TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 13, No. 1, Janua
ry 201
5, pp. 145 ~
150
DOI: 10.115
9
1
/telkomni
ka.
v
13i1.671
2
145
Re
cei
v
ed Se
ptem
ber 18, 2014; Revi
se
d Octob
e
r 26,
2014; Accept
ed No
vem
b
e
r
20, 2014
A Breeding Estimated Particle Filter Research
Xiong Fang
Exp
e
rim
ental
Center, Hu
na
n Internatio
na
l Econom
ics Univ
ersit
y
,
Cha
ngsh
a
, Chi
na, postco
de: 410
20
5
email: matl
ab_
b
y
s
j
@com.co
m
A
b
st
r
a
ct
As the
nor
ma
l partic
l
e
filter
has
an
ex
p
ens
iv
e
co
mpu
t
ation an
d
d
e
gen
eracy pro
b
le
m, a
prop
agati
on-
pr
edicti
on particl
e
filter
is
prop
osed. In
this s
c
he
me,
particl
es after tra
n
sfer are
pr
opa
g
a
t
e
d
und
er the dist
ributi
on of
state noise, an
d
then the pr
o
duce
d
filia
l pa
rticles
are us
ed to predict
the
corresp
ond
in
g pare
n
t particle
referrin
g
to me
asure
m
en
t, in w
h
ich step the
new
est meas
ure infor
m
ation
i
s
add
ed int
o
esti
mati
on. T
heref
ore pre
d
icted
particl
e w
oul
d
be clos
er to the true st
ate, which i
m
pr
oves
the
precisi
on of pa
rticle filt
er. Experi
m
e
n
t result
s have prov
ed
the e
fficiency
of the algorith
m
an
d the gre
a
t
pred
o
m
in
anc
e in little p
a
rticle
s case.
Ke
y
w
ords
: state estimation, p
a
rticle filter, pa
rtic
le de
gen
era
cy, importa
nce
dens
ity functio
n
.
Copy
right
©
2015 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
Particle filter
method [1] th
e optimal Ba
ye
s filtering
a
nd Monte
Ca
rlo samplin
g
method
s
evolved, the
core ide
a
i
s
to sp
rea
d
in
the
state
spa
c
e u
s
in
g a
set of ran
dom
sam
p
le
s wit
h
associated weights to ap
proximate the
posteri
o
r
probabilitydensity, the mi
nim
u
m
variance of t
h
e
sampl
e
m
ean
inste
ad
of th
e integ
r
al
op
eration,
to o
b
t
ain state
e
s
ti
mates.
Du
e t
o
the
limitatio
ns
of the pa
rticle
filter is
not li
near an
d noi
se
Ga
u
ssi
an assumptio
n
s in
the
field of non-li
nea
r,
n
on-
Gau
ssi
an oc
ca
sion
s su
ch
as
t
a
r
get tracking,
sig
n
a
l
processing,
autom
atic
control
ha
s
b
een
widely u
s
ed.
However, the stand
ard p
a
rticle filt
er
wide
sp
rea
d
large a
nd pa
rticle deg
rad
a
t
ion
probl
em, whi
c
h the particle de
gradati
on will largely impact t
he estimation accuracy and
robu
stne
ss of
the pa
rticle fi
lter. In ord
e
r t
o
solve th
e p
a
rticle
deg
ra
d
a
tion proble
m
, the poste
rio
r
probability distribution cl
oser
to the importance of the
probability density function.
Do
ucet
et al
[3]
extended Ka
lman filter
(EKF) to gen
erate th
e
im
portan
c
e
de
nsity functio
n
, however
EKF
introdu
ce
s m
o
re erro
r
in
the
mod
e
l
li
neari
z
at
io
n a
nd n
o
ise G
a
ussian
a
s
su
mptions,
so
th
e
improvem
ent
effect is not
very satisfa
c
tory.
