Frequency-dependent Factor Expression of the GTD Scattering Center Model for the Arbitrary Multiple Scattering Mechanism
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摘要: 几何绕射理论(GTD)模型是一种重要的散射中心模型,能准确描述雷达目标主要散射机理的频率依赖行为,但目前在频率依赖因子与散射机理类型之间尚未建立明确、一般的数学关系。该文从射线理论出发,结合几何光学(GO), GTD, 物理绕射理论(PTD)和驻相法(SPM)等方法,推导了理想电导体(PEC)目标任意多次散射机理的频率依赖因子数学表达式。该表达式具有简洁、统一的解析形式,指出散射中心频率依赖因子与形成散射中心的射线反射次数、射线经过的几何元素维数以及射线场焦散情况等因素有关。一系列典型组合体目标的电磁仿真与微波暗室测量数据验证了提出公式的有效性。该文提出的频率依赖因子表达可应用于正向参数化建模中频率依赖因子的正向推算。Abstract: This paper presents a derivation of a formula with a concise and uniform analytic form by the Stationary Phase Method (SPM) plus Geometrical Optics (GO), the Physical Theory of Diffraction (PTD), and Geometrical Theory of Diffraction (GTD) to calculate the frequency-dependent factor for the arbitrary multiple scattering mechanism, validated by the simulated and measured data of a series of canonical ensembles, validated by the simulated and measured data of a series of canonical ensembles. Although the GTD model, a scattering center model, can accurately describe the frequency-dependent characteristic of several main scattering mechanisms of the radar target, no explicit and general expression relates the frequency-dependent factor to the type of scattering mechanism. The derived formula relates the scattering center’s frequency-dependent factor with bounce times, dimensions of all the encountered geometrical elements, and a caustic type of ray contributing to the scattering center and can be applied to determine the parameter value of frequency-dependent factor of the GTD model and its derived versions in the forward parametric modeling.
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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.
In 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).
With 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.
4. 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.
We 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.
Some 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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表 1 GTD模型频率依赖因子取值及其对应的散射机理类型
Table 1. The values of frequency-dependent factor of GTD model and corresponding mechanisms
频率依赖因子取值 散射机理类型 1 平板、二面角、三面角的反射 1/2 单弯曲曲面的反射 0 双弯曲曲面的反射、直边的绕射 –1/2 曲边的绕射 –1 尖顶、角的绕射 表 2 6种典型体尺寸参数列表
Table 2. Size parameters for 6 canonical objects
典型体名称 尺寸参数 方形平板 边长500 mm,厚度10 mm 圆柱体 (1)直径200 mm,长300 mm;(2)直径150 mm,长300 mm 球体 (1)直径100 mm;(2)直径300 mm 半圆锥体 (1)直径50 mm, 100 mm;(2)直径125 mm, 400 mm 直角四面体 (1)底边200 mm,棱边200 mm,劈角20°;(2)底边350 mm,棱边350 mm,劈角50° 圆盘 半径500 mm,厚度8 mm 表 3 20种组合体目标及其中产生的二次反射/绕射机理的几何结构示意与频率依赖因子取值
Table 3. Types of double reflection/diffraction mechanisms, 20 combination objects, corresponding geometric diagram and theoretical values of the frequency-dependent factor
散射机理类型 组合体名称 几何示意图 理论α值 镜面反射-镜面反射 平板-平板(垂直) 1 圆柱-平板(垂直、平行) 1/2 球-平板 0 圆柱-圆柱(垂直、平行) 1/2 球-圆柱 0 球-球 0 边缘绕射-镜面反射 直劈-平板(垂直、平行) 0 直劈-圆柱(垂直、平行) 0 直劈-球 –1/2 曲劈-平板 –1/2 曲劈-圆柱 –1/2 曲劈-球 –1/2 边缘绕射-边缘绕射 直劈-直劈(垂直、平行) –1/2 曲劈-直劈 –1 曲劈-曲劈 –1 表 4 基于20种组合体仿真数据的二次散射机理形成散射中心的频率依赖因子估计与理论值对比
Table 4. Comparison of theoretical frequency-dependent factor values by proposed formula and estimated ones by simulation data for scattering centers induced by double scattering from 20 combination objects
