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 in- formation. In this paper, we contribute a method to ana- lytically 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 inde- pendently) 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 and show an im- provement in terms of various signal distance metrics when comparing the three axes before and after derotation.

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