Mer
w
e and
D
oucet
[4
] propo
sed
u
s
ing u
n
sce
n
ted
Kalman filter (UKF
) in
ste
ad of the EK
F pro
d
u
c
e
s
t
he imp
o
rtan
ce den
sity fun
c
tion, to o
b
ta
in
highe
r estim
a
tion accuracy
, but also gre
a
tly increa
se
the amount of
computatio
n. In addition, the
method u
s
ed
to generate
the importan
c
e den
sity
Gauss - the Hermitian filter method [5],
the
state pa
ram
e
ter de
co
mpo
s
i
t
ion and a
nne
aling
coe
fficie
n
t method [6]
,
nonlinea
r int
e
ra
ctive multi
-
model
app
ro
ach
[7], the
se
con
d
-o
rd
er ce
ntral
di
fferen
c
e filte
r
in
g metho
d
[8]
and
qu
adrature
Kalman filter
(QKF) [9]. In
varyi
n
g
de
gr
ee
s
,
th
es
e me
th
o
d
s
impr
o
v
e th
e
pr
ec
is
io
n o
f
th
e
p
a
r
t
ic
le
filter, but also redu
ce the
real-time na
ture of
the algorithm. In this pap
er, the probl
ems
of
existing p
a
rti
c
le filtere
d
al
gorithm
pro
p
o
se
d breedi
n
g
to improve
the estimate
d
accuracy of
th
e
particl
e filter the e
s
timated
particl
e filter
at the
sam
e
t
i
me ta
king
i
n
to a
c
count th
e
re
al-time,
an
d
achi
eved go
o
d
results.
2. Principles of Particle Filter
Con
s
id
er the
gene
ral no
nli
near
system,
the
state eq
uation an
d o
b
se
rvation eq
uation is
as
follows
:
1
(,
)
(,
)
kk
k
k
kk
k
k
f
h
xx
u
zx
v
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 1, Janua
ry 2015 : 145 –
150
146
Whe
r
e,
k
x
is the system
stat
e vector
k
z
for the sy
stem of
observation v
e
ctors,
k
u
and
k
v
, res
p
ec
tively, for s
y
s
t
em s
t
atus
tran
sfe
r
of noise an
d obse
r
vation
noise,
()
k
f
and
()
k
h
,
respe
c
tively, for the tran
sfe
r
of
the
state
of the syste
m
and o
b
se
rvat
ion fun
c
tion
s.The pu
rp
ose
o
f
the filtered
i
s
to
estim
a
te the
state i
n
format
io
n
can n
o
t be
di
rectly o
b
tain
ed by
ob
serving
assumptio
n
s
to estim
a
te t
he a
m
ount
o
f
the fun
c
tion
0:
()
k
g
x
of th
e
syst
em
state.Du
e
to the
gene
ral no
nli
near
system
s, the posterio
r
pro
bability
0:
1
:
(|
)
kk
p
xz
is not easy to see
k
an ea
sy
sampli
ng a
n
d
with simil
a
r po
sterio
r p
r
obability dist
ribution in
stea
d of
0:
1
:
(|
)
kk
p
xz
sampli
ng
assumptio
n
0:
1
:
(|
)
kk
q
xz
,
0:
()
k
g
x
by the following equ
atione
stimate:
0:
0
:
0:
0:
((
)
(
)
)
[(
)
]
((
)
)
kk
k
k
kk
Eg
w
Eg
Ew
xx
x
x
(
2
)
1:
0
:
0
:
0:
0:
1
:
(|
)
(
)
()
(|
)
kk
k
kk
kk
pp
w
q
zx
x
x
xz
Estimates
using the Mo
nte Ca
rlo m
e
thod to
samp
le from the
referen
c
e
dist
ributio
n
0:
1
:
(|
)
kk
q
xz
,
0:
()
k
g
x
mathemati
c
al expectatio
n
:
()
()
0:
0
:
()
()
1
0:
0
:
0:
()
1
0:
1
1
()
()
(
(
)
)
()
()
1
()
N
ii
kk
k
N
ii
i
k
kk
k
N
i
i
kk
i
gw
N
Eg
g
w
w
N
xx
xx
x
x
(
3
)
()
()
()
0:
0:
0:
1
()
(
)
()
N
ii
i
k
kk
k
k
k
i
ww
w
xx
x
Whe
r
e,
()
0:
i
k
x
is the i-th sam
p
li
ng parti
cle
s
. If the state estimation p
r
o
c
e
ss fo
r opti
m
a
l
estimation, th
e refe
ren
c
e
distrib
u
tion d
epen
ds
only on the p
r
ob
a
b
ility density function
of
1
k
x
and
k
z
, and therefore ca
n ge
t the right values
recursive
form:
()
()
()
()
()
1
0:
1
0
:
1
()
()
11
:
(|
)
(
|
)
()
(
)
(|
,
)
ii
i
ii
kk
k
k
kk
k
k
ii
kk
k
pp
ww
q
zx
x
x
xx
xx
z
(
4
)
Whe
r
e,
()
(|
)
i
kk
p
zx
calle
d the likeliho
od an
d cha
r
a
c
teri
zation
of
the i-th p
a
rti
c
le from
state
1
k
x
to
k
x
an
d the
deg
ree
of si
milarity;
system
atic o
b
se
rvation
va
lue
k
z
,
()
()
1
(|
)
ii
kk
p
xx
transition probability of
the i-th particl
e state
1
k
x
to
k
x
.
