Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 2, No. 2,
May 2016, pp
. 344 ~ 350
DOI: 10.115
9
1
/ijeecs.v2.i2.pp34
4-3
5
0
344
Re
cei
v
ed
Jan
uary 2, 2016;
Re
vised Ma
rc
h 3, 2016; Accepte
d
March
19, 2016
Improved UFIR Trackin
g
Algorithm for Maneuvering
Target
Shoulin Yin*, Jinfeng Wa
ng, Tianhua
Liu
Soft
w
a
re Co
lle
ge She
n
y
a
ng
Normal U
n
iv
ersit
y
, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 3527
20
214
@
qq.com
A
b
st
r
a
ct
Mane
uveri
ng t
a
rget trackin
g
is a target
moti
on esti
mation pr
ob
le
m, w
h
ich can d
e
scribe th
e
irregu
lar targ
e
t
mane
uver
ing
motio
n
. It h
a
s bee
n w
i
de
ly used in th
e field of mi
li
tary and civil
i
a
n
app
licati
ons. In
the man
euv
ering tar
get trac
king, the
perfo
rma
n
ce
of Ka
l
m
a
n
filter (KF
)
and
its i
m
pro
v
e
d
alg
o
rith
ms
de
p
end
o
n
th
e acc
u
racy
of pr
oce
ss no
ise
st
atisti
cal prop
erties. If
there exists d
e
viati
on betw
e
en
process n
o
ise
mod
e
l a
nd t
he actua
l
pro
c
ess, it
w
ill gener
ate the p
hen
o
m
en
on of
estimati
on er
ro
r
incre
a
sin
g
. Un
bias
ed finit
e
i
m
p
u
ls
e respo
n
se (UF
I
R) filter does n
o
t nee
d pri
o
ri
kn
ow
ledg
e of n
o
is
e
statistical pro
p
e
rties in th
e fil
t
ering pr
ocess.
T
he exis
tin
g
UF
IR filters ha
ve t
he pro
b
le
m that g
ener
al
i
z
e
d
nois
e
pow
er
g
a
in(GNPG) d
o
e
s not ch
an
ge
w
i
th me
as
ure
m
e
n
t of in
nov
ation. W
e
pr
o
pose
an i
m
pro
v
ed
UF
IR filter b
a
s
ed
on
meas
ure
m
e
n
t of
inn
o
va
tion w
i
th
r
a
tio
d
y
na
mic
ad
aptiv
e adj
ustment
a
t
adj
acent ti
me.
It
perfects the mane
uveri
ng d
e
tect-abi
lit
y. T
he simu
lati
on res
u
lts show
that
the improv
ed
UF
IR filter has th
e
best filterin
g effect than KF
w
h
en proc
ess no
i
s
e is not accur
a
te.
Ke
y
w
ords
:
Ma
neuv
erin
g targ
et tracking, UF
IR, KF
,
GNPE,
Adaptiv
e ad
jus
t
ment
Copy
right
©
2016 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
Maneuve
r
ing
target t
r
ackin
g
[1] i
s
ve
ry d
i
fficult
y
in the ra
dar target t
r
ackin
g
pro
c
e
ss.
KF
is widely use
d
in
th
e state estimation
wh
ich uses
process n
o
ise of
state
e
quatio
n to a
dapt ta
rget
maneuve
r
ing.
In fact, target mane
uvering
stat
e i
s
un
kno
w
n
whi
c
h results in difficult
y of
determi
ning p
r
ocess noi
se
of state
equat
ion. Finally, it has an effe
ct
on the accu
racy of filterin
g
.
