A Dynamic Approach To Sensor Network Deployment For Target Detection In Unstructured, Expanding Search

Areas

by

Julio Vilela

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Mechanical and Industrial Engineering University of Toronto

© Copyright by Julio Vilela 2015

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A Dynamic Approach To Sensor Network Deployment For Target

Detection In Unstructured, Expanding Search Areas

Julio Vilela

Master of Applied Science

Mechanical and Industrial Engineering

University of Toronto

2015

Abstract

This thesis presents a novel dynamic deployment strategy for a network of static sensors using a

probability model of target motion to detect un-trackable targets. The focus herein is on the

dynamic and optimal deployment of the static sensor network. The network nodes are

determined at regular time intervals throughout the search based on available real-time

information. Optimality is achieved based on maximizing the probability of finding the target

through the use of the novel iso-cumulative curve. It is adaptable to terrain variation, presence of

obstacles, and can be re-calculated whenever target information, like a clue, is found to re-locate

search effort. Simulations showed that the proposed methodology increases the success rate of

target interception and reduces the mean detection time compared to uniform coverage-based

approaches. In addition, the methodology was applied to a wilderness search and rescue scenario,

where static sensors assisted mobile sensors in intercepting a target.

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Acknowledgments

The successful completion of this thesis was a result of many hours of doodling, reflection,

programming, dedication to research, and most importantly, the discovery of oneself. However,

this work would not have been accomplished without the crucial help of many individuals, to

whom I would like to thank.

First and foremost, I would like to thank my supervisors, Prof. Beno Benhabib and Prof. Goldie

Nejat. Prof. Benhabib was a continuous presence, source of inspiration, as well as a source of

feedback throughout the last two years. He was there “to protect me from myself”. Without his

ongoing questioning and critiquing of my ideas, none of this work would have been a reality. He

taught me what research is about – an ongoing battle with oneself to obtain answers nobody else

has. The capability to develop a concept, explain it clearly, and validating, is an acquired skill

that I have started to master, and will be taking on beyond my academic life. Prof. Benhabib,

with his joyful persona and rigorous work ethic, has inspired me to become a better researcher. I

tried to enjoy every moment along the way, and he made that possible. I enjoyed doing my

masters. I would also like to thank Prof. Nejat, who also supervised my work and provided

immense feedback while I developed my methodology and while I did paper revisions. Writing

papers with Prof. Nejat is like sculpting with sand: it takes a while to get it done, but the final

result is aesthetically pleasing. I wish both my supervisors great success to their already very

successful careers, and I sincerely hope that future graduate students can experience the same

support and help that I received from them. It was a privilege to have them as my supervisors.

I am eternally grateful to Ashish Macwan, who took his time to explain to me his research. Some

of my work complements his, and without his dedication and answers to my endless questions,

none of this would have been possible. It was a pleasure working alongside him, and assist him

with his work. He was an integral part to my adaptation to graduate school, and I wish him all

the best in his career.

My experience in graduate school was highly influenced by other graduate students, especially

the ones at The Computer Integrated Manufacturing Laboratory at the University of Toronto.

They provided a lively and friendly atmosphere to conduct research, as well as a joyful

playground for discussions and socializing. Many thanks to Evgeny Nuger, Mario Luces,

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Bejamin Corcoran, Arta Alagheband, Masih Mahmoodi, Justin Kim, Kerry Zhou, and Mengzhe

Zou. I wish you all the best in your careers, whether they are in academia or in industry. I would

also like to extend my gratitude to Alex Hong, Wey-Hao Chang, Veronica Marin and Pieter

Luitjens from the Autonomous Systems and Biomechatronics Laboratory at the University of

Toronto. They made me laugh. A lot. Thank you.

I would also like to give special thanks to summer students Raymond Ly and Lucas Sardinha De

Arruda. They provided vital help to my research and offloaded a lot of computer programming

tasks, as well as literature review hours, from my shoulders. I am eternally grateful to both of

them, and I wish you both all the best.

I would like to thank Julie Roy, my partner in crime and soulmate. You have been there to

support me and laugh with me. Graduate school, and life, would have never been this joyful and

pleasant without you. Thank you for being there for me.

Last but not least, I would like to thank my family: my sister Joana, my mother Maria de Fátima,

and my father Júlio Jose. You provided continuous moral support throughout my entire life, and

especially while I completed my masters. Today, I am a better person thanks to you. You have

taught me what life is about, and that honesty, hard work, and perseveration, are essential

ingredients to conquer dreams. I know you will always be there for me. I would have never

achieved all my goals without your support. You might live in another city, but your presence is

constant in my heart. Special thanks as well to Joly for her soft furriness and endless positive

energy. Obrigado por tudo.

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Table of Contents

Acknowledgments ................................................................................................................................ iii

Table of Contents .................................................................................................................................. vi

List of Figures ...................................................................................................................................... vii

Nomenclature and Acronyms ............................................................................................................... ix

Introduction....................................................................................................................................... 1

1.1 Thesis Objectives ...................................................................................................................... 3

1.2 Thesis Organization................................................................................................................... 4

Literature Review ............................................................................................................................. 5

2.1 Static-Deployment Strategies .................................................................................................... 6

2.1.1 Probabilistic .................................................................................................................. 6

2.1.2 Deterministic................................................................................................................. 7

2.1.3 Applications .................................................................................................................. 9

2.2 Dynamic-Deployment Strategies ............................................................................................ 12

2.3 Mobile-Target Behavior .......................................................................................................... 15

Static Sensor Network Deployment ................................................................................................ 17

3.1 Problem Statement .................................................................................................................. 18

3.1.1 The untrackable target ................................................................................................ 18

3.1.2 The static sensors ........................................................................................................ 19

3.1.3 The environment ......................................................................................................... 19

3.2 Methodology ........................................................................................................................... 21

3.2.1 Deployment Planning – Stage I .................................................................................. 22

3.2.2 Deployment Execution – Stage II ............................................................................... 37

3.2.3 Redeployment – Stage III ........................................................................................... 38

3.2.4 Determining the search parameters ............................................................................ 40

3.3 Hybrid deployment strategy .................................................................................................... 42

Performance Studies ....................................................................................................................... 47

4.1 Comparative study .................................................................................................................. 47

4.1.1 Simulated Target ......................................................................................................... 48

4.1.2 Simulated Experiments ............................................................................................... 49

4.2 WiSAR Case Study ................................................................................................................. 54

Conclusions and Recommendations ............................................................................................... 60

References............................................................................................................................................ 63

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List of Figures

Fig. 1. Illustration of the iso-cumulative curves. (a) A target PDF along a ray; (b) Iso-probability

curves, at t; and (c) Propagated iso-probability curves, at t+Δt. .................................................. 16

Fig. 2. (a) Google Earth terrain image of Mount Robson Provincial Park, BC, Canada; (b)

Simulated 3D terrain in TerreSculptorTM based on height map data from (a). ............................. 20

Fig. 3. Summary of proposed methodology.................................................................................. 21

Fig. 4. Overview of the deployment planning – Stage I. .............................................................. 23

Fig. 5. Example of a Target CPDF. .............................................................................................. 25

Fig. 6. Cumulative probability of success curves at multiple time instances, t* < t < Tmax. ......... 26

Fig. 7. (a) A target NCPDF along a ray; (b) Iso-cumulative curve, at t*. ..................................... 27

Fig. 8. Outline of iso-cumulative curve generation at deployment time t*. .................................. 27

Fig. 9. (a) Terrain with 4 rays; (b) sNCPDF plots for Tmax = 2.5 h for Rays 1,2 and 3; (c) Several

sCPDF propagations and the sNCPDF plot for Ray 4 in (a). ....................................................... 29

Fig. 10. The iso-cumulative curve at t*=1800 s, effective for the time interval t* < t < Tmax........ 30

Fig. 11. (a) Iso-cumulative curve propagation with obstacle presence. ....................................... 31

Fig. 12. Example of three iso-cumulative curves. ........................................................................ 33

Fig. 13. CPSO algorithm showing the locations of the static sensors for different stages of the

optimization process; (a) N = 1; (b) N = 20; (c) N = 500. ............................................................ 36

Fig. 14. Example of dynamic deployment of static sensors with three propagations of the iso-

cumulative curve, for tmin = 1800 s, tmax = 3000 s, and Δtint = 600 s. ............................................ 37

Fig. 15. An example of network redeployment due to clue find. ................................................. 39

Fig. 16. Hybrid deployment strategy. ........................................................................................... 42

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Fig. 17. (a) Originally planned path with no static sensors at time t; (b) Adjusted path with static

sensor avoidance at time t. ............................................................................................................ 44

Fig. 18. State of an example search at t*=2400 s. ......................................................................... 46

Fig. 19. (a) PDF of target travel direction change; (b) Examples of simulated target paths. ....... 48

Fig. 20. Optimal deployment networks; (a) NCPDF vs (b) VFA. ................................................ 49

Fig. 21. (a) Simulated target interception at t = 10382 s with 10 m sensing range; (b) Simulated

target interception at t = 5763 s with 40 m sensing range. ........................................................... 50

Fig. 22. (a) Simulated target without interception with 10 m sensing range; (b) Simulated target

intersection at t = 9155 s with 20 m sensing range. ...................................................................... 50

Fig. 23. (a) Simulated target interception using NCPDF at t = 5914 s; (b) Simulation with no

target interception using VFA. ...................................................................................................... 51

Fig. 24. Improvement of NCPDF over VFA for different search times and sensor detection sizes;

(a) Improvement in success Rate; (b) Reduction in mean detection time. ................................... 52

Fig. 25. Comparing success rate and mean detection time for different search time and varying

sensor detection radii. ................................................................................................................... 53

Fig. 26. Static sensor deployment configuration for the search. ................................................... 55

Fig. 27. Initial state of the search at 1800 s. ................................................................................. 56

Fig. 28. State of the search at 3724 s (clue located at ‘’). ......................................................... 57

Fig. 29. State of the search at 5573 s. ........................................................................................... 58

Fig. 30. Target interception by a mobile sensor at 5543 s. ........................................................... 59

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Nomenclature and Acronyms

Latin letters

a First optimal weight parameter

ai First model parameter in the logistic function

a1 Learning factor for local optimal position

a2 Learning factor for global optimal position

b Second optimal weight parameter

bi Second model parameter in the logistic function

cpj,i ith Control point with time j

dclue Distance along a straight line from the clue drop to the LKP

di Distance to a neighboring particle

dj Nearest neighbor distance of a particle

dmax Maximum distance traced by a target along a ray

D100* Location of the iso-probability curve with cumulative probability value of 1

Li Third model parameter in the logistic function

M Number of control points used for interpolation

nt Number of deployment instances

nsc Number of static sensors per curve

N Iteration number

Nnei Number of neighboring particles

Nprop Number of propagations of the CPDF

Nss Number of static sensors available at the start of a search

Nund Number of undeployed static sensors before redeployment

pi ith particle considered for the local optimal position.

pj jth particle considered for the global optimal position.

pnet Global optimal position of a static sensor

pss Local optimal position of static sensor

x

r Position of a target along a ray

rmax Optimal location along a ray

rran1 Random variable for local optimal position

rsens Random variable for global optimal position

t Time instance during a search

ti Time instance of a propagated CPDF

t* Deployment time during a search

tmin Minimum allowed deployment time during a search

tmax Maximum allowed deployment time during a search

Tclue Time of clue find belonging to the target

Tclue_drop Time of the clue drop by the target

Tclue_drop Estimated time of the clue drop by the target

Tmax Search time

T*max Search time for redeployment

THS Head start time

U Uniform distribution

vj Cumulative probability value

vmax Maximum speed of the target

vss Velocity of a particle in the PSO/CPSO algorithm

w Intertia factor

wi NCPDF weight

wini Initial NCPDF weight

wini

Normalized initial NCPDF weight

xss Position of a particle in the PSO/CPSO algorithm

X Random variable representing position of a target along a ray

xi

Greek letters

Δtapp Time intervals between CPDF propagations

Δtint Time interval between static sensor deployment

µν Mean of the nominal target speed PDF

σν Standard deviation of the nominal target speed PDF

Abbreviations

CG Computational Geometry

CPDF Cumulative Probability Density Function

CPSO Constrained Particle Swarm Optimization

GA Genetic Algorithm

GB Gigabyte

GHz Gigahertz

LKP Last Known Position

NCPDF Normalized Cumulative Probability Density Function

OF Objective Function

PDF Probability Density Function

PSO Particle Swarm Optimization

RAM Random Access Memory

UAV Unmanned Aerial Vehicle

UASN Underwater Acoustics Sensor Network

USAR Urban Search And Rescue

UWSN Underwater Sensor Network

VD Voronoi Diagram

VFA Virtual Force Algorithm

WiSAR Wilderness Search And Rescue

WSN Wireless Sensor Network

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Introduction

Recent development in hardware and software technologies has made the use of sensor networks

more popular in our lives. From mobile phones connecting multiple users, to motion detectors in

the gaming industry, sensors can be found in a very broad range of applications. Various works

have introduced sensor networks to assist humans in various tasks, including environmental

monitoring, border patrol, and target interception and tracking. Within robotics, examples can

also be found in urban search and rescue (USAR) and wilderness search and rescue (WiSAR).

These examples have shown that the presence of small sensing devices with low power

consumption can be of valuable assistance in reducing the human involvement in time-

consuming, and sometimes dangerous tasks.

However, one particular area that has lacked major development is that of the detection of

moving targets, assisted by sensor networks, in unbounded and possibly unstructured

environments. This is a scenario commonly found in WiSAR, where the main goal is to locate a

lost person in a remote area, far from urban settlements. In this case, locating refers to

determining the exact location of the target. In real life, this could be the case of a lost hiker in a

mountain, an elderly who deviated from a trail in a national park, or a child who escaped the

boundaries of a camping ground. Locating a moving target that is untrackable is not a trivial

problem to solve since the area where the target may be found (i.e. the search space), can grow

with time and can be in theory, infinitely large. One can never know in advance the exact motion

of the target, including its direction of travel, how often he/she changes direction, nor the rate at

which the target propagates. As such, a judicious distribution of search efforts must be

strategized to assist with the search. Such deployment should obey a generic motion model of

target motion in order to be resource-efficient and maximize the chances for target interception.

Moving search agents, in the form of humans, robots, or human powered vehicles can be of great

assistance in WiSAR, but they are constrained by their limited availably and often complicated

deployment logistics. Moreover, many WiSAR missions result in long hours of continuous

search. They can become physically demanding and impose psychological stress on human

search agents. Therefore, the help of autonomous robots and sensor networks is desired, as they

can resist better to drastic environmental changes, and provide long-term assistance with lower

performance degradation when compared to humans. Static sensors are small and cost-effective,

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and can be used at a large scale. In practice, they can be readily positioned (i.e. deployed) within

the search space by, for example, and airplane or unmanned aerial vehicle, at relatively minimal

costs. Although size and sensing range appear to be small, if not insignificant, relative to the

expanding search space, an optimal deployment can provide a meaningful contribution in the

search. In fact, it will be shown in this thesis that the presence of static sensors within the

environment will help to increase the success rate and reduced the mean detection times of target

interception. Since there exist several deployment strategies for only mobile sensors to detect un-

trackable targets, this thesis will focus exclusively on the deployment of static sensors. However,

a simple hybrid deployment strategy based on static and mobile sensors will also be proposed.

The motivation behind static sensors for target interception has been presented, and will be

proceeded by the thesis objectives (section 1.1) and the thesis organization (section 1.2).

Furthermore, a literature review (section 2) will be provided based on relevant research work,

showing that existing efforts to do not fully solve the problem at hand. The rest of the thesis will

focus on a detailed description of the methodology (section 3).

