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m
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ated
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tio
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in
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m
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m
ate
th
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s
ig
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al
s
o
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r
ce
d
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ec
tio
n
[
1
]
.
Fro
m
p
ast
t
wo
d
ec
ad
es,
m
a
n
y
al
g
o
r
ith
m
s
w
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d
er
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to
s
o
lv
e
th
e
p
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o
b
lem
o
f
DO
A
es
ti
m
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n
.
T
h
ese
alg
o
r
ith
m
s
ca
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b
e
b
r
o
ad
ly
class
if
ied
i
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to
:
i
)
C
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v
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t
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m
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o
d
s
,
ii
)
Su
b
s
p
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ce
m
eth
o
d
s
,
iii
)
Sp
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e
m
et
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T
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s
tan
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ar
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MU
SI
C
al
g
o
r
ith
m
p
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p
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in
[
2
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3
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,
d
ec
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m
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ltip
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icat
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esti
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ate
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co
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er
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n
t
s
i
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s
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ce
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.
I
n
[
4
]
,
an
i
m
p
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o
v
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a
n
d
m
o
d
i
f
ie
d
MU
SIC
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p
er
f
o
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f
t
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m
d
eter
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r
ates
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o
r
l
o
w
SN
R
r
e
g
io
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.
I
n
[5
,
6
]
,
th
e
p
er
f
o
r
m
an
ce
o
f
all
th
ese
s
u
b
s
p
ac
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b
ased
s
tan
d
ar
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DOA
esti
m
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g
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r
ith
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s
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an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
8
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8708
I
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lec
&
C
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p
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g
,
Vo
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11
,
No
.
4
,
A
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u
s
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0
2
1
:
3
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3058
3050
f
o
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th
at
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tec
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f
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p
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y
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t
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e
s
p
ar
s
e
n
a
tu
r
e
o
f
to
b
e
esti
m
ated
s
i
g
n
al
[
7
]
.
T
h
e
s
p
ar
s
e
b
ased
alg
o
r
ith
m
p
r
o
p
o
s
ed
in
[
8
,
9
]
is
b
ased
o
n
t
h
e
o
r
th
o
g
o
n
al
m
atc
h
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n
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(
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I
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[
1
0
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,
a
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[
1
1
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1
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ased
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r
e
-
w
ei
g
h
ted
l1
m
i
n
i
m
izatio
n
is
p
r
o
p
o
s
ed
to
m
in
i
m
ize
t
h
e
co
m
p
le
x
it
y
o
f
DO
A
est
i
m
a
tio
n
al
g
o
r
ith
m
b
u
t
s
u
f
f
er
s
w
it
h
lo
w
p
er
f
o
r
m
a
n
ce
f
o
r
co
h
er
e
n
t
a
n
d
clo
s
el
y
s
p
ac
ed
s
i
g
n
a
l
s
o
u
r
ce
s
.
T
h
e
co
m
p
r
es
s
iv
e
s
e
n
s
i
n
g
b
ase
d
DO
A
est
i
m
a
tio
n
alg
o
r
ith
m
s
p
r
o
p
o
s
ed
in
[
1
3
-
1
6
]
ar
e
b
ased
o
n
th
e
s
i
m
p
le
least
s
q
u
ar
es
m
i
n
i
m
izatio
n
m
et
h
o
d
w
h
ich
o
f
f
er
s
g
o
o
d
MSE
,
r
eso
lu
tio
n
b
u
t
s
u
f
f
er
s
f
r
o
m
h
i
g
h
co
m
p
le
x
it
y
,
th
e
p
er
f
o
r
m
a
n
ce
o
f
B
P
an
d
OM
P
d
e
p
en
d
s
o
n
th
e
ar
r
a
y
-
s
teer
in
g
m
atr
ix
[
9
]
,
an
d
it
d
eg
r
ad
es
f
o
r
h
i
g
h
l
y
co
r
r
elate
d
ar
r
a
y
-
s
teer
i
n
g
m
atr
i
x
i
n
t
h
e
ca
s
e
o
f
DO
A
p
r
o
b
le
m
.
T
h
e
s
ca
lin
g
/
s
h
r
i
n
k
ag
e
o
p
er
atio
n
s
in
co
n
v
ex
r
elax
at
io
n
m
a
y
r
ed
u
ce
v
ar
ian
ce
f
o
r
in
cr
ea
s
e
in
s
p
ar
s
it
y
o
r
v
ice
v
er
s
a.
I
n
th
e
m
o
s
t
r
ec
en
t
y
ea
r
s
,
B
ay
esian
m
et
h
o
d
s
lik
e
m
ax
i
m
u
m
a
p
o
s
ter
io
r
i
(
MA
P
)
[
1
7
,
1
8
]
,
m
ax
i
m
u
m
lik
eli
h
o
o
d
(
ML
esti
m
atio
n
)
[
1
8
]
,
iter
ativ
e
r
e
w
ei
g
h
ted
l1
a
n
d
l2
al
g
o
r
ith
m
s
w
er
e
ap
p
lie
d
to
s
o
lv
e
t
h
e
DO
A
esti
m
atio
n
p
r
o
b
le
m
.
T
h
ese
B
ay
esia
n
alg
o
r
it
h
m
s
s
u
f
f
er
f
r
o
m
h
ig
h
MSE
,
ev
e
n
th
o
u
g
h
tr
u
e
p
r
io
r
s
ar
e
u
s
ed
.
I
n
[
1
7
]
,
MA
P
o
n
ly
g
u
ar
a
n
tees
m
ax
i
m
izatio
n
o
f
p
r
o
d
u
ct
o
f
lik
el
ih
o
o
d
an
d
th
e
p
r
io
r
o
f
th
e
u
n
k
n
o
w
n
s
p
ar
s
e
s
ig
n
al
.
ML
est
i
m
a
te
i
n
[
1
8
]
,
also
m
ax
i
m
izes
o
n
l
y
t
h
e
li
k
eli
h
o
o
d
f
u
n
ctio
n
b
y
as
s
u
m
i
n
g
p
r
io
r
o
f
u
n
k
n
o
w
n
to
b
e
eq
u
all
y
li
k
el
y
to
o
cc
u
r
.
Sp
ar
s
e
B
ay
es
ian
lear
n
in
g
(
SB
L
)
w
ith
r
ele
v
an
ce
v
ec
to
r
m
ac
h
in
e
p
r
o
p
o
s
ed
b
y
T
ip
p
in
g
in
[
1
9
]
an
d
r
e
-
r
ep
r
esen
ted
b
y
W
ip
f
i
n
[
2
0
]
f
o
r
lin
ea
r
r
eg
r
e
s
s
io
n
/s
p
ar
s
e
s
i
g
n
al
r
ec
o
v
er
y
p
r
o
b
le
m
led
a
b
r
o
ad
e
r
w
a
y
w
it
h
h
ig
h
er
p
er
f
o
r
m
a
n
ce
r
esu
lts
i
n
th
e
r
esear
ch
o
f
s
p
ar
s
e
s
ig
n
a
l
r
ec
o
v
er
y
.
I
n
t
h
i
s
p
ap
er
,
w
e
p
r
esen
t
th
e
d
etail
in
f
er
en
ce
o
f
Sp
ar
s
e
B
a
y
es
ian
l
ea
r
n
in
g
an
d
its
ap
p
licab
ilit
y
to
DOA
p
r
o
b
le
m
u
s
in
g
o
n
-
g
r
id
ap
p
r
o
ac
h
.
W
e
also
d
er
iv
e
th
e
u
p
d
atin
g
eq
u
atio
n
s
f
o
r
h
y
p
er
p
ar
a
m
eter
s
b
y
m
ax
i
m
izi
n
g
t
h
e
p
o
s
ter
io
r
o
f
h
y
p
er
p
ar
a
m
eter
s
f
o
r
n
o
n
ze
r
o
h
y
p
er
p
r
io
r
s
ca
lar
s
.
Fu
r
t
h
er
,
th
e
p
ap
er
is
o
r
g
an
ize
d
as
:
Sectio
n
2
d
escr
ib
es
th
e
s
ig
n
a
l
m
o
d
el
u
s
ed
f
o
r
DO
A
e
s
t
i
m
atio
n
f
o
r
a
u
n
i
f
o
r
m
l
in
ea
r
ar
r
a
y
.
Sect
io
n
3
d
escr
ib
es
th
e
b
asics
a
n
d
in
f
er
e
n
ce
o
f
th
e
Sp
ar
s
e
B
ay
e
s
ian
L
ea
r
n
i
n
g
tech
n
iq
u
e.
Sectio
n
4
d
escr
ib
es
ab
o
u
t
u
p
d
atin
g
o
f
t
h
e
h
y
p
er
p
ar
am
eter
s
o
f
SB
L
est
i
m
ate
b
y
p
r
o
p
o
s
in
g
a
m
et
h
o
d
o
f
m
ax
i
m
u
m
-
a
-
p
o
s
ter
io
r
o
f
th
e
h
y
p
er
p
ar
a
m
eter
s
.
S
ec
tio
n
5
s
u
m
m
ar
izes
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
I
n
s
ec
tio
n
6
,
th
e
r
es
u
lts
an
d
p
er
f
o
r
m
a
n
ce
a
n
al
y
s
i
s
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
ar
e
p
r
esen
te
d
.
