Detectability of Static and Moving Targets in Randomly Deployed Military Surveillance Networks

bewgrosseteteSoftware and s/w Development

Dec 13, 2013 (3 years and 9 months ago)

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1


Abstract

Military surveillance networks are t
he most
challenging Wireless Sensor Network (WSN
)

based
applications
.
In contrast
to the most of

other application
areas,
military
surveillance
network
s

are
usually
meant to
be
deployed randomly. Because of its probabilistic
nature, this deploying framework brings up
the
two most
important questions related to the deployment quality:
the network connectivity and the network coverage. This
paper addresses
the
typical
military surv
eillance
scenarios
.

It

aims to
provide
a qualitative analytical and
simulation
-
based

analysis on detectability of both static
and moving targets.
The analysis covers different aspects
of
the deployment modeling strategies and studies
the
ir
impact on detect
ing

the intruders or
on
securing a clear
path
from one site to another.

In order the barrier
coverage analysis to be conducted through simulations,
a special algorithm is developed.
It provides gap
identification and returns the number of
the
potentially
n
eeded
mobile nodes
for
the
strong barrier coverage to
be provided
.
The derived analytical and simulation results
and discussions show the degree the different
parameters influence the deployment quali
ty in realistic
implementations.


Index Terms


Military
Surveillance Networks, Network
Coverage, Wireless Sensor Networks.

I.

I
NTRODUCTION

W
ireless sensor network
s

(WSN
s) provide

a new
class of computer systems and expand

people

s ability
to remotely int
eract with the physical world [1
].
This
engineering area is
recognized to be a prom
ising tool in
many application areas such as:
mi
litary, industrial,
biomedical,
and environmental

surveillance and
monitoring
.

Beside
s

the ordinary distributed computing
issues, there are many additional aspects that
are to be
faced when dealing with
a
WSN
-
based application for a
specific purpose. Challenges are mainly related to the
low
-
rate, sho
rt
-
range, battery
-
supplied, memory and
computational
-
constrained nature of small computing
and communicating devices


senso
r nodes that are
organized into large scale dynamic networks.

While
some of the applications accentuate energy efficiency
as
the
primary goal, others can be more focused on
reliability, network coverage, or connectivity.
Even when
considering
only
one spec
ific field of interest
,

such as
for example military applications, different scenarios
result in totally different hardware, software and
communication architectures prioritizing

different
performance aspects.


Military applications
might
be the most deman
ding
ones among WSN
-
based applications.
Sensor network
nodes are deployed in an area by either placing them in
predetermined locations or having the nodes randomly
located
[2
]
. The second approach brings up greater
number of scientific and engineering
challenges. In
these situations, b
eside
s

other limitations

and aspects
,
one of the most

important
quality evaluation
parameters of the WSN
-
based
military
application
is
how well a deployed network can sense a physical
world
, i.e., how well it can provide t
he detection of the
military targets in a specific area.

In this

paper
,
target
detectabilty is evaluated through
military scenarios
that are analyzed both
analytically
and
via
simulations
. These scenarios are focused on
:
a)
detection
analysis
of the
static

target
s

in the
rectangular area (such are minefield
s
, biologically or
chemically contaminated areas
,

etc.)
, and
b)
detection
of the moving target
s

(such as armed soldiers or
vehicles).
In

the latter case, the barrier coverage
analysis is also performed.
G
lobal barrier coverage,
which requires much fewer sensors than full coverage,
is known to be
an
appropriate model of coverage for
movement detection application
s such as intrusion
detection [3
]. Therefore, a

special algorithm
on
finding
barrier gaps
and
th
eir mending with
mobile
sensor
nodes is developed.
This algorithm is more generic
than similar algorithms given in literature. While
similar
algorithms are developed strictly for uniform
-
normal
distribution of the network, this algorithm includes the
gap f
inding routines
from one point of
the
network to
another
,

for all
kinds of
the deployments

where
barrier

coverage is needed to be analyzed.
Coverage is
quantified
in terms of
the probability
for the
target
to be
detected
and the
number of
sensor
nodes
needed
to
cover

the area
(
i.e.
,

nodes’ density)

with a
certain
degree of target detection
/undetection

probability
.


The a
nalysis involves two
random deployment
strategies.
Uniform distribution is more appropriate
when there is approximately
an
equal probability for
the target to be situated anywhere on the area (such
is
the case of
mines in minefield
s

etc.). On the other
hand, when a sensor barrier or secure crossing path
has to be provided from the air, normal distribution
along the axis orthog
onal to the line of flight gives more
realistic approach to the application

design
.

In accordance to the design criterions given

in [4
]
,
the analysis
incorporates
random deployment
strategies
,
Boolean isotropic sensing area modeling,
a
distributed coverag
e scheme,
and sensor mobility
.

Analyzed networks belong to the third generation
sensor networks presented in [
5
].

In order to
firstly
describe

the general approach to the
analytical
detectability analysis of the
various military scenarios
,
and to provide a numerical reference point for testing
D
etectability of
Static

and
Moving

Targets in

Randomly Deployed
Military
Surveillance
Networks



Zhilbert Tafa

















V
eljko

Milutinovic,

Fellow IEEE

Department of Computer
Science










Department of Computer
Science


Belgrade University, Serbia















Belgrade University, Serbia


tafaul@t
-
com.me




















vm@etf.rs




2

the simulation framework (by comparing
these results

to
the simulation
outcomes
),
a set of analysis is conducted
analytically
.