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1.1 Thesis Objectives

The goal of this thesis is to design a methodology for static sensor network deployment

according to a probabilistic model of target motion to assist with the intersection of an un-

trackable moving target. To achieve this goal, this research will be subdivided into three tangible

objectives: 1) planning the deployment strategy, 2) executing the deployment strategy, and 3)

adapting to events during the search. Each objective will be achieved through a corresponding

stage: the deployment planning stage, the deployment execution stage, and the redeployment

stage.

For the deployment planning stage, the optimal locations and deployment times for the static

sensors will be determined off-line, according to the probabilistic target motion, number of static

sensors available, and type of environment under consideration. Once the optimal solution for

the first instance of deployment is determined, the solution will be propagated with time to

provide optimal deployment locations for future deployment instances. Therefore, each

deployment instance will have a corresponding set of optimal sensor locations.

For the deployment execution stage, sub-sets of static sensors will be ‘dropped’ at their

deployment locations, and only at their planned deployment times. The execution of the

deployment will follow the proposal of the planning stage for the duration of the search, unless

new information of the target becomes available (i.e., a target clue is found).

For the redeployment stage, a new deployment configuration with the remaining static sensors

will be planned and executed given current and possibly new information about the target (i.e. a

target clue found). This stage is a combination of the previous two stages (planning &

execution), and in the case of a clue find, the sensor deployment is centered at the location of the

found target clue.

The final objectives of the thesis are to demonstrate the effectiveness of the proposed

methodology through simulations, prove its superiority over current approaches, and integrate

the proposed strategy within a hybrid sensor deployment that also uses mobile sensors. This is

achieved through simulations for static sensor network deployment in a MATLAB©

environment.

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1.2 Thesis Organization

The structure of the thesis is as follows:

Chapter 1: This chapter presented the problem under consideration, namely static sensor

deployment, and outlined the objectives and organization of the thesis, was well as the

motivation behind the proposed methodology.

Chapter 2: This chapter presents a detailed literature review, showing that existing efforts do

not fully solve the problem at hand. Namely, they do not consider expanding search areas,

unstructured environments, nor probabilistic target motion.

Chapter 3: This chapter presents a novel methodology for static sensor network deployment for

the intersection of an un-trackable target in unstructured and expanding search areas. This

chapter discusses the off-line deployment planning stage, the on-line deployment execution

stage, as well as the procedure for redeployment upon a target clue find. Furthermore, the

integration of static sensor deployment with mobile sensor deployment is also presented as part

of a hybrid sensor deployment strategy.

Chapter 4: This chapter presents simulation results based on the evaluation of the novel

deployment methodology. The effectiveness of the thesis research work is evaluated in terms of

detection success and detection time, when compared to simpler, and more common deployment

approaches. In addition, a WiSAR case study is described in detail to illustrate the benefit of a

hybrid sensor deployment strategy in detecting an un-trackable target.

Chapter 5: This chapter presents a conclusion to the thesis and discusses future work to be taken

into consideration.

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Literature Review

The deployment of static sensor networks and/or autonomous teams of mobile sensors (i.e.,

sensors mounted on mobile platforms) has been proposed for a variety of unstructured-

environment exploration applications, including border security, target tracking and localization,

environment monitoring, observation of natural phenomena, such as ocean currents, air/water

pollution, or even seismic activities, and, more recently, for USAR and WiSAR missions. Some

progress has also been reported on the deployment of hybrid networks combining mobile sensors

with static sensor networks. Such hybrid solutions have been gaining popularity due to recent

availability of inexpensive and small wireless sensors.

In general, deployment strategies have either been classified as static, when sensor inter-node

separations remain constant once implemented, or as dynamic, when the network is

reconfigurable over time. In these approaches, two main types of sensor models have been

considered: binary models (i.e., when a sensor detects a target only when the target is within its

sensing range) [1], or probabilistic models (i.e., the probability of detecting a target is a function

of its distance to the sensor) [2,3]. Furthermore, several performance metrics have been proposed

for use in sensor-deployment strategies, which will be discussed in detail in this literature review.

They include, but are not restricted to, energy consumption, network connectivity, and network

coverage.

The main goal of this thesis is, thus, to propose a novel dynamic deployment strategy for a

network of static sensors by using a probability model of target motion. The goal of the network

is to intercept an un-trackable target in an unbounded and growing search space with varying

terrain. In order to show that no current effective solution to this problem exists, a review of the

pertinent literature for the deployment of static sensor networks is presented.

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2.1 Static-Deployment Strategies

Static deployment approaches refer to strategies where sensor locations (i.e., network nodes) are

planned in advance and, once deployed, these locations do not change with time. Static

approaches have been, typically, classified as probabilistic or deterministic. Probabilistic

deployments are based on stochastic placement of network nodes following a user-defined

probability density function (PDF) that may be uniform, Gaussian, or even Poisson.

Deterministic strategies, on the other hand, consider placement of nodes at fixed locations,

obtained according to some heuristics or objective functions. This sub-section discusses both

types of static deployments, and some applications.

2.1.1 Probabilistic

Probabilistic strategies are recommended for applications where areas of interest are not easily

accessible and/or rapid deployment may be desirable [4-6]. In [4], a methodology was presented

to provide early detection for forest fires using a wireless sensor network. A probability model

for forest fire was obtained and a k-coverage algorithm determined optimal locations for node

placement. In [5], an approach combined Gaussian and Poisson distributions to deploy nodes in

surveillance missions, where the spacing distance between sensor nodes followed any of the

above mentioned distributions. The goal was to efficiently distribute the resources in a uniform

manner while providing emphasis to hot spots that required higher surveillance. In [6], wireless

sensor networks (WSNs) were proposed to track targets in battlefields. Sensors were placed at

strategic locations according to a priori known target-motion models, and the certainty of target

tracking was provided by a Bayesian formulation.

Meanwhile, there are other deployment methods that determine the location of sensors by first

relying on a random distribution. In [7], a virtual force algorithm (VFA) enhanced the coverage

of a sensor network after an initial random distribution, by spacing static sensors away from each

other while maintain a certain maximum separation distance. After the planned locations of the

sensors were finalized, the sensor nodes were deployed. Finally, the sensors would relay

information to each while tracking a target based on a probabilistic localization algorithm used to

determine the likely position of the target. While the work in [8] brought more realism into the

tracking problem by accounting for the effect of varying terrain with VFA, it was shown in [9]

that optimization of sensor placement to maximize coverage constrained by detection

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imprecisions and terrain properties outperformed the random and uniform placement of static

sensors.

The proposal of hybrid systems, employing both static and mobile sensors, is also found in

methods that use random static sensor deployment, [10-13]. In [10], static sensors were randomly

deployed to perform environmental monitoring and surveillance tasks. More specifically, a

greedy algorithm optimally assigned mobile robots to visit specific static sensors whenever the

static sensors detected events within their sensing range. Meanwhile in [11], the problem of

coverage holes (i.e., unmonitored areas) was investigated. An initial random deployment of static

sensors resulted in holes, and an algorithm based on graph theory dictated the movement of

mobile sensors to fill in the holes. The coverage-healing problem was also investigated in [12],

with the incorporation of a genetic algorithm (GA) to determine both the minimum number of

mobile sensors required to cover holes, as well as their corresponding locations. In [13] however,

the proposed method achieved the same task by re-locating the sensors with the assistance of

Voronoi Diagrams (VDs) and movement-assisted sensor deployment protocols, with the ultimate

goal of spreading static sensors uniformly. Clearly, none of these hybrid methodologies deploy

sensors to locate an untrackable target, with or without the help of a target motion model.

2.1.2 Deterministic

In contrast, deterministic approaches are static approaches that rely on heuristics and/or objective

functions to determine the deployment locations of sensor nodes. The solutions for these

strategies can be based on geometrical patterns, or heuristics and objective functions.

Many approaches have made use of complex geometrical patterns to achieve superior coverage

and network connectivity [14-16]. In [14], a hexagonal-based pattern was used to deploy sensors.

It was shown that, with this geometric approach, the connectivity, coverage and lifetime of the

network was maximized, and the deployment scheme was superior to conventional approaches,

like row spacing. In [15], several geometric deployment strategies for WSNs were compared. It

was shown that a seven-node hexagonal strategy outperformed others, such as square grid and

tri-hexagon tiling, by reducing sensor overlap and resulting in less static sensors needed to

achieve the same area coverage. In [16], given a number of regions, the spatial arrangement of

static sensors was optimized to minimize the number of sensors in order to achieve a connected

network.

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Meanwhile, sensor power consumption has also been commonly used, together with geometrical

patterns, as a metric for optimal deployment, [17-19]. In [17, 18], different spatial arrangements

based on geometrical patterns were considered: the bounded detection area was discretized into

different patterns (square, triangular, and diamond shapes), and two types of operating modes

(active and sleep) were considered for the sensors so that not all were operating at once.

Meanwhile the survey in [19] evaluated topology control in WSNs, by clustering deployment

techniques based on either network coverage or network connectivity. Methods like blanket

coverage (where every point in a network was covered by at least one sensor), barrier coverage

(covering continuous boundaries with sensor nodes), and sweep coverage (only covering select

points of interest within the network) were compared. When discussing connectivity issues, it

was shown that synchronized protocols were shown to be effective in minimizing network power

consumption, where individual sensors shared their working schedule with neighbors such that

not all sensors were active at once. Important conclusions drawn from this study were that a

simplified design of a sensor network, that is scalable and efficient, was preferred over more

complex integrated systems that attempt to unit several control protocols, and that a balance

between network coverage and network connectivity is not always easily achievable. Eventually,

the final design of a network would have to suit the application at hand, and none of these

applied to target localization according to target-motion models.

Other approaches like the ones in [20, 21] utilized GAs to solve for the optimal deployment of

static sensors according to fitness functions. In [20], a GA was used to optimally place static

sensors in a grid for maximum coverage in an environment with obstacles. Given a probabilistic

sensor model, the optimization was carried out to uniformly place a minimum number of sensors

in the search area. In [21], factors such as terrain features, sensor capabilities, and basic

probabilistic models of target behavior were considered to optimally deploy a network of sensors

in a bounded environment employing a hybrid steady-state GA. This strategy differed from [20]

in the sense that each generation of the algorithm was made up of two components: the steady-

state component replaced only one solution with a new offspring (i.e. another mutated solution),

while the hybrid component improved the offspring through local optimization.

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2.1.3 Applications

It is also important to discuss the static deployment of static sensors in the context of practical

applications, such as environmental monitoring, robotic related applications like USAR and

WiSAR, as well as underwater sensor networks (UWSNs) and border patrol.

Examples of deterministic, static approaches are found in environmental monitoring [22-24]. In

[22], linear sensor configurations radiating from the center of a volcano were proposed for

monitoring seismic activity. However, deployment of the sensors was based on human

experience and knowledge of volcano sites. In [23], a WSN deployment on redwood trees was

suggested to monitor temperature and humidity levels. The uniform inter-node spacing between

sensors placed along tree trunks captured enough data to accurately perform interpolation

between nodes. In [24], “globally distributed” (i.e. uniformly distributed) stations with GPS and

accelerometer data were used to track the epicenter of earthquakes. The combination of both

types of sensors allowed for a more complete description of seismic-related frequency spectra,

with higher accuracy in magnitude and phase detection. However, no reference was made as to

what spatial arrangement of sensor deployment would achieve better results.

Several deterministic deployment strategies have also been considered for USAR applications,

[25-28], most of which make use of heterogonous groups of agents. In [25], an autonomous

sensor network was deployed to provide support for rescue operations in damaged buildings. The

system, composed of stand alone sensors, gave human rescue agents vital information of the

rescue missions such as localization and mapping through GPS and radio based positioning. In

addition, these low power devices monitored areas around their vicinities and informed mobile

agents of possible threats and hazards areas to avoid. The sensor locations were determined

according to a priori knowledge of the affected building, forming a rectangular perimeter. In

[26], static sensors were manually deployed by mobile agents inside an unknown building to

locate victims. The sensors were placed randomly on the grounds of the collapsed building to

provide real-time path navigation information to mobile sensors through temperature gradients,

as well as assisting with simultaneous location and mapping. The work in [27] differed from [26]

in that light, temperature, and acceleration sensors, in addition to chemical-substance detectors

assisted with path-planning and safe navigation to mobile robots in simulated USAR scenes. The

algorithm combined data from heterogeneous sensors that were placed in a grid-like pattern,

10

hanging from ropes over the scene. In [28], the objective was to optimally deploy sensor teams

comprising of agents with high/low sensing capabilities, as well as enhanced/limited mobility to

maximize area coverage and assist with target localization in USAR environments. Mobile

robots deployed the static sensors according to a hierarchy of behaviors allowing for individual

decision making without compromising computational power. The robots moved around the

environment through a combination of random and uniform distribution based dispersal

algorithms.

Other deterministic strategies extend to WiSAR missions in [29-31]. In [29], a mission planner

was developed for teams of heterogeneous agents to assist with the retrieval of moving hikers. In

[30], static sensors acted as access points by collecting data from mobile agents. They helped

with localization and were strategically placed in locations where hikers were likely to pass by,

like trails and resting areas. However, both WISAR examples in [29, 30] neglected target motion

models to optimize for static sensor deployment for target interception. As another WiSAR

related example, the study in [31] analyzed cognitive tasks during the integration of unmanned

aerial vehicles (UAVs) with WiSAR missions. Emphasis was placed on human operators

enhancing the capabilities of mobile agents to acquire field data, without any consideration for

static sensor deployment through the UAVs. Clearly, there appears to be a gap in the study and

validity of static sensor deployment to support WiSAR missions.

Another area that has received extensive attention is UWSNs. It has been shown that land-based

deployment techniques, such as those discussed above, are not easily transferrable to underwater

cases due to communication constraints and the potential 3D nature of the problems in

underwater environments. UWSNs are, typically, deployed to maximize the efficiency of the

network defined by communication performance, power consumption, network reliability, or

fault tolerance. In [32], coverage optimization for submarine detection using Particle Swarm

Optimization (PSO) was proposed, where the optimal locations of the sensors are determined a

priori based on transmission range, attenuation, and water depth. In [33], various deployment

methodologies for underwater acoustics sensor networks (UASNs) were presented, where static-

based deployments could either be random [34] or deterministic [35]. For example, the work in

[34] placed sensors at different depths for monitoring purposes, where the initial deployment

location was decided based on random deployment and diffusion strategies. The presence of

exogenous forces such as winds and ocean currents rendered the stochastic placement of sensors,

11

proceeded by self-adjustment strategies, preferable. Meanwhile, in the cases were sensor

locations could be achieved with higher accuracy, geometrical strategies like grid-based

approaches in [35] were suggested, achieving minimal coverage overlap in order to track the

movement of a sinking object.

In addition, static sensor deployment has also been used for target tracking and detection [36-39].

In [36], Doppler shifts and radio signals were employed to track a target through nonlinear

observability decomposition, but the deployment locations of the static sensors were assumed to

be known a priori. In [37, 38], static sensors within a WSN were deployed in advance, according

to a 2D uniform random distribution. The network nodes acted as way points for mobile sensors

to navigate through the environment and track a moving target, where navigation was either

based on surface interpolation through radial basis function in [37], or a “pseudogradient” path

planner in [38]. Although a higher density and greater number of static sensors increased

interpolation accuracy and reduced travel distance, the deployment of network nodes was made

randomly and not according to the target’s motion model. Finally, the work in [39] proposed a

deterministic deployment scheme based on line-sets to maximize the likelihood of target

interception, but assumed that targets were moving in straight lines.

