A Generalized Closed-Form Solution for Magnetic Dipole Source Localization with Total-Field Magnetometers

Modern navigation, sensing, target-tracking, and identification applications require robust, simple, and noise-tolerant methods to reliably localize magnetic targets. Target localization is a non-linear inverse problem that typically requires highly sensitive sensors and dense measurements. Although modern, commercial high-sensitivity total-field magnetometers enable low-noise, compact arrays and very dense data sets, numerical inversion for a dipole’s location remains challenging and often provides non-unique solutions. This paper presents a detailed derivation of the novel closed-form solution for extracting the location of an unknown magnetic dipole target from data collected solely with an array of total-field magnetometers. The proposed solution relates the target location to magnetic data collected and array location, eliminating the need for other measured or a priori information such as local inclination or declination, sensor speed, or orientation. Simulations quantify numerical accuracy and demonstrate localization performance, and show that the localization performance remains reliable under a range of deployment formations, indicating that the approach is feasible for practical target localization scenarios.