Fin
all
y
,
s
ec
tio
n
7
co
n
clu
d
es t
h
e
p
ap
er
.
2.
S
I
G
NA
L
M
O
DE
L
F
O
R
SPAR
SE
DO
A
E
S
T
I
M
AT
I
O
N
C
o
n
s
id
er
‘
D’
n
u
m
b
er
o
f
ar
r
iv
i
n
g
s
ig
n
al
s
o
u
r
ce
s
s
(
n
)
=
[s
1
(
n
)
,
s
2
(
n
)
….
s
D
(
n
)
]
T
i
m
p
i
n
g
i
n
g
o
n
t
h
e
u
n
i
f
o
r
m
lin
ea
r
ar
r
a
y
o
f
‘
M’
s
en
s
o
r
s
w
it
h
a
u
n
if
o
r
m
s
p
ac
i
n
g
o
f
d
≤
λ
/2
,
w
h
er
e
λ
is
t
h
e
w
a
v
ele
n
g
t
h
o
f
th
e
ar
r
iv
in
g
s
i
g
n
als.
L
et
y
(
n
)
=
[y
1
(
n
)
,
y
2
(
n
)
….
y
M
(
n
)
]
T
b
e
Mx
1
o
b
s
er
v
ed
s
ig
n
al
s
a
m
p
le
s
r
ec
eiv
ed
b
y
‘
M
’
an
ten
n
a
ar
r
ay
s
e
n
s
o
r
s
.
Fo
r
s
i
m
p
lici
t
y
,
ass
u
m
in
g
a
s
in
g
le
s
n
ap
s
h
o
t
(
s
in
g
le
m
ea
s
u
r
e
m
en
t
v
ec
to
r
)
i.e
,
n
=1
,
th
e
p
r
o
b
lem
o
f
d
ir
ec
tio
n
o
f
ar
r
iv
al
est
i
m
a
ti
o
n
ca
n
b
e
m
o
d
eled
as in
(
1
)
.
y
(
n
)
=
A
(
θ
)
x
(
n
)
+
w
(
n
)
(
1
)
w
h
er
e
A
i
s
M
x
N
ar
r
a
y
s
teer
i
n
g
m
atr
i
x
g
i
v
en
b
y
(
2
)
an
d
a
(
θ
i
)
r
ep
r
esen
ts
th
e
ato
m
f
o
r
a
p
ar
ticu
lar
d
ir
ec
tio
n
an
g
le
θ
i
.
Fo
r
s
ea
r
ch
i
n
g
t
h
e
en
tire
a
n
g
le
s
p
ac
e
f
o
r
DO
A
a
p
ar
ticu
lar
g
r
id
o
f
‘
N
’
v
a
lu
es
o
f
a
n
g
les
ar
e
co
n
s
id
er
ed
.
E
ac
h
ato
m
is
a
v
e
cto
r
o
f
Mx
1
an
ten
n
a
ar
r
a
y
s
tee
r
in
g
v
ec
to
r
g
i
v
en
i
n
(
3
)
.
A
(
θ
)
=
[
a
(
θ
1
)
,
a
(
θ
2
)
…
.
.
a
(
θ
N
)
]
(
2)
a
(
θ
i
)
=
[
1
e
−
j
β
d
s
i
n
(
θ
i
)
e
−
j2
β
d
s
i
n
(
θ
i
)
e
−
j3
β
d
s
i
n
(
θ
i
)
…
…
…
e
−
j
(
M
−
1
)
β
d
s
i
n
(
θ
i
)
]
T
(
3
)
w
h
er
e,
β=2
π/λ,
x
(
n
)
=
[x
1
(
n
)
,
x
2
(
n
)
….
x
N
(
n
)
]
T
is
N
x
1
s
i
g
n
al
v
e
cto
r
th
at
n
ee
d
s
to
b
e
esti
m
ated
to
f
i
n
d
th
e
s
o
u
r
ce
s
ig
n
al
d
ir
ec
tio
n
s
in
p
r
esen
ce
o
f
an
te
n
n
a
ar
r
a
y
n
o
is
e
v
ec
to
r
w
(
n
)
=
[w
1
(
n
)
,
w
2
(
n
)
….
w
M
(
n
)
]
T
o
f
Mx
1
s
ize.
T
h
e
esti
m
ated
x
(
n
)
v
alu
e
s
ar
e
th
e
e
s
ti
m
atio
n
o
f
s
i
g
n
al
p
o
w
er
s
(
n
)
an
d
is
r
elate
d
b
y
(
4
)
.
x
i
(
n
)
=
{
s
j
(
n
)
θ
i
=
DOA
;
∀
i
=
1
,
2
…
N
0
e
l
s
e
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
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&
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n
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I
SS
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2
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8
8
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a
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s
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n
lea
r
n
in
g
s
ch
eme
f
o
r
s
p
a
r
s
e
DOA
esti
ma
tio
n
b
a
s
ed
o
n
ma
ximu
m
-
a
-
p
o
s
teri
o
r
i o
f
...
(
R
a
g
h
u
K
)
3051
T
h
e
m
o
d
el
i
n
(
1
)
tu
r
n
s
o
u
t
t
o
b
e
th
e
p
r
o
b
lem
o
f
s
p
ar
s
e
s
ig
n
a
l
r
ec
o
v
er
y
f
r
o
m
t
h
e
u
n
d
e
r
-
s
a
m
p
led
m
ea
s
u
r
e
m
e
n
t
s
y
[
1
3
]
.
3.
SPAR
S
E
B
AYES
I
AN
L
E
AR
NIN
G
I
NF
E
RE
NCE
C
o
n
s
id
er
a
s
in
g
le
s
n
ap
s
h
o
t
ca
s
e,
DOA
es
ti
m
atio
n
p
r
o
b
le
m
as
in
(
1
)
.
T
h
e
w
(
n
)
ar
e
in
d
ep
en
d
en
t
n
o
is
e
s
a
m
p
les
w
h
ich
is
a
s
s
u
m
ed
to
b
e
ze
r
o
–
m
ea
n
Ga
u
s
s
ian
r
a
n
d
o
m
p
r
o
ce
s
s
w
it
h
n
o
is
e
v
ar
ia
n
ce
σ
2
.
B
y
B
a
y
e
s
’
s
th
eo
r
e
m
[
1
9
]
,
th
e
p
o
s
ter
io
r
o
f
u
n
k
n
o
w
n
x
b
y
k
n
o
w
in
g
th
e
o
b
s
er
v
ed
an
ten
n
a
ar
r
a
y
r
ec
eiv
ed
s
ig
n
al
y
ca
n
b
e
ex
p
r
ess
es a
s
in
(
5
)
.
P
(
x
/
y
)
=
P
(
y
/
x
)
P
(
x
)
P
(
y
)
(
5
)
w
h
er
e,
P
(
y
/x
)
i
s
t
h
e
li
k
eli
h
o
o
d
o
f
o
b
s
er
v
ed
d
ata
f
o
r
t
h
e
e
s
ti
m
ated
u
n
k
n
o
w
n
p
ar
a
m
eter
‘
x
’
w
h
ic
h
i
s
as
s
u
m
ed
as
P
(
y
/
x
)
=
(
y
/
Ax
,
σ
2
)
,
w
h
er
e
th
e
n
o
tat
io
n
(
.
)
s
p
ec
if
ies
a
g
u
as
s
ian
d
is
tr
ib
u
tio
n
o
v
er
y
w
it
h
m
ea
n
A
x
an
d
v
ar
ian
ce
σ
2
.
T
h
is
ass
u
m
p
tio
n
is
d
u
e
to
an
o
th
er
as
s
u
m
p
tio
n
o
f
i
n
d
ep
en
d
en
ce
o
f
s
a
m
p
les
y
.
T
h
u
s
th
e
lik
eli
h
o
o
d
f
u
n
ctio
n
o
f
y
i
s
g
i
v
en
in
(
6
)
.
P
(
y
x
⁄
,
σ
2
)
=
1
(
2π
σ
2
)
M
/
2
e
xp
{
−
‖
y
−
Ax
‖
2
2
σ
2
}
(
6
)
T
h
e
p
r
i
o
r
o
f
u
n
k
n
o
w
n
‘
x
’
is
al
s
o
ass
u
m
ed
to
b
e
as
ze
r
o
m
ea
n
Gau
s
s
ia
n
p
r
io
r
d
is
tr
ib
u
tio
n
o
v
er
x
w
it
h
v
ar
ian
ce
[
1
9
,
2
0
]
.
T
h
e
Gau
s
s
i
an
p
r
io
r
o
f
a
s
in
g
le
s
a
m
p
le
o
f
x
(
i.e
,
x
i
)
is
g
i
v
e
n
in
(
7
)
.
P
(
x
i
γ
i
⁄
)
=
1
(
2π
γ
i
)
1
/
2
e
xp
{
−
x
i
2
2
γ
i
}
(
7
)
T
h
e
o
v
er
all
Gau
s
s
ia
n
p
r
io
r
f
o
r
all
i =
1
to
N
is
g
iv
e
n
in
(
8
)
.
