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Subband Information Geometry Detection Method Based on Orthogonal Projection for Weak Radar Targets
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摘要: 基于信息几何理论的雷达目标检测是一种新兴的技术，它将目标检测问题转化为流形上目标与杂波的区分问题，在低信杂比检测中具有优势。对于复杂背景下的弱小目标检测，目标与杂波难以区分，限制着检测性能。因此，该文基于矩阵信息几何检测器，提出一种基于正交投影的子带信息几何目标检测方法。该文利用滤波器组对雷达回波信号进行子带分解，并在矩阵流形上稳健估计子带内强杂波信号子空间，提出基于流形的正交投影方法以抑制强杂波，增强目标与杂波的区分性。最后，采用仿真数据和实测海杂波数据验证所提方法的有效性。结果表明，所提方法能够有效抑制强杂波，具有较好的检测性能。Abstract: Herein, a novel and effective method for detecting radar targets with a low signal-to-clutter ratio is proposed based on the information geometry theory. In the proposed method, the target detection problem is converted to distinguishing the target from a clutter background on a manifold. However, this is challenging when dealing with small and weak targets embedded in a complex and strong clutter background, which limits the detection performance. Therefore, to address this issue, an orthogonal projection based subband information geometry detection method is proposed. In this method, the received radar signal undergoes subband decomposition by a designed filter bank, and the robust estimation of clutter signal subspace in each subband is implemented on the matrix manifold. Subsequently, the suppression of the strong clutter is achieved through orthogonal projection based on the manifold, thereby improving the discrimination between the target and the clutter. Finally, the effectiveness of the proposed method is evaluated using simulated and real sea clutter data. The experimental results confirm that the proposed method effectively suppresses strong clutter and exhibits excellent detection performance.
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1. Introduction
Today, the research and application of Artificial Intelligence (AI) has become a major area of scientific and technological development. Developing AI is a major strategy for enhancing national core competitiveness and maintaining national security.
The Massachusetts Institute of Technology (MIT) has not established a new college for decades. However, in October 2018, MIT announced a new facility, the Schwarzman College of Computing[1], and the construction of the Stata Science Center (see Fig. 1) for computer science, AI, data science, and related intersections. Its purpose is to harness the powerful role of AI and big data computing in science and technology of the future. From Fig. 2, the SCR-615B radar built by MIT during World War II is on display in the Stata Science Center lobby. The MIT president also published an article in this year’s MIT newsletter[2] emphasizing the competition and challenges brought by AI.
Figure 1. MIT Stata Science Center
Figure 2. SCR-615B radar displayed in the hallIn 2016, the United States (U.S.) White House released three important reports titled Preparing for the Future of Artificial Intelligence, National Artificial Intelligence Research and Development Strategic Plan, and Artificial Intelligence, and Automation and Economic Report, which promoted the establishment of a Machine Learning and Artificial Intelligence (MLAI) subcommittee that would actively plan for the future development of AI[3]. In January 2018, the United States Department of Defense released a new version of the National Defense Strategy report, stating that the development of advanced computing, big data analysis, and robotics are important factors affecting national security. In June 2018, the U.S. Defense Advanced Research Projects Agency (DARPA) discussed for the first time the preliminary details of the U.S. Electronic Revival Plan. The implementation of this Electronic Revival Plan will accelerate the development of AI hardware. In September of the same year, DARPA announced its commitment to building a system based on common sense, contextual awareness, and higher energy efficiency[4]. In February 2019, U.S. President Trump signed an executive order titled To Maintain U.S. Artificial Intelligence Leadership, which aims to maintain U.S. global leadership in AI. On February 12, 2019, the U.S. Department of Defense website published a Summary of the 2018 Department of Defense Artificial Intelligence Strategy—Harnessing AI to Advance Our Security and Prosperity, which clarified the U.S. military’s strategic initiatives and key areas for deploying AI[5]. The U.S. Department of Defense plans to use DARPA’s Next Generation Artificial Intelligence (AI Next) and Artificial Intelligence Exploration (AIE) projects as benchmarks for exploring and applying AI technologies to enhance military strength. The AI Next project, which was announced in September 2018, is based on the two generations of AI technology that were led by DARPA over the past 60 years. It emphasizes the environmentally adaptive capability of AI. The main areas of this project are to explore new technologies that promote the Department of Defense’s automation of key business processes, improve the robustness and reliability of AI systems, enhance the security and flexibility of machine learning and AI technologies, reduce power consumption and avoid inefficient data collection and performance, and create the next generation of AI algorithms and applications[6]. The AIE program will focus on Third Wave applications and theories of AI and aim to adapt machines to changing conditions. It will streamline proposals, contracts, and funding processes. The goal is to accelerate the research and development of AI platforms to help the U.S. maintain its technical advantages in the field of AI.
