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I need to calibrate physical devices to align their measurements to a common nominal base. Figure below depicts curves of measurements to be aligned.

devices differences

As it can be seen from the picture the difference is mainly in shifts on the x axis which I assumed to be locally linear.

I have attempted sampling a few points along the axis and searching for a linear shift minimizing RMSE between the curves.

This solution seemed to cause over-fitting, in most cases I got measured points $x_1 < x_2$ being "fixed" to $x_1^\prime , x_2^\prime$ correspondingly such that $x_2^\prime < x_1^\prime$ which seems very unreasonable. Also I have expected to identical directions of adjacent shifts, yet some have been shifted right while their immediate neighbors have been shifted left.

I was wondering what other methods I could use in order to solve this issue.

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  • $\begingroup$ This sounds very much like DTW. $\endgroup$
    – whuber
    Commented Jun 28, 2020 at 13:49
  • $\begingroup$ This seems very interesting thanks! Do you have experience with it on physical measures? Do you have a nice example were I can see it used? $\endgroup$
    – Port
    Commented Jun 28, 2020 at 14:25

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