For thi
s
qu
est
i
on, many researche
r
s hav
e rep
r
e
s
e
n
te
d som
e
imp
r
o
v
ed schem
es. Wu C, et al [
2
]
prop
osed current
stati
s
tic maneuve
r
ing
target
tra
cki
ng strong tra
cki
ng filter. T
he ne
w sch
e
m
e
kept th
e m
e
ri
ts of
high
tra
cki
ng
preci
s
i
on that
the current statisti
cal mod
e
l
a
n
d
st
ron
g
tracking
filter (STF
)
h
ad in
tra
c
kin
g
ma
neuve
r
i
ng ta
rget. Li
u
Y,
et al [3]
pre
s
ente
d
a trackin
g
algo
ri
th
m
based o
n
spline fitting.The
assumptio
n
wa
s that
pre
d
iction
wa
s
without dynami
c
motion
mo
del
and it
wa
s o
n
ly based o
n
the curve fitting ove
r
t
he
measured d
a
t
a. Fan E, et al [4] sh
owe
d
a
f
u
zzy
l
ogi
c-
b
a
se
d
re
cur
s
i
v
e lea
s
t
squ
a
re
s f
ilt
er
in
situatio
ns o
f
observatio
n
s
with
un
kno
w
n
rand
om characteri
stics. It use
d
fuzzy logic in t
he sta
ndard re
cu
rsi
v
e least sq
ua
res filter by t
h
e
desi
gn of a
set of fuzzy if-t
hen rule
s. Shmaliy [5]
prop
ose
d
UFI
R
filter whi
c
h
co
u
l
d igno
re n
o
ise
statistical characteri
stics in the
filtering proce
s
s ba
sed
on optimal fin
i
te impulse re
spo
n
se (OFI
R)
filter and
em
bedd
ed u
nbi
ase
d
OFI
R
fi
lter. In orde
r to obtain
th
e be
st filter
perfo
rman
ce,
the
wind
ow len
g
th of
UFIR filter m
u
st
be
o
p
timal.
The
windo
w le
ngth
need
not
to a
s
sume
like K
F
[6-
7]
by
pri
o
ri knowl
edge.
It can
be obtai
ned by
me
a
s
ureme
n
t cal
c
ulatio
n. UFI
R
filter
ca
n
be
expre
s
sed
a
s
an
iterative f
o
rm
whi
c
h
re
duces the
calculatio
n. However, the
existing UFIR filte
r
’s
informatio
n g
a
in
only ch
a
nge
s with
space equ
at
io
n. We p
r
op
o
s
e a
n
impro
v
ed UFIR fil
t
e
r
algorith
m
. It
use
s
the dev
iation betwe
e
n
measure
m
ent results a
nd filtering result
s to amend
information gain dynami
c
ally. Im
proved UFIR filter has the a
daptive ability for maneuveri
ng
target tra
cki
n
g
. We apply i
t
into the tracking p
r
o
c
e
ss.
Simulation result
s sh
ow t
hat the impro
v
e
d
UFIR filter ha
s the be
st performan
ce.
2. Linear Sy
stem Model
Nonli
nea
r system ca
n
m
a
ke
line
a
ri
za
tion
a
s
th
e
pro
c
e
s
s of
e
x
tended K
a
l
m
an filter
(EKF) [9]. T
h
e adva
n
tage
of UFI
R
filter
can
not
be
aff
e
cted. S
o
we
only con
s
ide
r
a li
nea
r
syst
e
m
model. Di
scre
te time-varyin
g
linear
syste
m
model can
be expre
s
sed
as :
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 2, May 2016 : 344 –
350
345
State equatio
n :
n
n
n
n
n
w
B
x
F
x
1
(1)
Observation equatio
n
:
n
n
n
n
v
x
H
z
(2)
Whe
r
e
N
n
R
x
and
M
n
R
z
is state vector a
nd
observation
vector at
n
tim
e
r
e
spec
tively.
M
N
n
R
F
,
P
N
n
R
B
and
N
M
n
R
H
is st
ate-tra
n
sitio
n
matrix, pro
c
ess noi
se
gain matrix a
nd mea
s
u
r
e
m
ent matrix at
n
time respectively.Assuming p
r
o
c
e
s
s noi
se vecto
r
is
P
n
R
w
at
n
time. Measurement
noise vecto
r
is
M
n
R
v
at
n
time.There is
no relationshi
p
betwe
en the two noise vectors. And
0
}
{
n
w
E
,
0
}
{
n
v
E
,
0
}
{
T
j
i
v
w
E
.
