%shuru(n)为实际输入信号，biaozhun(n)为参照信号
M=1000;%时长
N=8;%阵元数
lamda=0.99;%遗忘因子
w=zeros(N+1,M+1);
e=zeros(1,M+1);
w(1,1)=biaozhun(0)/shuru(0);
for k=1:N
for i=1:k
sum1=0;
for j=1:i
sum1=sum1-shuru(j)*w(i-j+1,k+1);
end
w(i+1,k+1)=(sum1+biaozhun(i))/shuru(0); %式(8.11)
end
end
Y=zeros(N+1);
for i=1:N+1
for j=1:N+2-i
Y(i,j)=shuru(N+3-i-j); %式(8.2)
end
end
Ul=lamda^(1/2)*Y; %式(8.12)
dlq=zeros(N+1,1);
for i=1:N+1
dlq(i,1)=(lamda^(i/2)*biaozhun(N-i+1));
end
for k=N+1:M
rl=1;
dl=biaozhun(k);
Xl=zeros(1,N+1);
for j=1:N+1
Xl(1,j)=shuru(k+1-j);
end
for i=0:N
c=sqrt(Ul(i+1,N+1-i)^2+Xl(1,N+1-i)^2);
cos=Ul(i+1,N+1-i)/c; %式(8.41)
sin=Xl(1,N+1-i)/c; %式(8.42)
s1=sparse([1,i+2],[1,1],[cos,sin],N+2,1);
s2=zeros(1,i);
s3=eye(i);
s4=zeros(N-i+1,i);
s5=[s2;s3;s4];
s6=sparse([1,i+2],[1,1],[-sin,cos],N+2,1);
s7=zeros(i+2,N-i);
s8=eye(N-i);
s9=[s7;s8];
Ql=[s1,s5,s6,s9]; %式(8.40)
A=Ql*[Xl;Ul]; %式(8.39)
Xl=A(1,:);
Ul=A(2:N+2,:);
rl=rl*cos; %式(8.54)
B=Ql*[dl;dlq];%式(8.51)
dl=B(1,1);
dlq=B(2:N+2,1);
end
dlq=lamda^(1/2)*dlq;
Ul=lamda^(1/2)*Ul;
r=rl; %式(8.51)
e(1,k+1)=dl*r;%式(8.51)%误差
D=[dl;dlq];%式(8.51)
U=Ul;
w(1,1)=D(N+2,1)/U(N+1,1);
for i=1:N
sum2=0;
for j=1:i
sum2=sum2-U(N+1-i,i-j+1)*w(i-j+1,k+1);
end
w(i+1,k+1)=(sum2+D(N+2-i,1))/U(N+1-i,i+1); %式(8.46)
end
end
figure(8);
k=1:M+1;
hold on;
plot(k,e(1,k),'g');
title('QR-RLS');
grid on;
%axis([0,M,-8,8]);
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