TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4264 ~ 4
2
7
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.506
3
4264
Re
cei
v
ed
No
vem
ber 5, 20
13; Re
vised
De
cem
ber 3
1
,
2013; Accep
t
ed Jan
uary 2
4
, 2014
Resear
ch on Warehouse Tar
g
et Locating and
Trackin
g
Based on EKF and UKF
Bian Gua
ng-rong*, Kon
g
Fan-cheng,
Zha
ng Hong
-hai, Cao Jin
-
rong, Shi Hong-
y
a
n
Dep
a
rtment of Aviatio
n
Ammu
nitio
n
, Air F
o
rce Co
ll
eg
e of Service, XuZ
h
o
u
,
JiangS
u Provi
n
ce, Chi
na,
227, Z
hon
gsh
a
n
road, GuL
ou
District, Xu
Z
h
ou, Jian
gSu pr
ovinc
e
, P.R.China,
Postcode: 2
2
1
003, telp: +
8
6
1
895
22
018
90
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 4497
39
01@
q
q
.com
A
b
st
r
a
ct
T
h
is pap
er pre
s
ents a new
locatin
g
an
d trackin
g
metho
d
based o
n
W
S
N, EKF
and UKF
.
T
he
princi
pl
e of Lo
cation a
nd tra
cking is a
pply
i
ng maxi
mu
m l
i
keli
ho
od esti
mati
on a
l
gor
ith
m
of multil
ater
al
me
asur
e
m
ent
meth
od t
o
calc
ulati
ng th
e co
o
r
din
a
tes of th
e
unkn
o
w
n
no
de.
Accordi
ng to
mo
nitori
ng
mot
i
on
trajectory of th
e sa
me
unk
no
w
n
target no
de
w
i
thin
a c
ontin
uous
peri
od
of
time, th
e
moti
o
n
eq
uati
on c
a
n
b
e
establ
ishe
d. When th
e stat
e
equ
atio
n of w
a
reho
use tar
get
tracking syst
e
m
is
no
n-li
ne
a
r
, EKF and U
K
F
filterin
g al
gor
ithm are
resp
ec
tively a
p
p
lie
d t
o
acq
u
ir
i
n
g
the
state esti
mate
of the w
a
re
ho
use targ
et
moti
o
n
equ
atio
n, so as to achieve th
e effective tracki
ng of w
a
reho
u
s
e target.
Ke
y
w
ords
:
W
S
N, EKF
, UKF, Locatin
g, T
r
acking
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
Re
cent a
d
va
ncem
ents of
micro sen
s
ors technolo
g
y have allo
wed
a wi
de
rang
e of
Wirel
e
ss Se
n
s
or Netwo
r
ks (WS
N) im
ple
m
entation
s
to
be reali
z
ed.
WSN
are
use
d
in mo
nitorin
g
and dete
c
tin
g
informatio
n of detecti
on obje
c
ts i
n
many types of ind
u
st
rial an
d mili
tary
environ
ment
s. The info
rma
t
ion is
sent t
o
the
g
a
tewa
y node, in
order to
re
alize
monitori
ng a
n
d
tracking
the t
a
rget i
n
a
certain area. Wa
reho
use
targ
et locali
zatio
n
and trackin
g
system
co
nsi
s
ts
of many wi
reless
sen
s
o
r
node
s, tho
s
e nod
es in
cl
ude b
e
a
c
on
node
s a
nd
u
n
kn
own no
d
e
s
.
Beaco
n
nod
e
s
ca
n obtain
their pre
c
i
s
e l
o
cati
o
n
by ca
rrying BDS (GPS) positio
ning equi
pme
n
t.
Beaco
n
nod
e
s
are th
e refe
ren
c
e poi
nt of unkn
o
wn no
de location [1
].
The un
kn
own
node
can
be
person
nel, vehicl
es
, op
eration ma
chin
ery and
other mobile
node
s. By communi
catin
g
with n
earb
y
beacon
no
des or
the unkno
wn
no
des whi
c
h
h
a
ve
acq
u
ire
d
thei
r own po
sitio
n
informatio
n
,
t
he unkn
o
wn node
s
can
cal
c
ulate th
eir o
w
n p
o
sit
i
on
according
to
a certain
lo
cation al
gorith
m
. The
pap
e
r
firstly esta
b
lishe
d the
wareh
o
u
s
e ta
rget
locatin
g
and trackin
g
syste
m
model ba
sed on WS
N,
maximum like
lihood e
s
tima
tion algorithm
of
multilateral
m
easure
m
ent
method i
s
a
p
p
lied to
cal
c
ul
ating the
co
ordinate
s
of the
unkno
wn n
o
de.