In accordance to the results derived from all the
scenarios, discussion
s toward r
ecommendations on
optimal number of
static

and mobile sensor nodes are
given regarding
each of
the
presented
purpose
s
.

The
remainder of this

paper is organized as follows.
Section II reviews previous work on target coverage.
The analysis
framework and the p
roblem
formulation
are given in Section III
.
In
the
scope of this framework,
the

analytical
presentation on detection probability for
some of the military scenarios is

covered

in S
ection IV
.
The issues (such as creating the secure path w
ith
airdropped wireless sensors and break finding/mending
algorithm), that will later be analyzed only through
simulations, are also
described
in this s
ection. In
Section
V
, simulations are
accomplished on all of the
considered cases
,

while the gap finding

algorithm for
barrier coverage is described in more details.
Section VI
contains conclusions.


II.

R
ELATED
W
ORK

The
problem of target detection in military
surveillance network
s

is addressed in literature from
different points of view
.


A thorough analytical approach to the area coverage,
node coverage fraction, and detectability is given in [
6
]
.
Authors conduct a
general and strictly analytical
analysis to the
coverage problem regarding the
Boolean

and cooperative sensing models.
On the
other hand, a

strictly
simulation
-
based approach
on deployment
quality of uniformly distributed military sensor networks

using
Boolean and Elfe’s
detection
model
s

is given in
[
7
].
Anothe
r perspective is given in [
8
]

where
,

beside
the detectability

analysis
,
military targets are
additionally

classified

and tracked

on a relatively small
area using grid
-
based analysis of the deterministically
deployed network
.


Analytical approach to the path coverage is also
covered in [
8
], while more thorough analysis relate
d to
the issues such as full path coverage and

distribution of
the number of uncovered gaps over the path are
addressed in [
9
]
.

Critical conditions for the existence of barrier
coverage and an algorithm to construct sensor barriers
is presented in [
10
].
Au
thors of [
11
] estimate the density
needed to achieve coverage and connectivity in thin
strips of finite length for four models of coverage and
use the uniform deployment manner.
A network model
for barrier coverage
,
along with an

algorithm
to
con
struct bar
riers is proposed

in [
12
]
. T
he authors
compare line
-
based normal distributed vs. uniformly
distributed network
s

in terms of barrier coverage.
Similar work is
presented

in [
13
], where a probability
analysis of barrier coverage is additionally conducted.

Introdu
cing the nodes’ mobility to improve the
coverage is also one of the challenges addressed in
this paper.
Similar

effort
s

were
also made

in literature
.
T
he methodology of relocating the mobile sensors with
limited moving range
,

with the aim to minimiz
e the
variance in number of sensors among the regions is
presented

in [
14
]
.
Construction of the maximum
number of barriers with minimum sensor moving
distance along with the effects of the number of mobile
nodes on the barrier coverage are also covered in

[
15
].
An algorithm similar to the one used in
this
paper was
presented in [
16
]. This algorithm is designed only for
finding and mending gaps
in a network deployed
based on the normal distribution.



III.

T
HE
ANALYSIS
FRAMEWORK

Detectability

typically

means

the probability that a
sensor network can detect an object moving from point
S to point D. It is the function of the network density
,
the deployment manner (model and strategy),

and the
distance between
S and D
points
.
I
n military
applications
, it

measure
s the intrusion detection
either
in
the
sense of detecting the objects crossing the
specific area or in
the
so
-
called border coverage
.

In
this paper, we will refer to this kind of detectability as
detectability of the moving objects. On the other hand,
the
re are situations where the area has to be covered
with a certain number of sensors in order the detection
of the
static

targets (e.g. mines) to be provided, or in
preventive protection, where the aim is to inspect if a
certain path is clear from infiltrat
ion by
static
targets.
Although
this description relate
s

to the definition of the
area
or full
coverage concept as: the fraction of the 2
-
D
or 3
-
D geographical area that is in sensing radius of
one or more sensors; when dealing with the detection
of the st
atic
military
targets, we will adopt detectability
as a general term

while
reformulating the definition
s
from literature to

some extent.
We will refer to the
target
detectability
as a
measure of how well
military
targets (both static and mobile)
can be detected by a
sensor network.




In military applications, for the purpose of the outdoor
sensing,
magnetic,
microwave,
acoustic,
ultrasonic,
infrared
,

and

radar systems are typical.

These

sensors
differ in their sensing
characteristics
.
T
he detection
probability and the number of needed sensor nodes
,

depend
also
on the strength of the signal emitted from
the target itself.
For example
,

to detect an enemy tank
might require
a smaller
number of
(acoustic) sensors
,

because the acoustic signal

emitted by them is
stronger [
17
].
Furthermore, various environmental and
implementation conditions result in different
sensing,
exposure, and
detection models to be appropriate in
different applications
.
A classification of the
coverage
-
related models is
given in
[
17
] and
[
1
8
].

The b
inary model is the simplest
,

but also the most
usual
detecting

model
. Sensor detects the event or
target with the probability P=1 if the target is at the
distance D<Dt from the sensor node, where Dt

is the
threshold sensing distance. This model, however,
does
not

take into account the environmental conditions of
the transmission medium
into consideration such
as
obstacles and other signal deterioration aspects. An
object is treated as detected if it
is situated inside
the

3

sensing radius of a particular sensor. Such a
simplification may be acceptable in
the
cases where the
line
-
of
-
sight is ensured.

