Digital Signal Processing Reference
In-Depth Information
Fig. 6.3
Block diagrams of two offline covariance recursion algorithms for the PDAF: HYCA
[
46
] and MRE [
20
]. The corresponding output of each algorithm, denoted by
P
HYCA
(k
|
k)
and
P
MRE
(k
|
k)
, is a deterministic approximation to the filter calculated covariance,
P(k
|
k)
of the
PDAF
where
γ
G
is the
gate threshold
. Here,
1
)
is the measurement predicted by
the tracking filtering algorithm, which is in our case the PDAF, and
S(k)
is the co-
variance associated with the difference
z(k)
−
z(k
|
k
−
ˆ
z(k
|
k
−
1
)
, which is the
innovation
corresponding to the target-originated measurement.
•
Assuming that
λ(k)
and
V(k)
are the spatial clutter density and the volume of the
validation gate at time step
k
, respectively, the number of false measurements at
any time step
k
, denoted by
m
k
, is modeled as a random variable with probability
mass function (pmf)
μ
F
(m
k
;
λ(k)V(k))
where
μ
F
(m
;¯
m)
denotes the Poisson
pmf for the dummy variable
m
with mean
m
, i.e.,
¯
e
−
m
m
m
m
¯
μ
F
(m
;¯
m)
.
(6.4)
!
6.2.2 NSPP Techniques for the PDAF
There exist two NSPP algorithms proposed so far for the PDAF, namely, MRE [
20
]
and HYCA [
46
]. The block diagrams of these offline covariance recursion algo-
rithms are given in Fig.
6.3
. The steps of each algorithm are briefly summarized in
the following subsections.
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