Acco
rdi
ng to
monitori
ng m
o
tion traje
c
to
ry of the
same
unkno
wn target nod
e with
in a continuo
us
perio
d of time, the motion
equation
can
be esta
b
lish
ed. Whe
n
the
state equ
atio
n of wareho
u
s
e
target trackin
g
sy
stem i
s
n
on-lin
ea
r, EKF and
UK
F fil
t
ering
algo
rith
m are respectively applied
to
acq
u
irin
g the
state e
s
tima
te of the wa
rehou
se
ta
rge
t
motion equ
ation, so a
s
to achi
eve the
effective tracking of ware
h
ouse target.
2. Backg
rou
nd
2.1. Problem Statemen
t
Wa
reho
use t
a
rget
lo
cating
and
tra
c
king
syst
em
ba
se
d on
WS
Ns i
s
com
p
o
s
ed
of many
wirel
e
ss
sen
s
or no
de
s. These n
ode
s c
ontain
b
eacon n
ode
s an
d u
n
kn
own
nod
es.
The
prop
ortio
n
of beacon no
d
e
s in the net
work is
small
.
Beacon no
des
can g
e
t their o
w
n p
r
e
c
ise
locat
i
o
n
by
s
o
me me
an
s
su
ch a
s
ca
rr
y
i
ng
BDS (G
PS) po
sitioni
ng eq
uipme
n
t
s. Beacon n
ode
s
are
the refe
re
nce
poi
nts of unkno
wn nod
es
l
o
ca
tion. A
nd b
e
a
c
on
no
des a
r
e
arran
ged i
n
si
de
an
d
outsid
e
the wareh
o
u
s
e eve
n
ly. The un
kn
own n
ode
s
can be a
c
tive
node
s of pe
rson
nel, vehicl
es
and ware
hou
se eq
uipme
n
t
s. By communicating wi
t
h
nearby be
aco
n
nod
es
or the un
kno
w
n
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Wa
reho
use T
a
rget Lo
catin
g
and Trackin
g
Based o
n
EKF and… (B
i
a
n
G
u
a
n
g
-
r
o
n
g
)
4265
node
s
whi
c
h
have a
c
qui
re
d their o
w
n
positio
n info
rmation, the u
n
kn
own no
de
s can
cal
c
ula
t
e
their own po
sition accordin
g to a certain
locatio
n
algo
rithm. As is sh
own in Fig
u
re
1.
In
te
r
n
e
t
B
e
ac
on
No
d
e
U
n
kn
ow
n
Nod
e
Zi
g
b
e
e
Ga
t
e
w
a
y
Zi
gbe
e
Br
i
d
g
e
Lo
cat
i
n
g
an
d
T
r
ac
ki
n
g
S
e
r
v
er
Zi
gbe
e
Br
i
d
ge
Data
ba
se
Se
rv
e
r
Figure 1. Sch
e
matic Di
ag
ram of Wareh
ous
e Target Location an
d Tra
cki
ng Syst
em
2.2. Design
Analy
s
is of Ware
hous
e Targe
t
Local
ization an
d Tracking Sy
stem Based
on
WSN
The ba
si
c thought of wi
reless sen
s
o
r
net
wo
rks lo
cali
zation
ca
n be re
presented a
s
follows. Som
e
spe
c
ial n
o
des which o
c
cupy
a
ce
rtai
n propo
rtion
are
depl
oyed
in the
wi
rele
ss
sen
s
o
r
netwo
rks. T
h
is ki
nd
of n
ode
s
wh
ich
are calle
d
beaco
n
nod
es also have
strong en
ergy
and
can
be e
quipp
ed with
BDS(GPS)
p
o
sitioni
ng sy
stem, or can a
c
qui
re thei
r o
w
n
coo
r
din
a
tes
by other way
s
. By measu
r
ing the di
sta
n
ce
a
nd an
gle betwe
en u
n
kn
own nod
es an
d bea
con
node
s, or d
o
i
ng ce
rtain
calcul
ation a
c
cording to th
e relative po
sition relation
ship, thei
r o
w
n
coo
r
din
a
tes
can be worked
out [2].
