Aerospace and Electronic Systems Magazine January 2018 - 45

Xu et al.

Figure 14.

Micromotion simulation of a cone target via finite motion parameters. (a) Rotation. (b) Tumbling. (c) Procession. (d) Nutation.

GRFT/GFT can be defined in the future to improve target detection
and feature extraction in low SNR scenarios.

ULTRAHIGH-SPEED TARGETS
For the detection of the conventional air targets, radar normally
adopts narrowband matched filter based on narrowband assumption as 2vr / c << 1 / Tp B , where Tp, B, vr, and c represent pulse
duration, signal bandwidth, target's radial velocity, and the light
speed, respectively. That is, the scale effect, i.e., extension or conc + vr
traction in the duration of an echo with scale coefficient κ =
,
c − vr
can be ignored for this situation, and the echoes can be modeled as
the copies of transmitted pulses with the same pulse duration but
varied Doppler modulations. Nevertheless, the above assumption
may be violated for the detection of a far-range, ultrahigh-speed
space target. First, for far-range space search radar, the conventional microsecond-level duration will be enlarged to millisecond-level
to increase the echo energy [1-3]. Second, the GHz bandwidth has
been used to obtain high range resolution [1]. Third, high-speed
space targets, e.g. planet, satellite etc., may have a speed of tens
of Mach and far larger than conventional air targets. Let's take
a space target with vr = 3400m/s as an example. The two parts
2vr / c = 22.7 × 10−6and 1 / Tp B = 20 × 10−6 can be calculated for a

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JANUARY 2018

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space observation radar with B = 5 MHz and Tp = 10ms. Obviously,
the narrowband condition 2vr / c << 1 / Tp B cannot be satisfied in
this case. That is, the neglected scale effect should be effectively
compensated for the high-speed target detection. Furthermore, it
has been found in [39] that the conventional narrowband matched
filter may cause obvious performance loss on target detection
and parameter estimation due to the uncompensated scale effect.
Therefore, a wideband scaled Radon-Fourier transform (WSRFT)
[39] is proposed to jointly compensate the scale effect and realize
the long time coherent integration. That is, the scale effect caused
by high speed vr is compensated by WSRFT on the echo's duration
in accordance with the searched velocity.
To demonstrate the effectiveness of the proposed WSRFT, let's
take the results of ultrahigh-speed targets [34] in Figure 15 and
Figure 16 as an example. Figure 15(a) and Figure 15(b) show the
normalized gray-scale images of RFT and WSRFT outputs of five
orbit ultrahigh-speed targets in a formation on the range-velocity
plane, respectively. The range and velocity shifts can be observed
via RFT as Figure 15(a) without compensation of scale effect,
while all the peaks are precisely located at the targets' positions
via WSRFT as Figure 15(b). Also, Figure 16 shows the detection
c + vr
performance versus scale coefficient κ =
values. The dec − vr
tection performance of the RFT and WSRFT are almost identical

IEEE A&E SYSTEMS MAGAZINE

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