最小二乘法MATLAB程序及結(jié)果

最小二乘法MATLAB程序及結(jié)果針對(duì)辨識(shí)模型，有z(k)-+a1*z(k-1)+a2*z(k-2)=b1*u(k-1)+b2*u(k-2)+v(k)模型結(jié)構(gòu)，對(duì)其進(jìn)行最小二乘一次完成算法的MATLAB仿真，對(duì)比真值與估計(jì)值。更改a1、a2、b1、b2參數(shù)，觀察結(jié)果。仿真對(duì)象：z(k)-1.5*z(k-1)+0.7z(k-2)=u(k-1)+0.5*u(k-2)+v(k)程序如下：u=[-1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,1,1];%輸入信號(hào)為一個(gè)周期的M序列z=zeros(1,16);fork=3:16z(k)=1.5*z(k-1)-0.7*z(k-2)+u(k-1)+0.5*u(k-2);%以理想輸出值作為觀測(cè)值endsubplot(3,1,1)stem(u)subplot(3,1,2)i=1:1:16;plot(i,z)subplot(3,1,3)stem(z),gridonu,z%顯示輸入信號(hào)與輸出觀測(cè)信號(hào)L=14;HL=[-z(2)-z(1)u(2)u(1);-z(3)-z(2)u(3)u(2);-z(4)-z(3)u(4)u(3);-z(5)-z(4)u(5)u(4);-z(6)-z(5)u(6)u(5);-z(7)-z(6)u(7)u(6);-z(8)-z(7)u(8)u(7);-z(9)-z(8)u(9)u(8);。-z(10)-z(9)u(10)u(9);-z(11)-z(10)u(11)u(10);-z(12)-z(11)u(12)u(11);-z(13)-z(12)u(13)u(12);-z(14)-z(13)u(14)u(13);-z(15)-z(14)u(15)u(14)]%給樣本矩陣HL賦值。ZL=[z(3);z(4);z(5);z(6);z(7);z(8);z(9);z(10);z(11);z(12);z(13);z(14);z(15);z(16)]%給樣本矩陣ZL賦值c1=HL'*HL;c2=inv(c1);c3=HL'*ZL;c=c2*c3a1=c(1),a2=c(2),b1=c(3),b2=c(4)程序運(yùn)行結(jié)果如下：u=-11-11111-1-1-11-1-111z=Columns1through9000.50000.25000.52502.11254.30126.47316.1988Columns10through163.2670-0.9386-3.1949-4.6352-6.2165-5.5800-2.5185HL=001.0000-1.0000-0.50000-1.00001.0000-0.2500-0.50001.0000-1.0000-0.5250-0.25001.00001.0000-2.1125-0.52501.00001.0000-4.3012-2.11251.00001.0000-6.4731-4.3012-1.00001.0000-6.1988-6.4731-1.0000-1.0000-3.2670-6.1988-1.0000-1.00000.9386-3.26701.0000-1.00003.19490.9386-1.00001.00004.63523.1949-1.0000-1.00006.21654.63521.0000-1.00005.58006.21651.00001.0000ZL=0.50000.25000.52502.11254.30126.47316.19883.2670-0.9386-3.1949-4.6352-6.2165-5.5800-2.5185c=-1.50000.70001.00000.5000a1=-1.5000a2=0.7000b1=1.0000b2=0.5000程序運(yùn)行曲線：圖.1最小二乘一次完成算法仿真實(shí)例輸入信號(hào)與輸出觀測(cè)值分析:從仿真結(jié)果知,由于所用的輸出觀測(cè)值沒(méi)有任何噪聲成分,所以辨識(shí)結(jié)果也無(wú)任何誤差。更改仿真對(duì)象參數(shù):z(k)=0.5*z(k-1)-1.5*z(k-2)+0.5*u(k-1)+0.8*u(k-2);程序如下:u=[-1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,1,1];z=zeros(1,16);fork=3:16z(k)=0.5*z(k-1)-1.5*z(k-2)+0.5*u(k-1)+0.8*u(k-2);endsubplot(3,1,1)stem(u)subplot(3,1,2)i=1:1:16;plot(i,z)subplot(3,1,3)stem(z),gridonu,zL=14;HL=[-z(2)-z(1)u(2)u(1);-z(3)-z(2)u(3)u(2);-z(4)-z(3)u(