Closed-Form Position and Orientation Estimation for a Three-Axis Electromagnetic Tracking System

Electromagnetic tracking systems are a practical and cost-effective alternative to vision-based systems for virtual reality applications, providing a large working range without suffering from the line-of-sight problem. We present closed-form formulas for the optimal least-squares position and orientation estimates of an electromagnetic tracking system. A generic system consisting of three-axis sensor and generator coils-the coils need not be orthogonal-is considered, and a least-squares objective function for tracking is formulated. The optimal solution is then derived in closed form. Experimental validation via numerical simulations and hardware experiments confirm that our least-squares tracking algorithm can run in real time, and that tracking performance is more robust to measurement errors than existing methods.