SAR Target Physics Interpretable Recognition Method Based on Three Dimensional Parametric Electromagnetic Part Model
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摘要: 该文通过部件级三维参数化电磁模型(3D-PEPM)描述了复杂目标的电磁散射现象,并基于此模型提出了一种新的合成孔径雷达(SAR)目标识别方法。该方法首先根据雷达参数将3D-PEPM中各个散射体的散射响应投影到二维图像平面,预测每个散射体的位置和形状,然后根据3D-PEPM提供的先验信息评估3D-PEPM与SAR数据之间的相似程度,最后利用一种视角调整方法对整个过程进行优化,产生3D-PEPM和SAR数据之间的最终匹配分数,并根据该匹配分数完成识别决策。这种识别方法明确标识了SAR数据和3D-PEPM散射体之间的对应关系,具有清晰的物理可解释性,能够有效处理各种扩展条件下的SAR目标识别问题,仿真实验验证了该方法的有效性。Abstract: In this paper, a target’s electromagnetic scattering phenomenon is characterized by the Three Dimensional Parametric Electromagnetic Part Model (3D-PEPM) and a novel Synthetic Aperture Radar (SAR) target recognition method is proposed based on the model. The proposed method projects the individual scatterers in the 3D-PEPM to the 2D image plane to predict the location and appearance for each scatterer according to the radar parameters firstly. Then based on the prior information provided by the 3D-PEPM, the similarities between the 3D-PEPM and SAR data are evaluated. Finally, a view angle adjusting method is utilized to optimize the whole process to produce the final match score between the model and SAR data, and the recognition decision is made according to the match score. The proposed recognition method identifies clearly the correspondences of the scatterers between SAR data and 3D-PEPM and enjoys the explicit physical interpretability, so it can deal with SAR recognition problems under various extended operating conditions. Experiments on simulated data reveal the effectiveness of the proposed method.
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1. Introduction
Frequency Diverse Arrays (FDA) radar has recently drawn much attention among the researchers. FDA differs from the traditional phased array by using a small frequency increment across the array elements, which results in a range-angle-dependent beam pattern. FDA radar system is first proposed in Ref. [1]. In FDA radar, a uniform interelement frequency offset is applied across the array elements. FDA radar with uniform small and large frequency offset frequency has been investigated in Refs. [1–7]. Small frequency offset has been exploited to generate range-dependent beampattern, while large frequency offset can get independent echoes from the target.
Unlike the phased array, the range-angle dependency of the FDA beampattern allows the radar system to focus the transmit energy in a desired range-angle space. This unique feature of FDA helps to suppress the range-dependent interferences[8] and increases the received SINR consequently. Especially for the mainlobe interference and clutter, the FDA can achieve a significant improvement in SINR against the phased array because the FDA provides the increased Degrees Of Freedom (DOFs) in range domain. However, the FDA beampattern is shown to be periodic in range and time[2], which goes to maximum at multiple time and range values. With this multiple-maximum beampattern, the resulting SINR will be deteriorated when the interferers are located at any of the maxima. To improve SINR, FDA with Time-Dependent Frequency Offset (TDFO-FDA) was proposed to achieve a time-independent beampattern at the target location[9]. Nevertheless, the proposed beampattern is still periodic in range which will result in the loss of SINR. A nonuniformly spaced linear FDA with linear incremental frequency increment has also been studied in Ref. [10], and a nonrepeating beampattern has been obtained for range-angle imaging of targets. A uniformly spaced linear FDA with Logarithmically (Log-FDA) increasing frequency offset is proposed in Ref. [11]. The proposed strategy provides a nonperiodic beampattern with the single-maximum in space. In Ref. [12], the beampattern of FDA who transmits the pulsed signal has been studied. Lately, few more publications have done some work in decoupling the range-angle dependent beampattern of FDA[13–16]. All these papers only address the properties of the FDA beampattern, and they do not study the common rule for the FDA configuration to form a single-maximum transmit beampattern.
