An improved cross-correlation approach to parameter estimation based on fractional Fourier transform for ISAR motion compensation

Inverse synthetic aperture radar (ISAR) imaging is typically useful when there is a need to classify, recognize, or identify a moving target of interest. In fact, an ISAR image highlights two-dimensional (2-D) geometric features of a target, which can provide indications of target's type, size, and other salient information. Such information can be then used for target classification, recognition, and identification. In this chapter, we will provide five case studies on applications of ISAR imaging. Such case studies are chosen to diversify the type of application and to give additional indications about how to interpret ISAR images. Specifically, in the first case study (Section 12.1), we show an example of ground-based ISAR images of a noncooperative sailing ship. The ISAR techniques used to form the ISAR images are the range-Doppler (Chapter 3) and the ICBA (Chapter 5) techniques. Different time windows are chosen to show the effects of the coherent processing interval (CPI) length on the ISAR image. Since the radar is ground based, this represents a case where the ISAR image is formed by exploiting only the sea surface induced target's motions. The second case study (Section 12.2) refers to a scenario where the radar is carried by an aircraft and the target is a ship at sea. In this case, both the target and the platform motions concur to the ISAR image formation. Also in this case, the range-Doppler and ICBA are used to form the ISAR image sequence. The third case study (Section 12.3) concerns dual ground-based/satellite ISAR imaging of a noncooperative sailing ship. In this experiment two radars are used to image a sailing ship at the same time. Two techniques are here used to form the ISAR images: a refocus technique (see Chapter 8) to form the satellite ISAR image; and a range-Doppler with ICBA to form the ground-based ISAR image. In this case study, we show how a dual system is able to form ISAR images of the same target with different target's views and projections. This is a simple case of multiple-perspective ISAR images, which may be looked at as a way to improve a target's classification and recognition [1]. The fourth case study (Section 12.4) shows ISAR images of four aircrafts obtained by processing data acquired with a ground-base radar. This case study may be regarded as the classic ISAR imaging example. Four different airplanes have been selected to show how their characteristics are mapped onto ISAR images. Such characteristics can then be used by classifiers for recognition purposes.

Inverse synthetic aperture radar (ISAR) imaging of multiple warhead targets in the same antenna beam is a big challenge when they are overlapping in the same range bin. Existing methods are usually based on single target motion compensation and they can't get clear ISAR image of multiple targets. This paper presents a new algorithm for ISAR imaging of multiple targets based on Fractional Fourier Transform (FrFT) CLEAN method to separate signals of different targets. Firstly, signal model of multiple targets is given. Then analyzed each target has different Doppler history, the signals of a certain target in a range bin correspond to a batch of multicomponent liner frequency modulation (LFM) signals. Theoretical analysis and computer simulations show the proposed method can generate the images from multiple target echoes effectively.

For the Inverse Synthetic Aperture Radar (ISAR) imaging, the ISAR image obtained by the Range-Doppler (RD) or time-frequency analysis methods can not display the target's real shape due to its azimuth relating to the target Doppler frequency, thus the cross-range scaling is required for ISAR image. In this paper, a fast cross-range scaling method for ISAR is proposed to estimate the Rotational Angular Velocity (RAV). Firstly, the proposed method utilizes efficient Pseudo Polar Fast Fourier Transform (PPFFT) to transform the rotational motion of two ISAR images from two different instant time into translation in the polar angle direction. Then, a new cost function called integrated correction is defined to obtain the RAV coarse estimation. Finally, the optimal RAV can be estimated using the Bisection method to realize the cross-range scaling. Compared with the available algorithms, the proposed method avoids the problems of precision loss and high computational complexity caused by interpolation operation. The results of computer simulation and real data experiments are provided to demonstrate the validity of the proposed method.

In this paper, we analyze the effect of roll, pitch and yaw rotations on inverse synthetic aperture radar (ISAR) imaging of small craft. An ideal ISAR image of a target with regular motion can be derived from the image projection plane and the radar line-of-sight (LOS) unit vector. Roll, pitch and yaw rotations can induce time-varying Doppler shifts that can be analyzed through the rotation matrix and the effective rotation vector. We use a commercial small craft ISAR data accompanied with roll, pitch and yaw data collected by the Trimble Tans Vector system with 4 GPS antennas to study the effect of rotational motion on ISAR imaging. For a target with regular motion, perturbations of roll and pitch motions may make for image blurring if conventional motion compensation is used. In this case, advanced imaging algorithms, such as the polar reformatting algorithm, that compensate the perturbations may improve the image.

