TELKOM
NIKA
, Vol.13, No
.1, March 2
0
1
5
, pp. 221~2
2
9
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i1.1263
221
Re
cei
v
ed Se
ptem
ber 28, 2014; Revi
se
d De
ce
m
ber
22, 2014; Accepted Janu
ary 10, 201
5
Received Signal Strength Indicator Node Localization
Algorithm Based on Constraint Particle Swarm
Optimization
Songhao Jia
*
, Cai Yang
Dep
a
rtment of Comp
uter and
Information T
e
chno
lo
g
y
, N
a
n
y
a
ng N
o
rmal U
n
iversit
y
, Na
n
y
ang 4
7
3
061,
Hen
an, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: jsong
ha
o@1
26.com
A
b
st
r
a
ct
Becaus
e the
receiv
ed si
gn
al
strength
ind
i
c
a
tor (R
SSI) va
lue
gre
a
tly cha
nges, th
e dir
e
ct use o
f
RSSI val
u
e
ha
s more
errors
in th
e
positi
oni
ng
proces
s
as
the
bas
is to
c
a
lcul
ate t
he
po
sition
of
anch
o
r
nod
es. T
h
is p
aper
prop
oses
a RSSI no
de
local
i
z
a
ti
on a
l
gorit
hm
bas
e
d
on c
onstrai
nt particl
e sw
a
r
m
opti
m
i
z
at
ion (P
SO-RSSI). In the al
gorit
hm, p
a
rticle sw
arm
opti
m
i
z
at
ion is
used to se
lect anch
o
r no
des
set
w
h
ich are ne
a
r
the unknow
n
node.
T
h
e al
gorith
m
take
s
an ele
m
ent in
the
set,
a
n
d
me
asur
e
d
i
sta
n
ce
betw
een
it an
d
the oth
e
r el
e
m
e
n
ts in t
he s
e
t. T
hen,
the
max
i
mu
m l
i
kel
i
hoo
d
meth
od
i
s
used t
o
calc
ulate
the coor
din
a
te
s. Accordin
g to
the differe
nce
betw
een th
e ca
lculat
ed co
ordi
nates a
nd the
actual c
oord
i
n
a
t
es
of the
anch
o
r n
ode, th
e o
b
tai
n
coord
i
n
a
te of
unkn
o
w
n
n
ode
is corr
ected.
W
hen a
ll th
e
el
ements i
n
th
e
set
perfor
m
suc
h
oper
ation, th
e
statistical
meth
ods ar
e
use
d
to deter
mi
ne t
he co
or
di
nates
of the unk
no
w
n
nod
e. T
he al
go
rithm
e
m
bo
di
e
s
all the r
e
fere
nce p
o
ints
i
n
flu
ence
on p
o
sitio
n
in
g, corrects the error
prob
le
m
on a si
ng
le ref
e
renc
e no
de p
o
sitio
n
in
g in th
e past. T
he
si
mu
lati
on res
u
lt
s show
that
the effect of the PSO-
RSSI algor
ith
m
is more exc
e
l
l
ent.
Ke
y
w
ords
: co
nstraint
particl
e sw
arm o
p
ti
mi
z
a
t
i
o
n
, w
i
rel
e
ss se
nsor
n
e
tw
ork, RSSI alg
o
rith
m,
n
ode
locali
z
a
tion
1. Introduc
tion
With the
ra
pid d
e
velop
m
ent of i
n
tegrate
d
circuit, sen
s
o
r
and
wi
rele
ss netwo
rk
techn
o
logy, Wirel
e
ss
Se
nso
r
Networks
(WSN
) a
r
e more a
n
d
more
con
c
erne
d by all
the
cou
n
trie
s
in
t
he worl
d. Wireless se
nsor netwo
rk
i
s
m
a
inly compo
s
ed of th
e
sen
s
or n
ode, th
e
sin
k
node
and m
onitorin
g
cen
t
er, has t
he i
n
formatio
n proce
s
sing
and
informatio
n
comm
uni
cati
on
function.
Obt
a
in a
c
curate l
o
catio
n
info
rmation of
sen
s
or no
de
s an
d tran
smit th
em to the
co
ntrol
cente
r
, is cri
t
ical for WS
N. Accordi
n
g
to
whethe
r
need
rangi
ng
, positionin
g
algorithm
s
are
divided i
n
to
rang
e b
a
sed
localization
algorith
m
(Range
-ba
s
e
d
) and
rang
e
free l
o
calizat
ion
algorith
m
(Ra
nge-f
r
ee
). Th
e Ran
g
e
-
ba
sed algo
ri
thm
measures di
stance o
r
rang
e paramete
r
s of
unkno
wn no
de to locate.
It has the
advantag
e
of high positio
ning accu
ra
cy, but requires
addition
al ha
rdwa
re
su
ppo
rt. The Range
-free
algo
rith
m only de
pen
ds o
n
the
co
nne
ctivity of the
netwo
rk to a
c
hieve th
e p
o
sitioni
ng. Compa
r
ed
with
the Rang
e-b
a
se
d alg
o
rith
m, this alg
o
ri
thm
has t
he
relati
vely small p
o
we
r
con
s
u
m
ption, an
d
the po
sitionin
g
accu
ra
cy i
s
lo
we
r than
the
former
cal
c
ul
ation. Becau
s
e the ab
ove
two ty
pes of
locali
zation
algorith
m
s h
a
ve advanta
ges
and di
sa
dvan
tages, p
eopl
e
ca
re a
bout e
nergy
con
s
u
m
ption an
d p
r
eci
s
io
n po
siti
oning
and
ho
pe
to get the best service at minimum cost.
