TELKOM
NIKA
, Vol.13, No
.1, March 2
0
1
5
, pp. 349~3
5
6
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i1.1272
349
Re
cei
v
ed O
c
t
ober 2, 20
14;
Revi
se
d Ja
n
uary 2, 2015;
Acce
pt
ed Jan
uary 20, 201
5
Unscented Particle Filt
ering Algorithm for Optical-Fiber
Sensing Intrusion Localization Based on Particle
Swarm Optimization
Hua Zh
ang*, Xiaoping Jiang, Cheng
h
u
a
Li
Coll
eg
e of Elec
tronics an
d Informatio
n
Engi
n
eeri
ng, Hub
e
i
Ke
y
Lab
orator
y of Intellige
n
t Wireless
Commun
i
cati
o
n
s, South-Ce
nt
ral Univ
ersit
y
f
o
r Natio
nal
ities
,
W
uhan 43
007
4, Hube
i, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zhang
hu
a@
mail.scu
ec.edu
.cn
A
b
st
r
a
ct
T
o
improve th
e conver
ge
nc
e and
precis
i
on of in
trus
io
n loca
li
z
a
ti
on
in optic
al-fi
ber
sensin
g
peri
m
et
er prote
c
tion a
ppl
icati
o
ns, w
e
present
an a
l
gor
ith
m
b
a
sed
on a
n
u
n
scented
particl
e filter (UPF
). T
h
e
alg
o
rith
m e
m
ploys
particl
e
sw
arm opti
m
i
z
at
io
n (PS
O
) to mitig
a
te the sa
mpl
e
de
gen
eracy
an
d
impov
erish
m
en
t probl
e
m
of th
e partic
l
e fi
lter. By co
mp
ar
in
g
the pr
esent fit
ness va
lu
e of
particl
es w
i
th th
e
opti
m
u
m
fitn
es
s valu
e of th
e
obj
ective fu
n
c
tion, PSO
moves p
a
rticles
w
i
th insig
n
ific
ant UPF w
e
ig
hts
tow
a
rds the h
i
gher
like
lih
oo
d
regi
on
and
det
ermines
the
op
tima
l p
o
sitio
n
s
for particl
es w
i
th lar
ger w
e
i
ght
s.
T
he particl
es w
i
th larg
er w
e
ig
h
t
s results in a
n
e
w
sa
mp
le set
w
i
th a mor
e
ba
l
ance
d
distri
buti
on b
e
tw
een th
e
priors
an
d th
e l
i
kel
i
ho
od.
Simulati
ons
d
e
monstrat
e
th
at the
al
gorith
m
s
p
e
eds
up
conv
erge
nce
a
n
d
improves th
e p
r
ecisio
n of intru
s
ion l
o
cal
i
z
a
tio
n
.
Ke
y
w
ords
: opt
ical-fib
er sens
o
r
, intrusion l
o
ca
li
z
a
tio
n
, UPF
,
PSO
1. Introduc
tion
Optical
-
fibe
r
sen
s
o
r
-ba
s
ed
intrusi
on d
e
tecti
on te
ch
no
logie
s
are wi
dely used in
perim
eter
se
curit
y
pr
ot
ect
i
on
sy
st
e
m
s.
Re
ce
ntly, the optical
fiber se
nsi
n
g techn
o
logi
es availa
ble
for
intrusi
on d
e
tection i
n
clu
d
e
the interfe
r
ometer-ba
s
e
d
optical fibe
r se
nsor
s an
d the optical
time
domain
reflectometry (OTDR)-ba
s
e
d
o
p
tical fib
e
r
se
nsors,
and
ea
ch
of which h
a
s
cha
r
a
c
ters [1]
-
[8]. Among t
he te
chn
o
log
i
es, the
interferomete
r
-b
a
s
ed
opti
c
al-fi
ber
se
ns
ors are preferred
in
intrusi
on dete
c
tion for thei
r high se
nsitivi
t
y to vibrat
ional sign
als a
n
d
low cost. As is kno
w
n, it is
importa
nt to l
o
cali
ze th
e in
trude
r when
an intrusi
on
signal i
s
d
e
tected in a
pe
ri
meter
prote
c
t
i
on
system. Gen
e
rally,
the un
derg
r
o
und
i
n
trusi
on sig
nal
s
to be
dete
c
te
d are a
c
o
u
sti
c
(or vibratio
n
a
l)
sign
als g
ene
rated by the i
n
trude
r. Whe
n
an intrus
i
o
n occu
rs, the
time of arriv
a
l (TOA
) of the
intrusi
on si
gn
al is used to locate the p
o
sition of the intrude
r ap
proxi
m
ately [9].
