The current procedure to detect and identify unexploded ordnance (UXO) using electromagnetic induction (EMI) time-domain sensors is based on two steps. First, data are acquired over large areas in dynamic mode, and locations of interest are flagged based on measured field amplitudes. Second, sensors return to the flagged areas for more in-depth cued interrogation, providing high-quality data for subsequent identification and classification. Flagging based on field amplitude, however, has potential drawbacks: The magnetic field in the EMI regime exhibits a 1/R6 drop-off with range, and a deep UXO may not produce a strong response while still being potentially hazardous. To address this problem, we propose in this paper an inversion method based on Kalman and extended Kalman filters meant to do the following: 1) work with dynamic data; 2) provide both position and polarizability estimates; and 3) operate in real time (less than 100 ms in our case). Such full characterization of the target, albeit limited to within the 2.7-ms interrogation time window of the dynamic mode associated with the sensors studied here, provides useful information when deciding whether to continue with the cued interrogation. We validate the method for two popular EMI sensors, the second-version Man Portable Vector (MPV-II) and the MetalMapper, operated in very different settings: The MPV-II is used to interrogate a limited region of space atop a single target, whereas the MetalMapper is driven over long lanes along which several targets and clutter items are present.