Recursive Bayesian Method for Magnetic Dipole Tracking With a Tensor Gradiometer

Previous magnetic dipole localization algorithms using gradient data attempt to find the position of the magnetic source at the measurement time only. Based on the direct inversion of the magnetic gradient tensor, these methods provide results that can be highly sensitive to temporal noise in data. To avoid a temporally scattered solution, a recursive approach is proposed that is promising for estimating the trajectory and the magnetic moment components of a target modeled as a magnetic dipole source using data collected with a gradiometer. In this study, the determination of target position, magnetic moment, and velocity is formulated as a Bayesian estimation problem for dynamic systems, which could be solved using a sequential Monte Carlo based approach known as the "particle filter." This filter represents the posterior distribution of the state variables by a system of particles which evolve and adapt recursively as new information becomes available. In addition to the conventional particle filter, the proposed tracking and classification algorithm uses the unscented Kalman filter (UKF) to generate the prior distribution of the unknown parameters. The proposed method is then demonstrated by applying it to real data collected when an automobile was passing by a gradiometer either on a straight or a curved track. The results indicate that the recursive method is less sensitive to noise than the direct inversion solution, even if not all the components of the gradient tensor were used.