TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 6254 ~ 6258
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.538
1
6254
Re
cei
v
ed
De
cem
ber 1
7
, 2013; Re
vi
sed
March 31, 20
14; Accepted
April 15, 201
4
A Novel Wireless Sensor Network Node Localization
Algorithm Based on BP Neural Network
Li Cheng*
1
,
Zhang Hongl
ie
1
,
Song Guangjun
2
,
Liu Yanju
3
1
Colle
ge of Co
mputer an
d Co
ntrol En
g
i
n
eeri
ng, Qiqih
a
r Uni
v
ersit
y
,
Qiqih
a
r, Heil
on
gjia
ng, 1
610
06
, P. R. China
2
School of Mathematics, Ph
ys
ics and Inform
at
ion Sci
enc
e, Z
heji
ang Oce
a
n
Univ
ersit
y
,
Z
housh
an, Z
h
e
jian
g
, 31
600
0, P. R. China
3
Computer C
e
nter, Qiqihar U
n
iversit
y
,
Qiqih
a
r, Heil
on
gjia
ng, 1
610
06
, P. R. China
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: lcxsn
h
@
163.
com
A
b
st
r
a
ct
T
he acc
u
rate
l
o
cali
z
a
tio
n
of
w
i
reless se
nso
r
netw
o
rk n
ode
is o
n
e
of the
supp
orting
tec
hno
log
i
e
s
of netw
o
rk app
licatio
n. A nov
el loc
a
li
z
a
t
i
on
alg
o
rith
m of w
i
reless se
nsor
netw
o
rk nod
e base
d
on BP n
eura
l
netw
o
rk is
put f
o
rw
ard i
n
th
e
p
aper. T
h
is l
o
ca
li
z
a
tio
n
al
gorith
m
c
onstructs t
he BP
n
eutral
netw
o
rk
mod
e
l
i
n
accord
ance w
i
th the nu
mber o
f
the anchor n
o
de firstl
y, and t
hen trai
ns the
netw
o
rk by the anch
o
r no
de a
n
d
estimates the l
o
catio
n
of the unknow
n no
d
e
. Moreover
, the virtual a
n
c
hor no
de is in
troduce
d
into this
alg
o
rith
m i
n
or
der to re
ali
z
e
i
t
s optimi
z
a
t
i
on,
w
h
ic
h incr
eas
es the a
n
ch
or
nod
e scal
e
i
n
the n
e
tw
ork an
d
improves
the
local
i
z
a
ti
on
ac
curacy
of the
no
de.
T
h
e si
mu
lati
on
exp
e
r
iment r
e
sults
in
tw
o differ
ent
cond
itions
sh
o
w
that co
mp
ar
ed w
i
th
Ce
ntroi
d
a
l
gor
ith
m
an
d DV-H
op
al
go
rithm, t
he
loc
a
li
z
a
ti
on
al
gor
ith
m
of
this p
aper
esti
mates
the
loc
a
tion
of the
unk
now
n n
o
d
e
mo
re prec
ise
l
y a
n
d
i
m
pr
oves
the
locati
on
accur
a
cy
mor
e
effectivel
y. T
h
is algorith
m
de
monstrate
s
its merits gre
a
tly.
Ke
y
w
ords
: w
i
reless se
nsor n
e
tw
ork, BP neural netw
o
rk, an
chor no
de, virtual a
n
ch
or nod
e
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The wirel
e
ss sen
s
o
r
n
e
two
r
k
i
s
comp
osed
of
do
ze
ns or eve
n
thou
san
d
s
of the
sen
s
o
r
node
s a
nd th
ese
se
nsor n
ode
s are mo
stly deploy
e
d
in are
a
s
of complex envi
r
onment, even
in
some a
r
ea
s
out of perso
n
nel’s rea
c
h in
the method of random
se
eding [1]. A small amount
o
f
the
kn
own
no
des are usua
lly
depl
oyed
whe
n
the
sen
s
or network i
s
con
s
tru
c
tin
g
. The
s
e no
d
e
s
carry out
self-localization
by GPS with a high
co
st, so not all the
node
s in
sen
s
or
network h
a
ve
the fun
c
tion
of self-l
ocalization. Thu
s
, t
o
re
a
lize the
high-preci
s
io
n lo
ca
lization
of the
node
has
become o
n
e
of the hot i
s
sue
s
in the
wirel
e
ss
se
nso
r
net
wo
rk resea
r
ch in
orde
r to m
eet
requi
rem
ents of
application
s
.