As the inte
rfe
r
omete
r
-ba
s
e
d
syste
m
s
use co
ns
ecutive lase
r p
u
lses,
the interval
b
e
twee
n
the lase
r bei
ng sent out a
nd the intrusi
on sign
al
arriving at the receiver
can
not
be determin
ed.
Thus,
the T
O
A of the
i
n
trusi
on
sig
n
a
l cann
ot
be
accu
rately measured, which
affect
s the
pre
c
isi
on of i
n
trusi
on l
o
cal
i
zation. T
o
ge
t the pre
c
i
s
e
TOAs
of the i
n
trusi
on
sign
als, ma
ny sig
n
a
l
pro
c
e
ssi
ng
algorith
m
s
were
employe
d
[11]. Ho
wever, the a
ppro
a
che
s
suffer from t
h
e
measurement
erro
rs for the
fast speed of
the lase
r pro
pagatin
g in the optical fiber, the errors of
the time limit the pre
c
i
s
ion
of the intru
s
io
n localiz
ation
to tens of m
e
ters [
12]. Many re
sea
r
ch
ers
have worke
d
on this proble
m
and va
rio
u
s
signal
processing algo
rithms have
b
e
en
em
ployed to
obtain
a p
r
e
c
ise
TOA i
n
o
p
tical-fib
e
r se
nsin
g lo
ca
li
za
tion [13],[14]. To i
m
prove t
he p
r
e
c
isi
o
n
of
intrusi
on lo
calizatio
n, we
have previously us
ed th
e geom
etrica
l position
s
of
the distri
but
ed
sen
s
o
r
s an
d
the differe
nces i
n
relative
TOAs to e
s
tim
a
te the po
sition of the i
n
trude
r
[15]-[1
6
]
.
State estim
a
tion-b
a
sed m
e
thod
s d
e
m
onstrate
hig
h
pre
c
isi
on.
Ho
wever,
as th
e mea
s
u
r
em
ent
equatio
n i
s
nonlin
ear,
th
e conve
r
ge
n
c
e
sp
eed
i
s
poo
r
and
t
he p
r
e
c
i
s
ion
is subje
c
t
to
measurement
erro
rs.
In this pap
er,
a parti
cle filter is u
s
ed to h
andle the
pro
b
lem of nonli
nearity in opti
c
al-fib
e
r
sen
s
in
g intru
s
ion
lo
cali
zati
on. To
avoid
the d
ege
neracy p
r
obl
em
and
sam
p
le i
m
poveri
s
hm
e
n
t
after re
sam
p
ling, we em
ploy the un
scente
d
pa
rticle filter (UP
F
) an
d use
particl
e swa
r
m
optimization (PSO) to mai
n
tain diversit
y in the
pa
rticle
s. A se
rie
s
of si
mulati
ons
demo
n
st
rate
that the prop
ose
d
algo
rith
m improve
s
p
r
eci
s
io
n
and
conve
r
ge
nce whe
n
there is no prior intru
der
loc
a
tion.
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 : 349 – 3
5
6
350
2. Intrusion localiza
t
ion in optical-fib
er sensing p
e
rimeter pro
t
ec
tion
In
optical-fib
er se
nsi
ng p
e
rimete
r prot
ecti
on
sy
st
e
m
s,
int
r
ude
r
s
gen
erate vi
bration
a
l
sign
als that
can be d
e
tect
ed by
the opt
ical-fib
er
sen
s
ors. Afte
r th
e dete
c
ted si
gnal
s have b
een
pro
c
e
s
sed an
d analyze
d
, the time intervals bet
ween t
he lase
r pul
se being sent and the 0-p
h
a
se
of the intru
s
io
n sig
nal
wave
forms
bein
g
receive
d
c
an
be calculated
. This inte
rval
is the time
th
at
the vibrationa
l sig
nal
s ta
ke
to p
r
op
agate
from
t
he i
n
truder to th
e
sensor,
and
is call
ed
the
T
O
A
of the intrusio
n sign
al.
