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基于高斯混合聚类的阵列干涉SAR三维成像

李杭 梁兴东 张福博 吴一戎

陈慧, 田湘, 李子豪, 等. 共形FDA-MIMO雷达降维目标参数估计研究[J]. 雷达学报, 2021, 10(6): 811–821. DOI: 10.12000/JR21197
引用本文: 李杭, 梁兴东, 张福博, 等. 基于高斯混合聚类的阵列干涉SAR三维成像[J]. 雷达学报, 2017, 6(6): 630–639. DOI: 10.12000/JR17020
CHEN Hui, TIAN Xiang, LI Zihao, et al. Reduced-dimension target parameter estimation for conformal FDA-MIMO radar[J]. Journal of Radars, 2021, 10(6): 811–821. DOI: 10.12000/JR21197
Citation: Li Hang, Liang Xingdong, Zhang Fubo, Wu Yirong. 3D Imaging for Array InSAR Based on Gaussian Mixture Model Clustering[J]. Journal of Radars, 2017, 6(6): 630-639. doi: 10.12000/JR17020

基于高斯混合聚类的阵列干涉SAR三维成像

DOI: 10.12000/JR17020
基金项目: 国家部委基金
详细信息
    作者简介:

    李杭:李   杭(1989–),男,江苏人,学士,中国科学技术大学;博士生,中国科学院电子学研究所;研究方向为阵列干涉SAR高精度3维成像。E-mail: aaronli@mail.ustc.edu.cn

    梁兴东(1973–),男,陕西人,博士,北京理工大学;研究员,中国科学院电子学研究所;研究方向为高分辨率合成孔径雷达系统、干涉合成孔径雷达、成像处理及应用、实时数字信号处理。E-mail: xdliang@mail.ie.ac.cn

    张福博(1988–),男,河北人,博士,中国科学院电子学研究所;助理研究员,研究方向为多通道SAR 3维重建、新体制雷达、阵列雷达信号处理。E-mail: zhangfubo8866@126.com

    吴一戎(1963–),男,安徽人,博士,中国科学院电子学研究所;研究员,中国科学院院士,中国科学院电子学研究所;研究方向为微波成像理论、微波成像技术和雷达信号处理。E-mail: wyr@mail.ie.ac.cn

    通讯作者:

    梁兴东   xdliang@mail.ie.ac.cn

  • 中图分类号: TN957.52

3D Imaging for Array InSAR Based on Gaussian Mixture Model Clustering

Funds: The National Ministries Foundation
  • 摘要:

    阵列干涉SAR具备高程分辨能力,单次航过即可生成观测场景的3维点云分布,解决叠掩问题。但是,由于阵列干涉SAR阵元数目有限、基线长度较短,高程向分辨率受到限制,加之城区建筑物的叠掩现象,常规方法重建结果定位精度较差,难以提取建筑物有效特征。针对这个问题,该文提出了一种基于高斯混合聚类的阵列干涉SAR 3维成像方法,首先通过基于压缩感知(Compressive Sensing, CS)的超分辨算法获得场景区域的3维点云分布,然后利用密度估计方法提取出建筑物的散射点,之后使用高斯混合模型(Gaussian Mixture Model, GMM)对建筑物3维点云进行聚类,最后利用系统参数完成各个区域的SAR图像反演,实现建筑物的3维成像。通过国内首次机载阵列干涉SAR实验的实际数据,验证了该文算法的有效性,并获得了真实的建筑物3维成像结果。

     

  • In recent years, Frequency Diverse Array (FDA) radar has received much attention due to its range-angle-time-dependent beampattern[1,2]. Combining the advantages of FDA and traditional phased array Multiple-Input Multiple-Output (MIMO) radar in the degree of freedom, the FDA Multiple-Input Multiple Output (FDA-MIMO) radar was proposed in Ref. [3] and applied in many fields[4-9]. For parameter estimation algorithm, the authors first proposed a FDA-MIMO target localization algorithm based on sparse reconstruction theory[10], and an unbiased joint range and angle estimation method was proposed in Ref. [11]. The work of Ref. [12] further proved that the FDA-MIMO is superior to traditional MIMO radar in range and angle estimation performance, and the authors of Ref. [13] introduced a super-resolution MUSIC algorithm for target location, and analyzed its resolution threshold. Meanwhile, high-resolution Doppler processing is utilized for moving target parameter estimation[14]. The Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) and PARAllel FACtor (PARAFAC) was proposed in Ref. [15], which is a search-free algorithm for FDA-MIMO.