With the pioneer work on FDA radar, we aim to decouple the range and angle in the beampattern and provide a nonperiodic beampattern with the single-maximum in the illuminated range-angle space. In this paper, we propose a basic criteria for the FDA configuration, in which the element spacing and frequency increment are configurable, to form a single-maximum beampattern through mathematical analysis. This single-maximum beampattern, unlike the multiple-maxima beampattern, can help to further suppress range-dependent interferences, causing improved SINR and increased detect ability. The proposed rule for the FDA configuration will be helpful to design the FDA.
The rest of the paper is organized as follows. In Section 2, the basic FDA model has been described and the basic criterion is derived for the FDA configuration to form a single-maximum beampattern through mathematical analysis. Moreover, several specific conditions are introduced. In Section 3, the beampattern has been plotted for the specific conditions discussed in Section 2. Finally, in Section 4 we conclude the paper.
2. Design and Mathematical Analysis of FDA
2.1 System description
Consider an array of M transmit elements, we assume that the waveform radiated from each antenna element is identical with a frequency increment, as shown in Fig. 1. The radiated frequency from the m-th element is
fm=f0+Δfm, m=0,···,M−1 (1) where Dfm is the frequency increment of m-th element with reference to the carrier frequency f0. Specifically, Df0 = 0.
Considering a given far-field point, the phase of the signal transmitted by the m-th element can be represented by
ψm=2πfm(t−rmc) (2) where c and rm are the speed of light and the distance between the m-th element and the observed point, respectively.
The range difference between individual elements is approximated by
rm=r0−dmsinθ0 (3) where θ0 is the desired angle, dm is the spacing between the m-th element and the first element. Specifically, d0 = 0.
So the phase difference between the m-th element and the first element is
Δψm=ψm−ψ0=2π(fm(t−rmc)−f0(t−r0c))=2πΔfmt−2πfmdmsinθ0c+2πΔfmr0c (4) In Eq. (4), the third term is important because it shows that the FDA radiation pattern depends on both the range and the frequency increment. Taking the first element as the reference for the array, the steering vector can be expressed as
a(θ,r,t)=[1,···,exp(−j2π−Δfm(tc+r)+fmdmsinθc)]T (5) where [·]T denotes the transpose operator.
In the pusled-FDA, for
t∈[−Te2,Te2] , Te is the pulsewidth, the maximum value of phase variance[12] during the pulse duration can be derived asξ=maxm2πΔfmTe (6) When the phase variance
ξ is small enough, the beampattern of the pulsed-FDA can be viewed as quasi-static. Actually, in practical radar systems, duty cycle other than pulse duration is often used to describe the characterization of the pulsed-waveform. Then, the phase varianceξ can be further written as|ξ|=maxm2π|Δfm|frdt=2πdtmaxmρm≪1 (7) where dt is the duty cycle, which is usually small. Eq. (7) holds when
maxmρm is also small.So under the condition Eq. (7), the time t can be neglected. So Eq. (5) can be simplified as
a(θ,r)=[1,···,exp(−j2π−Δfmr+fmdmsinθc)]T (8) 2.2 Transmit beampattern analysis
Throughout this paper, we assume a narrow-band system where the propagation delays manifest as phase shifts to the transmitted signals and Eq. (7) is satisfied. To steer the maximum at an expected target location (
θ 0, r0), the complex weights are configured as a(θ 0, r0), so the transmit beampattern can be expressedAF(θ,r)=|aH(θ0,r0)a(θ,r)|=|M−1∑m=0exp(j2πΔfm(r−r0)−fmdm(sinθ−sinθ0)c)| (9)
where [·]H denotes the conjugate transpose operator.
It is easy to see that the beam direction will vary as a function of the range and angle, which means the beampattern is range-angle dependent. Since the beampattern is coupled in the range and angle, the target’s range and angle cannot be estimated directly by the FDA beamformer output. Note that the beampattern is also related to Dfm and dm, so the desired single-maximum beampattern can be obtained by setting the proper Dfm and dm.
