A system, based on the principle of magnetic induction coupling, to track a particle nonintrusively in three dimensions is presented. It 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 of finding the three-dimensional position as well as orientation of the particle from the voltages induced in the antennae. In Part II the focus is on the actual system development, including all hardware and data acquisition aspects. The results presented here are comprehensive, as they include details of hardware/electronics, comparison of induced voltage model and actual measurements, and a set of actual tracking results. Through test experiments that include a variety of real-time trajectories, this system is tested and its success is demonstrated. Results of real trajectories of a single ball rising in a mass of other spheres in a vibrated bed are also shown. 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. ©1998 American Institute of Physics.