The l
o
calization te
chn
o
log
y
re
sea
r
ch
o
n
wi
rel
e
ss
se
nso
r
network is mainly
divided i
n
to
two
catego
ri
es: o
ne i
s
t
he rang
e-b
a
s
ed
loca
lization alg
o
rithm
;
anothe
r i
s
the range
-f
ree
locali
zation
al
gorithm.
Co
n
s
ide
r
ing
the f
a
ctors of
volu
me, ene
rgy
a
nd
co
st of the
se
nsor net
work
node
[2], the
ra
nge
-free
l
o
cali
zatio
n
al
gorithm
is
m
o
re
practi
cal.
The
range
-f
ree
lo
calization
algorith
m
tha
t
is co
mmonl
y used i
n
cl
u
des
Ce
ntroid
algorith
m
[3
], DV-Ho
p
al
gorithm [4, 5
]
,
Amorph
ou
s a
l
gorithm
[6, 7
], APIT algori
t
hm [8], etc.
I
n
rece
nt yea
r
s, the l
o
calization te
chn
o
l
ogy
resea
r
ch o
n
wirel
e
ss
se
n
s
or n
e
two
r
k
mainly fo
cu
ses
on i
m
proving lo
cali
zati
on a
c
cu
ra
cy, for
example, no
n
linear l
e
a
s
t squares
are u
s
ed to
re
sea
r
ch the
nod
e l
o
cali
zatio
n
in
[9]; fine-grai
ned
hop-co
unt is used to re
search the no
de locali
zati
o
n
in [10]; virtual cent
ral n
ode is u
s
ed
to
resea
r
ch the
nod
e lo
cali
zation in [1
1], and
so
on.
In additio
n
, som
e
ex
cell
ent lo
calization
algorith
m
s ha
ve bee
n
wide
ly applied
to t
he d
a
ily
prod
uction
an
d lif
e [12]. Th
e p
aper ad
opts
BP
neutral n
e
two
r
k an
d the virtual an
cho
r
no
de to re
sea
r
ch the locali
zat
i
on algo
rithm.
The remain
d
e
r of the p
a
p
e
r is
org
ani
ze
d as follo
ws. The lo
cali
zati
on algo
rithm
based on
BP neural n
e
twork i
s
prese
n
ted ca
refully
in Sect
ion 2,
includi
ng co
nstru
c
ting BP
neural netwo
rk
model, trai
nin
g
network a
n
d
estim
a
ting l
o
catio
n
, setti
ng virtual
an
chor
node
an
d
relo
cating
the
node. The
n
, the simul
a
tion
experiment
s and analy
s
is
are sho
w
n in
Section 3, wh
ich proves th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel
Wirel
e
ss Sensor
Network Node
Loca
lization
Algorithm
Based o
n
BP… (Li Ch
eng
)
6255
sup
e
rio
r
ity of this al
gorith
m
. In Sectio
n 4, con
c
lu
si
ons
are give
n with th
e i
m
porta
nce a
n
d
pra
c
tical valu
e of this algorithm.
2. Localiza
t
ion Algorith
m
Based on
BP Neur
al Net
w
o
r
k
This alg
o
rith
m u
s
e
s
a
key data
value
that is the
mi
nimum
hop
b
e
twee
n the
n
ode. An
d
the minimum
hop i
s
dete
r
mine
d by th
e followi
ng
method
s: the
anchor nod
e bro
a
d
c
a
s
ts its
locatio
n
information to the neighb
or no
de, inclu
d
ing
the hop (Its initial value is 0.) and its ID
informatio
n; the receiving
node
sto
r
e
s
t
he h
op;
if the
receiving
nod
e get
s the
ho
p from
the
sa
me
anchor nod
e
and the
hop i
s
big
ger t
han
the sto
r
ed
o
ne, the ne
wly
-re
ceive
d
ho
p
is ign
o
red; a
nd
then there exists the h
op
plus 1,
whi
c
h
is broad
ca
st to the neigh
bor n
ode
con
t
inuou
sly, so
the
minimum h
o
p
to each an
chor n
ode i
s
st
ored
by t
he n
e
twork n
ode.
The alg
o
rith
m is divide
d i
n
to
four ste
p
s in
detail as follo
wed [13].
