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Curvilinear Flight Synthetic Aperture Radar (SAR): Analysis, Methods, and Applications

A special issue of Remote Sensing (ISSN 2072-4292). This special issue belongs to the section "Remote Sensing Image Processing".

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 28902

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Guest Editor
Department of Electrical Engineering, City University of Hong Kong, Hong Kong, China
Interests: radar systems; adaptive beam-forming; tracking algorithms; systems engineering; remote imaging
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The utilization of range and Doppler information to produce synthetic aperture radar (SAR) images is a technique used in diverse fields, including air-to-ground imaging of objects, terrain, and oceans. The conventional SAR systems, which are mounted on aircrafts or satellites at certain heights, have been extensively investigated in the past several decades and found to be particularly useful under poor weather or illumination conditions. In the literature, the velocity is usually assumed as a constant value with a linear flight path. However, in practical environments, variations from this ideal model are inevitable. Small deviations, such as in airborne or spaceborne SAR, are mainly caused by atmospheric turbulence or rotation of the earth. Larger variations from the ideal path challenge the traditional design and processing technology, such as those experienced by SAR systems on drones, missiles, helicopters, or hypersonic vehicles engaging in high-acceleration “pop-up” maneuvers to perform post-earthquake change detection and monitoring of curvilinear areas of interest (corridor mapping), i.e., rivers, nearby (potential) flooding areas, and traffic routes. Nevertheless, the above highlight the need to devise new observation configurations based on multifrequency, multiantenna, or even multiplatform SAR systems.

This Special Issue is devoted to highlighting the most advanced research studies on curvilinear flight SAR technologies, methodologies, and applications. Papers dealing with fundamental theoretical analyses as well as those demonstrating their application in real-world and emerging problems are welcomed. This journal publishes original papers and occasionally invited review articles in all areas related to curvilinear flight SAR, including, but not limited to, the following suggested topics:

  • New SAR systems mounted on drones, CubeSats, missiles, helicopters, hypersonic vehicles, and automobile with curvilinear trajectories;
  • Monostatic and bistatic SAR algorithms with curvilinear flight paths;
  • Curvilinear flight SAR ground moving target indication (GMTI);
  • Curvilinear flight interferometric SAR (InSAR) and tomographic SAR (TomoSAR);
  • Curvilinear flight SAR three-dimensional (3-D) imaging;
  • Curvilinear flight SAR image target recognition;
  • Multichannel, multifrequency, and multiantenna SAR;
  • Digital beam-forming (DBF) SAR imaging approaches;
  • Real-time SAR processing system designs and algorithms

Prof. Dr. Hing Cheung So
Prof. Dr. Shiyang Tang
Prof. Dr. Alfonso Farina
Guest Editors

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Keywords

  • Synthetic aperture radar (SAR)
  • Curvilinear flight
  • SAR processing
  • SAR ground moving target indication (GMTI)
  • Three-dimensional (3-D) SAR
  • Real-time SAR processing
  • SAR interferometry
  • SAR tomography
  • SAR image target recognition
  • Other SAR applications

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Published Papers (13 papers)

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11 pages, 3333 KiB  
Communication
Super-Resolution Technique of Multi-Radar Fusion 2D Imaging Based on ExCoV Algorithm in Low SNR
by Dawei Song, She Shang and Dazhi Ding
Remote Sens. 2023, 15(8), 2108; https://doi.org/10.3390/rs15082108 - 17 Apr 2023
Viewed by 1293
Abstract
Limited by the hardware, the bandwidth of the transmitted signal is not wide enough for super resolution; this is the same for cross resolution, which is limited by the observation angle. In this paper, we propose a technique for imaging fusion using 2D-imaging [...] Read more.