P
(
x
γ
⁄
)
=
∏
{
1
(
2π
γ
i
)
1
/
2
e
xp
{
−
x
i
2
2
γ
i
}
}
N
i
=
1
(
8
)
T
o
d
ef
in
e
p
r
io
r
o
f
u
n
k
n
o
w
n
x
,
w
e
r
eq
u
ir
e
a
n
o
th
er
p
ar
a
m
e
ter
γ
w
h
ic
h
i
s
v
ar
ian
ce
o
f
u
n
k
n
o
w
n
x
.
T
h
u
s
t
h
e
γ
ca
n
b
e
ca
lled
as a
v
e
cto
r
o
f
h
y
p
er
p
ar
a
m
eter
s
o
f
u
n
k
n
o
w
n
‘
x
’
[
2
1
,
22
]
.
Hen
ce
,
to
co
m
p
lete
l
y
d
e
f
i
n
e
all
th
e
d
is
tr
ib
u
tio
n
s
,
th
e
h
y
p
er
p
ar
am
eter
s
γ
an
d
n
o
is
e
v
ar
ian
c
e
σ
2
n
ee
d
s
to
b
e
esti
m
ated
w
h
i
ch
ca
n
b
e
d
o
n
e
b
y
d
ef
in
i
n
g
th
e
h
y
p
er
p
r
io
r
s
o
f
γ
an
d
σ
2
as in
(
9
)
an
d
(
1
0
)
.
P
(
γ
)
=
∏
ga
mma
{
γ
i
a
⁄
,
b
}
N
i
=
1
(
9
)
P
(
σ
2
)
=
∏
ga
mma
{
σ
2
c
⁄
,
d
}
N
i
=
1
(
1
0
)
W
e
h
av
e
ch
o
s
en
g
a
m
m
a
d
is
t
r
ib
u
tio
n
b
ec
au
s
e
t
h
e
h
y
p
er
p
ar
a
m
eter
s
γ
and
σ
2
ar
e
s
ca
le
p
a
r
a
m
eter
s
[
2
3
,
2
4
]
w
h
er
e:
g
a
m
m
a(
γ
/
a,b
)
= G
(
a)
-
1
b
a
γ
a
-
1
e
−
b
γ
(
1
1
)
w
it
h
G(
a)
=
∫
t
a
−
1
e
−
t
dt
∞
0
is
th
e
g
a
m
m
a
f
u
n
c
tio
n
an
d
a,
b
,
c,
d
ar
e
all
h
y
p
er
p
r
io
r
p
ar
am
eter
s
.
Af
ter
d
ef
i
n
i
n
g
t
h
e
lik
eli
h
o
o
d
an
d
p
r
io
r
s
(
5
)
ca
n
b
e
r
e
-
w
r
i
tten
a
s
[
1
9
]
.
P
(
x
/
y,
γ
,
σ
2
)
=
P
(
y
/
x
,
σ
2
)
P
(
x/
γ
)
P
(
y
/
γ
,
σ
2
)
(
1
2
)
P
(
x
/
y
,
γ
,
σ
2
)
P
(
y
/
γ
,
σ
2
)
=
P
(
y
/
x
,
σ
2
)
P
(
x/
γ
)
(
1
3
)
B
y
p
l
u
g
g
i
n
g
in
(
6
)
an
d
(
8
)
o
n
r
ig
h
t
h
a
n
d
s
id
e
o
f
(
1
3
)
an
d
s
i
m
p
lify
i
n
g
g
i
v
e
s
an
o
t
h
er
Gau
s
s
ia
n
d
is
tr
ib
u
tio
n
f
o
r
P
(
x
/
y,
γ
,
σ
2
)
an
d
P
(
y/
γ
,
σ
2
)
as in
(
1
5
)
an
d
(
1
8
)
r
esp
ec
tiv
el
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
4
,
A
u
g
u
s
t 2
0
2
1
:
3
0
4
9
-
3058
3052
P
(
x
/
y,
γ
,
σ
2
)
P
(
y/
γ
,
σ
2
)
=
1
(
2
π
σ
2
)
M
/
2
e
x
p
{
−
‖
y
−
Ax
‖
2
2
σ
2
}
∏
{
1
(
2
π
γ
i
)
1
/
2
e
x
p
{
−
x
i
2
2
γ
i
}
}
N
i
=
1
P
(
x
/
y,
γ
,
σ
2
)
P
(
y/
γ
,
σ
2
)
=
(
x
μ
⁄
,
Σ
x
)
(
y
0
⁄
,
Σ
y
)
(
1
4
)
E
q
u
atin
g
o
n
b
o
th
s
id
e
s
w
e
g
et
:
P
(
x
y
,
γ
,
⁄
σ
2
)
=
1
(
2π
)
N
/
2
|
Σ
x
|
1
/
2
e
xp
{
−
(
x
−
μ
)
T
(
x
−
μ
)
2
Σ
x
}
(
1
5
)
w
h
er
e
th
e
p
o
s
ter
io
r
m
ea
n
an
d
co
v
ar
ian
ce
o
f
u
n
k
n
o
w
n
x
ar
e
g
iv
e
n
i
n
(
1
6
)
an
d
(
1
7
)
r
esp
ec
ti
v
el
y
.
μ
=
σ
−
2
Σ
x
A
T
y
(
1
6
)
Σ
x
=
(
σ
−
2
A
T
A
+
Γ
)
−
1
(
1
7
)
w
it
h
Γ
=
d
iag
(
γ
1
−
1
,
γ
2
−
1
…
.
.
γ
N
−
1
)
.
I
n
(
1
4
)
w
e
g
et
o
n
e
m
o
r
e
r
es
u
lt
f
o
r
p
r
io
r
o
f
th
e
o
b
s
er
v
ed
ar
r
ay
r
ec
ei
v
ed
s
i
g
n
al
v
ec
to
r
.
P
(
y
γ
⁄
,
σ
2
)
=
1
(
2π
)
M
/
2
|
Σ
y
|
1
/
2
e
xp
{
−
(
y
)
T
(
y
)
2
Σ
y
}
(
1
8
)
w
it
h
Σ
y
=
(
σ
2
I
+
A
Γ
−
1
A
T
)
as
th
e
p
r
io
r
co
v
ar
ian
ce
o
f
o
b
s
er
v
ed
ar
r
ay
r
ec
eiv
ed
s
ig
n
a
l
v
ec
to
r
.
So
lv
i
n
g
(
1
6
)
an
d
(
1
7
)
f
o
r
th
e
k
n
o
w
n
v
al
u
e
s
o
f
h
y
p
er
p
ar
a
m
eter
s
γ
and
σ
2
r
esu
lt
s
i
n
m
ea
n
a
n
d
co
v
ar
ian
ce
o
f
p
o
s
ter
io
r
o
f
u
n
k
n
o
w
n
x
r
esp
ec
ti
v
el
y
.
T
h
e
p
o
s
ter
io
r
m
ea
n
o
f
u
n
k
n
o
w
n
x
is
its
el
f
t
h
e
est
i
m
a
tio
n
o
f
t
h
e
u
n
k
n
o
w
n
x
i.e
,
̂
=
,
p
lo
ttin
g
th
is
̂
esti
m
ate
w
it
h
r
esp
ec
t
to
th
e
o
n
-
g
r
id
s
ea
r
ch
a
n
g
le
p
o
in
t
s
g
i
v
e
s
th
e
DO
A
p
e
ak
s
an
d
h
e
n
ce
t
h
e
ar
r
iv
in
g
s
i
g
n
al
s
o
u
r
ce
’
s
d
ir
ec
ti
o
n
ca
n
b
e
esti
m
ated
[
2
5
]
.
I
n
p
r
ac
tical
s
itu
a
tio
n
s
,
th
e
h
y
p
er
p
ar
a
m
eter
s
γ
and
σ
2
w
il
l
b
e
u
n
k
n
o
w
n
an
d
t
h
er
e
ca
n
n
o
t
b
e
a
n
y
c
lo
s
ed
f
o
r
m
e
x
p
r
e
s
s
io
n
s
o
b
tain
ed
f
o
r
th
e
m
[
2
6
]
.
Hen
ce
,
a
n
iter
ati
v
e
esti
m
atio
n
o
f
h
y
p
er
p
ar
a
m
eter
s
γ
and
σ
2
h
as to
b
e
d
o
n
e.
4.
M
AXI
M
U
M
A
P
O
ST
E
RIO
R
O
F
H
YP
E
RP
ARAM
E
T
E
RS
T
o
iter
ativ
el
y
esti
m
ate
th
e
h
y
p
er
p
ar
a
m
eter
s
li
k
e
v
ar
ian
ce
o
f
p
r
io
r
o
f
u
n
k
n
o
w
n
an
d
v
a
r
ian
ce
o
f
n
o
is
e
σ
2
,
w
e
m
a
x
i
m
ize
t
h
e
p
r
o
b
ab
ilit
y
f
u
n
ctio
n
P
(
γ
,
σ
2
/
)
g
iv
e
n
b
y
(
1
9
)
.