2.1. Cons
tru
c
ting BP Ne
ural Ne
t
w
o
r
k
Model
In the localization are
a
, assume the
r
e ar
e M any pl
acem
ent nod
es totally, and make
m=
1, 2,...
, M
, where first N of M is set
as the an
ch
o
r
node a
nd th
e rest i
s
set
as the un
kn
o
w
n
node.
C
i
=(
x
i
, y
i
)
rep
r
e
s
e
n
t
s the positio
n coo
r
din
a
te
of node
i
. Mak
e
K
i
=[
k
i1
, k
i2
,...
, k
in
,..
.,
k
iN
]
rep
r
e
s
ent the
minimum h
o
p
between th
e an
cho
r
no
d
e
, whe
r
e
k
in
repre
s
e
n
ts th
e minimum
h
o
p
betwe
en a
n
chor
nod
e
i
a
nd an
ch
or
no
de
n
, a
nd
i=1,... , N
,
n =
1,... , N
, and
whe
n
i=
n
,
k
in
=0
.
Then
ma
ke
K
j
=[
k
j1
, k
j2
, …,
k
jn
, …,
k
jN
]
re
pre
s
ent th
e
minimum
hop
between
the
un
kno
w
n
no
de
and the a
n
ch
or no
de, wh
e
r
e
k
jn
rep
r
e
s
ents the mi
ni
mum hop
be
tween u
n
kno
w
n no
de
j
an
d
anchor nod
e
n
, and
j=(N+
1
, N+
2,..., M)
,
n=
1,... , N
. The unit numb
e
r
of BP neutral netwo
rk in
put
layer is N,
wh
ich i
s
dete
r
mi
ned by the
nu
mber
of
the a
n
ch
or n
ode, t
he unit n
u
mb
er of the
hidd
en
layer i
s
dete
r
mined
by the
experim
ent, and th
e uni
t
numb
e
r
of the outp
u
t lay
e
r i
s
2,
which
rep
r
e
s
ent
s the node
coo
r
di
nate
(x, y)
.
2.2. Training Net
w
o
r
k an
d Estimating
Location
After con
s
tru
c
ting BP ne
ural n
e
two
r
k model
su
ccessfully, the locali
zation
a
l
gorith
m
carrie
s out tra
i
ning net
work and estimati
ng location.
For the trai
ni
ng stag
e, the anch
o
r n
ode
is use
d
to train BP neutral netwo
rk, a
nd the
training
sam
p
le sele
ct
s all the an
cho
r
n
o
des i
n
wi
rele
ss sen
s
or
net
work. Th
e trai
ning inp
u
t is t
h
e
minimum
hop
betwe
en th
e
an
cho
r
no
de
, namely
K
i
=[
k
i1
, k
i2
,..., k
in
,.
.., k
iN
]
,
i=
1,... ,
N
,
n=1,... , N
.
And the trai
n
i
ng outp
u
t is
the co
rrespo
ndi
ng
po
sitio
n
of the an
chor n
ode, n
a
m
ely
C
i
= (
x
i
, y
i
)
,
i=
1,... , N
.
For the estim
a
ting stage, the estimatio
n
i
nput is the hop between
each un
kn
o
w
n nod
e
and ea
ch
an
cho
r
no
de, n
a
mely
K
j
=[
k
j1
, k
j2
, …, k
jn
, …, k
jN
]
,
j=
(N+
1
, N+
2,..., M)
,
n=1,... ,
N
. And
the estimatio
n
output is th
e positio
n of
the co
rre
sp
o
nding u
n
kno
w
n no
de, na
mely
C
j
=(
x
j
, y
j
)
,
j=
(N+
1
, N+
2,..., M)
.
2.3. Setting
Virtual Anch
or Node
By definition, the virtual node is d
e
fine
d as
the no
d
e
that does n
o
t exist in reality and
has no
com
m
unication a
b
ility of
the real node. Ho
weve
r, it is the artificial n
ode to make
the
locali
zation
al
gorithm
re
sult
more a
c
cura
te, and it
s ch
ara
c
teri
stic is that the
coo
r
dinate i
s
kno
w
n
or ca
n be cal
c
ulate
d
accu
rately [14].
In localizatio
n area, a
s
su
me that there ex
ist S virtual ancho
r node
s, and its location
c
o
or
d
i
na
te
is
C
l
=(
x
l
, y
l
)
.
Ma
ke
s
K
l
=[
k
l1
, k
l2
,...
, k
ln
,..
