TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.1, Jan
uary 20
14
, pp. 388 ~ 3
9
7
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i1.4142
388
Re
cei
v
ed
Jun
e
25, 2013; Revi
sed Aug
u
st
26, 2013; Accepted Sept
em
ber 19, 20
13
Resear
ch on Space Target Recognition Algorithm
Based on Empirical Mode Decomposition
Xia Tian, Hou Chengy
u*,
and Shen Yiy
i
ng
Schoo
l of Elect
r
onics a
nd Info
rmation En
gin
e
e
rin
g
Harbi
n
Institute
of
T
e
chnolo
g
y
, Harbin, 15
00
01, PR Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: houc
y@
hit.e
du.cn
A
b
st
r
a
ct
T
he sp
ace tar
g
et reco
gniti
on
alg
o
rith
m, w
h
ic
h is
bas
ed
on t
he ti
me
seri
es
of rad
a
r cross
sectio
n
(RCS), is prop
osed i
n
this p
aper to
solv
e the pro
b
le
ms
o
f
space target
recogn
ition i
n
the active rad
a
r
system. In the
alg
o
rith
m, EMD met
hod is
a
ppli
ed for the
fi
rst time to extract the eig
en o
f
RCS time ser
i
es
.
T
he nor
ma
li
z
e
d instanta
n
e
o
u
s
frequenc
ies o
f
high-freq
ue
nc
y intrinsic
mo
d
e
functions
obt
ain
ed by EMD
are
used
as the
ei
gen v
a
lu
es for
the reco
gniti
o
n
, and
an
effect
ive target rec
ogn
ition cr
iteri
on is
establ
ish
e
d
.
T
he effectiven
ess an
d the st
abil
i
ty
of the al
gorith
m
ar
e ve
rified by
bot
h
s
i
mulati
on data and
r
eal data. In
add
ition,
the
al
gorith
m
cou
l
d
r
educ
e th
e
esti
mati
on
bi
as
of
RCS c
ause
d
b
y
in
accurate
ev
alu
a
tion,
an
d
it is
of great sign
ific
ance i
n
pro
m
ot
ing the targ
et re
cog
n
itio
n ab
ili
ty of narrow
-
band rad
a
r in pr
a
c
tice.
Ke
y
w
ords
: time series of RC
S, emp
i
rica
l m
ode d
e
co
mposi
t
ion, target rec
ogn
ition
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
Rad
a
r cross se
ction (RCS
)
is
th
e avail
able info
rmat
ion for
almo
st all types of
eigen
instru
mentati
on rada
rs. Ho
w to m
a
ke th
e be
st u
s
e
of
the spa
c
e ta
rget’s
RCS inf
o
rmatio
n i
s
v
e
r
y
important to
prom
ote the t
a
rget
recogni
tion ab
ility
of
narrow-band rada
r commissioned
[1]. RCS
is correlate
d
with many
factors, such
as the
ta
rg
et confo
r
mati
on an
d structure, the target
attitude, rada
r ob
se
rvation
angle
and
e
x
ternal env
i
r
onment, et
c. A small flu
c
tuation in the
s
e
factors
cha
n
ges
RCS g
r
e
a
tly. For exa
m
ple, a ti
ny
cha
nge i
n
th
e attitude of
a high
-fre
que
ncy
target
woul
d
cau
s
e
a
cha
nge in
RCS
of dozen
s d
e
c
ibel
s, an
d th
e co
mpli
cate
d environme
n
t in
pra
c
tice
wou
l
d lead to the extremely
complex ch
ange
s in RCS. These woul
d make
the
cal
c
ulatio
n of the target structur
e inform
ation from th
e target RCS
more difficult
. Therefore, how
to use the RCS information
is a big pro
b
l
e
m in
the field of rada
r target recognitio
n
[2].
No
wad
a
ys u
s
ing the ta
rget
RCS i
n
form
ation
to reco
gnize the ta
rget co
uld
be
achi
eved
by the ta
rget
RCS time
serie
s
.
Whe
n
the g
r
ou
nd
radar
stays
m
o
tionle
s
s an
d
the ta
rget
flies
along a defini
t
e track, the chang
es of the
target
motion
track a
nd its attitude are continuo
us, an
d
a function i
n
whi
c
h the target ech
o
inte
nsity fluc
tuat
es ove
r
time is forme
d
. According to
ra
dar
equatio
n, the
ech
o
inten
s
it
y sequ
en
ce
could b
e
tran
sformed i
n
to
RCS
seq
uen
ce. Be
cau
s
e
the
spa
c
e ta
rget
RCS time
se
ries in
clu
de pl
enty of
information, its ex
isting ei
gen
could b
e
u
s
ed
to
recogni
ze the
new targ
et, whi
c
h is the
main re
se
arch conte
n
t of this pa
per.
Two ki
nd
s of method
s are
often used to
extrac
t the ei
gen of RCS time seri
es. O
ne is the
traditional
sta
t
istical a
nalytical meth
od.
