Non-linear Kalman filters for tracking a magnetic dipole

The problem of tracking a vessel modelled at a distance by an equivalent magnetic dipole is investigated. Tracking a magnetic dipole from magnetic field measurements is a complex non-linear problem. The determination of target position, velocity and magnetic moment is formulated as an optimal stochastic estimation problem, which could be solved using the non-linear Kalman filtering methods. The estimation performance of the following non-linear filters is compared: the extended Kalman filter (EKF), two Kalman filters based on the Stirling’s interpolation formula, and the unscented Kalman filter (UKF). To evaluate the algorithms, the theoretical Cramer-Rao lower bounds (CRLB) of estimation error are derived for this problem. Results obtained on simulated track show that the target position, velocity and moment can be accurately determined. It is shown that the unscented Kalman filter (UKF) is the best non-linear Kalman filter for this application.