%?計(jì)算函數(shù)f的雅克比矩陣，是解析式
syms?a?b?y?x?real;
f=a*exp（-b*x）;
Jsym?=?jacobian（f[a?b]）


%?擬合用數(shù)據(jù)
data_1=[0.25?0.5?1?1.5?2?3?4?6?8];
obs_1=[19.21?18.15?15.36?14.10?12.89?9.32?7.45?5.24?3.01];

%?2.?LM算法
%?初始猜測(cè)s
a0=10;?b0=0.5;
y_init?=?a0*exp（-b0*data_1）;
%?數(shù)據(jù)個(gè)數(shù)
Ndata=length（obs_1）;
%?參數(shù)維數(shù)
Nparams=2;
%?迭代最大次數(shù)
n_iters=50;
%?LM算法的阻尼系數(shù)初值
lamda=0.01;

%?step1:?變量賦值
updateJ=1;
a_est=a0;
b_est=b0;

%?step2:?迭代
for?it=1:n_iters
????if?updateJ==1
????????%?根據(jù)當(dāng)前估計(jì)值，計(jì)算雅克比矩陣
????????J=zeros（NdataNparams）;
????????for?i=1:length（data_1）
????????????J（i:）=[exp（-b_est*data_1（i））?-a_est*data_1（i）*exp（-b_est*data_1（i））];
????????end
????????%?根據(jù)當(dāng)前參數(shù)，得到函數(shù)值
????????y_est?=?a_est*exp（-b_est*data_1）;
????????%?計(jì)算誤差
????????d=obs_1-y_est;
????????%?計(jì)算（擬）海塞矩陣
????????H=J‘*J;
????????%?若是第一次迭代，計(jì)算誤差
????????if?it==1
????????????e=dot（dd）;
????????end
????end

????%?根據(jù)阻尼系數(shù)lamda混合得到H矩陣
????H_lm=H+（lamda*eye（NparamsNparams））;
????%?計(jì)算步長(zhǎng)dp，并根據(jù)步長(zhǎng)計(jì)算新的可能的\參數(shù)估計(jì)值
????dp=inv（H_lm）*（J‘*d（:））;
????g?=?J‘*d（:）;
????a_lm=a_est+dp（1）;
????b_lm=b_est+dp（2）;
????%?計(jì)算新的可能估計(jì)值對(duì)應(yīng)的y和計(jì)算殘差e
????y_est_lm?=?a_lm*exp（-b_lm*data_1）;
????d_lm=obs_1-y_est_lm;
????e_lm=dot（d_lmd_lm）;
????%?根據(jù)誤差，決定如何更新參數(shù)和阻尼系數(shù)
????if?e_lm????????lamda=lamda/10;
????????a_est=a_lm;
????????b_est=b_lm;
????????e=e_lm;
????????disp（e）;
????????updateJ=1;
????else
????????updateJ=0;
????????lamda=lamda*10;
????end
end
%顯示優(yōu)化的結(jié)果
a_est
b_est

?屬性????????????大小?????日期????時(shí)間???名稱(chēng)
-----------?---------??----------?-----??----

?????文件????2871808??2011-11-03?00:14??Levenberg-Marquardt\Levenberg-Marquardt.ppt

?????文件???????1640??2011-11-03?00:03??Levenberg-Marquardt\LM.m

?????目錄??????????0??2011-11-03?00:32??Levenberg-Marquardt

-----------?---------??----------?-----??----

??????????????2873448????????????????????3