TELKOM
NIKA
, Vol.13, No
.2, June 20
15
, pp. 703 ~ 7
1
0
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i2.1434
703
Re
cei
v
ed
Jan
uary 17, 201
5
;
Revi
sed Ma
rch 1
8
, 2015;
Acce
pted April 10, 2015
Sensor Node Easy Mo
ving Monitoring Region Location
Algorithm in Internet of Things
Dongh
ua Fe
ng*
1,2
, Yahong Li
2
1
School of co
mputer scie
n
ce
and tech
nol
og
y, W
uha
n Univ
ersit
y
of T
e
chn
o
lo
g
y
,
W
uhan 4
3
0
070
, Hubei, Ch
ina
2
Dept. of computer and Inform
ation En
gi
neer
i
ng, Nan
y
a
n
g
Institute of techn
o
lo
g
y
,
Nan
y
a
ng
473
0
04, Hen
an, Ch
i
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: n
y
668
8@q
q
.
c
om
A
b
st
r
a
ct
Becaus
e of the influe
nce from geogr
aph
ical l
o
cati
o
n
, w
eather and oth
e
r kinds of circu
m
stances
i
n
mo
nitor
ed
are
a
s, the s
h
ift o
f
the n
o
d
e
l
o
c
a
tion
a
nd
no
n
-
unifor
m
distri
butio
n, this
pa
per
prop
ose
d
a
n
improve
d
D
V
-Hop
loc
a
tion
al
gorith
m
. F
i
rst
of all, th
e
pack
age
structure
by ch
ang
in
g th
e a
n
chor
no
de
s t
o
reduc
e the
n
u
m
b
e
r of
ho
ps
data
acqu
isiti
o
n p
hase
n
ode
data stor
ag
e; i
n
troduc
ing
w
e
i
ghts to th
e av
e
r
age
hop d
i
stanc
e calcul
atio
n ph
as
e the or
ig
in
al
avera
ge h
op di
stance calc
ulat
ion
meth
od w
a
s impr
ove
d
, an
d
betw
een the
n
ode a
nd a
n
ch
or nod
e dista
n
c
e calcu
l
ate
d
on the b
a
sis
of referenc
e a
n
chor n
o
d
e
s a
r
e
different; then,
iterative refi
ne
me
nt
of nod
e locali
z
a
tio
n
stage throu
gh
the
use of mu
ltilat
e
ral
me
asure
m
en
t
meth
od
an
d T
a
ylor s
e
ries. F
i
nally, s
i
mul
a
tio
n
ex
peri
m
ent o
f
this
metho
d
,
and
co
mp
are
d
w
i
th the ex
isti
ng
meth
ods, th
e r
e
sults pr
ove t
hat the
met
h
o
d
in th
is
p
aper
can gr
eatly r
educ
e p
o
sitio
n
i
ng
errors w
i
th
out
add
ing
hardw
a
r
e equ
ip
ment a
nd n
e
tw
ork traffic, impr
ov
e th
e positi
o
n
i
ng
a
ccuracy, a bett
e
r soluti
on to t
h
e
prob
le
m of no
d
e
loca
li
z
a
ti
on n
e
tw
orking
mon
i
toring ar
ea.
Ke
y
w
ords
: Internet of T
h
in
gs
, Sensor Nod
e
,
Monitori
ng Re
gio
n
, Loca
l
i
z
a
t
i
o
n
1. Introduc
tion
The Inte
rnet
of Thin
gs wa
s firstly p
r
op
ose
d
by
Auto-ID La
boratory of
Ma
ssa
c
hu
setts
Institute of Tech
nolo
g
y in 1999, and it’s basi
c
a
lly a
n
intelligent netwo
rk
whi
c
h conn
ect
s
o
n
e
thing to anoth
e
r throu
gh th
e sen
s
o
r
network, RFI
D
transceive
r
, two-dim
e
n
s
iona
l code, GPS and
other hardware. At present
, the Internet of Things
is
widely used i
n
agri
c
ulture, industry, military
and environm
ent fields to a
c
compli
sh dat
a
acq
u
isitio
n and re
al-time
monitori
ng.