    Moreover, the research of conformal array has received more and more attention. Conformal array is a non-planar array that can be completely attached to the surface of the carrier[16]. It has significant advantages such as reducing the aerodynamic impact on the carrier and smaller radar cross section[17]. In addition, conformal array can achieve wide-angle scanning with a lower SideLobe Level (SLL)[18]. Different from traditional arrays, the element beampattern of conformal array needs to be modeled separately in the parameter estimation due to the difference of carrier curvature[19-21].

    As far as we know, most of the existing researches on FDA-MIMO are based on linear array, while there is little research on the combination of FDA-MIMO and conformal array[22]. In this paper, we replace the receiving array in the traditional FDA-MIMO with conformal array. Compared with conventional FDA-MIMO, conformal FDA-MIMO inherits the merits of conformal array and FDA-MIMO, which can effectively improve the stealth and anti-stealth performance of the carrier, and reduce the volume and the air resistance of the carrier. For conformal FDA-MIMO, we further study the parameters estimation algorithm. The major contributions of this paper are summarized as follows:

    (1) A conformal FDA-MIMO radar model is first formulated.

    (2) The parameter estimation Cramér-Rao Lower Bound (CRLB) for conformal FDA-MIMO radar is derived.

    (3) Inspired by the existing work of Refs. [23,24], a Reduced-Dimension MUSIC (RD-MUSIC) algorithm for conformal FDA-MIMO radar is correspondingly proposed to reduce the complexity.

    The rest of the paper consists of four parts. Section 2 formulates the conformal FDA-MIMO radar model, and Section 3 derives a RD-MUSIC algorithm for conformal FDA-MIMO radar. Simulation results for conformal FDA-MIMO radar with semi conical conformal receiving array are provided in Section 4. Finally, conclusions are drawn in Section 5.

    For the convenience of analysis, we consider a monostatic conformal FDA-MIMO radar which is composed by a M-element linear FDA transmitting array and a N-element conformal receiving array, as shown in Fig. 1. d denotes the inter-element spacing, the carrier frequency at the mth transmitting element is fm=f1+Δf(m1), m=1,2,,M where f1 is the transmission frequency of the first antenna element, which is called as reference frequency, and Δf is the frequency offset between the adjacent array elements.

    Figure  1.  Conformal FDA-MIMO radar

    The complex envelope of the transmitted signal of the mth transmitting element is denoted as φm(t), assume the transmitting waveforms have orthogonality,

    Tpφm(t)φm1(tτ)dt=0,m1m (1)

    where τ denotes the time delay, Tp denotes the pulse duration, and () is conjugate operator. The signal transmitted from the mth element can be expressed as

    sm(t)=am(t,θ,ϕ,r)φm(t),0tTp (2)

    where

    am(t,θ,ϕ,r)=exp{j2π((m1)Δfrcf1(m1)dsinαc(m1)Δft)} (3)

    is the mth element of the transmitting steering vector according to the phase difference between adjacent elements, the angle between far-field target and transmitting array is denoted as α=arcsin(sinθcosϕ), where arcsin() denotes arcsine operator, α can be calculated by using the inner product between the target vector and unit vector along the X-axis. θ,ϕ,r are the elevation, azimuth and range between the target and the origin point, respectively. The phase difference between adjacent elements is

    Δψt0=2π(Δfrcf1dsinαcΔft) (4)

    where c is light speed. For far-field target P(r,θ,ϕ), the transmitting steering vector is

    a0(t,θ,ϕ,r)=[1,exp{jΔψt0},,exp{j(M1)Δψt0}]T (5)

    For the conformal receiving array, as shown in Fig. 1(b), the time delay between target P(r,θ,ϕ) and the nth receiving array element is

    τn=rn/c (6)

    where rn is the range between target and the nth receiving array element. For far-field assumption, the rn can be approximated as

    rnrpnr (7)

    where r denotes the range between the target and the origin point, pn=xnex+yney+znez denotes the position vector from the nth element to origin point, and r=sinθcosϕex+sinθsinϕey+cosθez is the unit vector in target orientation, where ex,ey and ez are the unit vectors along the X- , Y- , and Z-axis, respectively. (xn,yn,zn) are the coordinates of the nth element in the Cartesian coordinate system. For simplicity, we let u=sinθcosϕ, v=sinθcosϕ, so the time delay τn=(r(uxn+vyn+cosθzn))/c. The time delay between the first element and the nth element at the receiving array is expressed as

