronized. They operate at at a xed transmit power level of
0 dBm and use ZigBee channel 26 for transmission with CSMA mode is disabled.
The experiments were conducted during regular oce hours so as to make sure that
the evaluation is done in a realistic scenario. The ground truth was measured by marking
points on the
oor at every turn to be made and measuring time it took to go from one
point to the next. This system doesn't need to go through any training phase. All it needs
is the topology information of the beacon nodes and the dimensions of the localization
space. This makes a system like this readily deploy able and easy to use in emergency
situations. Next we present the algorithm used and the server architecture.
Once the target node picks up the beacon packet it measures the RSS corresponding
to that packet and relays this information along with a time-stamp and the source in-
formation to the server where it is processed to generate a RSS vector corresponding to
its time-stamp, which is then used to generate location estimates. In the next section we
present the results from the real world deployment described above.
5.6.1 Real world Results
The best way to evaluate a localization algorithm is to see the trace of the estimated
locations of the target node and compare it with the ground truth. The ground truth of
93
target node's movement is presented in Fig 5.10. The target node starts from point A
moves around the space and ends its path at B. Path A to B covers almost the entire
oor
starting from a room coming out to the corridor and walking through the corridor and
coming back to the entrance of the room where the target node originally started from.
The target node was being carried by a volunteer who walked at a normal pace. The
results presented show how the new algorithm improves upon SBL in step wise manner.
Figure 5.10: Target node's movement as it goes from point A to point B
The Fig 5.11(a) presents SBL algorithm output just by itself; these results are evalu-
ated by considering the localization space to be the entire building
oor. The SBL results
clearly demonstrate that the worse case estimates can have very large error and the vari-
ance of error is also very high, which, in turn, has an adverse eect on the condence
interval of the estimates.
Next in Fig 5.11(b), we present location estimates when the localization space is the
entire building
oor and the sequence of sequences (SOSBL) algorithm is used to generate
94
(a) Localization estimates using SBL.
(b) Localization estimates using SOSBL.
Figure 5.11: Location estimates using SBL and SOSBL as the target node traverses the
path shown in Fig 5.10.
95
Figure 5.12: Error in location estimates for SBL and SOSBL.
these estimates. The estimates plot a very clear and well dened path of the target node
as it moves around the localization space. The average error of SOSBL estimates is
almost 40% lower then that of SBL estimates. The Fig 5.11(b) shows these estimates on
the
oor-plan.
The localization error comparison for SBL and SOSBL is shown in Fig 5.12. The
average localization error goes down from 8:9m to 5:6m, which is approximately 40%
improvement in accuracy. The SBL and SOSBL estimation errors are positively co-
related, but the variance (42:1) in SBL error is almost three times more than variance
(14:3) in SOSBL error . This shows that SOSBL skips the outliers in the input. These
results are in accordance to the ones given by simulations.
5.6.1.1 Incorporating Floor Plan
The real world SOSBL results presented above do not utilize building
oor-plan informa-
tion for improving the accuracy. It is very clear from Fig 5.11(b) that the path estimate
can be improved if we can use the
oor-plan information, essentially saying that the tar-
get node cannot walk through walls. In this part of the results we rst present a simple
96
method to incorporate this information as a part of transition probability matrix used by
SOSBL and then next we present the results.
The
oor-plan information can be encoded in the transition probability matrix, by
essentially utilizing the shortest walking distance between two points in presence of ob-
stacles instead of utilizing shortest walking distance when there are no obstacles. This
means that the probability of going from one state to the other state, if the two were on
the opposite sides of a wall would reduce signicantly, even if the actual distance (without
the wall) between the two was really small. The shortest distance is used as an input to
Equation 5.14, rest of the parts of the SOSBL algorithm remain exactly the same without
any change.
Figure 5.13: Location estimates using SOSBL when utilizing building
oor-plan, as the
target node traverses the path shown in Fig 5.10.
For calculating the shortest distance between two points in presence of obstacles we
rst convert the
oor-plan into a bit map where the walls and other obstacles are denoted
by zeroes and open space by ones. Next we evaluate two algorithms for calculating
97
shortest distance using this bit map. First, we use Dijkstra's algorithm [19] to compute
the shortest path between two points represented as nodes of a graph, but due to bad
computational time, determined that it is not practical to use it in this scenario. The
second algorithm we utilize is based on the
ood ll [86] algorithm with eight directions.