Border-monitoring applications have also been explored in [40-42]. In [40] the inclusion of low-

power static sensors reduce false alarm rates, provide higher monitoring resolution through local

vibration measurements, and relay data across the sensor network. Static sensors were deployed

manually or randomly, depending on the easiness to field access, according to a k-barrier

coverage requirement. Meanwhile in [41], a hierarchical network was used for target

localization, where different sensors performed different roles (e.g., basic sensing, relaying, and

dissemination to base stations). In [42], several border surveillance examples with WSNs were

presented, including a “stealth detection” strategy with synchronized cameras along a passage

line, and a target detection methodology based on a Pursuer-Evaders game. However, these

border monitoring methods were restricted by a non-growing detection area, were limited to a

single instance of deployment at the start of operations, and no generic target motion model was

considered to assist with deployment.

12

2.2 Dynamic-Deployment Strategies

Dynamic deployment approaches differ from static approaches in that the networks are

reconfigurable, namely, the locations of the deployed sensors may vary with time. Typically,

dynamic deployments are less common that static deployment strategies, and they determine

deployment locations through either an on ongoing re-adjustment of the system to achieve a

desired configuration, or through re-deployment subject to time-based or event based events.

Whenever an optimal solution is difficult to obtain due to the complexity of the problem, a

deployment strategy that is on-line reconfigurable is preferred, as it allows near-optimal

solutions to be obtained after several iterations. Computational geometry (CG) and VDs are

typical methods used in dynamic strategies for sensor network deployment, [43-45]. In VDs,

sensor locations in 2D space are planned by re-drawing artificial polygons, called Voronoi

polygons, centered on guesses for sensor deployment positions. As sensors move to improved

locations within their polygons, the VDs are updated until no further improvements can be

obtained. For example in [43], VDs were used to deploy sensor nodes in order to maximize

coverage and sensor life, while minimizing for energy use during displacement and data packet

exchange. Meanwhile in [44], the adopted strategy first divided a search region into Voronoi

polygons and, then, a GA placed sensor nodes in each polygon region so as to fill up coverage

holes and avoid overlap with nodes within the same Voronoi polygon and adjacent Voronoi

regions. In [45], an artificial potential field (APF) method adjusted sensor-node positions within

a detection area based on directional sensing models. The positions were iteratively updated to

maximize coverage by concentrating more efforts on hot targets.

Dynamic deployment strategies are also commonly found in situations where global information

of the environment is unavailable, or as part of a distributive system without access to a control

station, or in time-triggered changing scenarios [46-49]. In [46], a fuzzy-logic system (FLS) was

used to improve the coverage of an UWSN after an initial random deployment. Sensors would

re-locate their positions based on the number of and distance to nearby sensors, and the step size

of such re-location would be determined by the FLS. In [47], sensors would first be deployed

along the seabed and their locations, at different depths, would then be optimized by reducing

coverage overlap, performed by clustering sensors and solving the graph-coloring problem. In

[48], sensors were relocated based on time-triggered events due to sensor failure, where

13

redundant sensors were first identified through a Grid-Quorum solution, and then relocated

through a cascaded movement. In [49], routing protocols were evaluated for WSNs, where static

and mobile sensor networks were considered. During data package exchanged, it was concluded

that networks comprising of static sensors outperformed dynamic sensors, since the mobile

sensors induced a higher delay during end-to-end data transfer, as well as a lower data

throughput.

Environmental monitoring applications also make use of dynamic deployment strategies, through

either taking into account environmental factors that can affect unwanted sensor displacement

[50], or through the use of hybrid systems to support mobile sensors [51]. The work presented in

[50] determined deployment locations for sensors subject to external forces, like winds and

currents, which would displace sensors with time. Sensor dynamics and environmental forecasts

were employed to predict sensor displacements, and a near optimal solution for the deployment

locations was obtained through a combination of computational geometry and quadratic

programming. Although the strategy did not re-locate sensors actively, it accounted for the

displacement of the sensors subject to external forces to guarantee deployment optimality.

Differently, in [51], a team of heterogeneous mobile sensors was used to monitor harmful algal

blooms in the ocean. The deployment followed a hierarchical approach, where quadrotors first

scanned target areas and, once certain features were detected, autonomous surface and

underwater vehicles were deployed to collect samples, acting as static sensors. Re-deployment of

surface and underwater sensors continued until sufficient data had been collected by the entire

sensor network.

Examples of dynamic deployments can be also found in UASNs. Besides the static approaches

which were previously discussed, other methods can be further categorized, according to [33], as

“self-adjusted” deployments, or “movement-assisted” deployment strategies. In “self-adjusted”

deployments, sensors changed their depth along the water bed to maintain application

requirements. Uniform coverage based approaches gave equal emphasis to all underwater areas,

like the work in [52] that took into account water currents to deploy sensors using rigidity-driven

mobile strategies. Meanwhile, methods for non-uniform coverage like the ones in [53, 54] were

targeted for event detection. However, in “movement-assisted” deployment strategies,

deployment was assisted by mobile sensors which transported static sensors underwater. These

strategies were meant for monitoring tasks, and were justified by the fact that mobile-sensor

14

assisted deployment was more cost-effective. Examples included autonomous underwater

vehicles driven deployment over predefined trajectories in [55], and data collection with sonar-

equipped underwater sensors in [56] through algorithm variants of NP-complete problems.

Dynamic approaches can also be found in target tracking applications, [57]. In particular, the

authors in [57] developed a strategy where a swarm of mobile targets were tracked by mobile

sensors with finite sensing range. Several cases were explored, where initial deployment was

based on geometrical patterns, and if sufficient tracking sensors existed then handover

techniques were used for tracking. However, the search space was assumed to be finite, and the

targets were assumed to be trackable. Furthermore, in the event that the number of sensors was

insufficient to cover the entire search space, tracking was deemed non-effective.

In the literature, APF-based algorithms are preferred for dynamic deployment problems, where

the environment is unpredictable and individual sensor nodes need self-arrangement to maintain

the optimality of the deployment with time. Alternatively, CG methodologies and VDs are

preferred for applications where sensors may potentially fail or their functionality is impacted by

environmental factors, and they are also used in large search spaces. Compared to grid-based

methods, VD-based strategies remain computationally efficient since they only rely on the

number of sensors in the network, and not on the size of the search space.

It is clear from the literature review that an existing method for sensor deployment to achieve

target localization using a target motion model does not exist, where the method must be scalable

to an expanding search area. The notion of an ever expanding search space is essential for target

localization, since localization is not guaranteed and the exact motion of a target is not known a

priori. Geometrical-based strategies could achieve target localization but they would be

inefficient, since they tend to deploy resources uniformly. Clearly, as the target propagates with

time, the points of interest within the search space would vary, and as such, non-uniform

coverage would be more desirable. Furthermore, to add complexity to the problem, deployment

based on trackable targets is not useful in this thesis since the target is assumed to be non-

trackable. As stated in [19], generic deployment methods are inconvenient since they do not

adapt well to specific applications. Therefore, since no current solution exists, the motivation

becomes to design a methodology that can deploy a sensor network to intercept an un-trackable

target within and expanding search space.

15

2.3 Mobile-Target Behavior

In order to solve the deployment problem, a target motion model needs to be considered. This

target motion model will assist in optimally deploying search resources within the search space.

In order to effectively intercept more than one type of target, a generic model of target motion

that can adapt to the uniqueness of targets, like target physiology and target psychology, must be

used. This sub-section summarizes the chosen target motion model, and explains how the current

search strategy associated with this motion model cannot directly solve for the deployment

problem at hand.

In [58], a target motion model was proposed using the novel concept of iso-probability curves.

These curves defined regional boundaries where the target could be located within with a certain

probability. They were generated according to a PDF that modeled the target behavior, with an

expected propagation speed (i.e., outward motion from the last known position (LKP) with

occasional random motion-direction and speed variations). The estimation of the probabilistic

target behaviour was supported by data from search and rescue (SAR) organizations [59].

For mobile targets, at the start of the search, every possible direction of travel from the LKP was

considered, defined as a straight-line ray, where the target-motion PDF was overlaid over such a

direction. At any given point in time, a distribution for the probable position of the target along

the ray could be obtained. Each cumulative-probability value along the ray was referred to as a

control point. Namely, each control point represented the limit of how far the target could be

located from the LKP corresponding to a (cumulative) probability value. Fig. 1(a) shows an

example PDF along a ray, with several control points. The length of a ray, at a given time t, was

determined by the distance covered by the target, travelling at the maximum outward

propagation rate of vmax. This total length, in turn, has a cumulative probability value of 1.

An iso-probability curve was determined by the collection of all the control points on all possible

rays, emanating from the LKP, with the same cumulative probability value. Due to terrain

variation along any direction, a control point pertaining to the same cumulative probability value

could vary in distance from the LKP. Fig. 1(b) shows an example of five iso-probability curves,

calculated based on a search time of t, which were interpolated from control points found along

12 distinct rays. Each of these curves delimits the region within which we would expect the

target to be with a certain probability, which for this case are 30%, 40%, 50%, 60% and 70%.

16

As the search progresses, however, due to the dynamic nature of the problem, the iso-probability

curves would propagate outwards in order to keep up with the probabilistic target-motion model.

Fig. 1(c) shows the new locations of the five iso-probability curves in Fig. 1(b) after Δt.

Fig. 1. Illustration of the iso-cumulative curves. (a) Target PDF along a ray based on speed

histogram; (b) Iso-probability curves, at t; and (c) Propagated iso-probability curves, at t+Δt.

The iso-probability curves described above could be used to deploy mobile sensors in search of a

mobile target. However, since the curves propagated in time to mimic the target motion, the

deployed mobile sensors needed to propagate forward with them in order to remain optimal over

time. Namely, they would be used to distribute the search effort over space and time in an

optimal way. Such an optimal-deployment strategy for mobile sensors was suggested by in [60].

The strategy selected both the number and positions of the iso-probability curves, as well as the

number of sensors assigned to each curve. The optimization procedure utilized the weighted

contribution of the search-time and success-rate objective functions to determine the optimal iso-

probability curves. After deployment, the mobile sensors remained on their respective iso-

probability curves at all times as the curves were propagated during the search [61]. As the

search progressed, however, new data about the target could become available. In such a case,

for example after finding a verifiable target clue, the optimal re-calculation of the iso-probability

curves and deployment of the mobile sensors would be repeatead as often as necessary.

The strategies in [60, 61] that translate the sensors forward in tandem with the propagation of the

iso-probability curves would not be possible for static sensors. Thus, a new strategy that

principally is based on the use of iso-probability curves needs to be developed for the

deployment of a static sensor network. The main requirement is to maintain the optimality of the

deployed static sensors for as long as possible.

-800 -600 -400 -200 0 200 400 600 800-800

-600

-400

-200

0

200

400

600

800Time = 0hr 30min 0sec

-800 -600 -400 -200 0 200 400 600 800-800

-600

-400

-200

0

200

400

600

800Time = 0hr 30min 0sec

Iso-probability

Curve Control

Point

A ray

LKP

0 200 m 0 200 m

(a) (b) (c)

A ray

LKP

Control

Points

Target

PDF

17

Static Sensor Network Deployment

The method for solving a static sensor network deployment during the search for an un-trackable

moving target involves both planning and execution. Deploying static sensors to assist with such

detection within a search area is referred to herein an as the search effort. To assist with this,

first, one must plan the locations for the static sensors to be located during the search in an off-

line fashion, and then, execute the deployment on-line. Since the target to be detected is assumed

to follow a probabilistic location model, which is typically found in the form of a PDF, it follows

that the planning of the deployment locations must adhere to the probabilistic model. Having

said this, the method must be adaptable to unstructured and expanding environments, with

possible terrain variation and presence of multiple obstacles. This guarantees that the deployment

tries to mimic as accurately as possible the target behaviour in the environment. In addition, the

method must be able to re-assign the search effort whenever new information about the target

becomes available, namely, through the detection of a target clue. In such events, a new

deployment scheme with the remaining number of static sensors must be planned and executed.

The proposed methodology in this thesis addresses the static sensor network deployment

problem by determining an optimal spatial configuration of the static sensors that maximizes the

likelihood of detecting an un-trackable target during a time-limited search. This chapter outlines

the details of the deployment methodology and it is presented as follows. The chapter starts with

a description in section 3.1 of the problem that the thesis is attempting to address. Afterwards,

section 3.2 discusses the methodology in detail, which is sub-divided into the deployment

planning stage (sub-section 3.2.1), the deployment execution stage (sub-section 3.2.2), and the

redeployment procedure (sub-section 3.2.3). Meanwhile, section 3.3 explains how the static

sensor network deployment is meant to be incorporated with mobile sensors as part of a hybrid

sensor deployment strategy.

18

3.1 Problem Statement

Before outlining the deployment methodology, a description of the problem the thesis is trying to

address is presented in this section. The problem consists in finding an optimal deployment

configuration for a set of static sensors to detect an un-trackable target. Such deployment must be

optimal in the sense that it maximizes the likelihood of detecting the target during a finite-timed

search, Tmax. The search time, Tmax, is defined herein as the period of time where the sensors are

capable of detecting a target. A detection is successful only when a target is detected by a sensor

during the search. During this time, if a target has been detected (i.e. a target comes in the

vicinity of a sensor), the search is labelled as “successful” and is terminated. However, if the

target is not detected within the time Tmax, the search is terminated and labeled as “unsuccessful”.

The deployment of all static sensors must occur at any point in time, through either one or

multiple instances of deployments of sub-sets of sensors, as long as the deployment times fall

within the starting time for the search, and the defined total search time, Tmax. Therefore, the first

deployment would be at tmin, and the last deployment would be at tmax , where tmax Tmax.

In order to solve this problem, three key factors come into play. These are the untrackable target,

the static sensors to de deployed, and the environment where the target is found. This section

describes all factors and how they shape the deployment problem.

3.1.1 The untrackable target

An untrackable target is an agent that cannot be tracked, i.e., the location of the target is not

known at any point in time. In this thesis, the behavior of a target is assumed to follow a

probabilistic model, in the form of a PDF identical to the one in [58]. According to this model,

the target’s only known previous location is its LKP, given by a 2D coordinate. In addition, a

head start time THS indicates how long ago the target was seen at the LKP. From this, a target-

location PDF is defined in any direction, or ray, emerging from the LKP. Then, the target is

assumed to move away from the LKP (i.e. outward), along any ray, at an outward propagation

rate following a uniform distribution with mean speed µν and standard deviation σν. Although a

typical, realistic target can change heading directions and vary its own moving speed while it

adjusts to its environment, it will still have an overall outward propagation motion radiating

away from the LKP, and its motion still abides by the target-location PDF.

19

Furthermore, it is assumed, in this model, that a target can leave clues behind. A clue is defined

as a piece of evidence, belonging to the target, providing immediate information about the

target’s location. Although in practical cases, clues can be false positives clues (i.e. clues that do

not belong to the target), it is assumed in this research work that the clues do indeed belong to

the right target being searched for. It is envisioned that once a clue location is determined during

the search, the deployment must be re-configured around this new location which estimates the

new and latest known position of the target.

3.1.2 The static sensors

The static sensors are the agents responsible for detecting a target during the search. It is

assumed, in this work, that a total of Nss static sensors are available for deployment, and the

sensors have a binary sensing model, with a radial detection range of size rsens. In a practical

situation, a static sensor would be any piece of stationary hardware that has sensing capabilities

and can detect target motion within a distance rsens. This means that if a target were to step into

the vicinity of a sensor, (i.e. be found within a distance of rsens meters or less away from the

center of a sensor), the sensor would detect the target, and the search would terminate. It is

important to note that, since static sensors can only detect a moving target, and clues are

stationary pieces of evidence, a clue cannot be detected by a static sensor. However, a clue can

be detected by another agent employed in the search such as a mobile sensor.

In addition, static sensors are static in the sense that their locations, once deployed, cannot

change during the search. It is envisioned, herein, that the locations for the deployment of static

sensors be first determined in advance (i.e. off-line), prior to actual deployment execution, which

happens regularly during the search (i.e. on-line). Clearly, if a static sensor’s location has been

planned off-line but its deployment not been executed yet, then its planned location may be

changed, which may be the case during search-effort relocation due to a clue find.

