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Target Localization and Tracking in a Random Access
Sensor Network
A Thesis Presented
by
Kivanc KERSE
to
The Department of Electrical and Computer Engineering
in partial fulfillment of the requirements
for the degree of
Master of Science
in
Electrical Engineering
in the field of
Communication and Signal Processing
Northeastern University
Boston, Massachusetts
August, 2013
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Abstract
Wireless Sensor Networks (WSNs) are commonly used to monitor physical or environmental
parameters such as temperature, sound, velocity, etc. Such networks find application in
different areas including military, environmental, medical and industrial ones. For
applications that require long term monitoring, data collection with limited resources (power,
bandwidth) is a challenging problem. In addressing these challenges, we study a network
architecture that relies on integrating sensing and random channel access to achieve energy
efficiency. Specifically, this thesis focuses on the use of WSNs for target localization and
tracking. In a random access framework, distributed sensor nodes transmit data packets to the
fusion center at will, maintaining a given average transmission rate. The fusion center
discards erroneous packets and those packets that have collided, and uses the remaining ones
to recover the target information. Target localization is formulated as a sparse recovery
problem, whose solution is sought through norm-1 regularized minimization techniques. This
solution feeds the subsequent tracking phase, where the knowledge of target signatures is
exploited to design an adaptive algorithm of low complexity. An adaptive framework is also
developed, in which loss of tracking triggers a new localization phase. System performance is
illustrated through computer simulation, showing that target localization and tracking can be
achieved using only a fraction of sensors’ measurements, conveyed in a random access
fashion.
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Acknowledgement
Foremost, I would like to express my sincere gratitude to my advisor Prof. Milica Stojanovic
for the useful comments, remarks and guidance through the learning process of this master
thesis. Furthermore, I would like to thank Fatemeh Fazel for introducing me to the topic, her
patience and her support through my academic adventure.
I would also like to thank to my friends Melis Yetkinler, Seyhmus Guler, Umut Orhan, Mert
Korkali, Cem Bila, and my fellow lab mates in Northeastern University CDSP Lab: Yashar
M. Aval, Parastoo Qarabaqi, Rameez Ahmed and Osso Vahabzadeh for energizing
conservations, academic supports and all the fun we have had in the last two years.
Last but not the least; I would like to thank my family; my parents Mualla-Ilhan Kerse and my
brother Can Kerse for supporting me in every way throughout my life.
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Contents
1 Introduction .......................................................................................................................... 1
2 Background ........................................................................................................................... 4
2.1 Wireless Sensor Networks ............................................................................................... 4
2.2 Compressed Sensing and its Application in WSN ........................................................... 8
2.3 Target Localization and Tracking Methods .................................................................... 10
3 System Framework ............................................................................................................ 15
4 Localization and Tracking ................................................................................................. 18
4.1 Random Access Compressed Sensing (RACS) ............................................................. 18
4.2 Target Localization Using Random Access WSN .......................................................... 21
4.2.1 Field Model ......................................................................................................... 22
4.2.2 Localization Algorithm ....................................................................................... 23
4.3 Target Tracking Algorithm ............................................................................................. 25
5 Simulation Results and Analysis ....................................................................................... 28
5.1 Synthetic Data Model .................................................................................................... 28
5.2 Localization Results for a Single Target ........................................................................ 29
5.3 Tracking Results for a Single Target .............................................................................. 34
5.4 Re-localization Mechanism ............................................................................................ 35
5.5 Localization and Tracking Results for Multiple Targets ................................................ 37
5.6 Localization and Tracking Results in the Presence of Sensing Noise ............................ 44
6 Conclusion ........................................................................................................................... 47
Bibliography ....................................................................................................................... 49
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List of Figures
3.1 System framework. N sensors distributed through field and have one-hop connection
with Fusion Center (FC). .............................................................................................. 16
4.1 Sample field model at a specific time instant with number of targets is K=5, amplitude
of all targets is Ak(t) =1 and decay rate 𝛽k=0.3 ............................................................. 22
4.2 Using 40% of the sensor measurements, target localization accurately finds the location
and the amplitude of the targets for the sample field model given at Figure 4.1. ........ 24
4.3 The average normalized recovery error plotted versus the % of the total number of
samples, for single target localization. As noted for localization recovery error below
10-2
at least 40% of the samples are required.. ............................................................. 25
4.4 The flowchart of the tracking algorithm ........................................................................ 27
5.1 Synthetic field model. A single target located at 3+j15 with unit amplitude 0.3 decay
rate 𝛽=0.3 moves in a direct line with a constant speed.. ............................................ 29
5.2 The average normalized recovery error of the localization algorithm plotted versus the
% of the total number of samples, for a single target. As noted for localization
recovery error below 10-2
at least 40% of the samples are required............................. 30
5.3 Actual field vs. recovered field using different number of samples as well as target
localization results. ....................................................................................................... 33
5.4 Recovery error performance using the tracking algorithm in Equations 4.17-18 for
different target speeds. .................................................................................................. 34
5.5 A second target enters to the field. (a) n = 0, (b) n = 10, (c) n = 20, (d) n = 40 ............. 36
5.6 The observed error E is monitored for a single target scenario. When a second target
enters the field, the value of the observed error exceeds the threshold value Ethres which
then triggers the recalibration mechanism... ................................................................. 37
5.7 The recovery error plotted versus the % of the total number of samples, for recovery of
three targets. As noted for localization recovery error around 10-2
at least 40% of the
samples are required.. ................................................................................................... 38
5.8 Recovery error performance using the tracking algorithm in Equations (4.17-18) for
three targets.. ................................................................................................................ 39
5.9 A fourth target enters to the field. (a) n = 0, (b) n = 20, (c) n = 40, (d) n = 50 .............. 40
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5.10 The observed error E is monitored for three target scenario. When a fourth target
enters the field the value of the observed error exceeds the threshold value Ethres and
triggers the recalibration mechanism. ........................................................................... 41
5.11 Routes of the moving targets. ....................................................................................... 42
5.12 Recovery error performance using the tracking algorithm in Equations (4.17-18) for
three targets, where the target routes are given in Figure 5.11... .................................. 42
5.13 The average normalized recovery error of the localization algorithm plotted versus the
% of the total number of samples, for different number of targets.. ............................ 43
5.14 The average normalized recovery error of the localization algorithm plotted versus the
% of the total number of samples, for three targets in the presence of sensing noise.. 45
5.15 Recovery error performance using the tracking algorithm in Equations (4.17-18) for
three targets in the presence of sensing noise.. ............................................................. 46
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Chapter 1
Introduction
Wireless Sensor Networks (WSNs) are composed of spatially distributed, self powered
autonomous sensors that monitor specific characteristics of their surroundings and wirelessly
deliver the gathered information to a network command location. WSNs find applications in
several fields, e.g., agricultural irrigation, medical applications, military and environmental
surveillance, flood control, fire detection, etc. In this thesis, we focus on the use of WSNs for
target localization and tracking.