As in Re
f. 3, a po
wer
sp
ectral den
sity function i
s
a
ppli
e
d
to obse
r
ve
RCS time
serie
s
, but it fails to
extract recogniti
on index for its insuffici
ent
recogni
za
ble
ability. In R
e
f. 4, a fighter and a h
e
l
i
copte
r
are take
n as the
targets, multi
p
le
distrib
u
tion m
odel
s, such a
s
,
2
distri
but
ion an
d lo
gn
ormal
dist
ribu
tion are a
ppli
ed to
study t
he
statistical di
stribution
chara
c
teri
zation
of
the RCS time
se
rie
s
, but it
need
s n
u
me
rous
sa
mple
s
to
verify. In Ref. 5 the metho
d
of analyzi
n
g time se
rie
s
with ARMA
model i
s
appl
ied to extract
the
pre
c
e
ssi
on
p
e
riod
of balli
stic ta
rget, b
e
ca
use RC
S
time se
rie
s
of the movin
g
sp
ace targ
et is
often non-sta
t
ionary time seri
es, it is very
difficult to be extract
ed and reco
gnized by the
conve
n
tional
time seri
es [
6
, 7] analysis. Therefor
e,
the other o
ne, i.e.
non-stationa
ry sig
nal
analytical me
thod, is ad
o
p
ted by man
y
schol
ar
s n
o
w. Fra
c
tion
al Brownian
motion mod
e
l is
introdu
ce
d in
Ref. 8 to an
alyze the
RCS time seri
es. The pre
s
e
n
t resea
r
ch is
mainly ba
sed
on
the applicatio
n of wavelet tran
sform a
n
d
fuzzy cl
a
ssifi
cation to extract the eigen
and re
cogni
ze
the sp
ace target [9-1
2]. Howeve
r, the
wavelet a
nal
y
s
is
po
ss
es
se
s a p
o
o
r
t
i
me
re
solut
i
on
in
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
TELKOM
NIKA
TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 388 – 3
9
7
389
low fre
quen
cy part and a
poor frequ
en
cy re
solutio
n
in the high freque
ncy pa
rt
. Furtherm
o
re, it
depe
nd
s on the sele
ction
of wavelet function, whi
c
h
limits its application. In
order to se
arch
for
the good nat
ure of time-freque
ncy loca
lization,
a ne
w method for analyzing th
e time-freq
u
e
n
cy
of nonline
a
r,
non-station
a
r
y sign
al, i.e. Hilber
t-Hu
a
ng Tra
n
sfo
r
m (HHT
), was p
r
op
osed
b
y
Norden
E. Huang
et al
i
n
19
96 [1
3], modifie
d
in
1999
[14].
HHT i
s
proved
to p
o
sse
s
s
all
advantag
es o
f
the wavelet analysi
s
, an
d its spe
c
tral
stru
cture i
s
more a
c
curate. Moreove
r
, the
results with
clear phy
sical meanin
g
co
ul
d be obtai
ne
d dire
ctly from spatial do
main. Since the
EMD, the very core of HHT, wa
s pro
posed,
it has been highly
con
c
erned
by domesti
c and
oversea
s
sch
o
lars sp
eci
a
lizing in such fields
a
s
atmo
sph
e
ri
c scien
c
e
s
, physical oce
ano
gra
p
h
y
,
remote
sen
s
i
ng, mech
ani
cal engine
erin
g and lif
e sci
ences, etc. T
he method h
a
s bee
n wid
e
ly
use
d
in su
ch asp
e
ct
s as fa
ult diagno
stic testing,
noise silen
c
ing a
nd multi-scal
e sepa
ratio
n
. For
example, the method is a
p
p
lied by
Loutridis et al to test the fault of machin
e roto
r and excelle
nt
perfo
rman
ce
is achieved [
15]. The EMD method i
s
proved to po
ssess excelle
nt filter prope
rties
by Fland
rin [1
6]. It is also
u
s
ed
by Lin
Zh
enshan
et
al t
o
analy
z
e th
e
temperature
cha
nge
s in t
h
e
northe
r
n hem
isph
ere over the
pa
st
400 years and re
sults i
n
that climate tempe
r
ature chan
g
e
s
regul
arly in
di
fferent time
scale [1
7]. In this
p
ape
r, E
M
D a
nalysi
s
woul
d be
pe
rformed
on
RCS
time seri
es to
explore the e
ffect
ive method to extract the eige
n.
2. Introduc
tion to EMD P
r
inciple
HHT i
s
comp
ose
d
of EMD and Hil
bert
Tran
sfo
r
m. In HHT eve
r
y signal a
r
e a
s
sumed to
be
comp
ose
d
of
several
Intrinsi
c
Mo
de Fu
nctio
n
s (IMF), i
n
which
IMF
sh
ould m
eet t
w
o
con
d
ition
s
bel
ow:
Within the en
tire time cou
r
se, the numb
e
r of cr
o
s
sin
g
zero is equ
ivalent to the number of the
extreme poi
nts or differs by
one at most.
Any point on
the sig
nal, th
e mea
n
s
of b
o
th the up
pe
r envelop
e an
d the lo
we
r e
n
velope
are
zero,
namely, the signal
s are lo
cally symmetri
c
al alo
ng the
time axis.