Re
ceived Si
gnal Stre
ngt
h Indicator
(RSSI
) lo
cati
on alg
o
rithm
is a rang
e
based
locali
zation
a
l
gorithm. It use
s
the
rel
a
tionship bet
wee
n
co
mm
unication di
stance
s
a
nd
the
received si
gn
al stren
g
th, to calculate the coo
r
di
nat
es of unkno
wn nod
es. T
he co
st of RSSI
locatio
n
algo
rithm is lo
w, so the
appli
c
ation is
ve
ry extensive. At pre
s
ent, this algorith
m
ha
s
some
sho
r
tcoming
s
, for example, the mea
s
ur
ed
position e
r
ror is la
rge
r
under
differen
t
environ
ment.
No
w, a lot
of schola
r
s a
nd expe
rt
s
st
udy the RSS
I
algorithm.
S. Elango et
al
pre
s
ente
d
a low cost ZigB
ee ba
sed WSN impleme
n
tation for in
door p
o
sitio
n
monitoring i
n
a
home autom
a
t
ion applicatio
n. The real
-time kno
w
le
dg
e of the location of person
nel, assets, a
nd
portabl
e in
struments
ca
n i
n
crea
se h
o
m
e
automat
io
n
control effici
ency [1]. Jo
sé Antonio G
ó
mez
Martin et
al p
r
esented
a re
sea
r
ch
a
nd a
develo
p
ment
of a fin
g
e
r
pri
n
t-indo
or-po
s
i
t
ioning
syste
m
usin
g the Re
ceived Sign
al
Strength Indication of a
Wirel
e
ss Sen
s
or
Network [2]. In
this stu
d
y,
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 1, March 2
015 : 221 – 2
2
9
222
the autho
rs u
s
e the Interdi
sci
plina
r
y Institut
e for Broadba
nd Te
ch
nology real-lif
e test bed a
n
d
pre
s
ent an a
u
tomated me
thod
to optim
ize and
calib
rate the
experimental d
a
ta
before
offeri
n
g
them to a
po
sitionin
g
en
gi
ne. In a p
r
e
p
roce
ssi
ng l
o
ca
lization
step,
they introd
uce a n
e
w
meth
od
to provide
bo
und
s fo
r the
range, th
ereb
y further im
p
r
oving the
a
ccura
cy of
ou
r
simple
a
nd fa
st
2D lo
cali
zatio
n
algo
rithm b
a
se
d on
co
rrected
dista
n
ce circle
s [3].
Byoungsu Le
e and Se
ung
wo
o
Kim develo
p
ed the
de
sig
n
technol
ogy
of a
se
nsi
n
g
platform
for
the HWR to
perfo
rm a
rol
e
of
both he
alth a
nd life
care i
n
an
aging
society. A fusi
on alg
o
rithm
usin
g RSSI a
nd trilate
ratio
n
is
also
propo
se
d for the
agil
e
self
-lo
c
ali
z
a
t
ion [4].
Gadd
i Blumro
se
n
et al propo
se
d a n
e
w t
r
a
c
king
system
ba
se
d on
exploitat
i
on of
Re
ceiv
ed Sign
al
Strength In
dicator m
e
a
s
urem
ents i
n
WSN.
The
system i
s
ev
aluated in i
n
d
oor
con
d
ition
s
and
ac
hiev
es tra
c
king
resol
u
tion of a
few ce
ntimet
ers
whi
c
h is compatible with t
heoretical bounds [5]. A.LAKSHMI
et al proposed novel energy
efficient algo
rithm FDPCA for Wi
rele
ss Sensor
Netwo
r
ks. Paramete
rs like End to End Delay an
d
Re
ceived
Signal Strengt
h Indi
cato
r a
r
e
co
nsid
er
e
d
for exerci
sing the
influ
ence o
n
tran
smit
power. The
p
r
opo
se
d algo
rithm ca
n effe
ctively sa
ve e
nergy
without
degrading th
e throu
ghput
of
the netwo
rk
and redu
ce t
he ene
rgy consumpti
on
of the netwo
rk [6].Tho
se
document
s p
u
t
forwa
r
d th
e i
m
provem
ent
measures
of the RSSI
alg
o
rithm, but th
ese m
e
thod
s can
only re
d
u
ce
the
effect
s of
tran
sie
n
t disturban
ce. More
over
, th
e po
sitioni
ng
accu
ra
cy i
s
not hi
gh, t
he
effic
i
enc
y
is
low.