Figure 1. Dist
ances fro
m
in
trude
r to sen
s
ors a
r
e e
qual
to the distan
ce that the aco
u
stic
sign
als
travels
from intruder to s
e
ns
ors
Figure 1 illustrates a di
stri
buted opti
c
al-fiber
sensing perimeter protection
syst
em. Let
the moment
at which the i
n
trude
r ge
ne
rates the vib
r
a
t
ional sig
nal
be t
0
, and the
TOA be t. The
time interval (t-t0) in
clud
e
s
the time taken by
the vibration
a
l sig
n
a
l to arrive at
the sen
s
or a
nd
the time for the laser to p
r
opag
ate alon
g the optical
fiber. As the
sensor lo
catio
n
s a
r
e fixed, the
prop
agatio
n t
i
me of the l
a
ser in the
opt
ical fibe
r i
s
al
most
con
s
tan
t
and
can
be
pre
-
calib
rate
d.
Thus, the g
e
o
m
etrical relati
onship bet
we
en the i
th
sen
s
or a
nd the in
trude
r is:
22
2
-(
-
)
(
-
)
(
)
0
x
xy
y
z
z
v
t
t
T
ii
i
I
i
i
（）
(1)
whe
r
e (x
i
, y
i
, z
i
) is the lo
ca
tion of the i
th
sen
s
or a
nd (x, y, z) is the location of the intrud
er. v
I
is
the spee
d at which the vibration
a
l sig
nal
gene
rate
d by the intruder i
s
tran
sported, t
0
is the
moment at which the intru
der ge
ne
rate
s the vibratio
nal sig
nal, T
i
is the time taken by the laser to
prop
agate
al
ong the o
p
tical fiber of the
i
th
s
e
ns
or
, an
d
t
i
is the m
o
ment at whi
c
h the int
r
u
s
i
o
n
sign
al in the i
th
sen
s
o
r
is d
e
tected by th
e receiver.
As the preci
s
e moment at
which the in
trude
r gen
era
t
es the vibrational si
gnal
a
nd the
prop
agatio
n spe
ed of the
vibrational signal are un
kno
w
n (i.e., t
0
and v
I
are unkn
o
wn), the
positio
n of th
e intru
der ca
nnot be
com
puted di
re
ct
ly by solvin
g E
quation
(1
). In previou
s
work,
we u
s
ed opti
m
al estimatio
n
and state
estimation
m
e
thod
s to obtain the be
st estimate of the
intrude
r’
s location
(
ˆ
ˆ
ˆ
,,
)
x
yz
.
2.1. Optimal estimatio
n-b
ased localization
If the intrusion sig
nal is
detecte
d by more tha
n
two sen
s
ors, t
0
can be ig
nore
d
by
con
s
id
erin
g the dista
n
ces
betwe
en the
sen
s
o
r
s:
22
2
2
2
2
-
(
-
)
(-
)
-
-
(
-
)
(-
)
(
-
-
(
-
)
)
i
xx
y
y
z
z
xx
y
y
z
z
v
t
t
T
T
ii
j
j
j
I
i
j
i
j
++
+
+
=
×
（）
（
）
(2)
whe
r
e
()
×
retu
rns th
e ab
sol
u
te value. T
hen, (x, y, z) and
I
v
can
b
e
compute
d
by optimal
estimation te
chni
que
s su
ch as the least-squ
a
re
s (L-S) method [15]. Howeve
r, the determin
a
te
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Uns
c
ented P
a
rtic
le Filtering Al
gorithm f
o
r Optic
a
l-Fiber Sens
ing Intrus
ion .... (Hua Zhang)
351
relation
shi
p
in Equation (2) doe
s not
con
s
id
er noi
se in the para
m
eters, resul
t
ing in impre
c
ise
estimate
s. In
particula
r, wh
en n
o
mo
re t
han fo
ur
se
nsors dete
c
t the
intru
s
ion
si
g
nal, the e
r
ror
in
the locatio
n
e
s
timation in
creases
con
s
id
erably.