The EMD a
p
p
roa
c
h
wa
s p
r
opo
se
d by Huang et al
to
resolve any g
i
ven sign
als.
This i
s
a
kind of expe
ri
ence sievin
g method.
Its proce
s
s is de
scribed b
e
lo
w:
As for a
n
y given sig
nal
X
(
t
), all of the extreme p
o
in
ts on
X
(
t
)
are identified a
t
first, and th
en
quad
ratic
spli
ne cu
rve is p
e
rform
ed on t
hem to con
n
e
c
t all points of
maximum values to form t
h
e
uppe
r envel
o
pe, and the l
o
we
r envel
op
e is devel
ope
d by the sam
e
way. The d
i
fference of the
data
X
(
t
)
and
the mean
s
m
1
of the upper a
nd the l
o
we
r envel
op
es i
s
re
co
rd
e
d
as
h
1
, then it
sho
w
s as f
o
ll
ow
s:
11
()
-
hX
t
m
(1)
The re
sidu
al
sig
nal
r
1
in
cludi
ng th
e
element
s of
the lo
wer o
r
der freq
uen
cy is give
n in
the
following formula:
11
()
-
rX
t
h
(2)
r
1
is ta
ke
n a
s
the
ne
w si
gnal. Th
e ab
ove sievin
g
steps a
r
e
re
p
eated o
n
it, until the resi
dual
sign
al of the nth orde
r be
comes m
onoto
n
ic fun
c
tion a
nd fails to sie
v
e IMF comp
onent
s.
-1
-
nn
n
rr
h
(3)
Mathemati
c
al
ly,
X
(
t
) coul
d
be exp
r
e
s
sed
as th
e sum
of
N
comp
on
ents of IMF
a
nd on
e resi
d
ual
item:
1
()
()
(
)
N
jn
j
Xt
h
t
r
t
(4)
3. Target
Re
cognition
Algorithm Ba
s
e
d on EMD
As sho
w
n in
(4), a
n
y sig
nal could
be
decompo
se
d into a
sum
of
N
IMF
s
and o
n
e
resi
dual
item.
As fo
r IMF
i
,
m
i
which
represe
n
ts th
e n
u
m
ber of
cr
ossing zero coul
d
be
calculat
ed,
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
Re
sea
r
ch on
Space T
a
rg
et Recognitio
n
Algorithm
Based o
n
Em
pirical Mod
e
...
(
H
o
u
C
h
en
gy
u)
390
and it
s n
o
rm
alize
d
in
stant
aneo
us freq
u
ency
F
i
is d
e
fined i
n
the
pap
er to
be
the ratio of
its
numbe
rs of crossing
zero to the length
H
of the time seri
es, which is expre
s
sed
as:
/,
1
,
2
,
3
,
,
ii
Fm
H
i
N
(5)
The e
nergy ratio
E
i
of IMF
i
is
defined
as th
e pe
rce
n
tage of th
e
energy
e
i
on
the total
sum of ea
ch I
M
F ene
rgy, its expre
s
sion i
s
as follo
ws:
1
/
1
00%
,
1
,
2
,
3
,
,
n
ii
j
j
Ee
e
i
N
(6)
The p
r
op
ertie
s
of the ta
rg
et RCS frequ
ency
c
oul
d b
e
often divid
ed into two p
a
rts, the
rapidly va
ryin
g pa
rt a
nd th
e sl
ow on
e. T
he latte
r
i
s
d
e
termin
ed
by the influ
e
n
c
e
s
of
ob
se
rvation
angle
an
d m
easure
m
ent
errors, et
c., while
the fo
rmer
i
s
relate
d to the
chan
ges in th
e ta
rget’s
confo
r
matio
n
, stru
ctu
r
e
an
d attitude. Ta
ken
the
ac
tua
l
high
-freq
u
e
n
cy target a
s
an exam
ple, t
h
e
energie
s
of th
e refle
c
ted
si
gnal
s from
th
e no
se
and
th
e win
g
of a
pl
ane a
r
e i
n
g
r
eat differe
nce
,
a
tiny cha
nge
i
n
the t
a
rg
et
attitude could
ca
us
e a
variance in
irrad
i
ation a
r
ea
a
nd m
a
ke
RCS
cha
nge
by d
o
ze
ns de
cibe
ls, thu
s
it i
s
see
n
t
hat th
e
high
freq
ue
ncy p
a
rt of
RCS tim
e
se
ries
rep
r
e
s
ent
s m
a
inly the p
r
o
p
e
rties of the
target. A
c
cord
ingly, if two
RCS time
se
rie
s
a
r
e th
e
sam
e
target, their n
o
rmali
z
e
d
instantaneo
us freque
nci
e
s (d
efined a
s
F
i
and
F
i
re
spe
c
tively) obtai
ned
by EMD sho
u
ld be
simila
r on th
e hig
h
frequ
en
cy. Based
on t
h
is
cha
r
a
c
teristic, fre
quen
cy
threshold
D
i
s
set in this
p
aper to
be th
e division
bet
wee
n
high f
r
e
quen
cy an
d low fre
que
ncy
of
IMFs. IMFs
a
r
e a
rra
nge
d i
n
de
scendi
ng
orde
r of
the
instanta
neo
u
s
fre
quen
cie
s
, and they are
recorded a
s
I
M
F
1
,I
MF2,
,I
M
F
N
. If there is
,1
,
2
,
3
,
,
j
F
Dj
N
(7)
IMF
j
would
be initially se
lected fo
r re
cogni
tion. It is assume
d th
at there a
r
e
M
high
freque
nci
e
s a
nd thei
r IMF
meets (7
). In
order to
red
u
ce
the
neg
a
t
ive effects of
high
-fre
que
n
cy
noises, the e
nergy thresho
l
d is set a
s
G
, if there is
,1
,
2
,
3
,
,
j
EG
j
M
(8)
IMF
j
woul
d
be sele
cted
as the
pa
rameter fo
r reco
gnition, o
t
herwi
se it
woul
d be
exclud
ed. Suppo
se if
K
IMFs meet th
e requi
rem
e
n
t
s and t
heir i
n
stanta
neo
us frequen
cie
s
are
taken
as the
eigen frequ
enci
e
s fo
r re
cog
n
ition, the
recognitio
n
i
ndex
R
woul
d be defin
ed
as
follows
：
''
(
)
/
1
00%
,
,
1
,
2
,
3
,
.
