Aerospace and Electronic Systems Magazine September 2017 - 55

Xu et al.

Figure 6.

Integration results with noise background. (a) MTD. (b) KT+MTD. (c) HT. (d) RFT.

threshold and peak searching. Nevertheless, it is found that GRFT
results will have a blunt response along acceleration. That is, the
response along acceleration has a broad mainlobe (Figures 7a and
7b). Therefore, it is not easy to discriminate multiple targets with
small acceleration differences.
To demonstrate the effectiveness of the proposed GRFT, some
real measured data are used for a near-range multiple target scenario. The main radar system parameters are identical to the previous simulations like those in Figure 6, but only the bandwidth is
reduced to 0.5 MHz. Figure 8a provides real measured data containing several moving targets with the obvious ARC effect in a
10-s observation time interval, and an obvious target called Target
1 is emphasized with a red ellipse. Figure 8b provides the result of
the MTD for Target 1, where the defocused response is generated
because of the uncompensated ARC effect of the moving target.
Figure 8c provides a three-dimensional (3D) result of the conventional MTD for Target 1, where a blunt peak is displayed. Figure 8d
provides a 3D result of the proposed second-order GRFT, and the
estimated motion parameters are compared in Table 1. Because the
Doppler ambiguity exists for Target 1, its estimated velocity by the
conventional MTD is ambiguous with one blind speed, i.e., about
200 m/s. On the contrary, the second GRFT can overcome the Doppler ambiguity and obtain accurate acceleration estimation, apart
from the range and radial velocities obtained by the MTD method.
What is more important is that because of the effective compensation of ARC and ADC, the peak of GRFT (Figure 8d) has about 12
SEPTEMBER 2017

dB SNR gain compared with the amplitudes of the MTD (Figure
8c).

MOTION PARAMETER ESTIMATION VIA GRFT,
GENERALIZED FOURIER TRANSFORM, OR
GENERALIZED RADON TRANSFORM
Apart from target detection, estimating target motion parameters,
e.g., range, velocity, and acceleration, as accurately as possible is
also the basic function of radar. It is then interesting to ask what the
optimal method and the inherent accuracy limitations are for motion
estimation of a radar maneuvering target. To answer these questions,
the optimal methods should be discussed for different kinds of radars. Some radar may have envelope-only or phase-only measurement, which are different from most coherent radars with the joint
envelope and phase measurement. For the former, the first example
is the early magnetron-based noncoherent radar, whose phase is affected by the uncertain pulse-by-pulse initial phase modulations.
The second case is the ISAR range alignment, which normally compensates for the target's unknown translational motion via envelope
shifting of high-resolution range profiles (HRRPs). For the latter,
there are also two typical examples. First, continuous wave (CW)
radar normally measures a vehicle's motions based on phase-only information. Second, some searching radar, e.g., over-the-horizon radar (OTHR) [8], has extremely low range resolution and the targets

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Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine September 2017