Magnetic Particle Tracking for Granular Flows: A Semi-Algebraic Solution

Magnetic Particle Tracking (MPT) is a non-invasive measurement technique often used to study dense granular flow, particularly for fluidization and rotating drum equipment. The basic principle of MPT relies on tracking the movement of a single magnetic tracer by means of measuring the magnetic field strength with a set of sensors. The difference between the sensor measurements and an estimate of the magnetic field, based on the position and orientation of the magnet can be solved by means of minimization techniques. MPT is therefore uniquely suited for the study of non-spherical particles, since it provides additional information on the orientation of the tracer. The performance of the localization is largely dependent on the signal-to-noise ratio and so far mostly relies on nonlinear optimization techniques. The definition of the magnetic field generated by a dipole is highly nonlinear and has five degrees of freedom. Here we present a semi-algebraic solution by decoupling the estimation of the position and orientation in separate algebraic solutions. The two estimates are mutually dependent, necessitating an iterative approach between the two. The main benefits of this new approach are the speedup and robustness of the algorithm, which are much higher than for the classical constrained nonlinear optimization techniques. It therefor allows both for fast screening of the initial data obtained by MPT and potentially could help screen sensor layout designs. Further improvements on this technique have been made with help of vectorization of the problem.