3. Particle Filter Problem
U
n
de
r
no
r
m
al c
i
rc
u
m
s
t
a
n
ce
s
,
a
fte
r
s
t
eps
ite
r
ative re
cursio
n, most
of the particles a
r
e
the right wei
ght become
s
very small, and only a fe
w pa
rticle
s h
a
ve a gre
a
ter weight. Thi
s
will
make
a larg
e
numbe
r of calcul
ation
s
wasted in the
s
e small
weig
hts pa
rticle
s
are alm
o
st zero,
and its
co
ntribution to th
e app
roximat
i
on po
ster
i
o
r prob
ability distrib
u
tion.Usually effe
ctive
sampl
e
si
ze
N
eff
measure
of the degre
e
of degrad
atio
n of the algori
t
hm.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Breeding E
s
tim
a
ted Particle Filter
Re
search (Xio
ng
Fang
)
147
*
1v
a
r
(
)
eff
i
k
N
N
w
(
5
)
Whe
r
e,
*(
)
(
)
(
)
1
(|
)
/
(|
,
)
ii
i
i
kk
1
:
k
k
k
k
wp
p
xz
xx
z
is cal
l
ed "true weig
ht".The effective sample
siz
e
ca
n not
be st
ri
ct
ly
cal
c
ul
ate
d
, but its estim
a
ted value:
2
1
1
()
ef
f
N
i
k
i
N
w
(
6
)
Whe
r
e,
i
k
w
is the form
ula
(4) defin
es a
regul
ar
wei
ghts.
eff
N
degra
dation of the
smalle
r
particl
es mea
n
s m
o
re
seve
rity. [3] prove
d
that wi
th th
e pa
ssage
of
time, the variance of
weig
ht
will increa
se,
therefo
r
e the
degr
adatio
n p
henom
ena
ca
n not be avoi
ded.
4. The Repr
o
ductiv
e
Estimated Par
t
ic
le Filter
Solve the de
grad
ation
pro
b
lems comm
only used
re
sampli
ng
prin
ciple, the
ba
sic idea
:
Whe
n
the p
a
r
ticle
set de
g
r
adatio
n bel
o
w
a
certai
n thre
shol
d (su
c
h as
eff
N
), the weight of the
particl
es
ba
sed on the im
portan
c
e
of sampling
re
sa
mpling to ge
nerate
a ne
w set of su
pp
ort
points
'
1
()
iN
ki
x
, to
the phase-out of the right value of
low particle, the
value of the right o
f
retention
of
the hig
h
p
a
rticle, the
r
eby
limiting the
deg
rad
a
tion
phe
nome
n
a
.
Re
sam
p
lin
g
particl
es, ho
wever, is n
o
longe
r inde
pe
ndent, high
-weight parti
cle
s
are
copi
ed
many times, and
low weight particles gradually di
sap
pea
r. After several iteration
s
, all parti
cles
a
r
e collap
s
ed t
o
a
point, resultin
g in a dilution
of the sampl
e
.
T
o
s
e
lec
t
ap
pr
o
p
r
i
a
t
e
c
l
os
e to
th
e tr
u
e
d
i
s
t
ributio
n of
the im
porta
nce of the
state
of the
system d
e
n
s
i
t
y function is
anothe
r com
m
on meth
od
to solve the d
egra
dation
problem
s. Usu
a
lly
usin
g EKF a
nd
UKF be
update
d
on
the current
particl
e, but
becau
se of i
t
s o
w
n filteri
n
g
estimation lin
eari
z
ation of
nonlin
ear
systems, and the
r
efore una
ble
to get rid
of the limitations of
lineari
z
atio
n
essentially. T
he
same
time
to ma
ke
u
s
e
of EKF an
d
UKF ea
ch
pa
rticle, p
r
ofile, th
us
greatly in
crea
sing th
e amo
unt of ca
l
c
ul
a
t
ion of the filtering
process,
is not cond
u
c
ive to re
al-ti
m
e
requi
rem
ents occa
sio
n
s a
pplication
s
.
Use oth
e
r m
e
thod
s [5
-9]
to gen
erate
the imp
o
rtan
ce
den
sity function will al
so a
ppea
r the sa
me pro
b
lem.
