Inverse Synthetic Aperture Radar Imaging: Principles, Algorithms, and Applications
The Doppler shift induced by the target motion and radar platform displacement can be obtained by time derivative of Equation 6 :. As can be seen from the Equation above, the ISAR echo module is not affected by the radial displacement of the aerostat-borne radar. Therefore, ISAR autofocus imaging can be achieved by implementing phase retrieval algorithm under the condition that the radar platform is unstable.
Inverse Synthetic Aperture Radar Imaging: Principles, Algorithms, and Applications
In addition to the platform displacement, the radar platform will experience a small amplitude of vibration due to the airflow. The traditional ISAR imaging technology is based on the motion parameters of the target, but the randomness of the platform vibration will bring more difficulties to the traditional ISAR imaging method.
With respect to the radar geometry model shown in Figure 1 , the echo of the radial vibration of the radar platform is analyzed. When the radar platform vibration occurs, the expression of R p 1 t in Equation 4 will change:.
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The distance r 1 t at this stage from the scattering point Q to the radar can be approximated as:. Therefore, the backscattered echoes from all the scatterers can be written as follows:. Seen from the above equation, the ISAR echo module is still not affected by the vibration of the aerostat-borne radar. Therefore, the method proposed in this paper can handle the difficulties of motion compensation in the above two cases. In the field of optical imaging, an imaged object is illuminated by a laser beam and projected onto an optical detection device, and its far field and near field Fourier transform are the same for an electromagnetic field.
Therefore, once the Fourier magnitude and phase value of the far field are known, the original target imaging result can be obtained. However, since the electromagnetic oscillation frequency of the light quantum is often greater than 10 15 Hz, the phase information cannot be directly recorded in the process of converting to electrons. The optical device first needs to measure the photon flux that is proportional to the Fourier amplitude spectrum of the imaged object, and then the phase retrieval algorithm is carried out for imaging.
As a popular imaging technology, Coherent Diffraction Imaging CDI is a method that combines X-ray diffraction, oversampling and phase retrieval. We rewrite the equation as:. To solve the problem of retrieval when the initial input Fourier amplitude spectrum is disturbed and mixed with noise, the OSS algorithm [ 27 ] adds iterative steps of frequency domain filtering after the support domain constraints of the traditional HIO algorithm [ 29 ].
Obtain a Fourier pattern X i K by performing the Fourier transform to x i n. W K is a normalized Gaussian function in Fourier domain, which is defined as:. The smoothing filter W K is only applied the density outside the support domain. From the analysis of Section 2. From the above equation, we can see that the radial motion of the radar platform does not have a negative effect on the amplitude of the received signal. In this way, the amplitude in Equation 20 is the same as that of the echo when the radar platform is stationary, which is the theoretical basis for phase retrieval algorithm to perform motion compensation.
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It should be pointed out that the classical phase retrieval algorithm tends to have a lower success rate if only the echo module information is used to recover the ISAR image. Moreover, the correctness of the recovery result cannot be guaranteed due to the lack of a priori information. Therefore, we propose an improved OSS phase retrieval algorithm that utilizes a priori information or error information , that is, the phase of the blurred image obtained by the classical imaging algorithm such as RD algorithm, cross-correlation method, etc.
Besides, the support domain size of OSS algorithm is set with respect to the blurred target image. The block scheme of this algorithm is shown in Figure 3. To verify the validity of the approach proposed in this paper, we conducted three sets of experiments. Table 1 shows the radar parameters and the target motion parameters used in the simulation. In Section 4. The hypothetical airplane composed of point scatterers and the ISAR echo signal modulus under the condition of a stable aerostat borne radar platform are shown in Figure 4.
It is assumed that the radar platform has a radial velocity v p and a radial acceleration a p. Consequently, The ISAR images with different radial displacements of radar platform are obtained as shown in Figure 5 , Figure 6 , Figure 7 and Figure 8 by applying the RD algorithm, cross-correlation method, minimum entropy method and the phase retrieval algorithm proposed in this paper. Imaging results with the radar platform displacement parameters P1. Imaging results with the radar platform displacement parameters P2.
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Imaging results with the radar platform displacement parameters P3. Imaging results with the radar platform displacement parameters P4. Different parameters from the experiments are listed in Table 2 for a more intuitive view. The motion parameters of the radar platform and maneuvering target in different experiments. As can be seen from Figure 5 a, RD algorithm can be applied to target imaging with slow motion under the condition of a stationary aerostat-borne radar platform.
However, RD algorithm is no longer applicable when radial motion of the radar platform occurs due to the air flow effects. The cross-correlation method can only estimate a fixed radial velocity within a preset interval, so when the radial velocity becomes large and the radial acceleration is small, Figure 6 b clearly demonstrates the success of the radial velocity compensation such that only the acceleration-based defocusing is noted in the ISAR image.
When the radial velocity becomes smaller and the radial acceleration is slightly larger, the resulting image is depicted in Figure 7 b and Figure 8 b where the image is highly distorted because of the large errors in the parameter estimation of the cross-correlation method. Compared with cross-correlation method, although minimum entropy method has a better performance in the parameter estimation the minimum entropy method can not only estimate the velocity value but also the acceleration value in a certain range, it must be set an appropriate search range and step length first, otherwise it is not possible to perfectly image the target scatterings.
