Abstract
In this paper, a fast method of estimating the position of a moving object for a magnetic motion capture system is presented. The system uses two quasi-uniform magnetic fields along the X-axis and the Z-axis and one gradient magnetic field having a null point at the origin. Each of these magnetic fields is produced sequentially by using two pairs of square coils wound along four edges of a cube where one pair is rotated through 90 degree from the other. A triaxial magnetometer is attached to the moving object to measure these magnetic field vectors. The position of the object is calculated from three scalar products among the measured magnetic field vectors. The calculation is done approximately by using a set of truncated Taylor serieses, where Wynn's vector epsilon-algorithm is used together to expand the area of convergence numerically. This method of calculation contains no iterative process and is much faster than the Gauss-Newton method. The position of the object is stably estimated by this method within a cubic area having an edge length of 60 percent of the side length of the coils. A prototype system using a triaxial Hall magnetometer was build. The experimental results show that the method works properly in a real system.
