disp_rand.m

本程序用matlab生成白噪声

function disp_rand    
%----------辨识与滤波仿真试验
clear,clc;
R1=1;R2=1;
k=1:34;
S=[0;0];E=eye(2);
x=ones(2,length(k));
y=ones(1,length(k));
K=ones(2,length(k));
xx=ones(2,length(k));
x(:,1)=[5;-5];
A=[0.9 0.1;-0.1 0.8];B=[1;1];C=[0 1];
P=5*eye(2);
%-----------初始化
nos1=randn(length(k),1);
nos2=randn(length(k),1);
%figure,hold on,
%subplot(2,1,1),plot(k,nos1,'ro-'),xlabel('k'),ylabel('nos1');
%title('仿真生成的白噪声');
%subplot(2,1,2),plot(k,nos2,'ro-'),xlabel('k'),ylabel('nos2');
%hold off;
%-----------仿真生成白噪声
sigma=P;
xx(:,1)=x(:,1);
%----------求得各个变量的初始值
for i=1:(length(k)-1)
    x(:,i+1)=A*x(:,i)+B*nos1(i);
    y(i)=C*x(:,i)+nos2(i);
end
%figure,hold on,
%subplot(3,1,1),plot(k,x(1,:),'r-'),xlabel('k'),ylabel('x1');
%title('利用模型生成的x(k),y(k)');
%subplot(3,1,2),plot(k,x(2,:),'g-'),xlabel('k'),ylabel('x2');
%subplot(3,1,3),plot(k,y,'b-'),xlabel('k'),ylabel('y');
%hold off;
%----------利用模型生成y(k)和x(k)
for i=1:(length(k)-1)
    K(:,i)=A*sigma*C'/(C*sigma*C'+R2);
    sigma=(A-K(:,i)*C)*sigma*A'+R1*eye(2);
    xx(:,i+1)=A*xx(:,i)+K(:,i)*(y(i)-C*xx(:,i));
end
%----------求得x(k|k-1)
figure,hold on,
subplot(2,1,1),plot(k,x(1,:),'r-',k,xx(1,:),'b-'),xlabel('k'),ylabel('x1');
title('x(k|k-1)和x(k)的对比曲线');
subplot(2,1,2),plot(k,x(2,:),'r-',k,xx(2,:),'b-'),xlabel('k'),ylabel('x2');
hold off;
%----------画出x(k|k-1)和x(k)对比曲线
Q=R1*eye(2);R=R2;
[sig,L,G,RR]=dare(A',C',Q,R,S,E);
fprintf('预报误差协方差稳态值为:')
sig
fprintf('预报误差协方差阵为:')
sigma
fprintf('预报误差的协方差阵与其稳态值之差为:')
sig-sigma
%----------求出稳态值sig并求sigma(k|k-1)与sig之差