]
[
T
n
n
n
w
w
E
Q
is the
pro
c
e
ss n
o
is
e cov
a
ri
an
ce
mat
r
ix
.
]
[
T
n
n
n
v
v
E
R
is the measurement
noise
covari
ance matrix.
3. The Improv
e
d
UKI
R Filter
3.1. The Improv
ed UKIR Filter Model
Assu
ming the
windo
w le
ngt
h of UKIR filter is
N
. Wh
en
we get the m
easure
m
ent value at
n
time.
N
measu
r
em
ent values a
r
e u
s
ab
le from
m
(
m=
n
-
N+
1
) to
n
time. And
m
≥
0
.
The estim
a
te
d value
n
x
ˆ
of target state ca
n be expre
s
sed
as:
m
n
m
n
m
n
n
Z
x
,
1
,
1
0
,
ˆ
(3)
W
h
er
e
g
r
n
h
r
n
h
r
n
g
h
i
i
r
n
g
r
h
r
F
F
F
F
1
,
,
T
m
n
m
n
T
m
n
m
n
H
H
H
,
1
,
,
1
,
)
(
,
T
T
m
T
n
T
n
m
n
z
z
z
Z
]
[
1
,
.
And
m
n
m
n
m
n
F
H
H
,
,
,
,
)
(
1
,
m
n
n
m
n
H
H
H
diag
H
,
T
T
m
n
T
m
n
T
m
n
m
n
I
F
F
]
[
1
1
1
,
1
0
,
,
.
For time-i
nva
r
iant sy
stem, (3)
can b
e
si
mplified into:
m
n
N
N
n
n
Z
F
x
,
1
1
1
ˆ
(4)
Whe
r
e
T
N
N
T
N
N
H
H
H
1
1
1
1
1
1
)
(
,
T
T
m
T
n
T
n
m
n
z
z
z
Z
]
[
1
,
.
And
1
1
1
ˆ
N
N
N
F
H
H
,
)
(
ˆ
1
N
N
H
H
H
diag
H
,
T
T
T
N
N
I
F
F
F
]
)
[(
1
1
.
From the ab
o
v
e equation
s
,
we can
kno
w
that UKIR
filter deal
s wit
h
filter for sig
nal with
ignori
ng noi
se
stati
s
tical
chara
c
te
risti
c
s.
Whe
n
N>
>1
, UKIR filte
r
i
s
n
e
a
r
ly the
most
optimal.
But
dimen
s
ion
of
matrix an
d vector will
in
crease
with
N
i
n
crea
sing. It
can
re
sult i
n
the computati
on
increa
sing.
Iteration UKIR filter
solves
this
problem.Estimated formula is
:
)
ˆ
(
ˆ
ˆ
1
1
a
a
a
a
a
a
a
a
x
F
H
z
K
x
F
x
(5)
Whe
r
e
T
a
a
a
H
G
K
(6)
1
1
1
]
)
(
[
T
a
a
a
a
T
a
a
F
G
F
H
H
G
(7)
a
G
is gen
eralized
noi
se
p
o
w
er gain (G
NPG) at
a
time. Initial c
o
nditions
i
x
ˆ
and
i
G
can
be
obtaine
d by UFIR.
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IJEECS
ISSN:
2502-4
752
Im
proved
UFI
R
Tra
c
king Al
gorithm
for Maneu
ve
ring
Ta
rget
(Shouli
n
Yin)
346
m
i
m
i
m
i
i
Z
x
,
1
,
1
0
,
ˆ
(8)
T
m
i
m
i
T
m
i
m
i
i
H
H
G
)
(
)
(
1
0
,
1
,
,
1
0
,
(9)
At the mome
nt
K<
<N
,
i=m
+
K-1
. Iteration variable
a
:
m+
K
≤
a
≤
n
. When
a=
n
, we get
the es
timation value
n
x
ˆ
.The time-inva
r
iant
system
can b
e
simplified a
s
:
)
ˆ
(
ˆ
ˆ
1
1
a
a
a
a
a
x
HF
z
K
x
F
x
(10
)
Whe
r
e
T
a
a
H
G
K
(11
)
1
1
1
]
)
(
[
T
a
T
a
F
FG
H
H
G
(12
)
m
i
m
i
m
i
i
Z
F
x
,
1
,
ˆ
(13
)
T
m
i
m
i
T
m
i
m
i
i
F
H
H
F
G
)
(
)
(
1
,
,
(14
)
Whe
r
e
i=m
+
K
-
1
. Iteration variabl
e
a
:
m+
K
≤
a
≤
n
.
