RLS-RELS模型.docxVIP

%题目2.7遗忘因子设为0.99%利用RELS算法计算题目2.9%用RLS-RELS解题目2.9%用BCRLS解题目2.10程序如下%题目2.7遗忘因子设为0.99clear;clc;Bushu=6000;lamda=0.99; %将遗忘因子设置被0.99randn (seed,1);e=sqrt(1)*randn(1,Bushu);%产生白噪声for k=1:60%给u进行赋值 for bushu=k*100-99:k*100 kk = mod(k,2); if(kk == 1) u(k*100-99:k*100)=1; else u(k*100-99:k*100)=-1; end k=k+1; endenda(1:Bushu)=1;b(1:Bushu)=1;%先设定出a和b，方便运算，而后对a（t）和b（t）进行定义for i=1:Bushu a(i)=0.5-0.15*sin(2*pi*i/2000); b(i)=0.81-0.2*cos(2*pi*i/2000);endy(1)=e(1);for i=2:Bushu y(i)=a(i)*y(i-1)+b(i)*u(i-1)+e(i);%产生CAR模型end%模型参数辨识sita(:,1)=zeros(2,1); %建立sita为2*1的矩阵p(:,1:2)=10^5*eye(2);%同理p矩阵为2*2的矩阵p(:,3:4)=10^5*eye(2);fai(:,1)=[0,0];for i=2:Bushu fai(:,i)=[y(i-1),u(i-1)]; sita(:,i)=sita(:,i-1) +p(:,2*(i-1)-1:2*(i-1))*fai(:,i)/(lamda+fai(:,i)*p(:,2*(i-1)-1:2*(i-1))*fai(:,i))*(y(i)-fai(:,i)*sita(:,i-1)); p(:,2*i-1:2*i)=1/lamda*(p(:,2*(i-1)-1:2*(i-1))-p(:,2*(i-1)-1:2*(i-1))*fai(:,i)*fai(:,i)*p(:,2*(i-1)-1:2*(i-1))/(lamda+fai(:,i)*p(:,2*(i-1)-1:2*(i-1))*fai(:,i)));end%对噪声方差进行估计for i=1:Bushu emixiu(i)=y(i)-fai(1:2,i)*sita(1:2,i);endtaoe(1)=emixiu(1)^2;for i=2:Bushu taoe(i)=taoe(i-1)+1/i*[emixiu(i)^2-taoe(i-1)]; %噪声方差用taoe表示end%作图并用合适的分区表示t=1:Bushu;subplot(2,2,1);plot(t,sita(1,t),r);title(a(t)μ?WLS2?êy1à??a(t)°?μ?ê?á2D?);for i=1:60line([i*100-99,i*100],[a(i*100-99),a(i*100)]);axis([0,Bushu,0,1]);endsubplot(2,2,2);plot(t,sita(2,t),r);title(b(t)μ?WLS2?êy1à??b(t)°?μ?ê?á2D?);for i=1:60line([i*100-99,i*100],[b(i*100-99),b(i*100)]);axis([0,Bushu,0.2,1.4]);endsubplot(2,1,2);plot(t,taoe,r);title(·?2?μ?RLS2?êy1à??μ?ê?á2D?);line([0,Bushu],[1,1])a(6000)b(6000)taoe(6000) %利用RELS算法计算题目2.9 clear;clc;Bushu=3000;randn (seed,8);e=sqrt(0.36)*randn(1,Bushu);%产生白噪声 %建立ARMA模型a1=-1.5;a2=0.54;d1=-1.2;d2=0.35;y(1)=e(1);y(2)=-a1*y(1)+e(2)+d1*e(1);for i=3:Bushu y(i)=-a1*y(i-1)-a2*y(i-2)+e(i)+d1*e(i-1)+d2*e(i-2);end %RELS算法 %赋予初值 sita(1:4,1)=zeros(4,1);ejian(1)=y(1);fai(1:4,1)=zeros(4,1);fai(:,2)=[-y(1),0,ejian(1),0];p(:,1:4)=10^5*eye(4); for i=2:Bushu sita(:,i)=sita(:,i-1)+[p(:,4*(i-1)-3:4*(i-1))*fai(:,i)*[