TELKOM
NIKA
, Vol.14, No
.1, March 2
0
1
6
, pp. 211~2
1
8
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v14i1.1731
211
Re
cei
v
ed Ma
rch 1
0
, 2015;
Re
vised Novem
ber 23, 20
15; Accepted
De
cem
ber 1
2
,
2015
Robust Localization Algorithm Based on Best Length
Optimization for Wireless Sensor Networks
Hua Wu
1
, Guang
y
uan Zhang
1
, Yang Liu
*1,2
, Xiaoming
Wu
1
, Bo
Zhang
1,3
1
School of Infor
m
ation Sci
enc
e & Electrical
E
ngi
neer
in
g/Sha
ndo
ng Ji
aoton
g Univ
ersit
y
,
Jina
n 25
035
7, Shan
do
ng, Chi
n
a
2
Nation
al Ke
y
Lab
orator
y of
CNS/AT
M
/Beihang U
n
ivers
i
t
y
3
School
e of Informatio
n
Scien
c
e & Engin
eer
i
ng/Sha
n
d
ong
Univers
i
t
y
*e-mai
l
: l
y
03
14
@12
6
.com
A
b
st
r
a
ct
In this pa
per, a
robust ra
nge-f
r
ee loc
a
l
i
z
a
tio
n
alg
o
rith
m by r
eali
z
i
n
g best h
op l
ength
opti
m
i
z
at
io
n i
s
prop
osed for n
ode l
o
cal
i
z
a
ti
o
n
prob
le
m in w
i
r
eless se
nsor n
e
tw
orks (W
SN
s). T
h
is algorit
hm is d
e
rive
d from
classic
DV-H
o
p
meth
od
b
u
t the cr
itical
h
o
p
len
g
th
betw
e
e
n
a
n
y r
e
lay
n
o
des
is
accurat
e
ly c
o
mput
ed
and
refine
d i
n
sp
a
c
e W
S
Ns w
i
th
arbitr
ary n
e
tw
ork co
nnectiv
i
ty. In case
of
netw
o
rk par
a
m
eters h
op
le
ng
th
betw
een
no
de
s can
be
d
e
ri
ved w
i
tho
u
t c
o
mplic
ated
co
mp
utatio
n and
further opti
m
i
z
e
d
usin
g
K
a
l
m
a
n
filterin
g i
n
w
h
ich
gu
ara
n
te
es ro
bustn
es
s eve
n
i
n
c
o
mplic
ated
e
n
viro
nment w
i
t
h ran
d
o
m
n
o
d
e
communic
a
tio
n
range. Esp
e
ci
ally se
nsor fus
i
on tech
ni
ques
used h
a
s w
e
ll
gain
ed ro
bust
ness, accuracy
,
scala
bil
i
ty, an
d
pow
er
efficie
n
cy ev
en
w
i
thout acc
u
rate
d
i
stance
or
an
g
l
e
measur
e
m
e
n
t w
h
ich
is
mor
e
suitab
le i
n
no
nl
ine
a
r con
d
itio
n
s
and p
o
w
e
r li
mite
d W
S
Ns e
n
viro
nment. Si
mu
lati
on res
u
lt
s indic
a
te it ga
i
ned
hig
h
accuracy
compar
ed w
i
th
DV-H
op an
d Centro
id meth
ods in
ran
d
o
m
co
mmu
n
icati
o
n
ra
ng
e
co
nd
iti
ons
w
h
ich prov
es it
gives c
har
acte
ristic
of hi
gh r
o
bustness. Als
o
it nee
ds re
la
tiv
e
ly littl
e co
mp
u
t
ation ti
me w
h
i
c
h
possess
es hi
g
h
efficie
n
cy. It can w
e
ll s
o
lve
local
i
z
a
ti
on
pro
b
le
m w
i
th
ma
n
y
unkn
o
w
n
nos
ed i
n
the
netw
o
rk
and res
u
lts pro
v
e the theor
eti
c
al an
alysis.
Ke
y
w
ords
: W
S
Ns, Local
i
z
a
t
i
on Alg
o
rith
m, Rob
u
stness, H
op Le
ngth Opti
mi
z
a
t
i
o
n
Copy
right
©
2016 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Wirel
e
ss
sen
s
or
networks (WS
Ns) a
r
e
comp
osed o
f
thousa
n
d
s
of tiny and i
n
telligent
sen
s
o
r
s
whi
c
h a
r
e
re
spo
n
s
ible
for thei
r o
r
ga
nizatio
n
, co
nfigu
r
ati
on a
n
d
wo
rking in
o
r
de
r
to
provide
sen
s
ing ta
sks a
s
sign
ed to th
em. As the
developm
ent
of low-co
st and l
o
w po
wer
sen
s
o
r
s, mi
cro-p
r
o
c
e
s
sor
and ra
dio fre
quen
cy circ
ui
try for inform
ation tran
smi
ssi
on, there is a
rapid
develo
p
ment of WSNs [1], whi
c
h
can
b
e
deploye
d
in
large
numb
e
rs a
nd p
r
ovi
de
unprecede
nte
d
opp
ortuniti
es fo
r vario
u
s
ki
nd of
ap
plicatio
ns,
su
ch a
s
milita
r
y surveilla
nce,
environ
menta
l
monitorin
g
, habitat monit
o
ring, a
nd st
ructu
r
al m
oni
toring et
c., [2-5]. The
r
e a
r
e
many chall
e
n
ges in the
s
e
broa
d appli
c
a
t
ions.