jj
j
j
RF
F
F
j
K
(9)
is recog
n
itio
n thresh
old, whi
c
h sh
ould
be o
ften th
e positive nu
mber le
ss th
an 0.5. If th
e
above fo
rmul
a is m
e
t, the
n
there is
1
i
S
, o
t
herwi
se
0
i
S
. Th
erefo
r
e, the t
o
tal re
co
gnition
coeffici
ent
S
is
s
h
own as
follows
:
1
/2
K
k
i
SS
K
(10
)
If
S
is greater than or e
q
ual to
/2
K
, they
woul
d be ide
n
tified to be the sam
e
target,
otherwise the
different targ
ets. Figure 1 is the flow
cha
r
t of the algori
t
hm pre
s
ente
d
by this pap
er.
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Vol. 12, No
. 1, Janua
ry 2014: 388 – 3
9
7
391
j
FD
j
E
G
/
2
SK
Figure 1. The
flowch
art of the al
go
rithm
pre
s
ente
d
by this pap
er
4.The Anal
y
s
is of Simulated
Data
At first, simulated data wo
uld be used to veri
fy the e
ffectiveness and
the stabil
i
ty of the
algorith
m
pre
s
ente
d
by thi
s
pa
per. Sh
o
w
n a
s
Fi
g
u
re
2, RCS Se
qu
ence 1 i
s
the
curve
of a
RC
S
value, whi
c
h cha
nge
s with
time, calcula
t
ed by r
ada
r RCS fluctu
ation statisti
cal
model form
ul
a,
descri
bed
as
Ref. 3. Supp
o
s
e if the
r
e i
s
a fixed
ra
da
r
station o
n
a
certain
gro
und
and it
s worki
n
g
wavele
ngth is 5cm, a jet levels off in the dire
cti
on
of the radar
at 30km aw
a
y
from it, the
flight
height i
s
3km
，
the flight
sp
eed i
s
0.5km/s. Th
e
seq
u
e
n
ce
len
g
th i
s
212
point
s a
n
d
the
sp
ent ti
me
is 32.12
se
co
nds.
Figure 2. RCS Sequen
ce
1
EMD is pe
rfo
r
med o
n
the RCS time series
an
d obtai
ned data is
shown as Fig
u
r
e 3. The
line at the bo
ttom is its en
velope inform
ation,
and IMFs are listed
in desce
ndin
g
orde
r of the
norm
a
lized in
stantan
eou
s frequ
en
cie
s
. The ene
rgy
pe
rce
n
tage of the norm
a
lize
d
instantan
eo
us
freque
nci
e
s o
f
each IMF is
sho
w
n a
s
Ta
ble 1.
0
5
10
15
20
25
30
-20
-15
-10
-5
0
5
10
15
20
25
30
ti
m
e
/s
RC
S
/
d
B
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Re
sea
r
ch on
Space T
a
rg
et Recognitio
n
Algorithm
Based o
n
Em
pirical Mod
e
...
(
H
o
u
C
h
en
gy
u)
392
Figure 3. EMD of RCS Se
quen
ce 1
Table 1. No
rmalize
d
insta
n
taneo
us fre
q
uen
cie
s
and
energy ratio
s
of Sequen
ce
1 and 2
IMF
1
2 3 4
5 6 7
8
Instantaneous
frequenc
y of
Sequence 1
0.7
453
0.3
821
0.2
028
0.1
415
0.0
755
0.0
472
0.0
283
0.0
189
Instantaneous
frequenc
y of
Sequence 2
0.7
547
0.3
538
0.1
981
0.1
085
0.0
472
0.0
283
No
ne
No
ne
IMF ener
g
y
ratio(%
)
of
Sequence 1
16.
14
11.
05
10.
71
7.9
9
6.7
5
20.
00
6.9
2
20.
45
IMF ener
g
y
ratio(%
)
of
Sequence 2
23.
