Translational Motion Compensation for Maneuvering Target Echoes With Sparse Aperture Based on Dimension Compressed Optimization

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.

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.

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.

In the current scenario of high-resolution inverse synthetic aperture radar (ISAR) imaging, the non-cooperative targets may have strong maneuverability, which tends to cause time-variant Doppler modulation and imaging plane in the echoed data. Furthermore, it is still a challenge to realize ISAR imaging of maneuvering targets from sparse aperture (SA) data. In this paper, we focus on the problem of 3D geometry and motion estimations of maneuvering targets for interferometric ISAR (InISAR) with SA. For a target of uniformly accelerated rotation, the rotational modulation in echo is formulated as chirp sensing code under a chirp-Fourier dictionary to represent the maneuverability. In particular, a joint multi-channel imaging approach is developed to incorporate the multi-channel data and treat the multi-channel ISAR image formation as a joint-sparsity constraint optimization. Then, a modified orthogonal matching pursuit (OMP) algorithm is employed to solve the optimization problem to produce high-resolution range-Doppler (RD) images and chirp parameter estimation. The 3D target geometry and the motion estimations are followed by using the acquired RD images and chirp parameters. Herein, a joint estimation approach of 3D geometry and rotation motion is presented to realize outlier removing and error reduction. In comparison with independent single-channel processing, the proposed joint multi-channel imaging approach performs better in 2D imaging, 3D imaging, and motion estimation. Finally, experiments using both simulated and measured data are performed to confirm the effectiveness of the proposed algorithm.

Motion compensation of high-speed moving target is a challenging task because of its time-varying orientation and rotation velocity. A novel approach for inverse synthetic aperture radar (ISAR) imaging is presented for both target translational motion and rotational motion nonuniformity compensation. The basic idea is to perform frequency tracking to every individual scatterer via a polynomial fitting technique. After maximizing the projection of one-dimension range alignment to polynomial function in range plane, the Doppler frequency drift of the strongest scatterer in the range cell is automatically tracked out and the multiple prominent point processing scheme is implemented to eliminate both the translational motion error and rotational motion nonuniformity. Further the orientation velocity can be estimated. Finally, a simulation example is provided to demonstrate the performance of the proposed approach.

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.

Conventional inverse synthetic aperture radar (ISAR) imaging with sparse aperture usually suffers from high side lobes and wide main lobes, which limit the applications of radar super‐resolution imaging, multi‐target resolution, and cognitive reconfiguration. This paper proposes a fast, super‐resolution imaging method employing continuous compressive sensing for sparse‐aperture ISAR. First, the received echo in each range bin is characterised as a linear combination of multiple frequencies shown in a continuous atomic set, established into an atomic norm minimisation (ANM) mode. Second, to improve the resolution and reduce the computational burden significantly, a locally convergent iterative algorithm based on the alternating direction method of multipliers, which iteratively performs ANM with a sound reweighting strategy, is implemented. Then, the low‐rank Toeplitz covariance matrix, which contains the information of the target, is obtained. Subsequently, the Vandermonde decomposition of the Toeplitz covariance matrix is performed to acquire the locations and intensities of the scattering points. Finally, the super‐resolution result is generated by depicting the estimated scatterers in the image. Extensive numerical experiments demonstrate that the proposal is highly effective in recovering the super‐resolution image and shows better performance than state‐of‐the‐art methods.

Translational motion compensation for geosynchronous orbit (GEO) targets represents a crucial yet challenging task in inverse synthetic aperture radar (ISAR) imaging. The maneuvering tendencies of GEO targets introduce nonlinear distortions to the range profile, posing significant difficulties for precise translation compensation. Additionally, the vast distance between the radar and GEO targets results in an extremely low signal-to-noise ratio (SNR) of the echo signals, thereby undermining the coherence between consecutive pulses. In light of these challenges, this paper introduces a robust method for translational motion compensation tailored to GEO targets. This approach leverages genetic algorithm improved particle swarm optimization (GAPSO) merged with the generalized Radon-Fourier transform (GRFT). Initially, we delve into the intricacies of GEO target behavior to pinpoint an optimal imaging interval. Subsequently, translational motion is modeled using a high-order polynomial and GRFT is utilized to estimate the associated parameters. Furthermore, GAPSO is employed to streamline the parameter search process, thereby reducing computational demands. The proposed method can not only achieve effective motion compensation under ultra-low SNR conditions but also maintain high computational efficiency. Both simulated results and electromagnetic calculation data results affirm the efficiency and robustness of our proposed method.

