function [ output_args ] = QR_TLS( input_args )%QR_TLS Summary of this function goes here%   Detailed explanation goes here%shuru(n)為實(shí)際輸入信號，biaozhun(n)為參照信號 M=1000;%時長 N=8;%陣元數(shù) lamda=0.99;%遺忘因子 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)%誤差                 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]);