Purpose: 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.

		  Approach: 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.

		  Practical implications: After derotaion, 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.

		  Findings: 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 improved EER of 0.16
		  (when using derotation) over an EER of 0.18 (when not using
		  derotation).

		  Originality: Without derotating time series, angular
		  information cannot be used for deciding if devices have
		  been moved together. To the best of our knowledge, this is
		  the first analytic approach to find the optimal derotation
		  of the coordinate systems, given only the two 3D time
		  acceleration series of devices (supposedly) moved together.
		  It can be used as the basis for further research on
		  improved classification towards acceleration-based device
		  pairing.<br>
<br><pre>@article{Mayrhofer_15_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},
  journal = {International Journal of Pervasive Computing and
  		  Communications (IJPCC)},
  year = {2015},
  volume = {11},
  number = {4},
  pages = {454--466},
  month = oct,
  issn = {1742-7371},
  note = {A preliminary version of this work was published in iiWAS
  		  2014.},
  doi = {10.1108/IJPCC-08-2015-0031},
  keywords = {mobile devices, acceleration time series, quaternion
  		  derotation, device authentication},
  pubtype = {article},
  url = {https://www.emeraldinsight.com/doi/abs/10.1108/IJPCC-08-2015-0031}
}
</pre>