From Figure 6 c, Figure 7 c, and Figure 8 c, the dominant motion effects of translational motion are successfully eliminated by the minimum entropy method, but the proposed method in this paper outperforms the minimum entropy method in Figure 6 d, Figure 7 d, and Figure 8 d. The echo modules with the different radial motion parameters of radar platform in Figure 6 , Figure 7 and Figure 8 are unchanged, which is the same as the ISAR echo module in Figure 5. It is verified that the radial motion of the radar platform does not affect the echo module, and the proposed method can be used for ISAR autofocus imaging.
The further check is performed by looking at the spectrogram of the received time pulses with respect to Figure 8 a,d, which can reflect the change in frequency shift in Equation 8. We can see from Figure 8 a that before the OSS phase retrieval algorithm is applied, the severe frequency shifts due to the target motion and radar platform motion have occurred in Figure 9 a. Spectrograms of time pulses.
We set up three sets of comparative experiments with different vibration parameters, and the resultant images are shown in Figure 10 , Figure 11 and Figure Compared with Figure 10 , the vibration frequency of the radar platform in Figure 11 remains unchanged and the vibration amplitude is larger. Different from Figure 10 , the vibration amplitude of the radar platform in Figure 12 remains unchanged and the vibration frequency is increased.
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In this case, the resultant ISAR images obtained by the traditional algorithm are broadly blurred in the range and Doppler domains where the higher the vibration frequency is, the more serious the overlap will be. From the analysis of Section 4. Imaging results with the radar platform vibration parameters P5. Imaging results with the radar platform vibration parameters P6. Imaging results with the radar platform vibration parameters P7.
The spectrograms of the time pulses in the received signal are also plotted in Figure 13 with respect to Figure 11 a,d. By analyzing the Doppler shift in this case obtained from Equation 13 , we find that since the rotation component of the target is small, the frequency shifts are mainly caused by the platform vibration and the target motion, so there exists significant fluctuation due to platform vibration in the frequency of time pulses in Figure 13 a.
As is obvious from Figure 13 b, all frequency values of the returned pulses are aligned successfully, which proves the good performance of the proposed method under the condition of the radar platform vibration. The motion parameters of the maneuvering target in Section 4.
In order to demonstrate the ISAR imaging results of the proposed method with different radial motion parameters under the condition of unstable radar platform, another set of experiment were carried out. As can be seen from Figure 14 and Figure 15 , the resultant ISAR images are clear and focused in both range and cross-range directions, verifying that the proposed method can perform autofocus imaging of the target with different motion parameters.
Imaging results with the radar platform displacement parameters P8. Imaging results with the radar platform vibration parameters P In this paper, a phase retrieval method for aerostat-borne ISAR autofocus imaging has been proposed. In general, the radial displacement and radial vibration of the radar platform due to airflow will affect the stability of the radar platform, making the range-Doppler ISAR image highly defocused and blurred.
Based on the aerostat-borne ISAR imaging geometry model, we can deduce that ISAR echo module is not affected by the radial displacement and the vibration of the aerostat borne radar under the condition of the moving maneuvering target. Therefore, combined with classic OSS phase retrieval algorithm and the prior phase information that the traditional ISAR imaging technology can provide, we theoretically prove that the proposed method can overcome the difficulties of motion compensation in the above cases.
In the experimental simulation, we compare the imaging results of the RD algorithm, cross-correlation method, minimum entropy method with the imaging results of the proposed method. The former three traditional methods cannot successfully eliminate the motion effects of radar platforms and maneuvering targets. The method can obtain resultant motion-free ISAR image after completely removing the phase error of the received signal, wherein the scattering centers around the target are well localized.
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Additionally, we also show some imaging results of the proposed method with different target motion parameters under the condition of quasi-stationary radar platform, which further expand the application conditions of this method. In summary, the results of this study provide a new way of thinking for the non-stationary platform ISAR imaging problem.
Of course, it is very important that the algorithm does not estimate any relevant motion parameters. The future work will focus on a new approach for fast autofocus imaging, where the convolutional neural network is applied to recover the original phase of the radar received signal. The authors are very grateful to the Editor and reviewers for their constructive comments that have an important role in further improving this work. All the authors made significant contributions to this work. The authors declare no conflict of interest.
The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results. National Center for Biotechnology Information , U. Journal List Sensors Basel v. Sensors Basel. Published online Oct 5. Find articles by Saixue Xia. Find articles by Qi Qin. Find articles by Ting Yang.
Author information Article notes Copyright and License information Disclaimer. Received Sep 14; Accepted Oct 3. Abstract As a powerful signal processing tool for imaging moving targets, placing radar on a non-stationary platform such as an aerostat is a future direction of Inverse Synthetic Aperture Radar ISAR systems.
Keywords: inverse synthetic aperture radar ISAR , non-stationary platform, maneuvering target, autofocus, phase retrieval, oversampling smoothness OSS.
Introduction ISAR imaging has been the focus of many researchers and operational users in the last few decades. Open in a separate window. Figure 1. ISAR Echo Analysis of Platform Fluctuation In addition to the platform displacement, the radar platform will experience a small amplitude of vibration due to the airflow. Phase Retrieval Principle In the field of optical imaging, an imaged object is illuminated by a laser beam and projected onto an optical detection device, and its far field and near field Fourier transform are the same for an electromagnetic field.
OSS Phase Retrieval Algorithm To solve the problem of retrieval when the initial input Fourier amplitude spectrum is disturbed and mixed with noise, the OSS algorithm [ 27 ] adds iterative steps of frequency domain filtering after the support domain constraints of the traditional HIO algorithm [ 29 ]. Figure 2.