TELKOM
NIKA
, Vol.12, No
.4, Dece
mbe
r
2014, pp. 93
3~9
4
1
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v12i4.136
933
Re
cei
v
ed Au
gust 19, 20
14
; Revi
sed O
c
t
ober 2
2
, 201
4; Acce
pted
No
vem
ber 1
0
,
2014
Two-Dimensio
nal Imaging Algorithm Based on Linear
Prognosis for Space Target in Bistatic ISAR System
Xueping Lu*,
Shapu Ren
Sh
ao
xing U
n
iversit
y
, Z
h
e
j
i
a
ng, 312
00
0, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: xu
epi
ngl
u_z
j
s
x@
16
3.com
A
b
st
r
a
ct
In bistatic
inv
e
rse synthetic a
perture radar (
B
i-ISAR) system
, its
image r
e
solution is
lower than
m
o
nostatic IS
AR system
. In
order to s
o
lve
this problem
,
t
he linear pr
ognosis
algo
rithm
is
adopted in the
imagi
ng
proc
e
ss and th
e i
m
a
g
in
g al
gorit
h
m
base
d
o
n
li
n
e
a
r
prog
nosis is prop
osed.
S
p
a
c
e target Bi-IS
A
R
imagi
ng
is
take
n as
ex
a
m
pl
e
i
n
the
res
earch.
T
he
on
e-di
me
nsio
nal
ra
nge
profil
e is
cre
a
ted thr
o
u
gh
pu
l
s
e
compressi
on
me
ho
d. Befor
e
the
a
z
i
m
ut
h
co
mpress
io
n, burg
e
n
tropy
maxi
mu
m al
gorith
m
in
Le
vion
s
recursive
meth
od
is
used
to
e
s
timate
the
pr
o
gnos
is co
effici
ents a
n
d
the
a
z
i
m
ut
h
ech
o
d
a
ta. T
h
e
n
F
our
ie
r
transformatio
n
is use
d
to c
o
mpr
e
ss the
a
z
i
m
uth
dat
a i
n
o
r
der to
get the
hig
h
res
o
luti
o
n
a
z
i
m
ut
h i
m
a
ge.
T
h
is imag
ing
meth
od ca
n o
b
tain th
e tw
o-di
me
nsio
nal
image w
i
th the r
e
sol
u
tion
equ
a
l
to the monos
tatic
ISAR or
even
hig
her th
an
it.
Simulati
on
ex
p
e
ri
ments
hav
e
verifie
d
the
eff
e
ctiven
ess a
n
d
ava
ila
bil
i
ty of t
he
algorithm
.
Ke
y
w
ords
: bistatic ISAR, levions
prognosis,
im
age resolution, tw
o-dimensional
imaging
1. Introduc
tion
Due to t
he
separated tran
smitting a
nd
receivi
ng
stat
ion, the bi
sta
t
ic Inverse S
y
nthetic
Aperture
Radar
(ISAR) can still
get the 2--D
(two-dimensional) objec
t image even
when
the
relative ra
da
r line of sig
h
t has
no rotational move
m
e
nt, which is t
he better
ch
a
r
acte
ri
stic tha
n
mono
static I
SAR. So, bistatic ISAR has the
hi
ghe
r imaging p
r
o
bability than
mono
static I
SAR
[1],[2]. Otherwise, when the receiv
ing st
ation is l
o
cated in t
he front, the imagi
ng
range
augm
ents
at the same t
i
me, whi
c
h could imp
r
ove
the detec
tio
n
and ima
g
in
g ability for st
ealth targ
ets
[3]-
[5]. In recent
years, the
main re
se
arch of bi
static
ISAR is focu
sed o
n
imagi
ng pri
n
cipl
e
and
variou
s co
mp
ensation alg
o
r
ithms [6]-[9].
Duri
ng th
e bi
static ISAR i
m
aging
process, the time
-varia
nt
bist
atic a
ngle
ca
n l
ead to
a
time-varia
nt
bistatic i
m
agi
ng resolution,
whi
c
h m
a
ke
s the
2-D im
age b
e
come
blurred [1
0]. The
movement
of
spa
c
e
targets is
co
mpli
cate
d, so
it
n
eed
s to ima
ge th
e
obje
c
t in
a
short i
n
tegratio
n
time and avoi
d blurring p
h
e
nomen
on of 2
D
image.
Becau
s
e
of t
he sho
r
t inte
gration
time,
the bistati
c
a
ngle a
nd im
a
ge resolution
can
be
looked a
s
the
con
s
tant d
u
ri
ng imagi
ng ti
me, whi
c
h
co
uld effectively
avoid ph
eno
menon
of ima
ge
blurring. At t
he
same
tim
e
, the ta
rget
ch
ar
a
c
te
risti
c
s have
rela
tively small
cha
nge
s
wh
en
imaging
du
ri
ng
small
ro
tation an
gel,
whi
c
h
can
de
crease t
he difficulty of movem
ent
comp
en
satio
n
. While the coh
e
re
nt integration time
become
s
sh
o
r
ter, the re
sol
u
tion is defini
t
ely
decrea
s
e
d
. So it is th
e p
r
ereq
uisite
to
resea
r
ch the
ISAR imagin
g
algo
rithm
whe
n
the
rot
a
tion
angle i
s
small
.
