I am trying to do curve fitting for some noisy data. I know how the curve should look like since I am aware of the physics behind it. for example, the first part of the curve should be increasing always. where the other half should always be decreasing. I tried to use polynomial fitting (which is implemented in MATLAB) but it seems that the fitted curve does not comply with what I expect. How Can I perform curve fitting that satisfy such conditions ?
Thanks.
You are not really giving us enough information. For example, from your description you could have a piece-wise linear (positive slope, increasing) and (negative slope, decreasing) go through your data. But I suspect you also want smooth (continuous, differentiable etc.)
So, why doesn't the polynomial work--- how many data points did you give it to fit? I had an example like this where I wanted to have a maximum at a certain point and some of my fitted polynomials didn't give that max.... so you have constraints? Or you have a family of parameterized curves, and you want to fit the best of these with your data? If there is a nonlinear curve that you know is suited to the data (say a Poisson Distribution) you may be able fit with non-linear methods.
Perhaps you could share some data and challenge the community to get a good parsimonious fitting model?
Professor O'Kelly.
Many Thanks for your response.
Attached to this response figures of the original curve and the fitted curve. I repeat here that I am aware of the physics behind the curve. I can tell that the curve should be increasing up to T = 4 seconds (approximately), then it will decay with time. If I try to use polynomial fitting (which is my first option since I need to perform differentiation for further processing), MATLAB will do a lousy job at the very beginning and along the curve tail. I am not expert in data fitting techniques. I did not consider other techniques because I don't really know which one serve my purpose the best.
Many thanks for your help.
Thanks for the example. I think you probably used a very high order polynomial. Anyway, would the spline option be helpful? The Matlab help shows some situations where it does a good job. (Regarding your data as points for each time of observation.) You can place a knot at T=4 to hold the curve in place and with just "eyeball" it looks like an S-shape curve from 0--4, and another from 4 onwards. So probably a low order spline would work?
https://www.mathworks.com/help/matlab/ref/spline.html
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