Matlab - Try various start points for gaussian fit, choose the one with highest rsquare and then plot

Question

I am batch processing 1000s of data. Sometime the peak positions and magnitudes change drastically, and the program struggles to find these peaks with a single start point value. I have to divide my data into smaller batches to change the start point values, which is time consuming.

Is it possible to try various start point values and select the one with the best rsquare?

ft = fittype('y0 + a*exp(-((x-xa)/(wa))^2), 'independent', 'x', 'dependent', 'y' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';

opts.StartPoint = [10 10 10 0]; % this is a, wa, xa and y0 - from the equation

[fitresult, gof] = fit(xData, yData, ft, opts);

alpha = gof.rsquare; % extract goodness of fit

if alpha < 0.98 % if rsquare (goodness of fit) is not good enough
    
for x = 100:10:500; y= 10:1:50 %these numbers are not set in stone - can be any number
    
opts.StartPoint = [10+x 10 10+y 0]; % tweak the start point values for the fit

[fitresult, gof] = fit(xData, yData, ft, opts); % fit again

Then select the start point with the best rsquare and plot the results.

% plot
f = figure('Name', 'Gauss','Pointer','crosshair');
h = plot(fitresult, xData, yData, '-o'); 

Answer 1

If they are difficulties in guessing, I suggest to use a different method which is not iterative and doesn't need guessed value of the parameters to start the numerical calculus.

Since I have no representative data of your problem, I cannot check if the method proposed below is convenient in your case. This depends on the scatter of the data and on the distribution of the points.

Try it and see. If the result is not correct, please let me know.

A numerical example with highly scattered data is shown below. With this example you can check if the method is correctly implemented.

NOTE : This method can be used to obtain some approximate values of the parameters which can be put as "guessed" values in the usual non-linear regression softwares.

For information : The method is a linear regression wrt an integral equation to which the Gaussian function is solution :

For the general principle, see : https://fr.scribd.com/doc/14674814/Regressions-et-equations-integrales