45
5.3
9
2.9
9
1.1
6
12.
02
54.
98
No
ne
No
ne
The stability of this algorit
hm woul
d be analyzed bel
ow, it would b
e
con
s
ide
r
e
d
from two
asp
e
ct
s, the pre
s
en
ce of
measurement
erro
r and o
b
s
ervatio
n
time error.
1) Co
nsi
d
e
r
in
g the pre
s
en
ce of measu
r
e
m
ent error
Even if it is
the highly
accurate rada
r equip
m
ent,
the set
of sampled
data
alway
s
in
c
l
ud
es
1
%
~
2
%
，
someti
mes
even a
s
mu
ch
as
10%~2
0% (f
or exam
ple,
whe
n
the
high
elevation tra
c
king i
s
p
e
rfo
r
med by
rada
r) of the d
a
ta
whi
c
h d
e
viat
e
seve
rely fro
m
the target true
value b
e
cau
s
e of the
com
p
reh
e
n
s
ive in
fluences or
e
ffects of
man
i
fold o
c
casi
o
nal fa
ctors [1
8].
Hen
c
e, the e
x
treme value
of the data is som
e
ti
me
s cau
s
e
d
by measure
m
ent
error, but not
b
y
the real extreme poi
nt of the data.
In
order to verify
the stabilit
y of the algorit
h
m, suppose if
maximum an
d minimum v
a
lue
s
have e
rro
rs i
n
mea
s
ureme
n
t, five maximum
values a
nd fi
ve
minimum val
ues
wo
uld b
e
exclud
ed a
n
d
wo
uld b
e
re
placed
with their m
ean
s of
two nei
ghb
oring
points.
The re
formed RCS Sequen
ce
i
s
reco
rde
d
as S
eque
nce 2, as sh
own in Figure 4.
EMD i
s
p
e
rf
orme
d o
n
t
he
RCS tim
e
serie
s
, a
n
d
the
norm
a
lize
d
in
stan
taneou
s
freque
nci
e
s o
f
each IMF a
nd the ene
rg
y perce
ntage
are shown a
s
Table
1. It is found that the
numbe
rs
of
IMF
of RCS Sequen
ce
1
and 2 obtain
ed
by
EMD are
differe
nt and two IMF
s
are
missi
ng, in t
he pa
per th
e
freque
ncy th
reshold
D
i
s
taken as 0.1
，
the en
ergy
thre
shold
G
is
5%
，
the recognition
th
re
shol
d
is 10%
(whi
ch
is
app
lied to all
dat
a belo
w
and
woul
d not
b
e
repe
ated late
r). By cal
c
ul
a
t
ion four IMF
s
in Se
que
nce 2 a
r
e id
enti
f
ied to be th
e
high
-freq
uen
cy
IMF, but the
ene
rgie
s of
IMF3 an
d IM
F4 a
r
e l
e
ss t
han th
e e
n
e
r
gy thre
sh
old, they could
be
0
5
10
15
20
25
30
-0.
2
0
0.
2
ti
m
e
/s
IM
F
1
0
5
10
15
20
25
30
-0
.
2
0
0.
2
ti
m
e
/
s
IM
F
2
0
5
10
15
20
25
30
-0.
2
0
0.
2
ti
m
e
/s
IM
F
3
0
5
10
15
20
25
30
-0
.
2
0
0.
2
ti
m
e
/
s
IM
F
4
0
5
10
15
20
25
30
-0.
2
0
0.
2
ti
m
e
/s
IM
F
5
0
5
10
15
20
25
30
-0
.
2
0
0.
2
ti
m
e
/
s
IM
F
6
0
5
10
15
20
25
30
-0.
2
0
0.
2
ti
m
e
/s
IM
F
7
0
5
10
15
20
25
30
-0
.
2
0
0.
2
ti
m
e
/
s
IM
F
8
0
5
10
15
20
25
30
-0.
2
0
0.
2
ti
m
e
/s
RE
S
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TELKOM
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Vol. 12, No
. 1, Janua
ry 2014: 388 – 3
9
7
393
rega
rd
ed a
s
high-f
r
eq
ue
ncy noi
se
s
and
would
b
e
exclu
ded.
Sequen
ce
2
relative to
th
e
recognitio
n
i
ndex of Seq
uen
ce 1
R
1
=1
.2
6%
,
R
2
=7.41%
are bot
h less tha
n
the re
cog
n
i
t
io
n
threshold
，
S
=2.
Whe
n
S
i
s
m
o
re
than
or
equal
to t
he h
a
lf of th
e reco
gnition
index
amou
nt
(
K
/2=
1
)
，
they coul
d be determined to
be the
sam
e
ta
rget. Therefore, the al
gorithm can
still work
whe
n
the se
q
uen
ce
s have
abno
rmal val
ues
cau
s
e
d
b
y
some mea
s
urem
ent errors.
Figure 4. RCS Sequen
ce
2 after the ab
norm
a
l value
s
are ex
clud
e
d
5. Consideri
ng the Pres
e
n
ce of Ob
ser
v
a
tion Time
Error
In order to
ensure the
successful compl
e
tion of
some t
a
sks, flight ve
hicles in the
military
field are
req
u
i
r
ed to a
pproa
ch the ta
rget i
n
the def
inite
dire
ction o
r
di
rectio
n inte
rval to maximize
the redu
ction
of
RCS
and
to co
nceal th
emselve
s
.