In Eq. (9), when m = 0, the exponential term is equal to 1. To obtain the maximum value of the beampattern, the exponential terms should be all equal to 1 for
m=1,2,···,M−1 . So the phase of the exponential term should be the integral multiple of2π , which can be expressed asΔfm(r−r0)−f0dm(sinθ−sinθ0)−Δfmdm(sinθ−sinθ0)c=Lm (10) where Lm is an integer, e.g. Lm = 0, ±1,···,
m=1,2,···,M−1 .The Eq. (10) can be rewritten as
r=Lmc+f0dm(sinθ−sinθ0)Δfm+dm(sinθ−sinθ0)+r0 (11) Since
dm(sinθ−sinθ0)≪r0 , the termdm(sinθ −sinθ0) in Eq. (8) can be neglected. The curves formed by Eq. (11) will be called as range-angle distribution curves throughout the paper. Then Eq. (11) can be approximately expressed asΔfm(r−r0)−f0dm(sinθ−sinθ0)=Lmc, m=1,2,···,M−1 (12) Rewrite Eq. (12) into matrix form as
Ax=b (13) where
A=[Δf1−f0d1Δf2−f0d2⋮⋮ΔfM−1−f0dM−1] ,x=[r−r0sinθ−sinθ0] ,b=[L1cL2c⋮LM−1c] , Lm = 0, ±1, ···,m=1,2,···, M – 1.To decouple the range and angle, the beam-pattern should have the unique maximum point in the range-angle distribution diagram, which means the Eq. (13) has the unique solution (
θ 0, r0). The necessary and sufficient condition of that the Eq. (13) has the unique solution isrank(A)=rank(˜A)=2 (14) where rank (·) is the rank of a matrix,
˜A=(A,b) . Whenrank(A)=rank(˜A)=1 , the Eq. (13) has infinite solutions, corresponding to the conventional FDA condition, which will be discussed in detail later.To satisfy rank (A) = 2,
dm≠PΔfm , P is a constant.To satisfy
rank(A)=rank(˜A) ,Lm=Qdm orLm=SΔfm , Lm is an integer, and assume that Q, S are the minimum non-zero constants to satisfy the equations. Sincedm≠PΔfm must be satisfied, the two equations cannot be hold at the same time but when Lm = 0,∀m=1,2,···, M–1.In the following, under the condition of
dm≠PΔfm,Lm=0,±1 ,···, we make a summary with different parameter configurations:(1) when Lm = 0, the Eq. (13) has the unique solution (
θ 0, r0);(2) when
Lm=Qdm≠0 ,Lm≠SΔfm , the Eq. (10) has the solutions(arcsin(sin(θ0)− kQλ0),r0),λ0=cf0,k=0,±1,±2,··· . When|sin(θ0)−kQλ0|≤1 , the angle grating lobes will occur at anglearcsin(sin(θ0)−kQλ0) in the beampattern. Otherwise, the Eq. (13) has no solution, resulting in no angle grating lobes;(3) when
Lm=SΔfm≠0,Lm≠Qdm , the Eq. (13) has the(θ0,r0+Skc) ,k=0,±1,±2,··· , which means the range grating lobes will occur atr0+Skc in the beampattern.Note that in array theory, when the adjacent element spacing is less than half the wavelength, the angle grating lobes will never appear. If
Qλ0=±1 andθ0=0∘ , where the element spacing isλ 0, then the grating lobes will occur at angle ±90°. ButLm=SΔfm can always be satisfied since Lm is an integer whose range is[−∞,+∞] . The range grating lobes will always occur at ranger0+Skc in the beampattern. The position of the range grating lobe changes with different S. For example, S = 0.01, the distance between the grating lobe and the mainlobe is 3000 km. So ifr0±Sc is out of the illuminated range space[Rmin,Rmax] , the beampattern has a single-maximum point (θ 0, r0) in the illuminated range space, which means the range and angle are decoupled.So we can conclude that the beampattern of the FDA is always range-periodic, the grating lobes will always occur at range
r0+Skc ,k=0,±1,±2,··· . To obtain the single-maximum beampattern in the illuminated range space[Rmin,Rmax] , the designing criteria for the FDA isdm≠PΔfm , and2Sc>Rmax−Rmin ,|sin(θ0)±Qλ0|>1 ,k=0,±1,±2,··· ,Lm=0,±1,··· ,m=1,2,··· ,M – 1, P is a constant, Q, S are the minimum non-zero constants to satisfy the equationsLm= SΔfm≠0 andLm=Qdm≠0 .Once the range and angle is decoupled, the target’s range and angle can be estimated directly by the FDA beamformer output. Also the 2-dementional MUSIC algorithm[16] for estimating the target’s range and angle can be used as well.