However, this model remains to
be the most frequently
used
model
to represent the
sensing field of the se
nsor nodes
, hence it is also used
in this paper.

Deployment strategy is also one of the very important
factors that influence the coverage issues.
While
deterministic deployment provides the exact knowledge
about the network coverage
and other network issu
es,
random

deployment
strategies (that are
considered in
this paper
)

deal with
the
probabilistic approach to most
of the WSN
-
related issues. Nevertheless
, as will be
shown, many exact conclusions can be derived.


This paper
involves
two deployment
strategies:

a)

T
he uniformly
and independently
distributed
sensors across

the
rectangular
region

(Fig
.

1)
.
Such a random initial deployment is desirable in
scenarios where prior knowledge of the field is not
available
[
7
]
.
This
deployment is
usually
realized
in
some manual way

or using artillery
.



Fig
.

1:
An

u
niformly distributed sensor network.

Description:
This form of distribution can be used in
detecting the static targets on the area
,
e.g. mines
(
depicted as crossed circles
)
, contaminated areas, etc.
;

and in detecting the moving objects
,

e.g. depicted with
the curve and the
arrows.


b)

Sensors are

thrown from the aircraft

in
nearly
-
linear manner (Fig
.

2
)
.
This approach present
s

a

typical
situation of the military network deployment
that usually aims to provide
barrier coverage

or to
secure
the

path between two geographical points
.




Fig
.

2
:

A line based WSN

deployment
.

Description:

Actual landing points of sensors deviate
from their targeted locations because of environment
factors.

Therefore, this deployment is modeled with
uniform distribution along x axis and normal distribution
along y axis. Vertical arrows present the moving
di
rection in
the
case of barrier coverage while horizontal
arrow
depicts

the moving direction
when clearance of
the terrain from the adversary elements has to be
provided.


Both scenarios
are based on the assumption

that
sensors are deployed to a region; they wake up,
organize themselves as
a
network, and start sensing
the area for a phenomenon. When
a
sensor detects an
event, it communicates to the sink node so that an
appropriate action is taken.
These models provi
de
the

framework for
classifying and
analyzing
sub
-
scenarios

such as
:

-

Assuring that a belt

region
is
clear
from military
objects or biological/chemical contaminations,
when the aim is
passing from one side of
the
region

to another.

-

Finding the p
robability of detecting the target that
moves along
an
arbitrary line.

-

Finding d
etectability of the target
that moves
perpendicularly to

the
length of the
belt
-
like
area
(
when
the target

does not know the position of
the sensor nodes

and suppose
s

for
the s
hortest
path to be the best one
)
.

-

Finding
solutions to provide
detectability of
a
moving
target
if it
knows the position of the
sensors
.

These sub
-
scenarios are hereafter
grouped into two
categories
, regarding the question of whether the
target is
static(on the land) or moving (from one point
to another).



IV.

A
NALYTICAL AND
SIMULATION
MODELING OF
THE
TARGET DETECTION
SCENARIOS

A.

D
etection of the static target
s.

Complete coverage means sensor networks can
sense the whole area of interest without any
vacancy
(or hole) [
19
].
Scenario A

involves
this
concept in
the
sense of finding the needed number of nodes
(both
analytically and using simulations)
that will satisfy
the
user requirements for a correct detection probability
(higher than 0.95) as
recommended
by

[
8
],
in
the
case
of uniformly and normally distributed network, where
the latter case area of interest will be a narrow passing
corridor along the line of flight of

the

supporting aircraft
.

In order to present the first case, l
et’s

assume that
there is a region A

that should be covered by sensors
uniformly
distributed across that region.

If (x, y) are
coordinates of each sensor

scattered on the area of
length
l

and width
w
, the probability density function of
the sensor location is:












otherwise
w
y
l
x
lw
y
x
f
,
0
0
,
0
,
1
)
,
(








(1
)

In this

case, i
f we denote the sensing radius with r
and the
rectangular area of interest with
A
, then the
probability that the event will be detected by only one
sensor is:


4

A
r
p
d

2
1
















…(2
)

Therefore, the probability that the event will be
detected by at least one of the N nodes can
analytically
be described with:

N
N
d
A
lw
r
p
p
)
1
(
1
)
1
(
1
2
1










…(3
)


If the region

A

is large
,

than (3
) can be approximated
with:

lw
Nr
A
e
p

2
1




















…(4
)

From here,

ρ

can be derived

as
:


A
p
r
A
N



1
1
ln
1
2















.
..(
5
)


This equation
gives
the required densit
y for a given
area coverage 0<
A
p
<1

in uniformly deployed sensor
network that embodies
the
binary sensing model
.
The
area dimensions used in simulations is 180x1200 m2,
while sens
ing radiuses are set to be r=10m and r=18
m.
According to the equation (5),
the
number of nodes

needed
to cover t
he region with the probability higher
than 0.95 for each
one
of the
sensing radius
,

should be
greater than

2060 and
637
,
respectively.

The detection
probability depends only on sensing radius and on
network density. Therefore, for the probability threshold

of 0.95, node density remains the same no matter how
large the area

is
.

