flch5rmleg2.m

《系统辨识及其MATLAB仿真》一书中第2、5、7章的原码。

clear               %清零

a(1)=1;b(1)=0;c(1)=1;d(1)=0;u(1)=d(1);z(1)=0;z(2)=0; %初始化
for i=2:1200          %产生m序列u(i)         
    a(i)=xor(c(i-1),d(i-1));
    b(i)=a(i-1);
    c(i)=b(i-1);
    d(i)=c(i-1);
    u(i)=d(i);
end
u; %若取去‘；’可以在程序运行中观测到m序列

v=randn(1200,1); %产生正态分布随机数
V=0;   %计算噪声方差
for i=1:1200
    V=V+v(i)*v(i);
end
V1=V/1200;   
for k=3:1200      %根据v和u计算z
 z(k)=1.2*z(k-1)-0.6*z(k-2)+u(k-1)+0.5*u(k-2)+v(k)-v(k-1)+0.2*v(k-2);
end

o1=0.001*ones(6,1);p0=eye(6,6);         %赋初值
 zf(1)=0.1;zf(2)=0.1;vf(2)=0.1;vf(1)=0.1;uf(2)=0.1;uf(1)=0.1;
   %迭代计算参数值和误差值
for k=3:1200
      h=[-z(k-1);-z(k-2);u(k-1);u(k-2);v(k-1);v(k-2)];
      hf=h;
     K=p0*hf*inv(hf'*p0*hf+1); 
     p=[eye(6,6)-K*hf']*p0; 
     v(k)=z(k)-h'*o1;
     o=o1+K*v(k) ;
       p0=p;
    o1=o;
    a1(k)=o(1);
    a2(k)=o(2);
    b1(k)=o(3);
    b2(k)=o(4);
    d1(k)=o(5);
    d2(k)=o(6);
    e1(k)=abs(a1(k)+1.2);
    e2(k)=abs(a2(k)-0.6);
    e3(k)=abs(b1(k)-1.0);
    e4(k)=abs(b2(k)-0.5);
    e5(k)=abs(d1(k)+1.0);
    e6(k)=abs(d2(k)-0.2);
     zf(k)=z(k)-d1(k)*zf(k-1)-d2(k)*zf(k-2);

     uf(k)=u(k)-d1(k)*uf(k-1)-d2(k)*uf(k-2);   
    
     vf(k)=v(k)-d1(k)*vf(k-1)-d2(k)*vf(k-2);  
   hf=[-zf(k-1);-zf(k-2);uf(k-1);uf(k-2);vf(k-1);vf(k-2)];    
 end 
 o1  %若取去‘；’可以在程序运行中观测到参数
 V1
  %绘图
 subplot(4,1,1)
k=1:1200;
plot(k,a1,'k:',k,a2,'b',k,b1,'r',k,b2,'m:',k,d1,'g',k,d2,'k');
xlabel('k')
ylabel('parameter')
legend('a1=-1.2,','a2=0.6','b1=1.0','b2=0.5','d1=-1.0','d2=0.2'); %图标炷
title('The parameter idendification of the RML');
end
subplot(4,1,2)
k=1:1200;
plot(k,e1,'k',k,e2,'b',k,e3,'r',k,e4,'m',k,e5,'g',k,e6,'k');
xlabel('k'); ylabel('error'); %title('误差曲线')
end
subplot(4,1,3)
k=1:1200;
plot(k,u);
xlabel('k');  ylabel('input'); %title('系统输入信号')
end
subplot(4,1,4)
k=1:1200;
plot(k,v);
xlabel('k'); ylabel('random noise'); %title('系统所加的随机噪声')
end