Digital Signal Processing Reference
In-Depth Information
some manipulations on the original form introduced in [
46
])
u
2
λ V(k,m
k
−
1
),P
D
,m
k
=
m
k
b(λ V(k,m
k
−
1
),P
D
)
c
n
z
(
2
π
1
g
2
)
n
z
/
2
P
G
m
k
+
n
z
g
n
z
m
k
I
2
λ V(k,m
k
−
1
),P
D
,m
k
(6.20)
1
n
z
×
where
I
2
(
·
,
·
,
·
)
and
b(
·
,
·
)
are defined in (
6.12
) and (
6.13
), respectively.
(ii)
Covariance Lumping:
N
{
Pr
m
k
}=
Pr
{
m
k
|
m
k
−
1
}
Pr
{
m
k
−
1
}
,
(6.21)
m
k
−
1
=
0
Pr
{
m
k
−
1
}
Pr
{
m
k
|
m
k
−
1
}
Pr
{
m
k
−
1
|
m
k
}=
,
(6.22)
{
m
k
}
Pr
N
P(k
0
P(k
|
k,m
k
)
=
|
k,m
k
−
1
,m
k
)
Pr
{
m
k
−
1
|
m
k
}
.
(6.23)
m
k
−
1
=
(iii)
Covariance Prediction:
P(k
F(k)P(k
k,m
k
)F
T
(k)
G(k)Q(k)G
T
(k).
+
1
|
k,m
k
)
=
|
+
(6.24)
(iv)
Output Covariance Calculation:
This is an optional part in the sense that it is
only for output purposes—it is not a part of the algorithm recursions:
N
P
HYCA
(k
|
k)
=
0
P(k
|
k,m
k
)
Pr
{
m
k
}
.
(6.25)
m
k
=
Similar to the MRE case, here, the output of the algorithm
P
HYCA
(k
|
k)
is a
deterministic approximation to the filter calculated covariance
P(k
|
k)
of the
PDAF.
6.3 NSPP-Based Detector Threshold Optimization
The NSPP techniques mentioned in the previous section have found several im-
portant application areas in the literature such as detector threshold optimization
[
20
,
22
,
48
], waveform optimization [
32
,
39
,
41
,
53
,
62
], multisensor tracking (as a
sensor selection criterion) [
52
,
54
,
55
], multitarget tracking (for the occlusion prob-
lem) [
36
], and multifunction radar resource allocation [
35
]. In this section, we focus
on the area of detector threshold optimization. We consider specifically the PDAF
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