Combining traditional inverse synthetic aperture radar (ISAR) imaging, interferometry technique and compressed sensing (CS), we studied the problem of interferometric ISAR imaging with sparse aperture. Based on the elaborate analysis of smoothed l0 algorithm in CS, we proposed joint smoothed l0 algorithm which is capable of maintaining coherence between ISAR images of different radars under sparse aperture, thus it could be applied to interferometric ISAR imaging. Besides, we discussed the relationship between sparsity degree and the precision of interferometric ISAR imaging result. Simulation results validate the effectiveness of proposed algorithm and rationality of our conclusions.

In this paper, performance efficiency analysis of compressive inverse synthetic aperture radar (ISAR) imaging for a complex, electrically large target is presented. In this context, physical optics (PO) is used as a high-frequency scattered field prediction technique and compressive sensing (CS) theory is applied to ISAR imaging by exploiting the sparse point scatterer structure of the target. Results prove that CS provides high resolution and accuracy in ISAR imaging even under the Nyquist sampling rate and linearly decreases computational time.

Sub-Nyquist sampling is a common means of interfering with inverse synthetic aperture radar (ISAR) imaging, which has been validated for the feasibility of 1-D compressive sensing (CS) ISAR imaging. In order to overcome the high computational complexity of 1-D CS-based ISAR imaging, the coupled 2-D CS algorithms are utilized to achieve ISAR imaging directly which has been proposed recently. In this paper, sub-Nyquist sampling jamming signals are utilized to induce multiple false-target ISAR images by using the coupled 2-D-CS algorithm. The jamming signals, which are formed by the intercepted radar signals under the sub-Nyquist sampling theorem and scattered by moving targets, are collected by ISAR to establish a 2-D super resolution model, and the finally reconstructed ISAR images are induced and show that the deceptive false-target images retaining the real target information. Simulated trails and real data of a Yak-42 plane are used to validate the correctness of the analyses and the finally well-focused false-target images greatly support the effectiveness of the sub-Nyquist sampling idea in the countermeasures of ISAR with coupled 2-D CS.

This letter presents an adaptive inverse synthetic aperture radar (ISAR) imaging algorithm based on evidence framework. This imaging algorithm iterates between sparse coding and parameter estimation until a fixed number of iterations is reached. An efficient Hessian update scheme is applied for sparse coding. In the parameter estimation step, the closed forms of parameters are obtained based on evidence framework. Experiments based on simulated and measured data are given to show the efficiency of the proposed ISAR imaging algorithm.

In order to obtain focused inverse synthetic aperture radar (ISAR) images, an accurate translational motion compensation is required. The phase adjustment step corresponds to fine compensation and must be properly designed. The authors introduce the Renyi entropy for autofocusing ISAR images. The Renyi entropy of order α is a generalisation of the standard Shannon entropy. When α tends to be the unity, the Renyi entropy tends to be the Shannon entropy. Here, we demonstrate that minimising the Renyi entropy for α = 2 is equivalent to maximising the contrast for ISAR autofocusing. Furthermore, it is also shown that maximising the peak value is equivalent to minimising the Renyi entropy for α tending to infinity. On the other hand, the authors propose to minimise the Renyi entropy with α = 0.5 to reconstruct an accurate ISAR image. Simulated data have been used to verify that, in terms of mean squared error, the proposed method with α =0.5 outperforms other autofocusing algorithms such as the method based on contrast maximisation or the one based on the minimisation of the standard Shannon entropy. The method has also been applied to real data.

Migration through resolution cells (MTRC) happened in large rotation angle inverse synthetic aperture radar (ISAR) imaging can be effectively eliminated by Polar Format Algorithm (PFA) under the far-field condition. However, traditional PFA is sensitive to range error, so it is difficult to be implemented into engineering. Aimed at this problem, a modified polar format algorithm for ISAR imaging is proposed in this paper. Firstly, echo data is compressed to one-dimensional (1-D) range profiles, envelope alignment and phase autofocus processing are applied to compensate the translational motion, and the target motion model is converted into a turntable model. Next, the rotation center of the target should be obtained, and its envelope would be compensated to range zero. Then, two 1-D interpolation operations are applied to process data from polar sector support region to Cartesian rectangular grid. Finally, Fast Fourier Transform (FFT) operations are carried out to get well focused the ISAR image. The new method needs no range information, and therefore the image quality is not affected by the range errors. Theoretical analysis and simulation results verified the effectiveness of the algorithm proposed in this paper.