Aiming at these p
r
o
b
lem
s
, based o
n
the analys
i
s
of the traditional RSSI p
o
sitioni
ng
algorith
m
, this pape
r prop
ose
s
RSSI node localiz
ation algo
rithm based on co
nstrai
nt parti
cle
swarm o
p
timization. Be
cau
s
e the pa
rticl
e
swarm
o
p
timization al
go
rithm ca
n iterative search t
h
e
optimal sol
u
tion, it is use
d
to find neighbo
ri
ng n
o
d
e
s set of the unkn
o
wn n
o
de, whi
c
h m
eet
certai
n
con
d
itions
or th
re
shold. Th
e no
des in th
e
set are
u
s
ed to
assist lo
cali
zation of u
n
kn
own
node. Sele
ct
a nod
e in t
he set as th
e refe
ren
c
e
node, oth
e
r
node
s in th
e
set a
r
e u
s
e
d
to
measure its l
o
catio
n
by th
e RSSI algo
ri
thm. Co
mp
ari
s
on
of actu
al
coo
r
din
a
te referen
c
e
nod
e,
the erro
r valu
e is
written d
o
wn. By u
s
in
g the
sa
m
e
method, the
coordi
nate
s
of
unkno
wn n
o
d
e
i
s
cal
c
ulate
d
. Then, the erro
r values of referen
c
e n
o
d
e
are u
s
ed t
o
modify coo
r
dinate
s
of the
unkno
wn n
o
de. When
al
l the no
de
s
in the
set
p
e
rform
the
o
peratio
n, the
coo
r
di
nate
s
o
f
unkno
wn no
de are cal
c
ulated by
using statisti
cal
method.
Th
e algorith
m
doe
s not ne
ed
addition
al ha
rdwa
re, du
e to
the introd
ucti
on of pa
rt
icle
swarm
algo
rithm, improve
s
the efficien
cy
and a
c
curacy
of positioni
n
g
. The si
mul
a
tion re
sult
s
sho
w
that the
PSO-RSSI a
l
gorithm i
s
m
o
re
acc
u
rate, and it has
less
error and better performanc
e
.
2. The Algori
t
hm Model
2.1. Particle s
w
arm optimiz
a
tion algorithm
Particle
swa
r
m optimization alg
o
rithm
is a
ki
n
d
of
evolutiona
ry
algo
rithm fo
r glo
bal
optimizatio
n. Inspired by
the
bi
rds
of pre
y
behavio
r, Dr R.Ebe
r
h
a
rt and Dr J.Ken
nedy
p
r
opo
se
d
the algo
rithm
.
In the opti
m
ization
pro
b
lem a
nd no
nlinea
r
p
r
o
c
e
ssi
ng com
b
in
ation
optimi
z
ation
probl
em, parti
cle swa
r
m op
timization alg
o
rithm ha
s ve
ry good effect
[7]-[9].
2.1.1. The principle of par
t
ic
le s
w
arm
optimiz
ation algorithm
Particle
swa
r
m optimizatio
n algorithm i
s
a
stocha
stic
particl
e swarm, and each particl
e
in the parti
cle
s
pop
ulation f
i
nds its
optim
al soluti
o
n
by iteration met
hod p
r
o
c
e
ss.
Assu
me that i
n
a D target se
arch sp
ace, a commu
nity compo
s
ed of
M particl
es.
D dimen
s
io
n
a
l vector said
one
of the particle
s
. As sh
own in equatio
n (1
).
12
(,
)
,
1
,
2
ii
i
i
D
x
xx
x
i
m
(1
)
x
i
said targ
et location of t
he parti
cle i i
n
the
D dim
ensi
on search spa
c
e. In the D dim
e
n
s
ion
sea
r
ch
spa
c
e
,
each
pa
rticl
e
po
sition i
s
a potential
solution, al
so
may be the
optimal
soluti
on.
Thro
ugh put x
i
into the obj
ective fun
c
tio
n
, the ad
aptat
ion value
s
ca
n be
cal
c
ulat
ed, and
mea
s
ure
the merit
s
of x
i
by the fitness val
ue. Assuming v
i
=(
v
i1
, v
i2
…v
iD
) is the speed
of p
a
rticle i. p
i
=( p
i1
,
p
i2
…p
iD
) i
s
th
e optimal
po
sition of the
pa
rticle i.
p
g
=(
p
g1
, p
g2
…p
gD
) is the
be
st po
sition of
pa
rticle
sw
arm so
f
a
r t
o
sear
ch.
Particle
swarm optimizatio
n algorith
m
u
s
ually ad
opts
the followin
g
two form
ula
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Recei
v
ed Signal Strength I
ndicator Node Loca
lization Algorithm
Based on .... (Songhao Ji
a)
223
k+
1
k
k
k
id
id
1
i
d
i
d
2
g
B
e
s
td
id
()
(p
x
)
()
(p
x
)
vv
c
r
a
n
d
c
r
a
n
d
(2
)
k+1
k
k+1
id
id
id
x
xv
(3
)
(1)
c
1
, c
2
is ca
lled le
arni
ng
factor.
In m
o
st
ca
se
s,
c1
=c2=2.
The
be
st ran
ge i
s
fro
m
0 to
4,
and the effect more than
4 or le
ss tha
n
0 optim
ization algo
rithm
s
is not very
good. Lea
rni
n
g
factors i
s
u
s
ed to g
u
ide
and p
r
om
ote
the optimal
particl
e to th
e optimal val
ue an
d the
e
n
tire
popul
ation of all particl
es [1
0, 11].
(2) r
1
, r
2
is a numbe
r of ran
dom dist
ributi
on value from
0 to 1.
2.1.2. Proces
s of par
t
icle s
w
a
r
m op
timization alg
o
rithm
The sta
nda
rd
particle
swarm optimiz
atio
n pro
c
ed
ure is as follo
ws:
Step 1
: Initialize the particle p
opu
lation.
