A Fast and Robust Magnetic Localization Technique Based on Elimination of the Orientation Variables From the Optimization

Abstract

Passive magnetic localization is a wireless motion tracking method that can determine position and orientation of objects with embedded magnets. The magnetic field around the magnetic object can be detected using magnetometers. Afterward, using an optimization algorithm, the difference between the measured and calculated magnetic field (from the mathematical model of the magnetic field produced around the magnetic object) is minimized. However, using numerical optimization methods faces two main challenges: low computation speed to reach desirable accuracy and convergence to a local minimum. In this paper, we propose a method to analytically calculate the magnet’s orientation in terms of the magnet’s position. Therefore, the optimization problem is solved only to find the position unknowns. The experimental results demonstrate that the average position error is 2.0 mm and orientation error is 2.3° for a cube magnet with a 5 mm edge length. According to the experiments, by employing this method, computation speed becomes 2.1 times faster with respect to the conventional method. Furthermore, in contrast to the conventional method, the proposed technique is robust with respect to the initial conditions and the technique always converges towards the global minimum and gives the correct solution regardless of the initial guess.