Choosing a method for nonlinear data-fitting to find parameters

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Nik 2017-7-31

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评论： Nik 2017-8-1

I'm currently trying to fit nonlinear experimental data to find two parameters. Using lsqcurvefit has been working well about 90% of the time, but I wanted to try to improve that. I have found other methods for fitting data, but I'm confused about the differences between them, and how to choose one. I tried using MultiStart in addition to lsqcurvefit, but that did not seem to improve the results. I also tried lsqnonlin without any luck. Do you have any recommendations about other methods/options to try? I have access to the majority of the toolboxes. Some people were discussing the use of robustfit, but I was confused about the implementation of that. Any insight would be greatly appreciated!

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Answer 1

Matt J 2017-7-31

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编辑：Matt J 2017-7-31

If lsqcurvefit is failing and your objective function is legal (differentiable, etc...), then it must be that you are deriving a bad initial guess in those failure cases. Since it is only a 2 parameter search, you should be able to derive a good initial guess of the optimum just by evaluating the least squares cost function on some coarse grid and either plotting them as a 2D surface or taking the minimum over the samples.

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John D'Errico 2017-8-1

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fminspleas will be more efficient here, as well as more robust, because it need to work with only the one nonlinear parameter, B. That means A does not need a starting value, nor is it really solved for in an iterative sense. This also makes the problem more robust, because the parameter search is now done in a 1-dimensional search space, instead of the 2-d space of the original problem.

You can even take advantage of the model form to use the expm1 function, since expm1(X)=exp(X)-1. This can be more accurate for some values of X. I doubt it is important here though.

funlist = {@(B,xdata) -expm1(-xdata*B)};

Nik 2017-8-1