Step 2
: Adaptive va
lue of each p
a
rticle i
s
cal
c
ulated.
Step
3
: Accordi
n
g
to the
value
of ea
ch
pa
rticle
cal
c
ul
ate
d
in
Step
2,
their i
ndividu
al optim
al
s
o
lution is
updated. At the s
a
me time, the
o
p
timal
so
lution of
grou
p is fou
nd, a
nd th
e
index value is stored.
Step
4
: Usi
ng th
e
formula
(2
)
and fo
rmul
a
(3
),
spee
d
and
po
sition
of ea
ch
pa
rticle
are
recalculated.
Step
5
: Judg
e
whe
t
her the
fitne
s
s value
rea
c
he
s the
pre
determi
ned
requireme
nts
or the
maximum nu
mber of itera
t
ions is rea
c
hed,
if met, then end the
iteration. Oth
e
rwi
s
e,
Step 2 is turn
ed.
2.2. The max
i
mum likelih
ood estima
t
ion method
Suppo
se no
d
e
p
1
(x
1
, y
1
), p
2
(x
2
, y
2
), p
3
(x
3
, y
3
)…p
n
(x
n
, y
n
) is the anchor no
de. M(x, y) is
the unknown
node. d
1
, d
2
, d
3
…d
n
is expre
s
sed a
s
the dista
n
ce
betwe
en an
chor no
de an
d
the
unkno
wn no
d
e
M. Acco
rdi
ng to the ge
o
m
etric
kn
owle
dge, the follo
wing e
quatio
n formula
ca
n
be
obtaine
d.
22
2
11
1
22
2
22
2
22
2
nn
n
(x
x)
(
y
y
)
(x
x)
(
y
y
)
...
(x
x)
(y
y
)
d
d
d
(4
)
In
the formula (4), the first equatio
ns, the second equations...the n-1 equations
seq
uentially
minus the n e
quation
s
, dra
w
the followi
n
g
equatio
n formula.
22
2
2
2
2
1n
1
n
1n
1
n
n
1
22
2
2
2
2
2n
2
n
2n
2
n
n
2
22
2
2
2
2
n-
1
n
n-
1
n
n-
1
n
n
-
1
n
n
n
-
1
2(
x
x
)
2
(
)
2(
x
x
)
2
(
)
..
.
...
...
2(x
x
)
2
(
)
yy
x
xyy
d
d
yy
x
x
xyy
d
d
y
yy
xx
y
y
d
d
(5)
The equatio
n
,
X= (A
T
A)
-1
A
T
b, i
s
dra
w
.
Acco
rdi
ng to
this
equ
atio
n, the u
n
kno
w
n
nod
e
locatio
n
of M can b
e
cal
c
ul
ated.
1n
1
n
n-
1
n
n-
1
n
2(
x
x
)
2
(
)
,
.
..
..
.
2(x
x
)
2
(
)
yy
x
XA
y
yy
(6
)
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930
TELKOM
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015 : 221 – 2
2
9
224
22
2
2
2
2
1n
1
n
1
n
2
2
22
22
n-
1
n
n-
1
n
n-
1
n
...
x
xyy
d
d
b
x
xy
y
d
d
(7)
3. The Desig
n
of Algorith
m
3.1. The idea
of algorithm
(1)
RSSI values
of all nodes i
n
WSN a
r
e colle
cte
d
, and the RSSI values a
r
e conv
erted to the
distan
ce
With the increa
se of distance, wi
rele
ss
sign
al wil
l
be regul
arl
y
attenuated
. This
attenuation h
a
s great influ
ence
on the positio
ning a
c
cura
cy of RSSI. So we should
choo
se
a
suitabl
e atten
uation mo
del
of wirel
e
ss si
gnal. The
co
mmonly used
wirel
e
ss cha
nnel p
r
op
agat
ion
attenuation
model
in
clud
es
Fre
e
Sp
a
c
e P
r
op
agati
on M
odel
(F
ree
-
Spa
c
e
M
odel) a
nd
L
og-
distan
ce
Distribution Mod
e
l
[12],[13].
The Free-Sp
ace mo
del is
sho
w
n in formula (8
):
)
lg(
10
)
lg(
10
44
.
32
0
f
k
d
k
Loss
(8)
Whe
r
ein, Lo
ss
rep
r
e
s
ent
s the ch
ann
el att
enuatio
n (unit: dB),
d said the
distan
ce
betwe
en the
test point an
d sou
r
ce di
stance (u
nit:
km), f represe
n
ts the si
gnal
freque
ncy (u
nit:
MHz), k said
attenuation fa
ctor.
Becau
s
e
of the sig
nal
interferen
ce
and
the
o
b
sta
c
le fa
cto
r
s, the
Log
-distan
c
e
Distri
bution
model is oft
en use
d
to determi
ne the relation
shi
p
betwee
n
si
gnal strength
and
distan
ce. The
Log-di
stan
ce
Distrib
u
tion
model is
sho
w
n in form
ula
(9):
X
d
d
k
d
PL
d
PL
)
lg(
10
)
(
)
(
0
0
(9
)
In formul
a (9
), d
rep
r
e
s
en
ts the
dista
n
c
e
between
the
curre
n
t n
ode
and
the
so
urce
node. PL(d
) i
s
the path loss at the recei
v
ing node. X
σ
said Ga
uss distribute
d
ra
ndom varia
b
l
e
s,
the averag
e value of which is 0. The ra
nge of it
is 4~10. k rep
r
e
s
ents the atte
nuation fa
ctor, in
different ci
rcu
m
stan
ce
s, its value
is different, which ra
nge is 2
~
5.
