Reliable localization under Global Positioning System-denied or visually degraded conditions remains a fundamental challenge for autonomous systems. Vision- and Light Detection and Ranging (LiDAR)-based approaches often degrade in low illumination, adverse weather, or appearance-changing environments, as they rely on stable surface texture or geometry. In contrast, ground-penetrating radar (GPR) captures subsurface electromagnetic reflections that remain relatively stable across lighting, seasonal, and weather variations, making it a promising complementary sensing modality for long-term localization. However, spatial variability in subsurface dielectric properties induces fluctuations in electromagnetic wave velocity, leading to geometric distortions in GPR echoes and unstable feature extraction. To address this challenge, we propose the Velocity-Invariant Feature Transform (VIFT), a physics-guided self-supervised learning framework for GPR keypoint detection and description. VIFT explicitly models wave-velocity-induced distortions through a continuous velocity space parameterized by a Beta distribution, and leverages velocity-conditioned wavefield migration as physically consistent data augmentation. A Siamese network is trained with velocity-consistency supervision to jointly learn repeatable keypoint score maps and discriminative local descriptors from unlabeled real GPR scans. To further enhance robustness, sparsity-aware, dispersion, distinctiveness, and orthogonality losses are incorporated to improve repeatability, spatial coverage, and descriptor discriminability. Extensive experiments on public benchmarks and large-scale real-world GPR datasets demonstrate that VIFT consistently outperforms traditional handcrafted methods and recent learning-based Vison and GPR methods, achieving a 5–10% improvement in keypoint repeatability over state-of-the-art methods, particularly under extremely sparse keypoint sampling regimes, while also improving matching accuracy and registration robustness under diverse subsurface conditions.

Ground penetrating radar (GPR) based localization has gained significant recognition in robotics due to its ability to detect stable subsurface features, offering advantages in environments where traditional sensors like cameras and LiDAR may struggle. However, existing methods are primarily focused on small-scale place recognition (PR), leaving the challenges of PR in large-scale maps unaddressed. These challenges include the inherent sparsity of underground features and the variability in underground dielectric constants, which complicate robust localization. In this work, we investigate the geometric relationship between GPR echo sequences and underground scenes, leveraging the robustness of directional features to inform our network design. We introduce learnable Gabor filters for the precise extraction of directional responses, coupled with a direction-aware attention mechanism for effective geometric encoding. To further enhance performance, we incorporate a shift-invariant unit and a multi-scale aggregation strategy to better accommodate variations in dielectric constants. Experiments conducted on public datasets demonstrate that our proposed EDENet not only surpasses existing solutions in terms of PR performance but also offers advantages in model size and computational efficiency.

As a promising technology for autonomous driving, localizing ground penetrating radar (LGPR) is a vehicle localization method that relies on prior maps and couples deeply with subsurface features. However, the unique characteristics of GPR data often lead to a significant number of mismatched candidates during localization. Previous learning-based GPR place recognition methods have primarily relied on 2D convolutional neural networks (CNNs), which struggle to effectively capture critical temporal information, limiting further performance improvements. To address this limitation, we propose a spatial-temporal U-shaped network (STU-Net) that leverages 3D convolutional neural networks to simultaneously extract spatial and temporal features from GPR image sequences. Additionally, residual dense blocks (RDBs) are integrated into the network to enable multi-scale feature extraction. Extensive experiments conducted on publicly available datasets demonstrate that our STU-Net achieves state-of-the-art performance, outperforming existing methods with significant improvements.

Ground-penetrating radar (GPR) , as a sensor for mapping and localizing subsurface features, has gained significant attention in robotic localization for complex environments. However, varying weather conditions change the subsurface dielectric constant, which weakens the registration correlation between real-time images and maps, thereby compromising localization stability. We design an image registration framework for localizing ground penetrating radar (LGPR) in multi-weather. Specifically, we first propose an adaptive hyperbolic receptive field that aims to significantly enhance the robust features in the GPR images, while improving both discrimination capability in map and reliability for image registration. Then, an image alignment module is introduced to eliminate the time-delay blurring problem caused by the variation of dielectric constant under multi-weather conditions. The proposed method was evaluated on three distinct datasets (simulated, publicly available, and self-constructed), demonstrating significant improvements in registration and localization performance. The average correlation coefficient on simulated data achieved a enhancement from 0.3796 to 0.7406 compared with baseline, validating the effectiveness of feature enhancement. Furthermore, measured datasets exhibited 15% higher average registration and localization accuracy than baseline. These results demonstrate that the method provides a reliable guarantee for the stable operation of LGPR systems in complex environments. The datasets will be released at: https://github.com/Eazin-bz/dataset_AHFT.git.

As a novel configuration of along-track Multistatic SAR (Multi-SAR), the high frame rate Along-Track Swarm SAR (ATS-SAR) has garnered significant attention in recent years due to its exceptional efficiency in reducing data acquisition time. Motivated by its potential for high-resolution imaging of moving targets, this paper investigates the application of ATS-SAR in moving target imaging. However, high frame rate ATS-SAR-based moving target imaging confronts two critical challenges: time-space coupling and partial data loss in moving target echoes. To address these challenges, we first conduct a comprehensive analysis and theoretical derivation of the moving target echo model under the high frame rate ATS-SAR configuration. Subsequently, we propose an innovative motion parameter estimation algorithm that exploits unique echo characteristics to achieve high-performance imaging. Furthermore, we introduce the highresolution, high frame rate ATS-SAR Sub-Aperture Collaborative Imaging algorithm for Moving Targets (MT-SACIm-ATS). Extensive simulations and a real measured experiment validate the effectiveness of the MT-SACIm-ATS algorithm, demonstrating imaging performance that closely approximates reference imaging results. Comparative analysis with several state-of-the-art algorithms further highlights the superiority of the proposed approach in terms of resolution and robustness.

