Convex optimization of measurement allocation for magnetic tracking systems

Magnetic tracking is a popular technique that exploits static and low-frequency magnetic fields for positioning of quasi-stationary objects. One important system design aspect, which substantially influences the performance of the tracking system, is how to collect as much information as possible with a given number of measurements. In this work, we optimize the allocation of measurements given a large number of possible measurements of a generic magnetic tracking system that exploits time-division multiplexing. We exploit performance metrics based on the Fisher information matrix. In particular, the performance metrics measure worst-case or average performance in a measurement domain, i.e. the domain where the tracking is to be performed. An optimization problem with integer variables is formulated. By relaxing the constraint that the variables should be integer, a convex optimization problem is obtained. The two performance metrics are compared for several realistic measurement scenarios with planar transmitter constellations. The results show that the worst performance is obtained in the most distant parts of the measurement domain. Furthermore, measurement allocations optimized for worst-case performance require measurements in a larger area than measurement allocations optimized for average performance.