A system for determining the position of a medical device having a sensor comprises a plurality of field radiators wherein each field radiator has a plurality of radiator elements. Each radiator element generates a magnetic field such that each magnetic field is distinct from one another due to the use of a different frequency through simultaneous energizing of the radiator elements. A signal processor is operatively connected to the field radiators and the sensor of the medical device for receiving a sensing signal from the sensor indicative of the magnetic field sensed at the sensor. The sensing signal defines a measured magnetic field at the sensor. The signal processor also has a desired range of accuracy for the system which is stored therein. The signal processor includes an initial position estimator for establishing an initial position estimate for the sensor; a magnetic field calculator for calculating the magnetic field at the initial position estimate; a steepest descent calculator for calculating a steepest descent of the calculated magnetic field to the measured magnetic field; and a new position estimate calculator for calculating a new position estimate of said sensor based on said steepest descent. The signal processor determines the position of the sensor when the new position estimate of the sensor is within the desired range of accuracy for the system. Alternative field radiator arrangements are also provided in conjunction with a novel algorithm utilizing a global convergent technique.