front_lrls.m

时域自适应滤波中基于先验概率的格型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

kb=zeros(M+2,N+2);
kf=zeros(M+2,N+2);
a=zeros(M+2,N+2);%derta
aD=zeros(M+2,N+2);
r=zeros(M+2,N+2);
sb=zeros(M+2,N+2);
sf=zeros(M+2,N+2);
el=zeros(M+2,N+2);
elb=zeros(M+2,N+2);
elf=zeros(M+2,N+2);
vi=zeros(M+2,1);

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

for k=0:M
    r(k+2,1)=1;
    elf(k+2,1)=shuru(k);
    elb(k+2,1)=elf(k+2,1);
    sb(k+2,1)=shuru(k)^2+lamda*sf(k+1,1);
    sf(k+2,1)=sb(k+2,1);
    el(k+2,1)=biaozhun(k);
    
    for i=0:N
        a(k+2,i+1)=lamda*a(k+1,i+1)+r(k+1,i+1)*elb(k+1,i+1)*elf(k+2,i+1);%(6.47)
        
        c1=(r(k+2,i+1)*elb(k+2,i+1))^2;
        r(k+2,i+2)=r(k+2,i+1)-c1/sb(k+2,i+1);%(6.100)
        
        elb(k+2,i+2)=elb(k+1,i+1)-kb(k+1,i+1)*elf(k+2,i+1);%(6.99)
        elf(k+2,i+2)=elf(k+2,i+1)-kf(k+1,i+1)*elb(k+1,i+1);%(6.98)
        
        kf(k+2,i+1)=a(k+2,i+1)/sb(k+1,i+1);
        kb(k+2,i+1)=a(k+2,i+1)/sf(k+2,i+1);
        
        sf(k+2,i+2)=sf(k+2,i+1)-a(k+2,i+1)*kf(k+2,i+1);%(6.31)
        sb(k+2,i+2)=sb(k+1,i+1)-a(k+2,i+1)*kb(k+2,i+1);%(6.27)
        
        %Feedforward Filtering
        
        c2=r(k+2,i+1)*elb(k+2,i+1);
        aD(k+2,i+1)=lamda*aD(k+1,i+1)+c2*el(k+2,i+1);%(6.101)
        el(k+2,i+2)=el(k+2,i+1)-vi(k+1,1)*elb(k+2,i+1);%(6.102)
        vi(k+2,1)=aD(k+2,i+1)/sb(k+2,i+1);%(6.103)
    end

end
figure(3);
k=0:M;
plot(k,el(k+2,N+2));
grid on;
title('基于先验误差的LRLS');
axis([0,M,-8,8]);