    Δτrn=τ1τn=u(xnx1)+v(yny1)+cosθ(znz1)c (8)

    And the corresponding phase difference between the first element and the nth element is

    ΔψRn=2πf1Δτrn (9)

    Consequently, the receiving steering vector is

    b(θ,ϕ)=[r1(θ,ϕ),r2(θ,ϕ)exp(jΔψr2),,rN(θ,ϕ)exp(jΔψrN)]T (10)

    where rn(θ,ϕ) is the nth conformal receiving array element beampattern which should be designed in its own local Cartesian coordinate system. In this paper, we utilize Euler rotation method to establish transformation frame between local coordinate system and global coordinate system[25,26].

    Then the total phase difference between adjacent transmitting array elements can be rewritten as

    Δψt=2π(Δf2rcf1dsinαcΔft) (11)

    where the factor 2r in the first term represents the two-way transmission and reception, and the correspondingly transmitting steering vector is written as

    a(t,θ,ϕ,r)=[1,exp{jΔψt},,exp{j(M1)Δψt}]T (12)

    Assuming L far-field targets are located at (θi,ϕi,Ri), i=1,2,,L and snapshot number is K. After matched filtering, the received signal can be formulated as following matrix (13,14)

    X=AS+N (13)

    where the array manifold A is expressed as

    A=[at,r(θ1,ϕ1,r1),,at,r(θL,ϕL,rL)]=[b(θ1,ϕ1)a(θ1,ϕ1,r1),,b(θL,ϕL)a(θL,ϕL,rL)] (14)

    where at,r(θ,ϕ,r) is the joint transmitting-receiving steering vector, S=[s(t1),s(t2),,s(tK)]CL×K and NCMN×K denote the signal matrix and noise matrix, respectively, where noise follows the independent identical distribution, and denotes Kronecker product.

    a(θ,ϕ,r)=[1exp{j2π(2Δfrcf1dsinαc)}exp{j2π(M1)(2Δfrcf1dsinαc)}] (15)

    which can be expressed as

    a(θ,ϕ,r)=a(θ,ϕ)a(r) (16)

    where

    a(r)=[1,exp(j2π2Δfrc),,exp(j2π(M1)2Δfrc)]T (17)
    a(θ,ϕ)=[1,exp(j2πf1dsinαc),,exp[j2π(M1)f1dsinαc]]T (18)

    and represents Hadamard product operator.

    The CRLB can be obtained from the inverse of Fisher information matrix[27,28], which establishes a lower bound for the variance of any unbiased estimator. We employ the CRLB for conformal FDA-MIMO parameter estimation to evaluate the performance of some parameter estimation algorithms.

    The discrete signal model is

    x[k]=at,r(θ,ϕ,r)s[k]+N[k],k=1,2,,K (19)

    For the sake of simplification, we take at,r as the abbreviation of at,r(θ,ϕ,r).

    The Probability Distribution Function (PDF) of the signal model with K snapshots is

    p(x|θ,ϕ,r)=1(2πσ2n)K2exp(1σ2n(xat,rs)H(xat,rs)) (20)

    where x=[x(1),x(2),,x(K)] and s=[s(1),s(2),,s(K)].

    The CRLB matrix form of elevation angle, azimuth angle and range is given by Eq. (21), diagonal elements {Cθθ,Cϕϕ,Crr} represent CRLB of estimating elevation angle, azimuth angle and range, respectively.

