Parameters to consider in non linear curve fitting

I have a complex (sum and multiplication of several elementary functions) function to fit with experimental data, but I could not reach the desired fit, the program does his work but the parameters are far from what they should be, I noticed that if I change the lb or ub it changes the results also if I change Beta0 it also affects the results. I need help and advise on the factors that I should consider to have the best fit

note: the experimental data are about 6000 points, I have around 15 parameters to find

thanks in advance

Answer 1

[Star Strider]

Without knowing more, I suggest you choose Beta0 to be close to what you expect the parameters to be as you can. I also suggest not restricting the parameters with lb and ub unless you know that, for instance, they must be positive or if you already know they should not exceed a specific value.

Fitting so many parameters will give any solver problems. Consider reducing them if you can.

[Zine]

Thanks Star, I tried this idea and it makes the values closer, thanks for that, but in some cases it creates complex numbers, so how to impose real values only so the program will not search in complex numbers, I should find as result only real results (no imaginary parts)

note: the modules of my complex results are very close to what I want to have

[Star Strider]

The only way I can think of to force real numbers is for the last lines of your objective function to return them as reals. For instance:

function (p,x) = fun(p,x)
    (code)
    p = abs(p);
end

That’s not recommended, but it is probably an experiment you can do to force the returned parameters to be real. If it fails to converge to what you consider a ‘correct’ solution, you can always remove the ’abs’ line and live with complex parameter estimates.

Answer 2

[Image Analyst]

Yeah, I don't know either from this description, so I'll just put in a plug for John's masterpiece: http://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling

Description   

If you could only download one curve fitting tool to your laptop on a desert island, this should be it.

For many years.......

[John D'Errico]

Blush. I suppose I'd take a good supply of batteries too. ;)

[Star Strider]

Interesting. I hadn’t seen it before.

Thanks for the link — and John for the work!

[Image Analyst]

John has lots of good ones I use: allwords, polyfitn (to do background correction of images), suite of min bounding objects, etc. It's worth everyone looking over his impressive File Exchange. There's something there for just about everybody.

[Star Strider]

I’ll search on his name from the link you provided. Thanks again.

(I’m just happy when someone occasionally downloads polyparci!)