This recursion technique is same as the one used for the paint bucket function for coloring
all the connected pixels of same color with a new color. We modify the algorithm such
that instead of changing color of the pixel, it updates its distance from the starting pixel
and keeps doing it until it nds the minimum distance. When the recursion ends minimum
distance from the starting point to all the pixels have been computed and because we use
eight neighbours the distances are same as computed by Dijkstra's algorithm. Another
benet of this algorithm is that we don't have to construct a graph which is required for
Dijkstra's algorithm. The complexity of this technique is O(M) where M is the number
of bits in the bit map.
Figure 5.14: Error in location estimates for SBL and SOSBL with building
oor-plan.
The results of SOSBL after incorporating building
oor-plan is presented in the
Fig 5.6.1.1. The improvement in the accuracy of the path can be seen clearly. The
path estimate shows how the target node moves from the room to the corridor through
98
the door and makes proper turns. The error plot shown in Fig 5.6.1.1 is similar to the ones
shown previously, the average error and error variance are further reduced in this case to
4:9m and 13:3 respectively from 5:6m and 14:3 when SOSBL didn't use
oor-plans. The
key benet of incorporating
oor-plan is better path structure estimation.
5.7 Conclusion
In this chapter, we presented Sequence of Sequences Based Localization (SOSBL) algo-
rithm. SOSBL utilizes a Hidden Markov Model (HMM) based mathematical model to
improve upon the accuracy of Sequence Based Localization algorithm. We have presented
extensive simulation and real world deployment results which demonstrate that SOSBL
estimate are signicantly better then the ones obtained by SBL algorithm. The aver-
age localization error is reduced from 8:9m in case of SBL to 5:6m for SOSBL without
oor-plan and 4:9m for SOSBL with
oor-plan. One of the other benet of SOSBL is
the estimates are less jittery, meaning that the outliers are ltered out and SOSBL with
oor-plan is capable of estimating better path structure.
The implementation of SOSBL involved careful tailoring of the underlying algorithms
and models. Multiple shortest distance algorithms were evaluated and a tailored version
of
ood ll algorithm was used. Similarly a lot of dierent hypotheses were tested for
calculating dierent probabilities and the best ones were picked. Also, few conditions
were added when calculating state probabilities for Viterbi algorithm to ensure smooth
working of SOSBL. All this has led us to develop and evaluate a very elegant technique
for indoor localization.
99
The results further raise the question: are there better ways to estimate the transition
and emission probabilities so as to further improve the accuracy? A simple minded idea
is to incorporate walls and doors when calculating the SBL regions itself in addition to
transition probability calculation. We believe this can further improve the estimates and
make the algorithm more powerful.
100
Chapter 6
Conclusions and Future Work
6.1 Summary
While deploying a real world indoor localization system based on SBL algorithm for an
interactive media project at USC in Spring semester of 2012, we uncovered that SBL's
assumption of having equal transmit power for all beacon nodes may not always be
true, which may lead to higher localization error. This led us to a detailed analysis and a
deeper understanding of how SBL algorithm can benet from non-uniform transmit power
of beacon nodes and what role an active network can play in a RSS based localization
system. Analyzing the problem further made it clear that the non-uniform transmit
power can improve the theoretical accuracy of SBL.
We started Chapter 3 by describing the eects of non-uniform beacon transmit power
on equal-RSS lines. We proved how it transforms the locus of equal-RSS points from
straight lines, in case of equal transmit power, to circles when the transmit power is
dierent. We also proved that the number of SBL facets generated by these circles is
O(n
4
). We demonstrated that the radius and center of these equal-RSS circles can be
101
varied by changing the dierence in transmit power of corresponding beacon nodes. We
used this new found degree of freedom to divide the localization space more uniformly.
This is presented as the Non-Uniform Sequence Based Localization (NU-SBL) algorithm,
where an optimized transmit power value is found for each beacon node in the given
topology using simulated annealing. We took the idea a step further to show that the
localization error can be further reduced if the optimization is done for a sub-section of
the localization space, making it a zoom like scenario; this algorithm is called NU-SBL-
ZOOM. Detailed simulation results are presented to substantiate these ndings.
