Graphics Programs Reference
In-Depth Information
1.5
1
0.5
0
-0 .5
-1
-1 .5
-4
-3
-2
-1
0
1
2
3
4
A ngle - radians
Figure 9.12c. Difference pattern corresponding to Fig. 9.12a.
The difference channels give us an indication of whether the target is on or
off the tracking axis. However, this signal amplitude depends not only on the
target angular position, but also on the targetÓs range and RCS. For this reason
the ratio (delta over sum) can be used to accurately estimate the error
angle that only depends on the targetÓs angular position.
∆Σ
⁄
Let us now address how the error signals are computed. First, consider the
azimuth error signal. Define the signals
S
1
and
S
2
as
S
1
=
AD
+
(9.9)
S
2
=
BC
+
(9.10)
The sum signal is , and the azimuth difference signal is
. If , then both channels have the same phase (since
the sum channel is used for phase reference). Alternatively, if , then the
two channels are out of phase. Similar analysis can be done for the ele-
vation channel, where in this case
Σ
S
1
=
+
S
2
∆
az
=
S
1
S
2
S
1
≥
S
2
0°
S
1
<
S
2
180°
S
1
=
AB
+
and
S
2
=
DC
+
. Thus, the
error signal output is
∆
Σ
ε
ϕ
=
------
cos
ξ
(9.11)
where
ξ
is the phase angle between the sum and difference channels and it is
equal to
0°
or
180°
. More precisely, if
ξ
=
0
, then the target is on the track-
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