Each node in the network measures the aggregate received signal strength from the
targets in the field and transmits this data along with additional information (e.g. location tag
of the node) to a central command station, which we will refer to as the Fusion Center (FC)
throughout this thesis. The FC collects data from different nodes, discards the erroneous
packets, and after processing the useful data recovers the map of entire field. Sensor nodes
are usually battery powered and battery recharging in the field is a hard task. Therefore, it is
important to maximize the lifetime of the nodes and the robustness of the network against
node failures.
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Bandwidth requirements and energy consumption are two main design challenges in
WSNs. Routing and scheduling algorithms can be used to improve the energy efficiency in
WSNs [1]. However, implementing routing and scheduling algorithms over a large-scale
sensor network can be challenging. Another method to reduce the energy consumption is by
integrating communication and channel access considerations into the data acquisition process
[2], [3]. In [2, 3], the authors propose a Random Access Compressed Sensing (RACS)
scheme, which combines random sensing with random channel access. In this approach, the
correlation among the sensor data is exploited to compress the data during the acquisition
process. By acquiring a sufficient number of sensor data full recovery can be achieved in an
energy efficient manner.
The idea behind [2] and [3] arises from the assumption that most signals of interest
have a sparse representation when expressed in a proper domain. E.g., most natural signals
have a sparse representation in the frequency domain [4]. Then, by using compressed sensing
techniques [5], the spatial map of the field is recovered using only a random subset of sensors’
measurements. In some cases, the signals of interest may have sparse representations in bases
other than the frequency domain. In addition, recovering the whole spatial map is not always
necessary, e.g. depending on the task, we may be interested in acquiring specific
characteristics of the field. In this thesis, by taking into account the target signatures, we find
an efficient basis for localization, and integrate random sensing with random channel access
for an energy-efficient network implementation. The localization algorithm is then used to
initialize a gradient-based tracking algorithm.
Furthermore, we propose an adaptive scheme in which the FC constantly monitors the
sensing process, adjust the per-node sensing rate when necessary, and uses the re-localization
mechanism to recalibrate the tracking algorithm. We show that target localization and
tracking can be achieved using a small fraction of sensors’ measurements.
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The thesis is structured as follows. Chapter 2 explains the relevant background
material. System framework is introduced in Chapter 3. Chapter 4 investigates the proposed
methodology and discusses the localization and tracking algorithms. Synthetic data models
are explained in Chapter 5 and simulation results for the proposed method are analyzed.
Concluding remarks are made in Chapter 6 and potential future work is discussed.
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Chapter 2
Background
2.1 Wireless Sensor Networks
Wireless sensor networks are crucial in enabling the development of smart
environments such as smart buildings, transportation systems, factories , etc, since they are
the only communication tool between the real world and the smart system. WSN technology
offers great benefits in many areas such as medical, environmental, industrial and military
applications. Different kinds of sensors are produced for different applications, e.g., one type
of sensors can measure physical properties like pressure, temperature and humidity, while
another type of sensors are capable of measuring motion properties such as position, velocity
and acceleration or sense identification properties such as fingerprints, voice and retinal scan
[6]. Since the potential usage of WSNs is widely variable, requirements, designs and
constraints differ depending on the applications. In this part, we will briefly describe a few
specific applications that can benefit from the methods proposed in this thesis.
Today, WSNs are commonly used in environmental applications such as tracking
small animals, insects and birds [27], monitoring natural events effects on crops [38],
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irrigation of fields [39], chemical and biological detection [7], biological monitoring of
marine, atmospheric and soil contents [40], flood control [41], forest fire detection [8],
pollution study [42] and so on.
Wildfires are one of the fatal threats in the world. It is reported in [9] that a total of
67,774 wildfires burned 9,326,238 acres in USA during 2012. One way to monitor and detect
wild fires is based on satellite monitoring [10]. But authors in [8] state that long scan periods
and satellites’ low resolutions restrict this techniques’ effectiveness. Authors then propose a
real-time forest fire detection application by using WSNs [8]. In this work, sensors are
programmed to collect data such as temperature and relative humidity and send their
measurements to a base station. At the base station, all collected data is analyzed to determine
the likelihood for the weather to cause a wild fire. In addition to that, if sensors detect smoke
or abnormal temperatures, they directly send an emergency data to the base station to report a
possible fire threat.
Another environmental application for WSNs is flood control. One example of flood
control mechanism established using WSNs is ALERT [7]. In basic ALERT installation,
several sensor types are deployed in the field, such as rainfall sensors, weather sensors, and
water level sensors. The sensors regularly gather data and transmit information to a
centralized database in a predefined manner. At the database, operators can examine the
information e.g., by displaying the average level of rainfall at a specific time for each rainfall
sensor, displaying the current rainfall for all sensors in a specific area, or displaying the sensor
locations where a certain amount of rainfall is observed. By querying the database, experts at
the base station analyze the circumstances and take the necessary precautions [11].
Besides environmental applications, WSNs have great impact on health applications
like telemedicine, telemonitoring of human physiological data and tracking and monitoring
patients’ locations and identifying patients’ health status [12], [13]. Telemedicine attracts
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increasing attention as one of the healthcare application using WSNs. The aim of
telemedicine is to improve health care access and reduce governments’ healthcare costs.
Using combination of computers and telecommunications, in [14] it is demonstrated that
telemedicine can improve the quality of healthcare by collecting and transmitting patients’
data to medical centers. In addition it is also explained in [14] that telemedicine allows
patients to leave the hospital early, even after a surgical intervention. Furthermore, in [15]
authors propose a work that enables to care for elderly people remotely. By using WSNs,
major incidents such as a fall, long term inactivity or unusual behavioral activities can be
detected. With the help of these small sensors, while patients’ freedom is provided, gathered
data allows the doctors to identify predefined symptoms earlier [16].
WSNs are a supplementary part of military command, control, communications,
computing, intelligence, surveillance, reconnaissance and targeting (C4ISRT) systems [7].
Since sensor networks consist of compact, disposable, low cost sensors, even the destruction
or failure of some nodes does not affect the whole military application as much as traditional
surveillance stations. Sensor networks are useful in military applications such as monitoring
friendly forces’ ammunition, location and equipments, tracking hostile targets, battle field
surveillance, battle damage assessment, and nuclear, biological and chemical (NBC) detection
[7]. Authors in [17] investigate the use of WSN network technology for ground surveillance
such as target detection and target tracking by using hybrid sensor networks that report the
gathered data to command centers. Since real-time tracking with WSNs is a challenging task
which requires robustness, high frequency sampling, complex signal processing and
coordination between sensors, authors propose a two layer system to address these challanges.
In the first layer, tiny, inexpensive nodes are used to perform acoustic, magnetic and optic
sensing. These nodes send the collected data to sparser, more complex and powerful nodes to
process. After the gathered data is processed in the second layer, location, signal power and
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all necessary information is sent to a command center. At the command center, experts can
make necessary analysis to track and detect the hostile targets’ locations.
These applications are only some examples of the possible applications of WSNs, and
each application has its own challenges and requirements. However, one main challenge in all
WSNs is that of energy consumption. Sensor networks consists of small, microelectronic
nodes that can only be equipped with a limited power source (<0.5 Ah, 1.2 V) [7]. Life time
of these micro devices is strongly dependent on their application. In other words, depending
on the application, the required energy to sense the surroundings varies and that variation
affects the battery life of the sensors. For multihop Ad-Hoc sensor networks, disfunctioning of
a few nodes because of battery drainage prompts rerouting, which forces the other nodes to
consume more energy and decreases the lifetime of the WSN. For these reasons, energy
consideration is an important research area and researchers propose different methods to
preserve energy.
