Non-linear parameter estimation (least squares)
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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.
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Greg Heath
2016-2-16
0 个投票
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
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