组合体名称 估计α值 理论α值 组合体名称 估计α值 理论α值 VV HH VV HH 平板-平板(垂直) 1.0000 0.9988 1 直劈-圆柱(垂直) 0.0383 0.0028 0 圆柱-平板(垂直) 0.5011 0.4949 1/2 直劈-圆柱(平行) 2.90e-4 –4.90e-5 0 圆柱-平板(平行) 0.5015 0.5753 1/2 直劈-球 –0.5040 –0.6427 –1/2 球-平板 0.0385 –0.1048 0 曲劈-平板 –0.4957 –0.4904 –1/2 圆柱-圆柱(垂直) 0.5499 0.5034 1/2 曲劈-圆柱 –0.3976 –0.4226 –1/2 圆柱-圆柱(平行) 0.5438 0.3807 1/2 曲劈-球 –0.5909 –0.6195 –1/2 球-圆柱 –0.0616 0.0831 0 直劈-直劈(垂直) –0.5000 –0.5000 –1/2 球-球 –0.0591 –0.0591 0 直劈-直劈(平行) –0.5000 –0.5000 –1/2 直劈-平板(垂直) 1.68e-4 –0.0053 0 曲劈-直劈 –0.9428 –1.1978 –1 直劈-平板(平行) –4.05e-7 –2.34e-6 0 曲劈-曲劈 –0.9428 –1.0302 –1 表 5 基于2种组合体仿真数据的三次散射机理形成散射中心频率依赖因子估计与理论值对比
Table 5. Comparison of theoretical frequency-dependent factor values by proposed formula and estimated ones by simulation data for scattering centers induced by triple scattering from 2 combination objects
组合体名称 几何示意图 估计α值 理论α值 垂直三面角结构 0.9934 1 双顶帽结构 0.5097 1/2 表 6 基于7种组合体暗室测量数据的二次散射机理形成散射中心的频率依赖因子估计与理论值对比
Table 6. Comparison of theoretical frequency-dependent factor values by proposed formula and estimated ones by meas urementdata in microwave anechoic chamber for scattering centers induced by double scattering from 7 combination objects
机理类型 组合体名称 几何示意图 估计α值 理论α值 边缘绕射-镜面反射 四面体-圆盘(垂直) 0.1589 0 边缘绕射-边缘绕射 四面体-四面体(垂直) –0.4829 –1/2 边缘绕射-镜面反射 四面体-圆柱(平行) –0.0485 0 镜面反射-镜面反射 平板-圆柱(平行) 0.5345 1/2 镜面反射-镜面反射 直二面角(垂直) 1.0314 1 镜面反射-镜面反射 圆柱-圆盘(垂直) 0.5048 1/2 镜面反射-镜面反射 双圆柱(垂直) 0.5115 1/2 -
[1] KELLER J B. Geometrical theory of diffraction[J]. Journal of the Optical Society of America, 1962, 52(2): 116–130. doi: 10.1364/JOSA.52.000116 [2] 黄培康, 殷红成, 许小剑. 雷达目标特性[M]. 北京: 电子工业出版社, 2005: 230–237.HUANG Peikang, YIN Hongcheng, and XU Xiaojian. Radar Target Signature[M]. Beijing: Publishing House of Electronics Industry, 2005: 230–237. [3] HURST M P and MITTRA R. Scattering center analysis via Prony’s method[J]. IEEE Transactions on Antennas and Propagation, 1987, 35(8): 986–988. doi: 10.1109/TAP.1987.1144210 [4] CARRIÈRE R and MOSES R L. High-resolution parametric modeling of canonical radar scatterers with application to radar target identification[C]. The IEEE 1991 International Conference on Systems Engineering, Dayton, USA, 1991. doi: 10.1109/ICSYSE.1991.161070. [5] POTTER L C, CHIANG D M, CARRIÈRE R, et al. A GTD-based parametric model for radar scattering[J]. IEEE Transactions on Antennas and Propagation, 1995, 43(10): 1058–1067. doi: 10.1109/8.467641 [6] 代大海, 王雪松, 肖顺平. 基于相干极化GTD模型的散射中心提取新方法[J]. 系统工程与电子技术, 2007, 29(7): 1057–1061. doi: 10.3321/j.issn:1001-506X.2007.07.010DAI Dahai, WANG Xuesong, and XIAO Shunping. Novel method for scattering center extraction based on coherent polarization GTD model[J]. Systems Engineering and Electronics, 2007, 29(7): 1057–1061. doi: 10.3321/j.issn:1001-506X.2007.07.010 [7] FULLER D F. Phase history decomposition for efficient scatterer classification in SAR imagery[D]. [Ph. D. dissertation], Air Force Institute of Technology, 2011: 67–150. [8] DUAN Jia, ZHANG Lei, XING Mengdao, et al. Polarimetric target decomposition based on attributed scattering center model for synthetic aperture radar targets[J]. IEEE Geoscience and Remote Sensing Letters, 2014, 11(12): 2095–2099. doi: 10.1109/LGRS.2014.2320053 [9] HALMAN J and BURKHOLDER R J. Sparse expansions using physical and polynomial basis functions for compressed sensing of frequency domain EM scattering[J]. IEEE Antennas and Wireless Propagation Letters, 2015, 14: 1048–1051. doi: 10.1109/LAWP.2015.2394474 [10] GERRY M J, POTTER L C, GUPTA I J, et al. A parametric model for synthetic aperture radar measurements[J]. IEEE Transactions on Antennas and Propagation, 1999, 47(7): 1179–1188. doi: 10.1109/8.785750 [11] AI Fazhi, ZHOU Jianxiong, HU Lei, et al. The parametric model of non-uniformly distributed scattering centers[C]. The IET International Conference on Radar Systems (Radar 2012), Glasgow, UK, 2012. doi: 10.1049/cp.2012.1712. [12] 冯艾茜, 郭琨毅, 盛新庆. 