P
(
γ
,
σ
2
/
y
)
=
P
(
y
/
γ
,
σ
2
)
P
(
γ
,
σ
2
)
P
(
y
)
(
1
9
)
T
h
e
h
y
p
er
p
ar
a
m
eter
s
γ
,
σ
2
is
m
u
t
u
all
y
in
d
ep
en
d
e
n
t
w
it
h
ea
c
h
o
th
er
an
d
also
th
e
p
r
o
b
ab
ilit
y
o
f
k
n
o
w
n
m
ea
s
u
r
ed
ar
r
ay
r
ec
ei
v
ed
s
ig
n
a
l
v
ec
to
r
is
a
co
n
s
ta
n
t.
T
h
u
s
,
m
a
x
i
m
izi
n
g
(
1
9
)
is
eq
u
iv
alen
t
to
m
a
x
i
m
ize
(
2
0
)
w
it
h
r
esp
ec
t to
γ
,
σ
2
.
P
(
γ
,
σ
2
/
y
)
∝
P(
y/
γ
,
σ
2
)
P
(
γ
)
P
(
σ
2
)
(
2
0
)
As
i
n
p
r
ac
tice,
w
e
ass
u
m
e
u
n
if
o
r
m
h
y
p
er
p
r
io
r
s
o
v
er
a
lo
g
a
r
ith
m
ic
s
ca
le
w
it
h
t
h
e
d
er
iv
ati
v
es
o
f
t
h
e
h
y
p
er
p
r
io
r
s
ter
m
s
g
o
e
s
to
ze
r
o
,
w
e
c
h
o
o
s
e
to
m
ax
i
m
ize
t
h
e
lo
g
ar
ith
m
ic
q
u
a
n
tit
y
o
f
(
2
0
)
w
it
h
r
esp
ec
t
to
lo
g
γ
an
d
lo
g
σ
2
.
T
h
e
lo
g
ar
ith
m
o
f
(
2
0
)
is
g
i
v
en
b
y
(
2
1
)
.
L
=lo
g
P
(
γ
,
σ
2
/
y
)
≅
lo
g
P
(
y/
lo
g
γ
,
lo
g
σ
2
)
+
l
ogP
(
l
og
γ
)
+lo
g
P
(
lo
g
σ
2
)
(
2
1
)
L
=lo
g
P
(
y/
lo
g
γ
,
lo
g
σ
2
)
+
∑
l
ogP
(
l
og
)
N
i
=
1
+lo
g
P
(
lo
g
σ
2
)
(
2
2
)
Hen
ce
m
a
x
i
m
izi
n
g
L
th
e
o
b
j
ec
t
iv
e
f
u
n
c
tio
n
i
n
(
2
2
)
w
it
h
r
esp
ec
t
to
lo
g
γ
an
d
lo
g
σ
2
g
iv
es
t
h
e
iter
ativ
e
esti
m
ate
o
f
γ,
σ
2
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
in
(
2
2
)
ca
n
also
b
e
w
r
itte
n
as i
n
(
2
3
)
.
L=
-
1
2
{
−
l
og
|
Σ
x
|
+
N
l
og
σ
2
−
l
og
|
Γ
|
+
σ
−
2
‖
y
−
A
μ
‖
2
+
μ
T
Γμ
}
+
∑
(
−
a
l
og
γ
i
−
b
γ
i
−
1
)
−
c
l
og
σ
2
−
d
σ
−
2
N
i
=
1
(
2
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
B
a
ye
s
ia
n
lea
r
n
in
g
s
ch
eme
f
o
r
s
p
a
r
s
e
DOA
esti
ma
tio
n
b
a
s
ed
o
n
ma
ximu
m
-
a
-
p
o
s
teri
o
r
i o
f
...
(
R
a
g
h
u
K
)
3053
4
.
1
.
T
he
v
a
ria
nce
o
f
un
k
no
w
n ‘
x
’
T
h
e
d
if
f
er
en
tia
tio
n
o
f
(
2
3
)
w
it
h
r
esp
ec
t to
lo
g
γ
i
g
i
v
es:
l
o
g
γ
i
=
1
2
[
1
−
γ
i
−
1
(
μ
i
2
+
Σ
xii
)
]
+
−
γ
i
−
1
(
2
4
)
Settin
g
t
h
is
(
2
4
)
to
ze
r
o
an
d
M
ac
k
a
y
[
2
7
]
,
lead
s
to
th
e
u
p
d
ate
in
(
2
5
)
.
=
(
μ
i
2
+
2b
)
γ
i
−
Σ
x
ii
+
2a
(
2
5
)
4
.
2
.
T
he
no
is
e
v
a
ria
nce
T
h
e
d
if
f
er
en
tia
tio
n
o
f
(
2
3
)
w
it
h
r
esp
ec
t to
lo
g
σ
2
w
e
g
et:
∂
L
∂
l
o
g
σ
2
=
1
2
[
N
σ
2
−
‖
y
−
A
μ
‖
2
−
tr
(
Σ
x
A
T
A
)
]
+
c
−
d
σ
−
2
(
2
6
)
w
h
er
e:
tr
(
Σ
x
A
T
A
)
=
σ
2
∑
(
1
−
N
i
=
1
γ
i
−
1
Σ
xii
)
an
d
s
etti
n
g
d
er
iv
ati
v
e
in
(
2
6
)
to
ze
r
o
an
d
r
e
-
ar
r
an
g
in
g
th
e
ter
m
s
w
e
g
et
σ
2
u
p
d
ate
as i
n
(
2
7
)
.
σ
2
(
n
ew
)
=
‖
y
−
A
μ
‖
2
+
2d
N
−
∑
(
1
−
N
i
=
1
γ
i
−
1
Σ
x
ii
)
+
2c
(
2
7
)
5.
T
H
E
P
RO
P
O
SE
D
AL
G
O
RI
T
H
M
Fo
r
a
s
in
g
le
s
n
ap
s
h
o
t
ca
s
e,
i
n
DO
A
est
i
m
at
io
n
,
i
n
itial
ize
t
h
e
n
o
is
e
v
ar
ia
n
ce
σ
2
a
n
d
th
e
p
r
io
r
v
ar
ian
ce
γ
o
f
u
n
k
n
o
w
n
x
to
a
v
alu
e
(
i.e
,
u
s
u
all
y
ta
k
en
as
1
)
.
Usi
n
g
(
1
7
)
w
ill
g
iv
e
t
h
e
co
v
ar
ian
ce
esti
m
ate
an
d
later
u
s
i
n
g
(
1
6
)
w
ill
g
i
v
e
th
e
f
ir
s
t
i
ter
ativ
e
esti
m
ate
o
f
μ
.
B
ef
o
r
e
p
er
f
o
r
m
i
n
g
th
e
2
nd
iter
ativ
e
esti
m
atio
n
o
f
Σ
x
an
d
μ
,
let
u
s
u
p
d
ate
t
h
e
h
y
p
er
p
ar
am
eter
s
γ
an
d
σ
2
u
s
i
n
g
(
2
6
)
an
d
(
2
7
)
,
w
h
er
e
t
h
e
p
ar
a
m
e
ter
s
/
v
ar
iab
les
i
n
t
h
o
s
e
eq
u
atio
n
s
r
ep
r
ese
n
t
th
e
v
al
u
es
o
f
1
st
iter
atio
n
.
No
w
u
s
in
g
t
h
ese
n
e
w
u
p
d
ated
v
alu
e
s
o
f
γ
an
d
σ
2
,
esti
m
ate
t
h
e
2
nd
iter
atio
n
v
alu
es
o
f
Σ
x
an
d
μ
.
R
ep
ea
t
th
ese
s
tep
s
u
n
til
a
p
ar
ticu
lar
s
to
p
p
in
g
cr
iter
io
n
is
ac
h
iev
ed
.
I
n
th
i
s
iter
ativ
e
p
r
o
ce
s
s
,
s
o
m
e
ele
m
e
n
ts
o
f
μ
v
ec
to
r
ten
d
t
o
b
ec
o
m
e
v
er
y
m
i
n
i
m
u
m
v
al
u
e
(
i.e
,
less
th
a
n
a
p
r
eset
th
r
es
h
o
ld
)
,
eq
u
atin
g
th
e
s
e
ele
m
en
ts
to
ze
r
o
,
r
esu
lts
i
n
s
p
ar
s
i
t
y
o
f
t
h
e
s
o
lu
tio
n
.
Fo
r
‘
L
’
n
u
m
b
er
o
f
m
u
ltip
l
e
s
n
ap
s
h
o
t/
m
u
ltip
le
m
ea
s
u
r
e
m
en
t
v
ec
to
r
(
MM
V)
ca
s
e
also
,
s
a
m
e
p
r
o
ce
d
u
r
e
ca
n
b
e
u
tili
ze
d
ex
ce
p
t
th
at
th
e
p
r
io
r
m
ea
n
o
f
u
n
k
n
o
w
n
‘
x
’
(
i.e
,
μ
)
is
a
m
atr
ix
,
i
n
w
h
ich
ea
c
h
r
o
w
co
r
r
esp
o
n
d
s
to
a
p
ar
ticu
lar
o
n
-
g
r
id
s
ea
r
ch
p
o
i
n
t
o
f
an
g
le
o
f
ar
r
iv
al.
