5.1. Simulation Experiment
Firstly, the effectiveness of the algorithm is verified by the simulation of a single scattering point target. The simulation parameters are shown in
Table 2. At
, the position of the target is at the center of the scene, and the coordinate is
. This paper is mainly aimed at the ground vehicle target. In a synthetic aperture time, it can be considered that the motion characteristics of the scattering points of each part of the target are the same [
32]; that is, the speed and acceleration of each part are the same, and there is no rotational motion. Rotating target detection and parameter estimation can be found in the literature [
33,
34].
The target trajectory after range compression is shown in
Figure 5a. It can be seen from the figure that the target trajectory has serious range migration caused by the target movement. After Hough-SOKT and third-order term migration correction, the DCCF constructed by the proposed method is shown in
Figure 5b, the target energy is corrected for the same range cell. However, the peak position of the DCCF constructed by KT-CICPF is shifted by the range cell, and its peak energy is dispersed into three range cells, as shown in
Figure 5c. The reason for this problem is the coupling between DCCF and the range migration caused by insufficient range migration correction, which directly affects the extraction of the chirp signal of Equation (
24). The DCCF after third-order correction is shown in
Figure 5b. The amplitude and Doppler spectrum of
extracted by the two methods are shown as
Figure 5d,e. It can be seen that the amplitude gain of the signal extracted by the proposed method is stronger and the Doppler spectrum is smoother, which conforms to the ideal chirped signal. However, the amplitude and Doppler spectrum extracted by KT-CICPF fluctuate greatly.
Figure 5f,g show the
–
parameter plane constructed by the two methods. Inside the red rectangle is a local magnification of the peak position.
Figure 5h shows the slice along
in the
–
plane. It can be clearly seen that the peak of the parameter plane constructed by the proposed method is more significant, while the parameter plane generated by KT-CICPF is energy-dispersive.
Figure 5i,j show the imaging results of the two methods, respectively.
Figure 5k,l are slices of the imaging results in the range direction and azimuth direction. It can be seen from the figure that the proposed method has a better focus. However, in the contrasting method, the target occupies multiple range cells due to the residual range migration, which reduces the resolution of the target.
The parameter estimation results obtained by the two methods are shown in
Table 3. It can be seen that the parameter estimation accuracy of the proposed method is relatively high, while the parameter error estimated by KT-CICPF is relatively large. Especially for the estimated value of
, the error of the KT-CICPF method reaches 7.01%, while the maximum relative error of the parameters estimated by the proposed method is only 0.21%. Therefore, it can be concluded that the proposed method has better parameter estimation performance.
In addition, the focusing performance of the moving target is shown in
Table 4. The theoretical range resolution is
m. According to Equation (
5), the Doppler bandwidth of the moving target in the synthetic aperture time can be calculated. So, the theoretical azimuth resolution is
m. As can be seen from the table, the resolution obtained by the proposed method is closer to the theoretical value than that obtained by KT-CICPF method. The azimuth resolution of the KT-CICPF method has a maximum broadening of about 26.51%. The theoretical values of the peak sidelobe ratio (PSLR) and integrated sidelobe ratio (ISLR) are −13.27 and −10.24 dB [
10]. For the proposed method, the range and azimuth PSLR/ISLR values have small deviations from the theoretical values.
Figure 5i,j show the imaging results of the two methods, respectively.
Figure 5k,l are slices of the imaging results in the range direction and azimuth direction. It can be seen that the proposed method has a better focusing performance.
In high-resolution SAR images, the target is often composed of multiple pixels. In order to verify the ability of the algorithm to maintain the target geometry, this paper carried out the simulation analysis of moving targets with “cross” distribution (hereinafter referred to as T1) and “circular” distribution (hereinafter referred to as T2). T1 consists of 15 strong scattering points. The azimuth and range intervals between the scattering points are both 0.5 m, and the coordinate distribution is shown in
Figure 6a, where the red squares represent the positions of the scattering points. T2 is composed of 63 scattering points uniformly distributed on the circumference, and its coordinate distribution is shown in
Figure 6b. In
Figure 6, the abscissa is the slant range, and the ordinate is the azimuth coordinate.
Two methods are used to process it.
Figure 7 and
Figure 8 show the processing results of T1 and T2, respectively.