To
this end, this
pa
per prese
n
ts
a ba
sed
on th
e th
e estimate
d
particl
e filter
bree
ding
method
s. Pro
posal di
stribu
tion due to th
e tran
sfer
of a prio
ri a
s
cu
rre
nt ob
serva
t
ion inform
ation
is mi
ssi
ng, the estimated
accuracy
of
t
he standard particl
e
filter.
This arti
cle
will be transferred
into the l
a
te
st ob
se
rvatio
n information
get the
pa
rticle
referen
c
e to the
ob
served val
ue
to
reproduce estimates, the
posteri
or
probability
di
stri
bution of
the particle di
stribution to better
reflect the tru
e
situation, to
improve the
accu
racy of the estimate
s
of the particle
filter.
The
ne
w al
g
o
rithm to
re
prod
uce th
e
particl
es in
st
ead
of u
s
ing
a
normal
G
aussia
n
distrib
u
tion, b
u
t the state t
r
an
si
tion n
o
ise distri
bution
stand
ard
br
e
eding parti
cle
distrib
u
tion. In
this ma
nne
r
is mo
re i
n
li
ne
with the
actual
si
tuati
on, an
d thu
s
also can
achieve a
high
er
accuracy
tha
n
the
Ga
ussi
an di
stri
butio
n. Particl
e
s (known a
s
th
e
mother pa
rticl
e
s) after tra
n
s
fer
to rep
r
o
d
u
c
e,
and
then
use the
estimat
e
, of the
pro
p
agation
of pa
rticle
s o
n
the
mother pa
rticl
e
s
can
be o
b
tain
ed a n
e
w e
s
timate of the
mother
pa
rtic
l
e
s. Th
ese Estimate parti
cl
es into
the lat
e
st
observation
i
n
formatio
n, a
nd the
r
efo
r
e
more
a
c
cu
rat
e
ly refle
c
t th
e true
state
of the
syste
m
.
Finally, using the estimat
ed part
icle estimate the
state will be
able to get
a more
accurate
estimate of th
e state. Rep
r
odu
ction e
s
ti
mated pri
n
ci
p
l
e is sh
own in
Figure 1.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 1, Janua
ry 2015 : 145 –
150
148
Figure 1. The
i-th particl
e p
r
opa
gation fo
recast p
r
o
c
e
ss
From Fig
u
re
1, we ca
n un
derstand the
particl
es fo
r repro
d
u
c
tion, due to the di
fferent
distan
ce
s a
w
ay from the real va
lue of
each proge
n
y
particle
s
, so the weight
is not the
sa
me.
After usin
g p
r
oge
ny parti
cles
weighte
d
estimate
s obt
ained m
o
ther particl
es
clo
s
er to th
e tru
e
value. The particle
s
multi
p
ly the number doe
s not
h
a
ve to generally take 10 to 20 can a
c
h
i
eve
good results. Breedi
ng e
s
timate parti
cle
filter algorith
m
step
s are a
s
follows:
Breedi
ng e
s
timate parti
cle
filtering algo
ri
thm:
1) Syste
m
ini
t
ialization.
k
= 0,
a
s
the
i
n
itial set of
p
a
rticle
s ba
se
d on
the
wei
ght of th
e
initial importa
nce d
e
n
s
ity sampling of N
particl
es
{,
1
/
}
i
k
N
x
.
2) Parti
c
le up
dates.L
et k = k + 1, the p
a
rtic
le
s a
c
cording to the transfe
r fun
c
tio
n
of the
system
state is upd
ated:
1
(,
)
ii
kk
k
k
f
xx
u
(
7
)
3) Pa
rticle
propag
ation.According
to th
e syste
m
to t
r
an
sfer th
e di
stributio
n of t
he noi
se
of the curre
n
t particle
s
repro
d
u
c
tion, simult
an
eou
sl
y calculate t
he weig
ht of each proge
ny
particl
es a
nd
is normali
zed
,
i.e. on
1,
2
,
,
c
cN
:
ic
i
kk
k
xx
u
(
8
)
(|
)
ic
ic
kk
k
wp
zx
，
1
c
N
ic
ic
ic
kk
k
c
ww
w
(
9
)
4) Pa
rticle
estimates.Bree
ding p
r
og
eny
parti
cl
es wei
ghted e
s
timat
e
s of
cu
rre
nt
particl
e,
the estimated
value of the curre
n
t particl
e:
1
ˆ
c
N
ii
c
i
c
kk
k
c
w
xx
(
1
0
)
5) After the e
s
timate of the
likeliho
od val
ue
cal
c
ul
ation
according to
the observe
d weig
ht
of each p
a
rticle, and norma
lization:
1
ˆ
(|
)
ii
i
kk
k
k
ww
p
zx
，
1
i
N
ii
k
kk
i
ww
w
(
1
1
)
6) State esti
mation.According to the estima
te
s of particle
wei
ght estimatio
n
system
status valu
es:
1
ˆ
ˆ
N
ii
kk
k
i
w
xx
(
1
2
)
7) Using Equ
a
tion (6
)
eff
N
.If
ef
f
th
r
e
s
NN
,
the resamplin
g, and the weights of all the
partic
l
es
is
res
e
t to 1 / N.
