批处理最小二乘参数估计.doc

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1、%批处理最小二乘参数估计(LS)考虑如下系统：式中x(k)为方差为1的白噪声。选用幅值为1的逆M序列作为输入信号u(k):clearall;a=[1-1.50.7]';b=[10.5]';d=3;%对象参数na=length(a)-1;nb=length(b)-1;%计算阶次L=20;%数据长度uk=zeros(d+nb,1);yk=zeros(na,1);%输入初值x1=1;x2=1;x3=1;x4=0;S=1;%移位寄存器初值，方波初值xi=rand(L,1);%白噪声序列theta=[a(2:na+1);b];%对象参数真值fork=1:Lphi(k,:)=[-yk;u

2、k(d:d+nb)]';%phi(k,:)为行向量，便于组成phi矩阵y(k)=phi(k,:)*theta+xi(k);%采集输出数据IM=xor(S,x4);ifIM==0u(k)=-1;elseu(k)=1;endS=not(S);M=xor(x3,x4);%产生M序列%更新数据x4=x3;x3=x2;x2=x1;x1=M;fori=nb+d:-1:2uk(i)=uk(i-1);enduk(1)=u(k);fori=na:-1:2yk(i)=yk(i-1);endyk(1)=y(k);endy=0.19340.97241.62593.29995.46266.08186.

3、17735.36873.08261.95940.7778-0.8051-2.4305-1.93721.11353.18652.84230.8226-1.9145-4.4135u=11-11-1-11-1-1-111-1-1-1-1-11-11phi=0000-0.1934000-0.9724-0.193400-1.6259-0.97241.00000-3.2999-1.62591.00001.0000-5.4626-3.2999-1.00001.0000-6.0818-5.46261.0000-1.0000-6.1773-6.0818-1.00001.0000-5.3687-

4、6.1773-1.0000-1.0000-3.0826-5.36871.0000-1.0000-1.9594-3.0826-1.00001.0000-0.7778-1.9594-1.0000-1.00000.8051-0.7778-1.0000-1.00002.43050.80511.0000-1.00001.93722.43051.00001.0000-1.11351.9372-1.00001.0000-3.1865-1.1135-1.0000-1.0000-2.8423-3.1865-1.0000-1.0000-0.8226-2.8423-1.0000-1.00001.9

5、145-0.8226-1.0000-1.0000thetaevaluation=inv(phi'*phi)*phi'*y'%计算参数估计值thetaevaluation=-1.50600.60310.88860.4924采样500组数据的参数估计值：thetaevaluation=-1.53620.68021.00680.4864