Energy harvesting is one way to increase the lifetime of the sensors by using sunlight,
ambient vibrations, and electromagnetic energy [18]. For now, efficiency of the energy
production using energy harvesting is low, however, this technique is used for low data rate,
long term applications. The main task of a sensor node in such applications is to detect events,
perform data processing and transmit the processed data. The energy consumption for each
task is different, but for all WSNs, data transmission consumes the most energy [19].
Therefore, while energy harvesting can sustain energy for processing or sensing, other
methods are required to sustain or preserve transmission energy.
Another approach for energy saving is duty cycling. Exploiting node redundancy, duty
cycling aims to adaptively select a small subset of nodes and keep them active to maintain
connectivity, while keeping the rest of the nodes in sleep mode to save energy. Finding the
optimal subset of nodes is called topology control. On the other hand, active nodes do not
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need to maintain their radio connection active at all time. These nodes can switch off their
radio connection when there is no network activity, which is called power management [22].
Furthermore, power management can be achieved in two different ways, depending on the
implementation layer of the network architecture: independent sleep-wake up protocols
implemented on top of MAC (medium access control) layer, network or application layer, or
integrated within the MAC protocol. However, this method faces challenges such as time
synchronization [21].
A different approach to energy saving in WSNs is hierarchical routing [37]. All
sensing is done by tiny, low-cost low-layer nodes and these nodes only communicate with
higher level nodes, which are designed to process data and transmit the processed data to
longer ranges. This technique usually requires clustering in which highly equipped, powerful
nodes become cluster heads, while less expensive sensing nodes only communicate with the
cluster heads. The main challenge is how to choose the cluster heads and how the cluster
heads should gather and process the data. Hierarchical routing can work with spatial
compression techniques, which will be discussed in the next section.
The abovementioned methods, of course, are not the only energy conserving solutions
for WSNs. By exploiting the advantages of each method, a combination of all solutions can be
used to find alternative or superior methods. We use methods inspired by compressed sensing
in the context of this thesis. In the following section we will discuss compressed sensing in
detail.
2.2 Compressed Sensing and its Application in WSN
Traditional methods for sampling signals follow Shannon’s theorem, or the so called
Nyquist rate, that indicates the sampling rate must be at least twice the maximum frequency
present in the signal [23]. Today, this principle is used nearly in all signal acquisition
protocols used in visual and audio electronics, medical imaging devices, radio receivers and
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communication devices. A novel sensing sampling model called compressed sensing or
compressive sampling (CS) offers an alternative technique to traditional methods in data
acquisition. Compressed sensing theory proves that certain signals can be recovered from far
fewer samples or measurements than dictated by their dimension [24]. CS relies on two
principles: sparsity and incoherence. While sparsity relates to the signals of interest,
incoherence relates to the sensing modality.
Sparsity infers that a discrete time signal can be represented with a few non-zero
elements compared to its finite length, or that the information rate of a continuous signal
might be much smaller than suggested by its bandwidth. In other words, the compressed
sensing theory exploits the fact that a signal has sparse or compressible representations in an
appropriate basis Ѱ. On the other hand, incoherence uses the duality between time and
frequency and relies on the idea that signals that have a sparse representation in Ѱ, must be
spread out in the domain which they are sampled. In other words, the incoherence property
expresses that the sampling waveforms must have a dense representation in Ѱ.
CS theory enables sensors to capture the information of a sparse signal very
efficiently. Then, by using ℓ1 optimization techniques, the full length signal can be
reconstructed using only a small number of samples. The CS theory is applied in different
areas in which the prerequisite of sparsity of the signal of interest in a certain basis is
satisfied. Due to the specific contents of medical images, using a proper basis, the image can
be saved in a much smaller file, while conserving the high resolution of the image. Authors in
[44] use the CS theory to archive and reconstruct medical images using files that occupy less
space than traditional medical image files. In seismology, due to the limited number of
available observations, geophysical data is usually sub sampled. In other words, the seismic
map is reconstructed from only a few samples. Authors in [45] use CS theory to reconstruct
the sub sampled geophysical data. CS theory is also used in radars for target tracking. Target
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localization and tracking applications usually are not delay tolerant. To achieve this delay
constraint, gathering the samples from the field should be done in a time efficient manner and
a fast reconstruction algorithm is required for recovery. The authors in [43] use CS theory to
achieve this goal.
2.3 Target Localization and Tracking Methods
Generally, target localization is achieved using the following methods:
Energy-based localization
Direction of arrival (DOA)
Time difference of arrival (TDOA)
TDOA methods require time synchronization among sensors ,which is not practical in
a large scale network [46] [47]. DOA methods require sensors to measure incoming signal
directions, hence additional processing at sensor nodes [48]. In this thesis, we focus on
energy-based localization methods, which rely on energy measurements at the sensors. An
energy-based method using Maximum-Likelihood (ML) is proposed in [49] [50]. The ML
source localization problems solved using multi-resolution projection [50], Expectation-
Maximization (E-M) algorithm [50] or semi definite programming methods [51].
If the goal is that of finding the target location (and not the amplitude), references [49]
[52] propose computing the energy ratios between sensors and determining the hyper-spheres
on which target resides. Another class of methods consider decentralized localization
algorithms which update the estimation one measurement at a time. Examples of such
methods are: distributed ML [53][54], projection onto convex sets [55] and kernel averaging
estimators [56].
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Various approaches have been proposed in the literature for target tracking by
considering scalability, overheads, accuracy and energy consumption. Current approaches can
be classified under five schemes: tree based methods, cluster based methods, prediction based
methods, mobicast message based methods and hybrid methods [26].
Tree based methods organize the sensor nodes in a hierarchical tree such that the
points in the tree graph represent the sensor nodes and the edges represent the communication
links between nodes. Dynamic object tracking protocol is a tree-based target localization and
tracking method, which reports the tracking data of a moving target to a moving base station
[27]. Base station or command center broadcasts a request message and only sensors that are
close to the target location reply back to the base station. To keep track of a moving target,
spatial neighbors of the active node are waken up. There are beacon nodes between the base
station and the sensing nodes, which keep track of the target location. During the target
tracking process, base station sends a query to an active beacon node and that beacon node
replies back to the base station with the next location of the target. The base station then
moves on to the next beacon node by declaring it as the active beacon node. This process
iteratively continues until the base station catches up with the target.
Another tree based method is called scalable tracking, which assigns a cost to each
link calculated by the Euclidian distance between the nodes [28]. The leaf nodes (sensing
nodes) are assigned to sensing the field and sending data to base station through intermediate
nodes. The intermediate nodes keep track of the detected target and if there is an update about
the target send the relevant information to the base station. One disadvantage of this method is
the high communication cost due to the possibility that an edge might consist of multiple
communication hops.