E
ac
h
o
f
t
h
e
s
e
r
o
w
s
o
f
μ
f
o
r
MM
V
ca
s
e
s
h
o
u
ld
b
e
tak
en
as
ab
s
o
l
u
te
m
ea
n
s
q
u
ar
e
v
al
u
es
o
f
all
th
e
ele
m
en
ts
o
f
t
h
at
p
ar
ticu
lar
r
o
w
.
T
h
is
μ
esti
m
ate
o
b
tain
ed
at
t
h
e
f
i
n
al
i
ter
atio
n
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
p
lo
tted
v
er
s
u
s
t
h
e
s
ea
r
ch
g
r
id
o
f
a
n
g
le
o
f
ar
r
iv
al
.
T
h
e
p
lo
t
s
h
o
w
i
n
g
p
ea
k
s
co
r
r
esp
o
n
d
in
g
to
th
e
p
ar
tic
u
lar
v
alu
e
o
f
a
n
g
le
o
f
ar
r
i
v
al
o
n
x
-
ax
is
,
i
n
d
icate
s
t
h
e
esti
m
ate
o
f
d
ir
ec
tio
n
o
f
ar
r
iv
a
l.
T
h
e
p
r
o
p
o
s
ed
DOA
esti
m
at
i
o
n
alg
o
r
it
h
m
b
a
s
ed
o
n
s
p
ar
s
e
B
ay
e
s
ian
lear
n
i
n
g
-
m
ax
i
m
u
m
a
p
o
s
ter
io
r
o
f
h
y
p
er
p
ar
am
eter
s
(
SB
L
-
M
A
P
-
H)
f
o
r
MM
V
ca
s
e
is
s
u
m
m
ar
ized
i
n
T
ab
le
1
.
T
ab
le
1
.
T
h
e
p
r
o
p
o
s
ed
SB
L
-
MA
P
-
H
DO
A
est
i
m
a
tio
n
a
l
g
o
r
ith
m
I
n
p
u
t
P
a
r
a
me
t
e
r
s:
Y
(M
xL
)
,
A
(M
xN
)
O
u
t
p
u
t
P
a
r
a
me
t
e
r
s:
μ
x
(N
x1)
1.
I
n
i
t
i
a
l
i
z
e
σ
2
=
1
,
γ
=
[
1
,
1
,
1
…1
]
,
a
,
b
,
c
,
d
p
a
r
a
me
t
e
r
s,
μ
m
in
&
D
O
A
se
a
r
c
h
g
r
i
d
.
2.
Γ
=
d
i
a
g
(
γ
1
−
1
,
γ
2
−
1
…
.
.
γ
N
−
1
)
3.
Est
i
m
a
t
e
Σ
x
=
(
σ
−
2
A
T
A
+
Γ
)
−
1
4.
Est
i
m
a
t
e
μ
=
σ
−
2
Σ
x
A
T
Y
=
[
μ
1
(
1
)
μ
1
(
2
)
⋯
μ
1
(
L
)
⋮
⋱
⋮
μ
N
(
1
)
μ
N
(
2
)
⋯
μ
N
(
L
)
]
5.
U
p
d
a
t
e
γ
i
ne
w
=
(
μ
i
2
+
2b
)
γ
i
γ
i
−
Σ
x
i
i
+
2a
γ
i
&
σ
2
(
ne
w
)
=
‖
y
−
A
μ
‖
2
+
2d
N
−
∑
(
1
−
N
i
=
1
γ
i
−
1
Σ
x
i
i
)
+
2c
6.
D
e
t
e
r
mi
n
e
μ
x
=
[
|
μ
1
(
1
)
|
2
+
|
μ
1
(
2
)
|
2
…
+
|
μ
1
(
L
)
|
2
|
μ
2
(
1
)
|
2
+
|
μ
2
(
2
)
|
2
…
+
|
μ
2
(
L
)
|
2
⋮
|
μ
N
(
1
)
|
2
+
|
μ
N
(
2
)
|
2
…
+
|
μ
N
(
L
)
|
2
]
7.
I
f
a
n
y
r
o
w
o
f
μ
x
i
s
l
e
ss t
h
a
n
a
t
h
r
e
sh
o
l
d
μ
m
in
,
t
h
e
n
e
q
u
a
t
e
t
h
e
r
o
w
o
f
μ
x
t
o
z
e
r
o
a
n
d
d
e
l
e
t
e
t
h
e
p
a
r
t
i
c
u
l
a
r
c
o
r
r
e
sp
o
n
d
i
n
g
c
o
l
u
m
n
i
n
A
mat
r
i
x
f
o
r
t
h
e
n
e
x
t
i
t
e
r
a
t
i
o
n
.
8.
R
e
p
e
a
t
f
r
o
m st
e
p
2
t
o
s
t
e
p
7
u
n
t
i
l
a
s
t
o
p
p
i
n
g
c
r
i
t
e
r
i
o
n
i
s
a
c
h
i
e
v
e
d
.
9.
P
l
o
t
μ
x
v
/
s t
h
e
D
O
A
se
a
r
c
h
g
r
i
d
p
o
i
n
t
s
a
n
d
l
o
c
a
t
e
t
h
e
p
e
a
k
s
t
o
e
st
i
m
a
t
e
t
h
e
d
i
r
e
c
t
i
o
n
o
f
a
r
r
i
v
a
l
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
4
,
A
u
g
u
s
t 2
0
2
1
:
3
0
4
9
-
3058
3054
6.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
N
I
n
th
is
s
ec
tio
n
,
th
e
e
x
p
er
i
m
en
tal
r
esu
lts
o
f
t
h
e
p
r
o
p
o
s
e
d
alg
o
r
ith
m
is
p
r
ese
n
ted
f
o
r
d
if
f
er
en
t
co
n
d
itio
n
s
o
f
v
ar
io
u
s
al
g
o
r
it
h
m
ic
p
ar
a
m
eter
s
.
Fo
r
t
h
e
s
i
m
u
latio
n
o
f
th
e
al
g
o
r
ith
m
,
MA
T
L
A
B
R
2
0
1
3
a
p
latf
o
r
m
h
as
b
ee
n
u
tili
ze
d
.
T
h
e
s
i
m
u
latio
n
r
e
s
u
l
ts
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
ar
e
co
m
p
ar
ed
w
it
h
s
ta
n
d
ar
d
DO
A
esti
m
atio
n
alg
o
r
it
h
m
s
li
k
e
MU
SI
C
[
2
,
3
, 2
8
]
,
MV
DR
[
2
9
,
3
0
]
an
d
th
e
r
ec
en
t stan
d
ar
d
alg
o
r
ith
m
l
1
-
SVD
[
1
1
,
1
2
]
.
C
o
n
s
id
er
i
n
g
a
u
n
if
o
r
m
li
n
ea
r
ar
r
a
y
(
U
L
A
)
o
f
M=
1
0
0
n
u
m
b
er
o
f
ar
r
a
y
ele
m
en
ts
w
it
h
a
n
i
n
ter
-
ele
m
e
n
t
s
p
ac
i
n
g
o
f
λ
/2
,
w
h
er
e
λ
s
tan
d
s
f
o
r
w
av
e
len
g
t
h
o
f
th
e
r
ec
eiv
ed
s
i
g
n
al
as
s
u
m
ed
t
o
b
e
as
1
m
.
L
et
u
s
ass
u
m
e
a
s
i
n
g
le
s
ig
n
al
s
o
u
r
ce
tr
an
s
m
itted
f
r
o
m
a
f
ar
-
f
ield
w
it
h
a
d
ir
ec
tio
n
o
f
0
0
w
it
h
r
esp
ec
t
to
th
e
v
er
tical
n
o
r
m
al
a
x
is
h
av
in
g
an
a
n
g
u
l
ar
f
r
eq
u
en
c
y
o
f
2
0
π
r
/s
is
i
m
p
in
g
i
n
g
o
n
th
e
UL
A
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
co
n
s
id
er
s
a
s
et
o
f
o
n
-
g
r
id
p
o
in
ts
f
o
r
s
ea
r
ch
i
n
g
t
h
e
d
ir
ec
tio
n
o
f
t
h
e
ar
r
i
v
in
g
s
i
g
n
al
w
it
h
a
0
.
5
0
s
tep
-
s
ize.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
s
i
m
u
lat
ed
f
o
r
L
=5
0
0
n
u
m
b
er
o
f
s
n
ap
s
h
o
ts
i
n
a
n
o
is
y
en
v
ir
o
n
m
e
n
t
w
it
h
S
NR
o
f
3
0
d
B
.
T
h
e
h
y
p
er
p
ar
am
eter
u
p
d
ati
n
g
d
ep
en
d
s
o
n
th
e
h
y
p
er
p
r
io
r
p
ar
am
eter
s
(
a,
b
,
c,
d
)
.
T
h
ese
p
ar
am
eter
s
h
ig
h
l
y
in
f
lu
e
n
ce
t
h
e
D
O
A
est
i
m
a
tio
n
r
es
u
lts
as
s
h
o
w
n
i
n
Fi
g
u
r
e
1
.
Fo
r
ab
cd
-
p
ar
am
eter
v
alu
e
s
eq
u
al
to
ze
r
o
,
th
e
DO
A
esti
m
atio
n
p
ea
k
i
s
les
s
s
teep
w
h
en
co
m
p
ar
ed
to
th
e
e
s
t
i
m
atio
n
p
ea
k
o
b
tain
ed
f
o
r
ab
cd
-
p
ar
a
m
eter
s
eq
u
a
l
to
0
.
