内容简介作者简介 - 科学与工程计算系

−0.
4x
−3.
2x
【例 4.10.2.2-1】取发生信号的原始模型为 y(
x)
= 3e
+ 12e
。x 在[0, 4]中取值;y 受
−a3x
−a4
x
到噪声 0.3*(rand(n,1)-0.5) 的污染。本例演示:如何以 y = a1e
+ a2e
为模型,通
过 fminsearch 从受污染数据中,估计出参数 a = [ a(
1),
a(
2),
a(
3),
a(
4)]
= [ a1,
a2
, a3,
a4
] 。
(1)
[xydata.m]
function [x,y,STDY]=xydata(k_noise)
%xydata.m
x=[0:0.2:4]';
yo=3*exp(-0.4*x)+12*exp(-3.2*x);
rand('seed',234)
y_noise=k_noise*(rand(size(x))-0.5);
y=yo+y_noise;
STDY=std(y_noise);
[twoexps.m]
function E=twoexps(a,x,y)
%twoexps.m
x=x(:);y=y(:);Y=a(1)*exp(-a(3)*x)+a(2)*exp(-a(4)*x);
E=sum((y-Y).^2);
(2)编写 M 脚本文件作为主文件
[exm041022_1.m]
%exm041022_1.m
k_noise=0.3;
[x,y,STDY]=xydata(k_noise);
a0=[1 1 1 1];
options=optimset('fminsearch');
options.TolX=0.01;
options.Display='off';
a=fminsearch(@twoexps,a0,options,x,y);
chi_est=twoexps(a,x,y)/STDY^2;
freedom=length(x)-length(a0);
Q=1-chi2cdf(chi_est,freedom);
%
y_est=a(1)*exp(-a(3)*x)+a(2)*exp(-a(4)*x);
ych='y_e_s_t=';
a1=num2str(a(1));a2=num2str(a(2));a3=num2str(a(3));a4=num2str(a(4));
char_y_est=[ych,a1,'*exp(-',a3,'*x) + ',a2,'*exp(-',a4,'*x)'];
plot(x,y,'b+');hold on,plot(x,y_est,'r');hold off,axis([0,4,0,16])
text(0.4,14,'y=3*exp(-0.4*x)+12*exp(-3.2*x)')
text(0.4,12,char_y_est),text(2.5,9,['chi2=' , num2str(chi_est)])
text(2.5,7,['freedom=' , num2str(freedom)])
text(2.5,5,['Q=' , num2str(Q)])
(3)
exm041022_1
23