Our work in chapter 3 laid the foundation for deriving a mathematical transform which
made it possible to implement the NU-SBL and NU-SBL-ZOOM techniques in a real world
settings without changing the transmit power of the existing or newly deployed beacon
nodes. The proposed transform makes it possible to use ZOOM technique simultaneously
for multiple target nodes. The Warped RSS Sequence Based Localization (WR-SBL) and
Enhanced Warped RSS Sequence Based Localization (EW-SBL) are practical equivalents
of NU-SBL and NU-SBL-ZOOM algorithms respectively. We also presented evaluations
conducted for both WR-SBL and EW-SBL on two dierent testbeds one using WiFI
and the other using ZigBee technology. We have shown that the EW-SBL technique of
localization improves the localization accuracy considerably.
Our second major contribution is detailed in chapter 5, where we demonstrated the
use an orthogonal technique to improve the localization accuracy of the SBL, that we
refer to as Sequence of Sequences Based Localization (SOSBL). We showed how the
problem of estimating ideal location sequences from the incoming ranked RSS sequences
can be modeled as a state estimation problem for a Hidden Markov Model (HMM).
102
The modeled technique works on top of the SBL implementation, where the estimated
location sequences given by SBL algorithm are treated as input observation sequence for a
hidden Markov process. We then presented mathematical approaches for calculating state
transition probability, emission probability and initial probability matrices and showed
how to use them to deduce the hidden states using Viterbi Algorithm. The presented
model takes into account target node walking model as well as log-Normal fading model
for improving location estimates. We evaluated SOSBL on a deployment, which showed
that it can reduce localization error by 40% over SBL. The SOSBL algorithm is capable
of ltering out the outliers and has a strong mathematical foundation.
6.2 Future Work
In this work, our main focus has been the design of better indoor localization algorithms
that use ranked RSS vectors instead of absolute RSS values. Our work has sparked many
ideas that can form the basis of future research, as we discuss below.
6.2.1 Optimum Node Density
The sequence centroid tables generated for implementing EW-SBL algorithm are based on
the assumption that the beacons from each and every beacon node deployed in a certain
distance are heard by the target nodes. But in real world, due to the walls and obstacles,
the RF signal is attenuated non-uniformly along dierent directions which immensely
impacts the accuracy of the algorithm. This raises the question: what should be the
node deployment density such that the average localization error is not greater than a
certain value? It is worth investing in an eort to come up with an empirical method that
103
would give us a value ofM for a given value of average error, whereM is the minimum
number of audible beacon nodes at any point on the
oor. This will complement the
traditional way of dening the node density as number of nodes per area by taking the
walls and obstacles into account.
6.2.2 Antenna Diversity
The beacon nodes used in our evaluation were simple, o-the-self available devices with-
out any special front end antenna. Use of multiple directional antennas on a single beacon
node can improve the RSS readings, by reducing the signal variance and hence signi-
cantly improving the results. This requires special hardware design and development but
it can potentially improve localization accuracy to a great extent.
6.2.3 Incorporation of Floor-Plans
SBL relies on the path loss model of RF channel for the purpose of localization and it
assumes that there are no obstructions in the localization space, which is not true in
case of indoor environments. It populates the sequence centroid table on the basis of this
model, but this model does not incorporate the attenuation caused by the walls which acts
as another source of error. Due to this the reference model used for any of the algorithms
is faulty. It is possible to incorporate the building map information in the model when
creating the sequence centroid table thereby reducing the error. Incorporating walls can
be implemented by modifying the path loss model as follows:
P
R
=P
T
P
d
0
10 log
d
d
0
X
i
G
i
W
i
dB
104
WhereW
i
dB
is the attenuation caused by wall of typei andG
i
is the number of such walls
between the receiver and the transmitter.
6.2.4 Dynamic Calibration of Model Parameters
Model parameters such as path loss exponent, variance
2
in signal strength and walking
speed are dynamic entities which
uctuates between a given range of values. At present,
these parameters are estimated once and manually fed to the system and are never up-
dated during a run. Thus, there is a need to run the parameter estimator periodically so
as to further improve the accuracy of the algorithms.
In our implementation, the path loss exponent estimation process involves using one
or more stationary target nodes whose actual location is known. RSS measurements are
taken on beacon packet reception, which are then used to evaluate the value. This
single requirement of having stationary target nodes for estimation makes it dicult
to turn this algorithm into a stand alone mobile application. In order to overcome this
hurdle, we propose to perform an on-line simultaneous localization and estimation of
value. This will not only enhance the performance, but also make it more versatile.
