有懂矢量嵌套阵 doa估计的原理吗，不太懂矢量阵去冗余怎么去，有了解的吗，有了解的吗

Question

有懂矢量嵌套阵 doa估计的原理吗，需要具体实现，不太懂矢量阵去冗余怎么去，有了解的吗，有了解的吗？

Answer 1

不知道你这个问题是否已经解决, 如果还没有解决的话:

• 你可以看下这个问题的回答https://ask.csdn.net/questions/216499
• 这篇博客你也可以参考下：团队协作OA解决方案
• 这篇博客也不错, 你可以看下团队协作OA解决方案
• 除此之外, 这篇博客: 角度测量(AOA/DOA)室内定位-迭代最小二乘和高斯牛顿法\MATLAB中的 3. 参考代码 部分也许能够解决你的问题, 你可以仔细阅读以下内容或者直接跳转源博客中阅读:
  

  clc;
  close all;
  clear all;
  N=50;%迭代次数
  deta=0;
  Runs=350;%Monte karlo
  ml_runx=0;
  ml_runy=0;
  ls_runx=0;
  ls_runy=0;
  %%initial varient
  ls_res=zeros(2,N);
  ls_v=zeros(2,N);
  ls_x=zeros(1,N);
  ls_y=zeros(1,N);
  %%ML变量定义
  ml_res=zeros(2,N);
  ml_v=zeros(2,N);
  ml_x=zeros(1,N);
  ml_y=zeros(1,N);
  d0=0.5;%迭代终止条件
  % T=1;%采样周期
  %target
  xp=20000;
  yp=20000;%目标位置
  vp=[xp;yp];
  x=zeros(1,50);
  y=zeros(1,50);
  %sensor 
  x1=0;y1=0;
  x2=15000;y2=5000;
  x3=30000;y3=0;%传感器位置，三个
  v1=[x1;y1];
  v2=[x2;y2];
  v3=[x3;y3];
  y=[y1,y2,y3];
  x=[x1,x2,x3];
  Z=zeros(3,1);%传感器量测数据
  z1=0;z2=0;z3=0;
  Z(1,1)=z1;
  Z(2,1)=z2;
  Z(3,1)=z3;
  
  %非线性函数
  h01=0;h02=0;h03=0;
  H0=zeros(3,1);
  H=zeros(3,1);
  
  %噪声
  w=zeros(3,1);
  Q=(pi/180)^2;%noise variance
  
  % hatv=zeros(2,1);%v=[x;y]
  %%
  % nonlinear funchtion h() matraix
  h01=atan2(yp-y1,xp-x1);
  h02=atan2(yp-y2,xp-x2);
  h03=atan2(yp-y3,xp-x3);%真实位置信息
  H0(1,1)=h01;
  H0(2,1)=h02;
  H0(3,1)=h03;
  
  for i=1:1:Runs;
      
  %white gassian noise
  w=sqrt(Q)*randn(3,1);
  %measuremen z
  Z=H0+w;
  z1=Z(1,1);
  z2=Z(2,1);
  z3=Z(3,1);
  %LS估计初值
  ls_x0=(x3*tan(z3)-x1*tan(z1)-y3+y1)/(tan(z3)-tan(z1)); %20060;%初始位置
  ls_y0=((x1-x3)*tan(z1)*tan(z3)-y1*tan(z3)+y3*tan(z1))/(tan(z1)-tan(z3));  %19770;y纵坐标初始位置
  ls_v0=[ls_x0;ls_y0];
  %ML估计初值
  ml_x0=ls_x0;
  ml_y0=ls_y0;
  ml_v0=[ml_x0;ml_y0];
  