Gene
rally, kn
own tran
smit node'
s
signa
l stren
g
th, the re
ceiving n
ode'
s si
gnal
stren
g
t
h
and the gai
n of the antenn
a, using form
ula (1
0
)
can g
e
t the chan
ne
l attenuation
value.
R
S
S
I
P
G
-
P
L
(d)
(10
)
In formula (1
0), P represe
n
ts tran
smit pow
er, G sai
d
antenn
a g
a
in. By formula (10
)
,
PL(d) can
be
obtaine
d. d
0
is the
refe
rence di
stan
ce, usually is
taken
a
s
1m.
Putting it into
formula (8), PL(d
0
)
can
b
e
obtaine
d. Putting PL(d
)
and PL(d
0
) in
to the formul
a (9
) ca
n get
the
requi
re
d dista
n
ce d.
(2) T
he intro
d
u
ction of pa
rticle swa
r
m op
timization alg
o
rithm
Pa
r
t
ic
le sw
arm a
l
g
o
r
i
th
m is
a pr
oc
es
s
o
f
fin
d
i
n
g
th
e p
a
r
t
ic
les
op
tima
l
s
o
lu
tio
n
th
r
o
ug
h
con
s
tant ite
r
a
t
ions. Th
e cu
rre
nt optimal
values
are u
s
ed to
find th
e glob
al opti
m
um. Based
on
the parti
cle
swarm
algo
ri
thm, the anchor n
ode
s a
r
e obtai
ned,
whi
c
h a
r
e n
ear a
r
o
und t
he
unkno
wn no
de. These a
n
ch
or no
de
s form a set. Becau
s
e th
e node
s in
WSN a
r
e ra
ndom
relea
s
e, thi
s
will ca
use so
me parti
cle
s
random m
o
vin
g
aro
und, not
to get the fastest
way to find
optimal
soluti
on. In order to avoid the
o
c
curren
ce
of su
ch a
situati
on, re
st
ri
ct
iv
e con
d
it
ion
s
a
r
e
adde
d, and t
he cou
r
se of
finding the
o
p
timal soluti
o
n
is im
prove
d
. In the com
pari
s
on
process,
the improved
method
rele
ase
s
the
nod
es
whi
c
h a
r
e
far from
the
optimal
soluti
on. By red
u
ci
ng
the times of compa
r
ison, the iter
ative am
ount is re
du
ced [14]-[16].
Specific
step
s are a
s
follo
ws:
Step l: initialization paramet
ers of PSO.
Step 2: Get the parti
cle swarm fun
c
tion
equatio
n:
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Recei
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ed Signal Strength I
ndicator Node Loca
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Based on .... (Songhao Ji
a)
225
2
ir
i
i
Ff
d
(11)
Among them,
22
ii
i
f
xx
y
y
.
Step 3: Com
pari
s
on
of the cal
c
ulate
d
particl
e soluti
on with the
resp
ective opt
imal
solutio
n
s, th
e
be
st solution
is fo
und. By
comp
ari
s
o
n
, better
valu
e are upd
ated and repl
aced.
Save the current be
st value of the optimal tr
aversal,
continu
e
to repeat, the global optima
l
solutio
n
are f
ound in the
whole po
pulati
on.
Step 4: Whe
n
the co
ndition is rea
c
he
d (arriv
ed at
the thre
shol
d
or the trave
r
sal is
compl
e
ted
)
, the algo
rithm i
s
end. All sol
u
ti
ons a
r
e so
rted, and the
optimal app
ro
achi
ng no
de
set is obtai
ne
d.
(3)
Cal
c
ulatin
g the coo
r
din
a
tes of the un
kno
w
n n
ode
Each an
ch
or
node of the set is taken o
u
t,
and its positionin
g
is m
easure
d
by other
anchor
nod
e
s
in the
set.
Then, the
maximum likelihoo
d meth
od is
used t
o
cal
c
ul
ate the
coo
r
din
a
tes o
f
the an
ch
or
node.
Com
p
a
r
iso
n
with th
e
actu
al
coo
r
d
i
nates, th
e e
r
ror value
is
obtaine
d. Th
e un
kno
w
n n
ode i
s
locate
d by usin
g th
e sam
e
meth
od, the coord
i
nate value i
s
obtaine
d. Accordin
g to
the
error value
of
an
ch
o
r
nod
e
s
, the
obtain
e
d
coo
r
dinate
s
of u
n
known
node a
r
e
co
rrected. Thi
s
recu
rsi
on, all the elem
ents i
n
the set pe
rf
orm
s
the sa
me ope
ration
,
until the el
em
ents in
the
co
llecti
on t
r
aversal i
s
compl
e
ted. Fina
lly, the meth
od of
statisti
cs i
s
use
d
to cal
c
ul
ate the final coordi
nate
s
of the unkno
wn
node [17]-[1
9
]
.