Limited by the hardware, the bandwidth of the transmitted signal is not wide enough for super resolution; this is the same for cross resolution, which is limited by the observation angle. In this paper, we propose a technique for imaging fusion using 2D-imaging super-resolution by using multi-radar data from different observation locations, and the resultant effective band is proposed. First, a sparse 2D parametric model based on GTD theory is introduced to construct a dictionary by matching the scattering theory of the radar observation target. Then, the multi-radar fusion imaging framework is constructed. Meanwhile, the 2D model’s sparse parameters are obtained in low SNR using an expansion-compression variance-component algorithm. Finally, radar echo data is expanded to realize the fusion imaging process. The simulation results show that the image quality is improved after multi-radar fusion, which is better than that of the single radar echo, verifying the effectiveness of our method. Full article
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23 pages, 8251 KiB  
Article
Joint Communication and Jamming System Design Based on Filter Bank Multicarrier Chirp Waveform: Using for Curvilinear Flight Scenario
by Gaogao Liu, Wenbo Yang, Yuqian Bao, Youming Wang and Peng Li
Remote Sens. 2023, 15(5), 1239; https://doi.org/10.3390/rs15051239 - 23 Feb 2023
Cited by 3 | Viewed by 2281
Abstract
A joint communication jamming waveform is proposed in this study based on the FBMC- chirp. To increase the number of false targets in a single pulse period, the chirp signal is modulated to different subcarrier groups. Since the subcarriers of the FBMC-OQAM signal [...] Read more.
A joint communication jamming waveform is proposed in this study based on the FBMC- chirp. To increase the number of false targets in a single pulse period, the chirp signal is modulated to different subcarrier groups. Since the subcarriers of the FBMC-OQAM signal are orthogonal, the signals are naturally orthogonal. This allows the transmitter and receiver to be separated and achieve multiple false target jamming, allowing the CFAR threshold to be raised by about 20 dB and protecting the target from detection. The ratio of the frequency shift of the designed jamming signal to the frequency modulation depends on the delay time, making the joint signal more robust in response to jamming and resistant to frequency modulation. The use of intercepted radar signals allowed channel estimation, providing high-speed digital transmission while ensuring multi-false-target jamming. The simulation results show that the joint signal has jamming effects on the pulse Doppler radar. The proposed FBMC chirp joint waveform requires about 20 dB less jamming signal ratio than the existing method, and thus the energy saved can ensure the robust performance of the communication subsystem in the joint communication jamming system. The proposed system has excelled in communication rate and bit error rate performance, ensuring that instructions are accurately and completely transmitted while implementing effective jamming. Full article
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18 pages, 5503 KiB  
Article
Back-Projection Imaging for Synthetic Aperture Radar with Topography Occlusion
by Zhanye Chen, Zhiqiang Zeng, Dongning Fu, Yan Huang, Qiang Li, Xin Zhang and Jun Wan
Remote Sens. 2023, 15(3), 726; https://doi.org/10.3390/rs15030726 - 26 Jan 2023
Cited by 2 | Viewed by 2433
Abstract
When synthetic aperture radar (SAR) is conducting remote sensing or terrain mapping, its radar beam is inevitably occluded by the variations in the under-test topography. Although back-projection algorithm (BPA) can theoretically directly solve the imaging problems of topography variations that most current SAR [...] Read more.
When synthetic aperture radar (SAR) is conducting remote sensing or terrain mapping, its radar beam is inevitably occluded by the variations in the under-test topography. Although back-projection algorithm (BPA) can theoretically directly solve the imaging problems of topography variations that most current SAR imaging algorithms cannot handle, these BPAs only solve the phase focusing of SAR echo signal, and do not consider the mismatch of SAR imaging results caused by topography occlusion. To solve the mis-imaging issue of the occluded area generated by BPA under the case of topography variation, a topography-based BPA (Topo-BPA) is proposed in this paper. Firstly, a new beam occlusion judgment algorithm based on spherical wave assumption is proposed, and its core is depression angle interpolation and depression angle updating. Then, the proposed Topo-BPA embeds the proposed beam occlusion judgment algorithm before the classical BPA, which not only did not reduce the focus depth of BPA, but improved the imaging accuracy of classical BPA. Finally, numerical experiments have demonstrated the superiority of the Topo-BPA’s performance in comparison with classical BPA. Full article
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23 pages, 8057 KiB  
Article
Focus Improvement of Spaceborne-Missile Bistatic SAR Data Using the Modified NLCS Algorithm Based on the Method of Series Reversion
by Zirui Xi, Chongdi Duan, Weihua Zuo, Caipin Li, Tonglong Huo, Dongtao Li and He Wen
Remote Sens. 2022, 14(22), 5770; https://doi.org/10.3390/rs14225770 - 15 Nov 2022
Cited by 8 | Viewed by 1641
Abstract
The speed and direction of a missile shifts sharply in the dive phase, making the azimuth frequency modulation (FM) rate change with the azimuthal position, leading to azimuth ambiguities and image distortion. To solve this problem, a modified nonlinear chirp scaling (NLCS) algorithm [...] Read more.