Ho
wever sen
s
or no
de lo
ca
lization
ha
s b
e
com
e
the
m
o
st imp
o
rtant
one, n
a
mely
how to
locali
ze un
kn
own
sen
s
o
r
s with smalle
st numbe
r of anch
o
rs tha
t
reduces
co
mputation time,
comm
uni
cati
on overhea
d
s
, and
ene
rg
y con
s
umptio
n
but with
hi
gh lo
cali
zatio
n
accu
ra
cy h
a
s
become a hot
rese
arch topi
c.
One
comm
on
way in the
world i
s
Glo
bal
Positionin
g
System (GPS
) syste
m
. But it is not
s
u
ita
b
l
e
in
WSN
s
b
e
c
a
us
e its
pe
r
f
or
man
c
e d
e
g
r
ad
es
dr
as
tic
a
lly
w
h
en
re
ce
iver
is in
in
d
o
o
r
o
r
locate
d in forest environ
ments. Mea
n
w
hile a
s
a result of con
s
traint
s in si
ze and p
o
wer
con
s
um
ption,
it is u
n
fea
s
i
b
le to e
quip
traditional
G
PS receivers for all
no
de
s in
WS
Ns.
Only
those that ha
ve the features of well fle
x
ibilit
y, convenient mainten
ance and lo
w-co
st upd
ate are
highly need
e
d
. Node lo
cal
i
zation i
s
one
of the importa
nt supp
orting
techn
o
logie
s
i
n
WSNs.
Nod
e
locatio
n
information
should b
e
inclu
ded in the colle
cted
informatio
n so as to
reali
z
e un
kn
o
w
n localizatio
n pro
c
e
ss in the physi
ca
l world. Until no
w many algo
rithms espe
cia
lly
desi
gne
d for WS
Ns environment
have
bee
n p
r
op
o
s
ed
an
d
can
be
so
rted
i
n
to range
-b
a
s
ed
categ
o
ry [6], su
ch a
s
Ao
A (Angle of
Arrival) m
e
a
s
urem
ent [7], ToA (Time
o
f
Arrival), TDoA
(Time
Differe
nce
of Arrival
)
[8, 9], a
nd
RSS (Rec
eived
Signal
Stren
g
th) [1
0, 11].
The
RSS
way
is
sup
e
rio
r
to
the te
chn
o
log
i
es
ba
sed
on
TDOA, TOA
and
AOA [1
0]. The
RSS
-
ba
sed
lo
cati
ng
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 1, March 2
016 : 211 – 2
1
8
212
techn
o
logy h
a
s the ch
aracteri
stics of
low co
st, no extra har
d
w
are req
u
ire
m
ents, ea
sy to
impleme
n
t, which
ha
s be
en wi
dely ap
plied. In
re
cent years, th
e sp
arse tra
n
sformation
and
comp
re
ssed
sen
s
in
g on WSNs lo
cating
resea
r
ch hav
e become the
acad
emic h
o
t
spot.
The
oth
e
r m
a
in catego
ry is
d
e
scri
bed
as ra
n
ge-f
r
ee
. This
one
o
n
ly employ
s
distan
ce
vector excha
nge
and
net
work
conn
ectiv
i
ty to fi
nd the
dista
n
ces be
tween
the
no
n-an
ch
or no
d
e
s
and th
e a
n
ch
or
node
s to realize n
ode
l
o
cali
zatio
n
by
pe
rformi
ng
a
tri-late
ration
or m
u
lti-late
ra
tion
techni
que
[
12, 13]
incl
u
d
ing
DV-hop
[14],
DV
-di
s
tance, APIT,
Eucli
dean,
Amorph
ou
s [
15],
Centroid a
n
d
others. The
differen
c
e
s
betwe
en
ran
ge-b
a
sed a
n
d
ran
g
e
-
free
are that
ran
ge-
based a
ppro
a
ch
es
have
highe
r a
c
curacy but m
o
re expen
sive
hardwa
r
e
a
nd hig
her po
wer
con
s
um
ption
are ne
ede
d a
nd ran
g
e
-
free
ones n
eed n
o
more
comp
licated h
a
rd
ware an
d po
wer
con
s
um
ption
but with rel
a
tively low po
sition esti
m
a
tio
n
error. Th
e para
m
eter th
at determin
e
s its
accuracy is d
e
rivation of h
op length b
e
twee
n two no
des.
In this pape
r, a robust ra
nge-f
r
ee lo
ca
lization alg
o
ri
thm by realizing best ho
p
length
optimizatio
n,
whi
c
h i
s
hi
gh
efficient
and
accu
rate
, i
s
prop
osed. T
h
is al
gorithm
i
s
d
e
rived
fro
m
cla
ssi
c t
w
o
-
di
mensi
onal
DV-Ho
p
m
e
tho
d
but th
e
criti
c
al
hop
len
g
th bet
wee
n
a
n
y
relay
nod
es is
accurately computed
an
d
refine
d in
space WS
Ns
with all
sen
s
ors de
ployed
ran
domly a
nd
arbitrary net
work
co
nne
ctivity. In case of
netwo
rk
para
m
eters hop l
e
ngt
h between
node
s can b
e
derived
with
o
u
t co
mplicate
d
computatio
n an
d fu
rth
e
r optimized
using Kalm
an fi
ltering i
n
whi
c
h
guarantee
s robu
stne
ss e
v
en
in compl
i
cated env
iro
n
ment
with random
nod
e
comm
uni
cati
on
rang
e. Espe
cially sen
s
or f
u
sio
n
tech
niq
ues u
s
e
d
in
this pap
er h
a
s well gain
ed ro
bu
stne
ss,
accuracy, scalability, and power efficie
n
cy even wi
t
hout accu
rate
distan
ce o
r
angle info
rma
t
ion
whi
c
h is mo
re
suitable in n
online
a
r cond
itions.