The Inte
rnet
of Thin
gs for m
onitori
ng
is m
o
stly lo
cated
in te
rri
tories with
so po
o
r
environ
ment
con
d
ition
s
th
at even
hum
an
can’t
app
roach. So i
n
such
a
r
ea
s th
e heli
c
o
p
ters
are
usu
a
lly appli
ed in
sp
re
ad
ing
sen
s
o
r
n
ode
s to a
c
q
u
ire
and
an
alyze th
e en
vironme
n
t da
ta.
Beside
s the
sen
s
o
r
no
de
s may
some
times
shift in
the environ
ment, su
ch
as in th
e o
c
ean
monitori
ng, sensor nod
es cha
nge
their
positio
ns by the
water flo
w
. So the
lo
cation
of
sen
s
or
node
s is con
s
tantly chan
g
i
ng as well as the
netwo
rk topology. Ho
wever, the
acqui
red da
ta
become
s
me
aningl
ess wit
hout the d
e
tai
l
ed lo
cation a
nd net
work to
pology info
rm
ation. Thu
s
it is
very importan
t
to locate the sen
s
o
r
nod
es for d
a
ta a
c
qui
sition a
n
d target moni
toring, e
s
pe
ci
ally
in the territori
es that se
nsor nodes can easily shift.
There are t
w
o bas
i
c
s
e
ns
or
nodes
loc
a
liz
a
tion methods
:
the Ranged-Bas
e
d method and
Ran
ge-Fre
e
method
re
sp
ectively. For
the forme
r
o
ne the lo
cati
on informatio
n is o
b
taine
d
with
addition
al hardwa
r
e an
d ex
tra dista
n
ce a
nd angl
e
information such as R
SSI [1], TOA [2], TDOA
[3] and AOA
[4]. But for the latter o
n
e
the co
nne
cti
v
ity information is
only ne
eded to
get the
sen
s
o
r
no
des position,
su
ch as
convex
prog
ram
m
ing
algorithm [5],
DV-Hop alg
o
r
ithm and M
D
S-
MAP algorith
m
[6]-[7]. Becau
s
e i
n
the
monitori
ng a
r
eas th
e
wirel
e
ss sen
s
o
r
n
ode
s net
wo
rk of
the Intern
et o
f
Thing
s
requi
res lo
w po
we
r con
s
umptio
n and
low co
st, the Rang
e
-
Free meth
od
is
better for the
Internet of Th
ings.
DV-Hop alg
o
rithm is a cla
s
sic
Ran
ge-Free met
hod, which h
a
s go
o
d
accuracy to
monitor
regio
n
s
with steady an
d uniformly distri
buted se
n
s
or node
s, but has po
or pe
rfo
r
man
c
e for th
e
non-unifo
rm
distrib
u
tion a
nd mo
bile n
e
twork. In
o
r
d
e
r
to imp
r
ove t
he alg
o
rithm t
he me
an
squ
a
re
error i
s
used
to cal
c
ul
ate t
he h
op di
stan
ce, a
nd
th
e a
v
erage
ho
p a
n
ch
or
nod
es
distan
ce
is used
to obtain
the
distan
ce
from
nod
es to
an
chor
no
de
s [8]
-
[9]. The
com
b
ination
of
RSSI and
DV-Hop
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 703 – 71
0
704
is al
so p
r
o
p
o
s
ed to
improve the a
c
curacy [9]-[
10]. Usi
ng the
DV-Hop meth
od
wi
th multi- an
ch
or
node
s, the di
stan
ce is o
b
tained by
mult
iplying the we
ighting facto
r
.
The above m
e
thod
s have the vital significan
c
e
to improve the locali
zation a
c
cura
cy and
redu
ce th
e p
o
sitioni
ng e
r
ror. But in the
se
cond
stag
e of the algo
rithm, an
cho
r
node
s ne
ed
to
store
b
r
oad
cast p
a
cket
s
again,
whi
c
h
increa
se
s th
e amo
unt of
data
storag
e nod
es an
d
the
node
s co
st and also
aff
e
cts
the existing
time
of
the n
e
two
r
k [11]. In thi
s
pap
er a
no
de
locali
zation
al
gorithm
ba
se
d on
DV
-Hop
algo
rith
m i
s
prop
osed, in
whi
c
h th
e
cal
c
ulatio
n of
DV-
Hop
algo
rith
m, the avera
ge ho
p di
sta
n
ce i
n
ho
ps and
n
ode co
ordin
a
te
po
sit
i
oning stag
es
have
been imp
r
ove
d
.