2.3 Specific examples
For the conventional FDA,
Δfm=mΔf , dm = md, Df and d are configurable parameters to control the frequency increment and the element spacing. When Lm = nm,n=0,±1,±2,··· ,m=1,2,···,M−1 , we can getrank(A)=rank (˜A)=1 . Under this circumstance, the Eq. (13) has infinite solutions. The solutions form the range-angle dependent curves, which have expressions as:r=f0dΔfsinθ−f0dsinθ0Δf+r0+ncΔf (15) In Eq. (15), the expression is no longer related to m, which means the range-angle curve for different element coincides with each other, as depicted in Fig. 2(a). In the range-angle distri-bution diagram, the curve is periodic in range, and the range difference between the adjacent curves is c/Df. The corresponding beampattern is depicted as Fig. 3(a).
For the Expf-FDA, whose frequency incre-ment is exponentially increased,
Δfm=(bm −1)Δf , dm = md. b is a configurable constant. The range solution rises when b gets larger. The range-angle distribution curves and the beampattern are depicted in Fig. 2(b) and Fig. 3(b), respectively.Likewise, for the Logd-FDA, whose element spacing is logarithmically increased,
Δfm=mΔf ,dm=log(m+1)d. When Lm = nm,n=0,±1, ±2,··· ,m=1,2,···,M−1 , we can getrank(A)= rank(˜A)=2 , so the range grating lobes will occur in the beampattern as depicted in Fig. 3(c), and the range difference between the grating lobe and the mainlobe is c/Df. The corresponding range-angle distribution diagram is depicted in Fig. 2(c).For another kind of FDA, called Expf-Logd-FDA, where the frequency increment is exponentially increased and the element spacing is logarithmically increased,
Δfm=(bm−1)Δf ,dm=log(m+1)d . The range-angle distribution curves and beampattern are depicted in Fig. 2(d) and Fig. 3(d), respectively.3. Simulations, Results, and Discussions
Bampattern expressed in Eq. (9) and the range-angle distribution curves expressed in Eq. (11) were simulated and plotted for different kinds of FDA discussed in Section 2. The results are discussed and compared with the different kinds of FDA. The illuminated range space is (0 km, 800 km]. To generate these plots, the values of the configurable parameters have been taken as listed in Tab. 1. To avoid angle grating lobes, the parameter d is less than half the wavelength.
