Indonesian
J
our
nal
of
Electrical
Engineering
and
Computer
Science
V
ol.
25,
No.
3,
March
2022,
pp.
1518
∼
1528
ISSN:
2502-4752,
DOI:
10.11591/ijeecs.v25.i3.pp1518-1528
❒
1518
An
experimental
e
v
aluation
of
localization
methods
used
in
wir
eless
sensor
netw
orks
Mostapha
Laaouafy
,
F
atima
Lakrami,
Ouidad
Labouidya,
Najib
Elkamoun
Departement
of
Ph
ysics,
Laboratory
of
Sciences
and
T
echnologies
of
Information
and
Communication,
F
aculty
of
Science,
Chouaib
Doukkali
Uni
v
ersity
,
El
Jadida,
Morocco
Article
Inf
o
Article
history:
Recei
v
ed
Apr
24,
2021
Re
vised
Dec
22,
2021
Accepted
Jan
10,
2022
K
eyw
ords:
Centroid
Localization
Localization
accurac
y
MinMax
Multilateration
T
rilateration
WSN
ABSTRA
CT
The
problem
of
localization
in
wireless
sens
or
netw
orks
has
recei
v
ed
considerable
attention
from
researchers
o
v
er
the
past
decades.
Se
v
eral
methods
and
algorithms
ha
v
e
been
proposed
to
solv
e
this
problem.
The
ef
fecti
v
eness
of
these
algorithms
depends
on
the
accurac
y
of
the
estimated
positions
and
t
he
information
required
to
calculate
the
coordinates.
In
this
paper
,
we
propose
to
e
v
aluate
four
of
the
most
commonly
used
localization
methods
in
sensor
netw
orks.
O
ur
study
considers
a
mathematical
description
of
the
studied
methods
in
order
to
e
v
aluate
their
comple
xity
,
and
then
a
practical
implementation
on
the
simulation
tool
Cooja
.
W
e
e
v
aluate
the
performance
of
the
studied
methods
as
a
function
of
the
number
of
deplo
yed
sensor
nodes
and
their
de
gree
of
mobility
in
terms
of
se
v
eral
performance
metrics.
The
objecti
v
e
is
to
r
e
v
eal
the
most
suitable
localizati
on
method
for
a
particular
case
of
deplo
yment.
Impro
v
ement
proposals
are
also
pro
vided
to
impro
v
e
the
most
rele
v
ant
localization
method
for
the
in
v
estig
ated
study
.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Mostapha
Laaouafy
Departement
of
Ph
ysics,
Laboratory
of
Sciences
and
T
echnologies
of
Information
and
Communication
F
aculty
of
Science,
Chouaib
Doukkali
Uni
v
ersity
Jabran
Khalil
Jabran
A
v
enue,
B.P
299-24000,
El
Jadida,
Morocco
Email:
mostapha.laaouafy@gmail.com
1.
INTR
ODUCTION
W
ith
the
proliferation
of
smart
objects,
localization
has
become
a
critical
component
in
deplo
ying
fu-
ture
IT
servi
ces
and
applications.
These
future
applications
will
mainly
in
v
olv
e
the
e
xchange
of
time-sensiti
v
e,
fresh
and
re
gular
information
for
monitoring
and
control,
as
in
the
case
of
autonomous
v
ehicles
[1].
Although
man
y
localization
met
hods
ha
v
e
emer
ged
for
ad
hoc
netw
orks,
fe
w
of
them
can
adapt
to
all
types
of
en
viron-
ments
and
support
the
multiple
constraints
of
wireless
communi
cations,
most
notably
wireless
sensor
netw
orks.
W
ireless
sensor
netw
ork
(WSN)
ha
v
e
become
increasingly
popular
in
recent
years
a
n
d
ha
v
e
attracted
a
great
deal
of
interest
from
researchers
due
to
their
wide
range
of
applications.
M
an
y
applications
rely
on
the
kno
wl-
edge
of
the
location
of
sensor
nodes.
An
e
v
ent
detected
by
a
sensor
is
only
useful
in
such
applications
if
information
about
its
geographical
location
is
pro
vided.
This
type
of
deplo
yment
requires
calculating
sensor
positions
in
a
x
ed
coordinate
system,
hence
the
need
for
localization
algorithms.