    CRLB=[CθθCθϕCθrCϕθCϕϕCϕrCrθCrϕCrr]=FIM1=[F11F12F13F21F22F23F31F32F33] (21)

    The elements of Fisher matrix can be expressed as

    Fij=E[2ln(p(xθ,ϕ,r))xixj],i,j=1,2,3 (22)

    In the case of K snapshots, PDF can be rewritten as

    p(x|θ,ϕ,r)=Cexp{1σ2nKn=1(x[k]at,rs[k])H(x[k]at,rs[k])} (23)

    where C is a constant, natural logarithm of Eq. (23) is

    ln(p(x|θ,ϕ,r))=ln(C)1σ2nKk=1(x[k]at,rs[k])H(x[k]at,rs[k]) (24)

    where ln() represents the logarithm operator. The first entry of Fisher matrix can be expressed as

    F11=E[2ln(p(x|θ,ϕ,r))θ2] (25)

    Correspondingly, the first derivative of natural logarithm is given by

    ln(p(x|θ,ϕ,r))θ=1σ2nKk=1(xH[k]at,rθs[k]aHt,rθs[k]x[k]+aHt,rθat,rs2[n]a+aHt,rat,rθs2[n]) (26)

    Then we can obtain the second derivative of

    2ln(p(x|θ,ϕ,r))θ2=1σ2nKk=1(x[k]H2at,rθ2s[k]2aHt,rθ2s(k)x[k]+2aHt,rθ2at,rs[k]2+aHt,rθat,rθs[k]2+aHt,rθat,rθs[k]2+aHt,r2at,rθ2s[k]2) (27)

    And then we have

    Kk=1x[k]=Kk=1at,rs[k]+N[k]=at,r(θ,ϕ,r)Kk=1s[k] (28)

    and

    Kk=1s2[k]=Kvar(s[k])=Kσ2s (29)

    where var() is a symbol of variance. Therefore, the PDF after quadratic derivation can be written as

    E[2ln(p(x|θ,ϕ,r))θ2]=Kσ2sσ2n(aHt,rθat,rθ+aHt,rθat,rθ)=2Kσ2sσ2nat,rθ2 (30)

    where denotes 2-norm. Similarly, the other elements of the Fisher matrix can also be derived in the similar way, so the Fisher matrix can be expressed as

    CRLB1=FIM=2Kσ2sσ2n[aθ2FIM12FIM13FIM21aϕ2FIM23FIM31FIM32ar2] (31)

    where

    FIM12=12[aHt,rθat,rϕ+aHt,rϕat,rθ],
    FIM13=12[aHt,rθat,rr+aHt,rrat,rθ],
    FIM21=12[aHt,rϕat,rθ+aHt,rθat,rϕ],
    FIM23=12[aHt,rϕat,rr+aHt,rrat,rϕ],
    FIM31=12[aHt,rrat,rθ+aHt,rθat,rr],
    FIM32=12[aHt,rrat,rϕ+aHt,rϕat,rr],
    σ2sσ2n=SNR

    Finally, the CRLB of conformal FDA-MIMO can be calculated by the inverse of Fisher matrix.

    The covariance matrix of the conformal FDA-MIMO receiving signal can be written as

    RX=ARsAH+σ2IMN (32)

    where Rs represents the covariance matrix of transmitting signal, IMN denotes MN dimensional identity matrix. For independent target signal and noise, RX can be decomposed as

    RX=USΛSUHS+UnΛnUHn (33)

    The traditional MUSIC algorithm is utilized to estimate the three-dimensional parameters {θ,ϕ,r}, MUSIC spectrum can be expressed as

    PMUSIC(θ,ϕ,r)=1aHt,r(θ,ϕ,r)UnUHnat,r(θ,ϕ,r) (34)

    The target location can be obtained by mapping the peak indexes of MUSIC spectrum.

    Traditional MUSIC parameter estimation algorithm is realized by 3D parameter search, which has good performance at the cost of high computational complexity. When the angular scan interval is less than 0.1°, the running time of single Monte-Carlo simulation is in hours, which is unpracticable for us to analysis conformal FDA-MIMO estimation performance by hundreds of simulations.

    In order to reduce the computation complexity of the parameter estimation algorithm for conformal FDA-MIMO, we propose a RD-MUSIC algorithm, which has a significant increase in computing speed at the cost of little estimation performance loss.