4
.
I
t
is
also
test
ed
w
ith
v
a
r
io
u
s
o
th
er
v
al
u
es
o
f
a,
b
,
c,
d
an
d
f
o
u
n
d
th
at
f
o
r
all
0
<a
,
b
,
c,
d
<0
.
5
g
iv
es
s
teep
est
esti
m
atio
n
p
ea
k
s
co
n
tain
i
n
g
m
ax
i
m
u
m
p
ea
k
o
n
l
y
at
t
h
e
a
ctu
al
a
n
g
le
o
f
ar
r
iv
al
o
f
t
h
e
r
ec
eiv
ed
s
i
g
n
al
a
n
d
co
m
p
lete
l
y
f
lat
r
esp
o
n
s
e
f
o
r
a
n
y
o
t
h
er
g
r
id
p
o
in
ts
.
T
h
e
v
er
y
h
ig
h
v
al
u
e
s
et
f
o
r
a,
b
,
c,
d
in
cr
e
ases
t
h
e
s
p
ar
s
it
y
i
n
th
e
e
s
ti
m
ated
r
es
u
lts
an
d
i
n
s
o
m
e
ca
s
es
w
i
th
w
ea
k
s
i
g
n
al
s
tr
en
g
t
h
,
t
h
e
ac
t
u
al
tr
u
e
DO
A
s
al
s
o
m
a
y
n
o
t
co
n
ta
i
n
th
e
est
i
m
a
tio
n
p
ea
k
s
.
He
n
ce
th
e
r
an
g
e
o
f
0
<a
,
b
,
c,
d
<0
.
5
is
t
h
e
o
p
ti
m
i
ze
d
o
p
tio
n
f
o
r
DOA
e
s
ti
m
atio
n
ap
p
licatio
n
.
Fig
u
r
e
1
.
DOA
e
s
ti
m
atio
n
f
o
r
v
ar
io
u
s
h
y
p
er
p
r
io
r
p
ar
am
eter
s
A
ll
t
h
e
n
e
x
t
a
n
al
y
s
i
s
co
n
s
id
er
s
ab
cd
-
p
ar
a
m
eter
s
as
0
.
4
.
C
o
n
s
id
er
in
g
M=
1
0
,
n
u
m
b
er
o
f
s
ea
r
ch
g
r
i
d
p
o
in
ts
as
N=
3
6
1
,
L
=1
0
0
,
n
u
m
b
er
o
f
s
i
g
n
a
l
s
o
u
r
ce
s
D=
3
w
it
h
ac
t
u
al
tr
u
e
DO
A
s
a
s
-
10
0
,
1
0
0
,
6
4
0
w
it
h
co
r
r
esp
o
n
d
in
g
an
g
u
lar
f
r
eq
u
e
n
cies
o
f
2
0
π,
4
0
π,
6
0
π
r
/s
r
esp
ec
tiv
el
y
an
d
a
n
o
i
s
y
e
n
v
i
r
o
n
m
e
n
t
w
it
h
SN
R
0
d
B
.
Fig
u
r
e
2
s
h
o
w
s
th
e
DO
A
e
s
ti
m
atio
n
p
ea
k
s
f
o
r
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
as
w
ell
a
s
v
ar
io
u
s
s
tan
d
ar
d
DO
A
esti
m
atio
n
al
g
o
r
ith
m
s
.
I
t
ca
n
b
e
o
b
s
er
v
ed
th
at
t
h
o
u
g
h
t
h
e
v
alu
e
o
f
S
NR
i
s
v
er
y
le
s
s
(
i.
e,
th
e
w
o
r
s
t
n
o
is
y
en
v
ir
o
n
m
e
n
t)
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
h
o
w
s
s
h
ar
p
DO
A
est
i
m
atio
n
p
ea
k
s
at
t
h
e
ac
tu
a
l tr
u
e
DOAs.
Fo
r
th
e
s
a
m
e
p
ar
a
m
etr
ic
co
n
d
itio
n
s
,
co
n
s
id
er
i
n
g
a
s
i
n
g
le
s
n
ap
s
h
o
t
ca
s
e
w
it
h
L
=1
also
g
iv
e
s
s
h
ar
p
DO
A
esti
m
atio
n
p
ea
k
s
in
d
ic
atin
g
th
e
ac
t
u
al
tr
u
e
DO
As
w
it
h
1
0
0
%
s
u
cc
es
s
r
ate
as
s
h
o
w
n
i
n
Fig
u
r
e
3
.
Fig
u
r
e
4
in
d
icate
s
th
e
esti
m
atio
n
ca
s
e
f
o
r
th
e
n
u
m
b
er
o
f
ar
r
a
y
ele
m
e
n
ts
M=
1
0
0
,
w
h
ich
s
h
o
w
s
th
at
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
p
er
f
o
r
m
a
n
ce
is
a
l
m
o
s
t
s
i
m
ilar
to
t
h
at
f
o
r
M=
1
0
w
i
th
r
e
s
p
ec
t
to
m
ea
n
s
q
u
ar
e
er
r
o
r
.
I
n
th
e
ca
s
e
o
f
v
er
y
clo
s
el
y
s
p
ac
ed
s
o
u
r
ce
s
ig
n
al
s
w
ith
ac
t
u
al
tr
u
e
DO
A
o
f
1
0
0
an
d
1
1
0
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
till
p
r
o
d
u
ce
s
s
teep
er
p
ea
k
s
w
it
h
clea
r
d
is
ti
n
g
u
is
h
ed
D
O
A
p
ea
k
s
as
co
m
p
ar
ed
to
o
th
er
s
ta
n
d
ar
d
alg
o
r
ith
m
s
a
s
s
h
o
w
n
in
F
ig
u
r
e
5.
Fig
u
r
e
6
in
d
icate
th
e
ca
s
e
o
f
v
er
y
clo
s
e
l
y
s
p
ac
ed
t
w
o
c
o
h
er
en
t
s
i
g
n
al
s
o
u
r
ce
s
w
it
h
an
an
g
u
lar
f
r
eq
u
en
c
y
o
f
2
0
π
r
/s
an
d
lo
ca
ted
at
0
0
an
d
1
0
.
T
h
e
r
esu
lt
i
n
Fig
u
r
e
6
ex
h
ib
it
s
t
h
e
h
i
g
h
-
r
es
o
l
u
tio
n
p
er
f
o
r
m
an
c
e
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
c
o
m
p
ar
ed
to
th
e
o
th
er
alg
o
r
ith
m
s
.
As
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
e
m
p
lo
y
s
th
e
p
r
o
b
a
b
ilit
y
o
f
t
h
e
m
ea
s
u
r
ed
a
n
ten
n
a
ar
r
a
y
s
ig
n
al
b
y
k
n
o
w
i
n
g
t
h
e
p
r
io
r
o
f
u
n
k
n
o
w
n
s
,
g
o
o
d
r
eso
lu
tio
n
,
e
v
e
n
f
o
r
co
h
er
en
t
s
i
g
n
al
s
o
u
r
ce
s
ar
e
o
b
t
ain
ed
.
T
h
e
ef
f
ec
t
o
f
ar
r
ay
s
e
n
s
o
r
n
o
is
e
ad
d
ed
u
p
w
ith
th
e
r
ec
eiv
ed
s
i
g
n
a
l
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I
n
t J
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lec
&
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m
p
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g
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SS
N:
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8
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n
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r
n
in
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ch
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r
s
p
a
r
s
e
DOA
esti
ma
tio
n
b
a
s
ed
o
n
ma
ximu
m
-
a
-
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teri
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3055
f
o
r
h
y
p
er
p
r
io
r
p
ar
am
eter
s
a,
b
,
c,
d
=0
is
as
s
h
o
w
n
i
n
Fi
g
u
r
e
7
.
C
o
n
s
id
er
in
g
L
=5
0
,
M=
1
0
0
an
d
a
s
in
g
le
s
o
u
r
ce
s
ig
n
al
w
it
h
ac
tu
al
tr
u
e
DO
A
o
f
0
0
,
th
e
DO
A
p
ea
k
b
ec
o
m
e
s
m
o
r
e
s
teep
er
alo
n
g
w
i
th
d
ec
r
ea
s
e
in
m
ea
n
s
q
u
ar
e
er
r
o
r
f
o
r
th
e
im
p
r
o
v
e
m
e
n
t in
S
NR
v
al
u
e.
Fig
u
r
e
2
.
DOA
e
s
ti
m
atio
n
f
o
r
L
=1
0
0
Fig
u
r
e
3
.
DOA
e
s
ti
m
atio
n
f
o
r
L
=1
Fig
u
r
e
4
.
DOA
e
s
ti
m
atio
n
f
o
r
M=
1
0
0
Fig
u
r
e
5
.
DOA
e
s
ti
m
atio
n
f
o
r
v
er
y
clo
s
el
y
s
p
ac
ed
s
o
u
r
ce
s
i
g
n
al
s
Fig
u
r
e
6
.
