Optimization of sensor positions in magnetic tracking

In recent years, magnetic tracking has been applied in many biomedical settings due to the transparency of the human body to low-frequency magnetic fields. One way to improve system performance and/or reduce system cost is to optimize the sensor positions of the tracking system. In this work, the sensor positions of a magnetic tracking system are optimized by exploiting an analytical model where the transmitting and sensing coils of the system are approximated by magnetic dipoles. In order to compare different sensor array layouts, two performance measures based on the Fisher information matrix are discussed and compared for the optimization of the sensor positions of a circular sensor array. Furthermore, the sensor positioning problem is formulated as an optimization problem which is cast as a sensor selection problem. The sensor selection problem is solved for a planar sensor array by the application of a convex relaxation. Several transmitter positions are considered and general results are established for the dependence of the optimal sensor positions on the transmitter’s position and orientation.