In this article, we address the problem of clutter covariance matrix estimation for radar adaptive detection. Traditional estimation methods are usually based on specific models. However, performance will experience degradation in the presence of model mismatch, which occurs commonly in reality. Therefore, we resort to the data-driven deep learning method and construct a network based on the convolutional neural network (CNN) to estimate the clutter covariance matrix. Besides, due to the unavailable ground truth of the covariance matrix of measured data, simulated data are usually applied for training as a compromise. We design a loss function according to the whitening metric, which makes it possible to train the network directly by measured data. Compared with traditional covariance matrix estimators, the proposed network estimator has higher whitening ability. Moreover, we exploit the obtained covariance matrix estimations to an adaptive detector to evaluate the detection performance. Results with the Intelligent Pixel (IPIX) datasets show that the detector applying the network covariance matrix estimator gains a higher probability of detection (PD).

The Wide-Angle Stare Synthetic Aperture Radar (WasSAR), as an emerging SAR observation mode, enables long-duration, multi-angular imaging of a scene, demonstrating remarkable advantages in three-dimensional (3D) information acquisition. A critical step in the process of 3D information extraction lies in accurately determining the displacement information between sub-aperture images captured from adjacent azimuth angles. During the WasSAR imaging process, spatial targets exhibit positional discrepancies in imaging results obtained from different azimuth perspectives, making pixel-wise displacement estimation in SAR images highly challenging, especially in complex scenarios. To address this challenge, this study proposes an innovative displacement estimation method for WasSAR imagery tailored for 3D information extraction. The proposed approach begins with brightness equalization preprocessing to harmonize the brightness distribution between two images, ensuring the accuracy of subsequent processing steps. This is followed by an initial estimation using block-based registration techniques based on the Enhanced Correlation Coefficient (ECC). Finally, an improved optical flow algorithm is employed to achieve precise displacement estimation, significantly enhancing the accuracy and reliability of displacement information estimation between SAR images. A series of experiments were conducted using Ku-band Mountain scene datasets acquired by the National University of Defense Technology. The experimental results include a comprehensive comparative analysis with several existing displacement estimation methods, showcasing the superior performance of the proposed algorithm across multiple key performance metrics. The proposed algorithm’s performance in 3D information extraction applications was also evaluated, confirming its effectiveness and high practicality.

Localizing ground penetrating radar (LGPR) has been proven to be a promising technology for robot localization in various dynamic environments. However, the extreme scarcity of underground features introduces false candidate matches and brings unique challenges to this task. In this paper, we propose a sequence-based framework for LGPR to address the aforementioned issues. Specifically, we first introduce a trainable strategy to extract robust underground features in multi-weather conditions. By further using sequential information, our LGPR system can observe richer underground scene contexts, and the associated multi-frame scans could also improve the performance of underground place recognition. We demonstrate the superiority of our proposed method by comparing it against several recent state-of-the-art baseline methods applied to GPR image tasks. Experimental results on large public and self-collected datasets show that our proposed framework significantly improves the performance of various baselines in different scenarios.

Due to its rapid data acquisition capabilities, the Along-Track Swarm SAR (ATS-SAR) system offers a distinct advantage in simplifying the motion states of moving target. This paper addresses challenges encountered in ATS-SAR moving target imaging, specifically focusing on issues related to partial aperture data loss and the spatiotemporal non-equivalence of the ATS-SAR moving target echo. A novel ATS-SAR imaging method for moving target is introduced. Initially, the ATS-SAR moving target echo model is established. Subsequently, the proposed algorithm designs a phase compensation function that contributes to the accurate reconstruction of the complete echo for ATS-SAR moving target, resulting in outstanding imaging performance.

In this paper, an efficient method for parameter estimation of polynomial phase signal (PPS) is proposed. Instead of the existing methods based on parametric ergodic search or phase differentiation, the proposed method adaptively tracks the PPS phase through extended Kalman filtering (EKF), termed as APT-EKF. Firstly, based on the smoothness assumption of the local phase, a state-space model describing the PPS phase is constructed. Then, by solving the state-space model through EKF, the PPS phase can be tracked. Finally, the least square estimation (LSE) is performed for the inversion of PPS coefficients, and the O’Shea refinement strategy is implemented to enhance the estimation accuracy, thereby achieving the Cramér-Rao lower bound (CRLB). Compared with most existing studies, the proposed method occupies an obvious advantage in signal-to-noise ratio (SNR) threshold and computational efficiency. It is suitable for the arbitrary order PPS. Moreover, this article provides a comprehensive analysis of the parameter initialization, performance bounds, and computational complexity of the proposed method. Both simulation and experiment results are provided to demonstrate the effectiveness of the proposed method.

