Fitting A Gaussian Curve to a Time Series in Matlab

Question

I have some raw data of vegetation indices of a place. When I plot them on a time series I get a result as follows:

Now we can fit some Gaussian Model which is of the form

Where "n" is the number of terms/Gaussian. Matlab does provide this kind of functionality but for max of n=8.

So Can I get some help on how can I fit such type of functions in Matlab?

Answer 1

There's a good reason why Matalb stops at some n, Think about it for a second, count how many data points you actually have (say 100), how many free parameters you actually need to fit (3xn), so if you want to fit say 15 Gaussians, you need at least 45 conditions , add noise and the fact that you need several pixels (more than 3) per Gaussian for the fit to work, this requires probably more pixels than you have and a long optimization process. Of course, if you try to fit you'll still get an answer, but it won't be robust (garbage in garbage out), or single valued.

This is what I would do: Since the Gaussian width in your data is limited say 30 pixels, I'd split the data into several parts (that overlap by at least some pixels), and try to fit a smaller # of Gaussian each time to each segment. Say you take the range 0<x<30, then 10<x<40, etc... and in each find the 3-4 Gaussian separately. My intuition says this will be quicker and more robust.

If you still want to fit all of them at once, you can use something like this fex file...