    At first, we define

    V(θ,ϕ,r)=aHt,r(θ,ϕ,r)HUnUHnat,r(θ,ϕ,r)=[b(θ,ϕ)a(θ,ϕ,r)]HUnUHn[b(θ,ϕ)a(θ,ϕ,r)] (35)

    Eq. (35) can be further calculated by

    V(θ,ϕ,r)=aH(θ,ϕ,r)[b(θ,ϕ)IM]H×UnUHn[b(θ,ϕ)IM]a(θ,ϕ,r)=aH(θ,ϕ,r)Q(θ,ϕ)a(θ,ϕ,r) (36)

    where Q(θ,ϕ)=[b(θ,ϕ)IM]HUnUHn[b(θ,ϕ)IM],

    Eq. (36) can be transformed into a quadratic programming problem. To avoid a(θ,ϕ,r)=0M, we add a constraint eH1a(θ,ϕ,r)=1, where e1 denotes unit vector. As a result, the quadratic programming problem can be redefined as

    {min (37)

    The penalty function can be constructed as

    \begin{split} L(\theta ,\phi ,r) =& {{\boldsymbol{a}}^{\rm{H}}}(\theta ,\phi ,r){\boldsymbol{Q}}(\theta ,\phi ){\boldsymbol{a}}(\theta ,\phi ,r) \\ & - \mu \left({\boldsymbol{e}}_1^{\text{H}}{\boldsymbol{a}}(\theta ,\phi ,r) - 1\right) \\ \end{split} (38)

    where \mu is a constant, because {\boldsymbol{a}}\left( {\theta ,\phi ,r} \right) = {\boldsymbol{a}}\left( {\theta ,\phi } \right) \odot {\boldsymbol{a}}\left( r \right), so we can obtain

    \begin{split} \frac{{\partial L(\theta ,\phi ,r)}}{{\partial {\boldsymbol{a}}(r)}} =& 2{\rm{diag}}\left\{ {{\boldsymbol{a}}(\theta ,\phi )} \right\}{\boldsymbol{Q}}(\theta ,\phi ){\boldsymbol{a}}(\theta ,\phi ,r) \\ & - \mu {\rm{diag}}\left\{ {{\boldsymbol{a}}(\theta ,\phi )} \right\}{\boldsymbol{e}}_{\boldsymbol{1}}^{} \end{split} (39)

    where {\rm{diag}}( \cdot ) denotes diagonalization.

    And then let \dfrac{{\partial L(\theta ,\phi ,r)}}{{\partial {\boldsymbol{a}}(r)}} = 0, we can get

    {\boldsymbol{a}}\left( r \right) = \varsigma {{\boldsymbol{Q}}^{ - 1}}(\theta ,\phi ){\boldsymbol{e}}_1^{}./{\boldsymbol{a}}(\theta ,\phi ) (40)

    where \varsigma is a constant, ./ denotes the division of the corresponding elements, which is opposite of Hadamard product. Substituting the constraint {\boldsymbol{e}}_1^{\rm{H}}{\boldsymbol{a}}(\theta ,\phi ,r) = 1 into {\boldsymbol{a}}\left( r \right) , we can obtain \varsigma = 1/({\boldsymbol{e}}_1^{\rm{H}}{{\boldsymbol{Q}}^{ - 1}} \cdot(\theta ,\phi ){\boldsymbol{e}}_1 ), then {\boldsymbol{a}}\left( r \right) can be expressed as

    {\boldsymbol{a}}\left( r \right) = \frac{{{{\boldsymbol{Q}}^{ - 1}}\left( {\theta ,\phi } \right){{\boldsymbol{e}}_1}}}{{{\boldsymbol{e}}_1^{\rm{H}}{{\boldsymbol{Q}}^{ - 1}}\left( {\theta ,\phi } \right){{\boldsymbol{e}}_1}}}./{\boldsymbol{a}}\left( {\theta ,\phi } \right) (41)

    Substituting {\boldsymbol{a}}\left( r \right) into Eq. (37), the target azimuths and elevations can be estimated by searching two-dimensional azimuth-elevation spectrum,

    \begin{split} \hfill \lt \hat \theta ,\hat \phi \gt =& {\text{arg}}\mathop {\min }\limits_{\theta ,\phi } \frac{1}{{{\boldsymbol{e}}_1^{\text{H}}{{\boldsymbol{Q}}^{ - 1}}(\theta ,\phi ){{\boldsymbol{e}}_{\boldsymbol{1}}}}} \\ =& {\text{arg}}\mathop {\max }\limits_{\theta ,\phi } {\boldsymbol{e}}_1^{\text{H}}{{\boldsymbol{Q}}^{ - 1}}(\theta ,\phi ){{\boldsymbol{e}}_{\boldsymbol{1}}} \end{split} (42)

    Given azimuth-elevation estimations obtained by mapping the L peak points, the range information can be obtained by searching range-dimensional spectrum,

