A new approach for locating an underground line described herein remains accurate in the face of bleedover by including both amplitude and phase from at least two magnetic field strength sensors in the measurement set. A numerical optimization step is introduced to deduce the positions and currents of each of several cables, of which one is the targeted cable and the others are termed bleedover cables. Furthermore, some embodiments of the method accounts for practical problems that exist in the field that relate to reliable estimation of cable positions, like the phase transfer function between transmitter and receiver, the estimation of confidence bounds for each estimate, and the rejection of false positive locates due to the presence of noise and interference.