Estimating parameter uncertainties using fminunc and hessian

Dear Sir/Madam,

I have experimental data which is often described in litrature using the Kraus model (shown below). I am trying to identify the parameters (, and m) in the Kraus model via optimisation.

I wanted to calculate the errors present in the parameters too. I have used both lsqcurvefit and fminunc for the optimisation process. Both functions give me identical optimised parameters but the standard error returned by both functions vary. For lsqcurvefit I use the output jacobian matrix with the nlparci tool to dermine 95% confidence interval and back track to calculate the standard errors.

[x,resnorm,residual,exitflag,output,lambda,jacobian] = lsqcurvefit(___)

ci = nlparci(x,residual,'Jacobian',J); %Returns 95% confidence interval

err = ((ci(:,2)-ci(:,1))./3.92);

For fminunc, the function I minimise is the sum of square residues by comparing the Kraus model with the experimental data. Fminunc returns the otimised parameters and the hessian matrix. The hessian matrix is what I use to determine the standard errors.

err = sqrt(diag(inv(Hessian)))

The standard errors I obtain for the paramters differ. Why is this so? I would really appreciate any help I get with this. Thank you.

Kind Regards,

Vin