Refocusing moving targets in synthetic aperture radar (SAR) poses inherent challenges. The difficulty is amplified when SAR raw data are missing in the azimuth direction, mainly because of the unknown motion parameters of non-cooperative targets. Estimating these parameters from SAR azimuth missing data (SAR-AMD) is notably more challenging than from complete echoes. To address this problem, we propose the MPE-CM method, a fast and robust motion parameter estimation method for SAR-AMD based on contrast maximization. Initially, following the range walk correction (RWC) by Keystone transform (KT), a coarse-focused image is derived in the range-Doppler (RD) domain by constructing a phase compensation function with varying focusing factors. Subsequently, the estimation of motion parameters is converted into the estimation of focusing factors, which is accomplished through the maximization of contrast in the coarse-focused image. Concurrently, we propose a Five-Point method to efficiently and robustly determine the focusing factor. Finally, the along-range and azimuth velocities can be retrieved from the estimated focusing factor and Doppler shift, where the Doppler shift is obtained by identifying the peak energy shift of the coarse-focused image. The proposed MPE-CM method, ensures computational efficiency through a fast and robust approach, while coherent processing improves its anti-noise performance. The experimental results demonstrate the effectiveness of the proposed MPE-CM method in SAR-AMD.

The acquisition of 3-D information in the observation scene has always been a prominent issue in the field of synthetic aperture radar (SAR). The emerging wide-angle staring SAR (WasSAR) utilizes its unique multiview observation performance to obtain offset information of the target position under different observation angles, enabling the acquisition of 3-D information of the observation scene. However, existing multiview 3-D information extraction methods suffer from large errors due to a lack of prior information about the observed scene. In order to address these challenges, this article analyzes the impact of the missing incidence angle information on the 3-D reconstruction results and proposes a 3-D information correction algorithm. The method only needs the single-channel echo information of the two azimuth angles of a single pass and the corresponding radar platform motion information and does not need to rely on any a priori information of the observation scene, which realizes the acquisition of 3-D information without a priori information in the real sense. Through simulation experiments, we quantitatively analyze the error transfer coefficient and confirm both accuracy and effectiveness through experimental data processing in Ku-band mountain scenes autonomously measured by our team. The proposed algorithm significantly enhances measurement precision and reliability, demonstrating a mean error reduction to just 49% and a root-mean-square error (RMSE) decrease to 46% compared to the traditional method, thereby confirming its superior performance and practicality.

The ambiguity function (AF) is a crucial tool in characterizing the range-angle response of a multiple-input multiple-output (MIMO) radar system, which is intricately influenced by the transmit waveforms, receiving filters and also antenna configurations. Notably, the role of antenna configurations is less explored compared to the well-studied areas of waveforms and filters. In this article, we incorporate antenna positions as an additional design parameter alongside waveforms and filters to optimize the AF in a specific range-angle bin. We employ the mainlobe-to-integrated-sidelobe-level-ratio (MISLR) as a quantitative metric to assess the performance. The resulting optimization problem is inherently nonconvex, encompassing binary and unimodular constraints. To address this challenge, we reformulate the problem, enabling an alternating optimization approach for antenna positions and waveforms. Each iteration involves solving a sequence of quadratic constrained quadratic programming problems for the binarily constrained antenna position optimization and updating the waveforms iteratively via an analytical expression. Our simulation results validate the effectiveness of the proposed method as it achieves higher MISLR with the same number of antennas compared to conventional approaches. Moreover, the optimized antenna configurations notably enhance the balance between angular ambiguity and resolution.

Ground penetrating radar (GPR) images typically depict underground targets as hyperbolas, which pose a challenging detection task due to their low amplitude and resolution. To address this, we propose a robust and efficient feature descriptor based on a modified phase symmetry (PS) model. Specifically, we enhance the PS model to better represent hyperbolas in GPR images and introduce a weighted phase symmetry histogram descriptor (WPSHD) as a local structure descriptor. The proposed descriptor is used as the feature input to the classifier to realize the hyperbola recognition. The proposed method is compared with two baselines and state-of-the-art (SOTA) methods, such as histogram of oriented gradient (HOG), edge histogram descriptor (EHD), and histogram of oriented vector phase symmetry (HOVPS). Our validation experiments on both public datasets and real-world data show that our proposed algorithm improves hyperbola detection in GPR images, as demonstrated by qualitative and quantitative analyses.

Ground moving targets with complex motions often appear seriously dislocated and smeared in synthetic aperture radar (SAR) imagery due to non-cooperative motion. Refocusing such targets in SAR is challenging because of unknown motion parameters. In this paper, a novel SAR moving target imaging method based on adaptive phase tracking (MTIm-APT) is proposed. First, the Hough transform (HT) and the second(2nd)-order Keystone transform (SOKT) are performed to correct the range migration. Second, the Doppler phase can be adaptively tracked based on the improved extended Kalman filter (EKF). With the tracked Doppler phase, the motion parameters required for moving target imaging is estimated. Finally, the moving target is well-focused after motion parameters compensation since the high-order Doppler phase errors are efficiently eliminated. Unlike existing research that only considers the 2nd- or third(3rd)-order Doppler phase, the proposed method considers higher-order Doppler parameters which can be simultaneously estimated, thus eliminating error propagation effect. More importantly, due to the suboptimal filtering characteristics of EKF, the proposed method maintains excellent imaging performance at lower signal-to-noise ratio (SNR) than classical PGA. On the other hand, our method has a certain advantage in computational efficiency. Both simulated and real data processing results are provided to validate the feasibility and effectiveness of the proposed SAR MTIm-APT method.