The techniques of accurate cross-range scaling and motion compensation both play significant roles in inverse synthetic aperture radar (ISAR) imaging. This paper proposes a new method to estimate motion parameters for ISAR targets scaling as well as motion compensation. With a time-varying autoregressive (TVAR) model, the pole histories of dominant scatters can be obtained. According to the time-frequency relationship, motion parameters including the effective rotational velocity and the coefficients of phase error are extracted. Using these parameters, we can not only scale the image but also compensate phase error to focus the image. Simulation and real-data experiments illustrate its feasibility and robustness. (6 pages)

Compressive Sensing(CS) has been widely utilized in Inverse synthetic aperture radar(ISAR) imaging since real ISAR data is easier to be non-completed, and CS-based methods can obtain high-quality imaging results using under-sampled data. However, traditional CS-based methods need pre-defined parameters, sparse transforms and iterative reconstruction processes. Optimal parameters as well as transforms are tough to be hand-crafted, and iterative reconstruction consumes plenty of time, which limit practical applications in ISAR imaging. Given that Convolution Neural Network(CNN) has great power to learn rapidly, we compose CNN with traditional Iterative Shrinkage-Thresholding Algorithm(ISTA) to propose CNN-ISTA(CIST)-based ISAR imaging method. CIST is capable of learning optimal parameters and transforms throughout the training (i.e. the optimization process is interpretable) instead of manually defined. Compared with traditional state-of-the-art CS imaging methods, the experimental results demonstrate that our proposed CIST-based imaging method is superior in both imaging quality and computational efficiency.

For inverse synthetic aperture radar (ISAR) imaging of maneuvering targets, the Doppler frequency induced by an arbitrary scatterer on the target is time-varying, and hence, the traditional range-Doppler (RD) algorithm is not appropriate for obtaining focusing ISAR images. In such a scenario, a novel ISAR technique, called the range instantaneous Doppler derivative (RIDD) algorithm, has been recently proposed, and two different kinds of well-focused ISAR images, named range-Doppler centroid (RDC) frequency image and range-Doppler frequency rate (RDR) image, can be obtained. In order to improve the accuracy of the target classification and recognition, the scaling approach for the RIDD algorithm must be taken into consideration. In this article, the point spread function (PSF) representations and cross-range scaling factors of the RDC image and the RDR image obtained by the RIDD algorithm are demonstrated analytically. On the basis of the PSFs and cross-range scaling factors, a novel imaging and scaling approach for the RIDD algorithm in the presence of a low SNR environment based on smoothed integrated high-resolution time–frequency-rate representation (SIHR) combined with coherent integrated smoothed generalized cubic phase function (CISCF) is proposed. As the proposed algorithm has high estimation accuracy and good antinoise capability, precise parameter estimation of the received signal can be achieved. Hence, high-quality scaled RDC and RDR images of the target can be reconstructed by the proposed approach. Experimental results of simulated data and real measured data verify the correctness of the PSF representations and demonstrate the effectiveness of the imaging and scaling approach proposed in this article.

Inverse synthetic aperture radar (ISAR) imaging for the target with micro-motion parts is influenced by the micro-Doppler (m-D) effects. In this case, the radar echo is generally decomposed into the components from the main body and micro-motion parts of target, respectively, to remove the m-D effects and derive a focused ISAR image of the main body. For the sparse aperture data, however, the radar echo is intentionally or occasionally under-sampled, which defocuses the ISAR image by introducing considerable interference, and deteriorates the performance of signal decomposition for the removal of m-D effects. To address this issue, this paper proposes a novel m-D effects removed sparse aperture ISAR (SA-ISAR) imaging algorithm. Note that during a short interval of ISAR imaging, the range profiles of the main body of target from different pulses are similar, resulting in a low-rank matrix of range profile sequence of main body. For the range profiles of the micro-motion parts, they either spread in different range cells or glint in a single range cell, which results in a sparse matrix of range profile sequence. From this perspective, the low-rank and sparse properties are utilized to decompose the range profiles of the main body and micro-motion parts, respectively. Moreover, the sparsity of ISAR image is also utilized as a constraint to eliminate the interference caused by sparse aperture. Hence, SA-ISAR imaging with the removal of m-D effects is modeled as a triply constrained underdetermined optimization problem. The alternating direction method of multipliers (ADMM) and linearized ADMM (L-ADMM) are further utilized to solve the problem with high efficiency. Experimental results based on both simulated and measured data validate the effectiveness of the proposed algorithm.

With the development of multi-functional radar systems, inverse synthetic aperture radar (ISAR) imaging with sparse-aperture (SA) data has drawn considerable attention in the recent years. Motion compensation and imaging are among the most significant challenges that SA-ISAR imaging frequently faces. In this paper, we focus on the autofocus scheme, in which a modified eigenvector-based autofocus method is proposed. In the method, different weights are endued to different range cells according to their signal-to-noise ratios (SNRs). Using the weights, the contribution from the range cells with high SNR is enhanced, yielding accuracy improvement in phase error estimation. What is more is that to improve the estimation precision, an iterative scheme is introduced. Experimental results show that the proposal is not only robust to severe noise but also applicable to ISAR imaging with different SA patterns. Detailed comparisons are given in order to show the superiorities of the proposal in phase adjustment for ISAR data.