In March 2017, France released its Artificial Intelligence Strategy, built a new AI center, and developed data storage and processing platforms, automatic learning technology platforms, and network security platforms[7]. The German Brain Science strategy focuses on robotics and digitization. In 2012, the Max Planck Institute for Scientific Research in Germany cooperated with the U.S. in computational neuroscience[8]. Japan also attaches great importance to the development of AI technology. In 2017, the Japanese government issued the Next Generation Artificial Intelligence Promotion Strategy to clarify its focus on AI development and to promote the extension of AI technology to strong AI and super AI levels[9].
China released the New Generation Artificial Intelligence Development Plan in July 2017 and formulated a three-step goal for the national AI strategy. By 2030, China’s AI theory, technology, and applications will generally reach world-leading levels and become the world’s major AI innovation center[10]. Currently, China is showing very strong scientific research mobilization in the research and application of AI. For example, in August 2017, the National Natural Science Foundation of China (NSFC) released Guidelines for Emergency Management of Basic Research in Artificial Intelligence, which outlines plans to fund research in 25 research directions in three foundational aspects of the AI frontier, including intelligent autonomous movement bodies, intelligent decision-making theory, and key technologies of complex manufacturing processes[11]. We believe that, driven by innovation, China will achieve significant development in the research, application, and industrial fields of AI and AI technology, occupying an important territory in the world of AI.
In this paper, we propose the development of AI technology in the field of space remote sensing and target recognition. In 2017, we hosted the Institute of Electrical and Electronics Engineers’ (IEEE) Remote Sensing Intelligent Processing Conference[12] and published some papers in the IEEE Transactions on Geoscience and Remote Sensing/Geoscience and Remote Sensing Letters[13-16]. We have also published several discussions in the Science & Technology Review [17,18], highlighting concepts regarding physical intelligence and microwave vision. Here we focus on Synthetic Aperture Radar (SAR) target monitoring and information perception and discuss the research on AI information technology against the physical background of the interaction between electromagnetic waves and targets, i.e., the use of this physical intelligence to develop microwave visions that can perceive target information on the electromagnetic spectrum that cannot be recognized by the human eye.
2. Multisource Multimode SAR Information Perception
In the 1950s, SAR images were only single-mode RCS grayscale images used for monitoring military targets. Later, in the 1970s, the development and application of this technology began to make great strides in civilian fields of study, such as ocean wind fields, terrestrial hydrology, vegetation, snow, precipitation, drought, the monitoring and evaluation of natural disasters, and the identification of surface changes, to name a few. Various applications have various needs, and the theoretical and technical issues associated with different scientific connotations have strongly promoted the comprehensive development of SAR technology. Since the beginning of the 21st century, SAR satellite technologies have developed rapidly, with the realization of full polarization, interference, and high- resolution to produce a multisource multimode full-polarization high-resolution SAR (hereinafter referred to as multimode SAR) information technology (see Fig. 3).
Figure 3. Overview of SAR development in various countriesWith the improvement in spatial resolution to meters and decimeters, the perception of multimode SAR remote sensing information has produced a field of science and technology that has great significance for civilian and national defense technology. SAR in the 21st century promotes the research and application of Automatic Target Recognition (ATR). Based on the presence or absence of a one-dimensional to a two-dimensional object map, three-dimensional object feature recognition is achieved, along with identification of multi-dimensional object morphology.
However, SAR information perception and target feature inversion and reconstruction are not accomplished by human vision. The interaction between electromagnetic waves and complex targets and their image-scattering mechanisms provide the physical basis for SAR imaging. We have studied the theoretical parameter modeling, numerical simulation, and physical and numerical characteristics in the frequency, spatial, time, and polarization domains, and have developed polarized SAR parametric simulation software, techniques for scattering and imaging calculations, and target classification, recognition, and feature reconstruction[19].
