最小二乘法MATLAB程序及结果.doc

最小二乘一次完成算法的MATLAB仿真 针对辨识模型，有z(k)-+a1*z(k-1)+a2*z(k-2)=b1*u(k-1)+b2*u(k-2)+v(k)模型结构，对其进行最小二乘一次完成算法的MATLAB仿真，对比真值与估计值。更改a1、a2、b1、b2参数，观察结果。仿真对象：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;%输入信号为一个周期的M序列z=zeros(1,16);for k=3:16 z(k)=1.5*z(k-1)-0.7*z(k-2)+u(k-1)+0.5*u(k-2);%以理想输出值作为观测值endsubplot(3,1,1)stem(u)subplot(3,1,2)i=1:1:16;plot(i,z)subplot(3,1,3)stem(z),grid onu,z %显示输入信号与输出观测信号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) %给样本矩阵HL赋值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) %给样本矩阵ZL赋值c1=HL*HL;c2=inv(c1);c3=HL*ZL;c=c2*c3a1=c(1),a2=c(2),b1=c(3),b2=c(4)程序运行结果如下：u = -1 1 -1 1 1 1 1 -1 -1 -1 1 -1 -1 1 1z = Columns 1 through 9 0 0 0.5000 0.2500 0.5250 2.1125 4.3012 6.4731 6.1988 Columns 10 through 16 3.2670 -0.9386 -3.1949 -4.6352 -6.2165 -5.5800 -2.5185HL = 0 0 1.0000 -1.0000 -0.5000 0 -1.0000 1.0000 -0.2500 -0.5000 1.0000 -1.0000 -0.5250 -0.2500 1.0000 1.0000 -2.1125 -0.5250 1.0000 1.0000 -4.3012 -2.1125 1.0000 1.0000 -6.4731 -4.3012 -1.0000 1.0000 -6.1988 -6.4731 -1.0000 -1.0000 -3.2670 -6.1988 -1.0000 -1.0000 0.9386 -3.2670 1.0000 -1.0000 3.1949 0.9386 -1.0000 1.0000 4.6352 3.1949 -1.0000 -1.0000 6.2165 4.6352 1.0000 -1.0000 5.5800 6.2165 1.0000 1.0000ZL = 0.5000 0.2500 0.5250 2.1125 4.3012 6.4731 6.1988 3.2670 -0.9386 -3.1949 -4.6352 -6.2165 -5.5800 -2.5185c = -1.5000 0.7000 1.0000 0.5000a1 = -1.5000a2 = 0.7000b1 = 1.0000b2 =0.5000程序运行曲线：图.1 最小二乘一次完成算法仿真实例输入信号与输出观测值分析:从仿真结果知,由于所用的输出观测值没有任何噪声成分,所以辨识结果也无任何误差。更改仿真对象参数: 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);for k=3:16 z(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),grid onu,zL=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)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)c1=HL*HL;c2=inv(c1);c3=HL*ZL;c=c2*c3a1=c(1),a2=c(2),b1=c(3),b2=c(4)程序运行结果如下：u = -1 1 -1 1 1 1 1 -1 -1 -1 1 -1 -1 1 1z = Columns 1 through 9 0 0 -0.3000 0.1500 0.2250 1.1875 1.5562 0.2969 -1.8859 Columns 10 through 16 -2.6883 0.1848 3.8248 1.9353 -6.0696 -6.2377 7.2855HL = 0 0 1.0000 -1.0000 0.3000 0 -1.0000 1.0000 -0.1500 0.3000 1.0000 -1.0000 -0.2250 -0.1500 1.0000 1.0000 -1.1875 -0.2250 1.0000 1.0000 -1.5562 -1.1875 1.0000 1.0000 -0.2969 -1.5562 -1.0000 1.0000 1.8859 -0.2969 -1.0000 -1.0000 2.6883 1.8859 -1.0000 -1.0000 -0.1848 2.6883 1.0000 -1.0000 -3.8248 -0.1848 -1.0000 1.0000 -1.9353 -3.8248 -1.0000 -1.0000 6.0696 -1.9353 1.0000 -1.0000 6.2377 6.0696 1.0000 1.0000ZL = -0.3000 0.1500 0.2250 1.1875 1.5562 0.2969 -1.8859 -2.6883 0.1848 3.8248 1.9353 -6.0696 -6.2377 7.2855c = -0.5000 1.5000 0.5000 0.8000a1 = -0.5000a2 = 1.5000b1 = 0.5000b2 =0.8000程序运行曲线：图.2 最小二乘一次完成算法仿真实例输入信号与输出观测值结论及问题分析:更改仿真对象参数后对比更改前,从仿真结果可以看出,无论输入参数如何变化，输出观测值在没有任何噪声成分下,辨识结果跟真值没有误