3.2. The algo
rithm implementa
tion pr
ocess
Based o
n
the
above pro
p
o
s
ed al
gorith
m
s, t
he implem
entation ste
p
s
are a
s
follo
ws:
Step 1: Anchor
nod
es p
e
riodi
cally
send it
s
info
rmation
to other nod
e within
the
comm
uni
cati
on
scope. T
h
is info
rmati
on in
clud
es
ID n
u
mbe
r
, Coordi
nate
po
sition info
rm
ation
and so on. Each n
ode
spread
s in turn.
Step 2: Acco
rding to
different an
cho
r
n
ode
s,
the un
kno
w
n n
ode
cla
ssifie
s
the
received
informatio
n. Whe
n
the
re
ceived signal
excee
d
s
a
ce
rtain th
re
shol
d, the ave
r
ag
e value
of
sa
me
anchor n
ode
RSSI is cal
c
u
l
ated.
Step 3: Acco
rding to RSSI
from stro
ng
to we
a
k
orde
r, the mappin
g
of RSSI value and
the di
stan
ce
between
un
kno
w
n
no
de
and
the
an
cho
r
n
ode
is esta
blished.
Particl
e
swarm
optimizatio
n algorith
m
is u
s
ed to de
rive a set of
anch
o
r nod
es a
d
ja
cent to the un
kno
w
n n
ode.
The an
cho
r
n
ode set: B_se
t = {b
1
, b
2
, …,
b
m
}
Step 4: Sele
ct an
ancho
r node i
n
the
set, the di
stance i
s
m
e
asu
r
ed
by th
e othe
r
element
s in the set. Then,
the maximum likeliho
od method is u
s
ed to calculat
e its coordina
tes
(x
i
, y
i
). Comp
ared
with the
actu
al
co
ord
i
nates (x
ri
, y
ri
),
obtaine
d the erro
r value
△
x
i
(
△
x
i
=x
ri
-x
i
),
△
y
i
(
△
y
i
=y
ri
-y
i
).
Step 5: Th
e
co
ordi
nate
s
of the u
n
kn
own
nod
e a
r
e obtain
ed
b
y
the sa
me
method,
expre
s
sed a
s
: (x, y). According to the e
r
ror val
ue fr
o
m
step 4, the
coo
r
din
a
te (x
, y) is co
rrect
ed.
Then, the coo
r
dinate
s
is o
b
t
ained, expre
s
sed a
s
: (x
ui
, y
ui
). Among them, x
ui
=x
+
△
x
i
，
y
ui
=y
+
△
y
i
.
Step 6: Another elem
ent in the set is taken to
do step
(4), until a col
l
ection iterate
s
over.
Step 7: According to the
ob
tained
coo
r
di
nat
e value
of the un
kno
w
n
node, the
me
thod of
statistics i
s
u
s
ed to
cal
c
ul
ate the finally
coo
r
di
n
a
te v
a
lue of it. Th
e co
ordinate
s
of the un
kn
o
w
n
node i
s
expre
s
sed a
s
the a
v
erage valu
e.
4. The Simulation Results and An
aly
s
is
Based on
co
nventional RSSI
algorithm
,
th
is pape
r p
r
opo
se
s a
RSSI node localizatio
n
algorith
m
based on co
nstraint particl
e swarm optimization. In orde
r
to verify the
performanc
e
of
the new
alg
o
rithm, sim
u
l
a
tion expe
ri
ment us
es t
he MATLAB
2012, which
provide
s
wi
rele
ss
sen
s
o
r
netwo
rk
simulatio
n
environm
ent
for the simu
lation experi
m
ents to hel
p better an
al
ysis
res
u
lts.
Evaluation Warning : The document was created with Spire.PDF for Python.
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93-6
930
TELKOM
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Vol. 13, No. 1, March 2
015 : 221 – 2
2
9
226
4.1. The algo
rithm implementa
tion pr
ocess
In orde
r to better test the perform
an
ce
of
the new algorith
m
, in the simulatio
n
of the
actual
enviro
n
ment, wi
rel
e
ss sen
s
o
r
n
e
twork
nod
e
s
rand
omly
deploye
d
in
a network
re
gion
[20],[21].
The expe
rime
ntal para
m
ete
r
setting
s are as follo
ws:
(1) T
he ra
nge
of measu
r
ed
regio
n
: the sq
uare a
r
e
a
of 100m * 10
0m
(2) Th
e total
numbe
r
of no
des is 10
0. A
m
ong
th
em, t
he a
n
chor no
des are
re
sp
ectively
10, 15, 20, 25, 30, 35, 40, 45,
and
50. The po
si
tions of the
unkno
wn no
des a
r
e rand
omly
gene
rated by
MATLAB 201
2. The simul
a
tion run
s
100
times.
(3) Commu
ni
cation radiu
s
: Communi
cation radi
us
of node is 1
0
-10
0
m; the starting
value is set 50m.
(4) T
he si
mul
a
tion expe
rim
ent
usin
g the
sha
d
o
w
ing
m
odel which ha
s refe
ren
c
e
di
stan
ce
d
0
=1 an
d P (d
0
) = -40.
(5) G
a
u
ssi
an
distrib
u
tion varian
ce x
σ
=2.
All the simula
tion data are
averag
e valu
es, obtain
ed throu
gh ma
ny simulatio
n
s.