The po
sitioni
ng prin
cipl
e of ware
hou
se target
loca
lization an
d trackin
g
syste
m
is to
cal
c
ulate the
coo
r
din
a
tes
of the unkno
wn no
de
s wi
th node p
o
sit
i
on cal
c
ul
atio
n method. T
he
maximum likelihoo
d estim
a
tion metho
d
of the multila
teral mea
s
u
r
ement is
use
d
to cal
c
ulate
the
coo
r
din
a
tes o
f
the unkno
wn node
s [1].
The multilate
ral mea
s
u
r
eme
n
t method i
s
often appl
i
ed t
o
cal
c
ul
ating t
he coordinate
s
of the
unkno
wn nod
es. As sh
own in Fig.2, there are n refe
ren
c
e node
s M
1
(x
1
,y
1
),M
2
(x
2
,y
2
),…,M
n
(x
n
,y
n
)
,
a
nd
their
distan
ce
t
o
un
kn
own n
o
de
N i
s
re
spe
c
tively r
1
(t),r
2
(t),
…,r
n
(t).We
set
the coo
r
dinate
s
of
N a
s
(x
(t),
y
(t)).Th
en the coordi
nate
s
sati
sfy Equation (1).
…
M
1
M
4
M
5
M
n
M
2
M
3
N
Figure 2. Sch
e
matic Di
ag
ramof Maximu
m Likelih
ood
Estimation al
gorithm of Mu
ltilateral
Measurement
Method
Equation (2) can be a
c
qui
re
d by the ma
ximum likeli
hoo
d estimation m
e
thod.
)
(
)
)
(
(
)
)
(
(
)
(
)
)
(
(
)
)
(
(
2
2
2
2
1
2
1
2
1
t
r
y
t
y
x
t
x
t
r
y
t
y
x
t
x
n
n
n
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4264 – 4
273
4266
)
(
)
(
)
(
2
)
(
2
)
(
)
(
)
(
2
)
(
2
2
2
1
1
2
2
1
1
2
2
1
2
2
1
1
2
2
1
1
2
2
1
t
r
t
r
y
y
y
y
y
x
x
x
x
x
t
r
t
r
y
y
y
y
y
x
x
x
x
x
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
(2)
Applying syst
em of linear e
quation
s
，
it can be expressed a
s
)
(
)
(
t
b
t
AX
, where:
)
(
2
)
(
2
)
(
2
)
(
2
1
1
1
1
n
n
n
n
n
n
y
y
x
x
y
y
x
x
A
)
(
)
(
)
(
)
(
)
(
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
2
2
1
t
r
t
r
y
y
x
x
t
r
t
r
y
y
x
x
t
b
n
n
n
n
n
n
n
n
n
)
(
)
(
)
(
t
y
t
x
t
X
Whe
r
e x(t) re
pre
s
ent
s co
ordinate
s
of un
kno
w
n n
ode
N on x dire
ction at time t;
y(t) rep
r
e
s
ent
s co
ordi
nate
s
of unkno
wn
node
N on y dire
ction at time t;
r
n
(t) re
present
s the dista
n
ce from refe
re
nce n
ode M
n
to unkn
o
wn n
ode N at time
t.
The
co
ordi
na
tes of
the
no
de
N
can
be
acq
u
ire
d
by
stand
ard
mini
mum m
ean
varian
ce
estimation m
e
thod.
The co
ordinat
es is:
)
(
)
(
)
(
ˆ
1
t
b
A
A
A
t
X
T
T
(
3
)
Wa
reho
use target tra
c
kin
g
based on
wirel
e
ss sen
s
or n
e
two
r
ks is applying
wirel
e
ss
sen
s
o
r
netwo
rk to monito
r, identify and track m
o
vin
g
wareho
use
target within
the monitori
n
g
area. Wareh
ouse target
tracking
syst
em can m
o
n
i
tor motion chara
c
te
risti
c
s information
o
f
wareho
use t
a
rget
an
d
wa
reho
use ta
rg
et
attribut
e information in real time. From the acqui
ri
ng
pro
c
e
s
s of po
sition a
nd vel
o
city of the m
obile tar
gets,
it must be th
a
t
mult
iple sen
s
or nod
es wo
rk
together to
co
mplete the target tracking.