    P\left({\hat \theta _i},{\hat \phi _i},r\right){\text{ }} = \frac{1}{{{\boldsymbol{a}}_{t,r}^{\rm{H}}\left({{\hat \theta }_i},{{\hat \phi }_i},r\right){{\boldsymbol{U}}_n}{\boldsymbol{U}}_n^{\rm{H}}{{\boldsymbol{a}}_{t,r}}\left({{\hat \theta }_i},{{\hat \phi }_i},r\right)}} (43)

    For conformal array, different array layouts produce different element patterns. We select the semi conical conformal array which is shown in Fig. 2 as the receiving array for the following simulation.

    Figure  2.  Conformal FDA-MIMO semi conical receiving array

    The simulation parameters are provided as follows: M = 10,N = 7,{f_1} = 10\;{\rm{GHz}},\Delta f = 3\;{\rm{kHz}}, d = \lambda /2 = c/2{f_1} and c = 3 \times {10^8}\;{\rm{m}}/{\rm{s}}.

    We first analyze the computational complexity of the algorithms in respect of the calculation of covariance matrix, the eigenvalue decomposition of the matrix and the spectral search. The main complexity of the MUISC algorithm and our proposed RD-MUISC algorithm are respectively as

    O\left(KL{({MN})^2} + 4/3{({MN})^{\text{3}}}{{ + L}}{\eta _1}{\eta _2}{\eta _3}{({MN})^2} \right) (44)
    O\left(KL{({MN})^2} + 4/3{({MN})^{\text{3}}}{{ + L}}{\eta _1}{\eta _2}{({MN})^2} + L{\eta _3}{({MN})^2}\right) (45)

    Where K and L denote snapshot number and signal sources number, {\eta _1},{\eta _2} and {\eta _3} represent search number in three-dimensional parameter \theta ,\phi ,r , respectively.

    From Eq. (44) and Eq. (45), we can see that the main complexity reduction of the RD-MUSIC algorithm lies in the calculation of the spectral search function. With the increase of the search accuracy, the complexity reduction is more significant.

    The computational complexity of algorithms is compared in Fig. 3. It can be seen from Fig. 3 that the difference of computational complexity between the two algorithms gradually increases with the increase of search accuracy. In the case of high accuracy, the computational efficiency of RD-MUSIC algorithm can reach more than {10^3} times of the traditional MUSIC algorithm. The simulation results show that RD-MUSIC algorithm has advantage in computing efficiency for conformal FDA-MIMO.

    Figure  3.  Comparison of computational complexity under different scan spacing

    In order to illustrate the effectiveness of the RD-MUSIC algorithm for a single target which is located at ({30^\circ },{20^\circ },10\;{\rm{km}}), we first give the parameter estimation probability of success with 1000 times Monte Carlo simulation, as shown in Fig. 4, the criterion of successful estimation is defined as the absolute difference between the estimation value and the actual value is less than a designed threshold \varGamma . More specifically, the criterion is \left| {\hat \theta - \theta } \right| < {\varGamma _\theta },\left| {\hat \phi - \phi } \right| < {\varGamma _\phi },\left| {\hat r - r} \right| < {\varGamma _r} , and suppose {\varGamma _\theta } = \varGamma \times {1^\circ },{\varGamma _\phi } = \varGamma \times {1^\circ },{\varGamma _r} = \varGamma \times 100\;{\rm{m}}, in the simulation, as well as the search paces are set as \left[ {{{0.05}^\circ },{{0.05}^\circ },0.05\;{\rm{km}}} \right], respectively. From Fig. 4, we can see that the probability of success gets higher as \varGamma gets bigger, which is consistent with expected.

    Figure  4.  The parameter estimation probability of RD-MUSIC algorithm with different thresholds

    Then, we consider the single target parameter estimation performance, Fig. 5 shows the RMSE of different algorithms with the increase of SNR under 200 snapshots condition, and Fig. 6 demonstrates the RMSE of different algorithms with the increase of snapshot number when SNR=0 dB. As shown in Fig. 5 and Fig. 6, the RMSEs of conformal FDA-MIMO gradually descend with the increasing of SNRs and snapshots, respectively. At the same time, the performance of traditional algorithm is slightly higher than RD-MUSIC algorithm. When the number of snapshots is more than 200, the difference of RMSEs is less than {10^{ - 1}} . Therefore, the performance loss of RD-MUSIC algorithm is acceptable compared with the improved computational speed. Note that, here we set 100 times Monte Carlo simulation to avoid running too long.