Indeed,
the
localization
of
nodes
is
an
essential
task
in
deplo
ying
a
sensor
netw
ork
to
locate
the
v
arious
e
v
ents
occurring
in
the
monitored
area
and
de
v
elop
protocols
for
routing
the
collected
information,
and
data
aggre
g
ation.
The
performance
of
a
localization
method
depends
mainly
on
its
accurac
y
b
ut
also
on
ener
gy
and
po
wer
consumption.
Sensor
netw
orks
present
particular
ph
ysical
and
transmission
constraints
[2],
which
com-
J
ournal
homepage:
http://ijeecs.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
1519
plicates
the
de
v
elopment
of
a
generic
localization
method
re
g
ardless
of
the
deplo
yed
application.
Locating
mobile
nodes
in
a
sensor
netw
ork
consists
of
determining
these
nodes’
positions
autonomously
and
period-
ically
without
using
a
x
ed
infrastructure.
Some
applications
rely
mainly
on
the
detection
and
reporting
of
the
e
v
ents,
which
require
the
kno
wledge
of
the
e
xact
coordinates
of
nodes
detecting
the
e
v
ent.
Localizat
ion
is
also
necessary
for
close-range
applications
that
allo
w
dif
ferent
users
who
are
ph
ysically
close
to
each
other
to
share
some
of
their
information
and
locate
a
v
ailable
data.
The
importa
nce
of
localization
in
sensor
netw
orks
also
re
v
eals
itself
in
the
management
of
certain
functionalities
specic
to
sensor
netw
orks,
such
as
geographic
routing.
T
o
help
netw
ork
designers
in
determining
which
techniques
are
appropriate
for
their
applications,
au-
thors
in
[3]
present
a
classication
to
compare
dif
ferent
localization
techni
qu
e
s.
This
classicat
ion
is
based
on
se
v
eral
k
e
y
features
lik
e
the
pres
ence
of
anchor(s),
implementation
manner
,
range
measurements,
and
in-
frastructure
type.
Chelouah
et
al.
[4]
pro
vides
a
detailed
classication
of
man
y
algorithms
of
localization
in
mobile
WSNs
(MWSNs).
Localization
techniques,
anchor
-based/cooperati
v
e,
netw
ork
mobility
,
and
informa-
tion
state
are
all
f
actors
that
go
into
the
classication.
Shieh
et
al.
[5]
addresses
the
localization
problem
using
heuristic
optimization
approaches,
whil
e
Darak
eha
et
al.
[6]
proposes
a
distrib
uted
Range-Free
localization
algorithm
called
distrib
uted
cooperati
v
e
and
range-free
localization
algorithm
for
WSNs
(DCRL-WSN),
which
of
fers
high
accurac
y
.
F
or
both
approaches,
the
authors
propose
distrib
uted
algorithms,
which
means
that
the
sensor
nodes
are
responsible
for
processing
and
e
x
ecuting
these
algorithms,
this
can
increase
the
cost
of
com-
putation
and
subsequently
the
po
wer
consumpti
o
n,
leading
to
a
rapid
decrease
in
netw
ork
lifetime,
especially
in
hostile
re
gions.
Zhang
et
al.
[7]
propose
a
three-dimensional
localization
algorithm
that
combines
recei
v
ed
signal
strength
indicator
(RSSI)
and
time
of
arri
v
al
(T
O
A)
ranging
information,
as
well
as
a
single
mo
v
able
anchor
node
to
determine
the
precise
dist
ance
between
the
unkno
wn
node
and
the
anchor
node.
The
maximum-
lik
elihood
estimation
method
based
on
obtained
ranging
v
alues
is
used
to
estimate
the
position
of
unkno
wn
nodes.
Simulation
results
sho
w
that
the
proposed
algorithm
had
lo
wer
localization
ener
gy
consumption
and
higher
localization
accurac
y
,
b
ut
it
requires
a
lar
ge
computing
capacity
.
Zhang
and
W
u
[8]
de
v
elop
a
localization
algorithm
that
allo
ws
estimat
ing
the
positions
of
se
v
eral
sources
in
a
three-dimensional
space
using
direction-of-arri
v
al
(DO
A);
the
results
of
the
simulations
sho
w
that
the
proposed
method
could
reduce
the
computational
cost
without
compromising
the
accurac
y
of
the
estimate.
