# How to compare 3D accelerometer data in time series?

I'm trying to find similarity between two time series of 3D accelerometer data:

Just by looking at the graphs I can tell that red-circled parts looks pretty similar to me, but I would like to get algorithm telling me exactly how similar they are.

Suppose if I put left side on identical to itself it should yell a similarity of 100%.

There is also a time-shifting involved but I think if I could compare series of 10 points, I could simply compare another series by shifting it by one point and get a result that I want?

FYI: both data sets are recorded by trying to do the exact same action, i.e. lifting hand up and down and doing that at the same exact moment each time - start lifting at 0 seconds starting putting it down at 1 second. (If that's of any help)

• Have a look at the book "Information Retrieval for Music and Motion" by Meinhard Müller (springer.com/de/book/9783540740476). Especially the parts about Audio Indexing and Motion Templates should be very helpful. – LiKao Jun 22 '17 at 8:48

Other than correlation, you may also want to read about Dynamic Time Warping, DTW, which has the ability to ignore time delays and shifts in time. DTW Also, lowpass & highpass digital filters can help you to cancel out the very high frequency parts if you just care about low frequency segments, as shown in the picture.

A very simple attempt would be to correlate the recording with the live data. Provided that you properly normalise the result, you can get a similarity measure. Using correlation you would also circumvent the problem of small offsets that disturb other measures like the L2-norm. Maybe you can take a look: http://en.wikipedia.org/wiki/Cross-correlation

Here is another StackExchange question (with useful advice) on the problem of similarity measures for time series: https://quant.stackexchange.com/questions/848/time-series-similarity-measures

In my field we use a lot of machine learning techniques to do exactly this! When animals are equipped with accelerometers, we'd try to automatically assign the data to behaviours or activity types. Perhaps you could use some of the same techniques in your case? Here are two examples I was able to find that are open access, so you should be able to read the papers wherever you are.

https://movementecologyjournal.biomedcentral.com/articles/10.1186/s40462-014-0027-0

http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0088609

Good luck!!