Figure 1. Algorithm proced
ure of DV
-Ho
p
2. DV-Hop Al
gorithm
There are th
ree stag
es in t
he DV-Ho
p
al
gorithm:
(1) O
b
tain Ho
p cou
n
t of nodes
The an
ch
or
node
s in th
e
radiate
data
packet
a
r
e
denote
d
a
s
(ID, x, y, hop) in the
netwo
rk,
of which
ID i
s
the
ID n
u
mbe
r
o
f
anchor
no
d
e
itself, x an
d
y are
the
po
sition
of an
ch
or
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Sensor Node
Easy M
o
vi
ng
Monitori
ng Region Locati
on Algorithm
in Internet .... (
D
onghua Feng)
705
node
s, ho
p is the initial v
a
lue of h
op count 0.
Whe
n
the no
de receive
s
thi
s
packet at the
first
time, the dat
a pa
cket is
saved
and
h
op count
i
s
adde
d by on
e. Whe
n
the
node
secon
d
ly
receives data
pa
cket with
the same
ID,
the o
r
igin
al
data p
a
cket i
s
repla
c
e
d
if
the current
h
op
cou
n
t is le
ss t
han the exi
s
ting hop
co
unt, and is tran
smitted. This p
r
ocedu
re
stop
s until all IDs
of
anchor n
ode
s on longe
r ch
ange.
(2)
Cal
c
ulate
the averag
e h
op dista
n
ce
The average
hop di
stan
ce
hopValu
e
fro
m
the
ith anchor no
de to the othe
r M-1
anch
o
r
node
s is
cal
c
ulated u
s
ing t
he formul
a (1
)
1
1
1
1
()
M
ij
j
i
M
ij
j
dist
p
p
ho
pVa
l
ue
hop
(1)
In the fo
rmul
a (1),
()
ij
di
st
p
p
i
s
the
total dista
n
ce
between
an
chor nod
e
i
an
d an
ch
or
node j,
1
1
M
ij
j
hop
is the
total jump between a
n
chor node i and a
n
ch
or no
de n
u
mbe
r
j
.
Whe
n
all the
averag
e ho
p dista
n
ces
of eac
h an
ch
or no
de
s are
cal
c
ulated, t
he data
packet
s
are
begin
n
ing to
be broad
ca
st
ed in the
net
work. And
ea
ch n
ode
only
save
s the first
data pa
cket.
(3) Locate the Node.
Once obtai
ni
ng the
hop
co
unt of all a
n
chor
nod
es
an
d the ave
r
ag
e
hop
dista
n
ce
of ea
ch
anchor no
de,
the no
de l
o
cation
can
be
easily
acq
u
ired
u
s
ing
the three sid
ed measurement
o
r
the maximu
m likeliho
od method. The
DV-Hop alg
o
rithm flow can be expressed a
s
sh
own in
Figure (1
).
3. The Improv
ed DV-Hop Algorithm
3.1. The dra
w
b
a
ck o
f
DV
-Ho
p
algorithm
As the
cla
ssi
cal m
e
thod
of Ran
g
e
-
Free,
DV
-Hop
algo
rithm can
be
easily a
c
hi
eved wit
h
very low cost
, and is only
suitabl
e for n
ode lo
cation i
n
homo
gene
ous m
onitori
n
g
are
a
s. But in
actual
dete
c
tion a
r
ea
s, b
e
ca
use of e
n
vironm
ent
al
factors, no
des
are ofte
n non
-u
niformly
distrib
u
ted
an
d shifting
all t
he time, which lead
s
to
an
error th
at th
e cal
c
ul
ated
gap di
stan
ce
of
the averag
e
hop usi
ng
the traditiona
l DV-Hop al
gor
ithm i
s
far from the
actual di
sta
n
ce.
Mean
while
a
s
the
averag
e ho
p di
stan
ce
of ea
ch
a
n
ch
or
nod
e a
r
e n
o
t ide
n
tical, and th
e n
on-
anchor n
ode
s only re
ceiv
e the first averag
e
hop
di
stan
ce value,
so the average no
de ho
p
distan
ce h
a
s
a large
r
erro
r, whic
h affects the locali
zati
on accu
ra
cy.