On the other hand, the scenario which is also the
most usual in

military
application (
F
ig. 2), gives
a
different dependency
. The situation when sensors are
thrown from the aircraft intuitively would be more
accurately expressed if sensor distribution is considered
to be nearly uniform along the axis of flight, while it is
Gaussian in the orthogonal direction.
T
he probability
distribution along the y axis (orthogonal to the flight line
-
axis) is:

2
2
2
)
(
2
1
)
(







y
e
y
f









(
6
)


where μ is the mean that represents the line of flight
and the
2

is the y
-
axis offset variance which
represents the m
easure the positions of sensors are
expected to vary along the y
-
axis due to the influence of
many factors such as: wind, variable flight speed,
inertia
, terrain characteristics,

etc.
Although the
influence
of these
factors

is not treated separately on
each of them
,
a simple
model
given
above
can serve as
an approximation when a combined influence of all
these factors can be
estimated and
encapsulated into
the concept of σ.

According to the 68
-
95
-
99.7 rule for
the Gaussian d
istribution, 68% of the nodes are likely to
be situated in proximity ±σ to the flight line. Similarly,
95% and 99.7% of the number of nodes are expected to
fall within the distance ±2σ and ±3σ from the line of
flight, respectively.

The aim i
n the scenario

is
a secure path
between S
and D

(horizontal arrow in Fig.

2)

to be provided from
the air. A
n approximation is made by considering that
(almost) all the nodes lie at interval a<x<b,
-
3σ<y<3σ.
In most of the cases the
portion of the area with the
width
sma
ller than
σ will
provide satisfactory space for
the

vehicles
or

solders to pass.
In these cases,
If the
number of all nodes is N, the number of nodes which
are expected to lie on the interval ±
Δy

is determined by
the appropriate area under the curve of

nor
mal
distribution given in (6
)
.

While small value of Δy
intuitively gives better area coverage, the influence of
the border effect becomes high

(Fig
.

3
). Therefore, the
analysis of this sub
-
scenario is conducted using
simulations and the results are evaluated in
the
next
section.




Fig
.

3
:

The i
nfluence of the border effect on coverage
in a narrow area

(r ~ h)
.


Description:

S
ensing radiuses (circles) of some of the
nodes
(
that
belong to the valuated
region
)

lie outside
the region and vice versa.


B.
Detection of the moving target

Now, let’s
assume

that the target moves

from point S
to point D

across the area where the uniforml
y
distributed network is deployed, as depicted in Fig
.

1
.


The target will be
detected if at least one sensor
is
situated to the proximity smaller than r along the target
moving path

t
.

If

the number of sensors per unit area (density) i
s
denoted by ρ
, and the area is denoted by
A
,

then the
locations of the sensors located in a region A, N(A) can
be modeled as a stationary two
-
dimensional Poisson
process. The distribution of the number of nodes
on
a
given area A, for a given density
ρ

is then:


!
)
(
)
)
(
(
k
A
e
k
A
N
P
k
A

















(
7
)


If the area around line p is denoted by
Y
, the
n t
he
probability of an object not being detected is equal to
the probability that none of the sensor nodes are within
the detecting zone
of the path
t
,
precisely:


0
)
(
(

Y
N
P

















…(8)


When
the trajectory
can be
interpolated by
analytical
functions
)
(
x
f
i
, each w
ith starting and ending point
s

5

i
A

and
i
B
, respectively, the probability of detecting the
moving target
(while relying on relation 7)
along each of
paths

i

w
ill be:








Bi
Ai
i
r
x
f
r
di
e
P
)
))
(
(
1
2
(
2
2
'
1











…(
9
)


However,
as mentioned in
the
case A,
i
n
many
military
applications
,
either
due to

the

geographical terrain
constraints
,

or
the way the sensors are deployed
, the
region of interest may have long extension in
only
one
particular direction.
This situation can be modeled with
the two
-
dimensional strip. If the width of the strip h is
much large
r than sensing range, i.e. h>>r, then
boundary effects can be ignored. In this scenario,
the
most
important coverage issue

is related to the
detection of the target that crosses the strip
. There are
two situations of target crossing the strip
-
like region:
when
a
target does not know the p
ositions of the
sensors and when

it knows these positions.
When the
target does not know
the
positions

of the sensor nodes
,
it cannot plan the best path
hence

it
traverses the
region
without predictable and systematic pattern.
In
the
case of a strip
-
like region
,
the best assumed path for
crossing the width of the strip without being detected by
sensors is the path perpendicular to the length of the
strip.
We will refer to this situatio
n as vertical
detectability. In

the

presented scenario, vertical
detectability
is
a good measure of coverage quality

(F
ig
.

4
).



Fig. 4
:

The WSN in a s
trip
-
like area
.

Description:

In this example, the target has two
solutions to remain undetected by sensor network while
passing from one edge of the strip (S) to another (D).


In order to analyze this scenario,

l
et’s denote
again
the area of
the detecting zone with
A.

Using the same

approach as in
(
8
),
and assuming
that
h<<l

(
l
-
the length of the field),
the probability that an
object
,

while
moving along path from S to D
,

will be
detected in
the
case of two
-
dimensional strip area is:


rh
e
Pd

2
1




















…(
10
)


Therefore,

d
P
rh


1
1
ln
2
1












…(1
1
)



As can be noted, if any of the parameters
ρ
,
h,

l

and
r

in
the case
of
moving along
a
n arbitrary

curve
line,
and ρ,
h, and

r

in
the case
presented

in Fig.

4

is

large;

the
probability of the target detection will approach to one.
In other words, in situations
where a moving line
length, the sensing range or/and the deployment
density are large, it is almost impossible for the object
to

cross

the network without being detected.