8) Re
peat ste
p
s 2 to 7.
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TELKOM
NIKA
ISSN:
2302-4
046
A Breeding E
s
tim
a
ted Particle Filter
Re
search (Xio
ng
Fang
)
149
5. Algorithm Validation
In orde
r to ve
rify the effectiveness of the
al
gorithm, th
e stan
dard p
a
rticle filter
(with re
-
sampli
ng
ste
p
estimate
particl
e filter) and
the
bree
ding of
this pap
er,
a comp
ara
t
ive
analysi
s
.Refe
r
en
ce
s a
cla
ssi
c
example
he
re, th
e
st
ate eq
uation
and
ob
se
rvation e
quatio
n,
r
e
spec
tively:
1
1
2
1
25
0.5
8
c
o
s[
1.2(
1
)
]
1
k
kk
k
k
x
x
xk
u
x
(
1
3
)
2
0.05
kk
k
zx
v
(
1
4
)
Among them
, the state n
o
ise
2
~(
0
,
)
ku
uN
,and o
b
s
ervatio
n
noi
se
2
~(
0
,
)
kv
vN
,
22
1
uv
. Simulation
particl
e n
u
mb
er 5
0
is
sel
e
cted,
the num
ber
of pa
rticl
e
s of
pro
pag
ation
10, the
50
iteration
s
of th
e two
al
gorit
hms,
re
spe
c
ti
vely, to obtai
n si
mulatio
n
results sho
w
n in
Figure
2.
Fi
g
u
re 3 sho
w
s the
er
ro
r
cu
rve of the t
w
o
algo
rithm
s
. As
can be se
en,
the stan
d
a
rd
particl
e filter
due to in
suffi
cient
simulati
on samp
le
s
prod
uced la
rge erro
rs
, m
any of the st
ate's
estimated
ve
ry accu
rate.
The p
r
op
ose
d
algo
rith
m
can well e
s
tim
a
te the
state
of the sy
stem,
althoug
h the numbe
r of pa
rticle
s is very
small,
but still
achieve
d
a h
i
gh estimate
of effect.
Figure 2. State estimated e
ffect of the two
algorith
m
s
Figure 3. Co
mpari
s
o
n
of two alg
o
rithm
s
es
timate error
In this pape
r, the filtering estimate the
root mean
squa
re erro
r (Root Mea
n
Square
Error, referred to as
RMS
E
) to measure
the accuracy of filtering its definition:
1/
2
1
1
ˆˆ
RM
S
E
(
)
)
MC
N
ii
kk
k
i
MC
N
x(
x
x
(
1
5
)
RMSE value
is l
o
wer, th
e hig
her the
accuracy. T
h
e nu
mbe
r
of
pa
rticle
s
we
re ta
ke
n
50,100 ...... 4
00, breeding
the number
of particl
es i
s
still set to 10, two algorithms
simulati
on
RMSE values were
cal
c
ulat
ed in a differe
nt numbe
r of particl
es.
As ca
n be
seen from T
a
ble 1 the the
prop
agation
estimate the
runni
ng tim
e
of the
particl
e filter (PGPF) is
2 to 3 times of the st
an
dard p
a
rti
c
le
filter (PF). This i
s
estim
a
ted
prop
agatio
n
due to the
pa
rticle
s, thereb
y incre
a
si
ng t
he amo
unt of
comp
utation.
