最小二乘法MATLAB程序及結(jié)果

1、最小二乘遞推算法的MATLAB仿真針對(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)行最小二乘遞推算法的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)+0.7*z(k-2)=u(k-1)+0.5*u(k-2)+v(k)程序如下：L=15;y1=1;y2=1;y3=1;y4=0; %四個(gè)移位寄存器的初始值for i=1:L; %移位循環(huán) x1=xor(y3,y4); x2=y1; x3=y2; x4=y3; y(i)=y4; %取出作為輸出信號(hào)

2、，即M序列 if y(i)0.5,u(i)=-0.03; %輸入信號(hào) else u(i)=0.03; end y1=x1;y2=x2;y3=x3;y4=x4;endfigure(1);stem(u),grid onz(2)=0;z(1)=0;for k=3:15; z(k)=1.5*z(k-1)-0.7*z(k-2)+u(k-1)+0.5*u(k-2); %輸出采樣信號(hào)endc0=0.001 0.001 0.001 0.001; %直接給出被識(shí)別參數(shù)的初始值p0=106*eye(4,4); %直接給出初始狀態(tài)P0E=0.; c=c0,zeros(4,14); e=zeros(4,15);for

3、 k=3:15; %開始求k h1=-z(k-1),-z(k-2),u(k-1),u(k-2); x=h1*p0*h1+1; x1=inv(x); k1=p0*h1*x1; %開始求k的值 d1=z(k)-h1*c0;c1=c0+k1*d1; e1=c1-c0; e2=e1./c0; %求參數(shù)的相對(duì)變化 e(:,k)=e2; c0=c1; c(:,k)=c1; p1=p0-k1*k1*h1*p0*h1+1; %求出P(k)的值 p0=p1; if e20.5,u(i)=-0.03; else u(i)=0.03; end y1=x1;y2=x2;y3=x3;y4=x4;endfigure(1)

4、;stem(u),grid onz(2)=0;z(1)=0;for k=3:15; z(k)=z(k-1)-1.5*z(k-2)+u(k-1)+1.5*u(k-2);endc0=0.001 .0001 0.001 0.001;p0=106*eye(4,4)E=0.;c=c0,zeros(4,14);e=zeros(4,15);for k=3:15; h1=-z(k-1),-z(k-2),u(k-1),u(k-2); x=h1*p0*h1+1; x1=inv(x); k1=p0*h1*x1; d1=z(k)-h1*c0;c1=c0+k1*d1; e1=c1-c0; e2=e1./c0; e(:,

5、k)=e2; c0=c1; c(:,k)=c1; p1=p0-k1*k1*h1*p0*h1+1; p0=p1; if e2=E break; endendc,ea1=c(1,:);a2=c(2,:);b1=c(3,:);b2=c(4,:);ea1=e(1,:);ea2=e(2,:);eb1=e(3,:);eb2=e(4,:);figure(2);i=1:15;plot(i,a1,r,i,a2,:,i,b1,g,i,b2,:)title(Parameter Identification with Recursive Least Squares Method)figure(3);i=1:15;pl

6、ot(i,ea1,r,i,ea2,g,i,eb1,b,i,eb2,r:)title(Identification Precision)程序運(yùn)行結(jié)果:p0 = 0 0 0 0 0 0 0 0 0 0 0 0 c = Columns 1 through 9 0.0010 0 0.0010 0.4447 -1.2248 -0.9996 -0.9999 -1.0001 -1.0001 0.0001 0 0.0001 0.0001 0.3757 1.4987 1.4997 1.5000 1.5000 0.0010 0 -0.2489 0.6385 1.0560 1.0000 1.0001 0.9999

7、0.9999 0.0010 0 0.2509 1.1382 1.5557 1.4997 1.4995 1.4995 1.4996 Columns 10 through 15 -1.0001 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 1.5000 1.5000 1.5000 1.5000 1.5000 1.5000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 1.4996 1.4996 1.4999 1.4999 1.4999 1.4999e = 1.0e+003 * Columns 1 through 9 0 0 0

8、 0.4437 -0.0038 -0.0002 0.0000 0.0000 -0.0000 0 0 0 0 3.7564 0.0030 0.0000 0.0000 -0.0000 0 0 -0.2499 -0.0036 0.0007 -0.0001 0.0000 -0.0000 0.0000 0 0 0.2499 0.0035 0.0004 -0.0000 -0.0000 0.0000 0.0000 Columns 10 through 15 0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000程序運(yùn)行曲線:圖4. 輸入信號(hào)圖5. a1,a2,b1,b2辨識(shí)仿真結(jié)果圖6. a1,a2,b1,b2各次辨識(shí)結(jié)果的收斂情況結(jié)果總結(jié)及問題分析: 辨識(shí)結(jié)果與程序運(yùn)行曲線表明,大約遞推到五步時(shí),參數(shù)辨識(shí)的結(jié)果基本達(dá)到穩(wěn)定狀態(tài)。在參數(shù)更改前后運(yùn)行結(jié)果可以看出，輸出觀測(cè)值在沒有任何噪聲成分下，估計(jì)值與真