Alt
hough

the scenario presented in Fig. 4

can be
described as a kind of barrier coverage, it still enables
the target to remain undetected if
the target
knows the
position of the sensors while crossing the barrier from

one side to another.
In these situations
,
an area

is
considered to be
barrier covered if there exist
s

a set of
sensors that can be ordered as a chain across the
horizontal direction
(
F
ig. 5
)

such that the sensing
ranges of adjacent sensors overlap and the sensing
range at both ends of the chain intersects both
bou
ndaries of the rectangular area
.




Fig.

5
:

Construction
of
the b
arrier coverage.

Description:

Vertical edges
provide sensing
coverage
within distance r
.
This is because these two edges are
considered to be accessible.
Consequently, each one
of the sensing nodes within distance 2r from the edges
is considered to be connected and is treated as a
starting point of
the
barrier const
ruction

algorithm
.
Nodes
i

and
j

are considered to be connected if the
distance

between them is
r
d
ij
2

.
In this example,
local barriers are colored with red lines, while gaps are
colored with black lines between the nodes.

It
shows
the way the developed algorithm aims to find gaps
(and fill them) in order to ensure full barrier coverage.
In this simulated situation, t
wo barriers
are
proposed
by the
algorithm
(S1
-
D and S2
-
D)
, while only S2
-
D is

selected to be

optimal in
the
sens
e of
the
minimum
number of mobile nodes needed to cover the gaps

and
to create the full barrier coverage
.


V.

S
IMULATION RESULTS AN
D
THE
DISCUSSIONS

In order to
statistically
analyze, and compare
different aspects of the typical military surveillance
scenari
os, a s
imulation
environment
for the two
-
dimensional rectangular field
is
developed in Java.
A
djustable parameters

of the simulator
were
:
field
dimensions
,
the
number of sensor nodes,

the sensing
range
,
the normal distribution
parameter
σ
, and the
width of interest
in
the
case of path coverage analysis
.

The most typical sensing radius values in military
applicati
ons range between 10m and 18 m
;

hence
these two ranges are considered as the reference
points
.
Another reason why we consider these values
is that higher radiuses rapidly improve coverage

6

performance and therefore does not
present

the critical
area of research.

Our f
irst simulation address
es

the efficiency of
deployment based on normal distribution
over the one
based on uniform distribution in
the
case the
cover
age
of

the strip region with the
target detection
probability of
more than 0.95

is needed
.
This scenario includes the
results from the relation (5) where, in order the
detection probability of

0.95
for the sensing radiuses r =
10m and r = 18
m

to be provided
,
the
network density
should take values 0.00954055 and 0.002944,
respectively. While these values depend only on
sensing radius
in a
network deployed
by
following the
uniform distribution

pa
ttern
,
determining the total
number of nodes thrown from the aircraft that enable
efficiently coverage of a path from S to D (Fig. 2)

depend also on σ

and the width of interest
.

The
experiment in proceeding
takes
σ values of 10

and 30,
and the radiuses of 10m and 18
m. If the area length is
large enough

compar
ed

to the area width
, the precise
length
value is irrelevant

and the results are applicable
to any value of the
length
.

In this

simulation, the region
is 1200
m long.

A
ccordi
ng to the
mentioned 68
-
95
-
99.7
rule, 99.7
% of the sensor nodes will fall within the

width of the area. This

is why we consider the uniform
-
normal scenario where σ=10 and σ=30

to be
comparable with the scenario
s

of uniform
ly

distribut
ed
network

over the
area of 60m and
180
m

in
width,
respectively
.

On t
he other hand, approximately 68
% of
the nodes will fall within the central ±σ region
. This
means that if the
(secure)
path with the detection
probability of 0.95 for a relatively narrow width of the
region
has to be provided
, the width of the strip of
interest can be ±σ or narrower
.
W
e refer to the overall
density as:


ρ = (Number of sensor nodes)/Area


U
sing simulations,
we find the number of nodes that
need to be airdropped in order the ratio between area
of
uncovered regions and
2σl

(l


length of the field) to
take the average values smaller than 0.05. T
he
total
number of nodes
needed to be airdropped in order
to
cover the ±σ wide region around the line of flight with
the detection probability of
0.95

and

the ratio of

overall
density
for normal
-

and uniform
-
based

deplo
yment
manner is given in Table I
.



σ=10
=
rZ㄰
=
σ=30
=
rZ㄰
=
σ=10
=
rZㄸ
=
σ=30
=
rZㄸ
=
乵k
扥b
=
=
潦=摥s
=
㌷P
=
ㄱN
M
=
ㄳN
=
㌳P
=
ρn/ρu
=
〮MPP
=
〮MPP
=
〮㘳
=
〮MOP
=
TABLE

I:

Number of nodes and the ratio between the
densities of networks deployed in line
-
based manner
and those based on uniform distribution

when a strip
region of 2σ is
supposed to
provide the detectability
with probability of 0.95
.

Description:

The area of 6σ
x1200 m2 is covered with
sensors. The overall number of nodes deployed in this
region in order to cover the strip of 2σx1200 m2 with
the probability of at least 0.95 is derived.


The main conclusion from
T
able
I
is that,
when the
aim is
the detection prob
ability
(of static targets) of
0.95

to be achieved
, line based distribution

provides

40
-
50% of savings in
the
sense of number of sensor
nodes
over the
normal distribution.