The co
ntribut
ion of this paper i
s
as fo
llows. A robu
st 3D nod
e locali
zatio
n
base
d
on
prob
ability de
nsity functio
n
analysi
s
i
s
prop
osed a
n
d
in this
algo
rithm the b
e
st hop len
g
th
is
comp
uted
by
usi
n
g
re
gion
al di
re
ction
e
s
timation
an
d refined
by
data fu
sion
t
e
ch
nolo
g
y wi
th
relatively low computatio
n
time and powe
r
co
nsu
m
ption. It has a high ro
bust lo
cali
zat
i
on
accuracy and
rob
u
stn
e
ss. The comm
uni
cation
ra
nge
is n
o
t fixed b
u
t ran
domly
cha
nge
d, whi
c
h
make
s it mo
re suita
b
le in
compli
cted
e
n
vironm
ets.
This b
r
e
a
k th
roug
h the bi
g
gest rest
raint
in
wirel
e
ss sen
s
or networks.
The re
st of the pap
er i
s
orga
nized a
s
follows. Se
ction II gives some
ba
sic
probl
em
statement
an
d pa
ram
e
ter
definition
s
. Hop le
ngth
opt
i
m
ization
with
Kalman filteri
ng a
r
e
de
scri
bed
in Section III. Section IV describes the
whol
e lo
cali
zation al
gorithm and
Section V illustrates the
theoreti
c
al an
d simulatio
n
result
s. Finally, concl
u
si
on
s are liste
d in section VI.
2. Problem Statement a
n
d Paramete
r Defini
tions
2.1. Problem Statemen
t
In ra
nge
-free
localization
algorith
m
s di
st
an
ce betwe
en
u
n
kno
w
n node
s and
a
n
ch
ors
i
s
the key pa
ra
meters an
d b
e
com
e
s the
core p
r
o
c
ed
u
r
e in
the lo
calizatio
n alg
o
r
ithms.
No
rm
ally
this distan
ce
is com
puted
by hop length
and
hop cou
n
ts between
unkno
wn and
ancho
rs. On
ce
the three
sim
ilar di
stan
ce
s are
obtaine
d
the
un
kno
w
n co
ordi
nate
s
can
be
com
puted by m
u
lti-
lateration m
e
thod
s.
In den
sely
d
eployed
WS
Ns,
a
sho
r
te
st multi-ho
p p
a
th bet
wee
n
any pai
r
of th
e sen
s
o
r
node
s m
a
y b
e
existe
d. By disch
a
rgi
ng
one
hop
awa
y
from the
st
art no
de, the
accum
u
lative
distan
ce i
s
likely to be in
cre
a
sed by o
ne tran
sm
i
ssi
on ran
ge [16]
. As suppo
se
d in the front all
node
s
have t
he
same
p
r
o
perty, the
dist
anc
e b
e
twe
e
n
any
pair of
the sen
s
ors
(
St
a
r
t
E
n
d
) can
be a
p
p
r
oxim
ately estim
a
ted by
the t
r
a
n
smi
ssi
on
ra
nge
multiply
the corre
s
po
nding
ho
p
co
unts
betwe
en the
m
[17]. That is also the co
re co
n
c
e
p
t of cla
ssi
c DV
-Hop pro
pag
atio
n algorith
m
.
But in some
bad
enviro
n
m
ent, the d
e
n
s
ity of node
s i
s
very lo
w
whi
c
h i
s
not ad
e
quate to
con
s
tru
c
t a straight and
shorte
st multi-hop path b
e
twee
n two se
nso
r
s. In this situation it is
impossibl
e fo
r a
n
inte
rme
d
i
ate sen
s
o
r
to
be l
o
cated
cl
ose
to the
b
o
unda
ry of th
e
last
one,
whi
c
h
make
s t
he e
s
timated di
sta
n
ce
is far fro
m
the true
va
lue. It mea
n
s
a lot of l
o
cali
zation
erro
rs
are
introdu
ce
d.
In order to
o
v
erco
me thi
s
problem
ho
w to
optimi
z
e
and
refine th
e ho
p le
ngth
betwe
en
node
s be
com
e
critical and
determi
ne
s the final locali
zation accu
ra
cy.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Rob
u
st Lo
cali
zation Algo
rit
h
m
Based on
Best Length
Optim
i
zation for Wi
rele
ss…
(Hua
Wu
)
213
2.2. Parameter De
finition
s
In the
real
WSNs,
sen
s
or
nod
es are
sp
rin
k
led
by
low flying
ai
rplan
e
s o
r
u
n
mann
ed
grou
nd
vehicles, all
of th
em a
r
e
out
of co
nt
rol,
which
ma
ke
s
regula
r
ity and
topolo
g
y of
th
e
netwo
rk o
r
th
e affirmato
r
y
pattern
ha
rd t
o
be
go
tten.
There a
r
e
two ki
nd
s of
no
des in th
em,
one
is calle
d
a
n
ch
or nod
e with definitely
kno
w
n po
sition coordi
nate
s
an
d
the
othe
r
i
s
unkno
wn nod
es
whi
c
h nee
ds to be realized. They are
sprin
k
le
d
together at the
same time. Furthe
rmo
r
e,
all
sen
s
o
r
nod
es are assu
med
to be omni-di
r
ectio
nal
, ho
mogen
eou
s a
nd station
a
ry to some exte
nt,
whi
c
h i
s
to
sa
y the wh
ole n
e
twork
ca
n b
e
se
en
as
sta
t
ic or re
garde
d as a
spe
c
ia
l sna
p
shot of
a
mobile ad h
o
c
se
nsor net
work. Some p
a
ram
e
ters
used in this alg
o
rithm are de
fined as follo
ws.