The ISAR i
m
aging
be
comes
sp
ectrum estimatio
n
pro
b
lem
whe
n
the m
o
vement
comp
en
satio
n
is a
c
compl
i
she
d
a
s
re
searche
d
i
n
t
he p
ape
r [1
1
]. So, the
imaging
p
r
oble
m
in
small i
n
tegration time
ca
n
be
chan
ged
i
n
to a hi
gh
-re
solutio
n
spe
c
trum e
s
timati
on p
r
obl
em
with
sho
r
t d
a
ta
se
quen
ce. A
s
f
o
r th
e p
r
obl
e
m
of hi
gh-re
solution
sp
ectrum e
s
timatio
n
with
sho
r
t d
a
ta
seq
uen
ce, th
ere
are t
w
o
ki
nds of
pro
c
e
s
sing
me
th
od
s as introdu
ce
d in
the
pap
e
r
s [12],[13]. T
he
firs
t k
i
nd is
spec
trum es
timation method bas
ed
on spec
trum func
t
i
ons
s
u
c
h
as
MUSIC, ESPRIT
and so on. This metho
d
could get the
highe
r freq
ue
ncy re
solutio
n
but it has the fake am
pli
t
ude
informatio
n a
nd it is al
so
sen
s
itive to n
o
ise. Th
e se
con
d
kin
d
is
spe
c
tru
m
e
s
timation meth
od
based o
n
DFT data
extrapol
ation. T
h
is m
e
thod
com
p
lie
s with
some prin
ciple
s
which
extrapolate
s
new data
ba
sed
on
t
he
e
x
istent data.
Then
all th
e
data a
r
e
u
s
e
d
to a
c
com
p
l
i
sh
spe
c
tru
m
esti
mation ba
se
d on DF
T m
e
thod which will equival
e
n
t
ly increa
se
data length
a
nd
improve
s
spe
c
trum
re
soluti
on. The seco
nd metho
d
ha
s attra
c
ted m
o
re attentio
ns beca
u
se it has
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 933
– 941
934
high resolutio
n
, small
calculation works and the hi
g
h
e
r po
ssibility of reali
z
ation.
So the se
co
nd
method
is a
dopted
in thi
s
p
ape
r to
rese
arch
the
2-D ima
g
ing
algo
rithm fo
r bi
static ISA
R
according to
spa
c
e targets.
2. Echo modeling of spac
e targe
t
in bista
t
ic ISAR s
y
stem
The imagi
ng
geomet
ry rel
a
tionship of moving targ
et in bistatic IS
AR system i
s
sho
w
ed
in Figure 1.
()
m
t
Figure 1. Geo
m
etry relation
ship of bi
static ISAR
In Figure 1,
L
is the ba
selin
e of bistatic radar; T i
s
tra
n
smitting
station; R is rece
iving
station; y axis is the
bisect
or of
ta
rget
when
startin
g
the ob
se
rvat
io
n and
is th
e
ran
ge di
re
ction
of bistatic ra
dar al
so;
0
is bistatic an
gle
;
ci
is the bistatic angle of scatter
i
c
in target, and
0
ci
is thought to
be co
rre
ct
；
do
t
O
is the cent
er of pha
se;
ci
is the angl
e b
e
twee
n po
sition
vec
t
or
i
Oc
of scatter an
d the
negative
direction
of y a
x
is;
V
is
the target veloc
i
ty;
m
t
is
the
rotation an
gl
e of bisecto
r
durin
g imagin
g
pro
c
e
ss.
If we ma
ke the
assumption
that the bistatic
rada
r is id
ea
lly synch
r
o a
nd LFM
sign
al is tran
smit
ted with the
echo
whi
c
h
is sam
p
led
in
interme
d
iate freque
ncy an
d desample it
to baseba
nd
frequen
cy, the echo of scatter
i
c
can b
e
denote
d
thro
ugh (1
) a
s
follows.
2
0
ˆ
()
ˆ
,
()
()
ˆ
ex
p
2
ex
p
ci
m
rc
i
m
c
i
p
ci
m
c
i
m
tR
t
c
s
t
t
r
ect
T
Rt
Rt
jf
j
t
cc
(1)
Whe
r
e
ˆ
t
is the time-in-p
u
lse
;
m
t
is the pul
se tran
smitting
time;
0
f
is ca
rrier freq
uen
cy;
is freq
uen
cy slop
e;
p
T
is pul
se
width;
ci
is t
he non
-b
ack
scattering i
n
tensity of scat
ter
i
c
in
the
th
i
range bi
n
.