., k
lN
]
represent th
e minimum
h
op bet
wee
n
the
virtual anchor node and the
anch
o
r no
de,
where
k
ln
rep
r
esents the m
i
nimum hop b
e
twee
n virtua
l
anchor n
ode
l
and an
cho
r
n
ode
n
, and
l = 1, 2,..
. ,
S
,
n
=
1,... , N
.
Because the
virtual node has
no abilities of
comm
uni
cation and i
n
formation transf
erri
ng,
the minimum
hop i
s
dete
c
t
ed directly be
tween th
e
virtual an
cho
r
n
o
de an
d the an
cho
r
no
de, an
d
the dista
n
ce
from virtual
node to
a
n
ch
or
node
is conve
r
ted
to hop. In
the sim
u
lat
i
on
experim
ents,
the hop is first calculated
, and then
the distan
ce i
s
compa
r
e
d
with the wirele
ss
rang
e of the node.
The traine
d B
P
neu
ral n
e
twork i
s
used
to esti
mate
th
e lo
cation
of
all the virtu
a
l
anchor
node
s. The in
put of the network i
s
the m
i
nimum
ho
p b
e
twee
n the virtual an
ch
or
and the an
ch
or
node, whi
c
h i
s
de
scribe
d as
K
l
=[
k
l1
, k
l2
,..
., k
ln
,.
..,
k
lN
]
,
l
=
1, 2,...
, S
,
n =
1,...
, N
. T
he output of the
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 625
4 –
6258
6256
netwo
rk i
s
the estimation l
o
catio
n
of the
corre
s
po
ndin
g
virtual anch
o
r nod
e, that is,
C'
l
= (x
l
, y
l
)
,
l=
1, 2,...
, S
.
For the vi
rtu
a
l an
cho
r
no
de, its e
s
tim
a
tion lo
catio
n
and it
s a
c
tual location
can
be
comp
ared an
d figured
out, which is ba
sed on the fact
that the assumption of th
e virtual an
ch
or
node
lo
cation
is
kn
own a
s
rest
rictive
co
ndition
s, nam
ely
C'
l
and
C
l
. For th
e
com
parative
re
sul
t
,
sele
ct Q virtual an
cho
r
nodes
with small error, whi
c
h sets the min
i
mum hop
as
K
q
=[
k
q1
,k
q2
,...
,
k
qn
,...,k
qN
]
,
q=
1, 2,...
, Q
,
n=
1,...,
N
.
2.4. Reloca
ting Unkn
o
w
n
Node
After obtaini
ng the
trai
n
ed virtual
a
n
ch
or
nod
e, BP neu
ral
netwo
rk ne
e
d
s to
be
recon
s
tru
c
ted
.
At the mo
ment, the tra
i
ned virtual a
n
ch
or n
ode i
n
netwo
rk is added into t
h
e
anchor
nod
e. Therefore, the unit n
u
mb
er of BP
ne
u
r
al net
wo
rk i
nput layer ha
s be
en
cha
n
ged
becau
se the
numbe
r of the anchor n
o
d
e
has alte
red
.
And then the netwo
rk tra
i
ning is
carrie
d
out ag
ain
accordin
g to S
e
ction 2.2. T
he
training
comp
letion me
an
s
that all the
u
n
kn
own n
ode
s
are relo
cated.
3. Simulation Experimen
t
and An
aly
s
is
For
simulatio
n
experim
ent
s in this
pape
r, a se
rie
s
of simulatio
n
ex
perim
ents a
r
e ca
rrie
d
out on
Matla
b
softwa
r
e
by usi
ng
Ce
ntro
id lo
cali
zation
algo
rithm,
DV-Ho
p
lo
cali
zation al
gorith
m
,
the BP localization alg
o
rit
h
m without th
e virtual
anch
o
r nod
e, the RN-BP locali
zation alg
o
rit
h
m
with the
untrained
virtual
anchor no
de,
and
the
V
N
-BP locali
zati
on al
gorith
m
with the
train
e
d
virtual an
ch
o
r
n
ode
with
small
erro
r
resp
ective
ly. In the s
i
mulat
i
on expe
rim
e
nts, the
wi
rel
e
s
s
sen
s
o
r
netwo
rk no
de is di
stribute
d
in the are
a
of
100m
×100m
randomly. Be
cau
s
e p
r
edi
ct
ion
results of BP
neutral
netwo
rk a
r
e affe
cte
d
by the init
ia
l weight to
so
me extent, in orde
r to en
su
re
that the simul
a
tion expe
rim
ent re
su
lts
ref
l
ect the me
rits of the al
gorithm c
o
rrec
t
ly, the s
i
mulation
experim
ents
are carried o
u
t in the sam
e
experim
ent
al con
d
ition
s
for many times, su
ch a
s
50
times, and th
en the avera
ge locali
zatio
n
error value
s
are ta
ken
and analy
z
ed
. The simulat
i
on
experim
ents
and pe
rform
a
nce an
alysi
s
are carried
o
u
t in two different experi
m
ental con
d
itio
ns,
namely ch
an
ging the an
ch
or nod
e scale
and the total numbe
r of the node.
