Detecting if two or multiple devices are moved together is
		  an interesting problem for different applications. However,
		  these devices may be aligned arbitrarily with regards to
		  each other, and the three dimensions sampled by their
		  respective local accelerometers can therefore not be
		  directly compared. The typical approach is to ignore all
		  angular components and only compare overall acceleration
		  magnitudes – with the obvious disadvantage of discarding
		  potentially useful information. In this paper, we
		  contribute a method to analytically determine relative
		  spatial alignment of two devices based on their
		  acceleration time series. Our method uses quaternions to
		  compute the optimal rotation with regards to minimizing the
		  mean squared error. The implication is that the reference
		  system of one device can be (locally and independently)
		  aligned with the other, and thus that all three dimensions
		  can consequently be compared for more accurate
		  classification. Based on real-world experimental data from
		  smart phones and smart watches shaken together, we
		  demonstrate the effectiveness of our method with a
		  magnitude squared coherence metric, for which we show an
		  im- proved EER of 0.16 (when using derotation) over an EER
		  of 0.18 (when not using derotation).<br>
<br><pre>@inproceedings{Mayrhofer_14_OptimalDerotationShared,
  author = {Mayrhofer, Ren\'e and Hlavacs, Helmut and Findling, Rainhard Dieter},
  title = {Optimal Derotation of Shared Acceleration Time Series by
  		  Determining Relative Spatial Alignment},
  booktitle = {Proc. {iiWAS} 2014: 16th International Conference on
  		  Information Integration and Web-based Applications \&
  		  Services},
  year = {2014},
  pages = {71--78},
  address = {New York, NY, USA},
  month = dec,
  publisher = {ACM Press},
  note = { {Winner of the iiWAS 2014 best paper award}},
  booktitle_short = {Proc. {iiWAS} 2014},
  day = {4--6},
  documenturl = {http://www.mayrhofer.eu.org/downloads/publications/iiWAS2014-Quaternion-Derotation.pdf},
  doi = {10.1145/2684200.2687876},
  eventurl = {http://www.iiwas.org/conferences/iiwas2014/},
  isbn = {978-1-4503-3001-5},
  keywords = {Accelerometer time series; spatial alignment; quaternion
  		  rotation},
  location = {Hanoi, Vietnam},
  pubtype = {conference},
  url = {https://dl.acm.org/citation.cfm?id=2687876}
}
</pre>