Nod
e
relative
positionin
g
error can be
rep
r
e
s
ente
d
by the deviation of estima
ting the
positio
n and t
he actu
al location. As sho
w
n in form
ula
(12):
%
100
)
(
)
(
2
2
R
y
y
x
x
e
r
e
r
i
(1
2)
Among them,
(x
r
, y
r
) said t
he a
c
tual no
de po
sition i
n
formatio
n, (x
e
, y
e
) rep
r
e
s
ents the
estimated n
o
de po
sition in
formation, R
said n
ode
co
mmuni
cation
radiu
s
.
The average
locali
zation
error rate is
expr
e
s
sed a
s
all node
s averag
e erro
r rate. As
sho
w
n in formula (1
3):
n
n
i
i
1
(13
)
Among th
em,
n
rep
r
e
s
ent
s the
nu
mbe
r
s of u
n
kno
w
n no
de
s,
δ
said
n
e
two
r
k averag
e
locali
zation e
r
ror
rate.
4.2. Influenci
ng Factors
The pe
rform
a
nce
s
of two a
l
gorithm
s on the
locatio
n
error a
r
e ob
se
rved throug
h numbe
r
of anchor
no
des, total n
u
m
ber
of nod
es a
nd
com
m
unication
radiu
s
. In ord
e
r to imp
r
ov
e the
simulatio
n
a
c
curacy, thi
s
pape
r u
s
e
s
statistical m
e
thod
s. The
fol
l
owin
g a
r
e
1
00 me
asure
m
ent
res
u
lts.
(1) Effect
s of numbe
r of an
cho
r
nod
es o
n
positio
ning
pre
c
isi
o
n
Thro
ugh
cha
nging
the
nu
mber of a
n
chor
nod
es, t
he different
effects
of two ki
nd
s of
algorith
m
abo
ut positionin
g
erro
r ca
n be
obse
r
ved. T
he an
cho
r
no
de numb
e
r chang
es fro
m
10
to 50, and each in
crea
se
of 5. Co
mpared the erro
r rate of the two
algorithm
s,
the result is as
s
h
ow
n
in
F
i
gu
r
e
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Recei
v
ed Signal Strength I
ndicator Node Loca
lization Algorithm
Based on .... (Songhao Ji
a)
227
Figure 1. Effects of num
ber of anc
ho
r no
des o
n
po
sitioning p
r
e
c
isi
o
n
Figure 1
sho
w
s th
at, in th
e wh
ole
wirel
e
ss sen
s
or n
e
twork, the t
o
tal numb
e
r
of node
s
are fixed, the chang
e of anch
o
r
no
de
s have ce
rtain
degree of influen
ce on the
positionin
g
e
rro
r.
Overall,
with
the incre
a
se in the n
u
m
ber
of
an
chor
node
s, t
he po
siti
oni
n
g
accu
ra
cy
of th
e
traditional
RS
SI algorithm
and the PSO
-RSSI algorit
h
m
co
rresp
ond
ing in
cre
a
se, and the
error
is
redu
ce
d. Co
mpari
ng the t
w
o curve
s
in
the Figure
1,
in the pro
c
e
ss
of increa
sed from 1
0
to 50
anchor no
de
s, the PSO
-RSSI algo
rith
m is bette
r than th
e o
r
ie
ntation of th
e commo
n
RSSI
algorith
m
wit
h
high
a
c
curacy a
nd lo
w
error. T
h
is
sh
ow th
at the
PSO-RSSI al
gorithm
improve
s
positio
ning a
c
curacy, re
du
ce the positio
n
i
ng error fun
c
tion.
But more
th
an a
ce
rtain
ran
ge, thi
s
setting i
s
n
o
t
too large
role. Thi
s
sh
ows that
positio
ning
error chan
ge
is
not obvio
us,
whe
n
a
n
chor
node
s
are a
d
ded to
a
certa
i
n nu
mbe
r
. T
h
is
time, location
erro
r is not redu
cing by si
mply increa
si
ng the numb
e
r
of anchor n
ode
s.
(2) Effect
s of total numbe
r of node
s on p
o
sitioni
ng pre
c
isi
o
n
In the
co
nditi
on of
un
cha
n
ged
of the
an
cho
r
nod
es p
r
opo
rtion
an
d
the total
nu
mber of
node
s i
n
crea
se
s, the
pe
rfo
r
man
c
e
of th
e two
alg
o
rith
ms
perfo
rma
n
ce
a
r
e
as sh
own
in
Figu
re
2.
With the
nu
mber of no
d
e
s in
crea
se
s,
it is
can
be
see
n
fro
m
th
e Figu
re
2 th
at the po
sitio
n
ing
errors of th
e
two alg
o
rithm
s
sho
w
a
do
wn
ward tre
n
d
.
Unde
r th
e same
con
d
itio
ns, the
avera
ge
positio
ning error of PSO-RSSI algorithm is far le
ss th
an the origin
al RSSI algorithm. With the
increa
se of t
he nu
mbe
r
o
f
node
s, nod
e dist
ri
bution
is mo
re
uniform a
nd
rea
s
on
able,
whi
c
h
redu
ce
s the i
n
fluen
ce on t
he accu
ra
cy of positioni
ng
.