3.2. The Improv
ed DV-Ho
p
Algorithm
In order to
overcome th
e sho
r
tcomin
gs,
the DV-Hop algo
rithm
is improve
d
in three
asp
e
ct
s belo
w
in this pa
pe
r.
3.2.1 Obt
a
in
Hop cou
n
t o
f
node
Firstly it is
essential to i
m
p
r
ove the
dat
a
stru
cture of
anchor
nod
e
s
b
r
oa
dcast
packet
(ID, x, y, hop
, hop val
ue,
path). So
the
data
st
ru
ctu
r
e was extend
ed
with two fi
elds:
hop
value
and path, wh
ere hop
valu
e
is
the way distan
ce
an
d
path i
s
th
e
prop
agatio
n
path. Th
ese
t
w
o
fields
are p
r
e
pare
d
fo
r th
e
se
con
d
stage
witho
u
t in
itial
i
zation
in th
e
first
stage.
Th
e an
ch
or no
d
e
s
broa
dcast the
data packet by the flooding method in the wh
ole net
work. Each n
ode only sav
e
s
the minimum
hop packet
sent by the anch
o
r no
de
with the sam
e
ID by the classical DV-Hop
algorith
m
. Th
e process g
o
e
s o
n
u
n
til all
the no
n-a
n
chor
nod
es
ob
tain the mini
mum ho
p p
a
c
ket
from all an
ch
or nod
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 703 – 71
0
706
3.2.2. Calcul
ate the av
erage hop dist
a
n
ce
In this
stage,
there
are two way
s
to im
prove th
e alg
o
rithm: firstly cha
ngin
g
the
ancho
r
node ave
r
ag
e hop dista
n
c
e calcul
atio
n method by
introdu
cing
the weighte
d
value secon
d
ly
cal
c
ulatin
g the distan
ce o
f
the commo
n node
s to
different an
chor no
de
s accordi
ng to the
averag
e hop
distan
ce of di
fferent an
cho
r
node
s
The
path
of
any two
an
chor
nod
es in
the m
onitori
ng a
r
ea
is
shorte
r, then
the a
ngle
betwe
en th
e
cente
r
n
ode
path a
nd t
w
o
an
cho
r
n
ode
s i
s
la
rge
r
,
so the
path i
s
nearly
a
strai
ght
line, finally th
e error of the averag
e hop
distan
ce
i
s
smaller. So it is in need to i
n
trodu
ce the
hop
distan
ce
wei
g
hts of a
n
cho
r
node
s.
Nam
e
ly the av
e
r
a
ge ho
p di
stan
ce from the
a
n
ch
or
nod
e i
to
other an
cho
r
node
j(
11
jM
,
M
is
the total n
u
m
ber of a
n
c
hor
nod
es) ha
s different deg
rees
of importan
c
e
.
The cal
c
ulat
ion of the wei
ghts is
sho
w
n
in formula (2
):
1
1
ij
i
j
ij
M
ij
i
j
j
hop
w
hop
(2)
whe
r
e
ij
w
is the value of path cal
c
ulatio
n from the an
chor n
ode
i
to the ancho
r n
ode
j
;
ij
hop
is the hop co
unt from the anc
hor i to the anchor n
o
d
e
j;
ij
is
th
e
a
n
g
le
o
f
th
e
c
e
n
t
e
r
n
ode
k in th
e p
a
th from th
e an
ch
or n
ode
i to t
he an
ch
or
no
de j a
nd t
w
o
anchor no
de
s, whi
c
h i
s
sho
w
n
in formula (3):
22
2
cos
2
ik
k
j
ij
ij
ik
k
j
hop
hop
hop
hop
hop
(3)
In the formul
a (3
), the
ho
p count in
th
e pat
h i
s
used to
repl
ace
the a
c
tual
d
i
stan
ce
value to es
timate the
cos
ij
value, then calcul
ation weight
s from the a
n
chor n
ode i to
the othe
r
anchor n
ode
s is obtaine
d. Eventually the weig
ht
ed a
v
erage h
op d
i
stan
ce of ea
ch an
ch
or no
de
is:
1
1
()
M
ij
ii
j
j
ij
dist
p
p
hopvalue
w
hop
(4)
Whe
n
obtaini
ng the weig
hted avera
ge h
op dist
an
ce h
op value of each an
ch
or n
ode
s,
data p
a
cket
s is b
r
o
a
d
c
a
s
ted in th
e
wh
ole net
wo
rk
i
n
flood
way,
and th
e data
stru
cture h
e
re is
(ID, hop val
u
e, path). The
initial value of
path
i
s
th
e
anchor no
de
ID. Wh
en
ea
ch
nod
e
re
cei
v
es
the data packet, the data packet is refe
rre
d with
the same ID p
a
cket in the first stage and the
hop value a
n
d
path are filled in the dat
a packet
s
.