Figure 3. Sch
e
matic Di
ag
ram of Wa
reh
ouse Target Tra
cki
ng Prin
ciple
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Wa
reho
use T
a
rget Lo
catin
g
and Trackin
g
Based o
n
EKF and… (B
i
a
n
G
u
a
n
g
-
r
o
n
g
)
4267
Wa
reho
use target tra
c
kin
g
is essential
l
y a es
timate problem of h
y
brid system,
in other
words, it is a
pplying di
screte sen
s
o
r
m
easure
m
ent
s to estimate the targ
et's
continuo
us
sta
t
e
,
the p
r
inci
ple i
s
sho
w
n
in
Fi
gure
3.
Re
sid
ual i
s
the
differen
c
e
bet
we
en the
sen
s
o
r
me
asure
m
e
n
t
and the stat
e predi
ction
value. Acco
rding to ch
a
n
ges of the resid
ual vecto
r
, the maneu
ve
r
detectio
n
an
d
mane
uver id
entificati
on
are co
ndu
cted.
In acco
rda
n
ce wi
th
c
e
r
t
a
i
n
c
r
iter
ia
o
r
logic
,
the motion
chara
c
te
risti
c
s of the target
s can be i
d
e
n
tified in re
al time. By the
filtering alg
o
ri
thm
the value
of state estimate
and p
r
e
d
ictio
n
of t
he ta
rg
e
t
can
be
obtai
ned. Th
erefore, the e
s
senti
a
l
fa
c
t
o
r
s
o
f
the w
a
r
e
ho
us
e
ta
r
g
e
t
tr
ac
k
i
ng
co
ns
is
t
of the mo
delin
g
of wa
reh
o
u
s
e targ
et moti
on
model, targ
et locatin
g
, targ
et reco
gnition
and filtering
algorith
m
s.
3. The War
e
house Ta
rge
t
Trackin
g
Resear
ch Bas
e
d on EKF a
nd UKF
Curre
n
tly, the most
com
m
on no
nline
a
r filt
erin
g al
gorithm i
s
E
x
tended Kal
m
an filter
(EKF) a
nd
Unscente
d
Kal
m
an filter
(UKF). EKF
ha
s a fe
w
disa
dvantage
s, in
cludi
ng that f
i
rst-
orde
r line
a
ri
zation accu
ra
cy is low a
n
d
it need to calcul
ate the
Ja
cobi
an mat
r
ix of nonline
a
r
function, whi
c
h ea
sily cau
s
e that EKF nume
r
ic
al sta
b
ility is poor
and even
divergin
g. UKF
is
based on UT
tran
sformati
on,
which
a
p
p
ly the frame
w
ork of Kalm
an
filter an
d
UT tran
sform
to
dealin
g with the nonline
a
r transmi
ssion
of the mean and cova
ria
n
ce for o
ne
step predi
ctio
n
equatio
n, rather than ap
ply approxim
ating nonli
n
e
a
r functio
n
. It need not to calculate the
Ja
cobi
an mat
r
ix by derivation.
3.1. Extende
d Kalman Filter (E
KF) o
f
Nonlinear
Discre
t
e Sy
stem
Comp
uting m
odel of EKF is as follo
ws:
(1) Predi
ction
equation
)
,
,
ˆ
(
ˆ
ˆ
1
1
1
1
1
1
1
,
1
k
k
k
k
k
k
k
k
k
k
q
u
x
f
U
x
Φ
x
(4)
)
,
ˆ
(
ˆ
ˆ
1
1
1
k
k
k
k
k
k
k
k
k
k
r
x
h
y
x
H
z
(
5
)
(2) State e
s
timation
)
(
ˆ
ˆ
1
1
k
k
k
k
k
k
k
z
z
K
x
x
(6)
(3) Filter gain matrix
1
1
1
)
(
T
k
k
k
T
k
k
k
k
T
k
k
k
k
Λ
R
Λ
H
P
H
H
P
K
(7)
(4)
O
n
e
-
step predi
ction co
varian
ce
eq
u
a
tion
T
k
k
k
k
k
T
k
k
k
k
k
k
k
1
,
1
1
,
1
,
1
1
,
1
Γ
Q
Γ
Φ
P
Φ
P
(8)
(5) Filte
r
cov
a
rian
ce
1
)
(
k
k
k
k
k
P
H
K
I
P
(9)
Acco
rdi
ng to (4) to (9), as l
ong a
s
the ini
t
ial values of
0
ˆ
x
and
0
P
are giv
en, according
to the me
asurem
ent valu
e
k
z
at time k,
the
state e
s
timation
k
x
ˆ
c
a
n
b
e
fig
u
r
e
d ou
t b
y
th
e
recursive alg
o
rithm at time
k.