Accurate translational motion compensation is crucial for inverse synthetic aperture radar (ISAR) imaging. At low signal-to-noise ratio (SNR), the performance of nonparametric methods is declining because the correlation of adjacent range profiles is severely destroyed by the noise. Fortunately, parametric methods can still work well at low SNR. However, existing parametric methods are time-consuming, which decreases ISAR imaging efficiency significantly. So, a fast parametric translational motion compensation method is studied for low SNR scenes in the paper, which is based on modified Adam (Madam) algorithm. By changing the updating strategy for weights and learning rate in Adam, Madam algorithm can significantly accelerate the convergence when estimating the motion parameters. To further improve the efficiency, a new objective function by combining image contrast and image entropy is proposed. When applied into measured Yak-42 data at low SNR, the proposed method can image about 10 times faster than particle swarm optimization (PSO) method and 2 times faster than Adam method. Therefore, the proposed method is an efficient translational motion compensation method for low SNR ISAR imaging.

A single algorithm for various radar imaging applications is presented. The idea behind the proposed approach is that any motion between radar and target can always be modelled as a composition of translational and rotational components. Novel techniques to estimate and compensate these two motion components are discussed and also validated by application to real radar data for different targets (ships, aircraft, ground). By the translational-rotational-motion-compensation algorithm, good results can be achieved, especially in cases characterised by evident variation of the rotation rate during the coherent processing time for imaging. This usually happens in aircraft, ship or ground mover inverse synthetic aperture radar (ISAR) imaging as well as in squinted or forward-looking SAR. In any case, the efficiency and the accuracy of the algorithm presented for translational motion compensation might be the initial step of alternative radar imaging processing. The simplicity of the proposed algorithms makes them suitable and convenient for real-time application even for compact and low-weight radar systems to be fitted on board unmanned aerial vehicles (UAV) or other airborne platforms. The proposed concept is the result of the authors' decennial experience devoted to achieve a single, simple, robust, reliable and efficient signal processing algorithm for several real-time radar imaging applications.

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.

In inverse synthetic aperture radar (ISAR) imaging of targets with complex motion such as the high maneuvering airplanes and fluctuating ships with oceanic waves, the azimuth echo signals can be modeled with cubic chirps after translational motion compensation, and then, the azimuth focusing quality will be deteriorated by the time-varying chirp rate. In this paper, a parameter estimation method of cubic chirps is proposed based on the discrete chirp Fourier transform (DCFT), which is generated from DCFT for quadratic chirps. Several properties of DCFT for cubic chirps are derived, and we show that the modified DCFT (MDCFT) is more appropriate to deal with the practical applications (e.g., ISAR imaging) than the original DCFT. Therefore, we put forward the imaging algorithm based on MDCFT, and then, simulation results confirm the validity of the proposed 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.

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.

Automotive targets undergoing turns in road junctions offer large synthetic apertures over short dwell times to automotive radars that can be exploited for obtaining fine cross-range resolution. Likewise, the wide bandwidths of the automotive radar signal yield high-range resolution profiles. Together, they are exploited for generating inverse synthetic aperture radar (ISAR) images that offer rich information regarding the target vehicle's size, shape, and trajectory which is useful for object recognition and classification. However, a key requirement for ISAR is translation motion compensation and estimation of the turning velocity of the target. State-of-the-art algorithms for motion compensation trade-off between computational complexity and accuracy. An alternative low complexity method is to use an additional sensor for tracking the target motion. In this work, we propose to exploit computer vision algorithms to identify the radar target object in the sensor field-of-view (FoV) with high accuracy. Further, we propose to track the target vehicle's motion through fusion of vision and radar data. Vision data facilitates the accurate estimation of the lateral position of the target and its lateral velocity which complements the radar's capability of accurate estimation of range and radial velocity. Through simulations and experimental evaluations with a monocular camera and Texas Instrument's millimeter wave radar, we demonstrate the effectiveness of sensor fusion for accurate target tracking for translational motion compensation and generation of high quality ISAR images.