Ibrahim
et
al.
[9]
suggested
a
ne
w
range-based
localization
algorithm
called
triple
mobile
anchors
for
localiza-
tion
(TMAL).
This
technique
is
based
on
three
mobile
sensors
that
come
together
to
create
a
mo
ving
triangle
capable
of
locating
unkno
wn
sensor
nodes
using
recei
v
ed
signal
strength
indicator
(RSSI).
The
simulation
re-
sults
sho
w
that
this
algorithm
gi
v
es
good
accurac
y
.
Ho
we
v
er
,
authors
did
not
c
o
ns
ider
ener
gy
consumption
since
the
y
assume
that
the
batteries
can
be
char
ged
to
a
v
oid
their
depletion.
In
this
paper
,
we
propose
a
mathematical
modeling
of
four
localization
methods
for
sens
o
r
netw
orks.
W
e
also
conduct
a
comparati
v
e
study
by
simulation
of
the
four
in
v
estig
ated
methods
using
the
Cooja
simu-
lator
.
Our
objecti
v
e
is
to
e
v
aluate
the
deplo
yment
limi
ts
of
the
e
v
aluated
methods
in
the
f
ace
of
the
increase
in
the
number
of
nodes
and
the
netw
ork’
s
mobility
.
Our
w
ork
is
intended
as
a
perspecti
v
e
for
the
impro
v
e-
ment/de
v
elopment
of
a
simple
and
reliable
localization
algorithm
while
considering
sensor
netw
orks’
limits
and
constraints.
The
rest
of
the
paper
is
or
g
anized
as
follo
ws:
Section
2
describes
the
research
method.
Section
3
presents
the
simulation
and
results,
while
section
4
concludes
the
paper
.
2.
RESEARCH
METHOD
Monitoring/controlling
an
area
of
interest
is
one
of
the
principal
purposes
of
wireless
sensor
netw
orks
(WSN)
[10].
The
anchors
are
particular
nodes
of
wi
tch
positions
are
kno
wn
and
allo
w
to
b
uild
a
complete
netw
ork
mapping,
which
is
required
because
a
measurement
reects
the
state
of
a
specic
point.
Localization
algorithm,
measurement
technologies
and
position
calculation
are
the
three
parts
that
b
uild
a
localization
system
[11].
When
there
is
no
kno
wledge
about
the
location
of
a
wireless
sensor
netw
ork’
s
elements
in
the
deplo
yment
en
vironment,
the
collected
data
may
become
of
limited
usefulness.
F
or
an
y
type
of
processing
operation,
it
is
necessary
to
estimate
the
location
of
these
sensors
at
an
y
gi
v
en
moment
and
with
a
high
accurac
y
.
This
can
be
performed
on
the
basis
of
the
assumed
kno
wn
position
of
anchors
and
an
inter
-sensor
range
measurements
such
as
recei
v
ed
signal
strength
indication
(RSSI)
[12].
The
localization
problem
is
still
one
of
the
important
subjects
of
man
y
research
in
dif
ferent
elds.
In
the
follo
wing
paragraphs,
we
present
a
description
of
four
methods
of
localization
most
deplo
yed
by
researchers
in
the
eld,
which
are:
T
rilateration
[13],
Centroid
[14],
An
e
xperimental
e
valuation
of
localization
methods
used
in
wir
eless
sensor
networks
(Mostapha
Laaouafy)
Evaluation Warning : The document was created with Spire.PDF for Python.
1520
❒
ISSN:
2502-4752
MinMax
[15]
and
Multi
lateration
[16].These
methods
ha
v
e
the
adv
antage
of
being
independent
of
satel
lites
and
GPS-based
geolocation
systems.
The
y
are
of
reduced
comple
xity
and
of
fer
high
accurac
y
.
This
mak
es
them
highly
recommended
for
embedded
systems
with
limited
battery
capacity
such
as
wireless
sensor
netw
orks.
2.1.
T
rilateration
This
method
is
based
on
the
kno
wn
distances
between
the
tar
get
and
se
v
eral
anchors
as
well
as
its
spatial
coordinates.