The v
alues
on
the
number of nodes are
derived from simulation of
the

2400σ m2 area
s while those on
ratio
of overall density
are invariant to
the length
changes
(
as long as

the
length
of a region
is much larger than
its
width).

While
the ρu (i.e., the density of
a network distributed
following the uniform distribution
that provides the
d
etection probability of 0.95) is a constant value, ρ
n

density can be derived from the Table I for various
parameters σ=10, σ=30, r=10, and r=18.

Second
simulation involves
uniform distribution of
sensor nodes across
a strip region of 1200m in l
ength
and 1
8
0
m in width. This scenario is
applicable

when
the aim is to achieve the barrier coverage
and
the
sensor distribution
across the area
can be considered
to be nearly
-
uniform.

The target is supposed to cross
the region vertically, i.e., perpendicularly to th
e

area
length, since it is the most probable solution for the
target to remain undetected
if

it does not know the
position of the sensor nodes. The probability
for
the
target

to remain

undetected is calculated as
quotient
between the non
-
covered vertical
regions and the
region length.

The
average
results
for
500 different
deployments

are shown in

Fig.

6
.



Fig
.

6
:
Probability

for
the target to remain undetected
while crossing the shortest path along the width of the
strip
.

Description:

Probability for the target to remain
undetected
while

crossing the
180x1200 m2 strip
-
like
rectangular

region

along the width, in networks
deployed based on
uniform
and normal
distribut
ion
.


Fig.

6

shows that,

in
the
case of 18
-
m
eter
-
sensing
radius

sensors
, the region is vertically covered
95%
and
97.2%
,

if more than
100 and
120 nodes are
deployed
, respectively
.
On the other hand, more than
190

sensor nodes
with the 10 meter
-
sensing radius
are
needed in order to

cover the same region wit
h the
probability hi
gher than 9
5
%.

These results are in
accordance with the relatio
n (11
). According to this
relation, the number of sensor nodes
with the 18
m
sensing radius
needed to vertically cover the 180x1200

0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0
20
40
60
80
100
120
Number of sensor nodes

r=10
r=18

7

m2 region with the probability 95% and 97.2%
is 99,857
and
119,
185, respectively
.

While the
intrusion
detection probability of vertical
crossing path r
emains the same
on

the case when the
network is uniformly distributed along the x
-
axis (area
length) and normally along the y
-
axis (area width)
, the
barrier covera
ge intuitively should show different
results.

In this sense, two different deployment styles
are evaluated.
An algorithm is used to find the number
and the length of the gaps in both cases.
The aim is to
give the average number of the needed mobile sensor
nodes in order to
fill the
network
gaps
and make the
network barrier covered.

Let’s denote the
coordinates
of the node
i

with X
i

and
Y
i
, respectively
.
The left and the right edges will
generally be denoted by
S and D, respectively.

The
gap
finding
and gap filling
algorithm now
works
as follows
:

1)

Init
ialize the
minimum
number of gaps g = 0 and
the

minimum
number of
needed
mobile nodes m

= 0.

2)

Find the nodes that are
connected to the leftmost
edge.

If there are no such nodes, the network is
deployed uns
uccessfully.
In simulation, t
he
deployment is repeated.

3)

Perform a routine that construct
s

a connectivity
graph f
or each of these nodes,

i.e.,

find
the
nodes that are

situated in radius 2r
, add them to
the appropriate
sub
-
graph,

and continu
e
searching for their neighbors. Repeat the
searching routine for each newly included
neighbor

until there are no more neighbors to
be
added
.
The output from this r
outine

will be a
number of connected or trivial graphs G1 (V1,
E1), G2 (V2, E2)… Gn (Vn, En)
. In the GUI, the
connec
tion
s

to the neighbor
s

achieved in this
way are

depict
ed by red lines.


4)

If any of
the
node
s that belong

to G1, G2,..Gn
has

reached the distance 2r from the right

edge,
than the area is considered to be
strongly
barrier
covered and t
he
program terminates

returning
minimum number of gaps
g = 0 and
minimum
number of needed mobile nodes
m = 0
.

5)

If not, f
ind the rightmost node
i

from
graph

G1
.


6)

From the rest of the nodes (that do not belong to
any of the graphs) f
ind the node
j

which is
closest to
i

and where
X
j
>X
i
.

T
his node will be
positioned
at
a
distance larger than 2r

from node
i
, otherwise it would be reached by some of the
graphs.
Now c
onnect
i

and
j

(in GUI

depicted by
black line)
.

Increment
g
, a
nd find the parameter
m

If
:

0
)
2
mod(
)
2
(


r
r
d
ij



m
r
r
d
m
ij



2
2











(1
2
)

e
lse
:

m
r
r
d
m
ij




1
2
2











(
13
)

In (1
2
), quotient of the two
integers

is
the integer
number which returns the whole number part of
the result.
In simulation program, the d
istance
ij
d
is approximated to the integer value.

7)

Perform the routine
(such as one in step 3)
to
construct the connected graph starting from
the
point j.

8)

If the new rightmost node
i

(of the new graph)
has not reached the dist
ance smaller than 2r

from D, the
n repeat from step 6. Otherwise
return the values
g
1

and
m
1
.

9)

Repeat from step 5 for the graphs G2,…Gn.

10)

Return

g

=
MIN (g1, g1,

,
gn
)

and

m = MIN (m1,
m2,..
, mn
)
.