In the pap
er [
6
], it gets the
resea
r
ch re
sult t
hat wheth
e
r the ta
rget
moving tra
c
k
is in the
same
pl
ane
with b
a
seline
of bistati
c
rad
a
r, the
range
transfo
rmatio
n of
scatter can b
e
exp
r
e
s
sed
as
follows
(2).
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Two Dim
e
nsi
onal Im
aging Algorithm
Based on
Linear Prognosi
s for
Space .... (Xueping Lu)
935
()
()
()
()
()
2
c
o
s
[
(
)
]
c
o
s
[
]
2
ci
m
r
ef
m
r
o
t
i
m
m
re
f
m
i
c
i
m
Rt
R
t
R
t
t
Rt
r
t
(2)
Whe
r
e
0,
1
,
2,
m
tm
T
m
is
slow-tim
e;
()
m
t
is target time
-varying bi
sta
t
ic angl
e
durin
g the
i
m
aging
p
r
o
c
ess;
()
ref
m
R
t
is the
rang
e
cou
r
se
betw
een
target ph
ase
center
and
transmitting-receivin
g stati
on, whi
c
h i
s
the
tran
slatio
n
a
l movement
item of target
;
()
ro
t
i
m
Rt
is the
rotational
ran
ge item
of
scatter
i
c
. It can
be fou
nd f
r
o
m
type
(2) th
at in bi
static I
SAR ima
g
ing
,
the ra
nge t
r
a
n
sformation
can
still b
e
d
i
vided into t
w
o pa
rts, i.e, tran
slation
a
l
movement it
em
()
re
f
m
R
t
and
rotation
al movem
ent
item
()
roti
m
R
t
. So through
bi
static
ISAR syste
m
also
can
get
the
target im
age
throu
gh
ran
ge
comp
re
ssion, ra
nge
al
ignment, initi
a
l pha
se
correctio
n
, a
z
im
uth
comp
re
ssion
just as m
ono
static ISAR
system re
sea
r
che
d
in the p
aper [6].
Whe
n
the
rotational
angl
e
is
small
which is eq
ual
to i
n
tegratio
n of
sho
r
t time, th
e bi
static
angle
()
m
t
can b
e
thoug
ht a
s
the con
s
tan
t
approxim
ately. It is assumed th
at the co
nsta
nt
bistatic
ang
el
is tho
ught t
o
be
0
. If the tran
slation
a
l ran
ge item
()
ref
m
R
t
has bee
n t
o
tally
comp
en
sated
,
the range transfo
rmatio
n item of scatte
r
i
c
can b
e
sim
p
lified as type
(3)
0
()
2
c
o
s
[
(
)
]
c
o
s
[
]
2
ci
m
i
ci
m
Rt
r
t
(3)
At this time, target range
resolution
of
and a
z
imuth
resolution
ca
n be exp
r
e
s
sed a
s
types (4
), (5
) respe
c
tively, the expre
s
sio
n
s a
r
e a
c
cordan
ce with th
e re
sea
r
ch work i
n
the pa
per
[14].
0
2c
o
s
2
r
w
c
B
(4)
0
2c
o
s
2
a
ro
t
(
5
)
In the eq
uatio
ns m
ention
e
d
above,
w
B
is th
e tran
smitting
sign
al b
and
width;
ro
t
is
the
rotational
an
g
l
e of bi
se
ctor
durin
g ima
g
in
g process.
F
r
om types (4
)
and
(5), it
ca
n be fo
und
that
whe
n
the tra
n
smitting
sig
nal ban
dwi
d
th is fixed,
the target rang
e re
solution i
n
small rotation
angle
imagi
n
g
conditio
n
i
s
the
con
s
ta
nt. But the a
z
imuth
re
sol
u
tion is totally determind
ed
by
rotational
an
g
l
e
ro
t
. Wh
en
the i
m
aging
rotational
angl
e
ro
t
is sm
all, the
azi
m
uth resoluti
on
i
s
also
sm
all a
s
well,
whi
c
h
could n
o
t satisfy with
the d
e
m
and
s of im
a
g
ing
system.
So the ima
g
i
n
g
algorith
m
in small rotation
a
l
angle conditi
on sh
ould to
be re
sea
r
che
d
and imp
r
ov
ed.
3. Anal
y
s
is o
f
Bistatic ISAR resolution
As tran
smitti
ng statio
n an
d re
ceiving
st
ation
a
r
e
sep
a
rated
from
each othe
r in
bistati
c
ISAR system
, thus the
im
aging
re
sol
u
tion is relat
ed
with bi
static
angle. If the i
m
aging
bi
stati
c
angle i
s
, then the target range resoluti
on can be ex
pressed as following type (6) [14],[15].
