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):-2.06882.2674-1.16920.3671-0.00640.0082-0.01020.00290.0067-0.00550.00090.0007aa0.83604210AR系數(shù)估計(jì)

2、方差6ARinJ50.5521012ar索數(shù)估計(jì)如差6ARin：-D.5Burg最大熵譜估計(jì):3uiy大誼估計(jì)珀率諾0.611.622.633.5頻率matlab代碼：u=1;whileu<=50%50次仿真實(shí)驗(yàn)n=10000;w二randn(l,n);%生成零均值，方差為0.2的白噪聲w=w-mean(w);w=w/std(w);w=sqrt(0.2)*w;x(l)=l+w(l);x(2)=2+w(2);x(3)=3+w(3);x(4)=4+w(4);%由ar模型生成含噪信號(hào)；fori=5:nx(i)=2.760*x(i-1)-3.809*x(i-2)+2.654*x(i-3)-0.9

3、24*x(i-4)+w(i);endP(l+l)=l/n*sum(x."2);%計(jì)算預(yù)測(cè)誤差功率的初始值g(1,:)=x;f(1,:)=g(1,:);m=1;k=0;l=0;a(1,1)=1;P(1)=1;whileabs(P(m+1)-P(m)/P(m)>=0.01forj=m+1:nk=k+f(m,j)*g(m,j-1);l=l+f(m,j廠2+g(m,jl廠2;endK(m)=-k/(1/2*l);%求反射系數(shù)a(1,1)=1;ifm>=2forj=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

4、);endendP(m+l+l)=(l+abs(K(m)廠2)*P(m+1);%計(jì)算預(yù)測(cè)誤差功率forj=l:n%計(jì)算濾波器輸出f(m+1,j)=f(m,j)+K(m)*g(m,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;endfori=1:50ar二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(

5、fx)=fx'end%求階數(shù)和AR系數(shù)的方差和偏差var_p=var(M);fori=1:max(M)var_ar(i)=var(ar_coef(:,i+1);endbias_p=mean(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;fori=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fori=1:length(Pxx(1,:)mean_P

6、xx(i)=mean(Pxx(:,i);end%作圖plot(fxx(l,:),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