12
(,
,
,
)
N
Nn
n
n
: Total number of s
e
ns
ors
in 3D WS
Ns
with
i
n
as
the
it
h
node.
VL
L
L
: Locali
z
ation
spa
c
e i
s
a cu
be as the vol
u
me is
V
with si
de length
L
.
/
N
V
:
Nod
e
den
sity
in
th
e
l
o
cali
zatio
n
space whi
c
h subj
ect
s
to
3D
P
o
isso
n
distrib
u
tion [1
8] result
s fro
m
rand
om de
pl
oyment of sensor no
de
s in 3D spa
c
e.
0
()
i
Vn
:
The occu
pi
ed spa
c
e
re
gion with
i
n
n
ode
as the
center and
co
mmuni
cation
rang
e
i
r
as it
s radiu
s
which i
s
a
ran
dom v
a
riabl
e u
p
to i
t
self. We
can
find
3
0
()
4
/
3
ii
Vn
r
. In this
way the sp
ace regio
n
of ea
ch no
de is a
sph
e
re a
nd a
n
y node in it will be seen a
s
its neig
hbo
r.
()
NC
: The num
ber of all se
nsors
in o
ne
sph
e
r
e an
d obvio
u
s
ly
3
()
4
/
3
i
NC
r
and
i
n
is
the cente
r
of the sp
here.
c
N
: The n
u
mb
er of
one
sensor’
s
n
e
ig
hbor
s
and
it ca
n be
ea
sily compute
d
a
s
()
1
c
NN
C
.
(,
,
)
ii
i
i
A
XY
Z
: Ancho
r
no
de
i
A
with
(,
,
)
ii
i
X
YZ
as its
coo
r
din
a
t
e.
Its co
ordinates are
pred
efined
or from GPS b
e
ca
use an
ch
ors
are
a ki
n
d
of node diff
erent from ordinary o
n
e
s
with
high po
we
r a
nd ene
rgy.
In the
pro
p
o
s
ed al
gorith
m
the nu
mbe
r
o
f
hop
length
need
ed
dealt
by Kalma
n
fi
lter for
each time is
set a
s
50
0 to
reali
z
e o
p
tim
i
zation.
In the
model o
n
ly numbe
r of a
n
c
ho
r no
de
s can
be cha
nge
d manually, na
mely percent
age of ancho
rs
. The total numbe
r of se
nso
r
s i
s
fixed at
200, whi
c
h
ca
n well re
present the
real a
pplication env
ironm
ent. No
t
e
that percent
age of an
cho
r
s
in the
network is mu
ch
sm
aller tha
n
that
of u
n
kn
own sen
s
or
no
de
s
i
n
the real
WSN
environ
ment.
3. Hop Leng
th Analy
s
is a
nd Optimiza
tion
w
i
th Kal
m
an Filtering
3.1. Best
Ho
p Length
An
aly
s
is
Suppo
se the
r
e is a sen
s
o
r
node indi
cat
ed as
i
S
with random
comm
unication ra
n
ge
i
r
.
In this way all node
s in the sph
e
re fo
rme
d
by node
i
S
as its center a
n
d
rand
om ra
d
i
us
i
r
are the
neigh
bors of
node
i
S
, which i
s
shown in Fi
gure
1. So as sho
w
n in Fi
g
u
re 1
on
ce st
arting n
ode
i
S
is given th
e
hop le
ngth to
wards end
n
ode
i
E
is at e
a
c
h h
op i
s
de
noted a
s
i
R
whi
c
h i
s
al
so
a
rand
om varia
b
le.
i
S
i
r
i
E
i
r
Figure 1. Formation of hop
length
Fi
gure 2. Best hop length computation
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1
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214
As analyzed
before the
ad
jace
nt hop m
a
y not
on the straig
ht line con
n
e
c
ted fro
m
node
i
S
to
i
E
. A neighb
or
sen
s
o
r
no
de
j
n
who lo
cat
ed ne
are
s
t its boun
dary
sh
ould b
e
sele
cted as th
e
next hop
no
d
e
. Ju
st a
s
sh
own
in Fi
gu
re 1
i
R
is th
e p
r
o
j
ection
of
i
r
on l
i
ne
SE
. In Figure 1 it is
obviou
s
that
31
2
(1
,
2
,
3
)
i
RR
R
R
i
. However this
sp
ec
ial s
e
ns
or
n
o
d
e
3
n
shoul
d b
e
negle
c
ted for
its oppo
site d
i
rectio
n with
SE
, which mean
s for any rela
y sensor no
d
e
, only those
neigh
bors whose positio
n is clo
s
er
to the endin
g
node
E
tha
n
the curren
t senso
r
are
con
s
id
ere
d
for the next hop node. Anot
her proble
m
is how to cho
o
se bet
wee
n
1
n
and
2
n
. As
sho
w
n
in
Fig.1 both
1
n
and
2
n
are in th
e
sam
e
spa
c
e
ci
rcu
l
ar
con
e
A
SB
. He
re
we
c
a
ll
sp
heri
c
a
l
spa
c
e
S
as
1
V
an
d co
mpute
1
R
and
2
R
as
11
1
cos
Rr
and
22
2
co
s
Rr
.