One-bit synthetic aperture radar (SAR) imaging has garnered significant interest due to its ability to lower the cost of storing enormous amounts of data during sampling and transmission, as well as the expense of analog-to-digital converters (ADCs). However, existing one-bit SAR imaging methods suffer from high computational complexity and artifacts in the resulting images. To address these problems, the sparse logic regression model (SLR) solved by iterative hard threshold (IHT) is applied to one-bit SAR imaging, and a new SLR-IHT imaging method is proposed. The SLR-IHT method models the one-bit SAR imaging problem as an SLR task and optimizes the solution using the IHT framework. By leveraging the joint sparsity of the real and imaginary components, the proposed method enhances imaging quality while effectively suppressing artifacts. To accelerate computation, the Armijo step size criterion is employed to adjust the step size and support set during the iterative procedure. Moreover, a theoretical investigation into the convergence properties of the proposed method was conducted. Extensive simulations and real data experiments are conducted to evaluate the performance of the SLR-IHT method. The results demonstrate its superiority over existing one-bit SAR imaging techniques in terms of imaging quality and computational efficiency.

In order to solve the problem of SAR imaging with azimuth missing data, a novel missing data SAR imaging algorithm is proposed in this paper. In the algorithm, the complete echo can be recovered at the two-dimensional frequency-domain by using the generalized orthogonal matching pursuit (GOMP) algorithm. The simulation result verifies the effectiveness of the proposed algorithm. Since the proposed algorithm only needs to recover the echo corresponding to sparse target-located range gates, compared with the state-of-the-art SAR imaging algorithm with azimuth missing data, it shows the advantage in the computational complexity when the targets are sparse enough in the range direction and it has a better imaging performance than the state-of-the-art azimuth missing data algorithm in noiseless and noisy settings.

Isotropy edge detection filters for synthetic aperture radar (SAR) images, such as crater-shaped window (CSW), cannot keep both high edge resolution and good speckle suppression ability at the same time. In this letter, an edge detector-combined CSW and robust inhibition-augmented curvilinear operator (RUSTICO) has been proposed. First, the preliminary edge strength map (ESM) is calculated by using CSW. Second, the RUSTICO is applied to suppress the influence of speckle and obtain the improved ESM (IESM). Moreover, by using nonmaximum suppression and hysteresis thresholding on IESM, the one-pixel-wide edges are acquired. Finally, the missing edges at intersection areas are extracted by the linking method. The experimental results on simulated and real SAR images demonstrate that the proposed edge detector can yield accurate and integrated edge map.

Synthetic aperture radar (SAR) raw data missing occurs when the radar is interrupted for various reasons during the work. Different solutions have been proposed to this problem. In recent years, with the continuous deepening of the research on compressed sensing (CS), it has also been fully utilized in solving the problem of missing data. When using traditional greedy algorithms to recover missing data, we need to know the sparsity, but it is often unknowable in practice. This letter proposes to apply the sparsity adaptive segmented orthogonal matching pursuit (SAStOMP) algorithm to the recovery of SAR missing data. Simulation results show that the proposed method can recover missing SAR data under the condition of unknown sparsity and can adapt to a wider range of threshold parameters. It has good recovery performance for periodic and nonperiodic missing SAR raw data, thus improving SAR imaging results.

Recently, we have proposed the coprime tomographic synthetic aperture radar (TomoSAR) technique, whose baseline configuration conforms to the coprime array geometry. This technique is devoted to reducing the required number of acquisitions in the practical application where the number of flight passes is usually restricted due to cost consideration and temporal decoherence. This letter extends the tomographic reconstruction of the coprime TomoSAR to the atomic norm minimization (ANM) framework to pursue super-resolution. A compact ANM approach is proposed in this letter for the tomographic reconstruction of coprime TomoSAR in the presence of multiple looks data. Compared with the conventional ANM approach, the proposed approach compresses the dimension of the ANM model to a smaller size by two operations. One operation is that the equivalent covariance matrix is constructed to be conformed with the covariance matrix of the real acquisition data. The other operation is adopting the singular value decomposition (SVD) technique to reduce the look dimension of acquisition data. As a result, the compact approach reduces the computation complexity without performance loss. It is confirmed by simulation experiments.

Feature matching refers to the establishment of reliable correspondence between two sets of local features, which is an essential approach in remote sensing applications such as image registration and mosaicking. In this paper, a simple yet effective method, called frame-based locality preservation matching, is proposed for robust remote sensing image matching. We primarily focus on those images pairs that involve large-scale geometric transformations (e.g., extreme zoom). The key idea of our approach is to dig up the frame knowledge, such as the feature orientation and scale implied by common features like SIFT. The frame knowledge is free to obtain, and we find it to be of great significance in feature matching, especially for our focus -- large-scale geometric transformations. The proposed method can easily handle the geometric challenges and high outlier proportions, and significantly improves the performance compared to other state-of-the-art methods.

Road extraction is an important part of synthetic aperture radar (SAR) image interpretation. In recent years, circular SAR (CSAR) has attracted extensive attention from researchers owing to its ability of 360° observation. Due to the unique imaging geometry of CSAR, CSAR images contain more complete road information. However, the curvilinear-structured appearance of roads in CSAR images and the complexity of the scene result in difficulties in road extraction. The curvilinear structure detector (CSD) is capable of extracting the curvilinear structures with a specific width from complicated image scenes. Based on the traditional CSD, an improved CSD (ICSD) for local road area extraction from CSAR images is introduced in this article. First, by adopting ICSD, the edges of a CSAR image and centerlines of local roads are extracted, as well as their direction. Second, the local roads are obtained by geometrical and radiometrical rules. Finally, the missing intersections and edge pixels are repaired to acquire high-precision and high-quality extraction results of the local road area. The experimental results on different band CSAR images reveal that the proposed method exhibit enhanced performance than the three state-of-the-art methods.

