Digital Signal Processing Reference
In-Depth Information
Fig. 10.10
The structure of
the external archive [
32
]
10.4.3.2 Computation of Cost Function
After the propagation and measurement update, the cost function,
f
j
k
, is calculated
as the square error between the real measurement,
z
k
, and the
j
th estimated output,
z
j
k
. Therefore, the cost assigned to sample
j
at time
k
is defined as follows:
f
k
=
z
k
−
z
k
T
z
k
−
z
k
.
(10.20)
The propagated samples in the archive are sorted according to their cost in as-
cending order, i.e.,
f
k
≤
f
k
≤···≤
f
k
.
10.4.3.3 External Archive Update
In this method,
N
best solutions are stored in an external archive. The structure of
this archive is shown in Fig.
10.10
. During any iteration of the inner loop at time
k
,
M
new solutions (i.e.,
x
k
,
j
=
1
,...,M
) found by ants will be added to the archive.
Therefore, there will be
M
N
ants within the archive. To limit the archive length,
M
worst solutions from the total
M
+
+
N
solutions are then removed and
N
top
solutions are retained.
10.4.3.4 Pheromone Update
Each ant uses
d
PDFs to perform
d
selections (corresponding to dimensions 1 to
d
) to make a complete solution
x
k
. Each PDF is defined using a weighted sum of
several Gaussian PDFs, defined as follows [
32
]:
exp
,
N
μ
i
)
2
2
(σ
i
)
2
1
σ
i
√
2
π
(x
−
G
i
(x)
=
ξ
j
−
−∞ ≤
x
≤+∞
(10.21)
j
=
1
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