F
i
n
a
lly w
e
s
e
le
c
t
n
ode
2
n
as the next h
op nod
e for
12
RR
.
That is be
ca
u
s
e it is more clo
s
e to co
m
m
unication ra
nge of
node
i
S
.
As
an
alyze
d
before, pa
ra
meter
is criti
c
al be
cau
s
e it
can
de
cide
the size
of spa
c
e
regio
n
whe
r
e
the be
st rel
a
y hop n
ode
s lo
cate. In o
r
de
r to obtai
n the rational
, we supp
ose
there
is a
se
nso
r
nod
e
'
S
on
the i
n
terse
c
tion p
o
int of
SE
and sph
e
re
S
. In this
way the next
optimum hop
length to node
E
can
reach its maximum value
i
r
. The
spe
c
ial inte
rsection spa
c
e
regio
n
2
V
, which is form
ed b
y
sphe
re
S
and
'
S
, can b
e
a
perfe
ct estim
a
tion of the space ste
p
regio
n
for so
urce n
ode
S
. But
1
V
is bette
r
than
2
V
to be se
en a
s
the
opt
imum spa
c
e
becau
se
maximum projectio
n
of se
nso
r
nod
es i
n
21
()
VV
on
SD
is
/2
i
r
whic
h
has lo
w ac
c
u
ra
cy
, whi
c
h
make
s
/3
. In this way optimu
m
spa
c
e ho
p length can be
formed.
3.2. O
v
er
v
i
e
w
o
f
Kalman
Filtering Alg
o
rithm
Although
WS
Ns technol
og
ies
develop
e
d
very q
u
ickl
y, challe
nge
s asso
ciate
d
with the
scarcity of band
width and
powe
r
in wireless
commu
nicatio
n
s hav
e to be addressed. Fo
r the
state-e
s
timati
on p
r
oble
m
s
discu
s
sed h
e
r
e, ob
se
rv
atio
ns a
bout a
co
mmon
state a
r
e the
be
st h
op
length comp
uted
befo
r
e. To
pe
rform state
estima
tio
n
, sen
s
o
r
s m
a
y sha
r
e the
s
e o
b
servatio
ns
with ea
ch ot
her o
r
to form a fusion center for
cen
t
ralize
d
processing. In either sce
n
a
r
io,
the
comm
uni
cati
on co
st in terms of band
wi
dth and po
we
r re
quired to
convey obse
r
vations i
s
large
enou
gh to m
e
rit attention.
Also in
som
e
actual te
sting
environ
ment
(tempe
ratu
re,
pre
s
sure fiel
d,
magneti
c
fiel
d, etc.), the
stat
e ch
ange
s of se
nsor
no
de a
r
e al
mo
st con
s
e
c
utive
,
which fo
rms a
smooth
an
d contin
uou
s curve su
rface.
The
pa
rame
ters in Kalm
an filterin
g
can b
e
p
e
rfo
r
med
easily.
The Kal
m
an
filtering
(KF
)
o
ffers
an
eleg
ant, efficient
and
optimal
solution to
lo
calizatio
n
probl
em
s in WSNs when
the system at
hand
s
is di
st
ributed
and random m
e
a
s
urem
ents e
r
rors
exist [19]. In the pa
per, the
Kalman filter (KF)
b
a
sed approa
ch wa
s
sele
cted
in orde
r
to redu
ce
the effect
s
of hop
len
g
th
e
rro
rs b
e
twe
e
n
an
ch
ors
an
d un
kn
own n
ode
s a
n
d
to
obtain
prope
rty of
robu
stne
ss a
gain
s
t existin
g
errors in
di
stan
ce
me
asurem
ents. T
o
explore thi
s
point, co
nsi
d
er a
vector state
()
p
x
nR
at time
n
and
let the
kth
se
n
s
or colle
ct ob
servatio
ns
()
q
k
yn
R
. T
he
basi
c
line
a
r st
ate and ob
se
rvation model
s are:
()
(
)
(
1
)
()
()
()()
()
kk
k
nn
n
n
nn
n
n
xA
x
u
yH
x
v
(1)
Whe
r
e the driving noise v
e
ctor
()
n
u
is normal Gau
ssi
a
n
noise a
nd
uncorrelate
d across time
w
i
th covar
i
anc
e
matr
ix
()
u
n
C
while the
norm
a
l ob
se
rvatio
n noi
se
()
k
n
v
ha
s
cov
a
ri
an
ce m
a
t
r
ix
()
v
n
C
and is
un
correlated a
c
ross time an
d se
nsors. With
K
vector observation
s
()
k
n
y
available, the
optimum esti
mation of
()
x
n
ca
n be derive
d
usin
g equ
atio
n 1. The rud
e
colle
ction
of these o
b
servation
s
a
n
d
the p
r
o
c
e
s
s
of these
meas
urements
, however, inc
u
r relatively high
power
con
s
u
m
ption with
the pro
d
u
c
t of the numb
e
r
K
of sensors in the net
work. Th
e
comp
utation t
i
mes th
at pro
v
ided to Kal
m
an filterin
g can be co
ntrolled
by
th
e algorith
m
itse
lf
by
cha
ngin
g
parameters of the netwo
rk. An
d in
this
paper this
value is
s
e
t as
500.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Rob
u
st Lo
cali
zation Algo
rit
h
m
Based on
Best Length
Optim
i
zation for Wi
rele
ss…
(Hua
Wu
)
215
4. The Whol
e Algorithm
Realization
In this pa
rt whole alg
o
rith
m whi
c
h
reali
z
e lo
cali
zatio
n
for ea
ch
un
kno
w
n
se
nso
r
nod
e is
depi
cted. Th
e best ho
p length compu
t
ation is
given first an
d
then the whole lo
cali
zat
i
on
algorith
m
is d
e
scrib
ed.
