How can I fit parameters for a given equation and a given set of data?

I have this function:

and I measured theta(psi) and psi and I have many data series of these two quantities. theta-r and theta-s are constant and known. I don't know only alfa and n .

I would like to know if there is a way to find those two parameters ( alfa and n) that best fit my data series.

Thank you,

Ginevra

Answer 1

[Star Strider]

I can’t test this with your actual data, but I simulated them and verified that this runs:

Thtar = 3;
Thtas = 5;
% b(1) = alfa,    b(2) = n
ThtaPsi = @(b,psi)  Thtar + (Thtas-Thtar)./((1+(b(1).*abs(psi)).^b(2)).^(1-1/b(2)));
B = nlinfit(psi, Thta, ThtaPsi, [1 1])
fprintf(1,'\n\nEstimated Parameters:\n\t\talfa = %.6f\n\t\tn    = %.6f\n\n', B)

I used the Statistics Toolbox nlinfit function to do the nonlinear fit. You can also use lsqcurvefit, and with one additional statement, fminsearch to estimate the parameters.