Consider
a
netw
ork
with
three
anchors
B
1
(
x
1
,
y
1
)
,
B
2
(
x
2
,
y
2
)
and
B
3
(
x
3
,
y
3
)
and
a
mobile
node
M(x,y)
that
needs
to
identied
their
coordinates
[13].
T
o
be
gin,
the
recei
v
ed
signal
strength
indicator
(RSSI)
approach
must
be
used
to
determine
the
distances
between
the
mobile
node
and
the
three
anchors.
The
signal
strength
depends
on
distance
and
transmitting
Po
wer
v
alue
and
then
can
be
deplo
yed
to
calculate
the
distance
between
tw
o
sensors.
So,
the
RSSI
[17]
technique
estimates
the
distance
between
a
transmitter
and
a
recei
v
er
based
on
the
the
recei
v
ed
signal
po
wer
of
a
gi
ving
data/control
pack
et.
In
free
space,
the
general
formula
for
calculating
RSSI
is:
P
r
=
P
r
0
−
20
log
10
(
d
d
0
)
(1)
with:
-
d
:
is
the
dif
ference
in
distance
between
the
transmitter
and
recei
v
er
.
-
d
0
:
is
the
user
-specied
distance.
-
P
r
0
:
is
the
signal
strength
estimated
from
the
transmission
rate
at
the
start.
The
data
transfers
allo
wed
the
mobile
to
kno
w
anchor
positions
and
the
triplet
(
D
1
,
D
2
,
D
3)
has
been
produced
by
e
x
ecuting
the
distance
measurement
protocol.
The
mobile
node
can
estim
ate
its
position
by
using
(2)
and
(3)
as
a
guide.
(
X
−
X
1
)
2
+
(
Y
−
Y
1
)
2
=
D
1
2
(2)
(
X
−
X
2
)
2
+
(
Y
−
Y
2
)
2
=
D
2
2
(3)
As
sho
wn
in
Figure
1,
the
sought
position
is
the
point
where
the
circles
C
1(
B
1;
D
1)
and
C
2(
B
2;
D
2)
cross.
In
the
general
scenario,
C
1
and
C
2
intersect
at
M
and
M
′
.
Thanks
to
the
anchor
node
B
3
,
the
mobile
node
position
is
one
of
these
tw
o
points.
Figure
1.
T
rilateration
principle
[18]
2.2.
Centr
oid
As
sho
wn
in
Figure
2,
the
centroid
is
the
point
at
where
the
triangle’
s
three
medians
cross.
The
trian-
gle’
s
gra
vity
center
can
be
determined
by
taking
the
a
v
erage
of
the
X
and
Y
coordinates
of
all
triangle
v
ertices.
The
centroid
localization
method
relies
on
a
thick
layer
of
references,
with
each
mobile
node
recei
ving
noti-
cation
from
a
fe
w
beacons
[14].
By
determining
the
center
posit
ion
of
all
recei
v
ed
anchor
nodes
depending
on
the
assumption
of
round
radio
propag
ation,
e
v
ery
mobile
node
can
estimate
its
location.
The
centroid
localiza-
tion
mechanism
requires
no
cooperation
between
reference
nodes
and
pro
vides
a
decent
le
v
el
of
localization
accurac
y
.
All
anchors
must
communicate
their
coordinates
to
all
mobile
nodes
within
their
transmission
area
to
e
x
ecute
the
centroid
algorithm,
and
all
mobile
nodes
must
compute
their
location
M
(
x,
y
)
using
(4).
M
(
x,
y
)
=
(
x
1
+
x
2
+
x
3
3
,
y
1
+
y
2
+
y
3
3
)
(4)
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
25,
No.
3,
March
2022:
1518–1528
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
1521
Figure
2.
Centroid
principle
[18]
2.3.
MinMax
This
method’
s
principle
consists
of
associating
for
each
anchor
a
container
area
with
the
sensor
node
to
be
located,
as
sho
wn
in
Figure
3.
These
areas
are
constructed
as
(5)
[15].
(
X
i
−
dx
i
;
Y
i
−
dy
i
)
and
(
X
i
+
dx
i
;
Y
i
+
dy
i
)
;
i
=
A,
B
,
C
(5)
The
intersection
of
these
areas
forms
a
ne
w
zone
dened
by
(6).
