Burg算法估計(jì)模型參數(shù)

1、已知AR(4)過(guò)程：x(n)=2.760x(n-1)-3.809x(n-2)+2.654x(n-3)-0.924x(n-4)+w(n)試用Burg算法估計(jì)模型參數(shù)、階數(shù)和功率譜。實(shí)驗(yàn)仿真50次，給出估計(jì)結(jié)果的方差和偏差（用估計(jì)結(jié)果均值與真值的差來(lái)估計(jì)偏差）。用Burg算法對(duì)該AR過(guò)程估計(jì),50次實(shí)驗(yàn)得平均階數(shù)p=4.8，取整數(shù)即為P=5，階數(shù)方差var(p)=12.53，階數(shù)偏差為0.8。AR參數(shù)（平均）: -2.0688 2.2674 -1.1692 0.3671 -0.0064 0.0082 -0.0102 0.0029 0.0067 -0.0055 0.0009 0.0007AR參數(shù)方差

2、:AR參數(shù)偏差：Burg最大熵譜估計(jì)：matlab代碼：u=1;while u=0.01for j=m+1:n k=k+f(m,j)*g(m,j-1); l=l+f(m,j)2+g(m,j-1)2;end K(m)=-k/(1/2*l);%求反射系數(shù) a(1,1)=1; if m=2 for j=1:m-1%計(jì)算前向預(yù)測(cè)濾波器系數(shù) a(m,j)=a(m-1,j)+K(m)*a(m-1,m-j); a(m,m)=K(m); endendP(m+1+1)=(1+abs(K(m)2)*P(m+1);%計(jì)算預(yù)測(cè)誤差功率for j=1:n%計(jì)算濾波器輸出f(m+1,j)=f(m,j)+K(m)*g(m,

3、n-1);g(m+1,j)=K(m)*f(m,j)+g(m,n-1);endm=m+1;endM(u)=m-1;%記錄每次實(shí)驗(yàn)的階數(shù)u=u+1;endfor i=1:50ar=arburg(x,M(i);%估計(jì)AR系數(shù)ar_coef(i,1:length(ar)=ar;Px,fx=pburg(x,M(i);%估計(jì)功率譜Pxx(i,1:length(Px)=10*log10(Px);fxx(i,1:length(fx)=fx;end%求階數(shù)和AR系數(shù)的方差和偏差var_p=var(M);for i=1:max(M)var_ar(i)=var(ar_coef(:,i+1);endbias_p=me

4、an(M)-4;ar_r(max(M)=0;ar_r(1)=-2.76;ar_r(2)=3.809;ar_r(3)=-2.654;ar_r(4)=0.924;for i=1:max(M) mean_ar(i)=mean(ar_coef(:,i+1); bias_ar(i)=mean(ar_coef(:,i+1)-ar_r(i);end%50次實(shí)驗(yàn)功率譜平均for i=1:length(Pxx(1,:)mean_Pxx(i)=mean(Pxx(:,i);end%作圖plot(fxx(1,:),mean_Pxx);%作功率譜圖title(burg最大熵估計(jì)功率譜);xlabel(頻率);ylabel(功率譜密度);figure(2);plot(var_ar);%AR系數(shù)估計(jì)方差title(AR系數(shù)估計(jì)方差);xlabel(AR(n);ylabel(方差);figure(3);plot(bias_ar);%AR系數(shù)估計(jì)偏差title(AR系數(shù)估計(jì)偏差);xlabel(AR(n);ylabel(偏差);disp