Surface fitting (only one free parameter)... unfamiliar with fitting tools

Hi All!

I have a set of measured 2-D data that I'd like to fit to an analytic solution to back out one parameter of interest. Previously I would make a 'guess' vector of that parameter (I know fairly well its realistic range), compute the analytic surface for each guess, plot the MSE's between the analytic surfaces at each guess point and the measured data... choose the guess that minimizes the MSE.

Well, there's a bit to be desired with that method... I'm sure Matlab can do a better job (quicker and more accurate), but I'm not familiar with the fitting tools. I'm somewhat overwhelmed by all the options and I feel like this should be straight forward for someone who knows what they're doing.

So, here are some details on the problem... let me know what you all think. Thanks!

sensorData = % read in data

[~, R] = cart2pol(X, Y);

analytic = @(r0)exp(-3.44 * (R/r0).^(5/3));

% solving for r0. Always real and positive.