DOA
e
s
ti
m
atio
n
f
o
r
v
er
y
clo
s
el
y
s
p
ac
ed
co
h
er
en
t so
u
r
ce
s
ig
n
al
s
Fig
u
r
e
7
.
E
f
f
ec
t o
f
SN
R
o
n
D
OA
e
s
ti
m
atio
n
p
ea
k
s
-
1
0
0
-
8
0
-
6
0
-
4
0
-
2
0
0
20
40
60
80
100
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
s
p
a
t
i
a
l
a
n
g
l
e
s
e
a
r
c
h
g
r
i
d
(
d
e
g
r
e
e
s
)
n
o
r
m
a
l
i
z
e
d
r
e
c
e
i
v
e
d
s
i
g
n
a
l
p
o
w
e
r
S
p
a
t
i
a
l
S
p
e
c
t
r
u
m
:
D
O
A
E
s
t
i
m
a
t
i
o
n
p
e
a
k
s
S
N
R
=
-
1
0
d
B
S
N
R
=
0
d
B
S
N
R
=
1
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d
B
S
N
R
=
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d
B
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I
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&
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o
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11
,
No
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4
,
A
u
g
u
s
t 2
0
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1
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3
0
4
9
-
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3056
Fig
u
r
e
8
s
h
o
w
s
th
e
e
f
f
ec
t
o
f
n
u
m
b
er
o
f
s
n
ap
s
h
o
ts
‘
L
’
o
n
t
h
e
DO
A
esti
m
atio
n
p
ea
k
s
f
o
r
S
NR
=1
0
d
B
,
M=
1
0
0
an
d
ac
tu
al
tr
u
e
DOA
o
f
0
0
.
A
s
th
e
n
u
m
b
er
o
f
s
n
a
p
s
h
o
ts
i
n
cr
ea
s
es,
t
h
e
DO
A
p
ea
k
s
b
ec
o
m
e
m
o
r
e
s
teep
er
w
it
h
b
etter
p
er
f
o
r
m
an
ce
.
Fo
r
th
e
ca
s
e
o
f
in
cr
ea
s
e
i
n
n
u
m
b
er
o
f
ar
r
ay
ele
m
e
n
ts
i
n
th
e
U
L
A
,
th
e
DO
A
esti
m
atio
n
p
er
f
o
r
m
a
n
ce
i
n
cr
ea
s
es a
lo
n
g
w
it
h
t
h
e
in
cr
ea
s
e
i
n
esti
m
atio
n
s
u
cc
e
s
s
r
ate
as s
h
o
w
n
i
n
Fi
g
u
r
e
9.
Fig
u
r
e
8
.
E
f
f
ec
t o
f
s
n
ap
s
h
o
t
s
o
n
DO
A
est
i
m
a
tio
n
p
ea
k
s
Fig
u
r
e
9
.
E
f
f
ec
t o
f
ar
r
a
y
s
ize
M
Fo
r
a
s
in
g
le
s
o
u
r
ce
ar
r
iv
in
g
at
ac
tu
al
tr
u
e
DO
A
o
f
0
0
w
i
th
L
=5
0
an
d
M=
1
0
0
,
th
e
p
e
r
f
o
r
m
an
c
e
an
al
y
s
is
o
f
v
ar
io
u
s
s
ta
n
d
ar
d
a
lg
o
r
ith
m
s
co
m
p
ar
ed
w
i
th
th
e
p
r
o
p
o
s
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t
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d
en
co
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r
ag
e
m
e
n
t.
RE
F
E
R
E
NC
E
S
[1
]
X
.
Zh
a
n
g
a
n
d
R.
Ca
o
,
“
Dire
c
ti
o
n
o
f
A
rri
v
a
l
Esti
m
a
ti
o
n
:
In
tr
o
d
u
c
ti
o
n
,
”
W
il
e
y
En
c
y
c
lo
p
e
d
i
a
o
f
El
e
c
trica
l
a
n
d
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e
c
tro
n
ics
En
g
in
e
e
rin
g
,
2
0
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d
o
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/
0
4
7
1
3
4
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0
8
X
.
W
8
3
4
3
.
[2
]
M
.
De
v
e
n
d
ra
a
n
d
K.
M
a
n
ju
n
a
th
a
c
h
a
ri,
“
DO
A
e
sti
m
a
ti
o
n
o
f
a
s
y
st
e
m
u
sin
g
M
USIC
m
e
th
o
d
,
”
2
0
1
5
In
t
.
Co
n
f
.
o
n
S
ig
n
a
l
Pro
c
e
ss
in
g
a
n
d
C
o
mm
u
.
E
n
g
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e
.
S
y
s
t
,
G
u
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t
u
r
,
2
0
1
5
,
p
p
.
3
0
9
–
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1
3
,
d
o
i:
1
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1
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0
9
/S
P
A
CES
.
2
0
1
5
.
7
0
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8
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7
2
.
[3
]
R.
O.
S
c
h
m
id
t,
“
M
u
lt
ip
le em
it
ter
lo
c
a
ti
o
n
a
n
d
sig
n
a
l
p
a
ra
m
e
ter e
stim
a
ti
o
n
,
”
IEE
E
T
ra
n
s.
An
te
n
n
a
s P
ro
p
a
g
,
v
o
l.
3
4
,
n
o
.
3
,
p
p
.
2
7
6
–
2
8
0
,
M
a
r.
1
9
8
6
.
[4
]
Y.
Ga
o
,
W
.
Ch
a
n
g
,
Z.
Pe
i,
a
n
d
Z.
W
u
,
“
A
n
I
m
p
ro
v
e
d
M
u
sic
A
lg
o
r
it
h
m
f
o
r
DO
A
Esti
m
a
ti
o
n
o
f
Co
h
e
re
n
t
S
ig
n
a
ls
,
”
S
e
n
so
rs
a
n
d
T
ra
n
sd
u
c
e
rs
,
v
o
l.
1
7
5
,
p
p
.
75
–
82
,
J
u
l
.
2
0
1
4
.
[5
]
R.
K an
d
P
.
K.
N,
“
P
e
rf
o
rm
a
n
c
e
Ev
a
lu
a
ti
o
n
&
A
n
a
l
y
sis o
f
Dire
c
ti
o
n
o
f
A
rriv
a
l
E
sti
m
a
ti
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n
A
lg
o
rit
h
m
s u
sin
g
ULA
,
”
2
0
1
8
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
El
e
c
trica
l,
El
e
c
tro
n
ics
,
Co
mm
u
n
ica
ti
o
n
,
Co
m
p
u
ter
,
a
n
d
Op
ti
miza
ti
o
n
T
e
c
h
n
iq
u
e
s (
ICEE
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,
M
sy
u
ru
,
I
n
d
ia,
2
0
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8
,
p
p
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1
4
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7
–
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4
7
3
,
d
o
i:
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0
.
1
1
0
9
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ECCOT
4
3
7
2
2
.
2
0
1
8
.
9
0
0
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4
5
5
.
[6
]
H.
Krim
a
n
d
M
.
Vib
e
rg
,
“
Tw
o
De
c
a
d
e
s
o
f
A
rra
y
S
ig
n
a
l
P
ro
c
e
ss
in
g
Re
s
e
a
rc
h
:
T
h
e
P
a
ra
m
e
tri
c
A
p
p
r
o
a
c
h
,
”
IEE
E
S
ig
n
a
l
Pro
c
e
ss
in
g
M
a
g
a
zin
e
,
v
o
l
.
1
3
,
n
o
.
4
,
p
p
.
6
7
–
9
4
,
Ju
l
.
1
9
9
6
.
[7
]
Z
.
Ya
n
g
,
J
.
L
i,
P
.
S
to
ica
,
a
n
d
L
.
X
ie,
“
S
p
a
rse
M
e
th
o
d
s
f
o
r
Di
re
c
ti
o
n
o
f
A
rriv
a
l
Esti
m
a
ti
o
n
,
”
Aca
d
e
mic
Pre
ss
L
ib
ra
ry
i
n
S
ig
n
a
l
Pro
c
e
ss
in
g
,
v
o
l.
7
,
p
p
.
5
0
9
–
5
8
1
,
2
0
1
8
.
[8
]
A
.
A
ich
a
n
d
P
.
P
a
lan
isa
m
y
,
“
On
-
g
rid
DO
A
e
sti
m
a
ti
o
n
m
e
th
o
d
u
s
in
g
o
rth
o
g
o
n
a
l
m
a
tch
in
g
p
u
rsu
it
,
”
In
t
.
Co
n
f
.
o
n
S
ig
n
a
l
Pro
c
e
ss
in
g
a
n
d
C
o
mm
u
n
ica
ti
o
n
(
ICS
PC)
,
2
0
1
7
,
p
p
.
4
8
3
–
4
8
7
,
d
o
i:
1
0
.
1
1
0
9
/CS
P
C
.
2
0
1
7
.
8
3
0
5
8
9
6
.
[9
]
N.
M
o
u
ra
d
,
M
.
S
h
a
rk
a
s
,
a
n
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.
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w
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IEE
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q
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D.
M
a
li
o
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,
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.
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ti
n
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a
n
d
A
.
S
.
W
il
lsk
y
,
“
A
sp
a
rse
si
g
n
a
l
re
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stru
c
ti
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n
p
e
rsp
e
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so
r
a
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y
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
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g
n
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l
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e
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2
]
F
.