_0
2c
o
s
2
rc
w
c
B
(6)
Whe
r
e
_0
rc
is the
target rang
e resol
u
tion;
w
B
is the tran
smitting si
gnal b
a
n
d
width;
is
the imaging b
i
static an
gle;
c
is the tran
smi
tting spee
d of electro
m
ag
n
e
tic wave in free sp
ace.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 12, No. 4, Dece
mb
er 201
4: 933
– 941
936
It can b
e
fou
nd fro
m
type
(6) that a
s
th
ere
ex
ists bi
static ang
el, th
e bistati
c
ISRA rang
e
resolution i
s
lowe
r than
the mo
nostati
c ISAR rang
e re
solutio
n
2
w
cB
with the
sa
me si
gna
l
band
width. F
o
r the conve
n
ien
c
e of co
mpari
s
o
n
,
bistatic ISRA
system i
s
thought to be
an
equivalent m
ono
static ISAR syste
m
in the bi
secto
r
. If the transmit
t
ing ca
rrie
r
freque
ncy is
0
f
,
sign
al ban
dwi
d
th is
w
B
, bistati
c
angl
e is
, th
en the equiva
lent ca
rrie
r
freque
ncy of m
ono
static
rada
r is
00
co
s
2
ff
an
d the equiva
lent sign
al b
and
width is
cos
2
w
BB
. So the
resolution al
so coul
d be ex
pre
s
sed a
s
type (6
) re
porte
d in the pape
r [15]. This e
quivalent mo
del
can expl
ain why the ran
g
e
resolution i
s
de
cre
a
s
ed
with bistati
c
angel, so this model ha
s b
een
widely u
s
ed d
u
ring the exi
s
tent bistatic ISAR
re
sea
r
ch work of the
papers [13]-[
15].
The fre
que
ncy of echo
co
uld not b
e
ch
ange
d except
Dop
p
ler effe
cts of ta
rget.
And the
target scatte
ring e
c
ho freq
uen
cy and it
s band
widt
h
could n
o
t be chang
ed a
s
th
e existen
c
e
of
bistatic an
gle
.
So,
there must be som
e
cau
s
e
s
t
hat make the bi
static ran
ge re
solutio
n
different
from that of mono
static I
SAR system.
In the Fi
gure.1, it is sho
w
n that
the
wave di
stan
ce is
different from s
c
a
tter
1
c
and
2
c
in different ra
nge area
s.
2
c
1
c
Figure 2. Wa
ve distan
ce di
fference
In the Figu
re
2, the broken
line is
the
ra
nge-sa
me lin
e of bi
static radar.
10
tc
R
,
10
rc
R
denot
e
the
dista
n
ce betwe
en scatter
1
c
and tran
smitting, re
ceiving statio
n
s
, re
sp
ectivel
y
.
20
tc
R
,
20
rc
R
rep
r
e
s
ent the
distan
ce bet
wee
n
scatter
2
c
and tran
smitting, receiving
station, resp
ectively.
is
bistatic angl
e;
T
、
R
are
tran
smitting and
re
ceiving
statio
n re
sp
ectively
;
r
is the
radi
al
distan
ce
betwe
en scat
ter
1
c
and
2
c
. When the targ
et is far from
rada
r, the a
s
sumption of
far field is
satisfie
d. So
the
wave-f
rontier i
s
th
o
ught
to be p
l
ane-wave. T
he wave dist
ances
bet
we
e
n
transmitting, receivin
g
stations an
d
scatter a
r
e
pa
ralle
l. Und
e
r thi
s
assumptio
n
, the roun
d
wav
e
distan
ce diffe
ren
c
e
wp
R
betwe
en scatter
1
c
and scatter
2
c
can
be expre
s
se
d as bel
ow.
2c
o
s
2
wp
Rr
(7)
In the dem
o
n
stratio
n
of
scatter
wave
distan
ce
differen
c
e in th
e
Figure 1, no
matter
whe
r
e the
scatter is, the
main lob
e
width of e
c
ho a
fter
pul
se co
mpre
ssion
i
s
con
s
tant
b
e
cause
the echo
sig
nal width is consta
nt, if it onl
y
judges from the
echo chara
c
teri
stics ind
e
x.
Otherwise, th
e e
s
sen
c
e of
rad
a
r
ra
nge
resolving
ab
ili
ty is the e
c
h
o
time-d
elay resolvin
g. Wh
en
the matchi
ng
filter based o
n
FFT is u
s
e
d
to acco
mpli
sh rang
e prof
ile com
p
re
ssi
on, wheth
e
r t
he
rada
r i
s
mon
o
static o
r
bi
st
atic, if the
e
c
hoe
s of
t
w
o
scatters
are
n
eede
d to
be
disting
u
ished,
and
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Two Dim
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nsi
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Based on
Linear Prognosi
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Space .... (Xueping Lu)
937
the time-dela
y
of
the two scatters ech
o
after pul
se compressio
n is 3dB width
at least. And the
roun
d wave d
i
stan
ce difference
d
coul
d b
e
denote
d
as
belo
w
type (8
).
w
c
d
B
(8)
The rang
e re
solving
ability is the
width
of t
he sm
alle
st re
solving
range i
n
the t
a
rget
s.
