An apparatus for estimating corresponding length parameter(s) and longitudinal position(s) within a sensing volume of one or more transversely localized electric current segments, the apparatus comprising: (a) a computer system comprising one or more electronic processors and one or more digital storage media coupled thereto; (b) one or more magnetic field sensors movable longitudinally along a lateral periphery of the sensing volume through which an electric current flows in a generally longitudinal direction (i) through a first electrically conductive body at least partly within the sensing volume, (ii) through a second electrically conductive body at least partly within the sensing volume, and (iii) across a gap between the first and second conductive bodies as the one or more transversely localized electric current segments; and (c) one or more sensor actuators arranged so as to move the one or more movable sensors longitudinally along the sensing volume in response to sensor position control signals generated by and transmitted from the computer system, (d) wherein the computer system is (i) operatively coupled to the one or more movable sensors and to the one or more sensor actuators, (ii) structured and connected so as to receive signals from the one or more sensor actuators indicative of corresponding longitudinal positions of the one or more movable sensors along the sensing volume and signals from the one or more movable sensors indicative of the corresponding magnetic field components measured by the one or more movable sensors, and (iii) structured, connected, and programmed so as to generate, and transmit to the one or more sensor actuators, the sensor position control signals, and (e) wherein the computer system is structured, connected, and programmed so as to calculate corresponding estimated length parameter(s) and longitudinal position(s) of the one or more current segments, that calculation being based at least in part on (i) magnetic field components measured at multiple different longitudinal positions along the sensing volume and (ii) for each of those measured magnetic field components, a corresponding longitudinal position along the sensing volume at which that magnetic field component was measured by a corresponding one of the one or more movable sensors. (a) a computer system comprising one or more electronic processors and one or more digital storage media coupled thereto; (b) one or more magnetic field sensors movable longitudinally along a lateral periphery of the sensing volume through which an electric current flows in a generally longitudinal direction (i) through a first electrically conductive body at least partly within the sensing volume, (ii) through a second electrically conductive body at least partly within the sensing volume, and (iii) across a gap between the first and second conductive bodies as the one or more transversely localized electric current segments; and (c) one or more sensor actuators arranged so as to move the one or more movable sensors longitudinally along the sensing volume in response to sensor position control signals generated by and transmitted from the computer system, (d) wherein the computer system is (i) operatively coupled to the one or more movable sensors and to the one or more sensor actuators, (ii) structured and connected so as to receive signals from the one or more sensor actuators indicative of corresponding longitudinal positions of the one or more movable sensors along the sensing volume and signals from the one or more movable sensors indicative of the corresponding magnetic field components measured by the one or more movable sensors, and (iii) structured, connected, and programmed so as to generate, and transmit to the one or more sensor actuators, the sensor position control signals, and (e) wherein the computer system is structured, connected, and programmed so as to calculate corresponding estimated length parameter(s) and longitudinal position(s) of the one or more current segments, that calculation being based at least in part on (i) magnetic field components measured at multiple different longitudinal positions along the sensing volume and (ii) for each of those measured magnetic field components, a corresponding longitudinal position along the sensing volume at which that magnetic field component was measured by a corresponding one of the one or more movable sensors.