3.1. Experiment on Chan
ging the Anc
hor Nod
e
Scale
Of the
simul
a
tion expe
rime
nts o
n
cha
ngi
ng the
an
ch
o
r
n
ode
scale,
set the
total
n
u
mbe
r
of the nod
e as
15
0
, set the wi
rele
ss range
as
30
m
,
and
the sp
ecific re
sults are
a
s
sho
w
n
in
Figure 1.
Figure 1. Anchor no
de scal
e and lo
cali
za
tion error
5
10
15
20
25
10
15
20
25
30
35
40
45
50
A
n
c
h
o
r
no
de
s
c
al
e (
%
)
Lo
c
a
l
i
z
at
i
on er
ror
(
%
)
B
P
D
V
-
H
o
p
C
o
n
t
r
o
i
c
R
N
-
B
P
V
N
-
B
P
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel
Wirel
e
ss Sensor
Network Node
Loca
lization
Algorithm
Based o
n
BP… (Li Ch
eng
)
6257
The
simulati
on re
sult
s
show th
at wit
h
the
in
crea
se of the
an
cho
r
no
de
scale, the
locali
zation e
rro
rs of five d
i
fferent algo
rithms de
crea
se. In the sam
e
con
d
ition
s
, the locali
zatio
n
error of the BP localizatio
n algorithm o
f
this paper i
s
on average
14.754%
lo
wer tha
n
that of
Centroid lo
ca
lization
algo
ri
thm and
on a
v
erage
10.34
0%
lowe
r tha
n
that of DV-Hop l
o
calizatio
n
algorith
m
, an
d the erro
r curve of the B
P
locali
za
tion
algorith
m
drops fa
ste
s
t. The lo
cali
zati
on
error of the
RN-BP locali
zation al
go
rithm is o
n
averag
e
3.81
4
%
lower th
a
n
that of the BP
locali
zation
a
l
gorithm. Th
u
s
, the an
cho
r
nod
e scale
affects the
locali
zation
e
rro
r. Also, th
e
locali
zation e
rro
r of the VN-BP localiza
t
ion algorith
m
is on avera
g
e
2.452%
lo
wer tha
n
that of
the RN-BP locali
zatio
n
al
gorithm. So for the di
ffere
nt scal
e
stat
es of the an
cho
r
no
de, the
introdu
ction o
f
the virtual node re
du
ce
s
the localization error effe
ctively.
3.2. Experiment on Chan
ging the To
tal Number of Node
The sim
u
latio
n
experim
ent
s are
ca
rrie
d
out in differen
t
condition
s o
f
the total number of
the nod
e, and
set the a
n
ch
or no
de
scale
as
15
%
an
d the wi
rele
ss range
as
30m
, who
s
e
sp
ecif
ic
r
e
su
lts
ar
e
as s
h
ow
n
in
F
i
gu
r
e
2
.
Figure 2. Nod
e
Numb
er a
n
d
Localization
Error
In the exp
e
ri
ments, fo
r th
ese
five diffe
rent al
go
rith
ms, the
lo
cal
i
zation
erro
rs on th
e
whol
e ta
ke
o
n
a
gradu
ally de
crea
sing
trend.
