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The simultaneous detection and identification of multiple targets using electromagnetic induction (EMI) time-domain sensors remains a challenge due to the fast decay of the magnetic field with sensor-target distance. For example, the signal from a weak yet shallow target or clutter item can overshadow that from a much larger yet deeper unexploded ordnance (UXO), potentially resulting in erroneous localization and/or identification. We propose, in this paper, a method based on the Gauss-Newton algorithm for the inversion of multiple targets within the field of view of sensors operating at EMI frequencies (tens of hertz to a few hundred kilohertz). In order to minimize the number of unknowns to invert for, the polarizability tensor is written as a time-independent orientation matrix multiplied by a time-dependent diagonal intrinsic polarizability tensor. Similarly, position is supposed to be time independent so that both position and orientation angles are inverted only once using all time channels collected by the instrument. Moreover, using the dipole approximation, we are able to compute the Jacobian in closed form for instruments with either square or circular primary field coils, thus contributing to the speed of the algorithm. Validating results are shown based on the measurement data collected with two EMI sensors on various types of UXO.