We characterize the performance of a system based on a magnetoresistor array. This instrument is developed to map the magnetic field, and to track a dipolar magnetic source in the presence of a static homogeneous field. The position and orientation of the magnetic source with respect to the sensor frame is retrieved together with the orientation of the frame with respect to the environmental field. A nonlinear best-fit procedure is used, and its precision, time performance, and reliability are analyzed. This analysis is performed in view of the practical application for which the system is designed that is an eye-tracking diagnostics and rehabilitative tool for medical purposes, which require high speed ($\ge 100$~Sa/s) and sub-millimetric spatial resolution. A throughout investigation on the results makes it possible to list several observations, suggestions, and hints, which will be useful in the design of similar setups.