Howev
e
r, in
the
sa
me
con
d
ition
s
, in
compa
r
i
s
on,
the lo
cali
zatio
n
e
rro
r
of the
BP lo
calization al
gorith
m
i
s
o
n
avera
g
e
12.60
0%
lo
wer th
an th
at o
f
Centroid lo
ca
lization alg
o
ri
thm. When the numb
e
r o
f
the node is
100
, the experim
ent re
sults
sho
w
th
at the
localizatio
n
error
of DV
-Hop lo
cali
za
tio
n
algo
rithm i
s
obviou
s
ly lo
wer than
that
of
the BP neural
netwo
rk al
go
rithm. But
wh
en the num
b
e
r of the nod
e is over
20
0
,
the locali
zati
on
error of the B
P
neural
net
work lo
cali
zat
i
on algo
rithm
quickly de
creases a
nd i
s
obviously lo
wer
than that of
DV-Hop l
o
cal
i
zation
algo
rithm. Wh
en
th
e virtual an
chor n
ode i
s
i
n
trodu
ce
d in
the
locali
zation al
gorithm, the l
o
cali
zatio
n
error of
the RN-BP locali
zati
on algo
rithm is on averag
e
2.221%
lo
we
r than
that o
f
the BP ne
ural
network
locali
zatio
n
algorith
m
, which
sh
ows t
hat
introdu
cin
g
th
e virtual an
ch
or no
de into t
he lo
calizatio
n algo
rithm redu
ce
s the lo
cali
zation e
r
ror
effectively. At the
sam
e
ti
me, the l
o
calization
erro
r
of the V
N
-B
P locali
zatio
n
algo
rithm i
s
on
averag
e
3.9
12%
lowe
r than that of the RN-BP locali
zatio
n
algorithm, whi
c
h sh
ows th
at
introdu
cin
g
the trained virtu
a
l anchor n
o
d
e
impr
ove
s
th
e locali
zation
accuracy effe
ctively.
4. Conclusio
n
This pa
pe
r introdu
ce
s th
e con
c
e
p
t of BP neural netwo
rk into
the wirele
ss se
nso
r
netwo
rk n
ode
locali
zation,
usin
g BP neu
ral network to
train the an
chor no
de in o
r
de
r to redu
ce
the locali
zatio
n
error. At the sam
e
time, aiming
at an
chor n
ode
scal
e in
locali
zati
on area, it puts
10
0
20
0
30
0
40
0
50
0
5
10
15
20
25
30
35
40
45
50
N
u
m
ber o
f
nod
e
L
o
c
a
l
i
z
at
i
o
n er
r
o
r
(
%
)
BP
D
V
-
H
o
p
C
o
n
t
r
o
i
c
R
N
-
B
P
VN
-
B
P
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 625
4 –
6258
6258
forwa
r
d th
e
appli
c
ation of
the traine
d
virtual an
cho
r
nod
e so a
s
to improve t
he an
ch
or n
ode
scale an
d re
duce the localizatio
n erro
r. The si
m
u
l
a
tion re
sults
in two differe
nt experime
n
t
al
con
d
ition
s
sh
ow that the l
o
cali
zatio
n
error of
the V
N
-BP locali
zati
on algo
rithm
is mu
ch lo
we
r
than of the B
P
neural net
work lo
cali
zat
i
on alg
o
ri
thm
as
well a
s
t
hat of the RN-BP lo
cali
za
tion
algorith
m
. Moreove
r
, the results
sho
w
that t
he localizatio
n erro
r of the BP neural netwo
rk
locali
zat
i
on
al
gorit
hm
in m
o
st
ca
se
s is
l
o
we
r t
h
a
n
th
at of Ce
ntroi
d
localizatio
n
algorith
m
a
s
well
as that of
DV-Ho
p
lo
cali
zation alg
o
rith
m. To
su
m u
p
, the localization alg
o
rith
m ba
sed
on
BP
neural network of this pap
e
r
has th
e sup
e
rio
r
ity and the resea
r
ch value to some e
x
tent.
Ackn
o
w
l
e
dg
ements
This
work is supp
orted
b
y
the Nation
al Nature Science Foun
d
a
tion of Heil
ongjia
ng
Province, Ch
ina, No. F2
0
1204,
and
th
e Edu
c
ation
Dep
a
rtme
nt
of Heil
ongji
a
ng Province
o
f
Chin
a, No. 1
2531
765 a
n
d
No.12
5116
0
4
, and the
Program
s for Young Te
a
c
he
rs S
c
ie
ntific
Re
sea
r
ch
in
Qiqiha
r Univ
ersity No. 20
12k-M1
4
.T
he
autho
rs al
so
very g
r
ateful
ly ackno
w
le
d
ge
the helpful co
mments a
nd
sug
g
e
s
tion
s of the revi
ewers,
which ha
ve improved t
he pre
s
e
n
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