Figure 7a,d and
Figure 8a,d are the amplitude and spectrum of the chirp signal corresponding to the DCCF peak range cell, which are used to estimate the coefficient of the third-order term. The signal gain and resolution extracted in the proposed method are higher than those extracted by KT-CICPF.
Figure 8b,e are the
–
parameter planes constructed by the two methods for the target T2, respectively. From the figures, it can be seen that the peak in the
–
plane constructed by the proposed method is relatively concentrated and the coupling degree with range migration is small. The peak of the
–
plane constructed by the KT-CICPF is divergent. The reason for this phenomenon is that the residual range migration by the KT-CICPF method is larger, resulting in a large parameter estimation error. For the target T1,
Figure 8b,e illustrates the same phenomenon. In this paper, when constructing the
–
plane, Equation (
29) is used to compensate for the DCCF to reduce the influence of the third-order range migration on the
–
parameter plane.
Figure 7c,f and
Figure 8c,f show refocused results of the two methods. It can be seen that the imaging results of KT-CICPF methods are severely defocused in azimuth. The proposed method can better maintain the shape of the target.
5.2. Measured Experiment
In this paper, the real data collected by a four-channel airborne X-band SAR system are used to verify the performance of the proposed method. The system parameters are shown in
Table 5. The four channels are equally spaced in the azimuth direction, and the working mode of one-transmitter and four-receiver is adopted. In this paper, the target signal extracted after clutter suppression is imaged. The flight platform and cooperation targets are shown in
Figure 9a,b, respectively. There are three electric tricycles as cooperative targets in the experiment. Each target is equipped with a corner reflector, and a GPS device is installed to record the real-time position and speed information of the target as the true value of the target movement.
The imaging result of the stationary scene without processing of GMT is shown in
Figure 10a. The magnified images of T1–T3 are shown in
Figure 10b–d, respectively. As can be seen from the figure, targets moving along the radial direction are defocused and appear displaced in azimuth from their original position.
Taking the target T1 as an example, the processing results of each step of the proposed method are analyzed. The target signal after clutter suppression is shown in
Figure 11a.
Figure 11b,c are the two-dimensional time domain signal and range-Doppler domain signal after RCMC, respectively. It can be seen that the target energy is basically corrected to the same range cell after Hough-SOKT.
Figure 11d is the
–
parameter plane constructed by the proposed method, and
Figure 11e is the slice along
at the peak of the parameter plane obtained by the two methods. Obviously, the peak value obtained by the proposed method is larger, which verifies that the proposed method can can obtain higher coherent accumulation gain.
Figure 11f,g show the refocused results of T1 by two methods, the proposed method has better focusing.
Figure 11h,i are slices in the range and azimuth directions, from which it can be seen that the focusing of the target in the azimuth has been significantly improved. In
Figure 11f–i, the image is interpolated 16-fold in azimuth and range directions. The results verify that a better focusing performance can be obtained by the proposed method.
To verify the adaptability of the algorithm, the same processing is used for T2 and T3 as for T1.
Figure 12 shows the refocused results of the three targets by three methods. The magnified images of moving targets without processing of GMT are shown in
Figure 12a–c, respectively. The refocused results by the KT-CICPF method of T1–T3 are shown in
Figure 12d–f. The results by the proposed method are given in
Figure 12g–i. As can be seen from the figure, the focusing effect of the proposed method on T1–T3 is superior to that of KT-CICPF method.
In addition, the focusing performance of the moving target is shown in
Table 6. The theoretical range resolution is
m. According to the system parameters, the Doppler bandwidth in the synthetic aperture time is about 300 Hz. So, the theoretical azimuth resolution is
m. As can be seen from the table, the resolution obtained by the proposed method is closer to the theoretical value than that obtained by the KT-CICPF method. The azimuth resolution of the KT-CICPF method has a greater broadening. It is proved that the proposed method has better focusing performance.
The radial velocities of T1–T3 estimated by the proposed method are 1.3156 m/s, 1.6851 m/s and −0.5725m/s, respectively. The distances of the three targets to the sensor are 7339.3228 m, 7631.5370 m and 7736.4643. In accordance with Equation (
37), the three targets are shifted in azimuth by 140.7934 m, 187.5168 m and −64.5833 m, respectively. After azimuth shift correction, the positions of the three targets are indicated by pentagrams in
Figure 10a. The targets are basically positioned on the road. The accuracy of the estimated parameters is verified again.