Non-linear parameter estimation (least squares)

For the following equation, I need to determine three parameters: Sigma, Ps, and kf

y = (Sigma/(1-Sigma))*(1-exp(-X*(1-Sigma)/Ps)))*(exp(-X/kf)

The following are the experimental values: x = [54.5, 77.4, 99.1, 121.8, 148.2, 172.2, 195.4]

y = [0.250, 0.299, 0.341, 0.375, 0.389, 0.406, 0.408]

Constraints:

0 < Sigma < 1, Ps > 0, kf > 0

I need to find the parameters by minimizing the least square errors between predicted and experimental values. I also need to find the 95% confidence interval for each parameter.

Being new to MATLAB, I am unsure how to go about solving this problem. What options do I have, as in what functions can I use? How should I go about solving this problem? Any help/suggestion is much appreciated.

[Image Analyst]

Is this your homework?

Answer 1

[Greg Heath]

Always begin searches with the lookfor command. Follow up with help and doc

>> lookfor 'least square'

lscov - Least squares with known covariance.

lsqnonneg - Linear least squares with nonnegativity constraints.

spaugment - Form least squares augmented system.

spap2 - Least squares spline approximation.

lsqnonlin - solves non-linear least squares problems.

lsqcurvefit - solves non-linear least squares problems.

lsqlin - Constrained linear least squares.

plsregress - Partial least squares regression.

regress - Multiple linear regression using least squares.

plspcrdemo - Partial Least Squares Regression and Principal Components Regression >

Hope this helps.

Greg