2.2. State es
timation-ba
s
e
d localiza
t
ion
To u
s
e
state
estimation
m
e
thod
s to
esti
mate
a
nd tra
c
k an
intrude
r’s lo
cation, t
he
state
equatio
ns a
n
d
mea
s
u
r
em
ent model
are ded
uced a
s
follo
ws. Th
e location an
d sp
eed of t
h
e
intrude
r, the unkno
wn spe
ed of the vibrational
sign
a
l
, and the moment at whi
c
h the intru
d
e
r
gene
rated
the vibration
a
l si
gnal
s
are
co
ns
i
d
e
r
ed as
the
state parameters,
i.e
.,
0
[]
T
xy
z
I
X
x
y
z
v
v
vvt
. To simplify the problem
, we assum
e
that the speed at
whi
c
h th
e intruder is movin
g
is almo
st
consta
nt, i.
e., the vari
ation i
n
spee
d is ze
ro, an
d that t
he
spe
ed of the
vibrational
signal i
s
con
s
tant. Zero
-m
ean G
a
u
ssi
a
n
noi
se i
s
a
dded to
both
the
intrude
r spee
d and the vibrational si
gnal.
The state eq
uation is the
n
,
X
AX
W
(3)
W
h
er
e
000
1
0
000
0000
1000
00000
100
00000
000
00000
000
00000
000
00000
000
00000
000
A
(4)
and W i
s
the
noise ve
ctor of the state para
m
et
ers,
whi
c
h have
mean
s of ze
ro and
covari
ance
matrix
12
8
R
=
d
i
a
g
(
...
)
.
The mea
s
u
r
e
m
ent para
m
e
t
ers a
r
e the p
o
ints at
whi
c
h the intrusio
n signal
s arri
ve at th
e
s
e
ns
or
s
,
i.e
.,
12
[.
.
]
T
n
Yt
t
t
. From Equati
on (1
), we ha
ve
22
2
0
1
-(
-
)
(
-
)
ii
i
i
i
I
tx
x
y
y
z
z
t
T
v
（）
(5)
Then, the me
asu
r
em
ent model can be
written a
s
:
()
Z
GX
V
(6)
whe
r
e
()
G
de
no
tes the
me
a
s
ureme
n
t fun
c
tion ve
ctors noted
in E
q
uation
(5
) a
n
d V i
s
the
measurement
noise vector,
whi
c
h ha
s
mean m
and
co
varian
ce
matrix
12
n
tt
Q=di
a
g
(
.
.
.
)
t
.
As the me
asurem
ent equ
ations i
n
Equ
a
tion (6
) a
r
e
nonlin
ear, th
e un
scented
Kalman
filter (UKF) i
s
u
s
e
d
to
ob
tain hig
h
p
r
e
c
isi
on [1
6]. The al
gorith
m
yields go
od
perfo
rma
n
ce
in
tracking
the i
n
trude
r.
However, when
there
is
no
pri
o
r
kno
w
le
dge
of the int
r
u
s
ion lo
cation, t
h
e
algorith
m
is sl
ow to co
nverge.
3. PSO-base
d UPF Algori
t
hm for Intru
s
ion Localization
UPF i
s
a
pop
ular
state
esti
mation al
gorit
hm fo
r nonli
n
ear syste
m
s. In
UPF, UKF is
u
s
ed
to generate
sophi
sticate
d
prop
os
ed
distributio
n
s
that sea
m
le
ssly integrate the
current
observation [
18]. The co
mbination of
UKF with
a particle filter outperforms existing part
i
cle
filters, alb
e
it at the cost o
f
comp
utatio
nal
compl
e
xity. UPF also
suffers from
the deg
ene
ra
cy
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 : 349 – 3
5
6
352
probl
em an
d
the loss of pa
rticle dive
rsity
.
As PSO
is
simple, fas
t, and effic
i
ent, it c
an be us
ed
to
improve the p
e
rform
a
n
c
e o
f
the UPF algorithm.
3.1. PSO algorithm
PSO is
an
e
v
olutionary
computation
tech
niqu
e b
a
s
ed
on
the
b
ehavior of in
dividual
s
within a swa
r
m [17]. The individuals
find the
optimum solutio
n
using thei
r own previo
us
experie
nce a
nd that of the
i
r neig
hbo
rs.