L
iu
,
L
.
P
e
n
g
,
M
.
W
e
i,
P
.
Ch
e
n
,
a
n
d
S
.
G
u
o
,
“
A
n
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m
p
ro
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l1
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a
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o
rit
h
m
b
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se
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su
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sp
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,
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Pro
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In
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e
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tro
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9
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p
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–
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0
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.
[1
3
]
Ra
g
h
u
K
.
a
n
d
P
ra
m
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e
la
K
.
N
.
,
“
On
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rid
A
d
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p
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v
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ss
iv
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n
sin
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ter
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d
DO
A
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m
a
ti
o
n
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y
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m
p
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g
S
in
g
u
lar
V
a
lu
e
De
c
o
m
p
o
siti
o
n
,
”
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ter
n
a
ti
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n
a
l
J
o
u
r
n
a
l
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In
n
o
v
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ti
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e
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,
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no
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p
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,
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0
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9.
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4
]
S
.
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Y.
X
u
e
,
a
n
d
L
.
Ca
ri
n
,
“
Ba
y
e
sia
n
Co
m
p
re
ss
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S
e
n
sin
g
,
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in
I
EE
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T
ra
n
sa
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ti
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5
]
S
.
D.
Ba
b
a
c
a
n
,
R.
M
o
li
n
a
,
a
n
d
A
.
K.
Ka
tsa
g
g
e
lo
s,
“
Ba
y
e
sia
n
Co
m
p
re
ss
iv
e
S
e
n
sin
g
Us
in
g
Lap
lac
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P
rio
rs,
”
in
IEE
E
T
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sa
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ti
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s
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.
[1
6
]
J.
H.
En
d
e
r,
“
On
c
o
m
p
re
ss
iv
e
se
n
sin
g
a
p
p
li
e
d
to
ra
d
a
r,
”
S
i
g
n
a
l
Pro
c
e
ss
in
g
,
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o
l.
9
0
,
n
o
.
5
,
p
p
.
1
4
0
2
–
1
4
1
4
,
2
0
1
0
.
[1
7
]
J.
Ga
u
v
a
in
a
n
d
C.
H.
L
e
e
,
“
M
a
x
im
u
m
a
p
o
ste
rio
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e
stim
a
ti
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n
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o
r
m
u
lt
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a
riate
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a
u
ss
ian
m
i
x
tu
re
o
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se
rv
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s
o
f
M
a
rk
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v
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h
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in
s,
”
in
IE
EE
T
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n
s
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d
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s
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o
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2
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p
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2
9
1
–
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9
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9
9
4
.
[1
8
]
X
.
Zh
a
n
g
,
M.
e
l
K
o
rso
,
a
n
d
M
.
P
e
sa
v
e
n
to
,
“
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a
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im
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m
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h
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o
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a
n
d
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m
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ti
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re
se
n
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f
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I
RP
No
ise
,
”
2
0
1
6
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EE
I
n
ter
n
a
t
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o
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l
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e
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u
stics
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h
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n
d
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ig
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0
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4
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2
4
4
.
[1
9
]
M
.
E
.
T
ip
p
in
g
,
“
S
p
a
rse
Ba
y
e
si
a
n
L
e
a
rn
in
g
a
n
d
th
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Re
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n
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V
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a
c
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e
,
”
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o
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l
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f
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a
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e
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e
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rn
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g
Res
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a
rc
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,
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l.
1
,
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p
.
2
1
1
–
2
4
4
,
2
0
0
1
.
[2
0
]
D.
P
.
W
ip
f
a
n
d
B.
D.
Ra
o
,
“
S
p
a
rse
Ba
y
e
sia
n
lea
rn
in
g
f
o
r
b
a
sis se
l
e
c
ti
o
n
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
S
i
g
n
a
l
Pr
o
c
e
ss
in
g
,
v
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l.
5
2
,
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o
.
8
,
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p
.
2
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5
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8
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6
.
[2
1
]
Z.
Zh
a
n
g
a
n
d
B.
D.
Ra
o
,
“
S
p
a
r
se
S
ig
n
a
l
Re
c
o
v
e
r
y
W
it
h
T
e
m
p
o
ra
ll
y
Co
rre
late
d
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o
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rc
e
V
e
c
to
r
s
Us
in
g
S
p
a
rse
Ba
y
e
sia
n
L
e
a
rn
in
g
,
”
in
IEE
E
J
o
u
rn
a
l
o
f
S
e
lec
ted
T
o
p
ics
in
S
i
g
n
a
l
Pro
c
e
ss
in
g
,
v
o
l
.
5
,
n
o
.
5
,
p
p
.
9
1
2
–
9
2
6
,
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e
p
.
2
0
1
1
,
d
o
i:
1
0
.
1
1
0
9
/J
S
T
S
P
.
2
0
1
1
.
2
1
5
9
7
7
3
.
[2
2
]
Z.
Zh
a
n
g
a
n
d
B.
D.
Ra
o
,
“
Ex
ten
si
o
n
o
f
S
BL
A
lg
o
rit
h
m
s
f
o
r
th
e
Re
c
o
v
e
r
y
o
f
Blo
c
k
S
p
a
rse
S
ig
n
a
ls
W
it
h
In
tra
-
Blo
c
k
Co
rre
latio
n
,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
i
g
n
a
l
Pro
c
e
ss
in
g
,
v
o
l.
6
1
,
n
o
.
8
,
p
p
.
2
0
0
9
–
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0
1
5
,
A
p
r
.
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0
1
3
,
d
o
i:
1
0
.
1
1
0
9
/T
S
P
.
2
0
1
3
.
2
2
4
1
0
5
5
.
[2
3
]
N.
Hu
,
B.
S
u
n
,
J.
W
a
n
g
,
a
n
d
J.
Ya
n
g
,
“
Co
v
a
rian
c
e
-
b
a
se
d
DO
A
e
stim
a
ti
o
n
f
o
r
w
id
e
b
a
n
d
sig
n
a
ls
u
sin
g
jo
in
t
sp
a
rse
Ba
y
e
sia
n
lea
rn
in
g
,
”
IEE
E
In
t
.
Co
n
f
.
o
n
S
i
g
n
a
l
Pro
c
e
ss
in
g
,
C
o
mm
u
.
a
n
d
Co
m
p
u
t
in
g
2
0
1
7
,
p
p
.
1
–
5
.
[2
4
]
Z.
M
.
L
iu
,
Z.
T
.
Hu
a
n
g
,
a
n
d
Y.
Y
.
Zh
o
u
,
“
Dire
c
ti
o
n
-
of
-
a
rriv
a
l
e
stim
a
ti
o
n
o
f
w
id
e
b
a
n
d
sig
n
a
ls v
ia co
v
a
rian
c
e
m
a
tri
x
sp
a
rse
re
p
re
se
n
tatio
n
,
”
IE
EE
T
r
a
n
s.
S
i
g
n
a
l
Pro
c
e
ss
,
v
o
l.
5
9
,
n
o
.
9
,
p
p
.
4
2
5
6
–
4
2
7
0
,
S
e
p
.
2
0
1
1
.
[2
5
]
Q.
Hu
a
n
g
,
G
.
Zh
a
n
g
,
a
n
d
Y.
F
a
n
g
,
“
DO
A
Esti
m
a
ti
o
n
U
sin
g
B
lo
c
k
V
a
riatio
n
a
l
S
p
a
rse
Ba
y
e
sia
n
L
e
a
rn
in
g
,
”
in
Ch
in
e
se
J
o
u
r
n
a
l
o
f
El
e
c
tro
n
ics
,
v
o
l.
2
6
,
n
o
.
4
,
p
p
.
7
6
8
–
7
7
2
,
2
0
1
7
,
d
o
i:
1
0
.
1
0
4
9
/cje
.
2
0
1
7
.
0
4
.
0
0
4
.
[2
6
]
A.
C.
F
a
u
l
a
n
d
M
.
E.
T
ip
p
i
n
g
,
“
An
a
ly
sis
o
f
sp
a
rse
Ba
y
e
sia
n
lea
rn
in
g
,
”
Ad
v
a
n
c
e
s
in
Ne
u
r
a
l
I
n
fo
rm
a
ti
o
n
Pro
c
e
ss
in
g
S
y
ste
ms
,
v
o
l.
1
4
,
p
p
.
3
8
3
–
3
8
9
,
2
0
0
2
.
[2
7
]
D.
J.
C.
M
a
c
Ka
y
,
“
Ba
y
e
sia
n
I
n
terp
o
lati
o
n
,
”
Ne
u
ra
l
C
o
mp
u
ta
t
io
n
,
v
o
l.
4
,
n
o
.
3
,
p
p
.
4
1
5
–
4
4
7
,
1
9
9
2
.
[2
8
]
J.
L
i,
Y.
He
,
L
.
He
,
a
n
d
X
.
Zh
a
n
g
,
“
DO
D
a
n
d
DO
A
e
sti
m
a
ti
o
n
f
o
r
M
IM
O
ra
d
a
r
b
a
se
d
o
n
c
o
m
b
in
e
d
M
USIC
a
n
d
sp
a
rse
Ba
y
e
si
a
n
lea
rn
in
g
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