Digital Signal Processing Reference
In-Depth Information
Step 2:
Predict the detection result of each cell using (5), and calculate the corres-
ponding information gain using (6);
Step 3:
Select the cell
i
(
t
) with the maximal information gain to make the observa-
tion, and get the detection result {
z
(
t
),
i
(
t
)};
Step 4:
Produce a new beta distribution using (16) to update the probability densities
of
P
d
and
P
f
;
Step 5:
Let
. If
, then the algorithm ends, otherwise return to
Step 1
.
t
=
t
+
1
t
>
T
4
Simulation Result and Analysis
In the simulation, the sensor searches a static target within a 3×3 cell grid. The true
value of the detection probability and the false alarm probability are 0.8 and 0.2
which both are unknown. The prior target distribution probability of each cell is[8]
()
{
()
}
{
}
π
0
=
π
0 ,
k
=
1, 2,..., 9
=
0.065 ,0.11, 0.065, 0.11 ,0.30, 0.11, 0.065, 0.11, 0.065
k
Without loss of generality, assume that the true
position of the target is in the center cell of the
search region, the fifth cell. Now two kind of search
method are selected. For the first algorithm, the
sequence search method is adopted in which the
sensor searches each cell uniformly while the prob-
abilities of detection and false alarm are selected
artificially as 0.7 and 0.3 which denote the pessimis-
tic estimation of detection performance. The second
algorithm is based on the maximal information gain
with Shannon entropy and the beta distribution is
used to model the detection performance, and the
model parameters (
a
=14,
b
=6) and (
a
=6,
b
=14) are selected for the probabilities of
detection and false alarm, which average values are 0.7 and 0.3 respectively.
1
2
3
4
6
5
8
9
7
Fig. 1.
search region with 9 cells
0.9
6
prior distribution
sequence search method
proposed search method
initial PDF with (a=14,b=6)
updated PDF with 20 observations
0.8
4
0.7
2
0.6
0
0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P
d
0.4
6
initial PDF with (a=6,b=14)
updated PDF with 20 observations
0.3
4
0.2
2
0.1
0
0
1
2
3
4
5
6
7
8
9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P
f
Cell position number
Fig. 2.
Search results for two algorithms
Fig. 3.
PDF of
P
d
and
P
f
