Matlab曲线拟合优化

Question

我试图按照this tutorial将曲线拟合到dataset。曲线的等式应为

f(t) = log10((wpmcoeff./(t.^2)) + 
       ((1.038+3.*log(2.*pi.*1e6.*t)).*fpmcoeff./(t.^2))+(wfmcoeff./t) + 
       (ffmcoeff)+(rwfmcoeff.*t)).

我创建了以下代码：

clock='atomicclockgpsworld.txt';
data=importdata(clock);

carrier=10e6;

sig=data(:,2);
t=data(:,1);
sigsq=log10(sig.^2);
fun = @(coeff)sseval(coeff,t,sigsq);
x0 = rand(5,1);
bestx = fminsearch(fun,x0);
wpmcoeff = bestx(1);
fpmcoeff = bestx(2);
wfmcoeff = bestx(3);
ffmcoeff = bestx(4);
rwfmcoeff = bestx(5);
yfit=log10((wpmcoeff./(t.^2))+((1.038+3.*log(2.*pi.*1e6.*t)).*fpmcoeff./(t.^2))+(wfmcoeff./t))+(ffmcoeff)+(rwfmcoeff.*t);
semilogx(t,sigsq,'x');
hold on
semilogx(t,yfit);
saveas(gcf,'fit','png');

和相应的功能

function sse = sseval(coeff,t,sigsq)
    wpmcoeff = coeff(1);
    fpmcoeff = coeff(2);
    wfmcoeff = coeff(3);
    ffmcoeff = coeff(4);
    rwfmcoeff = coeff(5);
    sse = sum(sigsq - (log10((wpmcoeff./(t.^2))+((1.038+3.*log(2.*pi.*1e6.*t)).*fpmcoeff./(t.^2))+(wfmcoeff./t)+(ffmcoeff)+(rwfmcoeff.*t))));
end

但是产生的适应性很糟糕（我的y数据应该在大约-20到-22之间变化，但拟合产生的曲线达到1e59！）。任何人都可以建议我可能出错的地方吗？

当前输出与数据：

Answer 1

在你的函数sseval中，函数与第一个脚本中的函数不同。在函数中，您获取整个等式的log10，而在log10脚本中(wfmcoeff./t)停止：

第一个脚本：

log10((wpmcoeff./(t.^2))+((1.038+3.*log(2.*pi.*1e6.*t)).*fpmcoeff./(t.^2))+(wfmcoeff./t))+(ffmcoeff)+(rwfmcoeff.*t)

功能：

log10((wpmcoeff./(t.^2))+((1.038+3.*log(2.*pi.*1e6.*t)).*fpmcoeff./(t.^2))+(wfmcoeff./t)+(ffmcoeff)+(rwfmcoeff.*t))

第二件事是你没有采取差异的方块。所以在你的函数中将最后一行改为

sse = sum((sigsq - (log10((wpmcoeff./(t.^2))+((1.038+3.*log(2.*pi.*1e6.*t)).*fpmcoeff./(t.^2))+(wfmcoeff./t))+(ffmcoeff)+(rwfmcoeff.*t))).^2);

注意：配件有时很好，有时它真的很垃圾，所以运行脚本几次以获得合适的效果。几次后，我得到了以下内容：

找到的参数是：

wpmcoeff: 10.898483535691309
wfmcoeff: 22.933722400252414
rwfmcoeff: 3.601059651996531e-05
fpmcoeff: -0.324473127267299
ffmcoeff: -21.497862719234053