Each in
dividu
al in the swa
r
m tra
c
ks the
coo
r
din
a
tes
in
the proble
m
spa
c
e
that a
r
e a
s
soci
ated
with the
be
st
solutio
n
a
c
hi
eved
so fa
r. I
n
the
reali
z
ati
on
pro
c
e
s
s of
a PSO
algo
rithm, ea
ch
particl
e
co
rresp
ond
s to
a candi
date
sol
u
tion to
the
optimizatio
n
probl
em. T
h
e
direction
a
n
d
di
stan
ce th
at the p
a
rti
c
l
e
s
move
wit
h
in the
soluti
on
spa
c
e a
r
e d
e
t
ermine
d by their
spe
ed, a
nd the obj
ec
tive func
tion determines
the fitnes
s
value of
each initial p
opulatio
n. Th
e parti
cle
s
fol
l
ow the
cu
rre
n
t optimal pa
rticle, an
d an
optimal solut
i
on
is a
c
hieve
d
a
fter ea
ch g
e
n
e
ration. In
ea
ch g
ene
ratio
n
, the pa
rticl
e
s follo
w the
optimal soluti
on
bes
t
p
of the parti
cle itself, den
oted a
s
12
(,
,
,
)
T
bi
bi
bi
biN
Pp
p
p
, as
well as
the
optimal s
o
lution
be
st
g
of the whole
popul
ation, d
enoted a
s
12
(,
,
,
)
T
bb
b
b
N
Gg
g
g
.
For a
ra
ndo
m parti
cle
swarm
contai
nin
g
M pa
rticle
s,
the po
sition
s and velo
citie
s
of the
i
th
parti
cle i
n
N-dime
nsi
onal
spa
c
e
are
12
(,
,
,
)
T
ii
i
i
N
Xx
x
x
and
12
(,
,
,
)
T
ii
i
i
N
Vv
v
v
. After
determi
ning
bes
t
p
and
be
st
g
, each particl
e upd
a
t
es its positi
on and velo
city according
to the
followin
g
equ
ations:
11
2
2
(
k
1
)
(k
)
(
k
)
(
k
)(p
(k
)
)
(k
)(
(k
))
ii
b
i
i
b
i
vw
v
c
r
x
c
r
g
x
(7)
(k
1
)
(
k
)
(
k
)
ii
i
xx
v
(8)
whe
r
e
1
(k
)
r
~U(0, 1) and
2
(k
)
r
~U(0, 1) are use
d
to give t
he algorithm a sto
c
hasti
c nature,
(k
)
w
is the ine
r
tial
weig
ht, and
1
c
, c
2
are
accel
e
ration facto
r
s
use
d
to adju
s
t the maximu
m step
size o
f
bes
t
p
and
be
st
g
.
3.2. PSO-optimized UPF for optical-f
iber sensing i
n
trusion localiz
ation
In the PSO process, the p
a
rticle
swarm
se
a
r
che
s
for optimal sol
u
tions a
nd det
ermin
e
s
the optimal lo
cation
by upd
ating the p
a
rti
c
le velo
ci
ties.
Whe
n
UPF i
s
ap
plied to t
he e
s
timation
of
the intru
s
ion
locatio
n
, the PSO algo
rithm is u
s
ed
to optimize
the parti
cle
s
in
UPF. In the
algorith
m
, the parti
cle po
pulation in th
e PSO sup
p
li
es the p
a
rticl
e
s for
UPF. PSO quickly find
s
the target re
g
i
on, whi
c
h en
sures th
at the parti
cl
e set sea
r
ches
re
gion
s with a
high likelihoo
d of
contai
ning th
e optimal sol
u
tion. The alg
o
rithm procee
ds a
s
follows:
Step 1: Initialization
Initialize the
PSO param
e
t
ers. Set up
the PSO
parameters, su
ch as the nu
mber of
particl
es
N, acceleration coefficient
s C
1
and C
2
, and the maximum
numbe
r of iteration
s
.
Step 2: Initial
sampli
ng
Sample
N particles {x
0
i
, i = 1, 2, …, N} from the
prior di
strib
u
tio
n
with initial
weig
hts
{(
1
)
1
,
1
,
2
,
,}
i
wk
N
i
N
.