Figure 2. Effects of total nu
mber of no
de
s on po
sitioni
ng pre
c
i
s
ion
0
1
2
3
4
5
6
7
10
15
20
25
30
35
4
0
45
50
numbe
r of an
chor n
odes
The positioning error/
m
RSS
I
PSO-RSSI
10
20
30
40
50
60
70
80
90
100
100
1
3
0
1
60
190
2
20
250
Tot
al nu
mber
of
node
s
T
he a
verag
e pos
ition
ing e
rror
%
RS
S
I
PSO
-
RSSI
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228
(3) Effect
s of comm
uni
cati
on radi
us o
n
positio
ning p
r
eci
s
ion
The g
r
eate
r
t
he ra
diu
s
of communi
catio
n
nod
es,
cov
e
ring
more a
n
ch
or n
ode
s,
and vice
versa. Th
ere
f
ore, by cha
nging the ra
dius of
com
m
unication, its effect is observed o
n
the
algorith
m
of a
v
erage
po
sitioning
error. I
n
this exp
e
ri
ment, the nu
mber
of an
ch
or no
de
s is
a
fixed
value of 20, the other p
a
ram
e
ters are con
s
tant, and the com
m
unication radiu
s
is the
only
cha
nge qu
a
n
tity. Communication ra
d
i
us from 20
m accordi
n
g
to 5m each step until
the
comm
uni
cati
on ra
dius
of 50m, the effect of node co
m
m
unication ra
dius o
n
the al
gorithm of e
r
ror
is ob
serve
d
. The re
sult is
sho
w
n in Fig
u
re 3.
Figure 3. Effects of co
mmu
nicatio
n
radi
u
s
on po
sitioni
ng pre
c
i
s
ion
It is shown t
hat the com
m
unication
radius is
too large or
too small will
affect
the
positio
ning e
r
ror.
When
co
mmuni
cation
radiu
s
i
s
35
meters, the positio
ning e
r
ror i
s
smalle
st.
Therefore, a
c
cordi
ng to the situatio
n in pra
c
tical
appli
c
ation, the app
rop
r
ia
te sen
s
ors a
r
e
sele
cted.
Un
der th
e same
con
d
ition
s
, the ave
r
age
l
o
cali
zatio
n
error
of the PS
O-RSSI algorithm
is
signifi
cantl
y
less th
an t
he
RSSI algo
rithm, th
e
po
sitionin
g
a
ccura
cy i
s
signi
ficantly imp
r
o
v
ed.
This
sho
w
s th
at the new al
gorithm h
a
s b
e
tter perfo
rm
ance.
To su
m up,
by chan
gin
g
numb
e
r of
anch
o
r n
o
d
e
s, total nu
mber of n
o
d
e
s an
d
comm
uni
cati
on radi
us, p
e
rform
a
n
c
e o
f
PSO-RSSI
algorith
m
is better than the origi
nal RSSI
algorith
m
.
5. Conclusio
n
Due
to the i
n
fluen
ce of
env
ironm
ent, the
traditi
on
al
RSSI method
of po
sitioning
error is
large
r
. Beca
use
only co
nsid
er a
sin
g
le refe
re
nce nod
e, the
referen
c
e n
ode d
e
ci
de
the
coo
r
din
a
te of
unkno
wn n
ode
s is to
o l
a
rge. In o
r
d
e
r to solve this p
r
obl
em,
this pa
per
has
prop
osed
RS
SI node l
o
cali
zation
alg
o
rit
h
m ba
se
d o
n
con
s
trai
nt
pa
rticle swarm
o
p
timization. T
h
e
algorith
m
is
mainly manif
e
sted in u
s
i
ng the re
fe
rence nod
es
to modify the locatio
n
of the
unkno
wn no
d
e
. Particle swarm optimi
z
at
ion algo
rithm
is use
d
to select an
ch
or
node
s set ne
ar
the un
kn
own
nod
e. Th
en
the m
a
ximu
m likelihoo
d
method
is u
s
ed to
locate
the
node,
a
n
d
corre
c
t the
m
easure
d
coo
r
dinate
s
. Each
referen
c
e
no
de in th
e set
can
affect the
coo
r
di
nate
s
o
f
the unkno
wn
node. Thu
s
,
the influen
ce of r
and
om
factors on
node p
o
sitio
n
ing is
red
u
c
ed.
Simulation result
s sh
ow that the PSO-RSSI
alg
o
rithm is ind
eed better t
han the ori
g
inal
algorith
m
, red
u
ce
s the po
si
tioning erro
r
and imp
r
ove
s
the positioni
ng accu
ra
cy.
Ackn
o
w
l
e
dg
ements
This
work wa
s su
ppo
rted
by the Educa
t
ion
Dep
a
rtm
ent of Hena
n
province sci
ence and
techn
o
logy rese
arch p
r
oj
ect (1
2A520
0
33) an
d He
n
an Provin
ce
basi
c
an
d fro
n
tier technol
ogy
resea
r
ch proj
ect (11
230
04
1022
5).
0
1
2
3
4
5
6
20
25
30
35
40
45
50
co
mm
un
ic
at
io
n
ra
d
i
u
s
Th
e
pos
it
ion
in
g e
rr
or/
m
RS
SI
PS
O-
RSS
I
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ISSN:
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Recei
v
ed Signal Strength I
ndicator Node Loca
lization Algorithm
Based on .... (Songhao Ji
a)
229
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