normalizion_lrls.m

时域自适应滤波中基于后验概率的归一化格型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=0.9;%遗忘因子
constant=0.001;%small positive constant

a=zeros(M+2,N+1);%derta
aD=zeros(M+2,N+1);%dertaD
e=zeros(M+2,N+2);
eb=zeros(M+2,N+2);
ef=zeros(M+2,N+2);
bx=zeros(M+2,1);%x方差
bd=zeros(M+2,1);%d方差

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

bx(1,1)=constant;
bd(1,1)=constant;

for k=0:M
    bx(k+2,1)=lamda*bx(k+1,1)+shuru(k)^2;%input signal energy
    bd(k+2,1)=lamda*bd(k+1,1)+biaozhun(k)^2;%reference signal energy
    eb(k+2,1)=shuru(k)/sqrt(bx(k+2,1));
    ef(k+2,1)=shuru(k)/sqrt(bx(k+2,1));
    e(k+2,1)=biaozhun(k)/sqrt(bd(k+2,1));
    
    for i=0:N
        c1=sqrt((1-eb(k+1,i+1)^2)*(1-ef(k+2,i+1)^2));
        a(k+2,i+1)=a(k+1,i+1)*c1+eb(k+1,i+1)*ef(k+2,i+1);%(6.81)
        
        c2=sqrt((1-a(k+2,i+1)^2)*(1-ef(k+2,i+1)^2));
        eb(k+2,i+2)=(eb(k+1,i+1)-a(k+2,i+1)*ef(k+2,i+1))/c2;%(6.84)
        
        c3=sqrt((1-a(k+2,i+1)^2)*(1-eb(k+1,i+1)^2));
        ef(k+2,i+2)=(ef(k+2,i+1)-a(k+2,i+1)*eb(k+1,i+1))/c3;%(6.83)
        
        %Feedforward Filter
        c4=sqrt((1-eb(k+2,i+1)^2)*(1-e(k+2,i+1)^2));
        aD(k+2,i+1)=aD(k+1,i+1)*c4+e(k+2,i+1)*eb(k+2,i+1);%(6.89)
        
        c5=sqrt((1-eb(k+2,i+1)^2)*(1-aD(k+2,i+1)^2));
        e(k+2,i+2)=(e(k+2,i+1)-aD(k+2,i+1)*eb(k+2,i+1))/c5;%(6.88)
    end
    
end

  figure(1);
  k=0:M;
  hold on;
  plot(k,e(k+2,N+2),'b');
  title('基于后验误差的归一化LRLS error');
  grid on;
  axis([0,M,-8,8]);