Multimode SAR remote sensing produces a many series of images with multiple temporal and physical characteristics and rich and multiple types of complex data. Driven by remote sensing big data, remote sensing application technology has progressed in a broad range of areas. However, most of these are limited to traditional data statistical analysis and image processing technologies, which cannot meet the needs of multimode SAR technology and applications. In particular, it is difficult to realize the automatic recognition of various types of targets in the sky, land, and sea, as well as the perception and inversion reconstruction of fine-scale multi-dimensional information.
3. Big Data-driven AI Technology
In recent years, AI technology has attracted considerable attention from science and industry. Based on the recognition of local structure-features-whole target in the eye-retina-brain V1–V4 area, a simple perception rule was established to obtain visual perception ability. Using the method of computational neuroscience and driven by the fitting of big data, multi-layer convolution networks are constructed from the local structure and feature-vector space for large overall network calculations to realize the ability to perceive internal information, which is the basic idea of AI and deep learning.
Similarly, we must determine how to develop a new smart brain-like function suitable for the perception of SAR information from electromagnetic wave image scattering, which differs from computer vision processing that is usually based on optical vision. To do so, it is necessary to construct an intelligent information technology that can perceive SAR information from the microwave spectrum. We call this the electromagnetic AI–new scientific technology, i.e., from optical vision by the human brain to humanoid brain electromagnetic waves–microwave vision, which is driven by remote sensing big data under the guidance of the physics mechanism of multi-source multimode full-polarimetric high-resolution SAR.
Fig. 4 and Fig. 5 illustrate the physical basis of multimode SAR as a forward problem of electromagnetic-wave-scattering modeling simulation and an inverse problem of multi-dimensional information inversion and reconstruction. AI deep learning based on a brain-like computing neural algorithm is driven by various types of big data constrained by the physical background of multimode SAR remote sensing for processing perceptions of AI information for application in various fields.
Figure 4. Research and application of multisource and multimode SAR remote sensing information perception for space-ground-sea targets
Figure 5. Physical intelligence to application of remotely sensed big data4. Microwave Vision to Realize ATR Based on Physical Intelligence
Based on the SAR image-scattering mechanism, we developed a brain-like intelligent function for processing this type of big data to perceive SAR information. This is like seeing microwaves, i.e., microwave vision. Eventually, this technology will be able to perform automatic interpretations online and produce easy-to-accept visual representations and visual semantics. Known as microwave consciousness, this technology plays an important role in the technical methods of visual semantics, reasoning, decision-making, interactive detection, identification, interference, confrontation, and the attack of SAR scattered radiation fields.
In Fig. 6, we propose a combined forward and inverse theory for the creation of electromagnetic-wave-scattering and brain-like AI research to generate a new intelligent algorithm. This cross-discipline electromagnetic AI (EM AI) has important applications in Earth remote sensing, ATR, electronic countermeasures, and satellite navigation communications. Therefore, this proposal represents remote sensing-communication-navigation technology in electromagnetic space.
Figure 6. Artificial intelligence of space electromagneticsWe have recently edited a book series titled Spaceborne Microwave Remote Sensing[20], whereby 14 monographs will be published by Science Press in the next two years, eight monographs of which deal with the acquisition of SAR information (Fig. 7). These include the monograph Intelligent Interpretation of Radar Image Information, written by our laboratory team[21]. Based on the background and research status of SAR image interpretation, this monograph summarizes our laboratory’s latest research progress using deep learning intelligent technology in SAR ATR and polarized SAR feature classification, and provides sample data and program code for relevant chapters.
Figure 7. Spaceborne microwave remote sensing research and application seriesSome of the research conducted at our laboratory on intelligent information perception can be summarized as follows:
• We proposed an intelligent recognition algorithm for SAR targets[15]. The full convolutional network we proposed reduces the number of independent parameters by removing fully connected layers. It achieved a classification accuracy of 99% for a 10-class task when applied to the SAR target classification dataset MSTAR[22]. In addition, an end-to-end target detection–discrimination–recognition method for SAR images was implemented. Furthermore, we proposed a fast-detection algorithm for surface ship targets, established an SAR image ship target data set, and performed a ship target classification experiment based on transfer learning.
• We proposed a deep-learning training network algorithm in a complex domain[16], whereby we can train a Convolutional Neural Network (CNN) of a polarized SAR surface classification with complex multi-dimensional images in a polarized coherence matrix. This algorithm achieved state-of-the-art accuracy of 95% for a 15-class task on the Flevoland benchmark dataset[22].