3.1.3 The environment

The environment is defined as the search space under consideration, where the un-trackable

target is found but its exact location unknown, and where static sensors may be deployed. The

environments under consideration have features typically found in the wilderness, such as

unleveled terrain due mountains, valleys, rivers, and trails, as well as obstacles that force the

20

target to make detours, like boulders, swamps, ravines, Fig. 2. In addition to the target-location

PDF, the environment is the only information known a priori that may be used to solve the

deployment problem. Typically, terrain information will be provided in the form of height map

data. Incorporating the terrain information is vital since it affects the way the target behaves and

travels through the environment, and the target-location PDF can be scaled to reflect such

influence. Once the target motion is scaled to the environment under consideration, optimal

deployment locations can be determined for the static sensors.

With time, and as a target moves away from the LKP in any possible direction, the total area

where the target might reside will grow, rendering the search space found within the

environment to be expandable and theoretically infinite. Therefore, it is imperative that the

search time parameter, Tmax, for which a deployment configuration must be obtained, to be

determined at the start of the search. The search time, Tmax, provides an indicator of the total area

under consideration where the target might be found. This is because the maximum possible

distance, dmax, travelled by a target along a ray, can only be achieved by the fastest possible

target, moving at an outward propagation rate of µν+3σν. Since this bound includes

approximately 99% of all targets, it can be taken as the maximum distance where the fastest

target might have travelled (especially since the target’s exact speed is never known). The

approximation was shown to be reasonable in [58], and will therefore be employed herein.

Fig. 2. (a) Google Earth terrain image of Mount Robson Provincial Park, BC, Canada; (b)

Simulated 3D terrain in TerreSculptorTM based on height map data from (a).

(a) (b)

21

3.2 Methodology

The main goal of this thesis is to propose a novel dynamic deployment strategy for a network of

static sensors by using a probability model of target motion. The overall objective of the network

is to intercept un-trackable targets in unbounded and growing search spaces.

The novel static sensor network deployment strategy described herein is real-time dynamic. The

strategy uses as input the mobile-target location PDF, the characteristics and number of the

available static sensors, as well as terrain information for the search area. As the first stage, the

strategy plans the initial optimal deployment of all static sensors at hand. This planning stage

utilizes our originally developed methodology for the deployment and utilization of a team of

mobile sensors in search of a mobile target within an expanding search area in unstructured

environments [58, 60, 61]. The next stage in the deployment of the static sensors comprises the

time-phased ‘dropping’ of sensors at their optimal locations as the search progresses. Finally, as

real-time information about the target becomes available, recalculation of the optimal locations

of the remaining (non-deployed) static sensors is invoked, followed by their deployment. This

three-stage strategy is iterative in nature and continues until the complete network is deployed,

Fig. 3.

As outlined above, the deployment of the reconfigurable static sensor network is dynamic.

Namely, although in order to initiate the network deployment the entire optimal node-placement

process is carried out off-line, the sensors are dropped at the time-phased nodes only at

corresponding time instances. Subsequently, as the search progresses and new information

becomes available, if there are still un-deployed static sensors at hand, a new network is planned

as required for the remaining set of sensors. In addition, the dynamic process of dropping them at

appropriate time instances is re-initiated.

Fig. 3. Summary of proposed methodology.

Plan initial optimal

deployment of all

available static sensors

Execute deployment of

subset of static sensors at

their optimal locations

Recalculate optimal

locations for remaining

static sensors with current

& new available target

data

Stage I Stage II Stage III

22

Since the total search time for successfully locating a target cannot be estimated ahead of time,

the overall time interval during which the static sensors are dropped must be chosen a priori

based on the priority at hand. For example, for time-sensitive cases, the network can be deployed

quickly in the close vicinity of the LKP of the target. For less urgent cases, on the other hand, the

time interval used to drop the static sensors can be longer, allowing for a larger coverage area,

and potentially allowing network reconfiguration based on target data that becomes only

available after the search has started (e.g., clues found in the field by dynamic sensors in a hybrid

system). Thus, a longer time interval could improve the chances of success of finding the target,

though at a cost of longer search time. The deployment of the static sensor network is further

optimal in the sense that the sensor nodes are chosen to maximize the success of finding the

target within a given time interval.

3.2.1 Deployment Planning – Stage I

The first stage of the proposed deployment strategy, planning, is carried off-line. It aims to

identify the locations and the times the static sensors will be deployed, and remain optimal for

the entire search. Planning is subject to several intertwined critical constraints: 1) there exists a

finite number of sensors available for deployment, 2) once deployed the sensor locations cannot

be altered, and 3) the sensors’ effectiveness is a function of their spatial distribution as well as

the overall length of the search time until the target is located.

Since the search time to success (in locating a mobile target) cannot be estimated ahead of time,

the optimal distribution of the static sensors must be based on an a priori chosen time-based

criterion during which the sensors’ effectiveness can be maximized through an optimal

distribution. This time-period limit is chosen herein as a generic value, Tmax. One should note

that, although the static sensors can operate well beyond this point in time, their deployment is

based on Tmax, whose selection is discussed in sub-section 3.2.4.

Determining the locations for deployment of the static sensors given the chosen parameter Tmax is

referred to herein as the “planning” stage of the deployment. It is sub-divided into three sub-

tasks: 1) determining optimal locations along any potential direction of target travel (i.e., ray),

(2) propagating the optimal locations with time, and (3) spatially distributing the static sensors to

achieve a specific configuration that maximizes a coverage-based criterion. Fig. 4 summarizes

23

the planning stage, and the details for the three sub-tasks are found below in sub-sections 3.2.1.1,

3.2.1.4, and 3.2.1.5, respectively.

Fig. 4. Overview of the deployment planning – Stage I.

3.2.1.1 Defining the iso-cumulative probability curve

As part of the proposed dynamic deployment strategy, the static sensors are to be iteratively

deployed as the search progresses – namely, at a discrete number of predetermined time

instances, during a user-specified total deployment period, tmin < t < tmax, where tmin is the first

instance where a subset of static sensors is deployed, and tmax is the last instance by which all

static sensors are deployed. As proposed in this thesis, for the optimal deployment of a subset of

static sensors at any given time instance, t*, tmin < t* < tmax, first the corresponding spatial

potential location/region to deploy the static sensors must be determined, at which the probability

of locating the target, by this specific subset of sensors remains maximum for the entire

(cumulative) interval t* to Tmax.

As per the definition of the iso-probability curve above, let us first consider a single direction of

potential motion of the target – defined here by a straight-line ray. The ray originates at the LKP

(last-known position of the target), at time t = 0, and extends to a maximum distance, dmax, that

could be achieved by the target, if he/she were to travel along the ray at maximum propagation

rate vmax. Therefore, dmax defines the point on the ray corresponding to the 100% iso-probability

curve calculated at any given time t. Herein, we employ the same target location PDF used to

generate the iso-probability curves in [58]:

22

2

2

)(exp

2

1),(

vt

tr

ttrPDF

(1)

where r is the distance from the LKP, and (µν,σν) are the mean and standard deviation of the

nominal mean target propagation speeds PDF, respectively.

Determine optimal

deployment locations

at the current time,

valid until time Tmax

Propagate optimal

solution with time for

future deployment

instances valid until time

Tmax

Distribute static sensors

optimally across the time-

propagated solution

24

Unlike mobile sensors that could remain optimal by staying on their respective iso-probability

curves as these are propagating, static sensors, once deployed, can only remain globally optimal

momentarily. Thus, the definition of optimality is redefined herein, where sensing optimality is

required to be effective for a chosen time interval. For example, a static sensor deployed at time

t*, tmin < t* < tmax, would need to remain optimal from t* until the user-chosen Tmax.

In this thesis, the premise is that the static sensor deployment will remain optimal for a given

time interval, in the sense of maximizing the cumulative probability of success of locating the

target during t* < t < Tmax. Thus, the objective is, for time t* deployment, to search along a

considered single ray for the optimal point to place a static sensor at time t*. In order to

determine this cumulative maximum probability of success of locating the target by a static

sensor placed at a given point on the ray, we make use of Eq. (1).

As the first step, in our quest for the optimal point on the ray to place the static sensor at time t*,

the target PDF, Fig. 1(a), is integrated to yield a cumulative PDF (CPDF) and is superimposed

on the ray, Fig. 5. This CPDF can be used to calculate a metric describing the probability of the

target to be at any distance, r, from LKP (i.e., P(X ≤ r)) during the time interval [0, t*]:

2

)(1

22

1

2

)(exp

2

1

),(),(

*

*

*

0

22

2*

0

**

t

trerf

t

t

tx

t

dxtxPDFtrCPDF

r

x v

r

x

(2)

Where erf is the error function:

z

g

g dgezerf0

21)(

(3)

This metric, thus, represents the approximate (momentary) likelihood associated with locating

the target at t* by a sensor located at r.

25

Fig. 5. Example of a Target CPDF.

However, since the sensor is static, while the target is mobile, we need to consider the

cumulative likelihood associated with locating the target by a sensor which is located at r during

the entire search-time interval t* ≤ t ≤ Tmax. This objective can be achieved by continuously re-

evaluating the CPDF and re-calculating the probability P(X ≤ r). Since this process would be

computationally prohibitive to carry out, a discrete approximation is proposed. Namely, for a

sensor deployed at t*, only a limited number of CPDFs are evaluated at regular intervals of Δtapp

during the period t* ≤ t ≤ Tmax. The first CPDF is for t ϵ [0, t*], the next one is for t ϵ [0, t*+Δtapp],

until the last one is for t ϵ [0, Tmax], Fig. 6 (top three graphs, respectively).

The individual CPDFs need to be weighted, summed up, and normalized to yield a single

normalized CPDF (NCPDF) for t*, Fig. 6 (bottom graph):

),(),(

1

*i

N

i

i trCPDFwtrNCPDFprop

(4)

Where Nprop is the number of discrete intervals being considered, ti ϵ {t*, t*+Δtapp, t* +2Δtapp, … ,

Tmax}, a set of size Nprop, and wi is the normalized weight for the time interval 0 to ti.

The weights, wi, in Eq. (4) must be selected such that rmax is located at the 100% iso-probability

curve at time ti = t*. This would ensure that the first deployment, at time t*, is exactly on the

100% iso-probability curve for time t*. This also ensures that the deployment locations found for

subsequent deployment instances (i.e., for times t > t*) will be within their respective upper

bounds defined by their 100% iso-probability curves. Sub-section 3.2.1.3 outlines the proposed

strategy to select such weights.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Ta

rge

t C

PD

FDistance from LKP [m] dmax

Ta

rget

CP

DF

Distance from LKP [m]

26

Fig. 6. Cumulative probability of success curves at multiple time instances, t* < t < Tmax.

Since a normal distribution is assumed herein for the target motion, the 50% probability point on

the NCPDF would represent the best sensor location, at rmax, with the highest likelihood

associated with locating the target at t*:

NCPDF(rmax, t*) = 0.5 (5)

As per the above discussion on developing the iso-probability curves, one cannot guess the

direction of travel for the target ahead of time. Thus, at any time instance, t*, the rmax value must

be determined on several distinct rays, chosen in different potential target-motion directions. The

outcome is a set of rays with an optimal sensor location on each for time instance t*. These can

be viewed as the control points on the rays that determine the iso-probability curves. Thus, as in

obtaining the iso-probability curves, these rmax points can be connected, for example, via cubic

spline interpolation, to obtain the corresponding iso-cumulative curve (short for iso-normalized-

cumulative-probability curve) for time instance t*, Fig. 7(b). One should note that, there exists

only a single iso-cumulative curve that is obtained, versus many possible iso-probability curves.

Distance from LKP

C

um

ula

tive

Su

cces

s

CPDF for 0 < t < t*

CPDF for 0 < t < t* + 4Δ tapp

CPDF for 0 < t < Tmax

rmax

NCPDF

0.5

27

An iso-cumulative curve theoretically passes through all the points along all directions where the

likelihood of finding the target is maximum, at t*, for a given search time interval t* ≤ t < Tmax.

Furthermore, as noted above, as terrain may vary along any direction of travel, the target

propagation rate is adjusted uniquely to that ray and it is, therefore, expected that the distance of

the optimal sensor deployment locations from the LKP along any ray would be different. The

process for generating an iso-cumulative curve at deployment time t* is summarized in Fig. 8.

Fig. 7. (a) A target NCPDF along a ray; (b) Iso-cumulative curve, at t*.

Fig. 8. Outline of iso-cumulative curve generation at deployment time t*.

3.2.1.2 Adjusting to terrain and obstacles

Two typical features found in realistic land-based environments are unleveled terrain and

obstacles, which impact the determination of the iso-cumulative curve. This section describes

how these two features are taken into account when calculating and propagating the iso-

cumulative curve.

A ray LKP

NCPDF

rmax

rmax

Iso-cumulative

curve LKP

A ray

(a) (b)

Generate iso-cumulative

curve by connecting all rmax

points using cubic spline

polynomial method

Determine NCPDF

curve along ith Ray

by propagating PDF

for a time interval

t* < t < Tmax

Determine rmax along ith

Ray by solving for

28

3.2.1.2.1 Terrain influence

The terrain variation present in the scene can cause a moving target to both change its traveling

direction and its moving speed. As outlined in [58], the change in terrain, measured by the slope,

can impact the target’s behavior. Therefore, the NCPDF along a ray will look different

depending on which ray is considered.

An effective way of dealing with terrain is the scaling of the NCPDF to generate the iso-

cumulative curve, analogous to the scaling of the control points during iso-probability curve

generation. In particular, the CPDF must be propagated along a ray as outlined in sub-section

3.2.1.1 but scaled according to the target’s response to terrain variation as in [58]. This results in

what is referred to herein as the ‘scaled CPDF’, or sCPDF. Therefore, combining the sCPDF

through Eq. (4) would generate the ‘scaled NCPDF’, or sNCPDF.

However, obtaining an exact solution for the sNCPDF would be computationally prohibitive,

since all infinitesimally-small scaled points would have to be scaled along the ray for each

sCPDF instance, ranging from the LKP, all the way until the maximum distance covered by the

fastest target. Therefore, an approximation is needed to speed up computation. In this thesis, it is

proposed to approximate the sNCPDF by using the scaled control points used for the generation

of the iso-cumulative curve. For each CPDF defined at time ti, the control points for the iso-

probability curve at time ti can be computed and scaled to the current terrain. Since the control

points represent a cumulative probability value, they can be interpolated to form the sCPDF.

Since the target model assumes a normal distribution for the target speed, the sCPDF will

resemble, with some perturbations due to terrain, the cumulative distribution function (CDF) of a

normal distribution. To approximate this distribution, the logistic function is suggested, as it is a

monotonically increasing function, and ranges in the values 0 to 1. Given a finite number of M

control points along a ray at time ti, given by cpj,i for j = 1,2,…M, and each with cumulative

probability values vj, a non-linear regression can be performed to obtain the approximation to the

sCPDF. Namely, the approximation can be given by the logistic function in the form of:

)(

1),(

iibra

ii

e

LtrS

(6)

29

where r is any distance from the LKP along a ray, and {ai, bi, Li} are the model parameters for

time ti estimated with control points cpj,i. We can use Eq. (6) to define the sCPDF:

),(),( ii trStrsCPDF (7)

and consequently, define the sNCPDF for deployment time t*:

),(),(

1

*i

N

i

i trsCPDFwtrsNCPDFprop

(8)

where Nprop are the number of propagations, and wi the weights for the sCPDF propagations. A

height map generated in TerreSculptorTM is shown in Fig. 9(a), with several sNCPDF plotted in

Fig. 9(b), and several sCPDF propagations with the resulting sNCPDF for Ray 4 are in Fig. 9(c).