Step 3: Importance
sampli
ng
Sample particles
(k
)
i
x
from the prop
osed di
stribution:
k(
k
)
ˆ
ˆ
(x(k
)
/
x
(
k
1
),
Z
)
(
(
k
)
,
(
k
)
,
(
k
)
)
ii
i
x
qN
x
x
(9)
Step 4: Updat
e weig
hts
a. Obtain syst
em mea
s
ure
m
ents.
b. Acco
rding
to the new measu
r
em
e
n
ts,
cal
c
ulat
e and norm
a
lize pa
rticl
e
weights
according to:
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TELKOM
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Uns
c
ented P
a
rtic
le Filtering Al
gorithm f
o
r Optic
a
l-Fiber Sens
ing Intrus
ion .... (Hua Zhang)
353
((
k
)
/
(
k
)
)
(
(
k
)
/
(
k
1
)
)
(k
)
(
k
1
)
(
(
k
)
/
(
k
1
)
,
(k
))
ii
i
ii
ii
pz
x
p
x
x
ww
qx
x
Z
(10)
Step 5: Optimize the pa
rticl
e
s by PSO
a. Re
sampl
e
the wei
ghte
d
parti
cle
s
to obtain
part
i
cle
s
{,
}
ii
kk
x
w
with e
qual
weight
s
1
{,
}
i
k
xN
. Particles
with sm
aller wei
ghts are
elimi
nat
ed, an
d th
e num
ber of
particl
es with
larg
er
weig
ht
s in
cre
a
se
s.
b. The majo
ri
ty of particles move towa
rd
s
the hig
h
-li
k
elihoo
d regi
o
n
and a
r
e a
s
sign
ed a
new wei
ght
by com
p
a
r
in
g the
cu
rre
nt po
sition
s wi
t
h
the fitne
s
s
value of the
optimal p
a
rticles
**
(/
)
(
/
)
ii
i
i
kk
k
k
p
pz
x
p
z
x
.
c. Set the minimum move
ment threshol
d
α
for the partic
l
es
. If
p
, the
filter partic
l
es
remai
n
statio
nary; otherwi
se, the
filter p
a
rticle
s adj
ust
their spe
ed a
c
cordi
ng to Equation (7):
**
*
*
11
2
2
(k
1
|
k
)
(k
)
(
k
|
k
1
)
(
k
1
)(
(k
1
)
(k
|
k
1
)
)
(
k
1
)(
(k
1
)
(k
|
k
1
)
)
k
ii
p
i
g
i
vw
v
c
r
x
x
c
r
x
x
(11)
w
h
er
e
(k
1
|
k
)
k
i
v
is the
value of
(k
1
|
k
)
i
v
after k iteratio
ns.
The
sp
eed
d
e
termin
es the
directio
n
and di
stan
ce
moved by the particle
s
d. Redete
r
mi
ne the parti
cl
e positio
ns a
c
cordi
ng to Equation (8) to
obtain a ne
w particle
set
{,
}
ii
kk
x
w
.
Step 6: State
estimation
Comp
ute the
poste
rior
probability esti
mation
of th
e target
state at time k using
*
1
N
ii
i
kk
k
i
x
xw
.
Step 7: Set k = k+1, return
to Step 3, a
nd
co
ntinue t
o
estimate th
e poste
rio
r
probability
of the target state at the next time step.
In the
above
processe
s,
PSO move
s
the pa
rt
icl
e
s
in the
UPF
towa
rd
s
are
a
s
of
high
likeliho
od. Th
us, the o
p
timal po
sition is
determi
ned in
the re
sam
p
li
ng process b
y
compa
r
in
g th
e
pre
s
ent fitne
s
s value
with t
he optim
um fitness val
ue
o
f
the obje
c
tive functio
n
. M
odifying the p
r
ior
sampl
e
weig
h
t
s such that t
he resulting
p
a
rticle
s
have large
r
weig
ht
s results
i
n
a
new
sample
set
that assume
s a more bal
an
ced di
strib
u
tion between t
he prio
rs and
the likelih
ood.
4. Simulations and An
aly
s
is
To verify the performan
ce of the pro
posed alg
o
rit
h
m, the con
v
ergen
ce
sp
eed an
d
pre
c
isi
on of t
he p
r
opo
se
d
algorith
m
were co
mpa
r
ed
with that of t
he UKF
algo
rithm and
an
L-S
algorith
m
[15]
-[16]. The
si
mulation d
a
ta
in [15]
are u
s
ed,
whe
r
e th
e se
nsors a
r
e located in li
nes
and ro
ws as
sho
w
n in Fig
u
re 2, and th
e interv
als b
e
t
ween eve
r
y pair of the nei
ghbo
ring
sen
s
ors
are 50 mete
rs. The propa
gation speed
of the vibr
ational sig
nal g
enerated by the intrud
er was
assume
d to
be a con
s
tan
t
1000 m/s.