The bi
static range
-bin
widt
h is dete
r
min
ded by
the di
stan
ce bet
we
en the two i
n
terse
c
tion
dot
s,
whi
c
h a
r
e th
e dots of bi
static bi
se
ctor
intersec
te
d b
y
the two ra
ng-sam
e
line
s
with
the
sa
me
focus whi
c
h i
s
also verfied by the paper [16],[17
]. Th
e distance between t
he two dots is al
so the
distan
ce
bet
wee
n
the
two ra
nge
-sam
e line
s
. So,
wh
en th
e t
a
rget
ro
und
wave
di
sta
n
ce
differen
c
e i
n
the type (7) is the
same
a
s
sho
w
e
d
in t
y
pe (8
),
scatter
1
c
and
scatt
e
r
2
c
c
a
n
be
sep
a
rate
d in
rang
e axi
s
by
the squa
re.
And no
w,
the
distan
ce
differen
c
e
of
the two
s
c
atters
in
rang
e axis i
s
_0
rc
, which i
s
expre
s
sed i
n
the type (6).
The
re
so
lution is l
o
wer than
th
e
mono
static ISAR system
wi
th the same
signal ba
ndwi
d
th as
2
rw
cB
4. Imaging algorithm bas
e
d on lev
i
ons prognosis
4.1 Imaging flo
w
o
f
2-D image
The m
a
in eff
e
ct fa
ctor
of 2
-
D i
m
agin
g
in
small
rotatio
nal a
ngle i
s
t
he a
z
imuth
re
solutio
n
.
So in the following research, it is assumed
that o
ne-di
men
s
ion
a
l rang
e profile is obtaine
d
throug
h digit
a
l matching fi
lter pul
se
co
mpre
ssion
an
d the tra
n
sl
ational
comp
en
sation
ha
s be
en
ac
compli
sh
ed
.
The ISAR imaging p
r
oble
m
can be reg
a
rde
d
as spe
c
trum e
s
timat
i
on pro
b
lem j
u
st sam
e
as the pa
per [11]. The basic
step of lin
ear p
r
og
no
sis
is
firs
tly to es
timate the
filter c
oeffic
i
ents
and then extrapolate the d
a
ta to
the ne
eded extent.
The progn
osi
s
co
efficient
s are e
s
timate
d
based on th
e least mea
n
squa
re e
rro
r rule, whi
c
h
can e
n
sure t
he differen
c
e
value betwe
en
actual e
c
h
o
and the extra
polated d
a
ta
is the le
a
s
t. In ord
e
r to im
prove the a
z
i
m
uth sp
ect
r
u
m
estimation
re
solutio
n
, the range
echo i
s
estimated
to accord with
the
line
a
r pro
g
nosi
s
m
odel and
the azimuth d
a
ta integratio
n time is extended
, so the
azimuth
re
sol
u
tion is adva
n
ce
d.
If
some ra
ng
e
align
ed ra
nge echo co
uld
b
e
exp
r
e
s
sed as
1
()
,
,
(
)
nm
n
xt
xt
, s
o
the
extrapolate
d
ech
o
at time
n
t
of this rang
e coul
d be expressed a
s
1
()
(
)
ˆ
m
nm
n
i
i
x
ta
i
x
t
(9)
In the equati
on (9
),
()
m
ai
is the ith coefficient of the
m-orde
r filter. With the same
analysi
s
, the
ech
o
at time
1
nm
t
after
extrap
olated
of this ra
n
ge
echo
coul
d b
e
exp
r
esse
d by
(10
)
.
*
1
1
()
(
)
ˆ
m
nm
m
n
m
i
i
xt
a
i
x
t
(10)
In the equatio
n(10
),
*
()
m
ai
is the conj
ugate
co
mplex of
()
m
ai
.
If the former-l
atter pro
gno
sis is prosecuted by
p
times, then the ech
o
after pro
g
n
o
si
s
coul
d be exp
r
esse
d as
11
(
)
,,
(
)
,,
(
)
,
,
(
)
nm
p
n
m
n
n
p
xt
xt
x
t
x
t
. If the pulse re
peat cycle i
s
T
, then
the azimuth
resol
u
tion coul
d be improve
d
from
1
mT
to
1(
2
)
Tm
p
.
Combi
ned wi
th rang pul
se
compressio
n
,
2-D imagin
g
algorithm fl
ow ba
sed o
n
linear
prog
no
sis
wh
en the rotatio
nal ang
el is small whi
c
h is
demon
strated
as in the Fig
u
re 3.