Th
en the path
with the nod
e
ID is tran
smi
tted
to the neigh
b
o
r no
de. The
node o
n
ly accept
s and fo
rw
ard ea
ch d
a
ta packet this time, afterwa
r
ds
the re
ceive d
a
ta pa
ckets i
s
ab
ando
ned.
Whe
n
ea
ch
node o
b
tain
s
all the wei
ght
ed average h
op
distan
ce of al
l the anch
o
r
node
s,
then the dista
n
ce of the node to all anchor n
o
des i
s
obtain
ed
with the hop
cou
n
ts an
d the averag
e ho
p distan
ce in
the first pha
se.
3.2.3. Locate
the Nod
e
The
co
ordi
na
tes of
the
no
des a
r
e
esti
mated
by mu
ltilateral lo
cal
i
zation
metho
d
in th
e
node lo
cali
za
tion stage. Th
e locali
zatio
n
of node i
s
assume
d a
s
(
x
p
,
y
p
), and the coordinate o
f
anchor n
ode
s resp
ectively are (
1
x
p
,
1
y
p
), (
2
x
p
,
2
y
p
),…, (
nx
p
,
ny
p
), then the coo
r
din
a
tes o
f
the
node (
x
p
,
y
p
) is:
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TELKOM
NIKA
ISSN:
1693-6
930
Sensor Node
Easy M
o
vi
ng
Monitori
ng Region Locati
on Algorithm
in Internet .... (
D
onghua Feng)
707
1
2
22
11
22
22
22
()
(
)
()
(
)
()
(
)
xx
y
y
xx
y
y
x
nx
y
n
y
n
p
pp
p
d
p
pp
p
d
p
pp
p
d
(5)
Usi
ng Taylo
r
seri
es
sh
own
in the
[12] a
nd suppo
sin
g
the error in
X
and
Y
dire
ction of
(
x
p
,
y
p
) re
sp
ectivel
y
is (h, K), then:
22
(,
)
(
)
(
)
xy
x
n
x
y
n
y
fp
p
p
p
p
p
(6)
The erro
r value (h, K) ca
n
by estimat
ed by placing
the formula (6) in the(
x
p
,
y
p
). By
setting th
e th
reshold
a
c
cording to
eq
uat
ion (6) an
d
stoppin
g
the
iteration
p
r
o
c
e
s
s until m
eeti
ng
the accuracy
requi
rem
ents,
the
final posi
t
ioning coordi
nates (
x
p
,
y
p
) ca
n be obtain
ed.
3.3. The improv
ed DV-Ho
p
algorithm proced
ure
The im
proved DV
-Hop
al
gorithm
is ba
sed
on
the
b
a
si
c al
gorith
m
sho
w
n i
n
Figure
1
with improve
m
ents in thre
e stage
s ab
o
v
e,
and its flow ch
art is
sho
w
n in figure 2
.
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Vol. 13, No. 2, June 20
15 : 703 – 71
0
708
Figure 2. The
improved
DV-Ho
p
algo
rith
m pro
c
ed
ure
4. The simulation te
st
The
simul
a
tio
n
envi
r
onm
en
t is th
at the
r
e
are
20
0 o
r
50
0 sen
s
o
r
n
o
d
e
s
depl
oyed i
n
a
200
× 200 mo
nitoring a
r
e
a
, and the nod
e
distributio
n is non
-unifo
rm. The node
commu
nication
radiu
s
is
R=2
0
m, and the simulation
result is the average of 100 ti
mes.
