MATLAB: Fitting of raw data

Question

Hi All,

I would like to fit the data shown in the attached photo. The two plots are from two temperature sensors (resistance sensor) against time. From the figure, at one point, you can see the lines start to broaden. This happens due to high variation of the temperature (resistance of the sensor) at low temperatures. This broadening is actually a sin function variation with very small frequency 1.15Hz (0.0145 min). I would like to find the best fit or someway to find the average of these points to elimenate the broadening.

Thanks

Answer 1

You don't have any simple model that you can use, at least, you have not suggested any. And, even if somebody suggests using polyfit, DON'T BELIEVE THEM! A polynomial model will be poor here.

Therefore, you need to ue a spline model. A problem is the heteroscedasticity. (]Yes, it hurts even to try to type that word.) But I would suggest a simple set of weights that decrease linearly with time. So small weight means that you don't trust that point much. High weight means you think the point is likely to be accurate.

You have not included your actual data, only a picture. Else, I would show how to fit it using my SLM toolbox. But a wild guess as to the call would be...

W = 1.25*max(Time) - Time;
slm = slmengine(Time,SR,'knots',12,'increasing','on','weights',W,'plot','on');

If you don't want to see the curve fit plot, then don't turn it on. Note that you should ALWAYS plot your data, and the curve fit through it. Decide for yourself if the fit is adequate.

More knots will give you a better fit, but less smooth, chasing the bumps in the curve.

If you want it to follow those bumps in the top end, where the curve seems to jump down a little, then you can leave increasing to be 'off' (the default), or you can set a specific interval where it should only be on.

Find SLM for download (free of course) on the file exchange here:

https://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling

Note that SLM does use the optimization toolbox.

A simpler alternative to SLM would be to use a moving window average or moving median filter. Without the data, it is difficult to know how well it would work. And of course, you would need to choose the window size. A Savitsky-Golay filter might also be reasonable. The problem with any of the latter tools is the window length might need to vary with Time, so where it is more noisy, you need a wider window to smooth things out.