• We proposed a CNN using few samples for target ATR, which has good network generalization ability. We also studied the target recognition and classification ability of CNN feature-vector distribution under the condition of no samples[14]. Zero-sample learning is important for SAR ATR because training samples are not always suitable for all targets and scenarios. In this paper, we proposed a new generation-based deep neural network framework, the key aspect of which is a generative deconvolutional neural network, called a generator that automatically constructs a continuous SAR target feature space composed of direction-invariant features and direction angles while learning the target hierarchical representation. This framework is then used as a reference for designing and initializing the interpreter CNN, which is antisymmetric to the generator network. The interpreter network is then trained to map any input SAR image to the target feature space.
• We proposed a deep neural network structure for CNN processing to despeckle SAR-image noise[23]. This process uses a CNN to extract image features and reconstruct a discrete RCS Probability Density Function (PDF). The network is trained by a mixed loss function that measures the distance between the actual and estimated SAR image intensity PDFs, which is obtained by the convolution between the reconstructed RCS PDF and the prior speckled PDF. The network can be trained using either simulated or real SAR images. Experimental results on both simulated SAR images and real NASA/JPL AIRSAR images confirm the effectiveness of the proposed noise-despeckling deep neural network.
• Lastly, we proposed a colorized CNN processing method from single-polarized SAR images to polarized SAR images for scene analysis and processing[24]. This paper proposed a deep neural network that converts a single-polarized SAR image into a fully polarized SAR image. This network has two parts, a feature extraction network and a feature translation network that is used to match spatial and polarized features. Using this method, the polarization covariance matrix of each pixel can be reconstructed. The resulting fully polarized SAR image is very close to the real fully polarized SAR image not only visually but also in real PolSAR applications.
In addition, part of the work of our laboratory is to do the SAR-AI-ATR identification of—base on domestic and foreign SAR data including China’s GF-3 SAR data. do the SAR-AI-ATR identification of ground vehicles, airport aircraft, and sea surface ships. In addition, we proposed a CNN method for the inversion of forest tree heights by interferometric SAR, i.e., INSAR, and a method for constructing the reciprocal generation of optical images and microwave radar images by the contrast training of optical and microwave images. The above work can be found in related monographs[21].
5. Conclusion
Data is not synonymous with information. Big data is just material and a driver, and different data have different scientific connotations. Therefore, the use of simple and direct statistics in the analysis of big data cannot realize the perception of connotative information, especially in the imaging of multi-dimensional vectorized complex data of multimode microwave SAR, which is difficult to intuitively perceive by the human eye. In this paper, we proposed the use of AI driven by big data under the guidance of physics to retrieve information and develop new AI models and algorithms to meet the needs of SAR remote sensing physics and applications. Interdisciplinary AI research is very important. The realization of new EM AI technology will drive the development of multiple industries and applications.