Fig. 9. (a) Terrain with 4 rays; (b) sNCPDF plots for Tmax = 2.5 h for Rays 1,2 and 3; (c) Several

sCPDF propagations and the sNCPDF plot for Ray 4 in (a).

Ray 2

Ray 1

Ray 3

Distance from LKP [m]

(b)

(a)

Distance from LKP [m]

(c)

Cu

mu

lati

ve P

rob

abil

ity

Valu

e

Ray 4

Cum

ula

tive

Pro

babil

ity

Valu

e

0 500 1000 1500 2000 25000

0.5

1

T = 1800 s

0 500 1000 1500 2000 25000

0.5

1

T = 4200 s

0 500 1000 1500 2000 25000

0.5

1

T = 9600 s

0 500 1000 1500 2000 25000

0.5

1

sNCPDF - Ray 4

0 500 1000 1500 2000 25000

0.25

0.5

0.75

1sNCPDF - Rays 1,2 and 3

rmax

Control

points Logistic

regression

0 1000 m

30

Finally, an illustrative example for the iso-cumulative curve is presented. Consider a target

moving outward from the LKP, with a propagation rate defined by a normally-distributed target

PDF, where the first static sensor deployment is scheduled for t*=1800 s. The problem at hand is

to determine the corresponding rmax values along 12 distinct rays. The sNCPDF along each ray is

obtained by considering 12 distinct sCPDFs, for a search time of Tmax =10800 s. Fig. 10

illustrates the corresponding iso-cumulative curve for the example.

Fig. 10. The iso-cumulative curve at t*=1800 s, effective for the time interval t* < t < Tmax.

3.2.1.2.2 Obstacle influence

In addition to terrain, another factor that influences the computation and propagation of the iso-

cumulative curve is the presence of obstacles within the environment. Obstacles are regions in

space that cannot be physically traversed by the target, like boulders, swamps, and ravines.

It is assumed that since targets cannot pass through obstacles, they will be forced to circumvent

them and follow a path which roughly represents the obstacle perimeter. Therefore, the effect of

obstacles would only be considered when a ray that is used to calculate the NCPDF originates

from the LKP and intersects an area bounded by an obstacle. For these rays in particular, the

NCPDF would wrap around the obstacle to account for the target’s behavior and motion while

circumventing the obstacle.

To accomplish this, and in order for this adjustment to not impact the way terrain influence is

taken into account (see previous sub-section), the modified path due to obstacles will be

interpolated from the control points used to propagate the CPDF. This means that the control

-1000 -500 0 500 1000

-1000

-500

0

500

1000

LKP

Optimal location rmax

along Ray 1

Iso-cumulative

curve

0 200 m

Ray 1

Ray 8 Optimal location

rmax

along Ray 8

31

points will wrap around the obstacle boundary as long as the ray falls within the obstacle

boundary. An example is illustrated below in Fig. 11 where two rays pass through obstacles and

are then adjusted to account for the target behavior along the ray while circumventing the

obstacle. Since the wrapping of control points around obstacles is done together with scaling due

to terrain, as reported in [58], it follows that these new locations serve as interpolation points for

the sCPDF. Therefore, the distance of the control point from the LKP, at time t and used in Eq.

(7), is the distance along the adjusted ray due to the obstacle, where the total length of the ray is

bounded by vmaxt.

Fig. 11. (a) Iso-cumulative curve propagation with obstacle presence.

3.2.1.3 Computing the NCPDF Weights

In order to properly capture the nature of the target location PDF, our methodology proposes a

selection of weights that follows a power relationship in the form of:

bii atw (9)

where a,b ϵ ℝ, b < 0, ti is the time for a CPDF and wi is the corresponding normalized weight for

that distribution. If we refer to the location of the 100% iso-probability curve at time t* as D100* ,

express CPDF(D100

*,ti) as vi, and substitute Eq. (9) into Eq. (4), we obtain:

-400 -300 -200 -100 0 100 200 300 400-400

-300

-200

-100

0

100

200

300

400Time = 0hr 30min 0sec

0 100 m

obstacle

Adjusted ray

Adjusted ray

Control point

Iso-probability

curves

LKP

32

propprop

N

i

ibi

N

i

ii vatvwtDNCPDF

11

**100 5.0),( (10)

This yields our objective function:

prop

N

i

ibi vatOF

1

5.0 (11)

Therefore, in order to determine the weights wi in Eq. (4), all that is required is to determine the

appropriate power model fit, namely, the parameters a and b in Eq. (9). Their numerical values

are the ones that minimize the objective function in Eq. (11). In order to accomplish this goal, the

following is proposed:

1. Obtain an initial guess for the weights of each ith CPDF, named wini . This is carried out in

inverse proportion from the deployment time t* to Tmax. Namely, for every discrete time

interval ti, there is an initial weight wini . For example, the CPDF evaluated for t ϵ [0, t*] is

weighted by [Tmax/t*], the CPDF evaluated for t ϵ [0, t*+2Δtapp] is weighted by

[Tmax/(t*+2Δtapp)], and the last CPDF for t ϵ [0, Tmax] is weighted by [Tmax/Tmax].

2. Normalize the weights such that the sum of all weights is unity (i.e. ∑ winiNprop

i=1=1).

3. Perform a power regression in the form of Eq. (9) on the set of normalized weights of

Step 2, to obtain initial values for a and b.

4. Obtain an initial value for the objective function in Eq. (11).

5. Perform gradient descent to minimize Eq. (11). To achieve this, for example, a can be

fixed, and the expression in Eq. (11) is differentiated with respect to b to yield:

prop

N

i

ibii ttva

db

OFd

1

)ln())(( (12)

6. Once model parameters a and b are determined, the expression in Eq. (9) is sampled at

values of ti and the corresponding weights wi are obtained.

The selection of a power relationship tries to mimic the varying maximum likelihood of target

detection, which changes as a function of the standard deviation of the target-location PDF.

33

3.2.1.4 Propagating the iso-cumulative probability curve

The proposed network deployment strategy requires the static sensors to be dynamically

deployed starting at tmin, every Δtint, for nt time instances, until tmax, for a total search time

considered, 0 < t < Tmax. Since the (optimal) iso-cumulative curve is determined first at t*= tmin, it

is imperative that this curve be propagated with time in order to determine the locations for the

complete set of iso-cumulative curves, for static sensor deployment at t*= tmin, t*= tmin + Δtint, at

t*= tmin + 2Δtint, and so on, until t*= tmax.

Fig. 12 below illustrates three iso-cumulative curves for the example initiated above in Fig. 10,

for 1800 s, 2400 s, and 3000 s, respectively. Herein, propagation refers to the re-calculation of

the optimal iso-cumulative curve at consecutive static sensor deployment instances and not to the

actual physical motion of the sensors (or the curve itself).

Once a complete set of nt iso-cumulative curves is obtained, for the interval tmin < t < tmax, the

available set of static sensors need to be optimally placed on these according to the global

strategy described below in sub-section 3.2.1.5.

Fig. 12. Example of three iso-cumulative curves.

-1000 -500 0 500 1000

-1000

-500

0

500

1000

0 200 m

Iso-cumulative curve at t*=2400 s LKP

Iso-cumulative curve at t*=1800 s

Iso-cumulative curve at t*=3000 s

34

3.2.1.5 Distributing static sensors optimally

The deployment of the static sensor network needs to be further optimal in the sense that sensors

are dropped on the iso-cumulative curves at locations that maximize the success of finding the

target. A balanced distribution of search resources based on density is proposed herein for static

sensor deployment on any given curve. Namely, for an adopted complete time interval duration

for the deployment of the static sensors, tmin < t < tmax, the goal is to allocate the same search

effort at every time instance of deployment. Thus, for a total search time decided upon for the

optimization, Tmax ≥ tmax + Δtint, there would be nt number of unique instances of deployments.

During the deployment planning stage, the locations of the sensors are determined by: (1)

distributing the sensors across the set of all iso-cumulative curves, such that every curve location

has a certain number of sensors, and (2) positioning the sensors along each curve.

The total number of sensors available, Nss, needs to be distributed amongst the iso-cumulative

curves according to an equal density approach. The perimeter of the optimal iso-cumulative

curve typically increases as the search progresses, Fig. 12, though these lengths could be

estimated off-line. Therefore, the successive iso-cumulative curves would be assigned a

proportionally larger number of sensors according to:

tn

c

sssc Nn1

(13)

where nsc is the number of static sensors on Curve c. Although a distribution of sensors exactly

proportional to curve perimeters may not hold true, this method could still achieve an overall

homogenous distribution of search resources during the entire duration of the search. This

procedure is analogous to mobile sensor deployment with iso-cumulative curves presented in

[60].

Once the number of sensors nsc is determined for each propagated optimal iso-cumulative curve,

the positions of the sensors along each curve must be identified. Although the sensors are

deployed in subsets at each propagation instance, their actual positions need to be determined in

advance. This ensures that the static sensor network is optimal, while uniformly covering the

search space and not giving any bias to a specific direction of target travel.

35

The use of a PSO strategy [62], for example, can be utilized to position the sensor nodes on the

set of iso-cumulative curves such that distances between nodes are maximized. Just like any

CPSO algorithm, any particle (i.e., static sensor) is positioned at an initial location xss with an

assigned speed vss. The speed dictates the movement of the particle and is updated at each

iteration:

vss= wvss+(1-w)[a1rran1(pss

- xss)+a2rran2(pnet

- xss)] (14)

where

w is the inertia factor that dictates by how much the previous speed of the particle will

influence the next speed.

pss and pnet are the local optimal and global optimal positions, respectively.

a1 and a2 are learning factors associated with local optimal and global optimal positions,

respectively.

rran1 and rran2 are two independent random variables following U(0,1).

Therefore, at each iteration, the particle’s position is updated with its velocity:

xss = xss + vss (15)

Our strategy requires a local and global optimal position for each particle. In our case,

1) The local optimal position (pss) for each particle is the position that maximizes the

summation of all distances to all nearby particles (i.e., distance to other nearby static

sensors). If a particle pj has Nnei static sensors in its vicinity, and the distance of each

neighbor to particle pj is dj, then the following expression must be maximized:

neiN

j

jd

1

(16)

2) The global optimal position (pnet) is the particle position that maximizes the summation of all

shortest-neighbor distances of all particles. If there are Nss particles, and the nearest neighbor

of each particle pi is located at a distance di, the following expression must be maximized:

ssN

i

id

1

(17)

36

3) The unfeasible regions are defined by the segments of the iso-cumulative curve bounded by

obstacles, whereas the feasible regions are all the remaining segments of the curve.

The initial guess is shown in Fig. 13(a) for iteration N = 1, where sensors are equally spaced

within each propagation of the curve (i.e., sensors within the first curve are equally spaced out,

etc.). At each iteration, the particles move along their respective curve, following the defined

local and global optimal positions with some randomness, Fig. 13(b).

Since an iso-cumulative curve is generated based on a finite number of rays, it would be possible

for it to intersect an obstacle present in the scene. In order to account for such unfeasible regions,

where a static sensor cannot be placed within, a constrained-PSO (CPSO) algorithm, for

example, the ‘fly-back mechanism’ in [63], can be used. When a particle is displaced to an

unfeasible region (i.e., to a region within an obstacle boundary), its velocity vss is reduced such

that its final location xss is still found within a feasible region (i.e., outside an obstacle’s

boundary). The CPSO algorithm can run for a pre-defined number of iterations or over a time

period. In this example, it runs until a pre-defined iteration number, N = 500, Fig. 13(c).

It is to be noted that the final solution (i.e., final arrangement of the static sensors) might depend

on the initial guess for the first iteration, and global optima for all particles is not directly

obtained. In order to correct for this, it is suggested for the CPSO to be ran several times, and the

solution to be selected from the final iteration of the best CPSO instance.

Fig. 13. CPSO algorithm showing the locations of the static sensors for different stages of the

optimization process; (a) N = 1; (b) N = 20; (c) N = 500.

-1500 -1000 -500 0 500 1000 1500-1500

-1000

-500

0

500

1000

1500

-1500 -1000 -500 0 500 1000 1500-1500

-1000

-500

0

500

1000

1500

-1500 -1000 -500 0 500 1000 1500-1500

-1000

-500

0

500

1000

1500

(a) (b) (c) 0 500 m Obstacle

Static-sensor

Iso-cumulative

curve LKP

Unfeasible

region

37

3.2.2 Deployment Execution – Stage II

Once the positions of all static sensors are uniquely identified for all the iso-cumulative curve

propagations, the deployment execution can commence. In practical terms, execution refers to

the physical placement of the sensors on the field, at their respective optimal locations. The first

deployment is executed at tmin, while subsequent deployments are executed at time intervals of

Δtint. Finally, the last deployment instance will occur at tmax.

Let’s consider the example for three deployment instances with user-defined parameters, such as

deployment interval 1800 s < t < 3000 s, and Δtint. = 600 s. The sensors corresponding to the first

iso-cumulative curve propagation, at tmin = 1800 s, can be deployed as soon as the search begins,

Fig. 14(a). After Δtint, the next set of sensors can be deployed for the next iso-cumulative curve,

Fig. 14(b). The method continues until the last deployment instance happens at tmax., Fig. 14(c).

The main advantage of employing a dynamic strategy for static sensor network deployment is

that it can easily respond to on-line events, like a clue find. If a piece of evidence is found by a

mobile sensor, the search effort can be relocated and centered at this new LKP. Since the static

sensors are dropped at regular time intervals Δtint, there would be (undeployed) sensors available

as long as we have not reached the end time, tmax. Namely, a redeployment of the static sensors

could be carried out based on a new set of re-computed iso-cumulative curves. It is important to

note that herein, only a high-level deployment process is outlined, and not the specifics for the

deployment implementation. In practice, deployment could be carried out by UAVs using

navigation and localization strategies while ‘dropping’ the sensors on the field, like in [64].

Fig. 14. Example of dynamic deployment of static sensors with three propagations of the iso-

cumulative curve, for tmin = 1800 s, tmax = 3000 s, and Δtint = 600 s.

0 300 m

t*= 1800 s t*= 2400 s t*= 3000 s

(a) (b) (c)

38

3.2.3 Redeployment – Stage III

The third and last stage of the deployment methodology is the redeployment stage, which refers

to the deployment of all remaining search resources centered at a new location. In this thesis, the

methodology instantiates a redeployment event whenever new target information is acquired

during the search. In particular, redeployment occurs upon the retrieval of a clue within one of

the sensor’s sensing range. It is assumed that clue finds are positive finds (i.e. they belong to the

target in question). Clearly, this stage can happen for an infinite number of clue finds, as long as

there are still sensors left to deploy and the last deployment time, occurring at tmax, has not been

reached.

Redeployment implies a re-computation of the location and propagation of the iso-cumulative

curve, as well as the re-calculation of the new optimal positions for the Nund undeployed static

sensors. A redeployment due to a clue find, at time Tclue, would re-initiate the search, where the

first new iso-cumulative curve is now centered at the clue location. This is analogous to the

redeployment of the iso-probability curves due to a clue find in [58]. While the already deployed

sensors cannot change location, the planned locations for the remaining Nund sensors at time Tclue

that have not yet been deployed will have to be re-planned.

In order to re-configure the planning, a new search time parameter used to define the iso-

cumulative curve, T*max, is obtained. In order to do this, one simply re-defines the iso-cumulative

curve for the remaining search time, Eq. (18). The result obtained from Eq. (18) will be the new

Tmax valued used in Eq. (4), that determines the new location of the iso-cumulative curve:

cluemaxmax TTT *

(18)

However, the time values for the deployment times have to be updated in order to take into

account the time it took for the target to drop the clue. Instead of propagating the curve for the

current time, one must propagate the curve for a new deployment time, which is the current time

minus the time of the clue drop. Since the real time of the clue drop by the target is not known

(i.e. Tclue_drop), one must obtain a conservative estimate of this time, Tclue_drop. The conservative

estimate will, in turn, guarantee a prediction of the area that will bound the location of the target.