6.2.5 Using Other Physical Signals with SBL
Sequence based localization techniques are generic techniques and are not tied down to
only received signal strength measurements. They can be applied to any other physical
modality measurements which encode the distance information between two devices. It
will be interesting to see how does these techniques perform with respect to variance in
105
measured value of the physical signal. These techniques can work with ultra-sonic sensor,
time of
ight measurements and many others.
6.2.6 Merging SOSBL with WR-SBL and EW-SBL
SOSBL and EW-SBL are completely orthogonal to each other and they individually bring
improvements in accuracy with them; it is yet to be seen if the two can work together and
constructively add their gains. Although as the number of states increase, the time taken
by the SOSBL starts to increase prohibitively. Bringing the two algorithms will require
a layered approach where the EW-SBL location estimate are used as an observation for
SOSBL with a reduced state space size.
6.2.7 In-Corporation of Other Sensor Data and Walking Models
It is very common to nd accurate step counter class or API in most of the smart-phone
operating systems. Combination of of a step counter and magnetometer readings for
calculating the transition probabilities dynamically can potentially improve the location
estimate given by SOSBL algorithm. The SOSBL technique provides a framework where
SBL can be combined with dierent walking models and sensor data in a probabilistic
manner without compromising the core ideas of geometric modeling and easy of deploy-
ment, which makes it a powerful tool for use in non line of sight emergency scenarios
where other algorithms fail.
106
6.2.8 Machine Learning Framework for SOSBL
SOSBL can benet by incorporation of a learning algorithm based on forward-backward
algorithm for hidden Markov process. The system can be bootstrapped with the transition
and emission probabilities as described in this thesis then once the system becomes live
these values can be improved further and can be used to give better localization estimates.
6.2.9 Optimization Problem Formulation
In this work, we optimized to nd the transmit power (in NU-SBL) or the Warp vector
(in WR-SBL and ER-SBL) using simulated annealing. Obtaining provable approximation
guaranties for this combinatorial optimization problem can help evaluate the quality of
approximation. If we consider n beacon nodes with a predened topology dened by the
setS. If
!
P
n
T
=fP
T1
P
Ti
P
Tn
g is the transmit power vector for this given topology
then it can be proved thatAM
a
(
!
P
k
T
) is a non-negative monotonic sub-modular function.
WhereA is the total area of the localization space,M
a
(
!
P
k
T
) is a function that returns the
Max-Area value for the selectedk beacon nodes whose transmit power is given by vector
!
P
k
T
. For such sub-modular function a bound on greedy approximation of the optimal is
given by Theorem 1.
Theorem 1. For a non-negative, monotone sub-modular function f, let be a set of
size k obtained by selecting elements one at a time, each time choosing an element that
providesthelargestmarginalincreaseinthefunctionvalue. Let
beasetthatmaximizes
the value of f over all k-element sets. Then f() (1
1
e
)f(
); in other words,
provides a (1
1
e
)- approximation. [56]
107
Using the Theorem 1 we can derive the following bound on the greedy approximation
of optimal Max-Area.
M
a
(
!
P
ng
T
)
A
e
+ (1
1
e
)M
a
(
!
P
n
T
)
For all practical purposes M
a
(
!
P
n
T
)A hence neglecting the second term on right hand
side.
M
a
(
!
P
ng
T
)
A
e
This is a very loose bound, improving on this bound requires further investigation.
One of the approach to do so is to divide the localization space into zones the way it was
done for the Zoom and then use a similar formulation.
Another problem formulation to look at requires a mobile target node (a robot) whose
location is known at all times. Using the information generated by this robot we want to
improve the warp vectors for each zone so as to improve the accuracy of the localization.
It will be interesting to compare the warp vectors generated by the simulated annealing
and by this technique.
