Recent localization systems do not effectively estimate the location of a target in the presence of dynamic obstacles. This paper presents nonline- of-sight (NLOS) localization technique and system for a quiet and known environment based on the measured time-of-arrival (ToA) of first arrival low-frequency acoustic signals. The true ToA is estimated using the modelled map, and then compared with the detected ToA to update the target position. The strength of the proposed technique is that the positioning accuracy is not corrupted by small or known obstacles. The performance of the system was investigated using different techniques and experimental setups. The numerical results show successful localization of a target in various situations, demonstrating the effectiveness of the technique and the system as a possible solution to the NLOS localization problem.