(
max
(
X
i
−
dx
i
);
max
(
Y
i
−
dy
i
))
and
(
min
(
X
i
+
dx
i
);
min
(
Y
i
+
dy
i
))
;
i
=
A,
B
,
C
(6)
The
sensor
node
M
to
be
located
estimates
its
position
as
the
center
of
gra
vity
of
this
area
using
(7).
(
X
;
Y
)
=
(
max
(
X
i
−
dx
i
)
+
min
(
X
i
+
dx
i
)
2
;
max
(
Y
i
−
dy
i
)
+
min
(
Y
i
+
dy
i
)
2
)
;
i
=
A,
B
,
C
(7)
Figure
3.
MinMax
principle
2.4.
Multilateration
It
is
an
e
xtension
of
trilateration
[14]
that
uses
more
than
three
anchors
to
locate
sensor
nodes.
M
ul-
tilateration
minimizes
the
error
mar
gin
due
to
the
high
number
of
anchors.
The
multilateration
scheme
is
illustrated
in
Figure
4.
The
estimation
of
the
position
of
the
sensor
node
S
using
multilateration
results
from
the
solution
of
(8).
(
x
−
x
Ai
)
2
+
(
y
−
y
Ai
)
2
=
d
2
i
(8)
(
x
Ai
;
y
Ai
)
are
the
coordinates
of
the
anchors
A
i
whate
v
er
i
=
1
..n
(
n
>
3)
while
(
x
;
y
)
are
the
coordinates
of
the
sensor
node
S
to
be
computed.
An
e
xperimental
e
valuation
of
localization
methods
used
in
wir
eless
sensor
networks
(Mostapha
Laaouafy)
Evaluation Warning : The document was created with Spire.PDF for Python.
1522
❒
ISSN:
2502-4752
Figure
4.
Multilateration
principle
[19]
3.
SIMULA
TION
AND
RESUL
TS
There
are
fe
w
studies
on
modeling
and
simulating
localization
methods
in
wireless
sensor
netw
orks.
Authors
focus
generally
on
geolocalization
methods,
where
at
least
one
terminal
is
capable
of
being
located
using
a
satellite
positioning
system
and
a
GPS
recei
v
er
.
These
methods
are
kno
wn
for
their
high
precision
error
.
This
section
pro
vides
a
desc
ription
of
some
e
xamples
of
related
w
orks.
Sheltami
et
al.
[20]
proposed
that
three
kno
wn
localization
protocols
(ngerprint,
centroid,
and
D
V
-Hop)
are
e
v
aluated
in
terms
of
accurac
y
and
po
wer
consumption;
simulation
results
sho
w
that
ngerprint
is
v
ery
accurate
than
centroid
and
D
V
-Hop,
b
ut
the
latest
outperform
in
terms
of
po
wer
consumption
and
stability
.
Grigulo
and
Beck
er
[21]
focused
on
v
alidating
e
xperimentally
the
technique
named
ef
cient
geometry-
based
localization
(EGL).
This
technique
locates
static
sensor
nodes
in
an
e
xperimental
eld
with
an
ef
cient,
distrib
uted,
and
scalable
manner
.
A
unmanned
aerial
v
ehicles
(U
A
V)
system
with
autonomous
i
g
ht
and
a
lo
w-
cost
global
na
vig
ation
satellite
system
(GNSS)
recei
v
er
will
carry
the
mobile
sink
node.
The
EGL
technique
w
as
v
alidated
by
e
xperimental
re
sults
comparing
localization
with
real
time
kinematic
(R
TK)
and
standalone
GNSS
technique.
Priya
and
Ali
[22]
modeled
and
simulated
the
localization
problem
in
WSN
using
an
im-
pro
v
ed
D
V
-Distance
algorithm
combined
with
trilateration
method
to
pre
v
ent
increasing
localization
error
.
The
results
sho
w
that
the
estimated
and
the
e
xact
coordinates
are
v
ery
close.
In
a
pre
vious
w
ork
[18],
we
conducted
a
comparati
v
e
study
in
terms
of
precision
and
ener
gy
con-
sumption
of
the
most
well
kno
wn
and
free
localization
methods
that
are:
trilateration
and
centroid
methods.
The
current
w
ork
presents
an
e
xtension
of
the
pre
vious
study
by
simulating
4
localization
methods:
trilatera-
tion,
centroid,
MinMax
and
reduced
MinMax
(MinMax
method
with
a
minimal
number
of
anchors).