3.2. Impro
v
e
d
Iterativ
e UKIR Filter
In the mane
uvering ta
rg
et tracking,
noise ca
n cause a larg
e deviation
betwe
en
measurement
data a
nd filte
r
data. So
de
viation
ca
n
re
flect the m
a
n
euverin
g
status. Fo
rmul
a (7)
and
(1
2)
sh
o
w
that
G
N
PG
only h
a
s the
rel
a
tion
with
state
tran
siti
on m
a
trix an
d me
asure
m
ent
matrix. Each
filtering
re
sult of iterativ
e UKIR
filter is
obtain
e
d
by the
origi
nal in
depe
nd
ent
iteration
N-
K
measu
r
em
e
n
t result
s. The GNP
G
filtering p
r
o
c
e
s
ses of different time a
r
e
indep
ende
nt. So ch
angin
g
GNPG i
s
u
n
constraine
d. T
hus
we
defin
e a g
ene
rali
zed noi
se
po
wer
gain a
d
ju
stment co
efficien
t
to adaptive adju
s
t G
N
PG by deviat
i
on bet
wee
n
measurement
data a
nd filte
r
d
a
ta in
this pap
er.
That
can
fu
rth
e
r i
m
prove
the fi
lterin
g
effecti
v
eness
of UKIR
filter.
This p
ape
r select
s ro
ot mean
squ
a
re
k
of deviation as de
scripti
on of mane
u
v
ering
target. And
k
is expre
s
sed
by:
)
ˆ
(
)
ˆ
(
k
k
k
T
k
k
k
k
x
H
Z
x
H
Z
(15
)
Whe
r
e
is
di
mensi
o
n
s
of t
he target mot
i
on.
k
Z
is the
me
asu
r
em
ent da
ta at
k
time.
k
x
ˆ
is
the filtering re
sult at
k
time.
k
H
is
meas
urement matrix.
In orde
r to ref
l
ect the obvio
us man
euve
r
i
ng target tra
c
king, we set a
deviation rati
o
λ
.
Based o
n
ro
o
t
mean squ
a
re, the
λ
c
an be s
e
t:
K
k
k
k
1
/
(16
)
In fact, noi
se
ca
n
re
sult in
filtering
dive
rgen
ce. S
o
we sele
ct the
mean val
ue f
o
r
λ
to
remove the ef
fect of noise.
The ra
nge of
mean value i
s
half of wind
ow len
g
th.
At
k
time, the
gene
rali
zed n
o
ise p
o
wer g
a
in adju
s
tme
n
t coefficie
n
t is:
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ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 2, May 2016 : 344 –
350
347
k
k
j
j
k
N
0
2
/
1
(17
)
Whe
r
e
1
2
/
0
N
k
k
,
2
/
N
den
otes the integ
e
r pa
rt of
N/2
.
And
1
0
K
m
k
,
2
/
N
K
m
k
. So
the time of gene
rali
zed
noise po
wer gain
adju
s
tment st
arts at
2
/
N
K
m
. Formula (1
) and (1
2) ca
n be rep
r
esented a
s
:
1
1
1
]
)
(
[
T
k
k
k
k
T
k
k
k
F
G
F
H
H
G
(18
)
1
1
1
]
)
(
[
T
k
T
k
k
F
FG
H
H
G
(19
)
Along with th
e
iterative proce
s
s, the ef
fect of
initial batch pro
c
e
s
sing
le
ngth will
be
re
du
ce
d.
1
is able to en
sure filtering
conve
r
ge
nce. With
the increase of the n
u
mb
e
r
of iterations, the
covari
an
ce of
target locati
on tends to
decrea
s
e. We can get th
e explanation
of the improved
UKIR filter,
when the
devia
tion bet
ween
measurement
and filte
r
ing
re
sult i
s
bi
gge
r than
previou
s
time. We sh
o
u
ld increa
se t
he wei
ght of innovatio
n
s
in
GNPG to re
duce the filtering error.
