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This paper presents a non-line-of-sight (NLOS) localization technique and its system for a quiet and known environment that uses first-arrival low-frequency acoustic signals. The proposed technique first measures the time-of-arrivals (ToAs) of the first-arrival low-frequency sounds. The technique then estimates the location of a target by minimizing the differences between the measured ToAs and the corresponding ToAs estimated from the known map. The strength of the proposed technique is that the positioning accuracy is not corrupted by any small or known obstacle. The performance of the technique was investigated by its comparison to other techniques in both simulations and an experiment. The numerical results show successful localization of a target in various situations, demonstrating the efficacy of the technique and system as a feasible solution for NLOS mitigation.