### A New Tracking System for Three Magnetic Objectives

Abstract

We have implemented a new noninvasive multiobjective tracking system, which can be used for localization of an endoscope and monitoring of heart valve prostheses and gastrointestinal transit of solid oral dosage forms or nutrients. The marker is modeled as a magnetic dipole, and the magnetic field at some point is regarded as summation of those from three dipoles. By minimizing the squared errors of magnetic field values between measurements and calculation using a hybrid of the particle swarm optimization (PSO) algorithm and the clone algorithm, an iterative result can be obtained, which is taken as the initial guess of the Levenberg-Marquardt (L-M) optimization method, and the first point can be determined. Subsequently, the previous computed point is used as the next initial guess of L-M algorithm, and the successive points are calculated. The tracking results demonstrate that the average position error for three objectives is 3.7 mm and the average orientation error is 1.8 degrees when the objectives move randomly in the space surrounded by the sensor array.