Fitting of autocorrelation function

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Philipp Steffen 2012-1-5

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https://ww2.mathworks.cn/matlabcentral/answers/25400-fitting-of-autocorrelation-function

Hi,

I am not an expert in curve fitting and stuck with a problem where I want to fit a function to a measured data set in order to extract parameters.

The data set contains values of the autocorrelation of diffusing fluorescent particles (G(tau), measured using a confocal microscope. Tau is the correlation time.

I would like to fit the data set using the following equation:

G(tau) = 1/x(1)*x(2)*((1+tau/x(3))^-1)*(1+tau/x(4)^2*x(3))^(-1/2)

in order to extract the parameters x(1), x(2), X(3) and x(4)

In theory I should be able to fit the data set using the Levenberg-Marquardt non-linear least-squares fit. I was so far experimenting with lsqcurvefit and fminsearch to solve the problem but could not get a reasonable fit. I am not sure whether I have a conceptual problem here or whether it is a problem with my implementation. I therefore would appreciate your help a lot!

I tried so far:

    beta0=[]; 
    beta = lsqcurvefit(@fcspddeb,[4.09E3, 0.3, 0.1,3],fcsdatatrimmed(:,1),fcsdatatrimmed(:,2));

where fcspddeb is:

function [ G ] = fcspddeb( x, tau )
G = 1/x(1)*x(2)*((1+tau/x(3)).^-1).*(1+tau/x(4)^2*x(3)).^(-1/2)
end

This gives me a completely wrong fit.

Thanks a lot for your help in advance,

Philipp

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bym 2012-1-6

please format your code. for functions returning one variable, the brackets are not necessary, but I don't think that is the problem. Can you post a small subset of fcsdatatrimmed ?

Philipp Steffen 2012-1-10