Whe
n
the deviation
is small
e
r th
an previou
s
time,it sho
w
s
that the filtering re
sult is
accurate. So it
redu
ce
s th
e
weig
ht of inn
o
vations
app
rop
r
iately
whi
c
h
doe
s n
o
t
affect the filter
re
sult. At the
same time, th
e decrea
s
e of
the GNPG wi
ll be able to
improve the
converg
e
n
c
e rate of the filte
r
.
4. Maneuv
ering targe
t
tr
ac
king simulation.
The sim
u
latio
n
scene i
s
: Acceleration
-T
urn.
A
ccel
e
r
a
t
i
ng zon
e
:
0s
≤
t
≤
20s. Unifo
r
m
zone : 20s
≤
t
≤
40
s. Turnin
g zone : 40s
≤
t
≤
70
s.
Uniform zo
ne
: 70s
≤
t
≤
1
0
0
s
. As in figure 1.
Figure 1. Simulation sce
n
e
Simulation system is de
scrib
ed a
s
wh
ite noise m
o
del und
er re
ctang
ular
co
ordin
a
te
system. In th
e formul
a (1
) and (2),
x
is defined
as
d
i
spla
cem
ent, velocity and
accele
ration
9-
dimen
s
ion
a
l vector at
x-
y-
z
dire
ction.
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752
Im
proved
UFI
R
Tra
c
king Al
gorithm
for Maneu
ve
ring
Ta
rget
(Shouli
n
Yin)
348
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
5
.
0
0
0
0
0
1
0
0
0
5
.
0
0
0
0
0
1
0
0
0
5
.
0
0
0
0
0
1
2
2
2
T
T
T
T
T
T
T
T
T
F
,
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
H
,
I
B
.
Process noi
se covari
an
ce
Q
and
mea
s
u
r
eme
n
t noise covari
an
ce
R
:
1
0
0
0
0
5
.
0
0
0
0
1
0
0
0
0
5
.
0
0
0
0
1
0
0
0
0
5
.
0
0
0
0
0
5
.
0
0
0
0
0
0
0
0
5
.
0
0
0
0
0
0
0
0
5
.
0
5
.
0
0
0
5
.
0
0
0
25
.
0
0
0
0
5
.
0
0
0
5
.
0
0
0
25
.
0
0
0
0
5
.
0
0
0
5
.
0
0
0
25
.
0
3
3
3
2
3
2
3
2
3
2
3
4
2
3
4
2
3
4
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
Q
400
0
0
0
400
0
0
0
400
R
T
is
s
a
mple interval ,
T=0.
1
s.
The existin
g
maneuve
r
ing
target
tra
cki
n
g
algo
rithms
based on KF
can al
so
de
sign th
e
corre
s
p
ondin
g
tracking al
gorithm
s ba
sed on UF
I
R
filter. The advantag
e of ignorin
g noi
se
statistical cha
r
acte
ri
stics in
UF
IR filter cannot
cha
n
g
e
. So we
co
mpare the p
e
r
forma
n
ce of
KF,
UFIR a
nd im
proved
UFIR
in this pap
er.
Whe
n
target
trajecto
ry i
s
attache
d
zero mea
n
g
a
u
s
sian
white no
ise
(its
cova
ri
ance i
s
100), Kalma
n
filter may achieve the opti
m
al soluti
o
n
. The optimal
wind
ow le
ngt
h of UFIR filter
55
opt
N
[10] and le
ng
th of the bat
ch p
r
o
c
e
s
sin
g
K=
5
by cal
c
ulatin
g. Posi
tion mean
sq
uare
error (PMSE
)
is as figu
re 2
,
3, 4 with
known n
o
ise sta
t
isti
cal c
har
ac
t
e
rist
ic
s.
Figure 2. PMSE at x-axis
Figure 3. PMSE at y-axis
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IJEECS
Vol.
