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

[bym]

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]

sorry for the formatting issue. This was my 1st post in the answer section.

Here is a subset of fcsdatatrimmed:

2.80000000000000e-06 0.000247287500000137

3.00000000000000e-06 0.000222712500000055

3.20000000000000e-06 0.000247654999999902

3.60000000000000e-06 0.000216259999999968

4.00000000000000e-06 0.000242887500000011

4.40000000000000e-06 0.000258062499999934

4.80000000000000e-06 0.000293670000000024

5.20000000000000e-06 0.000224647500000064

5.60000000000000e-06 0.000252660000000127

6.00000000000000e-06 0.000239894999999990

6.40000000000000e-06 0.000236425000000207

7.20000000000000e-06 0.000248582500000039

8.00000000000000e-06 0.000201032500000142

8.80000000000000e-06 0.000219357500000017

9.60000000000000e-06 0.000208382499999882

1.04000000000000e-05 0.000200205000000064

1.12000000000000e-05 0.000211342499999878

1.20000000000000e-05 0.000223410000000035

1.28000000000000e-05 0.000188237499999966

1.44000000000000e-05 0.000197192499999943