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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.

kjetil b halvorsen
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Port
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  • This sounds very much like [DTW](https://stats.stackexchange.com/questions/22209). – whuber Jun 28 '20 at 13:49
  • 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? – Port Jun 28 '20 at 14:25

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