文档介绍：matlab基于最小二乘、全局化算法、遗传算法的参数识别最小二乘法:%递推公式,更新p0=p2;forn=2:N-1%%递推最小二乘法K0=p0*X(n,:)'*inv(1+X(n,:)*p0*X(n,:)');%计算,Theta_abs=Theta_abs+K0*(Y(n)-X(n,:)*Theta_abs);%计算估计值Theta;p3=p0-K0*X(n,:)*p0;%计算Pp0=p3;%误差平方和最小Y1=X(n,:)*Theta_abs;%递推值J=(Y(n,:)-Y1)*(Y(n,:)-Y1)'if(J<err)%设定平方误差最小,跳出循环break;end;end对于,,,,,,,,,,yk,ayk,1....,ay,n,buk,...,buk,n1na1nbab,1,,,,qyk,yk,1引进后移算子假定在初始条件0时z变换得到,n1,bb,bz,...bzYz01n,,bHz,,,,,n1,a,,Xz1,az,...,az1na,n,1,1a,Aq,1,az,...,az,,1n,aARX模型有:,,n,1,1b,,Bqbbz...bz,,,,01nb,,1,d,1,,,,,,A,,qyk,qB,,quk,vk,,vk;为均值为0的噪声项nnab上式可以改写为,,,,,,,,zk,,azk,i,buk,i,vk,k,1,2,..,l,,ii,1,1iiT,,,,zk,hk,,v(k)上式改写为最小二乘格式(3)对于(3)式的次观测构成一个线性方程组lT,,,,,,,,h(k)z(k1),...,z(kn),u(k1),...,u(kn),,,ab即,T,,,a,a,...,a,b,b,...,b,,1212nnan,Z,H,,,,,,,,,,,,,,,,,,Z,z1,z2,...,zl,Vv1,v2,...vlllz?znu?un,0,(1,)01,h1,,,,,,,,,,,,ab,,,,z?znu?un,(1),(2,)12,h2,,,,,,ab,,,,H,,l,,,,?,,,,,,hl,,zl?zlnul?uln,(),,(,1)(,),,ab,,l2TT取极小化准则函数,极小化,求得参,,J,,,,,,,,,,,J,zk,hk,,z,H,z,H,,lLL,1kTˆˆˆˆˆˆˆˆ,,,,a,a,...,a,b,b,...,b数的估计值,,,1212nnanl2TTˆˆˆ表示为了确定使准则最小的条件,将该式,,,,,,,,,,J,zk,hk,,Z,H,Z,H,,llllk,1对各参数求导,并令其结果等于零:,1,JTTTˆˆH,,,,,,HZ,H,,即,,HHHZ,只要矩阵是满秩的,则是20,HHllllllllllˆ,,正定的,使准则为极小的条件得到满足,最小二乘估计的递推算法(RLS)最小二乘法,不仅占用大量内存,而且不适合于在线辨识,为了解决这个问题,ˆˆ把它转化为递推算法:,,,,修正项k,1kz?znu?un,0,(1,)01,h1,,,,,,,,,,,,ab,,,,z?znu?un,(1),(2,)12,h2,,,,,,ab,,,,H,,l,,,,?,,,,,,hl,,zl?zlnul?uln,(),,(,1)(,),,ab,,,1,1,1TTTT若令,则,,,,,,P,P,hh,P,PhI,hPhhPP