How to get parameter values from lsqcurvefit?

I have been using lsqcurve fit to calculate two parameters so that my model fits my experimental data more accurately. I have written code and keep getting the exit message:

"Local minimum found.

Optimization completed because the size of the gradient is less than the default value of the function tolerance."

Does this mean the programme has succeeded? How do I get the values for my two parameters?

Thanks

Answer 1

[Star Strider]

Your estimated parameters are ‘x’ in this example from the documentation:

x = lsqcurvefit(fun,x0,xdata,ydata)

The warning (not error) indicates that lsqcurvefit has found a local minimum, not the global minimum that would produce the best parameter estimates. Use different initial parameter estimates (in this example, ‘x0’) and see if that produces a better fit. Another option is to use fminsearch, since it uses a derivative-free method, and sometimes succeeds when the gradient-descent solvers do not. If you have the Global Optimization Toolbox, the patternsearch function may find the global minimum most efficiently.

Example code using fminsearch:

x = ...;                                                        % Independent Variable
y = ...;                                                        % Dependent Variable

fun = @(b,x) ...;                                               % Objective Function

SSECF = @(b) sum((y - fun(b,x)).^2);                             % Sum-Squared-Error Cost Function
B0 = [...];                                                     % Initial Parameter Estimates
B = fminsearch(SSECF, B0);                                      % Estimate Parameters

Here, ‘B’ would be the estimated parameters.