behind_lrls.m

时域自适应滤波中基于后验概率的格型RLS算法

%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
constant=0.01;%small positive constant

a=zeros(M+2,N+1);
aD=zeros(M+2,N+1);
kf=zeros(M+2,N+1);
kb=zeros(M+2,N+1);

r=zeros(M+2,N+2);
sb=zeros(M+2,N+2);
sf=zeros(M+2,N+2);
eb=zeros(M+2,N+2);
ef=zeros(M+2,N+2);
e=zeros(M+2,N+2);

for i=0:N
    a(1,i+1)=0; aD(1,i+1)=0; %assuming x(k)=0 for k<0
    sb(1,i+1)=constant; sf(1,i+1)=constant;
    r(1,i+1)=1;
    eb(1,i+1)=0;
end

for k=0:M
    r(k+2,1)=1;
    eb(k+2,1)=shuru(k); ef(k+2,1)=eb(k+2,1); %(6.35)
    sb(k+2,1)=shuru(k)^2+lamda*sf(k+1,1); sf(k+2,1)=sb(k+2,1);%(6.36)
    e(k+2,1)=biaozhun(k);
    
     for i=0:N
         c1=eb(k+1,i+1)/r(k+1,i+1);
         a(k+2,i+1)=lamda*a(k+1,i+1)+c1*ef(k+2,i+1);%(6.51)
         r(k+2,i+2)=r(k+2,i+1)-eb(k+2,i+1)^2/sb(k+2,i+1); %(6.60)
         kb(k+2,i+1)=a(k+2,i+1)/sf(k+2,i+1);
         kf(k+2,i+1)=a(k+2,i+1)/sb(k+1,i+1);
     
         eb(k+2,i+2)=eb(k+1,i+1)-kb(k+2,i+1)*ef(k+2,i+1); %(6.34)
         ef(k+2,i+2)=ef(k+2,i+1)-kf(k+2,i+1)*eb(k+1,i+1); %(6.33)
         sb(k+2,i+2)=sb(k+1,i+1)-a(k+2,i+1)*kb(k+2,i+1); %(6.27)
         sf(k+2,i+2)=sf(k+2,i+1)-a(k+2,i+1)*kf(k+2,i+1); %(6.31)
         
         c2=eb(k+2,i+1)/r(k+2,i+1);
         aD(k+2,i+1)=lamda*aD(k+1,i+1)+c2*e(k+2,i+1); %(6.64)
         vi=aD(k+2,i+1)/sb(k+2,i+1); %(6.67)
         e(k+2,i+2)=e(k+2,i+1)-vi*eb(k+2,i+1); %(6.68)
     end
     
end
figure(1);
k=0:M;
plot(k,e(k+2,N+2),'b');
title('基于后验误差的LRLS');
grid on;
axis([0,M,-8,8]);