Code for derotating pairs of multi-dimensional (e.g. 3D) acceleration timeseries so that similarity between individual axes-pairs of timeseries is maximized
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This repository accumulates code for derotating pairs of multi-dimensional (e.g. 3D) acceleration timeseries, so that similarity between individual axes-pairs of timeseries is maximized. Doing so can be especially useful if the timeseries have been recorded by sensors of which the spatial alignment is unkown. Instead of comparing timeseries magnitudes with derotation the individual axes of the timeseries can be compared - which still contain changes in rotation during recording (but not their absolute spatial alignment).

An example when derotation can be useful would be: two 3D acceleration sensors record the same acceleration while being placed slightly apart from each other. Their exact spatial alignment is unkown, so they are rotated arbitrarily against each other on all axes. One possibility to compare their timeseries recordings is to calculate and compare their acceleration magnitudes, as this removes sensor rotation completely. Unfortunately, this includes the initial sensor rotation as well as changes in rotation while recording. In order to not discard changes in rotation during recording, instead of calculating timeseries magnitudes, the individual axes of timeseries can be derotated to maximize their similarity* while keeping their orthogonality (means the magnitude keeps uneffected by derotation). Maximizing similarity between timeseries is done by calculating the mean squared error per pair of axes. Using derotated, individual axes of acceleration timeseries opens new ways of comparisions, as changes in rotation are still contained the timeseries, which the absolute spatial alignment of the sensor is discarded with derotation.

For details see http://usmile.at/ or the corresponding publication:

Mayrhofer, R.; Hlavacs, H. & Findling, R. D. Optimal Derotation of Shared Acceleration Time Series by Determining Relative Spatial Alignment. Proc. iiWAS 2014: 16th International Conference on Information Integration and Web-based Applications & Services, ACM, 2014