  %ML迭代
  for t=1:1:N;
      if(t==1)
          ml_res(:,t)=ml_v0;
          ml_v(:,1)=ml_v0;
          ml_x(t)=ml_x0;
          ml_y(t)=ml_y0;
      else
          %H矩阵:ml_h
          ml_h(1,1)=atan2(ml_y(t-1)-y1,ml_x(t-1)-x1);
          ml_h(2,1)=atan2(ml_y(t-1)-y2,ml_x(t-1)-x2);
          ml_h(3,1)=atan2(ml_y(t-1)-y3,ml_x(t-1)-x3);
          %雅可比矩阵ml_J
          ml_J(1,1)=-(ml_y(t-1)-y1)/((ml_x(t-1)-x1)^2+(ml_y(t-1)-y1)^2);
          ml_J(1,2)=(ml_x(t-1)-x1)/((ml_x(t-1)-x1)^2+(ml_y(t-1)-y1)^2);
          ml_J(2,1)=-(ml_y(t-1)-y2)/((ml_x(t-1)-x2)^2+(ml_y(t-1)-y2)^2);
          ml_J(2,2)=(ml_x(t-1)-x2)/((ml_x(t-1)-x2)^2+(ml_y(t-1)-y2)^2);
          ml_J(3,1)=-(ml_y(t-1)-y3)/((ml_x(t-1)-x3)^2+(ml_y(t-1)-y3)^2);
          ml_J(3,2)=(ml_x(t-1)-x3)/((ml_x(t-1)-x3)^2+(ml_y(t-1)-y3)^2);
          %函数h的二阶梯度ml_JJ
          for i=1:3
              ml_JJ(i,1)=(2*(ml_y(t-1)-y(i))*(ml_x(t-1)-x(i)))/((ml_y(t-1)-y(i))^2+(ml_x(t-1)-x(i))^2)^2;
              ml_JJ(i,2)=-(2*(ml_y(t-1)-y(i))*(ml_x(t-1)-x(i)))/((ml_y(t-1)-y(i))^2+(ml_x(t-1)-x(i))^2)^2;
              ml_JJ(i,3)=((ml_y(t-1)-y(i))^2-(ml_x(t-1)-x(i))^2)/((ml_y(t-1)-y(i))^2+(ml_x(t-1)-x(i))^2)^2;
          end
          
          %一阶梯度矩阵ml_F
          ml_F(1,1)=1/Q*((z1-ml_h(1,1))*ml_J(1,1)+(z2-ml_h(2,1))*ml_J(2,1)+(z3-ml_h(3,1))*ml_J(3,1));
          ml_F(2,1)=1/Q*((z1-ml_h(1,1))*ml_J(1,2)+(z2-ml_h(2,1))*ml_J(2,2)+(z3-ml_h(3,1))*ml_J(3,2)); 
          
          %Hessian矩阵：ml_H
          ml_H(1,1)=((z1-ml_h(1,1))*ml_JJ(1,1)-(ml_J(1,1))^2+(z2-ml_h(2,1))*ml_JJ(2,1)-(ml_J(2,1))^2+(z3-ml_h(3,1))*ml_JJ(3,1)-(ml_J(3,1))^2)/Q;
          ml_H(2,2)=((z1-ml_h(1,1))*ml_JJ(1,2)-(ml_J(1,2))^2+(z2-ml_h(2,1))*ml_JJ(2,2)-(ml_J(2,2))^2+(z3-ml_h(3,1))*ml_JJ(3,2)-(ml_J(3,2))^2)/Q;
          ml_H(1,2)=((z1-ml_h(1,1))*ml_JJ(1,3)-(ml_J(1,1))*(ml_J(1,2))+(z2-ml_h(2,1))*ml_JJ(2,3)-(ml_J(2,1))*(ml_J(2,2))+(z3-ml_h(3,1))*ml_JJ(3,3)-(ml_J(3,1))*(ml_J(3,2)))/Q;
          ml_H(2,1)=ml_H(1,2);
          
          %ML迭代
          ml_v(:,t)=ml_v(:,t-1)-inv(ml_H)*ml_F;
      end
      
          ml_res(:,t)=ml_v(:,t);
          ml_x(t)=ml_v(1,t);
          ml_y(t)=ml_v(2,t);
         
  end
          for k=1:50;
          ml_runx=ml_runx+(xp-ml_x(k))^2;
          ml_runy=ml_runy+(yp-ml_y(k))^2;
          end 
    
  %%LS迭代
  for t=1:1:N;%迭代不超过50次
      if(t==1)
          ls_res(:,t)=ls_v0;
          ls_v(:,1)=ls_v0;
          ls_x(t)=ls_x0;
          ls_y(t)=ls_y0;
      else
          %H矩阵
          ls_h1=atan2(ls_y(t-1)-y1,ls_x(t-1)-x1);
          ls_h2=atan2(ls_y(t-1)-y2,ls_x(t-1)-x2);
          ls_h3=atan2(ls_y(t-1)-y3,ls_x(t-1)-x3);
          ls_H(1,1)=ls_h1;
          ls_H(2,1)=ls_h2;
          ls_H(3,1)=ls_h3;
         