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938
Figure 3. 2D i
m
aging al
gori
t
hm flow
4.2 Cons
tru
c
tion of prog
nosis filter c
o
efficients a
nd its order
The la
rg
er t
h
e line
a
r
prog
nosi
s
filter is,
the m
o
re
a
c
curate th
e p
r
ogno
si
s resul
t
is. But
the calculatio
n am
ount i
s
i
n
crea
sed
rap
i
dly also
, so the
bal
an
ce
betwe
en cal
c
ulation wo
rk of
algorith
m
a
n
d
p
r
og
no
sis
error is de
stroied. In
the
pape
r [1
7], it
sho
w
s that
wh
en
the A
u
to
Reg
r
e
ssive
(AR)
mod
e
l i
s
used to
extrapolate
dat
a,
the
m
o
st accurate pro
g
n
o
si
s re
sults
could
be o
b
tained
whe
n
the filte
r
o
r
de
r i
s
cho
s
en
to be
1/3
of the d
a
ta l
ength. Th
e L
e
vinso
n
p
r
og
nosi
s
of Burg
entro
py is u
s
ed
to
estimate th
e
filter or
der a
nd
its co
effici
ents.
Th
e
filter coeffici
ent
s
of
different filter orde
r a
r
e e
s
timated firstly
,
then
the progno
si
s erro
r powe
r
wi
th
different filter is
comp
ared an
d it chooses
the filter with
the smalle
st prog
no
sis e
r
ror po
we
r.
The
ba
sic st
eps to
get t
he p
r
o
gno
sis order
an
d it
s
coeffici
ents are
summ
arized
a
s
follows
.
Step1
：
Initial the prog
no
sis powe
r
erro
r and
its ba
ck-and-fo
rth pro
gno
sis e
r
ror;
Step2
：
Co
unt
the reflection
coefficie
n
t
m
K
that is used to
extrapolate d
a
ta;
Step3
：
Co
unt
the back-a
n
d
-
forth p
r
ogn
o
s
is filter
coeffi
cient
s via (11
)
;
*
11
()
()
(
)
,
1
,
,
1
()
mm
m
m
mm
ai
a
i
K
a
m
i
i
m
am
K
(11)
Step4
：
Co
unt
the progn
osi
s
error
power of
the filter with m-ord
e
r vi
a (12
)
2
1
(1
)
mm
m
PK
P
(12)
Step5
：
Co
unt
the
output
o
f
the filter wit
h
m
-ord
er,
re
p
eat Step2
to
Step5 u
n
til th
e p
r
og
no
sis
error power
m
P
hardly b
e
com
e
sm
aller. An
d the o
r
de
r a
nd coefficie
n
ts of p
r
og
no
si
s filter a
r
e g
o
t
at the s
a
me time.
4.3 Data e
x
trapolation le
ngth
The data extrapolatio
n len
g
th is also d
e
termin
ded b
y
progno
si
s
error , and th
e longe
r
the data
extrapolatio
n le
n
g
th is the
la
rge
r
the
p
r
o
gno
sis e
rro
r
will b
e
. So f
a
r, the
r
e
is
no
quantitative choo
se
stand
a
r
d
con
c
e
r
ne
d
on thi
s
p
r
obl
em. Wh
at co
uld be
de
cid
e
d
up i
s
th
at the
length of dat
a extrapolatio
n is relate
d with SNR
( si
g
nal-n
oise-rate
)
, and the hig
her the SNR
is
the lon
g
e
r
th
e data
extra
p
o
lation l
ength
will
be.
Othe
rwi
s
e
the
sh
o
r
ter
data
extrapolatio
n le
n
g
th
has to be
ch
ose
n
. In this pape
r, spa
c
e
target is cho
s
en a
s
the re
sea
r
ch obje
c
t
and the SNR of
spa
c
e ta
rget i
s
rel
a
tively low compa
r
ed t
o
re
sea
r
ch result of pa
pe
r [17] , it adopts the 1/2 le
ng
th
of ori
g
inal
dat
a len
g
th
as th
e data
extra
p
o
lation l
ength
thus it
can
i
m
prove
the
a
z
imuth
re
sol
u
tion
by two times
.
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TELKOM
NIKA
ISSN:
1693-6
930
Two Dim
e
nsi
onal Im
aging Algorithm
Based on
Linear Prognosi
s for
Space .... (Xueping Lu)
939
5. Simulation experimen
t
Simulation si
tuation and
scatter mod
e
l
are expre
s
sed in Figu
re 4 and Fig
u
re 5,
r
e
spec
tively.
Figure 4. Target moving si
mulation sce
n
e
Figure 5. Target scatter m
odel
In the Fi
gure
4,
circle
sta
nds for the t
r
ans
mitting
station a
nd
rh
o
m
boid
sta
nds for th
e
receiving sta
t
ion. Target
orbit heig
h
t is abo
ut
260
Km; target round radial
velocity is a
bout
3.5Km/s; In
the sim
u
latio
n
, it’s a
s
su
med that
t
r
a
n
slatio
nal
co
mpen
sation
has be
en to
tally
compl
e
ted. T
he targ
et orb
i
t data is
sim
u
lated
throug
h orbit
software.