At present, research on multimode remote sensing intelligent information and target recognition is still in the exploratory stage, and further research is needed to continue to develop new theories, methods, and applications of microwave vision.
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图 5 基于正交投影的子带信息几何检测流程图
Figure 5. Flowchart of subband geometric detection based on orthogonal projection
图 6 加入干扰信号后不同方法的平均影响函数值
Figure 6. Mean value of the influence function for different methods after adding interferences
图 7 K分布杂波下的检测概率(
K=n )Figure 7. Probabilities of detection for K distribution clutter (
K=n )
图 8 K分布杂波下的检测性能曲线(
K=2n )Figure 8. Probabilities of detection for K distribution clutter (
K=2n )
图 10 IPIX雷达数据的归一化检测统计量(
fd=160 Hz)Figure 10. Normalized detection statistics of the IPIX radar data (
fd=160 Hz)
图 11 基于IPIX雷达数据的检测概率(
fd=160 Hz)Figure 11. Probabilities of detection for the IPIX radar data (
fd=160 Hz)
图 12 基于IPIX雷达数据的检测概率(
fd=350 Hz)Figure 12. Probabilities of detection for the IPIX radar data (
fd=350 Hz)
图 13 海杂波与目标探测数据采集的试验场景
Figure 13. Sea clutter and target detection experimental scenario
图 14 数据集20210106150614_02_staring的归一化距离-脉冲图
Figure 14. Normalized range-pulse of data set 20210106150614_02_staring
图 15 NAU实验数据(目标位于4.84 km处)
Figure 15. Experimental data of NAU (the target is located at 4.84 km)
1 基于正交投影的子带信息几何检测方法
1. Subband MIG detection method based on orthogonal projection
输入：雷达待检测单元回波信号zD和杂波参考单元回波信号{zk}k∈[K]。 输出：检测决策：D(l)(ℜ(zD),ˉℜ({zk}k∈[K]))H1≷H0η(l),l=−L,−(L−1),⋯,0,⋯,L。 For l=−L,−(L−1),⋯,0,⋯,L: 1：首先基于子带滤波器，对雷达回波信号进行子带滤波，获得子带滤波信号z(l)D=L(zD)和{z(l)k=L(zk)}k∈[K]； 2：基于流形估计子带内的杂波信号子空间，并进行稳健的正交投影，得到目标增强信号˜z(l)D=P(z(l)D)和{˜z(l)k=P(z(l)k)}k∈[K]； 3：将基于流形正交投影后的信号表征为HPD矩阵，计算待检测单元HPD矩阵ℜ(zD)和杂波参考单元HPD矩阵{ℜ(zk)}k∈[K]，并计算
几何均值ˉℜ({zk}k∈[K])；4：计算几何检测统计量D(l)(ℜ(zD),ˉℜ({zk}k∈[K]))，并与门限η(l)进行比较，完成检测判决
D(l)(ℜ(zD),ˉℜ({zk}k∈[K]))H1≷H0η(l)。End 
下载: 导出CSV
表 1 不同方法的计算复杂度
Table 1. The computation complexity of different methods
方法 计算复杂度 本文方法 O(M(Kn3+n3+(n+Q)log(n+Q))) RD O(νKn3) LE O(Kn3) KLD O(Kn3) LD O(εKn3) FFT O(nlogn+Kn) ANMF O(n3+Kn2) SANMF O(M(n3+Kn2)) ME O(K(n3+n)) PS-GLRT O(n3+Kn2) 2S-Rao O(n3+Kn2)
下载: 导出CSV
表 2 数据文件19980204_155537_ANTSTEP参数
Table 2. Parameters of data file 19980204_155537_ANTSTEP
参数 数值 载频(GHz) 9.39 脉冲重复频率(Hz) 1000 距离单元数 28 脉冲数 60000 距离分辨率(m) 30
下载: 导出CSV
表 3 数据文件20210106150614_02_staring参数
Table 3. Parameters of data file 20210106150614_02_staring
参数 数值 载频(GHz) 9.3~9.5 脉冲重复频率(Hz) 1704 距离单元数 4346 脉冲数 6000 采样频率(MHz) 60 目标位置(km) 4.84
下载: 导出CSV
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[1] 许述文, 白晓惠, 郭子薰, 等. 海杂波背景下雷达目标特征检测方法的现状与展望[J]. 雷达学报, 2020, 9(4): 684–714. doi: 10.12000/JR20084XU Shuwen, BAI Xiaohui, GUO Zixun, et al. Status and prospects of feature-based detection methods for floating targets on the sea surface[J]. Journal of Radars, 2020, 9(4): 684–714. doi: 10.12000/JR20084 [2] 朱文涛. 海面慢速弱小目标雷达探测技术研究[J]. 科技视界, 2018(22): 64–67. doi: 10.19694/j.cnki.issn2095-2457.2018.22.030ZHU Wentao. Research on radar detection technology for slow and weak targets on the sea[J]. Science &Technology Vision, 2018(22): 64–67. doi: 10.19694/j.cnki.issn2095-2457.2018.22.030 [3] 陈小龙, 关键, 黄勇, 等. 雷达低可观测目标探测技术[J]. 