Feature matching is a fundamental technique in remote sensing image processing. This article proposes a new formulation of affine covariant feature matching for remote sensing images, where we suggest matching features by matching two sets of triplets. Compared with previous works, the formulation exploits the whole feature frame rather than the 2-D location to reject outliers. Besides, we also develop a new latent variable model to combine the feature frame and the SIFT ratio values, to enhance the convergence speed and success rate in challenging cases. We evaluate our model on three challenging datasets in terms of both qualitative and quantitative experiments. We also study the robustness to outliers since remote sensing images are typically affected by mismatches. The results demonstrate that the proposed method provides excellent matching performance with satisfying runtime and shows good robustness to outliers.

Hyperbola detection is an important application field of ground-penetrating radar (GPR) systems as underground threats and targets detected by these systems are presented in the form of a hyperbola. However, the low-amplitude hyperbola detection of deeply-buried targets and targets with low metal content has remained a major challenge due to the increase in the attenuation of radar echo with an increase in the detection depth and the features with low resolution extracted by existing methods. In this study, first, a high-level visual feature, namely, phase symmetry, is proposed to effectively improve the feature resolution and the robustness of amplitude change in GPR images. Then, we propose a handcrafted feature descriptor based on phase symmetry, namely, histogram of oriented vector phase symmetry (HOVPS) to improve the detection of hyperbola in GPR images. In constructing HOVPS, we first cite our previous work to enhance the descriptive ability of hyperbola in GPR images. Subsequently, we extend a phase symmetry model to develop a vector feature model [namely, vector phase symmetry (VPS)]. Finally, HOVPS is developed based on the VPS to extract structural information from GPR images. The proposed HOVPS describes the shape features in GPR images using a symmetrical structure, and it is used as the feature input of the classifier for hyperbola detection. The qualitative analysis of the proposed method is performed by comparing the performance of the proposed method for the extraction of features on different GPR data with those of other methods. In addition, we also provide quantitative analysis on different signal-to-noise ratio (SNR) test sets, and the results reveal that the proposed method outperforms various state-of-the-art methods (e.g., GPR histogram of oriented gradient (gprHOG), edge histogram descriptor (EHD), and log-Gabor (LG) feature).

Circular synthetic aperture radar (CSAR) observes the scene by 360 degrees, the characteristics of targets from different aspects can be obtained. The noncoherent imaging is more popular since more textural features and lower speckle noise can be acquired. However, due to the motion error of the radar platform and the topography of observation scene, the noncoherent imaging result of full aperture can not be derived by simply noncoherent superimposing the subaperture images. In this paper, based on the enhanced correlation coefficient (ECC), we proposed a registration strategy to obtain full aperture noncoherent imaging result of CSAR, and the experiments demonstrate the effectiveness of our method.

Holographic synthetic aperture radar (HoloSAR) tomography is an attractive imaging mode that can retrieve the 3-D scattering information of the observed scene over 360° azimuth angle variation. To improve the resolution and reduce the sidelobes in elevation, the HoloSAR imaging mode requires many passes in elevation, thus decreasing its feasibility. In this article, an imaging method based on iterative adaptive approach (IAA) and generalized likelihood ratio test (GLRT) is proposed for the HoloSAR with limited elevation passes to achieve super-resolution reconstruction in elevation. For the elevation reconstruction in each range-azimuth cell, the proposed method first adopts the nonparametric IAA to retrieve the elevation profile with improved resolution and suppressed sidelobes. Then, to obtain sparse elevation estimates, the GLRT is used as a model order selection tool to automatically recognize the most likely number of scatterers and obtain the reflectivities of the detected scatterers inside one range-azimuth cell. The proposed method is a super-resolving method. It does not require averaging in range and azimuth, thus it can maintain the range-azimuth resolution. In addition, the proposed method is a user parameter-free method, so it does not need the fine-tuning of any hyperparameters. The super-resolution power and the estimation accuracy of the proposed method are evaluated using the simulated data, and the validity and feasibility of the proposed method are verified by the HoloSAR real data processing results.

By introducing curvilinear structures extraction (CSE) instead of watershed algorithm (WA) or nonmaximum suppression (NMS) to edge strength map (ESM), an improved ratio of exponentially weighted averages (ROEWA) edge detector with better capacity for weak edges detection is proposed to extract smooth edges and edge direction of synthetic aperture radar (SAR) images. Using the ROEWA, the ESM is calculated. Then the CSE algorithm is employed to extracted edges, by acquiring eigenvectors and eigenvalues of the Hessian matrix, the improved ESM (IESM) is obtained, which ensures the good weak edge detection capacity and smoothness of edges. Experimental results on simulated and real SAR images show that the improved ROEWA based on CSE attains better performance than the one using WA or NMS.

Noncoherent signal model is widely applied to angular superresolution in forward-looking imaging radar. However, relative phase influences the resolvability of the model in coherent applications. We propose a coherent signal model by replacing the antenna power pattern with the antenna radiation pattern. Experiment results have demonstrated significant resolution improvements for forward-looking imaging in coherent scanning radars.

Holographic synthetic aperture radar tomography can realize full 3-D reconstructions of objects over 360° with very high resolution, and thus becomes an interesting 3-D imaging technique. However, due to the uncompensated platform motion errors, phase errors among different tracks usually exist in this imaging mode, which will hinder the 3-D image focusing. In this letter, a phase calibration method based on phase gradient autofocus is proposed to mitigate the influence of these phase errors. It exploits the space-invariant characteristic of the phase errors in a limited scene and uses an efficient and robust multibaseline autofocus to calibrate the phase errors among the multiple circular tracks. Experimental results with the GOTCHA real data are carried out to demonstrate the validity and feasibility of the proposed method.