W
e
also
pro
vide
some
perspecti
v
es
for
the
enhancement
of
the
localization
method
that
manifests
the
best
results.
3.1.
Simulation
platf
orm
The
COOJ
A
simulator
stands
for
COntiki
Os
Ja
v
a
simulator
.
It’
s
a
simulator
for
sensor
netw
orks.
The
Contiki
OS
is
a
portable
operating
system
de
v
eloped
for
de
vices
with
limited
resources,
such
as
sensor
nodes
[23],
[24].
Thanks
to
this
simulator
,
we
can
ef
ciently
test
a
code
written
in
C
language
without
using
real
ash
sensors.
W
e
can
a
llocate
an
y
nu
m
ber
of
nodes
o
v
er
a
gi
v
en
area.
W
e
then
visualize
in
real-time
(or
accelerated)
the
e
v
olution
of
the
netw
ork
topology
.
In
a
simulation,
we
ha
v
e
se
v
eral
windo
ws
lik
e
sho
wn
in
Figure
5:
-
The
netw
ork
windo
w
displays
the
netw
ork’
s
graphical
representation
and
sho
ws
us
all
nodes
in
the
sim-
ulated
netw
ork.
-
The
simulation
control
windo
w
is
where
the
simulation
is
started,
paused,
stopped
and
wholly
reloaded.
-
The
notes
windo
w
is
where
we
can
put
notes
for
our
simulation.
-
The
mote
output
windo
w
is
where
the
sensor
outputs
are
printed.
A
te
xt
eld
allo
ws
us
to
enter
a
lter
to
tar
get
a
particular
sensor
or
message
type.
-
The
timeline
windo
w
displays
all
communication
e
v
ents
in
the
simulation
o
v
er
time
and
v
ery
con
v
enient
to
understand
what
is
happening
in
the
netw
ork.
The
mobility
model
describes
the
mo
v
ement
pattern
of
mobile
nodes
and
ho
w
their
loca
lizations
change
in
term
of
speed
and
frequenc
y
.
This
model
denes
also
the
trajectory
of
mobility
.
In
this
w
ork,
we
use
The
random
mobility
model
where
mobile
nodes
that
change
their
positions
randomly
and
periodically
.
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
25,
No.
3,
March
2022:
1518–1528
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
1523
Figure
5.
Cooja
simulator
graphical
interf
ace
3.2.
Localization
accuracy
The
localization
accurac
y
[25]
is
e
v
aluated
by
analyzing
the
error
in
the
deri
v
ed
localization.
A
localization
method
is
m
ore
accurate
when
its
e
rror
is
s
maller
.
The
estim
ated
error
bet
ween
the
mobi
le
node’
s
e
xact
and
estimated
position
is
determined
using
(9).
E
r
r
or
=
p
(
x
exact
−
x
estim
)
2
+
(
y
exact
−
y
estim
)
2
(9)
3.3.
T
rilateration
implementation
The
netw
ork
topology
presenting
the
simulation
scenario
contains
14
s
ensor
nodes
deplo
yed
in
an
area
of
90
×
90
m
2
,
including
eight
mobile
de
vices
and
six
anchor
de
vices.
40
m
is
the
wireless
communication
range,
and
the
transmission
rate
is
40%.
The
mobile
node
starts
e
x
ecuting
the
algorithm
of
the
trilateration
method
by
broadcasting
a
Hello
message
within
its
transmission
range
to
all
anchors.
The
mobile
node
mea-
sures
the
RSSI
v
alue
for
each
beacon
when
a
neighbor
node
responds
to
the
Hello
message.
The
distance
between
mobile
nodes
and
neighbor
anchors
is
calculated
using
(1).
By
resolving
the
equation
system
created
by
(2)
and
(3),
we
obta
in
the
mobile
node
position.
The
(10)
and
(11)
are
the
equation
system’
s
solutions
using
Python
programming
language.