无翼平底弹头的属性散射中心模型改进与参数估计[J]. 北京理工大学学报, 2015, 35(9): 961–967. doi: 10.15918/j.tbit1001-0645.2015.09.016FENG Aixi, GUO Kunyi, and SHENG Xinqing. Modification and parameter estimation of attributed scattering center model for flat-based warhead without wings[J]. Transactions of Beijing Institute of Technology, 2015, 35(9): 961–967. doi: 10.15918/j.tbit1001-0645.2015.09.016 [13] LI Zenghui, JIN Kan, XU Bin, et al. An improved attributed scattering model optimized by incremental sparse Bayesian learning[J]. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(5): 2973–2987. doi: 10.1109/TGRS.2015.2509539 [14] TSENG N Y and BURNSIDE W D. A very efficient RCS data compression and reconstruction technique[R]. NASA-CR-191378, 1992. [15] 王菁. 光学区雷达目标散射中心提取及其应用研究[D]. [博士论文], 南京航空航天大学, 2010: 3–77. doi: 10.7666/d.d167227.WANG Jing. A study on radar optical region target scattering center extraction and its applications[D]. [Ph. D. dissertation], Nanjing University of Aeronautics and Astronautics, 2010: 3–77. doi: 10.7666/d.d167227. [16] BHALLA R and LING Hao. A fast algorithm for signature prediction and image formation using the shooting and bouncing ray technique[J]. IEEE Transactions on Antennas and Propagation, 1995, 43(7): 727–731. doi: 10.1109/8.391147 [17] MENSA D L. High Resolution Radar Imaging[M]. Dedham, MA: Artech House, 1981. [18] RAYNAL A M. Feature-based exploitation of multidimensional radar signatures[D]. [PHD dissertation]. The University of Texas at Austin, 2008. [19] ZHOU Jianxiong, SHI Zhiguang, CHENG Xiao, et al. Automatic target recognition of SAR images based on global scattering center model[J]. IEEE Transactions on Geoscience and Remote Sensing, 2011, 49(10): 3713–3729. doi: 10.1109/tgrs.2011.2162526 [20] CHIANG H C and MOSES R L. ATR performance prediction using attributed scattering features[C]. SPIE 3721, Algorithms for Synthetic Aperture Radar Imagery VI, Orlando, United States, 1999: 785–796. [21] 邢笑宇. 耦合散射中心模型频率依赖关系及其估计[D]. [硕士论文], 中国航天第二研究院, 2014: 18–28.XING Xiaoyu. EM scattering modeling and application research of complex targets in the typical environment[D]. [Master dissertation], The Second Academy of China Aerospace, 2014: 18–28. [22] YAN Hua, LI Sheng, LI Huanmin, et al. Monostatic GTD model for double scattering due to specular reflections or edge diffractions[C]. 2018 IEEE International Conference on Computational Electromagnetics, Chengdu, China, 2018. doi: 10.1109/COMPEM.2018.8496539. [23] HE Yang, HE Siyuan, ZHANG Yunhua, et al. A forward approach to establish parametric scattering center models for known complex radar targets applied to SAR ATR[J]. IEEE Transactions on Antennas and Propagation, 2014, 62(12): 6192–6205. doi: 10.1109/TAP.2014.2360700 [24] LI Qifeng, GUO Kunyi, SHENG Xinqing, et al. High precise scattering centers models for cone-shaped targets based on induced currents[J]. International Journal of Antennas and Propagation, 2017, 2017: 7482895. doi: 10.1155/2017/7482895 [25] 张磊, 何思远, 朱国强, 等. 