Since the trajectory deviations of a radar platform cause serious phase errors that degrade the focusing quality of synthetic aperture radar (SAR) imagery, an autofocus method is very important for high-resolution airborne SAR imaging. In this letter, an extended autofocus backprojection (EABP) algorithm is developed to accommodate the phase errors. Under the criterion of maximum image sharpness, the traditional ABP algorithm supports a broader class of collection and imaging geometries. However, it neglects the influence of SAR image energy distribution on the estimation of phase errors that make it inapplicable for SAR imaging, which has high dynamic range, such as low-frequency SAR imaging. By choosing regions and balancing the energy distribution of the data, the EABP algorithm is more efficient and useful to avoid the estimation error caused by the unbalanced energy distribution. Its performance has been demonstrated by using the experimental data that are acquired by a P-band airborne SAR system with a low-accuracy global positioning system.

The ultrawideband (UWB) bistatic forward-looking synthetic aperture radar (BFSAR) can realize the high-resolution imaging in the forward direction of the transmitter/receiver, so it has significant applications in both civil and military fields. However, compared to the general narrowband side-looking bistatic synthetic aperture radar systems, the UWB BFSAR systems have larger fractional signal bandwidth and more special acquisition geometry, which will affect the behavior of spatial resolutions. Current methods for spatial resolution analysis of the UWB BFSAR are unsuitable because they do not consider the effects of these two special issues. This letter analyzes the special behavior of spatial resolutions in the UWB BFSAR, and the straightforward gradient method is utilized and extended based on the analysis to calculate the spatial resolutions. The theoretical analysis shows that the range resolution can be calculated by the traditional gradient method directly but the Doppler resolution should be calculated by the extended method. Simulated results verify the correctness of the theoretical analysis and the validity of the proposed method.

Space-time adaptive processing based on clutter sparse recovery (SR-STAP) methods outperform traditional statistical-STAP algorithms in scenarios with limited training numbers. However, the computational burden of current SR-STAP methods is extremely heavy, particularly when the number of discretized angle and Doppler grid points is large, which hinders these methods from coming into practical use. This letter proposes a spectrum-aided reduced-dimension SR-STAP method to overcome this issue. The proposed method employs the clutter spectrum estimated by training samples to design the reduced-dimension dictionary. By solving a reduced-dimension sparse recovery problem, the computational load of the proposed method can be reduced significantly while only slightly degrading the performance of clutter suppression and target detection compared with current SR-STAP methods. Numerical experiments using both simulated and measured data validate the effectiveness of the proposed method.

In the last few years, interest in circular synthetic aperture radar (CSAR) acquisitions has arisen as a consequence of the potential achievement of 3D reconstructions over 360° azimuth angle variation. In real-world scenarios, full 3D reconstructions of arbitrary targets need multi-pass data, which makes the processing complex, money-consuming, and time expending. In this paper, we propose a processing strategy for the 3D reconstruction of vehicle, which can avoid using multi-pass data by introducing a priori information of vehicle's shape. Besides, the proposed strategy just needs the single-pass single-polarization CSAR data to perform vehicle's 3D reconstruction, which makes the processing much more economic and efficient. First, an analysis of the distribution of attributed scattering centers from vehicle facet model is presented. And the analysis results show that a smooth and continuous basic outline of vehicle could be extracted from the peak curve of a noncoherent processing image. Second, the 3D location of vehicle roofline is inferred from layover with empirical insets of the basic outline. At last, the basic line and roofline of the vehicle are used to estimate the vehicle's 3D information and constitute the vehicle's 3D outline. The simulated and measured data processing results prove the correctness and effectiveness of our proposed strategy.

Phase unwrapping (PU) is significant in reconstructing the digital elevation model of a scene from its interferometric synthetic aperture radar (InSAR) data. The classical minimum discontinuity (MD) PU algorithm by Flynn is highly accurate but involves time-consuming computation. To overcome this shortcoming, we proposed a preunwrapping-assisted MD (PAMD) PU method, which has high efficiency and the same unwrapping quality as Flynn's algorithm. In the PAMD method, the phase image is first unwrapped by the preunwrapping algorithm, which generates and optimizes the dipole cuts. The preunwrapping algorithm is fairly fast, and the obtained result is much closer to the optimal solution of MD; therefore, it can be further optimized by Flynn's algorithm efficiently. Tests on simulated and real InSAR data confirm the accuracy and the efficiency of the proposed method.

This paper presents an efficient raw signal generation method based on equivalent scatterer and subaperture processing for the one-stationary bistatic synthetic aperture radar (SAR). It considers the moving platform's motion error to generate the precise raw signal for real SAR systems. First, the imaging geometry in elliptical polar coordinates is built, and then, the scene is divided into several equidistant elliptical rings. Based on the equivalent scatterer model, the approximate SAR system transfer function is derived; thus, each pulse's raw signal is calculated by the convolution of the transmitted signal and transfer function, via the fast Fourier transform (FFT). To further improve the simulation speed, the subaperture and subscene processing is used. The transfer function for the same subaperture's pluses is calculated simultaneously by the weighted sum of all subscenes' equivalent scattering coefficient in the same equidistant elliptical ring, which is performed by the nonuniform FFT (NUFFT). This method only involves the FFT, NUFFT, and complex multiplication, which means the easier operation and higher efficiency. The implementation, limitation, and evaluation of the proposed method are discussed. Simulation results are given to prove the correctness and validity of the proposed method.

