Graphics Programs Reference
In-Depth Information
Processor Implementation And Simulated Results
The M
2
filter approach outlined in this section requires a very accurate track
of the centroid of the chaff cloud being probed. As described earlier, initiation
of track on the chaff cloud centroid is achieved with a MB range resolution
waveform (step 1). As an example, assume that an X-band radar (10 GHz) is
engaging one or more ballistic targets enveloped in a chaff cloud that contains
1 million dipoles occupying a 1-kilometer range extent. Assuming that the
chaff cloud velocity distribution can be accurately modeled by Gaussian statis-
tics, approximately 67% of these dipoles will reside in 333 meters of range
extent. With these assumptions, the combined average RCS of the dipoles
( ) contained within a radar range resolution cell of this length (333 m)
can be approximated by
RCS
D
0.18
N
D
λ
2
0.03
2
RCS
D
=
=
0.18
×
670 000
,
×
=
108.54
⇒
20.4
dBsm
(10.36)
The RCS of a typical ballistic Reentry Vehicle (RV) at forward aspect view-
ing angles can be
20
dBsm
or smaller. Therefore, the MB
C
chaff
⁄
S
for a typ-
ical RV enveloped by the chaff cloud assumed above can approach
40
dB
or
greater. Using an 8-msec pulsewidth and
30
dB C
chaff
⁄
S
, the theoretical, sin-
gle pulse, minimum rms track error is approximately
f
e
=
1
Hz
. At X-band
frequencies, this translates to a single pulse velocity error of
f
e
λ
2
v
e
=
-------
=
0.015
ms
⁄
(10.37)
Note that for a train of pulses, this velocity error can be reduced by a factor of
10 or more. Thus, for a typical X-band radar, theory suggests that the track pre-
cision of the chaff cloud centroid can approach 0.0015 m/s or better. This track
precision is much less than the WB range resolution capability of the radar and
therefore can be utilized to bootstrap the WB tracker (steps 2 and 3).
Assume a Gaussian chaff clutter velocity distribution and denote it . If
( relative to the cloud centroid velocity), the mini-
mum PRF required to meet the Nyquist sampling criterion is
v
g
v
g
=
1.8
ms
⁄
±
0.9
ms
⁄
2
v
g
λ
--------
PRF
=
f
r
≥
2
×
=
240
Hz
(10.38)
Also, assume that a bank of Doppler MTI's (step 4) can be formed to cover this
frequency range. Note that 256 is the closest 2
N
multiple for implementation
with the Fast Fourier Transform (FFT). Using a 256 point FFT design, each fil-
ter will contain approximately 1/256 of the total clutter velocities (about 0.03
m/s of velocity clutter per MTI Doppler filter). In addition, by utilizing the WB
track waveform, a very precise range-Doppler image can be formed (with each
range-Doppler resolution cell containing approximately 15 cm by 0.03 m/s of
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