The e
rro
rs in
TOAs
were
assume
d to
be belo
w
0.1
ms,
and the me
a
s
ureme
n
t noi
se was a
s
su
med to hav
e
zero mean
and a covari
ance of 0.1. The
intrude
r wa
s con
s
ide
r
ed
to be moving with a speed of
1 m/s, and
the initial
R =
diag(1,1,1,1,1
,
1,1,1). In our simul
a
tion
s, t
he likelih
ood functio
n
is defined
as the obje
c
tive
function, and
thi
s
was assum
e
d
to
ha
ve
the posterior pr
obability funct
i
on
|1
21
/
2
2
11
(
)
exp[
(
)
]
(2
)
2
i
ii
kk
k
k
k
vv
pz
x
z
z
, where
k
z
is the latest ob
servatio
n an
d
|1
i
kk
z
is the
predi
cted o
b
servation.
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9
30
TELKOM
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Vol. 13, No. 1, March 2
015 : 349 – 3
5
6
354
Figure 2. The
location
s of the
se
nsors for simul
a
tion [15]
4.1. The con
v
ergence speed and pr
e
c
ision of th
e
algorithms
Figure 3 de
pi
cts the
simul
a
tion re
sult
s
and the
stati
s
tical
re
sults
of the algo
rithms a
r
e
listed in table 1. As shown in the simulations
, the PSO algorithm optimizes the particle
s
in
efficien
cy and the particle
popul
ation in the PSO
sup
p
lies the pa
rticle
s for UPF. As PSO quickly
finds the targ
et regio
n
, the particl
e set
searche
s
regio
n
s with
a hig
h
likelih
ood o
f
containin
g
the
optimal
soluti
on. As
sho
w
n in Ta
ble
1, the propo
se
d algo
rithm
converg
e
s wit
h
in 50
iterati
o
ns.
Figure 3 Simulation re
sult
s for ea
ch alg
o
rithm
Whe
r
e a
s
th
e L-S an
d UKF algorithm
s re
quire mo
re than
200
iteration
s
. Th
us, the
prop
osed
alg
o
rithm ha
s a redu
ce
d com
putational
bu
rden,
which
make
s it suitable fo
r
re
al-t
ime
appli
c
ation
s
. The e
rro
rs gi
ven by the different
alg
o
rit
h
ms a
r
e a
p
p
r
oximately the same, alth
ou
gh
those from th
e pro
p
o
s
ed a
l
gorithm a
r
e l
e
ss than
0.1
m after 50 it
eration
s
. Thi
s
demon
s
trate
s
that the algori
t
hm can al
so improve the p
r
eci
s
io
n
of detection. The simulation
s de
monst
r
ate tha
t
the pro
p
o
s
ed
algorithm
o
u
tperfo
rms th
e others
in t
e
rm
s of both
pre
c
isi
on an
d conve
r
g
e
n
c
e
spe
ed.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Uns
c
ented P
a
rtic
le Filtering Al
gorithm f
o
r Optic
a
l-Fiber Sens
ing Intrus
ion .... (Hua Zhang)
355
Table 1. The
statistics of the algorith
m
s
Algorithms
Error o
f
the location
estimation(meters)
Number of
iterations(times)
L-S[15]
0.23
>200
UKF[16]
0.21
>200
The pro
posed al
gorithm
0.07
<50
4.2. The rob
u
stn
ess o
f
the algorithm
to the numb
e
r of th
e sen
sors
As in state-e
s
timation b
a
sed algo
rithm
s
, the
preci
s
io
n is subje
c
t to the numb
e
r of the
sen
s
o
r
s an
d
the erro
rs of
the location
e
s
tima
tion
und
er va
riou
s n
u
m
bers of th
e
sen
s
o
r
s which
detecte
d the
intrusi
on
are
listed i
n
Ta
bl
e 2. A
s
sho
w
n in T
able
2,
to get
high
e
r
p
r
e
c
isi
on, t
h
e
intrude
r
sho
u
l
d be d
e
tect
ed by mo
re
than 5
sen
s
ors sim
u
ltan
eou
sly for L
-
S algorithm.