Phase unwrapping (PU) for large-scale images is a new challenging problem in reconstructing a digital elevation model from synthetic aperture radar interferometry (InSAR) data. In this letter, we proposed a region-partition-based PU method that could improve the efficiency and decrease the processing memory of the large-scale PU problem for P-band ultrawideband (UWB) InSAR. The interferometric phase is flattened by the reference phase, which is generated from the shift estimation in the registration step. We refer to the residual phase as the misregistration phase (MRP), which corresponds to the error of the shift estimation. The MRP is unambiguous in most of the area with high coherence because of the large fractional bandwidth; thus, the regions that assuredly have the unambiguous MRP are partitioned out from the MRP image and referred to as the high-quality area. Meanwhile, the remaining low-quality areas are separated by the high-quality areas and are considered irregular tiles. After unwrapping the tiles by a minimum discontinuity PU algorithm either in parallel or in series, the full-size unwrapped result is obtained. The test performed on real P-band UWB InSAR data confirms the effectiveness and efficiency of our method.

Compressed sensing (CS) based radar imaging requires the use of a mathematical model of the observation process. Inaccuracies in the observation model may cause defocusing in the reconstructed images. In the observation process, the observation positions are usually not known perfectly. Imperfect knowledge of the observation positions is a major source of model errors in imaging. In this paper, a method is proposed to compensate the observation position errors in CS-based radar imaging. Instead of treating the observation-position-induced model errors as phase errors in the data, the proposed method can determine the observation position errors as part of the imaging process. It uses an iterative algorithm, which cycles through steps of target reconstruction and observation position error estimation and compensation. The proposed method can estimate the observation position errors accurately, and the reconstruction quality of the target images can be improved significantly. Simulation results and experimental results from rail-mounted radar and airborne synthetic aperture radar are presented to show the effectiveness of the proposed method.

This paper presents a sparse multiple-input and multiple-output (MIMO) array and sparse frequency ground-penetrating radar (GPR) imaging scheme based on compressed sensing (CS). Since the targets of interest for GPR are usually sparse, the number of the MIMO array elements and frequencies can be reduced using CS theory. Thus, the system complexity and data acquisition time can be reduced accordingly. Considering the serious clutter in forward-looking GPR, we propose two methods for the CS reconstruction in clutter environment. The first one is a clutter suppression preprocessing method, which can effectively suppress the azimuth clutter and short range clutter outside the reconstruction region and significantly improve the reconstruction result. The second one is to determine the regularization parameter for the CS reconstruction in clutter environment. We refer to this reconstruction process as basis pursuit declutter. The proposed imaging scheme can produce pointlike and less cluttered images of sparse targets using fewer array elements and frequencies. Results from simulated data, trihedral reflector, and real buried land mine experimental data are presented to show the validity of the proposed methods. The experimental data are acquired by the vehicle-mounted stepped-frequency forward-looking ground-penetrating virtual aperture radar, which is designed and developed by the National University of Defense Technology.

This paper focuses on the problem of moving human target detection in foliage environment, which is a challenge in a radar system. As a matter of fact, owing to the rough surfaces of trunks, branches, and leaves, there is always a lot of multipath clutter remaining which will severely influence the detection performance. In the study, a method combined with entropy weighted coherent integration (EWCI) and the Hough transform is put forward. The method can effectively suppress not only the stationary clutter but also the multipath clutter. The nonline-of-sight (NLOS) foliage-penetration measurements are set up and the results prove the superiority of our method.

To improve time of arrival (TOA) estimation in impulse radio ultra wideband (IR UWB) ranging under harsh conditions, a novel method based on the rank statistics of the received signals is proposed to detect the first path (FP) in dense multipath, in which the FP is not always the strongest. Under the energy detection (ED) receiver, many threshold based methods are proposed for TOA estimation in the AWGN. However, many of them do not work well under harsh conditions, for example, when the noise is non-Gaussian or when there are outliers in the received signal. In these situations, there will be more random large samples in the output of the ED receiver, which will affect the FP detection, as it will be hard to model the received signal. The proposed method can solve the problem and it does not require prior information. Simulation results demonstrate its effectiveness.

Stepped-frequency waveforms can achieve an ultrawide bandwidth by using a sequence of single-frequency pulses. The advantages of stepped-frequency waveforms are low hardware requirements and high resolution. However, the stepped-frequency waveform requires a long time period to transmit the signals, which limits its application in synthetic aperture radar (SAR). The available imaging range width is usually very narrow, unless the range and azimuth resolutions are both decreased. In this paper, a random-frequency SAR imaging scheme based on compressed sensing is proposed. If the targets are sparse or compressible, it is sufficient to transmit only a small number of random frequencies to reconstruct the image of the targets. This means that the limitations of the stepped-frequency technique for SAR can be overcome. The available imaging range width can be enlarged significantly, while the range and azimuth resolutions are both maintained. Random undersampling is very easy to implement for both range and azimuth dimensions, and no new hardware components are needed. Simulation and experimental results are presented to demonstrate the validity of the proposed method.

The compressed sensing (CS) synthetic aperture radar (SAR) imaging scheme can use random undersampled data to reconstruct images of sparse or compressible targets. However, compared to Nyquist sampling, the cost of the CS imaging scheme is the long reconstruction time, particularly for the conventional reconstruction strategy, which reconstructs the whole scene in one process. It also needs a large memory to access the sensing matrix used for reconstruction. In this paper, a segmented reconstruction strategy for the CS SAR imaging scheme is proposed. The whole scene is split into a set of small subscenes, so that the reconstruction time can be reduced significantly. The proposed method also needs much less memory for computation than the conventional method. In this proposed method, the range profiles are reconstructed first, and then, the range profiles can be split into subpatches. Subscenes can be reconstructed by using the subpatch data, and the whole scene can be obtained by combining the reconstructed subscenes. Simulation and experimental results are shown to demonstrate the validity of the proposed method.