Figure
6
represents
the
simulation
results
and
the
error
between
the
e
xact
and
estimated
positions
in
the
T
rilateration
localization
method’
s.
x
=
−
1
2(
x
1
−
x
2
)
×
(
x
2
1
−
2
x
1
x
2
+
x
2
2
+
y
2
1
−
2
y
1
y
2
+
y
2
2
)
(
y
1
−
y
2
)
×
(
−
D
2
1
y
1
+
D
2
1
y
2
+
D
2
2
y
1
−
D
2
2
y
2
+
x
2
1
y
1
+
x
2
1
y
2
−
2
x
1
x
2
y
1
−
2
x
1
x
2
y
2
+
x
2
2
y
1
+
x
2
2
y
2
+
y
3
1
−
y
2
1
y
2
−
y
1
y
2
2
+
y
3
2
−
q
(
−
D
2
1
+
2
D
1
D
2
−
D
2
2
+
x
2
1
−
2
x
1
x
2
+
x
2
2
+
y
2
1
−
2
y
1
y
2
+
y
2
2
)
×
(
x
1
−
x
2
)
×
q
(
D
2
1
+
2
D
1
D
2
+
D
2
2
−
x
2
1
+
2
x
1
x
2
−
x
2
2
−
y
2
1
+
2
y
1
y
2
−
y
2
2
)
+
(
D
2
1
−
D
2
2
−
x
2
1
+
x
2
2
−
y
2
1
+
y
2
2
)
×
(
x
2
1
−
2
x
1
x
2
+
x
2
2
+
y
2
1
−
2
y
1
y
2
+
y
2
2
))
(10)
y
=
1
2(
x
2
1
−
2
x
1
x
2
+
x
2
2
+
y
2
1
−
2
y
1
y
2
+
y
2
2
)
×
(
−
D
2
1
y
1
+
D
2
1
y
2
+
D
2
2
y
1
−
D
2
2
y
2
+
x
2
1
y
1
+
x
2
1
y
2
−
2
x
1
x
2
y
1
−
2
x
1
x
2
y
2
+
x
2
2
y
1
+
x
2
2
y
2
+
y
3
1
−
y
2
1
y
2
−
y
1
y
2
2
+
y
3
2
+
q
(
−
D
2
1
+
2
D
1
D
2
−
D
2
2
+
x
2
1
−
2
x
1
x
2
+
x
2
2
+
y
2
1
−
2
y
1
y
2
+
y
2
2
)
×
(
−
x
1
+
x
2
)
×
q
(
D
2
1
+
2
D
1
D
2
+
D
2
2
−
x
2
1
+
2
x
1
x
2
−
x
2
2
−
y
2
1
+
2
y
1
y
2
−
y
2
2
))
(11)
An
e
xperimental
e
valuation
of
localization
methods
used
in
wir
eless
sensor
networks
(Mostapha
Laaouafy)
Evaluation Warning : The document was created with Spire.PDF for Python.
1524
❒
ISSN:
2502-4752
Figure
6.
T
rilateration
localization
method
results
3.4.
Centr
oid
implementation
This
method’
s
e
xper
iments
are
carried
out
by
deplo
ying
in
an
area
of
90
×
90
m
2
in
the
Netw
ork
windo
w
of
Cooja
sim
ulator
16
sensor
nodes,
six
of
which
are
anchor
de
vices
and
10
of
which
are
mobile
de
vices.
The
wireless
communication
range
is
40
m,
and
the
transmission
rate
is
40%.
When
we
click
on
the
b
utton
start
in
the
simulation
control
windo
w
,
the
netw
ork
starts
to
communicate.
The
mobile
node
gets
data
from
the
rst
three
beacons
and
uses
(4)
to
compute
its
o
wn
position.
Figure
7
represents
the
results
of
simulations
and
the
precision
error
relati
v
e
to
the
centroid
method.
Figure
7.
Centroid
localization
method
results
3.5.
MinMax
implementation
T
o
simulate
this
method,
we
rst
congure
a
topology
that
contains
18
sensor
nodes,
e
ight
of
which
are
anchor
de
vices
and
10
of
which
are
mobile
de
vices.
The
topology
is
represented
in
the
Netw
ork
windo
w
of
the
Cooja
simulator
by
a
90
×
90
m
2
area
with
a
wireless
communication
range
of
40
m
and
a
transmission
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
25,
No.
3,
March
2022:
1518–1528
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
1525
rate
of
40%.
When
the
start
b
utton
is
pressed,
the
mobile
nodes
be
gin
e
xchanging
data
with
their
neighboring
anchors.