科技导报, 2017, 35(11): 30–38. doi: 10.3981/j.issn.1000-7857.2017.11.004CHEN Xiaolong, GUAN Jian, HUANG Yong, et al. Radar low-observable target detection[J]. Science &Technology Review, 2017, 35(11): 30–38. doi: 10.3981/j.issn.1000-7857.2017.11.004 [4] 陈小龙, 陈唯实, 饶云华, 等. 飞鸟与无人机目标雷达探测与识别技术进展与展望[J]. 雷达学报, 2020, 9(5): 803–827. doi: 10.12000/JR20068CHEN Xiaolong, CHEN Weishi, RAO Yunhua, et al. Progress and prospects of radar target detection and recognition technology for flying birds and unmanned aerial vehicles[J]. Journal of Radars, 2020, 9(5): 803–827. doi: 10.12000/JR20068 [5] WATTS S. Cell-averaging CFAR gain in spatially correlated K-distributed clutter[J]. IEE Proceedings-Radar, Sonar and Navigation, 1996, 143(5): 321–327. doi: 10.1049/ip-rsn:19960745 [6] ARMSTRONG B C and GRIFFITHS H D. CFAR detection of fluctuating targets in spatially correlated K-distributed clutter[J]. IEE Proceedings F (Radar and Signal Processing), 1991, 138(2): 139–152. doi: 10.1049/ip-f-2.1991.0020 [7] CONTE E, DE MAIO A, and RICCI G. Covariance matrix estimation for adaptive CFAR detection in compound-Gaussian clutter[J]. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(2): 415–426. doi: 10.1109/TAES.2002.1008976 [8] SANGSTON K J and FARINA A. Coherent radar detection in compound-Gaussian clutter: Clairvoyant detectors[J]. IEEE Aerospace and Electronic Systems Magazine, 2016, 31(11): 42–63. doi: 10.1109/MAES.2016.150132 [9] LIU Weijian, LIU Jun, HAO Chengpeng, et al. Multichannel adaptive signal detection: Basic theory and literature review[J]. Science China Information Sciences, 2022, 65(2): 121301. doi: 10.1007/s11432-020-3211-8 [10] RONG Yao, AUBRY A, DE MAIO A, et al. Adaptive radar detection in low-rank heterogeneous clutter via invariance theory[J]. IEEE Transactions on Signal Processing, 2021, 69: 1492–1506. doi: 10.1109/TSP.2021.3058447 [11] SHUI Penglang and SHI Yanling. Subband ANMF detection of moving targets in sea clutter[J]. IEEE Transactions on Aerospace and Electronic Systems, 2012, 48(4): 3578–3593. doi: 10.1109/TAES.2012.6324742 [12] 时艳玲, 林毓峰, 梁丹丹. 非平稳海杂波背景下子带分段ANMF检测器[J]. 系统工程与电子技术, 2018, 40(4): 782–789. doi: 10.3969/j.issn.1001-506X.2018.04.11SHI Yanling, LIN Yufeng, and LIANG Dandan. Subband segmented ANMF detector in non-stationary sea clutter[J]. Systems Engineering and Electronics, 2018, 40(4): 782–789. doi: 10.3969/j.issn.1001-506X.2018.04.11 [13] 时艳玲, 王磊, 李君豪. 基于投影空间下奇异值分解的海面小目标CFAR检测[J]. 系统工程与电子技术, 2022, 44(2): 512–519. doi: 10.12305/j.issn.1001-506X.2022.02.20SHI Yanling, WANG Lei, and LI Junhao. CFAR detection for small targets on sea surface based on singular value decomposition in projection space[J]. Systems Engineering and Electronics, 2022, 44(2): 512–519. doi: 10.12305/j.issn.1001-506X.2022.02.20 [14] YANG Yong, XIAO Shunping, and WANG Xuesong. Radar detection of small target in sea clutter using orthogonal projection[J]. IEEE Geoscience and Remote Sensing Letters, 2019, 16(3): 382–386. doi: 10.1109/LGRS.2018.2875705 [15] 王炜鹏, 冯远, 单涛. 采用改进型时频滤波的海杂波抑制方法[J]. 