In an industrial installation, there is a pipe containing a continuous stream of product A.
The temperature of product A is measured at sampling point 1, every hour.
It is also measured a bit downstream, at sampling point 2, every eight hours.
It is comparable to a water pipe with two thermometers a few hundred meters apart.
Continuous sensors would record the following trends. I have marked with vertical bars the samples taken.
The sampling times very rarely match.
Due to this, there may never be, for the same wave, repeated measurements.
1 2 ===|=======|= -> A A A -> =============
With several years of data for both measurements, I would like to determine the time product A takes to go from 1 to 2. The flow rate is assumed to be constant, but is not measured.
After reading a bit, it looks like correlation would be the right tool for the job, but it requires having datapoints for the same times.
That would require either downsampling the data from 1 a lot, or interpolate more data from 2, but both methods seem to be diminishing the quality of the data, and therefore of the end result.
Is cross-correlation the right tool for this job, or should I go an other way?