This time will be used to start propagating the iso-cumulative curve. First, it is assumed that the

target travelled a distance of dclue, which is the distance of a straight path from the LKP to the

39

location where the clue was dropped, Fig. 15. Therefore, if the target travelled at the fastest

possible target speed vmax., this would bound all possible target locations, and represent a

conservative estimate of the time of the clue drop Tclue_drop:

max

cluedropclue

v

dT _ˆ

(19)

Finally, the deployment time corresponding to the curve propagation is updated. If the original

interval for the deployment time was tmin < t < tmax, and the time of the clue find Tclue was in this

time interval (i.e. Tclue ϵ [tmin, tmax]), it follows that the deployment times ti used in Eq. (4) have to

be subtracted by Tclue_drop. The curve is then propagated forward at a rate of Δtint until the updated

tmax is reached and the additional iso-cumulative curve locations are determined.

During deployment execution, the remaining static sensors are deployed at time intervals of Δtint,

where their optimal locations were re-determined according to CPSO strategy formulated in sub-

section 3.2.1.5, while taking into account previously deployed sensors. As an illustrative

example, Fig. 15 displays the first new iso-cumulative curve after redeployment, due to a clue

find at Tclue = 3050 s, as well as two previous iso-cumulative curves prior to the clue find. In Fig.

15, it can be seen that the CPSO places redeployed static sensors (red) in a way that it maximizes

the distance with the respect to the already deployed sensors (orange).

Fig. 15. An example of network redeployment due to clue find.

-1000 -500 0 500 1000

-1000

-500

0

500

1000

First new iso-cumulative

curve centered at the clue

Iso-cumulative

curves centered

at the LKP

LKP

Clue

0 500 m

Static sensors for

post-planning

dclue

40

3.2.4 Determining the search parameters

As previously stated, there were several parameters used during the definition and propagation of

the iso-cumulative curve. These were the total search time Tmax, the time interval between

deployment instances Δtint, and the deployment time interval given by tmin < t < tmax. These user-

defined parameters can be tuned to adapt to different search strategies. This section describes

how they can be modified in order to accommodate real-life search missions, which are typically

planned by a search commander.

Deployment Rate, Δtint

As the first issue at hand, the time interval between deployment instances Δtint must be

determined. This parameter decides on the number of considered propagations of the iso-

cumulative curve, and is dictated by how often the search resources can be deployed in the

search space. In practice, this could be the rate at which an airplane or UAV would deploy the

static sensors along the search space. One must understand that a fast rate will deploy sensors

quickly, but will lead to more deployment instances within the deployment interval, and

therefore, a greater distance between sensor locations. On the other hand, a low rate will dictate a

small number of deployment instances, but there will be more sensors located at each

propagation of the iso-cumulative curve. Values can range from several minutes to few hours.

Deployment Interval, tmin < t < tmax

As the second issue at hand, the search commander needs to deal with deciding on the

deployment interval tmin < t < tmax. This is the period during deployment is planned for, and then

executed. Typically, tmin will be equal to the head start time THS, although it may be set to later in

the search depending on how fast can the first set of static sensors be deployed. Meanwhile, tmax

dictates the final deployment instance and this is usually chosen according to the urgency of the

search. For urgent cases, the static sensor network can be deployed quickly in the close vicinity

of the LKP, meaning that tmax will not be much greater than tmin. However, a quicker deployment

makes the search less flexible, since fewer search resources become available in the event of a

redeployment (sub-section 3.2.3). For less urgent cases, the deployment time interval can be

longer, thus, allowing for a larger coverage area and potentially a network that is dynamically

41

deployed based on clues found in the field. A larger interval could increase the chances of

success of finding the target, though at a longer search time.

Decisions made at this level have direct impact on the number of iso-cumulative curve

propagations nt, and their spread. A tight link exists between the deployment interval and the

deployment rate previously discussed, as the two factors combined determine the number of

propagations, nt, considered for the iso-cumulative curve. This is the number of deployment

instances that will occur during the search, and is quickly obtained from the equation:

int

mint

t

ttn max (20)

Search Time, Tmax

As the last issue at hand, the search commander needs to decide on the limit of Tmax, which is

used in Eq. (4). Since it would be impossible to estimate the (successful) search time a priori,

one needs to decide on the time period the static sensors remain effective. The influence of this

parameter on the determination of the iso-cumulative curve and its propagation is not critical.

Any value above tmax, but less than a rough guess of the total search time, would be acceptable.

Having said that, the search time Tmax determines the total search area that will be considered

during the search, since the boundary of the area is determined by the maximum distance dmax

covered by the fastest possible target at a rate of vmax. A higher Tmax value will ‘pull’ the iso-

cumulative curve propagations away from the LKP, as a longer search will cover a greater search

area. On the other hand, a lower Tmax value will pull the iso-cumulative curve closer to the LKP,

as less area needs to be considered and more emphasis is placed to earlier instances of the search.

Nevertheless, the iso-cumulative curves will always remain optimal for any given search time

parameter value.

Another constraint of course would be the battery life Tbatt of the static sensors, since the search

time must always be selected such that the sensors remain operational, i.e. Tmax Tbatt. The

operation time can be based on the hardware design of the sensors, or on other search strategies

by the search commander, like minimizing for power consumption. As it will be seen later in

section 3.3, Tmax does not have to be equal to the search duration of other sensor teams (like

mobile sensors), as this is a parameter exclusive to static sensors.

42

3.3 Hybrid deployment strategy

A hybrid deployment methodology is proposed herein for a set of mobile sensor agents

supported by an on-line reconfigurable network of static sensors in search of a mobile target in a

boundless unstructured environment. The methodology combines the use of iso-probability

curves for mobile sensor deployment, and their guidance, with the use of the above detailed iso-

cumulative curves for dynamic static sensor deployment, Fig. 16. The ultimate goal is increasing

the success rate of the search, as well as decreasing the average search time. The planned and

executed search effort is complementary but not redundant.

Fig. 16. Hybrid deployment strategy.

Integration of static

sensors with mobile

sensors

Deployment planning

of static sensors

Dynamic deployment

execution of static

sensors

Redeployment planning

of static Sensors

Search

End

Yes

No

Yes

No

No

Yes

Deployment

planning of mobile

sensors

Deployment execution

of mobile sensors

Redeployment

planning of mobile

sensors

Target PDF

Terrain

Number of

mobile sensors

Motion planning of mobile

sensors

Target PDF

Terrain

Number of

static sensors

Mobile sensor deployment

Static sensor deployment

Was target

found?

Was there a

clue find?

Is it time to

deploy?

43

It is intended herein, that the deployment of mobile and static sensors to happen concurrently,

and that the search to be executed by both types of search agents, at the same time. Since this

hybrid deployment is based off a centralized system, simple cooperation between search agents,

via the central controller, is possible. Mobile agents can detect the presence of clues dropped by

the target, which leads to the redeployment of both mobile and static agents. The reverse action

(i.e. static sensors detecting target clues) is not considered in this thesis because it is assumed

that static sensors can only detect target motion, but if considered, then, static sensors would also

be able to instantiate redeployment of both agent types.

When incorporating mobile sensors in the search, both deployment and path-planning of the

mobile sensors are required. After their deployment execution through iso-probability curves is

done according to [60], mobile sensors must have individual paths to guide them throughout the

search. These trajectories must maintain the optimal deployment of the search resources.

Namely, the mobile sensors must remain on their respective iso-probability curves at all times as

the curves are propagated during the search. For this goal, a robust path-planning methodology

was introduced in [61] that guided the mobile sensors along their respective iso-probability

curves as the latter were propagated. This path-planning methodology aimed at guaranteeing an

optimal distribution of the mobile sensors throughout the search.

Since the proposed methodology for static sensor network deployment is to be incorporated with

mobile sensors, it is important that coverage overlap by mobile and static sensors be minimized.

Coverage overlap is discouraged as it decreases the efficiency of the search by placing search

resources (i.e. mobile and static sensors) on the area at the same time. In order to achieve this,

mobile sensors are forced to detour around the detection area of the static sensors, considering

them as obstacles to avoid, Fig. 17. This is achieved by wrapping the planned path around the

perimeter of the static sensor sensing range. Since static sensors are assumed to have radial

sensing range, the wrapping can be done according to any standard bug algorithm for obstacle

avoidance, likes the ones presented in [65]. Wrapping the path implies that the destination point

at the destination curve has to be re-adjusted in order to conserve the optimal length of the

planned path.

44

During navigation, i.e. while the mobile sensors traverse their assigned paths to their propagated

iso-probability curves (i.e. destination curves), the mobile sensors should conduct their regular

optimality checks, just like in [61]. These are:

Check #1 - existence of feasible shortest path from next check-point to the destination

curve.

Check #2 - existence of feasible shortest path from current location to the destination curve.

Fig. 17. (a) Originally planned path with no static sensors at time t; (b) Adjusted path with static

sensor avoidance at time t.

Although path re-planning due to static sensors is not strictly mandatory, it can be executed and

still safeguard the optimality of the mobile sensor deployment. However, if the mobile sensors

plan their paths while taking into account the presence of static sensors, and Checks #1 or #2 fail,

then that means the static sensor sensing range is impeding the mobile sensor from remaining

along its optimal path. It is crucial that in this hybrid deployment strategy, for the static sensors

to have no impact on the optimality of the mobile sensor deployment, as it can deteriorate the

(a) (b)

Iso-probability curve of robot at

time t

Destination

curve of

robot at

time t

Originally

planned

path

Original

destination

point on

destination

curve

Static sensor and

its sensing range

Adjusted

path

Adjusted

destination

point

Mobile

sensor

45

performance of the search. In such cases, the destination point along the destination curve must

be re-adjusted iteratively until the checks pass and the optimality of mobile sensor deployment is

maintained.

In the cases where static sensors are significantly large relative to the static sensors (i.e. the

sensing range of static sensors occupies at least 30% of the space between propagated iso-

probability curves), wrapping of the original planned path is not feasible because it will cause the

mobile sensor to be away from its optimal iso-probability curve for a large fraction of its

traveling time. Since this is not optimal, it means that for very large static sensor sensing ranges,

the planned paths for mobile sensors can be re-adjusted so that a fraction of the path may overlap

with the area bounded by static sensors. Therefore, the goal becomes to re-plan the path such that

it minimizes the overlap with the static sensor sensing range, while guaranteeing the arrival of

the mobile sensor to its destination curve in due time. An acceptable level of overlap will not be

evaluated in this thesis, as very large sensors are, in practice, difficult to exist.

For the example initiated above (Fig. 12), Fig. 18 below shows the state of deployment for both

static and mobiles sensors at t*=2400 s. The iso-cumulative curves have been propagated (with

the mobile sensors on them) from the start of the search at 1800 s to the current 2400 s. The first

instance of static sensor deployment is also at time t*=1800 s, while the second instance is at

t*=2400 s, Fig. 18. The target has moved from the LKP outwards, while dropping clues every

600 s that can only be detected by the mobiles sensors. In the figure, the following can be

observed: mobile sensors (blue dots), static sensors (orange dots), target (red cross), clues (purple

triangles), iso-probability curves (black solid lines), and obstacles (green circles).

46

Fig. 18. State of an example search at t*=2400 s.

Time = 0hr 40min 0sec

0 300 m

LKP

Target clues

Target

Mobile sensor

Static

sensor

Iso-cumulative curve at

time t*=1800 s

Iso-cumulative

curve at time

t*=2400 s

47

Performance Studies

This section of the thesis describes the simulations that were performed to: (1) validate the

benefit of the proposed static sensor deployment methodology in comparison to others available

in the literature, and (2) illustrate in detail a WiSAR example based on the proposed hybrid

dynamic and static sensors approach. The simulations were conducted in MATLAB© 2013a,

running on a 64-bit MS-Windows workstation with Intel i7 at 3.40 GHz and 12 GB of RAM.

In order to validate the benefit of the proposed static sensor deployment methodology, a popular

alternative method was selected and modified for fair comparison. The alternative deployment

method is first described below, followed by an overview of the target model used in the

simulations, a description of the environment used, and an analysis of the results emerging from

the comparative study.

4.1 Comparative study

To the best of our knowledge, no other method currently exists in the literature that can deploy

static sensors according to our target location PDF. Therefore, in order to achieve a fair

comparison, we modified a virtual-force-algorithm (VFA) based deployment methodology [7], in

order to adopt the same target location PDF. VFA was selected, as it can scale to large static

sensor networks, as well as to large search spaces, with minimal complexity. It was also used in

[7] to localize a target. VFA is a distributed methodology where attractive and repulsive forces

act on individual nodes in a network to reposition the nodes and achieve an optimal

configuration. The optimal configuration is obtained when the attractive and repulsive forces

reach an equilibrium, whereby nodes do not change locations after several iterations. In our case,

repulsive forces were represented by nodes in close proximity to other nodes, as well as any

obstacles found in the environment. Attractive forces were nodes found far away from other

nodes. The attractive forces were set up such that VFA would achieve a uniform deployment

within the search area, where all nodes are equidistant to nearby nodes.

The search area used by the VFA was determined by employing the target location PDF.

Namely, the 100% iso-probability curve found at the end of the search, Tmax, defined the

bounding area for the deployment of all static sensors. This ensured that the static sensors were

48

deployed in the search space that enclosed 100% of the simulated targets. As the initial planning

stage, all available static sensors, Nss, were deployed at random locations within the search area,

and their final optimal locations were iteratively solved for via the VFA.

Initially, all of the available static sensors, Nss, were deployed at locations determined by a

hexagonal grid pattern within the search area [14] that achieved preliminary uniform coverage.

The final sensor deployment locations were iteratively solved for via the VFA. Although not

considered for this comparison study, VFA can accommodate the presence of obstacles by

considering them as repulsive forces. In theory, in order to achieve a dynamic deployment with

VFA, only sensors found within the area dictated by the 100% iso-probability curve at any

deployment time ti, for tmin < ti < tmax, could be deployed. However, since common VFA methods

do not dynamically deploy static sensors, it was decided that the VFA used herein would deploy

all Nss sensors at the start of the search.

4.1.1 Simulated Target

The simulated target used in the comparative study had a propagation rate represented by a

normal distribution, with a mean of 0.083 m/s, and a standard deviation of 0.028 m/s. The

starting heading angle of travel, emerging from the LKP, was uniformly distributed in the range

[0°, 359°]. At periodic intervals, the target changed its direction of travel that followed an

inverted normal distribution, in the range [-60°, 60°], Fig. 19. For each comparison, 15,000

different target motions were considered.

Fig. 19. (a) PDF of target travel direction change; (b) Examples of simulated target paths.

0 500 m

LKP

(a) (b)

-60 -40 -20 0 20 40 600

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Target Change in direction of travel [degrees]

PD

F

49

4.1.2 Simulated Experiments

The performances of our proposed deployment strategy (NCPDF) vs the VFA were compared

based on two metrics: success rate and mean detection time. The former represents the

percentage of successful searches that detected a target within the allocated search time Tmax,

whereas the latter is the average time that it took for the target to be found – only for successful

searches. The detection time for successful searches was recorded as the time, to the nearest

second, when a target entered the radial area bounded by a sensor.

The deployment methodologies were compared for three different total search times Tmax: 13500

s, 27000 s, and 45000 s. This resulted in search areas with radial distance of 2250 m, 4500 m,

and 7500 m, respectively. For each total search time, the optimal sensor deployment network

was obtained, for each method, and tested with respect to simulated targets following the

behavior outlined above. Furthermore, different sensor detection radii were used: 5 m, 10 m, 20

m, and 40 m. The number of sensors used was Nss = 148, selected from a uniform distribution

U(120,160). The simulated environment consisted of a flat terrain with no obstacles. Fig. 20

shows the deployment configurations for both methods, where the 100% iso-probability curve

limits the search area in both figures.