108
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Abstract (if available)
Abstract
Real-world deployments of indoor localization systems are frequently faced with requirements like low stationary beacon node density, calibration, initial learning phase, scalability, non-line of sight deployments, use of crowded frequency channels and many others. This makes the use of existing localization technology in a real world scenario very costly and difficult to use. Further, the dynamics of an indoor environment and signal interference can adversely effect the accuracy of any such system. Also, localization algorithms for indoor environment should have a low computational complexity for a real time operation and should be capable of identifying and serving multiple, possibly hundreds of users simultaneously. Addressing these challenges, we present two key innovations: (1) a deterministic transformation of the received signal strength vector that can improve the sequence-based localization accuracy and (2) an orthogonal state estimation of hidden Markov process based approach that can further improve the accuracy of sequence-based localization. ❧ Sequence-Based Localization (SBL) is a technique whereby a node is localized based on the ranked sequence of signal strengths obtained from a set of beacon nodes. SBL effectively partitions the area into regions corresponding to each of these unique ranked sequences. Prior work has developed SBL under the assumption that all beacon nodes have the same transmit power. As the part of the first innovation, in this work we consider beacon nodes with unequal transmit power for SBL and present heuristic algorithms for joint optimization of transmit power and beacon node placement. We show through comprehensive simulations that a novel enhancement of SBL utilizing optimized non-uniform transmit powers, coupled with careful beacon node placement, which we refer to as NU-SBL, can dramatically improve the area partitioning compared to traditional SBL. However, in evaluating these schemes under stochastic fading, we find that the original SBL with optimized location performs nearly as well or slightly better than NU-SBL in many cases. We introduce another scheme, that we refer to as NU-SBL-ZOOM, which further allows the power levels to be optimized non-uniformly so as to focus in on a particular smaller region within the larger localization space. NU-SBL-ZOOM is found to perform much better in terms of both area partitioning as well as location error in the presence of fading. ❧ In order to implement the non-uniform versions of SBL in a practical setting where it is not possible to access and alter the power setting of stationary beacon nodes, we derive a mathematical transform that essentially achieves the same results as if the transmit power of beacon nodes was being changed dynamically. Based on these transforms we present Warped RSS Sequence Based Localization (WR-SBL) and Enhanced WR-SBL (EW-SBL). We implement these two algorithms on two real-world systems: one a Wifi-based testbed for smart-phones and another a low-power wireless testbed. We show that the proposed enhancements significantly reduce average localization error compared to traditional SBL, with no additional hardware and little additional run-time complexity, enabling them to be readily deployed in practice. On the low-density WiFi testbed, we show a 5-fold reduction in average distance error for EW-SBL compared to LSE. ❧ For the second innovation, we turn our attention to probabilistic model based localization algorithms which generally divide the entire localization area into a fine mesh and based of sensor readings carefully compute the probability of target node's location at one of these grid points. We take a little different approach: we estimate the path of the target node and model the problem as a state estimation problem for hidden Markov process, where the ideal SBL sequences are treated as hidden states, essentially modeling the location of moving target node in terms of which SBL face it resides on. We treat the individual SBL sequence estimates of target node's location as mere observations and then use Viterbi algorithm to deduce the true underlying state transition sequence. We use a random walking model to calculate transition probabilities and the log-normal fading modal to compute emission probabilities. We call this scheme Sequence of Sequences Based Localization (SOSBL). We implement this technique on a 15 node testbed and show a 40% improvement in the localization accuracy of a moving target. Also, we show that this technique reduces the error variance by 3 times over SBL.
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Creator
Deora, Suvil
(author)
Core Title
Radio localization techniques using ranked sequences
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Publication Date
02/22/2016
Defense Date
12/11/2015
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
hidden Markov model,indoor localization,Internet of Things,localization,NUSBL,OAI-PMH Harvest,RF localization,SBL,sequence based localization,sequence of sequences,simulated annealing,SOBS,tracking,Viterbi algorithm,walking model
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application/pdf
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Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Krishnamachari, Bhaskar (
committee chair
), Govindan, Ramesh (
committee member
), Parker, Alice (
committee member
)
Creator Email
deora@usc.edu,suvildeora@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c40-211641
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UC11278479
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etd-DeoraSuvil-4127.pdf (filename),usctheses-c40-211641 (legacy record id)
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etd-DeoraSuvil-4127.pdf
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211641
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Dissertation
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Deora, Suvil
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texts
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University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
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Tags
hidden Markov model
indoor localization
Internet of Things
localization
NUSBL
RF localization
SBL
sequence based localization
sequence of sequences
simulated annealing
SOBS
tracking
Viterbi algorithm
walking model