A system with 3-D imaging capability can be implemented by using a frequency modulated continuous wave (FMCW) radar which synthesizes a two-dimensional (2-D) planar aperture. A millimeter-wave FMCW three-dimensional (3-D) imaging system can be used for the detection of concealed weapons and contrabands at airports or other security checkpoints, since millimeter-wave can readily penetrate common clothing material. A 3-D image can be formed by coherently integrating the backscatter data over the measured frequency bandwidth and the two spatial coordinates of the 2-D synthetic aperture. This paper presents a 3-D imaging algorithm for near field FMCW radar. This algorithm is an extension of the 2-D range migration algorithm (RMA). We derive the formulation in detail by using the principle of stationary phase (POSP). A 3-D version Stolt interpolation is used in this algorithm. Accurate image reconstruction and high computational efficiency of this algorithm are demonstrated through simulation results.

Inspired by recent advances in multistatic radar systems, the problem of sensor placement is investigated. Our study is motivated by the fact that it is not always clear what the placement of the radars giving the best performance for the targets of interest might be. To account for the issue, we derive the multistatic Cramér-Rao lower bounds (CRLBs) for range and velocity estimation as the fitness function. Then we use genetic algorithms (GAs) to perform the optimized sensor placement as one of global optimization. The simulation example indicates that our proposed approach is a flexible and effective tool and is capable of suggesting optimal sensor placement strategies to meet required radar performance goals.

An extended two-step focusing approach (ETSFA) for processing the squinted spotlight synthetic aperture radar (SAR) data is proposed in this paper. The effect of the squint angle on the azimuth coarse focusing is analyzed and discussed. Based on the analysis results, a nonlinear shift preprocessing method is introduced, which can completely remove the squint angle impacts on the azimuth coarse focusing. Furthermore, based on the squinted spotlight SAR imaging model and the preprocessed echo data, derivations of the azimuth coarse focusing with the deramping-based technique and precise focusing with the modified Stolt-based technique are carried out in detail. Moreover, to produce an acceptable image by the proposed ETSFA for high-resolution ($<$3 m) squinted spotlight SAR with large scene, a subscene processing method is introduced. The experimental results on simulated data prove the validity of the whole analysis and the proposed methods.

In this paper, an extended nonlinear chirp scaling (ENLCS) algorithm for focusing synthetic aperture radar data acquired at high resolution and highly squint angle is proposed. The whole processing of the ENLCS consists of the following three steps. First, a linear range walk correction is used to remove the linear component of target range cell migration (RCM) and to mitigate the range-azimuth coupling of the 2-D spectrum. Second, a bulk second range compression (SRC) is performed in the 2-D frequency domain for compensating the residual RCM, SRC term, and higher order range-azimuth coupling terms. Third, a modified azimuth NLCS (ANLCS) operation is applied to equalize the azimuth frequency modulation rate for azimuth compression. By adopting higher order approximation processing and by properly selecting the scaling coefficients, the proposed modified ANLCS operation has better accuracy and little image misregistration. The overall focusing procedure of the ENLCS algorithm only involves fast Fourier transform and complex multiplication, which means easier implementation and higher efficiency. The experimental results with simulated data prove the effectiveness of the proposed algorithm.

This paper presents a synthetic aperture radar (SAR) imaging system using a stepped frequency waveform. The main problem in stepped frequency SAR is the range difference in one sequence of pulses. This paper analyzes the influence of range difference in one sequence of pulses in detail and proposes a method to compensate this influence in the Doppler domain. A Stolt interpolation for the stepped frequency signal is used to focus the data accurately. The parameters for the stepped frequency SAR are analyzed, and some criteria are proposed for system design. Finally, simulation and experimental results are presented to demonstrate the validity of the proposed method. The experimental data are collected by using a stepped frequency radar mounted on a rail.

We propose here a new approach for synthetic aperture radar (SAR) imaging of ground moving targets. The unique characteristic of this approach is that range curvature (i.e., quadratic range migration) can be corrected by a simple processing step. A keystone transform is used to correct range walk (i.e., linear range migration) for all targets without knowing their velocities, and the range curvature is corrected in the range-Doppler domain. The advantage of this approach is that it is simple to implement and can correct range curvature for all targets in one processing step, so that it is computationally efficient. Simulation and experimental SAR data processing results are presented to demonstrate the validity of the proposed approach.

Phase adjustment by contrast enhancement (PACE) is an autofocus algorithm that is capable of performance that is unattainable by conventional techniques. It is a nonparametric method that requires no constraints on the type of phase error to be measured. The algorithm does not require special data culling techniques or the presence of isolated scatterers. However, the drawback of PACE algorithm is that the number of estimated variables is very large; it leads to a long computational time. The azimuth sampling frequency is commonly much bigger than the bandwidth of phase error in SAR image so that we can estimate part of the phase error variables and then obtain the whole variables by interpolation; this induces the interpolated phase adjustment by contrast enhancement (IPACE) algorithm. The IPACE algorithm can remarkably reduce the computational time while maintaining the accuracy. This letter has derived the detailed processing of IPACE, and the results of the experiments using real SAR data are presented to show the validity of the proposed algorithm.