The speed and direction of a missile shifts sharply in the dive phase, making the azimuth frequency modulation (FM) rate change with the azimuthal position, leading to azimuth ambiguities and image distortion. To solve this problem, a modified nonlinear chirp scaling (NLCS) algorithm was adopted to compensate for the azimuth FM rate. First, the geometric configuration and echo signal model of the spaceborne missile bistatic synthetic aperture radar (SAR) were built, and then the Doppler frequency correction was performed, and the 2-D spectrum of the signal was derived by the method of series reversion. Next, range migration correction and range compression were finished in the 2-D frequency domain. Following this, a modified NLCS algorithm was proposed to solve the space variance of Doppler phase problem. After compensating for the azimuth FM rate, the azimuth compression focusing was completed and the imaging result was obtained. Finally, by comparing the calculation amount, imaging effect, and performance index with the traditional NLCS algorithm, it can be concluded that the algorithm reduced the calculation amount by 1.0128 × 108 floating point operations per second (FLOPs) compared with the traditional NLCS algorithm, and the azimuth focusing effect of the edge point was greatly improved. Its resolution, peak sidelobe ratio (PSLR), and integrated sidelobe ratio (ISLR) were improved by 0.87 m, 3.32 dB, and 1.79 dB, respectively, which proved the effectiveness and feasibility of this method. Full article
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19 pages, 4018 KiB  
Article
A-BFPN: An Attention-Guided Balanced Feature Pyramid Network for SAR Ship Detection
by Xiuqin Li, Dong Li, Hongqing Liu, Jun Wan, Zhanye Chen and Qinghua Liu
Remote Sens. 2022, 14(15), 3829; https://doi.org/10.3390/rs14153829 - 8 Aug 2022
Cited by 22 | Viewed by 3053
Abstract
Thanks to the excellent feature representation capabilities of neural networks, target detection methods based on deep learning are now widely applied in synthetic aperture radar (SAR) ship detection. However, the multi-scale variation, small targets with complex background such as islands, sea clutter, and [...] Read more.
Thanks to the excellent feature representation capabilities of neural networks, target detection methods based on deep learning are now widely applied in synthetic aperture radar (SAR) ship detection. However, the multi-scale variation, small targets with complex background such as islands, sea clutter, and inland facilities in SAR images increase the difficulty for SAR ship detection. To increase the detection performance, in this paper, a novel deep learning network for SAR ship detection, termed as attention-guided balanced feature pyramid network (A-BFPN), is proposed to better exploit semantic and multilevel complementary features, which consists of the following two main steps. First, in order to reduce interferences from complex backgrounds, the enhanced refinement module (ERM) is developed to enable BFPN to learn the dependency features from the channel and space dimensions, respectively, which enhances the representation of ship objects. Second, the channel attention-guided fusion network (CAFN) model is designed to obtain optimized multi-scale features and reduce serious aliasing effects in hybrid feature maps. Finally, we illustrate the effectiveness of the proposed method, adopting the existing SAR Ship Detection Dataset (SSDD) and Large-Scale SAR Ship Detection Dataset-v1.0 (LS-SSDD-v1.0). Experimental results show that the proposed method is superior to the existing algorithms, especially for multi-scale small ship targets under complex background. Full article
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28 pages, 4886 KiB  
Article
Curvilinear Flight Synthetic Aperture Radar (CF-SAR): Principles, Methods, Applications, Challenges and Trends
by Zhanye Chen, Shiyang Tang, Yi Ren, Ping Guo, Yu Zhou, Yan Huang, Jun Wan and Linrang Zhang
Remote Sens. 2022, 14(13), 2983; https://doi.org/10.3390/rs14132983 - 22 Jun 2022
Cited by 7 | Viewed by 2559
Abstract
The research into curvilinear flight synthetic aperture radar (CF-SAR) is the inevitable result of the comprehensive practicality of SAR. The flight path of the SAR platform in real applications, which is highly nonlinear or curvy due to three-dimensional velocity and acceleration, cannot be [...] Read more.