With the total numbe
r of node
s is 200
and 500,
the
sen
s
o
r
nod
es positionin
g
e
rro
r are
simulate
d. Here th
e po
siti
oning
erro
r is the pe
rc
enta
ge of differen
c
e of th
e si
m
u
lated a
nd a
c
tual
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Sensor Node
Easy M
o
vi
ng
Monitori
ng Region Locati
on Algorithm
in Internet .... (
D
onghua Feng)
709
coo
r
din
a
tes
a
nd commu
nication ra
diu
s
. The results a
r
e comp
are
d
with the reference 10
and
11
as sho
w
n in
Figure 3 and
Figure 4:
Figure 3. Co
mpari
s
o
n
of positioni
ng error rate in the
total numbe
r of node
s 200
Figure 4. Co
mpari
s
o
n
of positioni
ng error rate in the
total numbe
r of node
s 500
As sh
own in
Figure 3 an
d
Figure 4, with
t
he increa
se
of the numb
e
r
of neig
hbo
r
node
s,
positio
ning e
r
ror of thre
e method
s are
signifi
cant
ly redu
ced. Ho
wever the method in this p
aper
cha
nge
s mo
re gently, because wh
en calcul
ating th
e
node di
stan
ce the avera
g
e
hop di
stan
ce of
different refe
ren
c
e a
n
cho
r
node
s i
s
used. A
nd the
angle
betwe
en differe
nt anchor
nod
e
s
is
taken i
n
to
consi
deration
whe
n
calcula
t
ing t
he ave
r
age
ho
p di
stan
ce. Due
to the itera
t
ive
refinem
ent u
s
ing
a Taylo
r
Serie
s
in t
he po
sitionin
g
, the po
sitioning
error
become
s
sm
aller.
Whe
n
the tot
a
l numb
e
r
of node
s i
s
20
0, the av
era
ge lo
cali
zatio
n
error
between the
pre
s
ent
method an
d referen
c
e 1
0
is red
u
ced by 12%, and
8% with refere
nce 11. When t
he total numb
e
r
of node
s is
500, the ave
r
age lo
cali
zat
i
on error
wi
th
the present method an
d referen
c
e 10
is
redu
ce
d by
2
0
%, and
12%
with
refe
ren
c
e
11. All
the
re
sults ab
ove proved th
at the p
o
sitioni
ng
accuracy of the method in
this pap
er
is highe
r
und
er the
same con
d
itions.
5. Conclusio
n
s
In ord
e
r to
re
duce the im
p
a
ct of e
n
viron
m
ental
fa
ctors for the
shifting of the
loca
tions o
f
sen
s
o
r
no
de
s, an im
prov
ed DV
-Hop a
l
gorithm i
s
p
r
opo
sed
whi
c
h is p
r
op
er f
o
r
sen
s
o
r
no
des
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ISSN: 16
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930
TELKOM
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Vol. 13, No. 2, June 20
15 : 703 – 71
0
710
motion a
nd
uneven
dist
ri
bute net
wo
rk. The th
ree
stage
s
of the DV
-Ho
p
al
gorithm
are
all
improve
d
: firstly when
obta
i
ning the
ho
p
co
unt, the
d
a
ta structu
r
e
is
chan
ged, t
here
b
y the d
a
ta
stora
ge
sp
ace in the
seco
nd
stage i
s
re
duced. In
the
averag
e
h
op distan
ce
calculation stage
the
previou
s
met
hod i
s
imp
r
ov
ed by
intro
d
u
c
ing
the
we
ig
hts into the calcul
ation, thus the ne
w jump
distan
ce form
ula is clo
s
e
r
to the actual node
ave
r
ag
e distan
ce. In the node p
o
sitioni
ng sta
ge,
firstly the initial node
coo
r
dinate
s
is ob
tained by
the
multilateral
cal
c
ulatio
n method an
d then
Taylor serie
s
of iterative refinement is i
m
pleme
n
ted. Simulation re
sults
sho
w
th
at the improv
ed
method
only
broa
dcast
s
d
a
ta pa
ckets t
w
o time
s
a
s
usu
a
l, and
wi
thout incre
a
si
ng the
netwo
rk
traffic an
d h
a
rd
wa
re d
e
vice, the
posit
ioning
er
ror
is redu
ced
g
r
eatly, whi
c
h
improve
s
th
e
positio
ning a
c
curacy an
d h
a
s a st
rong p
r
acticality.
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ces
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y
c
h
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R
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lti
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a
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hong L
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