4.1. Best
Ho
p Length
Co
mputa
t
ion
As in
dicate
d
befo
r
e, all
sen
s
o
r
s a
r
e
deploye
d
in
3D
WS
Ns,
subje
c
ting to
Poisson
distrib
u
tion
wi
th nod
e d
e
n
s
i
t
y
/
N
V
[18]. The
n
,
the p
r
ob
abili
ty of
m
sen
s
ors located
withi
n
a
s
e
ns
or
i
n
’s spa
c
e re
gion, na
mely
3
0
()
4
/
3
ii
Vn
r
,
can be
expresse
d a
s
followi
ng eq
uation:
3
0
3
0
4/
3
4/
3
,
!!
i
i
m
m
i
i
Vn
r
i
r
Vn
pm
r
e
e
mm
(2)
Ju
st as th
e
model expl
ai
ned a
nothe
r
equatio
n can
be written a
s
3
1
21
c
o
s
/
3
i
Vr
.
Similarly, the probability
of
m
sen
s
ors
can
be
lo
cat
ed in
a
sp
h
e
re
sp
ace
section
bet
we
en
(,
)
of a sensor’
s
transmissio
n range will be
as follows:
3
1
3
21
c
o
s
/
3
1
[2
1
c
o
s
/
3
]
,
!!
i
m
m
r
i
V
Vr
pm
e
e
mm
(3)
Expand it to
3D sp
ace as
sho
w
n in Fig
u
re 2. We su
ppo
se varia
b
le
x
to be the distan
ce
betwe
en
i
S
and
its next pote
n
t
ial forwardi
n
g
se
nsor. It is obviou
s
x
is a
rand
om va
ria
b
le an
d the
probability of
x
being le
ss th
an
D
can b
e
gi
ven as
D
can b
e
obtaine
d using followin
g
equatio
n.
33
0
2(
1
c
o
s
)
(
)
/
3
,,
,
,
i
N
i
m
rD
p
xD
p
m
r
p
m
D
e
(4)
And the probability density function
(P
DF) c
an
be computed by
differential using
the
followin
g
equ
ation.
33
21
c
o
s
/
3
2
21
c
o
s
(
0
)
i
x
rD
d
fD
p
x
D
dD
De
(5)
As the
definiti
on of
ho
p le
n
g
th
i
R
, the p
r
oj
ection
on
the
line
co
nne
cti
ng the
sou
r
ce an
d
the destinatio
n node
s, we
can ea
sily ge
t
cos
Rx
. Further th
e best hop le
ngth
()
OR
can b
e
comp
uted a
s
followin
g
:
00
co
s
i
r
x
f
DD
d
d
D
OR
(6)
Finally
on
ce node den
sity
is given,
we
can obtai
n the
best h
op len
g
th usi
ng e
q
u
a
tion
(6) fo
r ea
ch u
n
kn
own nod
e
s
.
4.2. Realiza
t
i
on of the Pr
oposed
Algo
rithm
The propo
se
d locali
zatio
n
algorithm
with best hop
length opti
m
ization a
n
d
Kalman
filtering me
ch
anism i
s
de
scribed expli
c
itl
y
in
this part and some ba
sic
symbol
s a
r
e listed first.
i
U
: ID of arbitrary unkno
wn n
ode
i
A
: ID of arbitrary ancho
r nod
e
_
_
i
Nu
m
N
e
i
U
: Numbe
r
of sensor
i
U
’s neig
hbors
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 1, March 2
016 : 211 – 2
1
8
216
_
_
i
Se
t
N
e
i
U
: Set of s
ens
or
i
U
’s neigh
bo
rs
c
H
: Hop co
unts
to arbitra
r
y anch
o
r no
de
L
H
: Hop length t
o
arbitrary an
cho
r
nod
e
First ea
ch u
n
k
no
wn
sen
s
o
r
node
i
U
initializes itself by setting its own
_
_0
i
Nu
m
N
ei
U
and
_
_{
0
}
i
Se
t
N
e
i
U
. And then they monit
o
r info
rmatio
n
pa
ckage
s f
r
om a
n
y an
chor n
ode
s to
con
s
tru
c
t the
con
n
e
c
tivity
of the netwo
rk. Equation
(6) is
used fo
r ea
ch u
n
kno
w
n to
comp
u
t
e
best
hop l
eng
th. Then
ea
ch an
ch
or
nod
e
i
A
floods i
n
fo
rmation
pa
cket over th
e
whole n
e
two
r
k,
whi
c
h in
clud
e
s
ID of a
n
cho
r
nod
e
i
A
, hop counts
c
H
to co
rresp
ondi
ng an
cho
r
no
de
i
A
an
d hop
length
L
H
to co
rre
sp
on
ding a
n
chor node
i
A
. As indicated
_
_0
i
Nu
m
N
e
i
U
and
_
_{
0
}
i
Se
t
N
e
i
U
. Once u
n
kno
w
n
nod
e receives
any a
n
cho
r
’s pa
cket
s it
che
c
ks if
it is fro
m
a
new
an
cho
r
.
If so, re
co
rds the ID
and
ren
e
ws
c
H
and
L
H
by
usin
g
1
cc
HH
and
()
LL
H
HO
R
. Otherwise
1
cc
HH
and
c
H
are
co
mpared. If the forme
r
i
s
smaller,
ren
e
w
c
H
or di
sca
r
d th
e pa
cket. After all
of abov
e is fini
she
d
,
unkno
wn n
o
d
e
re
bro
a
d
c
a
s
ts the p
a
cket.