3.2. Unsce
nted Kalman F
ilter (UKF
)
Differing fro
m
EKF, by
the un
scente
d
tr
ansfo
rma
t
ion UKF ca
n make the
nonlin
ear
system eq
uat
ions a
pply to stand
ard Kal
m
an filter
ing
system un
de
r the linear hy
pothe
sis, rath
er
than EKF ach
i
eve recursiv
e filtering by lineari
z
in
g
no
nlinea
r functi
on. UKF is a
kind of no
nlin
ear
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273
4268
gau
ssi
an
sta
t
e estimato
r ba
sed
on
minimum va
rian
ce
estim
a
te criteri
on,
It can
bett
e
r
approximate
the nonline
a
r characte
ri
stics of
the sta
t
e equation t
han EKF, and has a hig
h
e
r
estimation a
c
curacy while
the orde
r of cal
c
ulatio
n amount is a
s
same a
s
EKF, thus it arouse
s
the wide
sp
re
ad attention.
Assu
ming tha
t
nonlinea
r ga
ussian
syste
m
state equat
ion and me
asurem
ent equ
ation
are respec
tively as
follows:
)
,
(
)
,
,
(
1
1
1
1
k
k
k
k
k
k
k
k
k
v
x
h
z
w
u
x
f
x
(10)
Whe
r
e the p
r
ocess n
o
ise
k
w
and mea
s
urem
ent noi
se
k
v
are all
un
co
rrel
a
ted
zero
mean white Gau
ss n
o
ise, thei
r cova
ria
n
c
e are re
sp
ectively
k
Q
and
k
R
,
UKF filter algorithm s
t
eps
are as
follows:
(1) T
he stati
s
tical prope
rtie
s of
the initial state are as f
o
llows:
0
]
,
[
0
]
,
[
]
)
ˆ
(
)
ˆ
[(
)
,
(
)
(
ˆ
0
0
0
0
0
0
0
0
0
0
0
k
k
T
E
E
E
Cov
E
v
x
w
x
x
x
x
x
x
x
P
x
x
(11
)
(2) T
he expa
nsio
n state vector of
the
system is expressed a
s
follo
ws:
k
k
k
T
a
k
a
k
a
k
a
k
a
k
T
T
k
T
k
T
k
a
k
E
R
Q
P
x
x
x
x
P
v
w
x
x
]
)
ˆ
)(
ˆ
[(
]
ˆ
[
(12)
(3) Tim
e
’s u
p
dating
n
k
n
n
W
n
W
x
c
x
m
)
(
),
1
(
,
2
2
)
(
0
)
(
0
(13
)
x
x
c
i
m
i
n
i
k
n
W
W
2
,
2
,
1
,
)
(
2
1
)
(
)
(
(14
)
Without
con
s
i
derin
g the in
put functio
n
, weig
ht
i
W
can
be calcul
ated
by Equation
(13
)
and Equatio
n
(14), the
r
e are:
)
,
,
(
1
1
1
1
w
x
x
x
u
x
x
k
k
k
k
k
f
(
1
5
)
x
x
x
1
,
2
0
)
(
1
ˆ
k
k
i
n
i
m
i
k
k
a
W
(16
)
T
k
k
k
k
i
k
k
k
k
i
n
i
c
i
k
k
a
W
]
ˆ
][
ˆ
[
1
1
,
1
1
,
2
0
)
(
1
x
x
x
x
P
x
x
(17
)
]
,
[
1
1
1
v
x
x
x
h
z
k
k
k
k
k
k
(18)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Wa
reho
use T
a
rget Lo
catin
g
and Trackin
g
Based o
n
EKF and… (B
i
a
n
G
u
a
n
g
-
r
o
n
g
)
4269
1
,
2
0
)
(
1
ˆ
k
k
i
n
i
m
i
k
k
a
W
z
z
(19)
(4) Me
asure
m
ent’s up
dati
n
g
T
k
k
k
k
i
k
k
k
k
i
n
i
c
i
a
k
k
k
k
W
]
ˆ
][
ˆ
[
1
1
,
1
