Magnetic cubes-collocated coils as sensors for displacement positioning

We describe design and verification of a novel autonomous sensor system (Magnetic Cubes) for evaluating the distance between two points as well as the rotation matrix between the coordinate systems attached to the sensors. The system is based on two sensors, each comprising three orthogonal coils wound on foam cubes, and near-field coupling between the sensors, which operate the medium frequency band. Testing and verification of the designed system was done by performing various 2D and 3D movements, and comparing positions and orientations estimated by Magnetic Cubes with those measured by an optical motion capture system. In all cases, good agreement is obtained: the RMS error for the estimation of the distances between the cubes is less than 10 mm (less than 2%), while the RMS errors for the estimation of the Cartesian coordinates are less than 7%. The discrepancies between the results obtained from the two systems were also assessed by the Pearson correlation coefficient (greater than 0.9 for the Cartesian coordinates and greater than 0.99 for the distances between the cubes).