Cluster-based methods propose forming node clusters statistically, while certain
properties of each cluster are predetermined, such as the area covered by each cluster or the
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number of members in each cluster. Static clustering is investigated for an energy efficient
target tracking in [29] referred to as RARE. This algorithm is based on two principles that are
called RARE –Area and RARE-Node. The RARE-Area deactivates the nodes that are not
receiving useful data to participate in tracking which are mostly the nodes placed far away
from target location. On the other hand, RARE-node hinders the sensor nodes that supply
redundant information. Even though static clustering has a simple implementation, there are
some disadvantages to it. For instance, in terms of fault tolerance, static clustering prevents
the nodes in different clusters to share information gathered in their area, which reduces the
robustness of the overall system [26]. To solve this problem, dynamic clustering methods
propose to form clusters dynamically, depending on the occurrence of the monitored events
[30]. The authors in [30] propose a method that forms clusters by using Voronoi Diagrams.
When a certain signal threshold is exceeded and the event is detected by a cluster head, only
that cluster head will become active and form a cluster by forcing the sensors in its
neighborhood to join the cluster. The activated sensors then gather data from the field and
send it to the cluster head to execute a localization algorithm and send the target location to
the base station. Many other examples can be given for cluster based tracking methods, but
one thing is common in these methods: that they provide scalability and better usage of the
bandwidth [26].
Prediction based methods are a hybrid mixture of cluster-based and tree-based
methods. These methods conserve energy by predicting the targets’ next location and only
activating the sensors located within the predicted area. If the prediction is wrong, such that
the target changes its moving direction or that the target cannot be detected by the active
sensors, then an error correction mechanism is executed to locate the current position of the
target and continue the prediction based tracking [31]. Another proposed method for
prediction-based method is given in [32] and [33]. The authors propose a method that keeps
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most of the nodes in the field in standby mode, until they are awaken by an active node. The
next possible location for the moving target is calculated at both sensor nodes and base
station, using previous data. If the predicted location is correct, the nodes do not transmit any
data to the base station. By using the sleep-awake mechanism, the authors aim to conserve the
energy in the sensing procedure, and by using the prediction method they aim to conserve the
energy in the data transmission. The drawback of the prediction methods is that of data
association for multiple targets. In multi-target cases, it is a challenging problem to associate
target locations and predict each target’s movement. This problem is investigated in [34] and
a clustering based target tracking method is proposed as a prospective solution.
Mobicast message based methods are actually a modified version of the prediction
based tracking methods. The method is based on a spatio-temporal multicasting technique that
delivers messages which contain the location and time information about the monitored field,
to a group of nodes that change according to targets’ active location. By predicting the next
position of the target, mobicast messages are delivered to next possible active region, before
the target enters the predicted area. Authors in [35] propose a dynamic method called VE-
Mobicast (Variant-Egg-Based Mobicast) in which by predicting the target movement, the
sensor nodes forward a control packet to the next active region by assessing present and past
values to activate minimum number of nodes in the forward field. In addition, authors in [36],
improve the power efficiency of VE-Mobicast method by modifying the message delivery
system from node to node, to cluster base structure with a method called HVE-Mobicast
(Hierarchical Variant-Egg-Based Mobicast). The proposed method delivers control message
at two stages: cluster to cluster and cluster to node. In the first stage, the cluster head sends a
message to a new cluster head to wake up the sensor nodes within its area. In the second
stage, the cluster head wakes up the sensor nodes according to the arrival time of the target.
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The main challenge with the mobicast message based target tracking methods is the
synchronization requirement between nodes and the base station.
Each tracking technique has its own benefits and drawbacks. Combining their
advantages is one way to fulfill different requirements. These solutions are called hybrid
tracking methods. Authors in [37] propose a method of Hierarchical Prediction Strategy for
target trajectory prediction in hierarchical sensor networks. The proposed method divides the
network into clusters, as is done in cluster based tracking, then creates a hierarchy between
the sensing nodes and the cluster heads as is done in tree based tracking, and finally, by using
Recursive Least Square (RLS) technique, the target’s moving trajectory is predicted to
activate respective nodes, as is done in prediction-based tracking and mobicasting message-
based tracking, to increase the overall network efficiency.
The common concern in all target tracking methods is energy consumption and
network robustness. An alternative tracking method will be provided in Chapter 4, which
employs an adaptive gradient-descent method to track the movements of the targets in the
monitored field.
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Chapter 3
System Framework
In this thesis, we assume we have N static sensor nodes placed in a field and a single-
hop transmission to base station referred to, throughout the thesis, as the Fusion Centers (FC),
as shown in Figure 3.1. The sensor nodes are simple devices that contain electronic sensors to
collect data from surroundings, simple processing unit to pack up the gathered data with
header bits, a transceiver to communicate the packet to the fusion center and a battery to
supply power. As explained in Chapter 2, accessing the sensors to recharge and replace
batteries is expensive, difficult and in some cases dangerous. On the other hand, FC has
considerable computational power and supplying power to the FC is not as hard.
Sensors in the field periodically collect data and transmit the information gathered
from their surroundings to the FC. In long term monitoring and field surveillance applications,
even when nothing noteworthy happens in the field, constant data stream continues to keep
track of the monitored area. Sensors sense the field with the equipped instruments and after
adding header bits, transmits the packet to the FC. The FC collects all the incoming data from
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different sensors, and after processing the data, provides the reconstructed snapshot of the
monitored field.
Figure 3.1: System framework. N sensors distributed through field and have one-hop
connection with Fusion Center (FC).
System design should address five major requirements. First of all, the FC must be
able to recover the field using the information gathered from the sensors and the accuracy of
the recovered field should not exceed a threshold. As a second requirement, the required
number of transmissions should be minimized to conserve energy. Thirdly, the overall system
should be robust against sensor failures, and unexpected noise levels. As a fourth requirement,
the executed algorithm at the sensors should have low complexity to extend the battery life of
the sensors. As the last but not the least requirement, the number of samples necessary to
recover the field should be minimized. To meet these requirements, we propose a solution that
is inspired by Random Access Compressed Sensing techniques in [2] and [3] to perform
localization and tracking. The proposed methods will be discussed in the next section.
We assume N sensor nodes are located on a P x Q grid where P x Q = N. In other
words, N sensor nodes are uniformly distributed throughout the field. Sensors take
measurements with an average sampling rate of λ measurements per unit time. For now, we
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will follow the assumption in [2] and assume that the sensors are synchronized. This
assumption is later relaxed in [3] as will be discussed in Chapter 4. The sensors measure the
surroundings for aggregate received signal strength from all targets, each having a power
level Am. The measurements along with the location tag are formed into a packet of L bits.
The packet duration or the required time to transmit the packet, is Tp=L/B where B is
the transmission bandwidth. To preserve the energy each node senses the field with a fixed or
adaptively variable rate and sends the gathered data to the FC. Through this thesis, we will
assume sensors use an average sensing rate to sense the field. This sensing rate is given by
Equation (4.5) in chapter 4. Note that the sensors do not communicate with each other.
The Fusion Center has no energy consideration and has access to high computational
power. The role of FC is to collect the packets from the nodes, to process them and to recover
the time varying map of the field. Packet losses, erroneous packets, overlapping packets and
other communication failures are naturally expected because of the nature of wireless
communication and random access. Therefore, another role of the FC is to check all incoming
packets for errors and keep only the meaningful packets to process.