The wh
ole proce
s
s end
s whe
n
ancho
r node re
ceiv
es
pa
cket fro
m
all other a
n
ch
ors. For e
a
ch
time 500 co
mputed b
e
st
hop len
g
th to anch
o
r n
ode
s for ea
ch n
o
de are sto
r
ed
and dealt u
s
ing
Kalman
filter model
to pe
rfect
the coll
ected
dist
a
n
ce
data to a
n
ch
or n
ode
s. Th
e mo
st a
c
curate
distan
ce e
s
ti
mation can
be de
rived b
y
refining
th
ose di
stan
ce
estimation
s.
Finally all the
coo
r
din
a
tes
of all unkn
o
w
n no
de
s ca
n be de
rived
by other m
e
ch
ani
sms,
such a
s
tri
-
an
gle
method an
d multi-lateratio
n
algorith
m
.
5. Simulation Validation
The
simulatio
n
is
mad
e
in
the MATLAB
(R2
008
a)
sof
t
ware
an
d
so
me a
s
sumpti
ons we
made a
r
e list
ed first in the
followin
g
.
a)
The whol
e sensor network
i
s
ma
de u
p
of
total 2
0
0
no
de
s an
d
the 3
D
sen
s
ing
area i
s
3
100
100
100
m
.
b)
The pe
rcenta
ge of an
ch
ors can
be
chan
ged ma
nually
and comm
un
ication ran
ge is
a
rand
om
variable.
c)
The ob
se
rvation frequ
en
cy of
Kalman filtering i
s
set a
s
500.
The p
e
rfo
r
ma
nce i
ndexe
s
are l
o
calizatio
n er
ro
r, ro
ot mean
sq
uare
error
(RMSE) and th
e
locali
zation ti
me com
pared
with cla
ssi
c
DV-Hop a
nd
Centroid met
hod
s.
Figure 3. Erro
r com
pari
s
o
n
s
Figure 4. RM
SE
compa
r
isons
Figure 5. Time comp
ari
s
o
n
s
In the figure
above lo
cali
zation erro
rs
o
f
DV
-Hop, Ce
ntroid a
nd p
r
opo
sed m
e
th
od in thi
s
pape
r are given. The pe
rcentage of
an
cho
r
s i
s
chan
ged from 1
0
%
to 80%. O
f
cause too h
i
gh
percenta
ge i
s
un
reali
s
tic i
n
actu
al WS
N envir
onm
e
n
t. Here
we
just explo
r
e t
he pe
rform
a
n
c
e
deeply in
the
simul
a
tion p
r
ocess. T
he
error
of DV-Hop
stays at
a hig
h
level
no matte
r h
o
w
anchor no
de
s are
ch
ang
ed
. Centroid i
s
much
better than
DV-Hop.
The a
c
cu
ra
cy of Cent
roid
is
alway
s
high
e
r
in any situat
ion. The Cent
roid i
s
almo
st
100% better
at the most. Also Centroi
d
is
more
stable t
han DV
-Hop.
There is n
o
fluctuatio
n
of Centroid
whi
c
h is mu
ch diff
erent from DV-
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Rob
u
st Lo
cali
zation Algo
rit
h
m
Based on
Best Length
Optim
i
zation for Wi
rele
ss…
(Hua
Wu
)
217
Hop. Its lo
cal
i
zation e
r
ror
cha
nge
s bet
wee
n
17.5m
and 22.5
m
, whi
c
h is m
u
ch better tha
n
DV-
Hop.
Ho
wever
wh
en pe
rcentag
e of an
cho
r
s is lo
wer tha
n
10%, the
error of
our
prop
ose
d
method i
s
the
large
s
t. That
is becau
se t
oo few an
ch
o
r
s
can
not hel
p unkno
wn n
ode
s to com
p
ute
best h
op le
n
g
th and i
n
tro
duces l
o
ts of
accum
u
late
d erro
rs. But
as the
num
ber
of an
cho
r
s
increa
se, its
accuracy i
s
g
e
tting highe
r
and hig
h
e
r
. Just when the
value is 2
0
% it become
s
the
best of the three an
d it is stable
comp
a
r
ed with
the
others. And its er
ro
r goe
s
on bein
g
sma
ller
and smalle
r. The smalle
st error of
the
p
r
opo
se
d
on
e
is le
ss than
1
0
m, whi
c
h i
s
only 5% of th
e
side l
ength. T
he be
st value
of the pro
p
o
s
ed m
e
thod i
s
69.7% a
nd
34.8% better
comp
ared
with
DV-Hop a
nd
Centroid.
Figure 4 gives the root me
an squ
a
re error (R
MSE)
compa
r
ison
s of the three. DV-Ho
p
pre
s
ent
s an upward tre
n
d
and Centroi
d
keep
s st
a
b
l
e. The RMSE of Centroi
d
keep
s aro
und
4.5m and th
ere a
r
e alm
o
st no big flu
c
tuation
s
a
s
percenta
ge o
f
ancho
rs ch
ange
s. DV-Hop
fluctuate fiercely and the la
rge
s
t value can re
ach 8m,
which mea
n
s
the environ
ment makes
big
effects o
n
DV-Ho
p
and
sometime
s ca
nnot localize
itself. Our p
r
opo
sed i
s
def
initely the be
st. It
gives a do
wn
ward tren
d an
d better locali
zation p
e
rfo
r
mance. The b
e
st is le
ss tha
n
2m.