2, No. 2, May 2016 : 344 –
350
349
Figure 4. PMSE at z-axis
Figure 5. PMSE at x-axis
Figure 6. PMSE at y-axis
Figure 7. PMSE at z-axis
From figu
re 2
,
3, 4, we ca
n kn
ow that fi
lt
er pe
rform
a
nce
of KF is
sup
e
rio
r
to UKIR and
improve
d
UKIR
whe
n
n
o
ise stati
s
tical
chara
c
te
rist
i
c
s is kn
own. Th
e imp
r
oved
UKIR is si
milar t
o
UKIR.It proves that the KF
is optimal
when noi
se
statistical charact
e
risti
cs i
s
obtained.
However,
we cannot a
c
curately predi
ct the target movi
ng co
ndi
tion. We have assume
d that the pro
c
e
s
s
noise stati
s
tical prope
rties
may be
wro
n
g
. In ord
e
r to
verify the ro
bustn
ess u
n
d
e
r the
un
kno
w
n
pro
c
e
ss
noi
se statisti
cal
prop
ertie
s
, we adju
s
t the
pro
c
e
ss
noi
se
covari
an
ce as
16. Th
e
simulatio
n
re
sults a
r
e a
s
figure 5, 6, 7 with unkn
o
wn noise statisti
cal cha
r
a
c
teri
stics.
From figu
re 5
,
6, 7, we can kno
w
that the
estimatio
n
erro
r of KF significa
ntly incre
a
ses
whe
n
the
pro
c
e
s
s noi
se
st
atistical
prop
erties is kn
o
w
n. Ho
weve
r,
UFIR filter d
o
es
not n
eed
p
r
ior
informatio
n of
pro
c
e
s
s noi
se statisti
cal p
r
ope
rtie
s
in t
he filtering
proce
s
s. It represe
n
ts
stro
ng
er
robu
stne
ss for the inaccu
ra
te pr
ocess no
ise stati
s
tical
prop
ertie
s
. Moreove
r
, the improve
d
UFI
R
filter ca
n b
e
tter ad
apt to
the targ
et m
aneuve
r
ing
a
nd get
better filtering
perf
o
rma
n
ce tha
n
existing
UFIR filter by u
s
in
g the d
e
viatio
n bet
w
een
m
easure
m
ent a
nd filterin
g re
sults to ad
apt
ive
adju
s
t new ra
te gain matrix
.
5. Conclu
sion
In this pape
r, we pro
p
o
s
e
the improve
d
UFIR
filter to offset the deficie
ncy of existing
UFIR filter. We use it for m
aneuve
r
ing ta
rget
tra
cki
ng. The sim
u
latio
n
experim
ent
s sh
ow that:
1.
whe
n
the
kno
w
n i
n
itial valu
es
and
noi
se
statistical di
st
ribution
follo
w id
eal
co
ndit
i
ons, KF
is
slightly better than existing
UFIR filter;
2.
whe
n
n
o
ise statistical dist
ribution
i
s
un
know
n, UFIR f
ilter
sho
w
s th
e st
rong
er ro
bustn
ess
than KF;
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Im
proved
UFI
R
Tra
c
king Al
gorithm
for Maneu
ve
ring
Ta
rget
(Shouli
n
Yin)
350
3.
this pap
er’
s
new
scheme
can a
daptive
adjus
t ne
w rate gain matrix which sho
w
s a bette
r
filtering pe
rformance than e
x
isting UFIR f
ilter;
4.
though the n
e
w UFI
R
filter can im
prov
e the filt
er preci
s
ion, its a
m
ount
of co
mputation is
N
opt
times gre
a
ter than the
KF.
In the future,
we
will evaluate our scheme wi
th other UFIR filter
al
gorithm
s and
desi
gn a
UFIR filter wit
h
small am
ou
nt of computa
t
ion
for usin
g it in the maneuvering ta
rget
tracking.
Referen
ces
[1]
Sing
h AK, Bhaumik S. Quadrature f
ilters for mane
uveri
ng target trackin
g
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g (ICRAIE)
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u
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an E, Xi
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ig
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oot
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