The next chapter will discuss the used methodology, components of the system and
integration between different techniques in details. Random Access Compressed Sensing
(RACS) will also be explained in the next chapter. In addition, localization algorithm using
ℓ1 –minimization and target tracking algorithm will be discussed. Furthermore, the
localization algorithm will be used to initialize the tracking algorithm.
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Chapter 4
Localization and Tracking
4.1 Random Access Compressed Sensing (RACS)
The compressed sensing theory states that if a signal of dimension N has an S-Sparse
representation in a proper domain Ѱ, it can be recovered from random measurements obtained
in a sensing domain which is incoherent with Ѱ [5]. The authors in [2] propose a novel
scheme that is called Random Access Compressed Sensing.
At time t, the sensor node located at location zi obtains measurements from its
surroundings. This process is assumed to have a coherence time Tcoh, such that uzi (t1) ≅ uzi
(t2) where Tcoh≥ |t1-t2|. The authors define a collection interval time T, where T≤ Tcoh. The
acquired data is sent to the Fusion Center (FC) to build a map of sensing field denoted by
1,....,1,.....,
[ ] [ ]iz pq P P
q Q
U u u
(4.1)
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Many natural signals have sparse representation in the frequency domain, i.e. for
u = vec (U) and v = Ѱ -1
u, the vector v is sparse, where Ѱ -1
is the DFT transform matrix. In
other words, Fourier domain is an appropriate sparsity basis for many natural signals [3]. In
some cases, there may exist other bases that are good candidates to be a proper sparsity basis.
We will discuss an alternative basis suitable for target localization over a grid in the next
section.
In RACS, the sensor at position (p, q) on the grid measures the surroundings for signal
intensity, independently from the other nodes, at an average sensing rate λ measurement per
unit time. As explained in Chapter 3, sensors encode each measurement together with the
location tag into a packet of L bits. Afterwards, the modulated packet is transmitted to the FC
in a random access manner. Because of the nature of wireless communication and random
channel access, packets from different nodes may overlap at the FC. All incoming packets are
tested with a cyclic redundancy check (CRC) or a similar control protocol and failed packets
are declared as erroneous and simply discarded at the FC. The benefit of using compressed
sensing appears here, in that the FC can recover the monitored field as long as;
1) The selected subset of the received packets is chosen uniformly at random.
2) Sufficient number of measurements from field is gathered to enable the
reconstruction of the field.
The FC thus discards erroneous packets and collects the remaining useful packets over
an observation interval T. The observation interval is assumed to be shorter than Tcoh as stated
before. Thus, the process is approximated as fixed during the observation interval. At the end
of observation interval, the FC has collected the meaningful data which can be modeled as
(4.2)
where R is an M x N matrix, where M corresponds to the number of useful measurements
observed during T, z represents sensing noise and u is the data vector. To make it clear, rows
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of the matrix R are actually rows of an N x N identity matrix, which is uniformly and
randomly picked, with a single 1 in each row corresponding to the sensor node location that
has contributed a useful packet. Since each incoming packet carries a location tag, the FC can
easily construct the matrix R.
Note that the sensor measurements stored in u are not sparse but they have sparse
representation in the frequency domain, i.e., u=Ѱv, where Ѱ is the Inverse Discrete Fourier
Transform matrix. Therefore, Equation (4.2) can be written as
Ѱ (4.3)
If sensor noise is ignored, in order to reconstruct the field, the FC recovers v by solving the
following minimization problem:
ℓ
subject to Ѱ
(4.4)
where is the recovered sparse signal and ||.||ℓ1 is the ℓ1-norm of a vector. CS theory states
that, the solution to the convex optimization problem in Equation (4.4), ṽ, is unique and equal
to v as long as the number of uniform and random observations M is greater than Ns =
CSlogN. The constant C is independent of S and N. In other words, by supplying a sufficient
number of measurements, RACS ensures that the FC can recover the field.
Random selection is rendered possible to RACS by setting a sensing rate λ at sensors.
Authors in [3, 25] define a sensing rate λ based on the following parameter;
a) Length of the collection interval T, which is dictated by the statistical properties of
the monitored field.
b) Minimum number of packets that is required at the FC, which depends on the
properties of the signal of interest, as well as the specific task of the network.
The minimum sensing rate per node is stated in terms of system parameters as;
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where Tp is the packet duration, b is the packet detection threshold, s is the average number
of packets required to be collected in an observation interval T to meet the sufficient sensing
probability, γ0 is the nominal received signal-to-noise ratio (SNR), and W0(.) is the principle
branch of the Lambert W function [3].
Noting that, setting a sensing rate is a challenging task. If is too large, packet traffic
in the channel increases, which will cause too many collisions. On the other hand, if is too
low, the FC will not receive enough packets to recover the monitored field. However, the
lowest possible rate that achieves the reconstruction is preferable since a lower sensing rate
also means lower energy consumption.
To sum up, RACS combines random sensing with random access communication to
ensure the delivery of sufficient number of packets to the FC to reconstruct the field map by
solving a convex optimization problem. By doing so, RACS offers an energy-efficient method
for data collection in wireless sensor networks. A specific field model used through this thesis
will be explained and target localization by using a random access WSN will be discussed in
the next section.
4.2 Target Localization Using Random Access WSN
One of the application areas of WSNs is target localization and tracking as discussed
in Chapter 2. Throughout this thesis, we assume a grid network that has N = P x Q sensors,
with P and Q sensors in the x and y direction respectively.
(4.5)
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4.2.1 Field Model
We assume K targets are placed in a field, each generating a decaying signal such as
heat, sound, etc. Throughout this thesis we will assume an exponential signature model for the
targets, however, the proposed methods are not limited to exponential signature only and
other signal models can be accommodated. At time t, the measurement observed by the sensor
node i at location zi is given by
(4.6)
where ck (t) is the coordinate, Ak (t) is the strength, and k is the decay rate of the k-th target,
respectively. The process evolves over time as the targets move along unknown trajectories.
Sample field model is illustrated in Figure 4.1 over a 30x30 field at a given time t with K=5
targets, and Ak (t) =1 and k=0.3, for all targets.
Figure 4.1: Sample field model at a specific time instant with number of targets is K=5,
amplitude of all targets is Ak (t) =1 and decay rate k=0.3.
x
y
5 10 15 20 25 30
5
10
15
20
25
30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
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4.2.2 Localization Algorithm
Using Equation (4.6) and assuming that targets are located exactly on grid points, we
can replace the IDFT basis Ѱ that is used in RACS, as given by Equation (4.3), with the
following basis based on exponential signatures,
Ѱ
(4.7)
where Ѱ ∈ ℝNxN. The vector v ∈ ℝN in Equation (4.3) is now a sparse vector containing the
location and amplitude of the targets, such that it contains Ak at the position corresponding to
the location of the k-th target and zero elsewhere. We can generalize this setup to the case in
which the targets are not exactly located on grid points, i.e. the sensors are located on a P x Q
grid, while the targets can be located on a J1 x J2 grid, where J1 x J2 = J and J≥N. In this case
Ѱ ∈ ℝJxJ is given by
Ѱ
(4.8)
and v ∈ ℝJ consists of
∈ (4.9)
The FC then collects the useful packets over the collection interval T and at the end of
collection interval the useful data can be expressed by Equation (4.3). After that the FC
recovers v by solving the convex optimization problem
ℓ Ѱ ℓ
subject to ≥
(4.10)
Note that we need to impose the non-negativity constraint on the solution vector v,
since the components of the vector v contain the amplitude of the targets as given by Equation
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(4.9), i.e., a zero amplitude indicates that no target is located at that position. The localization
problem is then solved at the FC by using Equation (4.10). In Figure 4.2 it is illustrated that,
for the given field in Figure 4.1 (where the number of targets K=5, amplitude of all targets Ak
(t) =1 and the decay rate k=0.3), target localization is accurately achieved using 40% of the
all sensors.
