Consider a sensor measurement f that varies with both temperature T and the properties of the fluid being measured. The temperature changes through each day and the fluid properties can be assumed to vary less frequently. If I cross plot the data in Excel then by eye I can very easily draw a straight line through some points and translate that line horizontally and "voila" that same line fits through other clusters of plots. So if that line has slope -1/a then all I need to do instead of plotting f versus time I actually plot f + a T versus time I get a curve which does not have the temperature dependence and is now indicative of fluid property. Cool.
So my question is how to automate this extraction of a. My plan today is to set objective function as the L1 norm of the derivative of the time series and minimize over a as that might give a time series of many points with almost zero derivative and a few jump discontinuities where it decides the fluid has changed [as opposed to an L2 that would smear everything out].
But my thoughts are that this feature extraction is likely already covered in some text book somewhere and what I am really missing is the better vocabulary to look it up :-)
Any suggestions? Thanks