Fitting two arbitrary set of data without tool box

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Hello Matlab experts,

I have measurements of several vectors such that y(:,i) = [a1i,a2i,....ani]. This data set also includes measurement errors. Now I have a modeled solution such that ymodl =[b1, b2, b3,....bn]. I am trying to fit measurement data with modeled data using fminsearch as following:

 function errprd=sumsqerror(fitparam,vecdata,datatraj)
    a =fitparam(1);
    b =fitparam(2);
    ypred =  a*vecdata +b;
    errprd =  sum((ypred-datatraj).^2);
 fitfun = @(x)sumsqerror(x,evect,trajdata);
 [bestx,errsumsqr, existflag, output] = fminsearch(fitfun,x);

My hypothesis suggests that one of columns of y measurement matrix should fit with modeled vector.

Though, I was unable to find a solution with this algorithm. I will highly appreciate if someone could tell me a better procedure (if there is any) to optimize a fitting of any arbitrary set of data.

Thank you.

Kind regards,

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Arun 2018-10-19

ymeasurement_1traj.png

Dear Walter,

Attached is one trajectory, y(:,1); It is not linear. Do you still think polyfit will work here ?

Thanks and regards

Walter Roberson 2018-10-19

在 MATLAB Online 中打开

You have

ypred = a*vecdata +b;

That is a plain y = a * x + b prediction, which polyfit(x,y,1) will calculate pretty quickly. Or more directly,

ab = [evect(:), ones(numel(evect),1] \ trajdata(:);

When I look at your data I would say, that a*x+b is a poor fit for the data -- but it is the model implemented by your ypred.

The data you display is pretty low quality. It looks like you only have 16 datapoints. I would guess maybe sum of three gaussians, maybe sum of four gaussians would be needed. That would require either 6 or 8 parameters. I would expect a low quality fit considering the small amount of data.

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