信号处理, 2019, 35(2): 208–216. doi: 10.16798/j.issn.1003-0530.2019.02.006WANG Weipeng, FENG Yuan, and SHAN Tao. A sea clutter suppression method using improved time-frequency filtering method[J]. Journal of Signal Processing, 2019, 35(2): 208–216. doi: 10.16798/j.issn.1003-0530.2019.02.006 [16] CHENG Yongqiang, HUA Xiaoqiang, WANG Hongqiang, et al. The geometry of signal detection with applications to radar signal processing[J]. Entropy, 2016, 18(11): 381. doi: 10.3390/e18110381 [17] HUA Xiaoqiang, ONO Y, PENG Linyu, et al. Target detection within nonhomogeneous clutter via total Bregman divergence-based matrix information geometry detectors[J]. IEEE Transactions on Signal Processing, 2021, 69: 4326–4340. doi: 10.1109/TSP.2021.3095725 [18] HUA Xiaoqiang and PENG Linyu. MIG median detectors with manifold filter[J]. Signal Processing, 2021, 188: 108176. doi: 10.1016/j.sigpro.2021.108176 [19] CHEN Xixi, CHENG Yongqiang, WU Hao, et al. Heterogeneous clutter suppression via affine transformation on Riemannian manifold of HPD matrices[J]. IEEE Transactions on Geoscience and Remote Sensing, 2022, 60: 5109813. doi: 10.1109/TGRS.2022.3147494 [20] WU Hao, CHENG Yongqiang, CHEN Xixi, et al. Geodesic normal coordinate-based manifold filtering for target detection[J]. IEEE Transactions on Geoscience and Remote Sensing, 2022, 60: 5114615. doi: 10.1109/TGRS.2022.3183432 [21] ARNAUDON M, BARBARESCO F, and YANG Le. Riemannian medians and means with applications to radar signal processing[J]. IEEE Journal of Selected Topics in Signal Processing, 2013, 7(4): 595–604. doi: 10.1109/JSTSP.2013.2261798 [22] BARBARESCO F. Innovative tools for radar signal processing based on Cartan’s geometry of SPD matrices & information geometry[C]. 2008 IEEE Radar Conference, Rome, Italy, 2008: 1–6. [23] BARBARESCO F and MEIER U. Radar monitoring of a wake vortex: Electromagnetic reflection of wake turbulence in clear air[J]. Comptes Rendus Physique, 2010, 11(1): 54–67. doi: 10.1016/j.crhy.2010.01.001 [24] HUA Xiaoqiang, CHENG Yongqiang, WANG Hongqiang, et al. Matrix CFAR detectors based on symmetrized Kullback-Leibler and total Kullback-Leibler divergences[J]. Digital Signal Processing, 2017, 69: 106–116. doi: 10.1016/j.dsp.2017.06.019 [25] YANG Zheng, CHENG Yongqiang, WU Hao, et al. Enhanced matrix CFAR detection with dimensionality reduction of Riemannian manifold[J]. IEEE Signal Processing Letters, 2020, 27: 2084–2088. doi: 10.1109/LSP.2020.3037489 [26] 杨政, 程永强, 吴昊, 等. 基于黎曼流形监督降维的矩阵CFAR增强检测[J]. 信号处理, 2021, 37(11): 2013–2021. doi: 10.16798/j.issn.1003-0530.2021.11.001YANG Zheng, CHENG Yongqiang, WU Hao, et al. Enhanced matrix CFAR detection based on supervised dimensionality reduction of Riemannian manifold[J]. Journal of Signal Processing, 2021, 37(11): 2013–2021. doi: 10.16798/j.issn.1003-0530.2021.11.001 [27] ZHAO Wenjing, LIU Wenlong, and JIN Minglu. Spectral norm based mean matrix estimation and its application to radar target CFAR detection[J]. IEEE Transactions on Signal Processing, 2019, 67(22): 5746–5760. doi: 10.1109/TSP.2019.2945991 [28] WU Hao, CHENG Yongqiang, CHEN Xixi, et al. Adaptive matrix information geometry detector with local metric tensor[J]. IEEE Transactions on Signal Processing, 2022, 70: 3758–3773. doi: 10.1109/TSP.2022.3189179 [29] 高永婵, 潘丽燕, 李亚超, 等. 空/时对称阵列雷达非高斯杂波背景下多秩距离扩展目标检测方法[J]. 雷达学报, 2022, 11(5): 765–777. doi: 10.12000/JR22013GAO Yongchan, PAN Liyan, LI Yachao, et al. Multi-rank range-spread target detection method for space/time symmetric array radar under non-Gaussian clutter background[J]. Journal of Radars, 2022, 11(5): 765–777. doi: 10.12000/JR22013 [30] 丁昊, 薛永华, 黄勇, 等. 均匀和部分均匀杂波中子空间目标的斜对称自适应检测方法[J]. 雷达学报, 2015, 4(4): 418–430. doi: 10.12000/JR14133DING Hao, XUE Yonghua, HUANG Yong, et al. Persymmetric adaptive detectors of subspace signals in homogeneous and partially homogeneous clutter[J]. Journal of Radars, 2015, 4(4): 418–430. doi: 10.12000/JR14133 [31] 邹鲲, 来磊, 骆艳卜, 等. 