Table 1. Parameters for simulationsParameter Value Parameter Value Element number M 8 d 0.1 m Reference frequency f0 1 GHz b 1.4 {\Delta}f 1 kHz Desired point
( \theta_0, r0)(0°, 400 km) The range-angle distribution curves are de-picted in Fig. 2. The curves with different color represent the range-angle distribution for different elements except the reference element in the FDA. It is easy to see that the range-angle distribution of the elements are the same in conventional FDA, and the range difference between the adjacent curves is c/Df = 300 km, which is consistent with the analysis in Section 2. For the Expf-FDA and Expf-Logd-FDA,
Δfm =(1.4m−1)Δf , the range between the first grating lobe and the mainlobe is 3e6 km, which is not in the illuminated space. So the curves of the elements in the range-angle distribution diagram have the single intersection point, which means that the beampattern has the single-maximum point in the illuminated range space. But for the Logd-FDA, when Lm = nm, the distance between the grating lobe and the mainlobe is c/Df = 300 km according to the analysis in Section 2. So in the range-angle distribution diagram, the curves have 3 intersection points, the range difference between adjacent intersection points is 300 km.The beampatterns are depicted in Fig. 3. Similar to the range-angle curve in Fig. 2, the beampattern of the conventional FDA is a range-angle-dependent beampattern. For the Expf-FDA and Expf-Logd-FDA, the beampatterns have a single-maximum point in the illuminated space corresponding to the single intersection point in the range-angle distribution diagram. For the Logd-FDA, the beampattern has 3 range grating lobes corresponding to the 3 intersection points in the range-angle distribution diagram. For the latter 3 FDAs, the contour of the beampattern is an ellipse, which is because the range-angle distribution curves are tightly distributed. The direction of the major axis of the ellipse is corresponding to the most tightness distribution direction of the range-angle distribution curves.
In the meanwhile, we analyze the range and angle solutions of different FDAs in Fig. 4. The Expf-FDA and the Exp-Logd-FDA have the same range solution, and the range solution of conventional FDA and Logd-FDA are the same. That is because the bandwidth across the whole array is the same for each pair. The same situation occurs for the angle solution, if the arrays have the same array aperture, they have the same angle solutions.
We choose the target position at (400 km, 20°), and the transmit beampattern is depicted in Fig. 5. Similar to Fig. 3, we can see that the single maximum beam is formed at the target position.
4. Conclusions
In this paper, we propose a basic criteria for the FDA configuration to provide a single-maximum beampattern in the illuminated space. The single-maximum beampattern can be generated by configuring the element spacing and frequency increment of the FDA. Through the analysis, we can find out that the beampattern of FDA is always range-periodic. Results show that a single-maximum beampattern can be generated with the corresponding criteria by choosing the proper frequency increment. As this paper describes the transmitter only, designing an appropriate receiver is our future work.
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表 1 参数的统计模型
Table 1. Statistical model of parameters
特征属性 均值 方差 距离向位置 x x0 σ2x=f2Downrange 方位向位置 y y0 σ2y=f2Crossrange 幅度 log10(|A|) lg(|A|0) σ2A=0.5 长度 L L0 σ2L=(2fCrossrange)2 表 2 模型投影和从数据估计得到的散射体参数的对比
Table 2. Comparison between model projection and scatterer parameters estimated from data