In comp
ari
s
o
n
,
the EKF and
UKF filtering
algorith
m
to
predi
ct the
p
a
rticle
(respe
ctively referre
d
to as th
e E
P
F
and UPF) wi
ll
con
s
um
e more co
mput
ing
re
so
urce
s,
whil
e
con
s
ide
r
abl
e
a
c
curacy with the
prop
osed
alg
o
rithm. T
herefore,
bre
edi
ng e
s
timate
particl
e filter
to improve fil
t
ering
a
c
cura
cy
while al
so ta
king into acco
unt the
real
-time nature of the algorith
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 1, Janua
ry 2015 : 145 –
150
150
Table 1. Vari
ous p
a
rticl
e
filter algo
rithm
runni
ng time
comp
ari
ng (si
m
ulation len
g
t
h 50)
Algorithm
Run time (unit: s
e
conds)
N
=50
N
=100
N
=200
N
=300
N
=400
PF 0.0196
0.0239
0.0387
0.0584
0.0851
PGPF
0.0429
0.0686
0.1240
0.1862
0.2504
EPF 0.0534
0.0947
0.1703
0.2737
0.3735
UPF
0.0938
0.1736
0.3098
0.4892
0.6103
6. Conclusio
n
s and Ou
tlo
o
k
In this paper, the proble
m
of the degrad
ation
of the pre
s
en
ce
of particle filter the
estimated p
a
r
ticle filter p
r
opo
sed b
r
ee
ding imp
r
ove
d
at the sam
e
time taking
into account
the
real
-time filtering a
c
cu
ra
cy. Simulation results
sho
w
that the f
iltering p
e
rfo
r
man
c
e
of the
algorith
m
wh
en signifi
cant
chang
es in t
he numb
e
r
of
particle
s
is a
l
ways
stable.
The advanta
g
e
of breedi
ng e
s
timate parti
cle filter highe
r filteri
ng accura
cy and co
mputational e
fficiency is al
so
high, b
a
si
call
y to a
c
hieve
re
al-time
re
quire
ment
s with
fe
we
r
p
a
rticle
s. Ho
w
e
v
e
r, with
th
e
increa
se in th
e numb
e
r of
state dime
nsi
on in t
he
ca
se of rep
r
od
uction of pro
g
e
n
y particl
es f
e
w
will affect the accuracy of the
filter; thi
s
probl
em has
not yet been
verified. Breeding in the hi
gh-
dimensional state the estim
a
ted parti
cle filter
will be the next step in t
he research
direction.
Referen
ces
[1]
Che
n
Z
.
Ba
y
e
s
i
an F
ilteri
ng F
r
om Kalma
n
F
ilter to Particle F
i
lt
ers, and Be
yo
nd. 200
3.
[2]
Can
d
y
JV. N
onli
n
e
a
r Statis
tical Si
gn
al Pr
ocessi
ng - A
Particle F
i
lteri
ng Ap
pro
a
ch.
Im
aging for
Detectio
n an
d I
dentific
atio
n.
2007; 12
9-1
50.
[3]
Douc
et A, Godsill S, Andri
eu
C. On sequent
ial Mont
e Carl
o sampli
ng me
thods for Ba
ye
sian filteri
n
g
.
Statistics and
Co
mp
uting.
2
0
00; (10): 19
7–2
08.
[4]
Mer
w
e RVD, D
oucet A. T
he U
n
scente
d
Parti
c
le F
ilter. Cam
b
rid
ge: Cambr
i
dge U
n
ivers
i
t
y
,
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[5]
Yuan Z
e
-Ji
an,
Z
heng Na
nni
ng, the Gu Xi
nc
hu
n. Gaussi
an - Hermitia
n
particl
e filte
r
.
Journal o
f
Electron
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20
03; 31(7): 9
70-
973.
[6]
Du Z
hen
gco
n
g
,
T
ang Bin, Lee
can. H
y
brid a
n
nea
led
particl
e filter
. Physics.
200
6; 55(3): 99
9-10
04.
[7]
LU Na, Z
u
-R
en
F
eng. Non
l
i
n
e
a
r inte
ractiv
e p
a
rticle filter
alg
o
rithm.
Contro
l
and D
e
cisi
on.
200
7;
22(4)
:
378-
383.
[8]
Shi Yon
g
, HA
N Cho
ng. Ce
ntre secon
d
-or
der diffe
re
ntia
l
particle filter
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ithm. Xi'
an Jia
o
ton
g
Univers
i
t
y
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W
u
Chu
n
l
i
ng,
HAN C
h
o
ng.
Quadratur
e K
a
lman
partic
l
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ilter a
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o
rithm.
Xi'
an J
i
a
o
ton
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iversit
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Evaluation Warning : The document was created with Spire.PDF for Python.