子空间干扰非高斯杂波的抑制[J]. 雷达学报, 2020, 9(4): 715–722. doi: 10.12000/JR19050ZOU Kun, LAI Lei, LUO Yanbo, et al. Suppression of non-Gaussian clutter from subspace interference[J]. Journal of Radars, 2020, 9(4): 715–722. doi: 10.12000/JR19050 [32] CABANES Y, BARBARESCO F, ARNAUDON M, et al. Unsupervised machine learning for pathological radar clutter clustering: The p-mean-shift algorithm[C]. C&ESAR 2019, Rennes, France, 2019: 1–21. [33] AMARI S I. Information Geometry and Its Applications[M]. Tokyo: Springer, 2016: 1–376. [34] MOAKHER M. A differential geometric approach to the geometric mean of symmetric positive-definite matrices[J]. SIAM Journal on Matrix Analysis and Applications, 2005, 26(3): 735–747. doi: 10.1137/S0895479803436937 [35] MOAKHER M. On the averaging of symmetric positive-definite tensors[J]. Journal of Elasticity, 2006, 82(3): 273–296. doi: 10.1007/s10659-005-9035-z [36] HIAI F and PETZ D. Riemannian metrics on positive definite matrices related to means[J]. Linear Algebra and its Applications, 2009, 430(11/12): 3105–3130. doi: 10.1016/j.laa.2009.01.025 [37] ARSIGNY V, FILLARD P, PENNEC X, et al. Geometric means in a novel vector space structure on symmetric positive-definite matrices[J]. SIAM Journal on Matrix Analysis and Applications, 2007, 29(1): 328–347. doi: 10.1137/050637996 [38] MOAKHER M and BATCHELOR P G. Symmetric Positive-Definite Matrices: From Geometry to Applications and Visualization[M]. WEICKERT J and HAGEN H. Visualization and Processing of Tensor Fields. Berlin: Springer, 2006: 285–298. [39] CHERIAN A, SRA S, BANERJEE A, et al. Jensen-Bregman LogDet divergence with application to efficient similarity search for covariance matrices[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(9): 2161–2174. doi: 10.1109/TPAMI.2012.259 [40] ZHANG Xianda. Matrix Analysis and Applications[M]. Cambridge: Cambridge University Press, 2017: 1–723. [41] HUA Xiaoqiang, CHENG Yongqiang, WANG Hongqiang, et al. Robust covariance estimators based on information divergences and riemannian manifold[J]. Entropy, 2018, 20(4): 219. doi: 10.3390/e20040219 [42] ZHAO Wenjing, LIU Chang, LIU Wenlong, et al. Maximum eigenvalue-based target detection for the K-distributed clutter environment[J]. IET Radar, Sonar & Navigation, 2018, 12(11): 1294–1306. doi: 10.1049/iet-rsn.2018.5229 [43] MAO Linlin, GAO Yongchan, YAN Shefeng, et al. Persymmetric subspace detection in structured interference and non-homogeneous disturbance[J]. IEEE Signal Processing Letters, 2019, 26(6): 928–932. doi: 10.1109/LSP.2019.2913332 [44] LIU Weijian, LIU Jun, and HUANG Lei. Rao tests for distributed target detection in interference and noise[J]. Signal Processing, 2015, 117: 333–342. doi: 10.1016/j.sigpro.2015.06.012 [45] IPIX Radar File. IPIX radar dataset files in Grimsby on the shores of Lake Ontario[OL]. http://soma.mcmaster.ca/ipix. 1998. [46] 刘宁波, 董云龙, 王国庆, 等. X波段雷达对海探测试验与数据获取[J]. 雷达学报, 2019, 8(5): 656–667. doi: 10.12000/JR19089LIU Ningbo, DONG Yunlong, WANG Guoqing, et al. Sea-detecting X-band radar and data acquisition program[J]. Journal of Radars, 2019, 8(5): 656–667. doi: 10.12000/JR19089 [47] 刘宁波, 丁昊, 黄勇, 等. X波段雷达对海探测试验与数据获取年度进展[J]. 雷达学报, 2021, 10(1): 173–182. doi: 10.12000/JR21011LIU Ningbo, DING Hao, HUANG Yong, et al. Annual progress of the sea-detecting X-band radar and data acquisition program[J]. Journal of Radars, 2021, 10(1): 173–182. doi: 10.12000/JR21011 -
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