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.

18

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)

19

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

20

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;

21

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)

22

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

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0.9

1

23

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

24

(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

25

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

26

(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

27

(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.

28

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

29

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

30

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

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0.8

0.9

1

31

(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

30

0.01

0.02

0.03

0.04

0.05

0.06

0 5 10 15 20 25 30

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30

x

y

Target Location and Estimate Position

sensor

target

detected target

x

y

recovered map with Ns=45

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30

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30

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Target Location and Estimate Position

sensor

target

detected target

x

y

recovered map with Ns=90

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30

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Target Location and Estimate Position

sensor

target

detected target

32

(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)

x

y

recovered map with Ns=180

5 10 15 20 25 30

5

10

15

20

25

30

0.1

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30

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Target Location and Estimate Position

sensor

target

detected target

x

y

recovered map with Ns=360

5 10 15 20 25 30

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30

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0.2

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0.9

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10

15

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30

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y

Target Location and Estimate Position

sensor

target

detected target

x

y

recovered map with Ns=450

5 10 15 20 25 30

5

10

15

20

25

30

0.1

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x

y

Target Location and Estimate Position

sensor

target

detected target

33

(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.

x

y

recovered map with Ns=720

5 10 15 20 25 30

5

10

15

20

25

30

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30

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sensor

target

detected target

x

y

recovered map with Ns=900

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30

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Target Location and Estimate Position

sensor

target

detected target

34

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

0.4

0.5

0.6

0.7

% Number of Samples

Reco

very

Err

or

Direct Tracking of a Single Target

Speed=0.1

Speed=0.5

Speed=1.0

Speed=1.5

35

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

36

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

37

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

0.05

0.1

0.15

0.2

Frame Number

E

0 10 20 30 40 500

0.05

0.1

0.15

0.2

Frame Number

Reco

very

Err

or

38

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.

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 3 Targets

39

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

0.1

0.2

0.3

0.4

0.5

0.6

0.7

% Number of Samples

Reco

very

Err

or

Direct Tracking of 3 Targets

Speed=0.1

Speed=0.5

Speed=1.0

Speed=1.5

40

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.

41

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

1

2

3

4

5

Frame Number

E

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1

Frame Number

Reco

very

Err

or

42

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

0.1

0.2

0.3

0.4

0.5

0.6

0.7

% Number of Samples

Reco

very

Err

or

Direct Tracking of 3 Targets

Speed=0.1

Speed=0.5

Speed=1.0

Speed=1.5

43

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

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 Multiple Target

#Targets=1

#Targets=3

#Targets=5

#Targets=7

#Targets=9

#Targets=10

#Targets=100

#Targets=150

#Targets=250

#Targets=350

44

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.

45

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

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 in the Presence of Sensing Noise

SNR=5dB

SNR=25dB

SNR=50dB

No Noise

46

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

0.1

0.2

0.3

0.4

0.5

0.6

0.7

% Number of Samples

Reco

very

Err

or

Direct Tracking of 3 Targets in the Presence of Sensing Noise

SNR=5dB

SNR=25dB

SNR=50dB

No Noise

47

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

48

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.

49

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