When
the algorithm

terminates,

only one
of
the
graphs G1, G2,
… Gn

will
be selected to
provide
the
full
barrier coverage
from S to D

(Fig
.

7
)
.
It will contain the
additional links created from the potentially added
mobile nodes.


Fig
.

7
:
The G
raphical
U
ser
I
nterface


Description:
Example of
50 nodes of 30
m
sensing range deployed
uniformly
on the rectangular area
200x900 m2.

Nodes are numerated.
In this implementation 4 gaps are found (between
nodes
44 and 48,
48 and 28, etc.). In order to mend those gaps, 5
additional
mobile
nodes are neede
d.

8


The r
ed
lines
present
the connections
of each sensor
with
its
neighbors while the black
lines

are the gaps that
are needed to be mended.


In a network
with
normal distribution

deployment
along y axis, this
greedy
algorithm gives the minimum
number of
potentially mobile
sensor nodes that
are
needed to be
added in order the network to provide the
full barrier coverage.
Still, in
the
case of
the
uniform
distribu
tion, there
are some specific situations whe
n

the
results
of this

algorithm
might
theoretically
slightly differ
from
the optimal (minimum) number of needed sensor
nodes
.
These
situations are excluded
from the analysis
and
will be addressed in a future work

(where the
research will be extended to the issues of energy
consumption and routing protocols)
.

Results
of the 500 deployments
for the uniformly
distributed network and uniform
-
normal distributed
network
(for σ = 30)
are shown in Fig
.

8

and
Fig. 9
,
respectively
.



Fig
.

8
:
Number of barrier gaps

(g)

and the minimum
number of additionally needed
mobile
nodes
(m)
for
achieving the
strong
barrier coverage

in a uniformly
distributed network
.

Description:

The chart gives
values
g

and
m

for two
different radiuses, with respect to

the number of sensor
nodes (horizontal

axe) on
uniformly distributed network
across the 180x1200m2 region.





Fig
.

9
:
Number of barrier gaps

(
g
)

and the minimum
number of additionally needed
mobile
nodes
(
m
)
for
achieving the
strong
barrier coverage

in a network
deployed based on normal distribution along vertical
axe perpendicular to the barrier direction.

Description:

The dependence of v
alues g and m

for
two different radiuses to the number of sensor nodes
a
cross the 180x1200m2 region

where the network is
deployed based on normal distribution along vertical
axe perpendicular to the barrier direction.

In the case of σ = 1
0 (where 60x1200 m2

region is
covered),
with increasing the number of nodes and
enlarging

the
sensing radius
,

the values of
g

and
m

become equal
. With decreasing
the parameter
σ, they
also have a tendency to become similar to the values
derived from the uniform distribution on the same area.
Table II gives the simulation results in the case
th
e
network
is
deployed based on normal distribution
(
σ =
10

and r = 18
m
)
.



n=80

n=120

n=160

n=200

n=240

g

9

4

2

0
-

67 %,
1

-

2
3 %

2


10 %

0
-

98%

1
-

2%

m

10

4

2

0
-

67 %,
1

-

2
3 %

2


10 %

0
-

98%

1


2%

TABLE II:

Dependence of
the
number of gaps

(g)

and
number of additionally needed mobile nodes
(m)
on
the number of initially deployed static nodes.

Description:

Table shows

the influence of the number
of nodes on optimizing the ratio g/m
.
In the sense of
energy efficiency

it is important to make a bal
ance
between the
m

and

the level of the probability needed
for a specific purpose, while keeping the ratio m/g as
closer to the value 1 as possible.



Results are
especially
important
when 200 and 240
nodes are deployed. In
the
first case, strong barrier
coverage is provided with the probability of 0.67

and
chances of having two breaks in the barrier are around
10%
. In the second case, the strong barrier coverage
probability is almost always provided.

Figures
8

and
9

show that, by increasing the number
of
static

(non
-
mobile) nodes, t
he
minimum
number of
0
10
20
30
40
50
60
70
80
120
160
200
g, m

Number of nodes

g, r=10
m, r = 10
g, r=18
m, r = 18
0
10
20
30
40
50
60
70
40
80
120
160
200
g, m

Number of nodes

g, r=10
m, r = 10
g, r=18
m, r = 18

9

gaps has the tendency to become
the same as
the
minimum
number of
mobile
nodes

needed
to
fill
these
gaps.
By enlarging
the
radius, this phenomenon is
achieved faster.
In fact, b
y
increasing
the number of
static nodes, and especially the sensing radius,
the
distance
s

between the
disconnected sub graphs
becomes smaller
. In this case, most of
the left and the
right edges of the gaps (
i

and
j
, respectively), will
satisfy
th
e inequality:


r
d
ij
4




















…(14
)


For example, when
160
-
200 nodes of 18m sensing
radius are deployed

(Fig.

8
)
,

the value of
g

becomes
approximately the same as the value
m

(
g

m
)
.

In line
-
based deployment
(Fig.

9
), this is achieved with the
smaller number o
f sensor nodes (approximately 12
0).

Figures 8

and
9

also show that the influence of
sensing radius on barrier coverage is much higher than
the influence of number of the deployed nodes. For
example, in
th
e
sense of barrier coverage, 40 nodes of
18m sensing radius
need less energy for
moving the
mobile nodes
than 200 nodes of
10m sensing radius.
This
degree of influence
is not
present in
the
case the
vertical coverage.