The research into curvilinear flight synthetic aperture radar (CF-SAR) is the inevitable result of the comprehensive practicality of SAR. The flight path of the SAR platform in real applications, which is highly nonlinear or curvy due to three-dimensional velocity and acceleration, cannot be described by the traditional uniform linear motion model. New mathematical models, signal characteristics, imaging algorithms, and system design criteria must be proposed and investigated for CF-SAR. This paper provides a comprehensive overview of CF-SAR. Firstly, the basic concept, unified model, and general signal characteristics of CF-SAR are defined, derived, and analyzed, respectively. Additionally, the advantages and drawbacks of current methodologies are reviewed. Discussions on the CF-SAR’s applications are presented from the perspective of typical platforms, new configurations, and advanced technologies, which are suitable means to fulfill the increasing user requirements. Finally, the challenges faced by CF-SAR are summarized, and some future trends for the study of CF-SAR are explored. Hopefully, this paper will serve as a reference for SAR researchers/engineers and stimulate the future development and actual application of CF-SAR. Full article
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23 pages, 9134 KiB  
Article
Fast Approach for SAR Imaging of Ground-Based Moving Targets Based on Range Azimuth Joint Processing
by Yuxiang Shu, Jun Wan, Dong Li, Zhanye Chen and Hongqing Liu
Remote Sens. 2022, 14(13), 2965; https://doi.org/10.3390/rs14132965 - 21 Jun 2022
Cited by 2 | Viewed by 1773
Abstract
The synthetic aperture radar (SAR) images of a moving target may be out of focus, given the motions of a non-cooperative target. Doppler ambiguities, including the Doppler center blur and spectrum ambiguity, will easily appear due to the limitations of pulse repetition frequency, [...] Read more.
The synthetic aperture radar (SAR) images of a moving target may be out of focus, given the motions of a non-cooperative target. Doppler ambiguities, including the Doppler center blur and spectrum ambiguity, will easily appear due to the limitations of pulse repetition frequency, which causes difficulty in moving-target imaging. Therefore, a robust fast Doppler ambiguity approach for SAR imaging of a ground-based moving target using range azimuth joint processing (RAJP) is presented. Firstly, the use of RAJP, based on a two-dimensional cross-correlation function and linear range cell migration (LRCM) compensation function, is proposed to simultaneously obtain the first- and second-order phase parameters in the fast-time and azimuth-frequency domains. Then, a corresponding azimuth reference function is constructed to image the moving target. Additionally, a principal component analysis-based operation is introduced to solve the mismatch with the LRCM compensation function. The couplings between the range and azimuth and between the first- and second-order parameters can be simultaneously decoupled by the proposed RAJP operation, which simplifies the processing steps. The developed approach can simultaneously obtain the first- and second-order parameters in the fast-time and azimuth-frequency domains, which avoids the propagation error of parameter estimation caused by the stepwise processing operation. The proposed method is relatively fast, given the need for fewer processing steps. The presented approach is robust in terms of Doppler ambiguity and handles the blind speed sidelobe well. In this study, simulated and real data are processed to verify the proposed approach. Full article
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18 pages, 8040 KiB  
Article
An Improved Spatially Variant MOCO Approach Based on an MDA for High-Resolution UAV SAR Imaging with Large Measurement Errors
by Yi Ren, Shiyang Tang, Qi Dong, Guoliang Sun, Ping Guo, Chenghao Jiang, Jiahao Han and Linrang Zhang
Remote Sens. 2022, 14(11), 2670; https://doi.org/10.3390/rs14112670 - 2 Jun 2022
Cited by 7 | Viewed by 1971
Abstract
For unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) imaging, motion errors cannot be obtained accurately when high precision motion sensors are not equipped on the platform. This means that traditional data-based motion compensation (MOCO) cannot be directly implemented due to large measurement [...] Read more.
For unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) imaging, motion errors cannot be obtained accurately when high precision motion sensors are not equipped on the platform. This means that traditional data-based motion compensation (MOCO) cannot be directly implemented due to large measurement errors. In addition, classic autofocusing techniques, such as phase gradient autofocus (PGA) or map-drift algorithm (MDA), do not perform well with spatially variant errors, greatly affecting the imaging qualities, especially for high-resolution and large-swath cases. In this study, an improved spatially variant MOCO approach based on an MDA is developed to effectively eliminate the spatially variant errors. Based on the coarse and precise MDA chirp rate error estimation, motion errors are optimally acquired by the random sample consensus (RANSAC) iteration. Two-dimensional (2D) mapping is used to decouple the spatially variant residual errors into two linear independent dimensions so that the chirp-z transform (CZT) can be performed for echo data correction. Unlike traditional approaches, the spatially variant components can be compensated without any measured motion information, which indicates that the proposed approach can be applied to the common UAV SAR system with significant measurement errors. Simulations and real data experiments were used to evaluate the performance of the proposed method. The simulation results show that the proposed algorithm is able to effectively minimize spatially variant errors and generate much better imaging results. Full article
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17 pages, 4178 KiB  
Article
Parameter Estimation for Sea Clutter Pareto Distribution Model Based on Variable Interval
by Yifei Fan, Duo Chen, Mingliang Tao, Jia Su and Ling Wang
Remote Sens. 2022, 14(10), 2326; https://doi.org/10.3390/rs14102326 - 11 May 2022
Cited by 3 | Viewed by 1635
Abstract
The generalized Pareto (GP) distribution model is often used to describe the amplitude statistical feature of sea clutter. Generally, the parameters of GP distribution are estimated by moments estimators. However, when the sea state is high, the appearance of sea spikes will increase [...] Read more.
The generalized Pareto (GP) distribution model is often used to describe the amplitude statistical feature of sea clutter. Generally, the parameters of GP distribution are estimated by moments estimators. However, when the sea state is high, the appearance of sea spikes will increase the echo of the anomalous scattering units, which leads to a decrease in the parameter estimation accuracy and target detection performance. To improve the parameter estimation accuracy, this paper proposes a novel parameter estimation method based on variable intervals. Considering the local properties of sea clutter, we take a variable interval of the entire sea clutter series for parameter estimation, where the interval position is selected according to the sea state conditions. For contrast, the bipercentile parameter estimation and truncate moment estimation are also introduced. Finally, the experiment based on the real measured X-band sea clutter datasets indicates that the proposed method outperforms the state-of-the-art moments estimators. Full article
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21 pages, 3429 KiB  
Article
An Efficient Ground Moving Target Imaging Method for Airborne Circular Stripmap SAR
by Yongkang Li, Tianyu Huo, Chenxi Yang, Tong Wang, Juan Wang and Beiyu Li
Remote Sens. 2022, 14(1), 210; https://doi.org/10.3390/rs14010210 - 4 Jan 2022
Cited by 7 | Viewed by 1958
Abstract
This paper studies the imaging of a ground moving target with airborne circular stripmap synthetic aperture radar (CSSAR). First, the range equation of a target moving with accelerations is developed. Then, a new range model of high accuracy is proposed, since the commonly [...] Read more.
This paper studies the imaging of a ground moving target with airborne circular stripmap synthetic aperture radar (CSSAR). First, the range equation of a target moving with accelerations is developed. Then, a new range model of high accuracy is proposed, since the commonly used second-order Taylor-approximated range model is inaccurate when the azimuth resolution is relatively high or the target moves with accelerations. The proposed range model also makes it easy to derive an accurate analytical expression for the target’s 2-D spectrum. Third, based on the proposed range model, the target’s 2-D spectrum is derived and an efficient imaging method is proposed. The proposed imaging method implements focusing via a phase multiplication in the 2-D frequency domain and utilizes the genetic algorithm to accomplish an efficient search of the parameters of the proposed range model. Finally, numerical experiments are conducted to validate the proposed range model and the proposed imaging method. Full article
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19 pages, 4396 KiB  
Article
A Study on the Range Equation Modeling for Multichannel Medium-Earth-Orbit SAR-GMTI Systems
by Yongkang Li, Tong Wang, Tianyu Huo and Laisen Nie
Remote Sens. 2021, 13(14), 2734; https://doi.org/10.3390/rs13142734 - 12 Jul 2021
Cited by 6 | Viewed by 1939
Abstract
This paper studies the range equation modeling of a ground moving target for multichannel medium-Earth-orbit (MEO) synthetic aperture radar (SAR) ground moving target indication (GMTI), an issue which is challenging to tackle due to the non-linear motion of the radar platform and the [...] Read more.