1
,
2
0
)
(
ˆ
ˆ
1
1
z
z
z
z
P
z
z
(20
)
T
k
k
k
k
i
k
k
k
k
i
n
i
c
i
a
k
k
k
k
W
]
ˆ
][
ˆ
[
1
1
,
1
1
,
2
0
)
(
ˆ
ˆ
1
1
z
z
x
x
P
x
z
x
(21
)
1
ˆ
ˆ
1
ˆ
1
ˆ
1
1
k
k
k
k
k
k
k
k
k
z
z
P
P
K
z
x
(22)
)
ˆ
(
ˆ
ˆ
1
1
k
k
k
k
k
k
k
z
z
K
x
x
(23)
T
k
k
k
k
k
k
k
k
k
K
P
K
P
P
z
z
1
1
ˆ
ˆ
1
ˆ
(24)
At this p
o
int,
the filtering
state an
d the
vari
an
ce
of
UKF at time
k
are
obtain
ed.
As th
e
function val
u
es by
Un
scen
ted Tra
n
sfo
r
mation a
r
e
n
o
t be line
a
ri
zed, not ign
o
ri
ng its hi
ghe
r-orde
r
terms, avoi
di
ng the
cal
c
u
l
ation of ja
cobian m
a
trix
(linea
r), thu
s
the e
s
tima
te of mean
and
covari
an
ce a
c
qui
red by UKF are mo
re
accurate than
EKF method.
4. Simulation Analy
s
is a
nd Comparis
on of EKF a
nd UKF
4.1. Precision Compariso
n
of EKF an
d UKF in th
e
Case o
f
Non
linearit
y
We a
s
sume t
he motion ch
ara
c
teri
stics
of ware
hou
se
targets a
r
e d
e
scrib
ed a
s
the non
-
linear
system
model, whi
c
h
are sh
own in
the following:
State equatio
n:
k
k
k
k
x
k
k
k
k
k
k
x
x
x
e
x
x
x
x
x
k
w
x
1
1
1
6
)
(
8
cos
3
,
3
,
2
,
1
,
1
,
2
1
,
3
1
,
2
1
,
1
1
,
3
(25
)
Measurement
equation:
k
k
k
k
k
x
x
x
v
z
,
3
,
2
,
1
2
(26
)
W
h
er
e
k
w
an
d
k
v
are
Ga
ussian
white
noi
se
，
a
n
d
their con
s
tant stati
s
tica
l
cha
r
a
c
t
e
ri
st
ic
s are a
s
f
o
llo
ws:
0
.
1
5
.
0
7
.
0
,
3
.
0
R
r
Q
q
(27
)
The the
o
retical initial valu
e of line
a
r system form
ul
a (2
5)
and
(26) i
s
assu
med a
s
follows
:
T
1
1
6
.
0
0
x
(28
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
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046
TELKOM
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KA
Vol. 12, No. 6, June 20
14: 4264 – 4
273
4270
Mean
while th
e initial value of the
state estimation is
set as follows:
I
P
x
0
0
0
ˆ
(29
)
And
0
ˆ
x
,
k
w
and
k
v
is not relevant.
UT t
r
a
n
sf
o
r
m
sy
mmet
r
i
c
s
a
mpling
st
r
a
t
egy
is
ap
plie
d to the sim
u
lation, pro
portionality
coeffici
ent
6
.
0
k
.
EKF and
UKF are
re
spe
c
tively applied
to estimatin
g
the sy
stem
state,
Figure 4 and
Figure 5 are
the estimation cu
rves of
nonlin
ear sy
stem state in the ca
se of two
kind
s of algo
rithm, Figure
6 and Figu
re 7 de
scri
be
the simul
a
tio
n
diag
ram of
estimation e
rro
r
and mea
n
sq
uare e
r
ror in t
he ca
se of UKF and EKF resp
ectively.