    Figure  5.  The RMSE versus snapshot for single target case
    Figure  6.  The RMSE versus SNR for two targets case

    Without loss of generality, we finally consider two targets which are located at ({30^\circ },{20^\circ }, 10\;{\rm{km}}) and ({30^\circ },{20^\circ },12\;{\rm{km}}), respectively, the remaining parameters are the same as single target case. Fig. 7 and Fig. 8 respectively show the RMSE of different algorithms with the increase of SNR and snapshot number in the case of two targets.

    Figure  7.  The RMSE versus snapshot for two targets case
    Figure  8.  The RMSE versus snapshot for two targets case

    It can be seen from Fig. 7 that the RMSE curve trend of angle estimation is consistent with that of single target case. The performance of traditional MUSIC algorithm is slightly better than that of RD-MUSIC algorithm. In the range dimension, the performance of traditional algorithm hardly changes with SNR, and RD-MUSIC algorithm is obviously better than traditional MUSIC algorithm. The proposed RD-MUSIC algorithm first estimates the angles, and then estimates the multiple peaks from range-dimensional spectrum, which avoids the ambiguity in the three-dimensional spectral search. Therefore, the RD-MUSIC algorithm has better range resolution for multiple targets estimation.

    In this paper, a conformal FDA-MIMO radar is first established, and the corresponding signal receiving mathematical model is formulated. In order to avoid the computational complexity caused by three-dimensional parameter search of MUSIC algorithm, we propose a RD-MUSIC algorithm by solving a quadratic programming problem. Simulation results show that the RD-MUSIC algorithm has comparative angle estimation performance with that of traditional MUSIC algorithm while greatly reducing the computation time. And the RD-MUSIC algorithm has better range estimation performance for multiple targets.

  • 图  1  阵列干涉SAR成像模型

    Figure  1.  Array InSAR imaging model

    图  2  观测场景光学图像

    Figure  2.  Optical image of the observed scene

    图  3  观测场景原始3维点云

    Figure  3.  Orginal 3D point clouds of the observed scene

    图  4  算法流程图

    Figure  4.  Workflow of proposed approach

    图  5  观测场景散射点密度图

    Figure  5.  Scatterer density map of the observed scene

    图  6  观测场景建筑物提取结果

    Figure  6.  Extracted building results of the observed scene

    图  7  不同窗口/阈值性能曲线图

    Figure  7.  Performance curve map with varying TH and GA parameters

    图  8  子类个数与偏差度关系图

    Figure  8.  Dispersion plot with number of clusters

    图  9  建筑物区域聚类结果

    Figure  9.  Clustered result of building areas

    图  10  K-means聚类结果

    Figure  10.  Clustered results of K-means

    图  11  各区域反演SAR图像

    Figure  11.  Inversed SAR images of all aeras

    图  12  地面区域SAR图像

    Figure  12.  Inversed SAR images of the ground

    图  13  观测场景2维SAR图像

    Figure  13.  2D SAR image of the observed scene

    图  14  观测场景干涉相位图

    Figure  14.  Interferometric phase image of the observed scene

    图  15  观测场景3维成像结果

    Figure  15.  3D imaging result of the observed scene

    表  1  阵列干涉SAR系统参数

    Table  1.   System parameters of array InSAR

    项目参数
    载频(GHz)15
    发射信号带宽(MHz)500
    脉冲重复频率(kHz)1
    载机高度(m)600
    飞行速度(m/s)70
    方位波束宽度(°)2
    距离波束宽度(°)27
    中心下视角(°)25
    下载: 导出CSV

    表  2  不同窗口/阈值质量评价表

    Table  2.   Quality evaluation with varying TH and GA parameters

    TH
    (点数/dm2)
    GA (dm2)
    1×12×23×34×45×5
    175.1274.8874.3771.8971.75
    281.2781.8681.7377.7178.07
    394.1293.8494.8294.6394.08
    487.4886.3286.4081.9877.56
    581.8984.7784.6878.2977.91
    667.2363.0267.1460.6251.83
    下载: 导出CSV
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  • 收稿日期:  2017-03-03
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