This paper studies the range equation modeling of a ground moving target for multichannel medium-Earth-orbit (MEO) synthetic aperture radar (SAR) ground moving target indication (GMTI), an issue which is challenging to tackle due to the non-linear motion of the radar platform and the Earth rotation. In the paper, the coordinates of the multichannel MEO SAR and the target, as well as the target’s range equation with respect to each channel, are developed. Moreover, an expression of concise form is derived for the target’s quadratic-approximated range equation, which will benefit the design of GMTI methods. Furthermore, theoretical analyses are conducted to reveal the dependency between the accuracy of the quadratic-approximated range equation and the parameters of the radar and the target. Numerical simulations are carried out to investigate the influence of the quadratic approximation of the range equation on the GMTI performance and to figure out the quadratic-approximated range equation’s scope of application. Full article
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18 pages, 816 KiB  
Article
Adaptive Beamforming for Passive Synthetic Aperture with Uncertain Curvilinear Trajectory
by Peng Chen, Long Zuo and Wei Wang
Remote Sens. 2021, 13(13), 2562; https://doi.org/10.3390/rs13132562 - 30 Jun 2021
Cited by 4 | Viewed by 2194
Abstract
Recently, numerous reconstruction-based adaptive beamformers have been proposed, which can improve the quality of imaging or localization in the application of passive synthetic aperture (PSA) sensing. However, when the trajectory is curvilinear, existing beamformers may not be robust enough to suppress interferences efficiently. [...] Read more.
Recently, numerous reconstruction-based adaptive beamformers have been proposed, which can improve the quality of imaging or localization in the application of passive synthetic aperture (PSA) sensing. However, when the trajectory is curvilinear, existing beamformers may not be robust enough to suppress interferences efficiently. To overcome the model mismatch of unknown curvilinear trajectory, this paper presents an adaptive beamforming algorithm by reconstructing the interference-plus-noise covariance matrix (INCM). Using the idea of signal subspace fitting, we construct a joint optimization problem, where the unknown directions of arrival (DOAs) and array shape parameters are coupled together. To tackle this problem, we develop a hybrid optimization method by combining the genetic algorithm and difference-based quasi-Newton method. Then, a set of non-orthogonal bases for signal subspace is estimated with an acceptable computational complexity. Instead of reconstructing the covariance matrix by integrating the spatial spectrum over interference angular sector, we extract the desired signal covariance matrix (DSCM) directly from signal subspace, and then the INCM is reconstructed by eliminating DSCM from the sample covariance matrix (SCM). Numerical simulations demonstrate the robustness of the proposed beamformer in the case of signal direction error, local scattering and random curvilinear trajectory. Full article
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18 pages, 5793 KiB  
Technical Note
Spatially Variant Error Elimination for High-Resolution UAV SAR with Extremely Small Incident Angle
by Xintian Zhang, Shiyang Tang, Yi Ren, Jiahao Han, Chenghao Jiang, Juan Zhang, Yinan Li, Tong Jiang and Qi Dong
Remote Sens. 2023, 15(14), 3700; https://doi.org/10.3390/rs15143700 - 24 Jul 2023
Viewed by 1341
Abstract
Airborne synthetic aperture radar (SAR) is susceptible to atmospheric disturbance and other factors that cause the position offset error of the antenna phase center and motion error. In close-range detection scenarios, the large elevation angle may make it impossible to directly observe areas [...] Read more.
Airborne synthetic aperture radar (SAR) is susceptible to atmospheric disturbance and other factors that cause the position offset error of the antenna phase center and motion error. In close-range detection scenarios, the large elevation angle may make it impossible to directly observe areas near the underlying plane, resulting in observation blind spots. In cases where the illumination elevation angle is extremely large, the influence of range variant envelope error and phase modulations becomes more serious, and traditional two-step motion compensation (MOCO) methods may fail to provide accurate imaging. In addition, conventional phase gradient autofocus (PGA) algorithms suffer from reduced performance in scenes with few strong scattering points. To address these practical challenges, we propose an improved phase-weighted estimation PGA algorithm that analyzes the motion error of UAV SAR under a large elevation angle, providing a solution for high-order range variant motion error. Based on this algorithm, we introduce a combined focusing method that applies a threshold value for selection and optimization. Unlike traditional MOCO methods, our proposed method can more accurately compensate for spatially variant motion error in the case of scenes with few strong scattering points, indicating its wider applicability. The effectiveness of our proposed approach is verified by simulation and real data experimental results. Full article
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