The
numbe
r for the sam
e
pre
c
isi
on in the
UKF al
go
rith
m and the propo
sed al
gori
t
hm are 3. Even
whe
n
there i
s
only one se
nso
r
whi
c
h
can dete
c
t
the intrude
r, the prop
osed alg
o
rithm can track
the intrud
er p
r
eci
s
ely. It demonst
r
ate
s
that the pr
op
osed algo
rithm i
s
ro
bu
st to the numb
e
r of th
e
s
e
ns
or
s
us
ed fo
r
lo
c
a
tio
n
es
tima
tio
n
.
Table 2. The
statistical errors
with vario
u
s num
be
rs o
f
sensors det
ecting the intrusio
n sig
nals
Algorithms
Number of
the se
nsors
Errors of th
e location
estimation(meters)
L-S
1 -
3 3.29
5 0.24
UKF
1 2.12
3 0.29
5 0.11
The pro
posed
algorithm
1 1.53
3 0.15
5 0.07
5. Conclusio
n
To imp
r
ove
the converge
nce
and
pre
c
isi
on of
i
n
trusio
n lo
cali
zation in
opti
c
al-fib
er
sen
s
in
g pe
ri
meter p
r
ote
c
t
i
on ap
plicatio
ns, we have
pro
p
o
s
ed
a
n
algo
rithm
based o
n
P
S
O
-
optimize
d
UP
F. In the propose
d
algo
rith
m, PSO
is employed to mitigate the sa
mple deg
ene
racy
and im
poveri
s
hme
n
t probl
em of the
particle filter.
By comp
ari
ng th
e present fitness value
of th
e
particl
es with
the optimu
m
fitness value
of the
obj
ective function,
PSO en
sure
s pa
rticl
e
s th
at
have in
sig
n
ificant
UPF
weights move
towards hi
gh
er li
kelih
ood
regio
n
s an
d
determi
ne
s t
he
optimal po
sit
i
on of pa
rticl
e
s
with larg
er we
ight
s. Simulation
s have dem
on
strated th
at the
prop
osed
alg
o
rithm
sp
eed
s u
p
conve
r
g
ence a
nd i
m
prove
s
th
e in
trusio
n lo
cali
zation
p
r
eci
s
i
o
n
comp
ared wit
h
previou
s
m
e
thod
s.
Ackn
o
w
l
e
dg
ements
This
wo
rk wa
s
supp
orte
d b
y
the Key Te
chn
o
logie
s
R&D Pro
g
ra
m
of Wu
han
Cit
y
, China
unde
r G
r
ant
No. 20
121
2521
825
an
d the Ge
ne
ral Prog
ram
of Nation
al
Natural Sci
e
nce
Found
ation of
China u
nde
r Grant
No. 61
2014
48.
Referen
ces
[1]
Juarez
JC,
M
a
ier, EW
, et
al.
Distribut
ed F
i
b
e
r-Optic Intrusi
on S
ens
or S
y
s
t
em.
Journ
a
l
of
Li
ghtw
a
ve
T
e
chno
logy.
2
005; 23(
6): 208
1-08
7.
[2]
Culsh
a
w
B. T
he o
p
tical
fiber
Sagn
ac i
n
terfe
r
ometer:
An ov
ervie
w
of
its pr
incip
l
es an
d
a
pplic
atio
ns.
Measur
e
m
ent
Scienc
e an
d T
e
chn
o
lo
gy
. 200
6; 17: 1-16.
[3]
Park
J.
F
i
b
e
r optic intrusi
o
n
sensor
usi
n
g
c
oher
ent optica
l
time doma
i
n
r
e
flectometer.
Appl. P
h
ys
.
200
3; 42: 348
1
-
348
2.
[4]
Z
hou Y, J
i
n
g
SJ, et al. St
ud
y
on
the
distri
buted
o
p
tical
fi
ber s
ensi
n
g
te
chno
log
y
f
o
r
pi
peli
n
e
safet
y
detectio
n
an
d l
o
catio
n
.
Journ
a
l of Optoel
ectronics · Las
er
. 200
8; 19(7): 92
2-92
4.
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 : 349 – 3
5
6
356
[5]
Jahe
d NMS, N
u
rmoh
a
mmad
i
T
,
et al.
Enhan
ced reso
luti
on
fiber optic stra
i
n
sensor
base
d
on Mac
h
-
Z
ehnd
er i
n
terfero
m
eter
an
d
di
sp
lace
ment
sensi
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