Figures
6, 8
, and
9

show

that
nodes with
the
smaller
sensing radius (
around
10
m

or smaller
)
are

generally
not

appropriate to provide the barrier coverage

(when
the target
aims to cross the strip and when it
knows the
position of the sensor nodes)
.
They can, however be
used to detect th
e target crossing the region
when

the
target does not know the position of the nodes and
when
the
communication (i.e., radio) radius is at least
several times larger than sensing radius.

On the other
hand, for the given area dimensions,

200 nodes of 18
m
sensing radius can almost surely provide vertic
al
coverage of the area (with

no
additional nodes
needed
)
whereas
only
3
-
6 nodes for σ=30
(Fig. 9)
and 1
-
2

mobile nodes
for σ
=1
0
(Table II)
placed

in network gaps
would be needed to achieve
both
full barrier a
nd vertical
coverage of the

region
.
I
n this case, if the energy
consumption of the mobile nodes is not critical, the
number of 80 deployed nodes would give good barrier
and vertical coverage performances of the network. In
this case about 20 additional nod
es would provide the
full barrier coverage of the network. This means that the
network would be fully covered by 100 nodes
, which is
less than a half of the needed number when the aim is
to achieve the strong barrier coverage at initial
deployment
.



It is obvious that barrier coverage is much more
meaningful in line
-
based (uniform
-
normal) deployed
network. In
the
case of uniform distribution, in order the
barrier coverage to be effectively
achieved

the
ratio
between the width and the sensing radius

sh
ould be as
small

as possible
.



VI.

C
ONCLUSIONS

AND FUTURE WORK

Observations
on engineering creativity
in scientific
research
([20]
-
[22]) state that

creativity in engineering
,
besides other limitations,

is constrained by feasibility
and practicality. It is
als
o
concerned with
and related to
conforming the observations and experimentation.
In
scope of this framework, t
his
research aims to analyze
the practical implementation of the WSNs in military
applications

i.e., target detection
.

We studied
detectability

in military sensor networks that are
deployed based on specific random distributions.
Depending on the purpose, network deployment is
modeled in two ways. If targets have the equal
probability to be positioned anywhere on the area, the
uniform distributio
n is used as a deployment style. On
the other hand,
in the case of airdropped wireless
sensors,
due to the environment factors such as wind
and geographic terrain, the sensors will be scattered
around the deployment line with some random offsets.
Besides
t
he
analytical approach, simulations are
conducted either to experimentally show the analytical
results or to
additionally investigate
the occurrence of
barriers and the path securing process.

S
imulation
s

provide the way the designer can
approximately asse
ss the number of nodes that are to
be airdropped if σ can be estimated.
Using simulation
results from various implementations of the network
based on normal distribution, and r
elying on analytical
results
derived from
the
case of
uniform distribution
(
wher
e the density
depend
s

only on sensing radius
and the probability of detection), one can
extract
the
needed number of nodes to cover the path of width σ
(or other) with the probability higher than 0.95.

A simulation on vertical detectability, in
the
case the
target crosses the strip
-
like region perpendicularly to
the length of the strip, exemplifies the influence of the
sensing radius on determining the number of sensor
nodes
when the is needed to provide a

certain
probability
value
.

In a network whe
re a number of mobile nodes are
supposed to cover the gaps in
order to provide
the full
barrier coverage, optimal
value in sense of
the
minimum number of mobile nodes is achieved when
the number of gaps equals the number of the needed
nodes. Simulations sh
ow that (except in
the
case of a
very densely deployed network) when the strip width is
expected to be much larger than the sensing radius
(e.g. 18 times larger), uniform distribution is generally
inappropriate. On the other hand
,

as the ratio between
the
width and the sensing radius decreases,
the
number of gaps statistically becomes similar to the
number of the additionally needed mobile nodes.
Furthermore, the
differences
on the degree the
deployment styles influence

the barrier coverage
issue
s

become sm
aller.

Decreasing the variance (by
performing the flight closer to the ground) is the best
method to improve the network deployment quality
when the sensors are thrown from the aircraft. When
this is unachievable,
the
decreasing
of
the ratio
between the
region

width and the sensing radius
and/or
increasing the number of nodes (with the

10

possibility of using mobile nodes)
remain
the

only

alternatives
.

Our future work will be focused on three
-
dimensional
(
analytical and simulation
)

analysis

of the influenc
e of

each of the

predictable
factors
on the positions
and the
sensing capacity
of the airdropped sensor nodes. This
approach is expected to provide greater number of
degrees of freedom for the designer, by increasing the
number of parameters that can be ad
justed.
Consequently,
the overall preciseness of the
derived
results

regarding the concrete implementation
is
expected to be improved
.



R
EFERENCES

[1]

M. Cardei and J. Wu, “Coverage in
Wireless Sensor N
etworks,”
in
Handbook of Sensor Networks
, M.Ilyas

and I. Mahgoub
(eds.), CRC Press, 2004.

[2]

R. Mulligan and H.M. Ammari, “Coverag
e in Wireless Sensor
N
etworks: A

survey,”
Network Protocols and Algorithms
, vol. 2,
no. 2, pp. 27
-
53, 2010.

[3]

A. Chen,
S. Kumar, and T.H. Lai, “Local Barrier Coverage in
Wireless Sensor N
etworks,”
IEEE Transactions on Mobile
Computing,
vol. 9, no. 4, pp. 491
-
504, 2010.

[4]

G. Fan and S. Jin, “Coverage Problem in Wireless S
ensor
N
etwork:

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