序号 模型投影得到的散射体参数 从数据估计得到的散射体参数 相似度 X(m) Y(m) L(m) A X(m) Y(m) L(m) A 1 –1.932 0.567 4.416 1.000 –1.932 0.487 4.265 1.000 0.643 2 –0.901 1.772 0.649 0.532 –0.900 1.780 0 0.193 0.254 3 0.181 1.212 0.708 0.458 0.182 1.210 0.695 0.095 0.902 4 0.181 2.400 1.057 0.328 0.183 2.394 0.868 0.114 0.705 5 0.181 –1.126 0.668 0.091 0.178 –1.168 0.633 0.048 0.841 6 –1.601 0 0 0.067 –1.730 –0.001 0 0.076 0.664 7 –1.068 –3.031 4.377 0.052 –0.929 –2.879 4.276 0.044 0.351 8 –0.772 –1.264 0.647 0.010 –0.770 –1.262 0.697 0.018 0.922 9 –1.431 0 0 0.008 –1.548 –0.002 0 0.045 0.689 10 0.338 –2.598 0.325 0.006 0.340 –2.324 0 0.001 0.227 -
[1] EL-DARYMLI K, GILL E W, MCGUIRE P, et al. Automatic target recognition in synthetic aperture radar imagery: A state-of-the-art review[J]. IEEE Access, 2016, 4: 6014–6058. doi: 10.1109/ACCESS.2016.2611492 [2] NOVAK L M, OWIRKA G J, BROWER W S, et al. The automatic target-recognition system in SAIP[J]. The Lincoln Laboratory Journal, 1997, 10(2): 187–202. [3] PARK J I, PARK S H, and KIM K T. New discrimination features for SAR automatic target recognition[J]. IEEE Geoscience and Remote Sensing Letters, 2013, 10(3): 476–480. doi: 10.1109/LGRS.2012.2210385 [4] NICOLI L P and ANAGNOSTOPOULOS G C. Shape-based recognition of targets in synthetic aperture radar images using elliptical Fourier descriptors[C]. SPIE 6967, Automatic Target Recognition XVIII, Orlando, USA, 2008. [5] MISHRA A K. Validation of PCA and LDA for SAR ATR[C]. The TENCON 2008 - 2008 IEEE Region 10 Conference, Hyderabad, India, 2008: 1–6. [6] 宦若虹, 杨汝良. 基于小波域NMF特征提取的SAR图像目标识别方法[J]. 电子与信息学报, 2009, 31(3): 588–591. doi: 10.3724/SP.J.1146.2007.01808HUAN Ruohong and YANG Ruliang. Synthetic aperture radar images target recognition based on wavelet domain NMF feature extraction[J]. Journal of Electronics &Information Technology, 2009, 31(3): 588–591. doi: 10.3724/SP.J.1146.2007.01808 [7] DONG Ganggang and KUANG Gangyao. Classification on the monogenic scale space: Application to target recognition in SAR image[J]. IEEE Transactions on Image Processing, 2015, 24(8): 2527–2539. doi: 10.1109/TIP.2015.2421440 [8] POTTER L C and MOSES R L. Attributed scattering centers for SAR ATR[J]. IEEE Transactions on Image Processing, 1997, 6(1): 79–91. doi: 10.1109/83.552098 [9] MOSES P L, POTTER L C, and GUPTA I J. Feature extraction using attributed scattering center models for model-based automatic target recognition (ATR)[R]. AFRL-SN-WP-TR-2006-1004, 2005. [10] LIU Xian, HUANG Yulin, PEI Jifang, et al. Sample discriminant analysis for SAR ATR[J]. IEEE Geoscience and Remote Sensing Letters, 2014, 11(12): 2120–2124. doi: 10.1109/LGRS.2014.2321164 [11] HUANG Yulin, PEI Jifang, YANG Jianyu, et al. Neighborhood geometric center scaling embedding for SAR ATR[J]. IEEE Transactions on Aerospace and Electronic Systems, 2014, 50(1): 180–192. doi: 10.1109/TAES.2013.110769 [12] DING Jun, CHEN Bo, LIU Hongwei, et al. Convolutional neural network with data augmentation for SAR target recognition[J]. IEEE Geoscience and Remote Sensing Letters, 2016, 13(3): 364–368. [13] CHEN Sizhe, WANG Haipeng, XU Feng, et al. Target classification using the deep convolutional networks for SAR images[J]. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(8): 4806–4817. doi: 10.1109/TGRS.2016.2551720 [14] ROSS T D, BRADLEY J J, HUDSON L J, et al. SAR ATR: So what’s the problem? An MSTAR perspective[C]. SPIE 3721, Algorithms for Synthetic Aperture Radar Imagery VI, Orlando, USA, 1999: 606–610. [15] KEYDEL E R, LEE S W, and MOORE J T. MSTAR extended operating conditions: A tutorial[C]. SPIE 2757, Algorithms for Synthetic Aperture Radar Imagery III, Orlando, USA, 1996: 228–242. [16] JONES III G and BHANU B. Recognition of articulated and occluded objects[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21(7): 603–613. doi: 10.1109/34.777371 [17] DIEMUNSCH J R and WISSINGER J. Moving and stationary target acquisition and recognition (MSTAR) model-based automatic target recognition: Search technology for a robust ATR[C]. SPIE 3370, Algorithms for Synthetic Aperture Radar Imagery V, Orlando, USA, 1998: 481–492. [18] HUANG Peikang, YIN Hongcheng, and XU Xiaojian. Radar Target Characteristics[M]. Beijing: Publishing House of Electronics Industry, 2006. [19] CHIANG H C, MOSES R L, and POTTER L C. Model-based Bayesian feature matching with application to synthetic aperture radar target recognition[J]. Pattern Recognition, 2001, 34(8): 1539–1553. doi: 10.1016/S0031-3203(00)00089-3 [20] ZHOU Jianxiong, SHI Zhiguang, XIAO Cheng, 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 [21] JACKSON J A. Three-dimensional feature models for synthetic aperture radar and experiments in feature extraction[D]. [Ph. D. dissertation], Ohio State University, 2009. [22] 文贡坚, 朱国强, 殷红成, 等. 基于三维电磁散射参数化模型的SAR目标识别方法[J]. 雷达学报, 2017, 6(2): 115–135. doi: 10.12000/JR17034WEN Gongjian, ZHU Guoqiang, YIN Hongcheng, et al. SAR ATR based on 3D parametric electromagnetic scattering model[J]. Journal of Radars, 2017, 6(2): 115–135. doi: 10.12000/JR17034 [23] GIUSTI E, MARTORELLA M, and CAPRIA A. Polarimetrically-persistent-scatterer-based automatic target recognition[J]. IEEE Transactions on Geoscience and Remote Sensing, 2011, 49(11): 4588–4599. doi: 10.1109/TGRS.2011.2164804 [24] TANG Tao and SU Yi. Object recognition based on feature matching of scattering centers in SAR imagery[C]. The 5th International Congress on Image and Signal Processing, Chongqing, China, 2012: 1073–1076. [25] MARTORELLA M, GIUSTI E, DEMI L, et al. Target recognition by means of polarimetric ISAR images[J]. IEEE Transactions on Aerospace and Electronic Systems, 2011, 47(1): 225–239. doi: 10.1109/TAES.2011.5705672 [26] SAVILLE M A, SAINI D K, and SMITH J. Commercial vehicle classification from spectrum parted linked image test-attributed synthetic aperture radar imagery[J]. IET Radar, Sonar & Navigation, 2016, 10(3): 569–576. [27] RICHARDS J A. Target model generation from multiple synthetic aperture radar image[D]. [Ph. D. dissertation], 1996, MIT. [28] 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 [29] ZHOU Jianxiong, SHI Zhiguang, and FU Qiang. Three-dimensional scattering center extraction based on wide aperture data at a single elevation[J]. IEEE Transactions on Geoscience and Remote Sensing, 2015, 53(3): 1638–1655. doi: 10.1109/TGRS.2014.2346509 [30] VOICU L I, PATTON R, and MYLER H R. Multicriterion vehicle pose estimation for SAR ATR[C]. SPIE 3721, Algorithms for Synthetic Aperture Radar Imagery VI, Orlando, USA, 1999: 3721. [31] CUI Xunxue, ZHANG Jichun, and ZHOU Pucheng. Hypothesis testing for target detection model in sensor networks[C]. The 7th International Conference on Fuzzy Systems and Knowledge Discovery, Yantai, China, 2010. [32] BOSE R. Lean CLEAN: Deconvolution algorithm for radar imaging of contiguous targets[J]. IEEE Transactions on Aerospace and Electronic Systems, 2011, 47(3): 2190–2199. doi: 10.1109/TAES.2011.5937291 [33] SHAFER G. A Mathematical Theory of Evidence[M]. Princeton: Princeton University Press, 1976. [34] FELZENSZWALB P F, GIRSHICK R B, MCALLESTER D, et al. Object detection with discriminatively trained part-based models[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 32(9): 1627–1645. doi: 10.1109/TPAMI.2009.167 期刊类型引用(7)
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