To cope with the disadvantage that many receiving channels will be needed in traditional Long Baseline Interferometer (LBI) localization system, a novel emitter localization method using ambiguous phase difference measurements by a rotating LBI is proposed. High localization precision can be achieved in a short observing period with no localization ambiguity, and the amount of receiving channels can be reduced to two. To cope with the strong nonlinear problem caused by the phase difference ambiguity, a multiple hypothesis nonlinear least square localization algorithm is proposed. Flow of the algorithm is presented. The algorithm has some advantages, such as small computation burden and strong ability on resolving localization ambiguity. Moreover, localization precision of the algorithm can approach Cramer-Rao lower bound. Feasibility of the localization method and performance of the localization algorithm are validated through computer simulations.