Figure 4. The
Estimation Value of Tra
c
ki
ng
State under E
K
F Algorithm
Figure 5. The
Estimation Value of Tra
c
ki
ng
State under
UKF Algorith
m
Figure 6. Estimation Error
unde
r the EKF and
UKF Algorith
m
Figure 7. Mean Squa
re Error u
nde
r the EKF
and UKF Alg
o
rithm
From Fi
gure
4 to Figu
re 7,
we
can
see
easily
, the val
ue EKF estim
a
tes
system
state is
bet
t
e
r in
som
e
ca
se
s,
st
at
e est
i
mat
i
o
n
err
o
r i
s
sm
all, but som
e
times the
state e
s
timation e
r
ro
r is
large, an
d the
state estimat
i
on mean vari
ance ac
cum
u
lates ra
pidly with time, because the EKF’s
poste
rio
r
me
an and va
ria
n
ce
of nonli
near
syste
m
state ca
n o
n
ly rea
c
h first ord
e
r T
a
ylor
approximatio
n. In the
cou
r
se
of filte
r
in
g the
no
n
line
a
r
system
formula
(25
)
an
d (26),
this first
orde
r ap
pro
x
imation pre
c
isi
on is hi
gh at som
e
point, can
meet the pra
c
tical
system
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Wa
reho
use T
a
rget Lo
catin
g
and Trackin
g
Based o
n
EKF and… (B
i
a
n
G
u
a
n
g
-
r
o
n
g
)
4271
requi
rem
ents,
and at
som
e
point it is
re
ally poor
whi
c
h m
a
ke
EKF state e
s
tim
a
tion erro
r la
rge,
and even div
e
rgin
g, while
UKF ca
n mai
n
tain effect
ively tracking t
r
ue valu
e of the targ
et state,
estimation
a
c
cura
cy i
s
b
e
tter than
EKF, becau
se
UKF
can
a
ppro
a
ch p
o
st
erio
r me
an
and
cov
a
ri
an
ce
o
f
nonline
a
r Gau
ssi
an sy
st
em st
at
e
at the a
c
curacy of
se
co
nd-o
r
d
e
r T
a
ylor
approximatio
n, this is the prima
r
y rea
s
o
n
t
hat UKF filtering a
c
cu
ra
cy is better tha
n
EKF.
4.2. Precisio
n
Comp
aris
on of E
K
F
a
nd UKF in
th
e Ca
se o
f
th
e Disc
ontinu
ous Situa
t
io
n of
Nonlinear Sy
stem Sta
t
e E
quation
We a
s
sum
e
the motion
chara
c
te
risti
c
s of
wa
reh
o
u
s
e ta
rget
s a
r
e de
scribe
d
as the
nonlin
ear
system model, which a
r
e sho
w
n in the follo
wing:
State equatio
n:
k
k
k
k
k
x
k
k
k
k
k
k
x
x
x
x
e
x
x
x
x
x
k
w
x
1
1
1
3
6
)
(
8
cos
3
,
1
,
3
,
2
,
1
,
1
,
2
1
,
3
1
,
2
1
,
1
1
,
3
(30
)
Measurement
equation:
k
k
k
k
k
x
x
x
v
z
,
3
,
2
,
1
(31
)
The
k
w
and
k
v
are
gaussia
n
whi
t
e noise, an
d their co
nsta
nt statistical p
r
o
pertie
s
are
as
follows
：
0
.
1
5
.
0
7
.
0
,
3
.
0
R
r
Q
q
(32
)
The theo
retical initial value of linear syst
em formula
(30) an
d (3
1) i
s
assu
med a
s
follows
:
T
1
1
6
.
0
0
x
(33
)
Mean
while th
e initial value of the
state estimation is
set as follows:
I
P
x
0
0
0
ˆ
(34
)
And
0
ˆ
x
,
k
w
and
k
v
is not relevant.
UT t
r
a
n
sf
o
r
m
sy
mmet
r
i
c
s
a
mpling
st
r
a
t
egy
is
ap
plie
d to the sim
u
lation, pro
portionality
coeffici
ent
6
.
0
k
.
EKF and
UK
F are respe
c
tively applied
to estima
tin
g
the
sy
stem stat
e, Figu
re 8
sh
ows
the e
s
timatio
n
curve
of the sy
stem
sta
t
e unde
r
UK
F filtering
alg
o
rithm, Fig
u
re 9
sho
w
s t
h
e
estimation
cu
rve of the system stat
us u
n
der EKF filteri
ng algo
rithm.
