Nonintrusive rigid body tracking technique for dry particulate flows. Part I. Theoretical aspects

Abstract

A unique system to nonintrusively track a particle in three dimensions is presented. It is based on the principle of magnetic induction coupling and consists of small transmitters mounted inside the particle being tracked, and a set of receiving antennae surrounding the experimental apparatus. In Part I of the sequence of two papers, the focus is on the theoretical aspects, in particular, on developing a computational technique to solve the inverse problem, i.e., find the three-dimensional position as well as orientation of the particle from the voltages induced in the antennae. The computational technique is based on the Levenberg–Marquardt algorithm, along with a scheme for providing good initializations. Through simulated experiments that include various levels of added noise in the voltage readings, the success of this algorithm is demonstrated and the feasibility of the overall technique is established. It is also shown that a system with three mutually orthogonal transmitters provides accurate results even with the noise in the voltage data. Although this system is intended for use in experimental studies of dry granular flows, it has wide applicability due to its nonintrusive nature, and is particularly useful when optical tracking techniques are not feasible.