Increase stability of curve fit

Hello,

I have a signal which I want to fit with the following function:

a*exp(-b*t) - c*exp(-d*t) + e*exp(-f*t)*cos(g*t) + h*exp(-k*t)*sin(l*t) + off

I know that my signal actually has this form and I also know the coefficients, but when I enter them as start points the fit does not exactly match the signal. How can I improve this?

I've chosen a Levenberg-Marquardt-alogorithm with LAR-robustness. Is the problem the large number of parameters?

Regards

twig

[Walter Roberson]

Could you attach some data for us to test with?

[twig27]

I've uploaded the signal time and coefficient vector. Unfortunately I cannot upload an .sfit-file, does this help?

Answer 1

[John D'Errico]

People think they have this great model. And computers can do anything. :) NOT TRUE.

A vast part of your data is constant, providing no information except what the value of that constant term at the end will be.

   ...
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11
   1.9608e-11

Essentially, about half of your data has no information content. The rest of it? Wildly insufficient to fit the model with all of those coefficients.

plot(time,data_transfer_out)

Sorry, but the fit that you got was worthless. Any attempts to fit that model, using any scheme on this data, will be a complete and utter waste of time.

On top of all that, sums of exponential models are notorious for being difficult to fit.

You can't get blood from a rock. And as bloodless rocks go? This one is highly anemic.