Figure
8
sho
ws
the
simulation
results
and
the
precision
error
for
the
MinMax
method.
Figure
8.
MinMax
localization
method
results
3.6.
Reduced
MinMax
implementation
T
o
simulate
this
method,
we
adopt
t
he
same
sensor
nodes
topology
used
to
e
v
aluate
the
MinMax
method,
b
ut
this
time
we
congure
only
three
anchor
nodes
whil
e
the
other
15
nodes
are
set
as
mobile
nodes
dispatched
in
an
area
of
90
×
90
m
2
with
a
transmission
rate
of
40%
and
a
communication
range
of
100
m.
In
this
method,
the
same
e
v
aluat
ion
principle
of
the
original
MinMax
method
is
replicated
b
ut
with
a
reduced
number
of
anchor
nodes
and
an
increased
transmission
range.
Figure
9
sho
ws
the
simulati
on
results
and
the
precision
error
obtained
for
this
method.
Figure
9.
Reduced
MinMax
localization
method
results
3.7.
Discussion
of
r
esults
T
o
compare
the
dif
ferent
simulated
methods,
we
will
refer
to
their
accurac
y
in
term
of
precision
err
o
r
s.
In
Figure
10
it
is
clear
that
the
localization
error
of
trilateration
and
centroid
methods
e
xceeds
four
meters
while
it
does
not
e
xceeds
one
and
a
half
meters
for
the
MinMax
method.
Therefore
we
can
deduce
that
the
MinMax
An
e
xperimental
e
valuation
of
localization
methods
used
in
wir
eless
sensor
networks
(Mostapha
Laaouafy)
Evaluation Warning : The document was created with Spire.PDF for Python.
1526
❒
ISSN:
2502-4752
method
is
more
precise
than
both
trilateration
and
centroid
methods,
while
the
reduced
MinMAx
method
allo
ws
locating
man
y
mobile
sensor
nodes
with
better
accurac
y
using
a
reduced
number
of
anchors.
Figure
10.
Localization
methods
error
comparison
In
terms
of
ener
gy
consumption
the
trilateration
method
is
the
most
consuming
because
it
uses
the
RSSI
technique
to
estimate
the
distance
between
anchors
and
the
mobile
node
before
running
i
ts
algorithm,
and
this
is
not
the
case
for
centroid
and
MinMax
methods.
T
o
locate
e
v
ery
mobile
node
using
MinMax
method
it
is
necessary
to
associate
for
each
anchor
a
pri
v
ate
container
area
which
increases
the
ener
gy
consumption
unlik
e
the
centroid
method
where
the
anchors
broadcast
their
coordinates
to
e
v
ery
mobile
node
in
their
transmission
area.
So
we
can
conclude
lik
e
sho
wn
in
Figure
11
that
the
centroid
method
consumes
less
ener
gy
than
the
trilateration
and
MinMax
methods.
Figure
11.
Localization
methods
po
wer
consumption
4.
CONCLUSION
W
e
presented
in
this
paper
a
mathematical
modeling
and
a
comparati
v
e
study
throught
si
mulation
of
four
basic
localization
methods:
trilateration,
centroid,
MinMax
and
reduce
d
MinMax.
Simulation
results
sho
w
that
the
MinMax
method
is
more
accurate
thand
other
methods,
while
the
centroid
method
is
concluded
to
be
the
best
in
terms
of
ener
gy
consumption.
F
or
the
centroid
and
trilateration
methods;
it
can
be
noticed
that
their
performance
deteriorates
signicantly
and
rapidly
as
the
number
of
mobile
nodes
increases.
The
reduced
MinMax
gi
v
es
a
v
erage
b
ut
acceptable
results
in
terms
of
accurac
y
and
ener
gy
consumption,
its
performance
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
25,
No.
3,
March
2022:
1518–1528
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
1527
also
de
grades
when
increasing
the
number
of
nodes
and
their
de
gree
of
mobility
,
b
ut
not
as
signicantly
as
the
other
methods.
W
e
are
currently
w
orking
on
impro
ving
the
reduced
MinMax
method
to
enable
its
scalability
while
inte
grating
a
better
netw
ork
management
especially
in
the
presence
of
a
high
number
of
mobile
nodes
or
anchors.
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