How to fit parameters in an m.file to a curve?

To understand my problem it would be best if you run this m file:

https://dl.dropbox.com/u/368757/curve_fitting_problem.m

In the following I refer to the variable names in the file:

It will plot a measured_signal in blue to which I want to fit a function (modeled_signal, shown in red). This function is generated in the same file. However, it is not a simple one line equation (with which all curve fitting tutorials that I found are dealing). It is rather a convolution of two functions one of which is constant and the other contains some variables which I want to optimize.

How can I tell matlab to fit the "modeled_signal" to the "measured_signal" by changing the three variables in lines 9-11 (tmax, alpha, mag)?

Thank you very much for your help!

Answer 1

[Seth DeLand]

Take a look at lsqcurvefit from the Optimization Toolbox. http://www.mathworks.com/help/toolbox/optim/ug/lsqcurvefit.html

You can write a function that takes in a vector with the parameter values and a vector with the xdata (t in your case), and then returns the values for the calculated modeled_signal. Then use lsqcurvefit to find the optimal parameters that fit your function to your ydata (measured_signal).

There's an example along these lines here: http://www.mathworks.com/products/optimization/examples.html?file=/products/demos/shipping/optim/datdemo.html

[Felix]

Thank you very much. It works now with this apporach. At first lsqcurvefit produced only complex numbers that made no sense, but this could be solved by setting reasonable boundaries for the solution.