A Three-Dimensional Localization System Based on Magnetic Fields and Induction

This paper describes a system for three-dimensional position measurement using magnetic fields, and the principle of electromagnetic induction. The system is designed to determine the position and orientation of a receiver relative to a transmitter. Both consist of three orthogonal coils. The magnetic flux density of the transmitting coils is modeled using the dipole equation, and the induced voltage in the receiver coils is modeled with Faraday's law of induction. The resulting equations are solved by minimizing a cost function using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. The transmitter consists of three amplifiers to drive the transmitting coils. The induced voltages in the receiving coils are amplified using two amplifier stages; measured using an analog-to-digital converter, and the fast Fourier transform on a STM32 microcontroller In determining the range of the system, an error of less than 10 cm is achieved in a radius of 3 m. In real-time tests, the receiver moves along a given trajectory and computes its position every 0.7 s.