We can see
from Figure
8, when th
e state
equ
a
t
ion sho
w
n i
n
formula
(3
0) is n
o
t
differentiabl
e
at some
po
int, UKF
re
mains effect
i
v
e trackin
g
f
o
r the
state
cha
nge
s, thi
s
i
s
becau
se
UKF
nee
d not to
cal
c
ulate
the
Ja
cobi
an m
a
trix, so it i
s
su
itable for no
n
linear sy
stem
s
filtering
while
the state fu
nction i
s
di
scontin
uou
s o
r
no
n-diffe
re
ntiable, while
EKF req
u
ires
nonlin
ear fun
c
tion should
be contin
uou
sly and differ
entiable whe
n
it calculate
Ja
cobi
an mat
r
ix.
Therefore, E
K
F failed to f
ilter the
nonli
near sy
st
em
state
su
ch a
s
formul
a (30) and
(3
1). A
s
is
sho
w
n in Fi
g
u
re 9, when
the sampl
e
numbe
r is
more tha
n
2
50, EKF has been un
abl
e to
pro
c
ee
d, pro
bably be
cau
s
e at some poi
nt it can't
solv
e the Ja
cobi
a
n
matrix of formula (3
0).
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4264 – 4
273
4272
Figure 8. The
System State Estimation
Curve
unde
r UKF Fi
ltering Algo
rithm
Figure 9. The
System State Estimation
Curve
unde
r UKF Fi
ltering Algo
rithm
5. Conclusio
n
s and rec
o
mmendation
s
The pa
per firstly establi
s
h
ed the ware
h
ouse
targ
et locatin
g
and t
r
ackin
g
sy
ste
m
model
based on wi
reless sen
s
or networks. Whe
n
the
st
ate equation
of wareh
o
u
s
e targ
et tra
cki
ng
system
is no
n-line
a
r, EKF
and
UKF
filtering
alg
o
rith
m are
re
spe
c
tively applied
to a
c
qui
ring
the
state estim
a
te of the syste
m
and sim
u
la
tion analysi
s
.
Simulation re
sults
sh
ow th
at, the value EKF estimate
d target tracking state i
s
b
e
tter in
some
cases,
state e
s
timati
on e
r
ror is small, but
so
metimes the
state e
s
timati
on e
r
ror is la
rge,
and the
stat
e estimatio
n
mean va
rian
ce a
c
cumul
a
tes
rapidly
wi
th time, because the EK
F’s
poste
rio
r
me
an and va
ria
n
ce
of nonli
near
syste
m
state ca
n o
n
ly rea
c
h first ord
e
r T
a
ylor
approximatio
n, this first o
r
de
r ap
proximation p
r
e
c
i
s
ion
i
s
high at
som
e
poi
nt,
can meet
the
pra
c
tical
syst
em requi
rem
ents, and at
some poi
nt it is really
poor
whi
c
h make
s EKF state
estimation
error la
rg
e, an
d even diverging, whil
e
UKF can ma
intain effectively tracking t
r
ue
value of
the t
a
rget
state,
e
s
timation
a
c
cura
cy i
s
b
e
tter th
an EKF,
be
cau
s
e
UK
F can
app
roa
c
h
poste
rio
r
me
an a
nd
cova
ri
ance of n
onli
near Ga
ussi
a
n
sy
stem
state at t
he accu
racy of
secon
d
-
orde
r Taylo
r
approximatio
n, this is the
fundame
n
ta
l
rea
s
on th
at UKF filtering a
c
cura
cy is
be
tter
than EKF.
Whe
n
the wareho
use target tra
c
kin
g
system
state equatio
n is nonli
n
ear a
nd
discontin
uou
s
，
EKF and UKF filtering algorithm a
r
e resp
ectively a
pplied to a
c
q
u
iring the
sta
t
e
estimate of
the system.
S
i
mulation re
sults sho
w
th
a
t, when
the
state equ
ation
of the
syste
m
is
not differentia
ble at some p
o
int, UKF re
mains e
ffe
ctive tracking of t
he state chan
ges, while EKF
filtering algo
ri
thm has faile
d and even u
nable to filter.
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