MATLAB: Double exponential fits, but single curves away from the data- why

Question

When I try single exponential fit (red line in attached pic) to my data (the part in blue on the attached graph), it seems to curve way from the values, and clearly does not fit. I used:

f=fit(newx(10000:11000), yy2(10000:11000), 'a*exp(-(1/b)*x)');
plot(f, newx(10000:11000), yy2(10000:11000))

I tried to filter and smooth the signal down to a single line, and I also tried cftool. When I use double exponential, it works, but for my calculations, I need a single exponential fit to get the b-coeff. Is there any reason why single exponential just does not work with this trace?

—–edit

I attached the whole trace, and I want to fit to points 10000:10500

Answer 1

very steep power laws can be notoriously difficult to fit, since small changes in x lead to big changes in y, it makes it hard on the fitting algorithms.

A trick you might try is (in your case) take the natural log of the data and then fit it to the natural log of your fit equation...

ln(a e^(-(1/b)*x))  = ln(a) - x/b;

so that now your fit problem has been reduced to a linear fit y = Mx+B, with M=-1/b and B = ln(a).

Also remember in matlab that the function for ln is log() which drives me crazy.