Figure 4 an
d
Figure
5 bo
th depict
s a
c
curacy
p
r
obl
ems of the t
h
ree. In all p
r
opo
se
d
method
outp
e
rform
s
both
the othe
r two
.
It not only
h
a
s th
e le
ast l
o
cali
zatio
n
e
r
ror but
also h
a
s
the be
st RM
SE. There i
s
anothe
r imp
o
r
tant ind
e
x
n
eed to
be a
n
a
lyzed, n
a
me
ly efficiency.
Here
we compute t
he localization time that the three ne
ed
ed, as sho
w
n
in Figure 5.
It is easy to
unde
rsta
nd
whe
n
fewe
r
node
s ne
ed
to be localized le
ss time
will be
need
ed. As
shown in Fi
gu
re 5 the th
re
e
all give
do
wn
ward
tre
nd as
unkno
wn no
des get small
e
r.
DV-Hop
and
Centroid
are
so
simpl
e
tha
t
they nee
d n
o
compli
cate
d computatio
n which ma
kes
them n
eed
le
ss lo
cali
zatio
n
time.
DV-Hop n
eed
s l
e
a
s
t time
no
m
a
tter h
o
w ma
ny nod
es ne
e
d
to
be localized. It is decide
d
by the algorit
hm itse
lf. Th
ere i
s
no mu
ch comp
utation and ju
st o
ne
comp
utation
pro
c
e
ss
whi
c
h save a lot o
f
time. C
entro
id is wo
rse than DV-Ho
p
, beca
u
se it has to
comp
ute the
cente
r
of
so
me an
ch
ors
many time
s.
So it co
nsum
es m
o
re time
than
DV-Ho
p
.
These two
al
gorithm
s a
r
e
both fast lo
calizatio
n al
go
rithms fo
r the
i
r sim
p
licitie
s.
And they ne
ed
less time than most of oth
e
r propo
se
d algorith
m
s n
o
w
.
But to some
extent our
propo
sed
one i
s
the m
o
st
co
mplex of the t
h
ree
so it nee
ds m
o
re
comp
utation t
i
me with
high
est a
c
curacy.
It not onl
y h
a
s lo
cali
zatio
n
process b
u
t
also the
r
e i
s
a
hop l
ength
o
p
timization
st
ep a
nd filte
r
i
ng p
r
o
c
e
ss,
whi
c
h i
s
una
voidable
for time
con
s
um
p
t
ion.
But com
pare
d
with
the
oth
e
r two the
tim
e
cost i
s
i
n
a
n
a
c
cepted
ra
nge. Th
e
wo
rst is ab
out 1
0
.
5
se
con
d
s
which is not a large value. But it r
ealize 90
% of all sensor’ localizatio
n deman
d an
d
accuracy i
s
much
better than the othe
r two. So it
is valuable to o
b
tain mu
ch hi
gher
accu
ra
cy but
give up som
e
time perform
ances in the
ac
tual u
s
e, which i
s
very meanin
g
ful.
6. Conclusio
n
Preci
s
e
lo
cati
ng target i
s
a preconditio
n
for
th
e p
r
a
c
tice
of
wirel
e
ss
sen
s
o
r
n
e
twork,
whi
c
h i
s
conn
ected to
the
quality of net
work
data
col
l
ection, d
a
ta
query, d
a
ta st
orag
e, an
d ot
her
appli
c
ation
s
.
The
ran
g
e
-
fre
e
ho
p le
ngth
optimizatio
n l
o
cali
zatio
n
al
gorithm
for 3
D
-WSNs l
o
ca
lize
the sen
s
ors
with the
hel
p
of an
cho
r
s. I
n
this
pa
per we pro
p
o
s
e a
rob
u
st
ra
nge
-free
lo
cali
zat
i
on
algorith
m
by
reali
z
ing
be
st hop le
ngth
optimizatio
n, whi
c
h i
s
hig
h
efficient an
d
accuracy. T
h
is
algorith
m
i
s
derived
from
cla
s
sic two
-
dimen
s
io
n
a
l
DV-Hop
met
hod
but the
critical h
op l
ength
betwe
en any
relay node
s is accu
rat
e
ly com
pute
d
and refine
d with all sensors depl
o
y
ed
rand
omly an
d
arbit
r
ary
net
work
co
nne
cti
v
ity. In
case
of network p
a
ramete
rs ho
p
length
betwe
e
n
node
s ca
n b
e
derived wit
hout com
p
licated com
put
ation and further optimize
d
using Kal
m
an
filtering in which gu
arant
ees
robu
stne
ss eve
n
in complicated e
n
vironm
ent with random n
ode
comm
uni
cati
on ran
ge. T
he re
sults of
the simula
ti
on experi
m
e
n
t indicate t
hat the algorithm
prop
osed in the pape
r is b
e
tter than the
traditional
m
e
thod in term
s of the locali
zation e
rro
r a
n
d
energy efficie
n
cy.
Ackn
o
w
l
e
dg
ements
Authors wi
sh
to thank th
e project
su
pporte
d by t
he Research
Fund
of Sh
ando
ng
Jiaoto
ng Univ
ersity (No. Z2
0130
6, Z201
419, Z201
52
8), Scien
c
e a
nd Technol
og
y Plan Project o
f
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ISSN: 16
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930
TELKOM
NIKA
Vol. 14, No. 1, March 2
016 : 211 – 2
1
8
218
Shando
ng P
r
ovince
(2
014
GGX10
1015
) and
Natu
ral
Scien
c
e F
o
u
ndation
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ando
ng Province
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