1、设:观察信号兀,兀,,讹);H = %,人hN_期望信号y(l), yy(L) w T线性FIR自适应滤波器原理框图十线性FIR自适应滤波器的输出:N1亍)=工 hkx(n - k) en) = yn) yn)k=o n=n2 斤=“2 H 厶$ LS Filter丿(H)=工护=(y(n)-y(n)2 = minn=n n=nxn=n2 n=n2丿(H)= /(“)= (y()-孑(MJ? =minn=W| n=nN_孑() =工处一“)k=二 正交原理(Principle of Orthogonality)H)= 0 =兀( - k)(n) = Q,k = O,1,.,N-1OH 心正交原
2、理:LS滤波器的输入x(nk)和误差0何正交,k =推论1:滤波器的输出和误差砒正交n=n2工孑()() = 0n=nx推论2:LS滤波等价于将期望信号y(n)进行正交分解y(n) = y(z2)+ e(zi)n=n2 n=n2 n=nb()= y2()+w2()1卩 y三 正则方程(Normal Equation)Nen) = y(n) -y(n) = y(n)工 hkx(n k)k=0 n=n2工 xn 一 k)e(n) = 0, k = 0,l,N _ n=nAN1 /Z/?2 /2工力7 工一一加)=k)y(n),k = 0丄,N-1 m=0 n=nA工饥(k) = z(-k),k =
3、 0,l”,N-l Normal Equationm=00H = z =Hls zk)=工 x(n 一 k)xn 一 m). m.k = 0,1,., N -1z(k) = yx(n-k)y(n),k = 0 丄,N-lH=/7=(QnxNz = z(0),z(-l),z(N + l)r/()= (y()-孑何=minn=n n=n四 selection of and n2(Data windowing) 7:卜 (3) Jx(n - k)x(n - m),m.k = O,1,N-1Z(-k) = x(n-k)y(n),k = 0,,N-17Z=7?I1) 比二1, n2=L+N-l,前后补零
4、N1(自相关法)2) 比=1, n2=L补零N丄后不补零(前加窗法)3) 比二N,兔二L+N丄前不补零后补零N-1 (后加窗法)4) 比二N,比二L,前后不补零(协方差法)五 Minimum Sum of Error Squaresn=n2 n=n2 n=n2Sy =工尸=工工九-吋n=nA 77=/?! n=nx=HrOH = Hrz = zrH h 匚1zLSi=-H = S-zrO-1z6.2标准RLS自适应滤波器(Standard RLS Adaptive Filters)n=fb n=n2丿(H)二乞孑的=工(y() 二 min%7)基本思想:假设在 1时刻得到滤波器系数的LS估计,
5、在时 刻新的数据到来后,按LS准则更新滤波器系数TRLSZH(n)=工龙I (0 = min 2 遗忘因子i=ix(i)=兀,无(i-l),.,x(i-N + l)r e(i) = y(/)-7*H(n) = h0 (必 % (心,hN_x (n)y(i) = Y 九)W - )= H气对乂(i) = xr(z)H(n)k=0y(0 = Hr(n)x(0 = xr(0H(n)dJH(n)门 吕、/、cn0H() ti0(n)H() = z() 一-1) 0(n),z(n)的递推计算()=20(n -1) + x(n)x7 (n)() =工矿M)xp)i=ln-=2 工 2,?l_/x(z)xr
6、(z) + x(n)x7(n)n 申一z(n) = 2nly(i)x(i) = 2 + x(n)y(n)i=l i=lz(n) = 2z(n-l) + x(n)y(n)i2)的递推计算0(n) = 2 (m -1) + x(n)xT (n)矩阵恒等式:(A + BCD尸二=Ar - A XB(C + DA XB) 1 DA 1玖 n) = l(n) A = 2O(n -1)B = x(n);C = 1,D = xT (n)P(n) = 2_1P(n-1)-2lP(n -l)x(n)l + xr(n)2_1P(n - l)x(n)-1 xr (n)AlP(n -1)P(n)=P( -1) - F
7、P(仃 1 严处Z)P(-l)l + 2_,xr(n)P(n-l)x(n)H(“)= (n)z(n) = P(n)z(n)H(n) = H(n-l) + k(n)(n)g()= y(n) -HT(n- l)x(n) 验前误差e(n) = y(n) -Hr (n)x(n)(幺(砒验后误差)忆/11/900乙()x(1 - %)丄H - + (T- )H =(wX(w)yf + (i- w)H(w)2x(n)yf-a- i/)h =(w)zC (w)x(w)iXl-w)z(t - w)d(w) 2x(w)耳一 (I w) z(i -w)d =(i/X(w)x + (I-i/)zy (T %)1(%
8、)八(两卫 一 (%)込亍=()z(w)d = (W) z(w)=(%)H(I - w)d(w) N 叭 _y -(-叽彳=(w)dz(m) = 2z(n -1) + x(n)j(n) H(n) = H(n-l) + k(n)(n)4) JH(n) = min = JRLS 的递推计算几/Hm 广胖2何n=jmin S) = S W-zr ()H(n) H 必Fy =化,(-l) + y2()min()= ) 一 Z 7 ()HRLS ()=Xsy O 一 1) + y $ (n) - &z( l) +O)y()5 H(n-l) + k(n) =2sy (一 1) zT(n - l)H(n -
9、1)+y()y() (n)H(w -1)- zr (n)k(n)(n)MMVCLAB6L(话(心+(I-町呷二S WW+(T-)u?Vr =为(叭 x(%lh -()+(【-) Ull7r = (m)(m)x(w)丄 h -(以朋M+(i-w)UVr = (w)(w)x(n)丄 h - (I-叭H(“) A - +(T- %)H(I - (I u) (3y = (w) U1U7 (w)x(w)2h =(w)H(w)2z-(w)as = (w)U!U7 g才盼-1)55)RLS算法总结 k l + 2_1xr(n)P(H - 1)x()初始化:H(0) = 0戶(0)=产1、 small positive contant for high SNR S = large positive contant for low SNRk()= ,2 + x7 (n)7i(n)歟)=y(n) - H7 (n - l)x(n),H(n) = H(n -1) + k(n)(),P(n) = 2_lP(n 一 1) 一 2lk(n)xr (n)P(n 一 1)
copyright@ 2008-2022 冰豆网网站版权所有
经营许可证编号:鄂ICP备2022015515号-1