Figure 4.2: Using 40% of the sensor measurements, target localization accurately finds the
location and the amplitude of the targets for the sample field model given at Figure 4.1.
In Figure 4.3, the average normalized recovery error performance of the localization
algorithm is illustrated for single target. With 40% of sensor measurements, we achieve a
recovery error below 10-2
for both target amplitude and target location, which means that the
error between the actual field and recovered field, is below 1%. Note that normalized
recovery error is defined as
where u(n) is the actual data and û(n) is the
recovered data in frame n. For target localization, 1% recovery error is considered acceptable.
In next section, we will present a tracking algorithm and an adaptive sensing mechanism,
0 5 10 15 20 25 30
0
5
10
15
20
25
30
x
y
target map
sensor
target
detected target
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which adaptively modifies the sensing rate to track moving targets in the field, aiming to
decrease the energy consumption without sacrificing the recovery error performance.
Figure 4.3: The average normalized recovery error plotted versus the % of the total number of
samples, for single target localization. As noted for localization recovery error below 10-2
at
least 40% of the samples are required.
4.3 Target Tracking Algorithm
Let us say that at some time using the localization algorithm given by Equation
(4.10), we have determined the number of targets K and the estimates Âk and ĉk for k ∈
{1,….,K}. We have also collected M observations, denoted by um where m denotes the index
of the collected packet from among the set of N possible measurement packets. We can form
an estimate
(4.11)
The error that we make in doing so is
0 20 40 60 80 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
% Number of Samples
Reco
very
Err
or
L1 minimization Recovery Error Performance for 1 Target
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(4.12)
This error can be measured since we have both um (observations from field) and ûm (estimate
data). We now define the observed squared error as
(4.13)
where the sum is taken over available observations in each collection interval. The relevant
error derivates are
(4.14)
and
(4.15)
where
(4.16)
Using these derivatives, we propose a gradient algorithm. Starting with the estimates
Âk (0), k (0), and working over n=1,2,…., a first order update is defined as
(4.17)
(4.18)
The parameters μ and v are the a-priori set step sizes. This type of update is the simplest;
however other types can be considered as well. It is also important to note that the algorithm
remains unchanged if the set of available observations changes with time (n).
The tracking algorithm in Equations (4.17-18) needs to be initialized using the
localization algorithm given in Chapter 4.2. Overall, once the number of targets and their
initial location is determined, tracking of those targets using Equations (4.17-18) may require
fewer samples. The network can thus reduce the per-node sensing rate, given by Equation
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(4.5), to save energy. For a given collection interval T, the per node sensing rate simply
follows from plugging s into Equation (4.5), where s in turn follows from Ns the number of
samples required for successful completion of the task (localization, tracking). Once the
number of targets and the target locations are determined, tracking the targets can be achieved
using lower number of samples in the subsequent intervals. To illustrate this point we
consider a simple tracking algorithm. Meanwhile, by monitoring the observed error E, the FC
will be able to detect major changes in the field and call for increasing the per-node sensing
rate to re-calibrate the tracking algorithm. To trigger this mechanism, the observed error E
should exceed a certain threshold Ethres. If the threshold is exceeded, the re-calibration
mechanism will be triggered at the FC to obtain the number and the location of the targets.
After the new locations are obtained and the tracking algorithm is re-calibrated, the FC will
continue with the tracking algorithm given above. In next chapter, a synthetic data model is
used to test the proposed localization and tracking methods.
Figure 4.4: The flowchart of the target tracking algorithm.
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Chapter 5
Simulation Results and Analysis
5.1 Synthetic Data Model
As explained in Chapter 4.2.1, we assume K targets are placed in a field and each
target generates an exponentially decaying signal. At time t, the measurement observed by the
sensor node i at location zi = xi + jyi is given by Equation (4.6).
For the first part of the simulations, we will assume that in the 30x30 field there is
only one target (K = 1) located at a position 3+15j and moving on a direct line with constant
speed. The decay rate of the target is assumed fixed at =0.3 and the target has a unit
amplitude Ak =1. Figure 5.1 illustrates this scenario.
In the second part of the simulation results, to demonstrate the system performance for
multiple targets, we will assume that K = 3 targets are placed in the 30x30 field located at
positions 3+5j, 25+3j, 25+25j and moving on direct lines with constant speeds. The decay rate
of the targets is assumed fixed at =0.3 and all targets have unit amplitude Ak =1. In addition,
the same scenario is examined when the targets change their moving directions during the
observation interval. Moreover, maximum number of targets that can be localized in an
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efficient manner will be determined. All results for multiple target case will be demonstrated
in Chapter 5.5.
In the third part of the simulation results, the performance of both localization and
tracking algorithms is tested in the presence of sensing noise. In this part, we will assume that
K = 3 targets are placed in the 30x30 field, located at positions 3+5j, 25+3j, 25+25j, and
moving on direct lines with constant speeds. The decay rate of the targets is assumed fixed at
=0.3 and all targets have unit amplitudes.
Figure 5.1: Synthetic field model. A single target located at 3+j15 with unit amplitude 0.3
decay rate =0.3 moves in a direct line with a constant speed.
5.2 Localization Results for Single Target
In Chapter 4.2.2, localization using random access WSN is explained and the
performance of the localization algorithm in Equation (4.10) is shown in Figure 4.3 and it is
reproduced here in Figure 5.2. To plot that figure, a single target with a decay rate =0.3 is
randomly placed at different locations, and for that specific location, different number of
samples is used to recover the field. By executing 1000 Monte Carlo simulation the average
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recovery error is plotted in Figure 4.3. In other words, for each number of samples, 1000
different subsets of the samples are used to recover the field.
Figure 5.2: The average normalized recovery error of the localization algorithm plotted versus
the % of the total number of samples, for a single target. As noted for localization recovery
error below 10-2
at least 40% of the samples are required.
From Figure 5.2, we note that, to achieve a recovery error below 1%, we need at least
40% percent of the total number of samples in the field. During our experiment, we used a
30x30 field, and all sensor nodes are placed on grid points, hence N=900 samples in total. To
achieve a recovery error below 1%, we thus need 360 samples. Snapshots of the recovered
field, using the localization algorithm for various numbers of samples are given in Figure 5.3.