雷达目标三维散射中心位置正向推导和分析[J]. 电子与信息学报, 2018, 40(12): 2854–2860. doi: 10.11999/JEIT180115ZHANG Lei, HE Siyuan, ZHU Guoqiang, et al. Forward derivation and analysis for 3-D scattering center position of radar target[J]. Journal of Electronics &Information Technology, 2018, 40(12): 2854–2860. doi: 10.11999/JEIT180115 [26] LIU Jin, HE Siyuan, ZHANG Lei, et al. An automatic and forward method to establish 3-D parametric scattering center models of complex targets for target recognition[J]. IEEE Transactions on Geoscience and Remote Sensing, 2020, 58(12): 8701–8716. doi: 10.1109/TGRS.2020.2989856 [27] LEE S W. Electromagnetic reflection from a conducting surface: Geometrical optics solution[J]. IEEE Transactions on Antennas and Propagation, 1975, 23(2): 184–191. doi: 10.1109/TAP.1975.1141040 [28] 汪茂光. 几何绕射理论[M]. 2版. 西安: 西安电子科技大学出版社, 1994.WANG Maoguang. Geometrical Diffraction Theory[M]. 2nd ed. Xi’an: Xidian University Press, 1994. [29] KOUYOUMJIAN R G and PATHAK P H. A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface[J]. Proceedings of the IEEE, 1974, 62(11): 1448–1461. doi: 10.1109/PROC.1974.9651 [30] PEREZ J and CATEDRA M F. Application of physical optics to the RCS computation of bodies modeled with NURBS surfaces[J]. IEEE Transactions on Antennas and Propagation, 1994, 42(10): 1404–1411. doi: 10.1109/8.320747 [31] MICHAELI A. Equivalent edge currents for arbitrary aspects of observation[J]. IEEE Transactions on Antennas and Propagation, 1984, 32(3): 252–258. doi: 10.1109/TAP.1984.1143303 [32] LING H, CHOU R C, and LEE S W. Shooting and bouncing rays: Calculating the RCS of an arbitrarily shaped cavity[J]. IEEE Transactions on Antennas and Propagation, 1989, 37(2): 194–205. doi: 10.1109/8.18706 [33] CARLUCCIO G, ALBANI M, and PATHAK P H. Uniform asymptotic evaluation of surface integrals with polygonal integration domains in terms of UTD transition functions[J]. IEEE Transactions on Antennas and Propagation, 2010, 58(4): 1155–1163. doi: 10.1109/TAP.2010.2041171 [34] 殷红成, 朱国庆, 董纯柱, 等. 基于自适应射线管分裂的多次反射计算方法[J]. 系统工程与电子技术, 2013, 35(4): 700–706. doi: 10.3969/j.issn.1001-506X.2013.04.04YIN Hongcheng, ZHU Guoqing, DONG Chunzhu, et al. Efficient multi-reflection computational method based on adaptive ray tube splitting[J]. Systems Engineering and Electronics, 2013, 35(4): 700–706. doi: 10.3969/j.issn.1001-506X.2013.04.04 [35] 侯兆国, 王超, 殷红成. 电大复杂目标电磁散射计算的特征基函数方法[J]. 制导与引信, 2009, 30(2): 24–29. doi: 10.3969/j.issn.1671-0576.2009.02.006HOU Zhaoguo, WANG Chao, and YIN Hongcheng. Characteristic basis function method for electromagnetic scattering computation of electrically large complex target[J]. Guidance &Fuze, 2009, 30(2): 24–29. doi: 10.3969/j.issn.1671-0576.2009.02.006 [36] FULLER D F and SAVILLE M A. The spectrum parted linked image test (SPLIT) algorithm for estimating the frequency dependence of scattering center amplitudes[C]. SPIE 7337, Algorithms for Synthetic Aperture Radar Imagery XVI, Orlando, United States, 2009. doi: 10.1117/12.819329. [37] QUINQUIS A, DEMETER S, and RADOI E. Enhancing the resolution of the radar target range profiles using a class of subspace eigenanalysis-based techniques[J]. Digital Signal Processing, 2001, 11(4): 288–303. doi: 10.1006/dspr.2001.0394. -