Fig. 20. Optimal deployment networks for Tmax = 13500 s; (a) NCPDF vs (b) VFA.

In order to illustrate the effect of sensor size on target interception for the proposed NCPDF

based methodology, several simulation examples out of the 15,000 different cases are presented

below. The example in Fig. 21 shows a simulated target that was intercepted using 40 m sensing

-3000 -2000 -1000 0 1000 2000 3000

-3000

-2000

-1000

0

1000

2000

3000

-3000 -2000 -1000 0 1000 2000 3000

-3000

-2000

-1000

0

1000

2000

3000

0 1000 m

(a) (b)

0 1000 m

50

range at an earlier time when compared to the interception using 10 m sensing range. In Fig. 22,

the target was not intercepted when using 10 m radial sensing range, but interception was

achieved with 20 m sensing range. Note that in both Fig. 21 and Fig. 22 the static sensor sizes

were drawn to scale.

Fig. 21. (a) Simulated target interception at t = 10382 s with 10 m sensing range; (b) Simulated

target interception at t = 5763 s with 40 m sensing range.

Fig. 22. (a) Simulated target without interception with 10 m sensing range; (b) Simulated

target intersection at t = 9155 s with 20 m sensing range.

LKP

Target

path

Static

sensor

Target

Interception

(a) (b) 0 100 m 0 100 m

(a) (b)

Target

Interception

0 100 m 0 100 m

Missed target

by few

meters

51

Another example presented herein shows the two methodologies side by side, as seen in Fig. 23.

In this example, the static sensors were not drawn to scale, but the example illustrates two

important aspects. The first one being that NCPDF achieved target interception for this Tmax = 3

hour search, while VFA did not. In addition, NCPDF achieved target interception using only 52

of the 148 available static sensors, whereas VFA deployed all 148 static sensors with no success.

Fig. 23. (a) Simulated target interception using NCPDF at t = 5914 s; (b) Simulation with no

target interception using VFA.

The overall results for all 15,000 target motions are shown in Fig. 24, where Fig. 24(a) shows an

increase in the relative improvement in success rate of our proposed NCPDF method over VFA,

as the allowed search time grows. In addition, the mean detection time was also reduced for our

method with respect to VFA across all detection radii and allowed search times, Fig. 24(b). More

detailed comparative results for the difference search times and sensor sizes used are given in

Fig. 25. As expected, it can be observed that the success rate increased with sensor detection

radius. Our proposed methodology detected targets consistently more often than VFA for any

detection radius, and this was also true across all total search times.

For example, in best comparative scenario for target-detection success rate, our method

outperformed the VFA by about 45% for detection radius of 5 m and search time of 45,000 s.

Similarly, in best comparative scenario for mean target-detection time, our method outperformed

(a) (b) 0 500 m 0 500 m

Target

Interception

52

the VFA by about 48% for detection radius of 40 m and search time of 45,000 s. In worst

comparative scenario for target-detection success rate, our method outperformed the VFA by

about 12% for detection radius of 40 m and search time of 45,000 s. Similarly, in worst

comparative scenario for mean target-detection time, our method outperformed the VFA by

about 32% for detection radius of 5 m and search time of 45,000 s.

(a) (b)

Fig. 24. Improvement of NCPDF over VFA for different search times and sensor detection sizes;

(a) Improvement in success Rate; (b) Reduction in mean detection time.

Other parameters that were examined included the total number of static sensors deployed Nss, as

well the time interval during which static sensors were deployed Δtint. As expected, greater Nss

yielded higher success rate and a lower mean detection time. Also, as expected, for Δtint, it was

noted that a shorter time interval placed emphasis on trying to find the target more quickly (e.g.,

emphasis on minimizing search time), at the expense of risking overall search success. Namely,

at the extreme case, dropping all the static sensors as soon as the search started on the optimal

iso-cumulative curve helped find the target quickly, when the target was indeed in the vicinity of

the curve. Otherwise, when the target was already beyond this curve, the sensors were wasted.

3.75 7.5 12.50

10

20

30

40

50

60

Search Time [hr]

% I

mpro

vem

ent

in S

uccess R

ate

5m 10m 20m 40m

3.75 7.5 12.50

10

20

30

40

50

60

Search Time [hr]

% R

eduction in D

ete

ction T

ime

5m 10m 20m 40m

% I

mpro

vem

ent

in s

ucc

ess

rate

% R

educt

ion i

n m

ean d

etec

tio

n t

ime

Search time [h] Search time [h]

53

Fig. 25. Comparing success rate and mean detection time for different search time and varying

sensor detection radii.

5 10 20 400

10

20

30

40

50

60

70

80

90

100

Detection Radius [m]

Succ

ess

R

ate

Search Time of 13500 s

VFA NCPDF

5 10 20 400

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4

Detection Radius [m]

Me

an D

ete

ctio

n T

ime

[s]

Search Time of 13500 s

VFA NCPDF

5 10 20 400

10

20

30

40

50

60

70

80

90

100

Detection Radius [m]

Succ

ess

R

ate

Search Time of 27000 s

VFA NCPDF

5 10 20 400

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4

Detection Radius [m]

Me

an D

ete

ctio

n T

ime

[s]

Search Time of 27000 s

VFA NCPDF

5 10 20 400

10

20

30

40

50

60

70

80

90

100

Detection Radius [m]

Succ

ess

R

ate

Search Time of 45000 s

VFA NCPDF

5 10 20 400

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4

Detection Radius [m]

Me

an D

ete

ctio

n T

ime

[s]

Search Time of 45000 s

VFA NCPDF

54

4.2 WiSAR Case Study

In order to illustrate the effectiveness of our proposed hybrid methodology for mobile target

detection, a WiSAR example is included herein. Information about the simulated target,

deployment parameters and configurations, as well as descriptions of events that happened

during the search are presented in detail.

In order to obtain the iso-cumulative curve and deploy the static sensors, it was assumed that the

target (i.e. a lost adult) had a mean outward propagation rate of 0.139 m/s from the LKP. This

was the mean target velocity corresponding to the target PDF, and the iso-cumulative curve was

defined and propagated according to this rate. However, the actual target shown in this example

travelled with an actual propagation rate of 0.119 m/s, which was slower than the rate used for

static sensor deployment. The target travelled with random variations of ±3σ = ±0.0139 m/s and

orientation deviations of ±3σ = ±15o occurring every 120 s. The head-start time THS for the target

was 1800 s, and the target left behind clues every 600 s. Eleven mobile and 148 static sensors,

with binary sensing models, were chosen. The static and mobile sensors had a radial target-

detection radius of 15 m and 10 m, respectively. In addition, the mobile sensors had a 3 m radial

clue-detection radius.

The deployment parameters for the static sensor network were chosen as: tmin= 1800 s, tmax=

7200 s, Δtint= 1800 s, and Tmax= 10800 s. Namely, the network started to be deployed at 1800 s,

with a total of nt = 4 iso-cumulative curves – one every 1800 s. The parameter selection

corresponded to a search with equal emphasis on success of target detection and minimal

detection time. The search region was defined by Tmax= 10800 s, and the initially planned static

sensor network had an optimal configuration of {22, 33, 42, 51} sensors on the four iso-

cumulative curves, respectively (Fig. 26). It can be observed in Fig. 26 that the static sensors

(orange) are located on their respective iso-cumulative curve propagations (blue), but only within

their feasible regions, which are segments outside areas covered by obstacles (green).

55

Fig. 26. Static sensor deployment configuration for the search.

-1000 -500 0 500 1000

-1000

-500

0

500

1000

Horizontal Distance from LKP [m]

Ver

tica

l D

ista

nce

fro

m L

KP

[m

]

56

Meanwhile, the initial optimal mobile-sensor deployment comprised five iso-probability curves,

with a mobile-sensor distribution per curve of {2, 2, 2, 2, 2}, with the 11th center sensor

travelling around the LKP throughout the search. This optimal configuration was achieved

according to the strategy presented in [60]. Fig. 27 below shows the overall deployment of both

static and mobile sensors at the start of the search, i.e., at 1800 s. Detection areas of the sensors

in the figure are exaggerated for illustration purposes, but, their relative positions are to scale:

mobile sensors (blue dots), static sensors (orange dots), target (red cross), clues (purple

triangles), iso-probability curves (black solid lines), and obstacles (green circles).

Fig. 27. Initial state of the search at 1800 s.

Horizontal Distance from LKP [m]

Ver

tica

l D

ista

nce

fro

m L

KP

[m

]

-1000 -500 0 500 1000

-1000

-500

0

500

1000

57

During the search, a clue was found by a mobile sensor at Tclue = 3724 s. After the clue find, all

sensor deployments were re-planned. The locations of the remaining two iso-cumulative curves

for the Nund = 93 static sensors were re-determined, with a new static sensor distribution of {40,

53}, respectively, with the first redeployment scheduled for immediate execution, and the last

(fourth) deployment to occur at 3724 s + Δtint =5524 s. The optimal number and locations of the

iso-probability curves were re-determined, according to [60], as nine, with a new mobile-sensor

distribution per curve being as {1, 1, 1, 1, 1, 1, 1, 1, 2}, respectively, plus the center robot. Fig.

28 below shows the state of the search immediately after re-deployment planning at 3724 s. The

target was eventually intercepted by a static sensor at 5573 s, Fig. 29 (target path shown as a red

line).

Fig. 28. State of the search at 3724 s (clue located at ‘’).

-1000 -500 0 500 1000

-1000

-500

0

500

1000

Ver

tica

l D

ista

nce

fro

m L

KP

[m

]

Horizontal Distance from LKP [m]

Static sensors due

to redeployment

58

Fig. 29. State of the search at 5573 s.

-1000 -500 0 500 1000

-1000

-500

0

500

1000

Ver

tica

l D

ista

nce

fro

m L

KP

[m

]

Horizontal Distance from LKP [m]

59

One must note that, the interception of the target is not guaranteed within the considered search

time of Tmax = 10800 s, neither can one a priori predict interception by a static or a mobile

sensor. For example, when a different target (and initial motion direction) was considered, with

an outward propagation rate of 0.147 m/s, interception was achieved by a mobile sensor at 5543

s, Fig. 30. It can be seen that the deployment of static sensors was efficient since not all static

sensors were needed to achieve target detection.

Fig. 30. Target interception by a mobile sensor at 5543 s.

-1000 -500 0 500 1000

-1000

-500

0

500

1000

Ver

tica

l D

ista

nce

fro

m L

KP

[m

]

Horizontal Distance from LKP [m]

60

Conclusions and Recommendations

This thesis presents a novel approach strategy for the deployment of a network of static sensors

when using a probability model of target motion. The strategy is novel in the sense that it is real-

time dynamic and makes use of the iso-cumulative curve to detect an un-trackable target in

unbounded and growing search spaces with varying terrain. The iso-cumulative curve was

generated to assist with the optimal deployment of the static sensors. The curve was propagated

with time, scaled according to the target’s response to terrain variation, and adjusted to obstacles

present in the scene. Consequently, sub-sets of static sensors were deployed in feasible regions

within the propagated curve in a time-varying dynamic manner.

In the event that new information of the target became available in the search, the deployment of

the remaining sensors could be re-calculated in order to shift the search effort, referred to as

redeployment. This did not only allow for concentrating search efforts closer to the most recent

location of the target, but allowed for search resources to be deployed more efficiently. If all

sensors were initially deployed, and a clue was detected during the search, no remaining sensors

would be available for redeployment.

Simulated experiments were carried out to validate the effectiveness of the proposed static sensor

network deployment strategy, namely showing that it could increase the success rate of a search

and reduce the mean detection time for target localization when compared to uniform coverage-

based approaches, existing in the literature, which did not consider the target-location PDF.

Furthermore, a realistic WiSAR search scenario was presented in detail, where target detection

was achieved through the application of a hybrid methodology that employed both static and

mobile sensor.

The work presented in this thesis served as the first steps for a deployment methodology that is

meant to be implemented in real-life with inexpensive hardware. Although mock searches could

be carried out to show the effectiveness in real-life, the optimal deployment of the sensors and

their impact on target interception was already validated in the simulations sub-section. Of

course, real life implementations would be accompanied with other problems, including how the

static sensors are ‘dropped’ on the field by possibly UAVs, or how the sensors are physically

designed to detect the target. However, the methodology was designed such that it would be

61

independent of the hardware used for deployment, which renders the deployment strategy more

flexible. As long as UAVs or other forms of search assistance physically deploy sensors at the

optimal location for that assigned deployment instance, the deployment would still remain

optimal. In addition, considering non-binary sensing models would have no effect in the

performance relative to other deployment approaches, since both approaches would suffer

equally from probabilistic target detection by static sensors.

However, some topics could be addressed in future work to render the methodology more easily

applied to real-life scenarios. This does not take away from the effectives of the work, but rather

enhances its capabilities and makes it more appealing for implementation. For example, the

target motion model carries a “probable direction of travel” component that was not explored in

this work. This represents a guess for the likelihood of travel direction of the target. Although

terrain and obstacles were considered when propagating the iso-cumulative curve, it was not

shown how the relative likelihood of travel amongst several rays impacted the creation of the

iso-cumulative curve. Having said that, likelihood of travel direction distorts the iso-probability

curves in a similar manner as terrain does, which was shown in [58]. Since the likelihood of

travel direction only impacts the position of the control points, this proposed strategy would

easily adapt to the likelihood of travel direction (if considered) because it would simply use these

same control points to generate the iso-cumulative curves.

Another topic that was not explored in this work was the issue of network connectivity. It was

assumed that the proposed strategy was part of a centralized system, where the main control

station had access to all deployed static sensors, and that target detection would be possible as

long as the target came within the vicinity of one of the static sensors’ sensing range. The data

collected by sensors regarding target detection would be received at the control station

instantaneously. To achieve this, data transfer could be accomplished through cellular networks,

although they are not always available. As an alternative, the network would relay data acquired

by the sensors, from sensor to sensor, until the data reaches the control station. Direct

implementation of data transfer protocols along a network could certainly be integrated with the

proposed strategy, but the data transfer effectiveness would be constrained by the distance

between sensor nodes inherited from the proposed strategy. Therefore, in order to incorporated

network connectivity, static sensors would have to be deployed according to the iso-cumulative

62

curve propagations, but the actual locations along the curves would also have to be optimized for

data transfer along the network.

Although extensive simulations presented in this thesis validated the proposed methodology, a

further comparative study could be carried out to determine the numeric benefit of the hybrid

approach over the approach solely based on mobile agents presented in [60]. The methodology

was designed so as to have no negative impact on the deployment and performance of a mobile

agent team searching for a target, but the exact improvement, in both success rate and mean

detection time is unknown. A new set of simulations with numerous target speeds and various

random paths would have to be conducted in order to obtain a number that realistically portrays

the benefit of the hybrid approach.

63

References

[1] Z. Wang, E. Bulut, and B.K. Szymanski, “Distributed energy efficient target tracking with

binary sensor networks,” ACM Trans. Sensor Netw., vol. 6, no. 4, pp. 32:1–32:32, July

2010.

[2] R. Stolkin, and I. Florescu, “Probability of detection and optimal sensor placement for

threshold based detection systems,” IEEE Sensors J., vol. 9, no. 1, pp. 57–60, Jan. 2009.

[3] L. Laxos, R. Poovendran, and J. Ritcey, “Detection of mobile targets on the plane and in

space using heterogeneous sensor networks,” Wireless Netw., vol. 15, no. 5, pp. 667–690,

Dec. 2007.

[4] M. Hefeeda and M. Bagheri, “Forest fire modeling and early detection using wireless

sensor networks,” Ad Hoc and Sensor Wireless Netw., vol 7, no. 3, pp. 169–224, June

2008.