0 20 40 60 80 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
% Number of Samples
Reco
very
Err
or
L1 minimization Recovery Error Performance for 1 Target
x
y
Actual Field
5 10 15 20 25 30
5
10
15
20
25
30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
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(a) Actual field
(b) Recovered field with 9 samples (1% of samples)
(c) Recovered field with 45 samples (5% of samples)
(d) Recovered field with 90 samples (10% of samples)
x
y
recovered map with Ns=9
5 10 15 20 25 30
5
10
15
20
25
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(e) Recovered field with 180 samples (20% of samples)
(f) Recovered field with 360 samples (40% of samples)
(g) Recovered field with 450 samples (50% of samples)
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(h) Recovered field with 720 samples (80% of samples)
(i) Recovered field with 900 samples (100% of samples)
Figure 5.3: Actual field vs. recovered field using different number of samples as well as target
localization results.
In Figure 5.3, the recovery result for different number of samples (9, 45, 90 180, 360,
450, 720, 900) is illustrated. With 9 samples, the actual target location and the detected
location differ greatly, however, with increased number of samples, the estimated location
improves, together with the amplitude prediction. With 360 samples, very low recovery error
is observed and after that point, the recovery performance almost stays at the same level. To
achieve target tracking with low recovery error, we proposed a method in Chapter 4.3 whose
aim is to conserve the energy by decreasing the required number of samples. In the next
section, the performance of the proposed tracking method will be illustrated over a given
field.
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5.3 Tracking Results for a Single Target
For the given exponential field model introduced in Chapter 5.1, the proposed tracking
method in Equations (4.17-18) is tested for different target speeds. In all cases, the target
moves with a constant speed on a direct line. The initial location of the target is 3+j15. For all
cases, the total duration of the event is limited to 10 frames. In other words, while for the
target with a speed of 0.1 frames per second, the total traveled distance is 1 pixel, for the
target with a speed of 1 pixel per frame, the total traveled distance is 10 pixels. For each value
of the speed (0.1, 0.5, 1.0 and 1.5), different number of samples is used and the average
recovery error is calculated. The recovery error for the tracking algorithm is plotted in Figure
5.4.
Figure 5.4: Recovery error performance using the tracking algorithm in Equations (4.17-18)
for a single target.
0 20 40 60 80 1000
0.1
0.2
0.3
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Direct Tracking of a Single Target
Speed=0.1
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Note that for slowly moving targets, tracking can be achieved using only a few
packets, such that, when target speed v=0.1 pixels/frame, using only 10% of the total number
of packets (Ns=90), a recovery error on the order of 0.01 is achieved (1% recovery error). This
value of Ns is 4 times lower than the value required for localization shown in Figure 5.2.
However, for targets with faster speeds, we still need a similar number of samples as that used
for target localization with ℓ1-regularized minimization. In the next section, we are going to
discuss re-localization mechanism for target tracking in case of erroneous tracking results.
5.4 Re-localization Mechanism
We assume that the tracking algorithm given in Chapter 4.3 knows the target location
at t=0 and applies the algorithm given by Equations (4.17-18) to track the target location in
subsequent frames. To initialize the tracking algorithm we propose to use the localization
algorithm given in Chapter 4.2 Equation (4.10). We also propose a re-calibration method, in
case that the tracking algorithm loses track of the target.
The main unexpected problem for the tracking algorithm would be the presence of an
unexpected target in the field. As it is explained in Chapter 4.3, the FC is able to detect major
changes in the field by monitoring the observed error E. We proposed a method in Chapter
4.3 that sets an error threshold Ethres to trigger the localization algorithm in order re-initialize
the tracking algorithm.
To present the performance of the proposed method, we consider the following
simulation scenario. We assume a single target is located at 3+j15 and is moving on a direct
line with a constant speed. In Chapter 4.3, we observed that the tracking algorithm requires
fewer samples, if the target speed is relatively small. Therefore, for this example, we will
assume that the target speed is 0.1 pixels/frame. The target decay rate is assumed to be fixed
at = 0.3. Initially, by setting Ns= 360, the localization algorithm accurately detects the
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location and the amplitude of the target. In the subsequent frames, the FC switches to tracking
mode, instructing the sensors to decrease their sensing rate to correspond Ns=90.
Meanwhile, throughout the subsequent frames, the FC monitors the observed error E. If E
exceeds a threshold Ethres (e.g. Ethres = 0.1 for this example), the FC sets Ns = 360 and triggers
the localization algorithm to recalibrate the tracking algorithm.
Figure 5.5: A second target enters to the field. (a) n = 0, (b) n = 10, (c) n = 20, (d) n = 40
For example, at frame n = 20 a new target enters the field as illustrated in Figure 5.5,
causing the observed error E to increase. The FC then sets Ns = 360 (corresponding to 40% of
the total number of samples), instructs the sensors to increase their sensing rate and uses
Equation (4.10) to recover the field. In doing so, the new number of targets and their positions
are determined. In the following collection intervals, the sensing rate can then be lowered to
save energy and the tracking algorithm in Equations (4.17-18) with the new estimates can be
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employed. In Figure 5.6, the observed error E vs. frame number is shown along with the
recovery error for each frame.
Figure 5.6: The observed error E is monitored for a single target scenario. When a second
target enters the field, the value of the observed error exceeds the threshold value Ethres which
then triggers the recalibration mechanism.
5.5 Localization and Tracking Results for Multiple
Targets
In this section, we use a similar setup as the one given in Chapter 5.2, with three
targets to show the performance of the proposed method in the case of multiple targets. Three
targets with same decay rate 0.3 are randomly placed at different locations. Using the Monte
Carlo Simulation structure as in Chapter 5.2, we note that recovery error performance for the
three target scenario has similar characteristics to that of the single target scenario.
0 10 20 30 40 500
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Figure 5.7 the recovery error plotted versus the % of the total number of samples, for recovery
of three targets. As noted for localization recovery error around 10-2
at least 40% of the
samples are required.
During our experiment, we used a 30x30 field, and all sensor nodes are placed on grid
points. We have 900 samples in total and to achieve a recovery error around 1%, we need at
least 360 samples. Similar to the single target results, a very low recovery error is achieved
with 360 samples and the recovery error almost stays at the same level after that point.
Similar to the single target case, we tested the proposed tracking method with three
targets. We assume all targets move with the same speed on direct lines. The initial locations
of the targets are 3+5j, 25+3j, 25+25j while each target moves on a different direction. The
total duration of the event is limited to 10 frames. The recovery error results for the three
targets are given in Figure 5.8.
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Figure 5.8: Recovery error performance using the tracking algorithm in Equations (4.17-18)
for three targets.
Similar to the single target scenario, for slowly moving targets, tracking can be
achieved using only a few samples. When the target speed v=0.1 pixels/frame, using only
10% of the samples, a recovery error around 1% is achieved. However, for targets with faster
speeds, we still need number of samples similar to that used for target localization.
In chapter 5.4, we tested the Re-localization mechanism for a single target scenario.
This time, we assume three targets are located at 3+5j, 25+3j, 25+25j and they move on a
direct line with constant speeds v = 0.1 pixels/frame. From Figure 5.8, we note that, the target
tracking algorithm requires fewer samples if the target moves with a relatively small speed.
The target decay rate is assumed fixed at =0.3 and is the same for all targets.
