Analytical and Experimental Investigation of a Tunnel Magnetoresistance Sensor Array System for Permanent Magnet Tracking

This paper presents the development of a five degree-of-freedom (DoF) cylindrical permanent magnet (PM) tracking system for estimating orientation and location. The system measures the effects of magnetic field changes caused by the PM through a tunnel magnetoresistance (TMR) sensor array Closed-form solutions for the magnetic flux densities are derived, and the Gaussian-Legendre quadrature method is applied to enhance computational efficiency. The Levenberg-Marquardt (LM) algorithm is employed to estimate location and orientation. These closed-form solutions were verified by finite element analysis software, and the LM methods were numerically validated. Experiments with a prototype confirm the analytical model’s accuracy in handling translational and angular displacements and demonstrate the validity of two cylindrical PMs’ location and orientation estimations.