When th
e orbit d
a
ta i
s
gene
rated, th
e orbit with consta
nt bistat
ic angle
i
s
ch
ose
n
to com
p
lete simul
a
tion and to avoid
the image bl
urri
ng cau
s
e
d
by the cha
nge of bistat
i
c
angl
e. The
target is ex
pre
s
sed by ideal
scatters and
the target mo
del in ran
g
e
-
azimuth
i
s
a
s
sho
w
n in Fig
u
re5. Th
e echo SNR
can
be
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93-6
930
TELKOM
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Vol. 12, No. 4, Dece
mb
er 201
4: 933
– 941
940
obtined
thro
u
gh
rada
r
equ
ation. In th
e
simulatio
n
, th
e smalle
st re
ceiving
SNR i
s
set to
be
1
4dB
and the
targ
e
t
RCS i
s
set
as 4
m
2
. Beca
use t
he
scatters a
r
e
sep
a
rate, res
p
ec
tively, s
o
the RCS
of every con
c
rete
scatter is 0.5m
2
. Simulation pa
ram
e
ters
of the ra
dar
system
are sh
own in th
e
Table 1.
Table 1. Simulation ra
da
r para
m
eters
paramete
r
index
paramete
r
index
Bistatic angel
120
Imaging
angel
2
Signal w
i
dth
950MHz
Pulse w
i
dth
60
s
Carri
er
frequenc
y
8GHz
Baseline
length
200Km
Acco
rdi
ng to the paramete
r
s in Table 1, t
he ran
ge re
solution and a
z
imuth resol
u
tion can
be exp
r
e
s
se
d a
s
0.3
3
r
and
0.85
96
a
r
e
sp
ectiv
e
ly
, throu
gh ty
pe
(4),
(5
). Sim
u
lation
results a
r
e sh
own in Fig
u
re
6 and Figu
re
7.
Figure 6. 2-D
image befo
r
e
azimuth d
a
ta extrapolatio
n
Figure.7 2-D image after a
z
imuth data extrapolatio
n
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TELKOM
NIKA
ISSN:
1693-6
930
Two Dim
e
nsi
onal Im
aging Algorithm
Based on
Linear Prognosi
s for
Space .... (Xueping Lu)
941
From the Fi
gure
6 we
can find that, bef
ore the
azimuth
data
extrapolatio
n ran
g
e
resolution is
s
m
aller than
the interval of s
c
atte
rs so
the scatters
coul
d be
tota
lly differentiat
ed
from rang
e p
r
ofile. But the
azimuth
re
sol
u
tion is
not
small en
oug
h, so th
e scatte
rs
could
not
b
e
differentiated
cle
a
rly fo
rm
azimuth
di
re
ction. Figu
re
6
is th
e
2-D i
m
age
after
d
a
ta extra
pola
t
ion
and be
ca
use
the azimuth
dopple
r
re
solution is im
proved, so the scatters
coul
d be totally
differentiated from
azi
m
uth dire
ction,
an
d the corre
c
t 2-D image i
s
ob
tained.
6. Conclusio
n
ISAR imagin
g
co
uld
be
seen a
s
high
-resol
ution
spe
c
trum
estim
a
tion p
r
oble
m
after the
movement co
mpen
sation i
s
com
p
leted. The sp
ace
target bistati
c
2
-
D imagi
ng problem in sm
a
ll
rotation an
gl
e is re
sea
r
ched in the p
aper. Simu
la
tion results
prove that this algo
rithm
can
improve resol
u
tion in azim
uth dire
ction
and ca
n be u
s
ed in p
r
a
c
tical environm
e
n
t.The re
sea
r
ch
on ho
w the al
gorithm
can b
e
use
d
in lower SNR is al
so perfo
rmed.
Referen
ces
[1] Marco
Martor
ella
，，
，
，
James
Palmer
John Homer
B
rad Littlet
on
I. Dennis Longstaff. On Bistatic
Inverse S
y
nth
e
t
ic Aperture Ra
dar.
IEEE Transactions on AE
S.
2007; 3: 112
5-11
34.
[2] Delis
le
GY.
，
H
a
iqi
n
g
W
u
. Movin
g
targ
et i
m
agi
ng
and
trajector
y
c
o
mp
utation
usi
ng
ISAR. I
EEE
Transactions on AES.
1994; 3
0
(3): 887-8
99.
[3] Chen
VC.
，
Shie Qian. Joi
n
t time-freque
n
c
y
transform
for radar ran
ge-D
opp
ler im
agi
ng.
IEEE
Transactions on AES.
1998; 3
4
(2): 486-
49
9.
[4]
Liu
Xi
n, Ch
in
a, Ren Y
ongf
eng, C
hu C
h
eng
qu
n.
Appl
i
c
ation
of Self
ada
ptin
g Ra
d
a
r Vid
eo Ech
o
Acquis
i
tion
S
ystem base
d
on LZ
W
Al
go
rithm.
T
E
LKOMNIKA Indo
n
e
sia
n
Jo
urna
l
of Electric
al
Engi
neer
in
g.