In
the
civil aviation system,
t
he
le
g whi
c
h is
expecte
d to b
e
pa
ssed in t
he flight plan
is pre-
plann
e
d
and eve
r
y l
eg is
a direct
ed flight, so t
h
e
track line of the space ta
rget possesses ce
rtai
n predictability. Howeve
r, the current RCS ti
me
seri
es o
b
tain
ed by observ
a
tion and the
previou
s
one
s have a
cert
ain error i
n
time be
cau
s
e
of a
tiny cha
nge
i
n
ra
da
r o
b
se
rvation time
or in
the
sp
ace
targ
et at
titude. Co
nsi
derin
g that t
h
e
algorith
m
sho
u
ld posse
ss a
definite stabil
i
ty in
the time, the middle section from 5
1
to 150 points
is cut off fro
m
the sequ
e
n
ce
with the
total length o
f
212 poi
nts
and i
s
u
s
ed
as the
refe
re
nce
seq
uen
ce,
re
corded
a
s
S
eque
nce 3.
Comp
are it
with Se
quen
ce
4
whi
c
h
i
s
tran
slation
a
l
over
time, then th
e
re
sult
s a
r
e
shown a
s
Figu
re
5. Fo
r exa
m
ple, if Seq
u
ence 4
ma
ke
s the
tra
n
sl
ation
motion by 1
0
points
rig
h
tward
s
relative t
o
Sequ
en
ce
3, it makes th
e tran
slatio
na
l motion by
1
0
%
relative to the original
seq
u
ence.
Figure 5. The
reco
gnition
result
s of Sequen
ce 4 rel
a
tive to Sequen
ce 3
0
5
10
15
20
25
30
-1
5
-1
0
-5
0
5
10
15
20
25
ti
m
e
/
s
RCS
/
d
B
-3
0
-2
0
-1
0
0
10
20
30
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
ti
m
e
/%
2S
/
K
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ISSN: 2302-4
046
Re
sea
r
ch on
Space T
a
rg
et Recognitio
n
Algorithm
Based o
n
Em
pirical Mod
e
...
(
H
o
u
C
h
en
gy
u)
394
The ratio
2/
SK
of the total
re
co
gnition
coeffi
cient
s of Se
q
uen
ce
4 relati
ve to Sequ
en
ce
3 to its total reco
gnition th
resh
old K/2 is
cal
c
ulate
d
to
cha
nge
with t
i
me, sh
own
a
s
the
solid li
ne
in Figu
re
5. If there i
s
2/
1
SK
，
the
same
target would
be
deter
mined,
so
it is th
e
corre
c
t
recognitio
n
whe
n
the
so
lid line
is a
bove the
da
sh li
ne. Se
e
n
from
the
above fig
u
re,
the
recognitio
n
ef
fects
of this
a
l
gorithm
is
co
mparat
ively stable
when
th
e overl
appi
ng
time of the
s
e
two
seq
uen
ces i
s
m
o
re than
75% of
the total len
g
t
h of the
se
q
uen
ce
s, exce
pt for the
da
ta
who
s
e time transl
a
tion are betwe
en 8% and 16%.
6. The Analy
s
is of the
Da
ta from the
Real Tes
t
The effectiveness and stabilit
y of the a
l
gorithm presented
here would be verifi
ed by a
grou
p of data
from the re
al
test in the followin
g
.
In the actual flight,
the high e
nd
of the fluctua
n
t
time spe
c
tru
m
of the
ai
rpl
ane’
s
RCS
would
be
mu
ch hig
h
e
r
. Wh
at is sho
w
n
a
s
Fi
gure
6 i
s
the
RCS time
se
ries in
real te
st, reco
rde
d
a
s
Sequ
en
ce
5, given addit
i
onally by
Ref
.
3, its length
is
217 poi
nts an
d the total time is 2.58 second
s.
Considering that the algorit
hm
should possess a defini
t
e st
ability in
the time, the
middle
se
ction f
r
om
51 to
150
poi
nts i
s
cut
off from S
eque
nce 5
with t
he t
o
tal len
g
th of
217
poi
nts
a
n
d
is used a
s
the refe
ren
c
e
sequ
en
ce, whi
c
h is
re
corde
d
as Se
quen
ce 6. Compa
r
e it wi
th
Sequen
ce
7
whi
c
h i
s
tran
slation
a
l over time, and
th
e re
sults
are
sho
w
n
as Fi
g
u
re 7. Se
en f
r
om
the figure, the
longer the ov
erlap
p
ing tim
e
of t
hese two sequ
en
ce
s, which i
s
gre
a
t
er than 70% o
f
the sequ
en
ce
’s total length
,
the better the simila
rity,
the more sta
b
le the algori
t
hm. Therefo
r
e,
this alg
o
rith
m coul
d be
con
c
lu
ded to
posse
ss a
def
inite sta
b
il
ity by the verificatio
n
of
the
simulate
d dat
a and the re
al
data.
