Non linear fit & error propagation

Dear Mathworks community,
I am currently facing the following problem : I have a set of data, X, and Y. I know that the uncertainty on Y is given by its square root. I want to use possibly a non linear fit to fit a gaussian function to it. I would like to propagate the error through the fit and take into account the fact that I know that there is an uncertainty on the measurement.
How is this possible with matlab ?
Cheers

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