[5] Y. Wang, M. Wilkerson, and X. Yu, “Hybrid sensor deployment for surveillance and target

detection in wireless sensor networks,” in Proc. 7th Int. Wireless Commun. and Mobile

Comput. Conf., Istanbul, 2011, pp. 326–330.

[6] B. Pannetier, J. Dezer, and G. Sella, “Multiple target tracking with wireless sensor network

for ground battlefield surveillance.” in Proc. IEEE 17th Int. Conf. Inform. Fusion,

Salamanca, 2014, pp. 1–8.

[7] Y. Zou and K. Chakrabarty, “Sensor deployment and target localization based on virtual

forces,” in Proc. IEEE 22nd Ann. Joint Conf. Comput. and Commun., San Francisco, CA,

2003, pp. 1293–1303.

[8] S. Li, C. Xu, W. Pan, and Y. Pan., “Sensor deployment optimization for detecting

maneuvering targets,” in Proc. 7th Int. Conf. Inform. Fusion, Stockholm, 2005, pp. 1629–

1635.

[9] S.S. Dhillon and K. Chakrabarty, “Sensor placement for effective coverage and

surveillance in distributed sensor networks,” in Proc. IEEE Wireless Commun. and Netw.,

New Orleans, LA, 2003, pp. 1609–1614.

[10] B. Coltin and M. Veloso, “Mobile robot task allocation in hybrid wireless sensor

networks,” in Proc. IEEE/RSJ Int. Conf. Intell. Robots and Syst., Taipei, 2010, pp. 2932–

2937.

[11] D.T. Nguyen, N.P. Nguyen, M.T. Thai, and A. Helal, “An optimal algorithm for coverage

hole healing in hybrid sensor networks,” in Proc. 7th Int. Wireless Commun. and Mobile

Comput. Conf., Istanbul, 2011, pp. 494–499.

[12] O. Banimelhem, M. Mowafi and W. Aljoby, "Genetic algorithm based node deployment in

hybrid wireless sensor networks," Commun. and Net., vol. 5, no. 4, pp. 273–279, Nov.

2013.

[13] G. Wang, G. Cao, and T. La Porta, “Movement-assisted sensor deployment,” IEEE Trans.

Mobile Comput., vol. 5, no. 6, pp. 640–652, June 2006.

64

[14] N. Hema and K. Kant, "Optimization of sensor deployment in WSN for precision irrigation

using spatial arrangement of permanent crop," in Prof. IEEE 6th Int. Conf. Contemporary

Comput., Noida, 2013, pp. 455–460.

[15] R.S. Rafi, M.M. Rahman, N. Sultana, M. Houssain, “Energy and coverage efficient static

node deployment model for wireless sensor networks,” Int. J. Sci. and Eng. Res., vol. 4, no.

4, pp. 382–387, Apr. 2013.

[16] K. Kar and S. Banerjee. “Node placement for connected coverage in sensor networks,” in

Proc. WiOpt’03: Modeling and Optimization in Mobile, Ad Hoc and Wireless Netw.,

Sophia Antipolis, 2003, pp.1–2.

[17] K. Yamamoto, H. Ozaki, T. Suzuki, T. Wada, K. Mutsuura, and H. Okada, “Barrier

coverage constructions for border security systems using wireless sensors,” in Proc. 40th

Int. Conf. Parallel Proc. Workshops, Taipei City, 2011, pp. 50–56.

[18] K. Yamamoto, H. Koyamashita, T. Wada, K. Mutsuura, and H. Okada, “Wave-type barrier

coverage for border security in wireless sensor networks,” in Prof. 7th Int. Conf. Comput.

and Convergence Tech., Seoul, 2012, pp. 78–83.

[19] M. Li, Z. Li, and A.V. Vasilakos, “A survey on topology control in wireless sensor

networks: taxonomy, comparative study, and open issues,” Proc. IEEE, vol. 101, no. 12,

pp. 2538–2557, July 2013.

[20] Y. Xu and X. Yao, “A GA approach to the optimal placement of sensors in wireless sensor

networks with obstacles and preferences,” in Proc. IEEE 3rd Consumer Commun. and

Netw. Conf., Las Vegas, NV, 2006, pp. 127–131.

[21] J. Seo, Y. Kim, H. Ryou, S. Cha, and J. Minho, “Optimal sensor deployment for wireless

surveillance sensor networks by a hybrid steady-state genetic algorithm,” IEICE Trans.

Commun., vol. E91–B, no.11, pp. 3534–3543, Nov. 2008.

[22] K. Lorincz, M. Welsh, O. Marcillo, J. Johnson, M. Ruiz, and J. Lees, “Deploying a wireless

sensor network on an active volcano,” IEEE Internet Comput., vol. 10, no. 2, pp. 18–25,

Mar. 2006.

[23] G. Tolle, J. Polastre, R. Szewcyk, D. Culler, N. Turner, S. Burgess, T. Dawson, P.

Buonadonna, D. Gay and W. Hong, “A macroscope in the redwoods,” in Proc. 3rd Int.

Conf. Embedded Netw. Sensor Syst., San Diego, CA, 2005, pp. 51–63.

[24] X. Li, X. Zhang, and B. Guo, “Application of collocated GPS and seismic sensors to

earthquake monitoring and early warning,” Sensors, vol. 13, no. 11, pp. 14261–14276, Oct.

2013.

[25] K. Känsälä and M. Korkalainen, “A versatile sensor network for urban search and rescue

operations,” in Proc. SPIE, 2011, doi:10.1117/12.898149.

[26] G. Kantor, S. Singh, R. Peterson, D. Rus, A. Das, V. Kumar, G. Pereira, and J. Spletzer,

“Distributed search and rescue with robot and sensor teams,” Field and Service Robot., vol.

24, no.1, pp. 529–538, Jul. 2006.

[27] K. Kotay, R. Peterson, and D. Rus, “Experiments with robots and sensor networks for

mapping and navigation,” Field and Service Robot., vol. 25, no. 1, pp. 243–254, Dec. 2006.

65

[28] J. Reich and E. Sklar, “Toward automatic reconfiguration of robot-sensor networks for

urban search and rescue”, in Proc. 5th Int. Conf. Auton. Agents and Multiagent Syst.,

Hakodate, 2006, pp. 18–23.

[29] E. Feo, L. Gambardella, and G.A. Di Caro, “GIS-based Mission Support System for

Wilderness Search and Rescue with Heterogeneous Agent,” in Proc. 2nd IROS Workshop

Robot. and Sensors Integration in Future Rescue Inform. Syst., Vilamoura, 2012, pp. 1–6.

[30] J. Huang, S. Amjad, and S. Mishra, “CenWits: a sensor-based loosely coupled search and

rescue system using witnesses,” in Proc. 3rd Int. Conf. Embedded Netw. Sensor Syst., San

Diego, CA, 2005, pp. 180–191.

[31] J.A. Adams, C.M. Humphrey, M.A. Goodrich, J.L. Cooper, B.S. Morse, C. Engh, and N.

Rasmussen, “Cognitive task analysis for developing unmanned aerial vehicle wilderness

search support,” J. Cognitive Eng. and Decision Making, vol. 3, no. 1, pp. 1–26, Mar. 2009.

[32] R.B. Manjula and S.S. Manvi, “Coverage optimization based sensor deployment by using

PSO for anti-submarine detection in UWASNs,” in Proc. Int. Symp. Ocean Electr., Kochi,

2013, pp. 15–22.

[33] G. Han, C. Zhang, L. Shu, N. Sun, and Q. Li, “A survey on deployment algorithms in

underwater acoustic sensor networks,” Int. J. Dist. Sensor Netw., vol. 2013, pp. 1–11, Nov.

2013.

[34] M.R. Senouci, A. Mellouk, and A. Aissani, “An analysis of intrinsic properties of

stochastic node placement in sensor networks,” in Proc. Global Commun. Conf., Anaheim,

CA, 2012, pp. 494–499.

[35] D. Pompili, T. Melodia, and I.F. Akyildiz, “Three-dimensional and two-dimensional

deployment analysis for underwater acoustic sensor networks,” Ad Hoc Netw., vol. 7, no. 4,

pp. 778–790, June 2009.

[36] G. Battistelli, L. Chisci, C. Fantacci, A. Farina, and A. Graziano, “Distributed tracking with

doppler sensors,” in Proc. IEEE 52nd Ann. Conf. Decision and Control, Florence, 2013, pp.

4760–4765.

[37] N. Deshpande, E. Grant, and T.C. Henderson, “Target-directed navigation using wireless

sensor networks and implicit surface interpolation,” in Proc. IEEE Int. Conf. Robot. and

Autom., Saint Paul, MN, 2012, pp. 457–462.

[38] N. Deshpande, E. Grant, and T.C. Henderson, “Target localization and autonomous

navigation using wireless sensor networks—A pseudogradient algorithm approach,” IEEE

Syst. J., vol. 8, no. 1, pp. 93–103, Aug. 2014.

[39] L. Lazos, R. Poovendran, and J. A. Ritcey, “On the deployment of heterogeneous sensor

networks for detection of mobile targets,” in Proc. 5th Int. Symp. Modeling and

Optimization in Mobile, Ad Hoc and Wireless Netw., Limassol, 2007, pp. 1–10.

[40] Z. Sun, P. Wang, M.C. Vuran, Z.A. Al-Rodhaan, A.M. Al-Dhelaan, and I.F. Akyildiz,

“BorderSense: Border patrol through advanced wireless sensor networks,” Ad Hoc Netw.,

vol. 9, no. 1, pp. 468–477, May 2011.

[41] R. Bellazreg, N. Boudriga, and S. An, “Border surveillance using sensor based thick-lines,”

in Proc. Int. Conf. Inform. Netw., Bangkok, 2013, pp. 221–226.

66

[42] E. Felembam, “Advanced border intrusion detection and surveillance using wireless sensor

network technology,” Int. J. Commun., Netw. and Syst. Sci., vol. 6, no. 5, pp. 251–259,

May 2003.

[43] M.R. Ingle and N. Bawane, “An energy efficient deployment of nodes in wireless sensor

network using Voronoi diagram,” in Proc. 3rd Int. Conf. Electr. Comput. Tech.,

Kanyakumari, 2011, pp. 307–311.

[44] N. Rahmani and F. Nematy, “EAVD: An evolutionary approach based on Voronoi diagram

for node deployment in wireless sensor networks,” in Proc. Int. Conf. Soft Comput. for

Problem Solving, Roorkee, 2011, pp. 121–129.

[45] H. Xiang, L. Peng, G. Liu, and C. Tang, “Multiple target coverage considering area

coverage in visual sensor networks,” Appl. Res. Comput., vol. 29, no. 9, pp. 3428–3431,

Sep. 2012.

[46] R. Mathur, M.K. Sharma, A. Misra, and D. Baveja, “Energy-efficient deployment of

distributed mobile sensor networks using fuzzy logic systems,” in Proc. Int. Conf.

Advances in Comput., Control and Telecomm. Tech., Trivandrum, 2009, pp. 121–125.

[47] K. Akkaya and A. Newell, “Self-deployment of sensors for maximized coverage in

underwater acoustic sensor networks,” Comput. Commun., vol. 32, no.7–10, pp. 1233–

1244, May 2009.

[48] G. Wang, G. Cao, T. La Porta, and W. Zhang, “Sensor relocation in mobile sensor

networks,” in Proc. IEEE 24th Int. Annu. Joint Conf. Comput. and Commun. Societies,

Miami, FL, 2005, pp. 2302–2312.

[49] P.T. Mahida, R. Patel, P. Patel, and S. Mody, “Performance evaluation of dynamic and

static sensor node in wireless sensor network,” Indian J. Comput. Sci. and Eng., vol. 4, no.

1, pp. 23–28, Feb. 2013.

[50] K. Baumgartner, S. Ferrari, and T.A. Wettergren, “Robust deployment of dynamic sensor

networks for cooperative track detection,” IEEE Sensors J., vol. 9, no. 9, pp. 1029–1048,

Sep. 2009.

[51] P. Alvarado, T. Taher, H. Kurniawati, and G. Weymouth, “A coastal distributed

autonomous sensor network,” in Proc. OCEANS’11 MTS/IEEE Conf., Kona, HI, 2011, pp.

1–8.

[52] N. Xia, Y. Zheng, H. Du, C. Xu, and R. Zheng, “Rigidity driven underwater sensor self-

organized deployment,” Chinese J. Comp., vol. 36, no. 3, pp. 494-505, Mar. 2014.

[53] N. Xia, C.S. Wang, R. Zheng, and J.G. Jiang, “Fish swarm inspired underwater sensor

deployment,” Acta Automatica Sinica, vol. 38, no. 2, pp. 295–302, Dec. 2012.

[54] N. Aitsaadi, N. Achir, K. Boussetta, and G. Pujolle, “Differentiated underwater sensor

network deployment,” in Proc. OCEANS’07 IEEE Conf., Aberdeen, 2007, pp. 1–6.

[55] P.V. Teixeira, D.V. Dimarogonas, K.H. Johansson, and J. Sousa, “Event-based motion

coordination of multiple underwater vehicles under disturbances,” in Proc. OCEANS’10

IEEE Conf., Sydney, 2010, pp. 1–6.

67

[56] G.A. Hollinger, U. Mitra, and G.S. Sukhatme, “Autonomous data collection from

underwater sensor networks using acoustic communication,” in Proc. IEEE/RSJ Int. Conf.

Intell. Robots and Syst., San Francisco, CA, 2011, pp. 3564–3570.

[57] A. Shukla, G. Ojha, S. Acharya, and S. Jain, “A customized flocking algorithm for swarms

of sensors tracking a swarm of targets,” in Proc. 2nd Int. Conf. Advanced Inform. Tech. and

App., Dubai, 2013, pp. 171–183.

[58] A. Macwan, G. Nejat, and B. Benhabib, “Target-motion prediction for robotic search and

rescue in wilderness environments,” IEEE Trans. Syst., Man Cybern. B, Cybern., vol. 41,

no. 5, pp. 1287–1298, Oct. 2011.

[59] D. Heth and E.H. Cornell, “Characteristics of travel by persons lost in Albertan wilderness

areas,” J. Environmental Psychology, vol. 18, no. 3, pp. 223–235, Sep. 1998.

[60] A. Macwan, J. Vilela, G. Nejat, and B. Benhabib, “Use of iso-probability curves in multi-

robot deployment for wilderness search and rescue,” Int. J. Robot. and Autom., no. 206–

4366, pp. 1–7, July 2015.

[61] A. Macwan, J. Vilela, G. Nejat, and B. Benhabib, “A multirobot path-planning strategy for

autonomous wilderness search and rescue,” IEEE Trans. Syst., Man Cybern. B, Cybern.,

vol. 45, no. 9, pp. 1784–1797, Nov. 2014.

[62] S. Ding, C. Chen, J. Chen, and B. Xin. "An improved particle swarm optimization

deployment for wireless sensor networks," J. Advanced Comput. Intell. and Intell. Inf., vol.

18, no. 2, pp. 107–112, Mar. 2014.

[63] S. He, E. Prempain, and Q.H. Wu, “An improved particle swarm optimizer for mechanical

design optimization problem,” Eng. Optimization, vol. 36, no. 5, pp. 585–605, Mar. 2004.

[64] G. Tuna, T.V. Mumcu, K. Gulez, V.C. Gungor, and H. Erturk, “Unmanned aerial vehicle-

aided wireless sensor network deployment system for post-disaster monitoring,” Emerging

Intell. Comput. Tech. and Appl., vol. 304, no. 1, pp. 298–305, July 2012.

[65] J. Ng and T. Bräunl, “Performance comparison of bug navigation algorithms,” J. Intell.

Robot. Syst., vol. 50, no. 1, pp. 73–84, Sep. 2007.