Figure 6. RCS Sequen
ce
5
Figure 7.
The
reco
gnition
result
s of Sequen
ce 7 rel
a
tive to 6
0
0.
5
1
1.
5
2
2.
5
-1
5
-1
0
-5
0
5
10
15
20
ti
m
e
/s
RC
S
/
d
B
-4
0
-30
-2
0
-10
0
10
20
30
0
0.
5
1
1.
5
2
2.
5
ti
m
e
/
%
2S
/
K
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ISSN: 2302-4
046
TELKOM
NIKA
TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 388 – 3
9
7
395
In the followi
ng a group of data from t
he real
test
woul
d be used to illust
rat
e
that the
algorith
m
po
sse
s
ses th
e a
d
vantage
s, such
as it
co
ul
d re
du
ce
so
me erro
rs i
n
t
he calculatio
n of
RCS which a
r
e ca
used by
inaccurate e
v
aluation.
Th
e data is com
posed of poin
t
track data a
n
d
energy info
rmation o
b
tai
ned
by the
si
gnal
dete
c
tio
n
of a
rada
r
system. T
he
RCS
co
uld b
e
derived from the mono
stati
c
rad
a
r p
r
op
a
gation eq
uat
i
on given by kerr [19], and i
t
is describ
ed
as
3
4
222
(4
)
/
(
)
rt
t
r
t
r
P
RP
G
G
F
F
(11
)
In the eq
uatio
n,
r
P
and
t
P
are resp
ectively th
e po
we
r of th
e re
ceive
d
si
gnal a
nd
of th
e
transmitted signal,
r
G
and
t
G
are the po
wer g
a
in of the
receivin
g antenna a
nd of the
transmitting antenn
a
sep
a
rately;
is the wavelen
g
t
h,
t
F
is the p
r
opa
gation fa
ctor
of the
dire
ctional di
agra
m
from the tran
smittin
g
antenn
a to the target,
r
F
is the propa
gat
ion factor of
the dire
ction
a
l
diagram fro
m
the targ
et to the re
ceivin
g anten
na, a
nd R i
s
the
di
stan
ce fro
m
the
rada
r to the target.
The ra
dar
eq
uation is p
e
rf
orme
d on re
al time
comp
utation of the RCS of the target,
resulting
in th
e RCS
se
que
nce
ne
ede
d.
A pul
se
Do
p
p
ler processi
ng i
s
perfo
rm
ed o
n
every
30
pulses,
what
we
got fro
m
this fo
rm
s a
p
o
int on th
e
seque
nce of 1
17 p
o
ints i
n
t
o
tal. The ta
rg
et
fails to be d
e
tected
whe
n
sign
al to noise rati
o i
s
co
mpa
r
atively low, then velocity su
per-
resolution
alg
o
rithm
woul
d
be ap
plied to
re
con
s
tru
c
t t
he lo
st targ
et [20] in orde
r to com
p
leme
nt
the data. The
target is the
civil airpla
ne
whi
c
h
flies in
the spe
ed of
0.26 km/
s
fro
m
about 78
km.
The
RCS
se
quen
ce
s
of the ai
rpla
ne
s on th
e
sam
e
flight, sho
w
n
as Figu
re 8
and
Fig
u
re
9
respe
c
tively, are
obtain
e
d
by dete
c
tin
g
at di
ffe
rent
time a
nd
re
corded
a
s
S
eque
nce 8
a
nd
Sequen
ce 9.
Figure 8. RCS Sequen
ce
8
Figure 9. RCS Sequen
ce
9
EMD is
perf
o
rme
d
on th
ese t
w
o
RCS sequ
en
ce
s respe
c
tively. Thro
ugh th
e re
sults
sho
w
n a
s
Ta
ble 2, the re
cognition in
de
x of the data
from the real rest is
foun
d to be greater t
han
the previo
us
data. If the total re
cog
n
ition co
efficient
meets the e
quation
S
=2
，
the sam
e
targe
t
woul
d be still
identified.
It is kn
own th
at the rada
r e
quation
given
by
ke
rr is
not
com
p
re
hen
si
ve for n
o
t re
ckoni
ng
in som
e
un
certain rada
r
para
m
eters.
Therefore, a
certai
n
erro
r wo
uld exist in the RCS
seq
uen
ce
s
we got. The
errors in
the
co
mputati
on
of RCS
ca
used
by these
pa
rameters
sho
u
ld
be a fixed val
ue or
at mo
st a fluctuatin
g
slo
w
ly
varyin
g functio
n
rel
a
tive to RCS,
whi
c
h
woul
d
not
signifi
cantly affect the normali
zed in
stantane
ou
s freque
ncy on
high ban
d extracted by EMD.