          %J矩阵
          ls_J(1,1)=-(ls_y(t-1)-y1)/((ls_x(t-1)-x1)^2+(ls_y(t-1)-y1)^2);
          ls_J(1,2)=(ls_x(t-1)-x1)/((ls_x(t-1)-x1)^2+(ls_y(t-1)-y1)^2);
          ls_J(2,1)=-(ls_y(t-1)-y2)/((ls_x(t-1)-x2)^2+(ls_y(t-1)-y2)^2);
          ls_J(2,2)=(ls_x(t-1)-x2)/((ls_x(t-1)-x2)^2+(ls_y(t-1)-y2)^2);
          ls_J(3,1)=-(ls_y(t-1)-y3)/((ls_x(t-1)-x3)^2+(ls_y(t-1)-y3)^2);
          ls_J(3,2)=(ls_x(t-1)-x3)/((ls_x(t-1)-x3)^2+(ls_y(t-1)-y3)^2);
          %噪声R
          R=eye(3)*Q;
          
          ls_v(:,t)=ls_v(:,t-1)+inv(ls_J'*inv(R)*ls_J)*ls_J'*inv(R)*(Z-ls_H);%最小二乘迭代位置状态拟合
      
      end
      
  %         deta=hatx(t)-hatx(t-1);%判断迭代终止；
  %          if deta<=d0
  %           break;
  %          end
           
         ls_res(:,t)=ls_v(:,t);
         ls_x(t)=ls_v(1,t);
         ls_y(t)=ls_v(2,t);
         
  end
         for k=1:50;
         ls_runx=ls_runx+(xp-ls_x(k))^2;
         ls_runy=ls_runy+(yp-ls_y(k))^2;
         end
  end
  %Monte karlo runs
  ml_Runs_x=sqrt(ml_runx/(Runs*N))
  ml_Runs_y=sqrt(ml_runy/(Runs*N))
  ls_Runs_x=sqrt(ls_runx/(Runs*N))
  ls_Runs_y=sqrt(ls_runy/(Runs*N))
  %fisher 信息
         %J矩阵,代入真值
          J(1,1)=-(yp-y1)/((xp-x1)^2+(yp-y1)^2);
          J(1,2)=(xp-x1)/((xp-x1)^2+(yp-y1)^2);
          J(2,1)=-(yp-y2)/((xp-x2)^2+(yp-y2)^2);
          J(2,2)=(xp-x2)/((xp-x2)^2+(yp-y2)^2);
          J(3,1)=-(yp-y3)/((xp-x3)^2+(yp-y3)^2);
          J(3,2)=(xp-x3)/((xp-x3)^2+(yp-y3)^2);
  % FI(1,1)=((z1-h01)*JI(1,1)+(z2-h02)*JI(2,1)+(z3-h03)*JI(3,1))/Q;
  % FI(2,1)=((z1-h01)*JI(1,2)+(z2-h02)*JI(2,2)+(z3-h03)*JI(3,2))/Q;
  FIM(1,1)=((J(1,1))^2+(J(2,1))^2+(J(3,1))^2)/Q;
  FIM(2,2)=((J(1,2))^2+(J(2,2))^2+(J(3,2))^2)/Q;
  FIM(1,2)=(J(1,1)*J(1,2)+J(2,1)*J(2,2)+J(3,1)*J(3,2))/Q;
  FIM(2,1)=(J(1,1)*J(1,2)+J(2,1)*J(2,2)+J(3,1)*J(3,2))/Q;
  ml_MSE=inv(FIM);
  ml_CRLB_x=sqrt(ml_MSE(1,1))
  ml_CRLB_y=sqrt(ml_MSE(2,2))
  %LS:MSE
  ls_MSE=inv(J'*inv(R)*J);
  ls_CRLB_x=sqrt(ls_MSE(1,1))
  ls_CRLB_y=sqrt(ls_MSE(2,2))
  
  %结果比较
  t=1:1:10;
      figure(1);
      plot(t,ls_res(1,t),t,ml_res(1,t),'r--')
      title('Estimation of East Position')
      xlabel('Iteration j'), ylabel('The East Position');
      legend('ILS','ML')
      hold on; 
      figure(2);
      plot(t,ls_res(2,t),t,ml_res(2,t),'r--')
      title('Estimation of North Position')
      xlabel('Iteration j'), ylabel('The North Position');
      legend('ILS','ML');
  
      figure(3);
      plot([x1 xp],[y1 xp],'-o');hold on; 
      plot([x2 xp],[y2 yp],'-o');hold on;
      plot([x3 xp],[y3 yp],'-o');hold on;
      plot(xp,yp,'*');
      axis([-10000 50000 -10000 50000]);
      xlabel('East(m)'), ylabel('North(m)');
  

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