2014; 12(
2): 133
3-13
42.
[5]
Xu
e-tao Y
u
,
Xi
ao-
pin
g
R
u
i,
F
eng L
i
. Lo
calizat
i
on M
e
thods
of W
e
ig
hted
C
entro
id
of dBZ
o
n
W
eatherR
adar
Echo
Maps
in V
e
ctor F
o
rmat.
T
E
LK
OMNIKA Indo
nesi
an J
our
na
l of El
ectrica
l
Engi
neer
in
g.
2013; 11(
2): 103
3-10
40.
[6]
Jingfa
ng W
a
n
g
. Multitarget
Directio
n
Measur
ement o
n
Bistatic MIMO Radar.
TE
L
K
OM
N
I
KA
Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
ng.
2014; 1
2
(9): 6
819-
682
6.
[7] Z
hang
Ya-
b
i
a
o
，
Z
hu Z
hen-bo
，
T
ang Z
i
-
y
u
e
，
et al. Bistatic inverse S
y
nth
e
tic Aperture
Rad
a
r Imag
e
Formation.
Jou
r
nal of Electro
n
i
cs & Informati
on T
e
chn
o
l
o
g
y. 2006; 28(
6): 969-9
72.
[8]
Z
hu Yu-Pen
g, Z
hang Yu
e-H
u
i, W
ang Hon
g
-
Q
iang, et
al.
Mode
lin
g an
d Simulati
on of
Bistatic ISAR
Imagin
g
for Moving T
a
rget.
Journa
l of System Si
mu
lati
on
. 200
9; 9: 2696-
269
9,27
04.
[9]
Don
g
Ji
an, Sh
ang
Ch
ao-
Xua
n
, Gao M
e
i-Gu
o, et a
l
. R
e
se
arch
on
Bi
sta
t
i
c
ISAR Speed
Compensation
of Space T
a
rget.
Journal of
Chin
a Acad
e
m
y of Electronic
s
and Infor
m
ati
on T
e
chn
o
l
ogy
.
2010; 1: 78-
85.
[10]
Don
g
Jia
n
. Stu
d
y
on k
e
y tech
nol
ogi
es of sp
ace ta
rg
et bist
atic ISAR ima
g
i
ng. Sh
iji
azh
u
a
ng: Ordna
nce
Engi
neer
in
g C
o
lle
ge D
i
sserta
t
ion
. 200
9.
[11]
Lia
ng
Hu
a-Qia
ng, H
e
M
i
ng-Y
i
, Z
han
g
Lin-
Xi
.
Super-r
esol
ut
ion
ISAR
imag
ing
bas
ed
o
n
beam-s
pac
e
MUSIC].
Applic
ation R
e
se
arch
of Computers.
2007; 2
4
(12):
361-
363.
[12]
He Son
g
-Hu
a
, Chen
g F
an-Y
ong, Ch
en W
e
i-Bin
g
,
et al. Band-l
i
mited
Sign
al Sp
ectru
m
Estimatio
n
Based
o
n
D
a
ta E
x
tropo
lati
o
n
a
nd M
a
xim
u
m L
i
kel
i
ho
od
Criteri
on.
J
o
urna
l of
Hu
na
n U
n
ivers
i
ty
(Naturn
a
l Scie
nce).
200
9; 36(
3): 85-88.
[13]
Luo Ji
ng-
ya
ng.
Applic
atio
n of
spectrum estim
a
tion i
n
hi
gh-re
soluti
on ra
dar i
m
agi
ng. Ch
ang
sha:
Hun
a
n
Univers
i
ty Diss
e
ratio
n
.
200
7.
[14]
Victor C. C
h
e
n
,
Andr
e des Rosiers,
Lipps Ron.
Bi-static
ISAR ra
nge-
do
p
p
ler
i
m
a
g
in
g
a
nd r
e
sol
u
tio
n
analysis.
IEEE Radar Confer
ence. 2009: 1-5.
[15] Z
hao
W
e
i-Li
，
Z
hang Qun
，
Z
hu Xia
o
-pe
ng. Stud
y
of Bistatic
ISAR Motion Correctio
n Algorit
hm.
Fire
Contro
l & Co
mma
nd C
ontrol.
201
2; 37(6): 10
0-10
2.
[16] Yang
Z
h
en-Qi
，
Z
hang Yon
g
-
S
hun, L
uo Yo
ng-Ju
n.
Bistati
c
radar i
m
a
g
i
n
g system
. Be
ij
ing: Defe
nse
ind
u
st
y
pr
ess. 199
8.
[17]
Li Bi
ng, C
i
L
i
n-
Lin, W
a
n
Jia
n
-
W
ei, et al. C
o
m
pariso
n
of ISAR Res
o
luti
on
Improveme
n
t Based
on
T
w
o
Cross Spectra
Extra
pol
atio
ns.
Radar Sci
enc
e and T
e
ch
no
l
ogy.
200
6; 4(6)
: 358-36
2, 381.
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