covariance between the estimated parameters from curve fitting toolbox

Hello,

I have collected data (x,y) from a sine wave. Now I want to fit a model to this data, e.g: y=A*sin(B*x+C) or y=E + A*sin(B*x) + D*cos(B*x).

Is there a way to estimate this parameters (A to D) with matlab, outside the curve fitting toolbox? The latter can provide me the parameters and confidence intervals, but i'm interested in the covariance between the estimated parameters.

If not, is there another way to calcualte the parameters and covariance between the estimated parameters A to D?

Thanks a lot.

Bram

Answer 1

[Matt J]

There is lsqcurvefit in the Optimization Toolbox. However, the Curve Fitting Toolbox does let you return the Jacobian, which is presumably what you would use for your covariance analysis,

https://www.mathworks.com/help/curvefit/fit.html?searchHighlight=fit&s_tid=doc_srchtitle#bto2vuv-1-output

[Bram Stegeman]

Thank you. with MSE and Jacobian from output Optimization Toolbox I can calculate covariance matrix.

[Mirta Dumancic]

How?

[Matt J]

It is the 7th output argument of lsqcurvefit

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