0 20 40 60 80 1000
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Speed=0.1
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Figure 5.9: A fourth target enters to the field. (a) n = 0, (b) n = 20, (c) n = 40, (d) n = 50
Initially, by setting Ns = 360, the localization algorithm accurately detects the locations
and the amplitudes of the targets. In the following frames, the FC switches to tracking mode,
and instructs the sensors to decrease the sensing rate , which corresponds to Ns = 90. At
frame n = 40, a fourth target enters the field as illustrated in Figure 5.9, hence causing the
observed error E to exceed a threshold Ethres =1.5 for this example. The FC sets Ns = 360,
instructs the sensors to increase their sensing rate and uses Equation (4.10) to recover the
number and location of the targets. In the following collection intervals, the sensing rate is
lowered and the FC switches back to the tracking algorithm as given by Equations (4.17-18).
In Figure 5.10 the observed error E vs. frame number is shown along with the recovery error
for each frame.
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Figure 5.10: The observed error E is monitored for three target scenario. When a fourth target
enters the field the value of the observed error exceeds the threshold value Ethres and triggers
the recalibration mechanism.
Until this point, we assumed that each target moves on a direct line with constant
speed. We use a similar setup given at the beginning of Chapter 5.5 to study the performance
of the proposed methods in the case of targets that change their moving direction. The initial
locations of the targets are 3+5j, 25+3j, 25+25j while each target moves in a different
direction. The total duration of the event is limited to 10 frames, while the targets change their
moving direction every three frames. Routes of the moving targets is given in Figure 5.11 and
the recovery error results for the are given in Figure 5.12.
0 10 20 30 40 500
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2
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Figure 5.11: Routes of the moving targets.
Figure 5.12: Recovery error performance using the tracking algorithm in Equations (4.17-18)
for three targets, where the target routes are given in Figure 5.11.
0 20 40 60 80 1000
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Speed=0.1
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The recovery error performance given in Figure 5.12 is almost the same as the one
given in Figure 5.8. This results shows that even when the targets change their moving
directions, tracking can be achieved successfully.
The maximum number of targets that can be localized depends on field size and the
decay rate of the targets. For all given examples, we assume targets are located in a 30x30
field with a fixed decay rate =0.3. We then use recovery error performance to find an
estimate for the maximum number of targets can be successfully located (with an error rate
around 10 -2
).
Figure 5.13: The average normalized recovery error of the localization algorithm plotted
versus the % of the total number of samples, for different number of targets.
As noted from Figure 5.13, with 40% of the samples, localization recovery error is
around 10-2
for three targets. For five targets, to achieve a recovery error around 10-2
at least
50% of samples are required. In other words, Figure 5.13 illustrates that, it is possible to
0 20 40 60 80 1000
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L1 minimization Recovery Error Performance for Multiple Target
#Targets=1
#Targets=3
#Targets=5
#Targets=7
#Targets=9
#Targets=10
#Targets=100
#Targets=150
#Targets=250
#Targets=350
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locate more targets but to do so, it is necessary to increase the number of samples. Throughout
the thesis, we focus to locate targets with 40% of samples, therefore, for a 30x30 field and the
decay rate =0.3, the limit is three targets for the proposed localization algorithm to detect
targets’ locations using 40% of samples with a recovery error around 1%.
5.6 Localization and Tracking Results in the
Presence of Sensing Noise
Heretofore, we assumed that the sensing noise z in Equation (4.3) is negligible.
However, in order to show the performance of the localization and tracking algorithm in case
of sensing noise, in this chapter, we will assume that three targets are located in a 30x30 field,
with a fixed decay rate =0.3. To test the performance of the localization algorithm, we use
the same Monte Carlo Simulation structure as in Chapter 5.2. We add white Gaussian noise to
sensor measurements. The SNR is measured in terms of the signal power to the noise power
ratio. For example if the SNR is 10 dB, that means
. In other words,
signal power is 10 times greater than noise power. In Figure 5.14, it is showed that, in case of
high SNR, target localization can be accurately achieved.
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Figure 5.14: The average normalized recovery error of the localization algorithm plotted
versus the % of the total number of samples, for three targets in the presence of sensing noise.
To test the performance of the tracking algorithm in presence of sensing noise, we
assumed that exact target amplitudes and locations are provided to tracking algorithm. We
then used the same simulation scenario as that of Chapter 5.3, but this time we add white
Gaussian noise to sensor measurements. In Figure 5.15, the error performance of the tracking
algorithm is illustrated for SNR values 5, 25 and 50 dB, along with the no noise case. In
Figure 5.15, it is shown that, in case of high SNR, target tracking can be accurately achieved.
0 20 40 60 80 1000
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Reco
very
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L1 minimization Recovery Error Performance in the Presence of Sensing Noise
SNR=5dB
SNR=25dB
SNR=50dB
No Noise
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Figure 5.15: Recovery error performance using the tracking algorithm in Equations (4.17-18)
for three targets in the presence of sensing noise.
0 20 40 60 80 1000
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0.2
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0.4
0.5
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% Number of Samples
Reco
very
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Direct Tracking of 3 Targets in the Presence of Sensing Noise
SNR=5dB
SNR=25dB
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No Noise
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Chapter 6
Conclusion
We studied the design of an adaptive random access sensor network for target
localization and tracking. Taking the target signatures into account, we determined an
efficient basis for localization, and integrated random sensing with random channel access for
an efficient network implementation. We then used sparse recovery algorithms based on ℓ1-
regularized minimization for target localization. The minimum required number of samples to
successfully achieve localization was investigated.
In addition, we proposed a simple target tracking algorithm, to enable tracking using
only a small number of samples, with an acceptable recovery error margin. We highlighted
that the proposed tracking method requires fewer samples to recover the field as compared to
the localization algorithm, in case of slowly moving targets.
We then developed an adaptive framework in which the FC iteratively adjusts the per-
node sensing rate such that target localization and tracking are achieved using minimal
resources. In other words, the network is capable of adaptively adjusting the sensing
parameters in accordance with the variations in the field. We proposed a solution that enables
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the FC to switch between localization and tracking algorithms, in case the tracking algorithm
loses track of the targets due to unexpected circumstances in the field.
Finally, the random access adaptive sensing scheme was illustrated using a few
example scenarios. Firstly, performance of localization algorithm is investigated for single
target scenario. Then tracking results are illustrated. After showing the benefits of the tracking
algorithm, a specific scenario was illustrated for our proposed adaptive solution, which
enables the FC to switch between localization and tracking algorithms. Same scenarios are
repeated for multiple targets and it is illustrated that the proposed methods work well in single
target and multi-target scenarios. Then, the maximum number of targets for localization
algorithm is determined for a specific case and performances of the localization and tracking
algorithms is illustrated in presence of sensing noise.
There are many opportunities for future research to improve the proposed tracking
algorithm. Energy efficiency analysis and error performance comparison with other tracking
algorithms can be done as future research. The proposed method can be improved to enable
tracking targets with higher speed using fewer samples than required for ℓ1- regularized
minimization. Also, alternative adaptive control mechanism can be investigated. We focused
on a network in which each sensor node has only a one hop distance to the FC. For different
topologies, the proposed tracking algorithm’s performance analysis would be another future
research. For multiple target tracking, the proposed method requires target association which
can be done by clustered target tracking methods as a future work.
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