Suppo
se if the experim
ent
is made
und
er the
c
onditi
on that the o
t
her pa
ram
e
ters
rem
a
in th
e
same, an
d th
e distan
ce fro
m
the rada
r to the tar
get d
e
tected i
s
not
pre
c
ise e
nou
gh to use, th
en
the data we o
b
tained i
s
onl
y as follows:
4
3
222
/(
4
)
/
(
)
rt
t
r
t
r
RP
P
G
G
F
F
(12)
0
1
2
3
4
5
6
7
0
2
4
6
8
10
12
14
16
ti
m
e
/s
RCS
/
d
B
0
1
2
3
4
5
6
7
-5
0
5
10
15
20
ti
m
e
/s
RCS
/
d
B
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
Re
sea
r
ch on
Space T
a
rg
et Recognitio
n
Algorithm
Based o
n
Em
pirical Mod
e
...
(
H
o
u
C
h
en
gy
u)
396
Table 2.
Data
colle
ction of RCS sequ
en
ce
s from the real test
IMF
1 2 3
4
5
Instantaneous fr
equenc
y
of Se
qu
ence 8
0.6686
0.2674
0.1337
0.0622
0.0267
Instantaneous fr
equenc
y
of Se
qu
ence 9
0.6436
0.2348
0.1453
0.0513
0.0256
Energ
y
percenta
ge (%
) of Sequ
e
n
ce 8
33.12
44.96
8.38
8.52
5.02
E
n
er
gy
per
centage (
%
) of Sequence 9
54.
85
28.
56
6.
61
6.
55
3.
43
Sequence 9 r
e
lativ
e to Sequence 8
R1
R2
R3
S
K/2
3.
74%
12.
19%
8.
68%
2
1.
5
As far as Se
quen
ce 8 is concern
ed,
4
/
R
is seen a
s
a whole, re
corde
d
as Seque
n
c
e
10 after the
modificatio
n
. The algo
rith
m is appli
e
d
to extract the no
rmali
z
e
d
instanta
n
e
ous
freque
ncy of Sequen
ce 1
0
.
Its results a
r
e co
mpa
r
ed
with the origi
nal data, sho
w
n a
s
Table
3.
The valu
es
of their
re
co
gnition in
dex,
R
1
,
R
2
an
d
R
3
a
r
e ve
ry small, a
nd t
hey are in
h
i
gh
simila
rity an
d co
uld b
e
determi
ned t
o
be the
sa
me targ
et. Accordi
ngly, the erro
rs in
the
cal
c
ulatio
n of RCS cau
s
ed
by some ina
c
curate ev
alua
tion of slowly
varying pa
ra
meters co
uld
be
ignored in the
algorithm, which
woul
d be
valuable for the appli
c
atio
n in engin
eeri
ng pra
c
tice.
Table 3. Experime
n
tal dat
a colle
ction b
y
ignoring the
distan
ce
R
IMF
1 2
3 4
5
Instantaneous fr
equenc
y
of Se
qu
ence 8
0.6686
0.2674
0.1337
0.0622
0.0267
Instantaneous fr
equenc
y
of Se
qu
ence 10
0.6410
0.2564
0.1282
0.0598
0.0256
Energ
y
percenta
ge (%
) of Sequ
e
n
ce 8
33.12
44.96
8.38
8.52
5.02
Energ
y
percenta
ge (%
) of Sequ
e
n
ce 10
33
．
76
44
．
99
8
．
56
8
．
05
4
．
64
Modification relative to the original
sequence
R1 R2
R3
S
K/2
4.13%
4.11%
4.11%
3
1.5
Finally, in order to verify the effectivenes
s of the
algorith
m
, three group
s of
data of
Sequen
ce
1,
5 a
nd
8 a
r
e
co
mpa
r
ed
la
terally an
d th
e data
obtai
n
ed i
s
colle
cte
d
a
s
T
able
4.
Shown
as
Ta
ble 4, Sequ
e
n
ce
1, 5 an
d
8 belo
ng to
di
fferent types
of target
s, an
d the re
co
gnit
i
on
index obtaine
d by matchin
g
two of them are
very great, almo
st greate
r
than
the recogniti
on
threshold
. All
S of theirs are all less than
/2
K
, so they are reco
gni
zed a
s
the different target
s.
Table 4. Re
cognition p
a
ra
meters coll
ection of Seque
nce 1,5 ,an
d
8
R1
R2
R3
S
K/2
Same Targ
et
？
8 relative to 1
10.29%
30.02%
34.07%
0
1.5
No
5 relative to 1
0.46%
17. 98%
22.73%
1
1.5
No
8 relative to 5
9.88%
14.68%
14.68%
1
1.5
No
7. Conclusio
n
The pa
per i
s
the first to propo
se th
at EMD is u
s
ed
to analyze
RCS time se
ries. Th
e
effectivene
ss
and stability of
the
propo
sed alg
o
rithm
are ve
rified b
y
a gro
up of
simulate
d d
a
ta
and t
w
o
gro
ups of
data
from the
rea
l
test. Th
i
s
algorith
m
co
uld ig
nore th
e e
rro
rs in
the
cal
c
ulatio
n of RCS cau
s
e
d
by some ina
c
curate
eval
u
a
tion of slowl
y
va
rying parameters, whi
c
h
is of great si
gnifica
nce to explore the
ability of
the
active narro
w-ban
d ra
dar t
o
recogni
ze t
he
target.
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046
TELKOM
NIKA
TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 388 – 3
9
7
397
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