This thesis proposes two acoustic localisation techniques that are accurate in Non-Line-of-Sight (NLoS) conditions and system implementation of the proposed techniques. Such conditions can cause positive bias errors, namely NLoS errors, in the measured Time-of-Arrivals (ToAs) of first-arrival signals received by microphones and thus reduce the positioning accuracy. The primary issue of the thesis is to precisely estimate and correct the NLoS errors by modelling the received first-arrival signals. The first proposed technique uses multiple on-ground microphones to locate a sound source. The proposed technique approximately estimates and corrects the NLoS errors based on an initial guess of the sound source position and a map. The localisation is then achieved by iteratively correcting the ToAs and updating the sound source location. The strength of the proposed technique is that its accuracy is not notably affected by small or known obstacles. The proposed technique is implemented into two localisation systems of controlled and uncontrolled sound sources. The performance of the proposed technique is investigated by its comparison with three other time-based localisation techniques in series of experiments and simulations, showing at least 10% improvement by the proposed technique under various background noise levels. The second proposed technique localises a sound source using a single on-ground microphone subject to an assumption of a single diffraction in the first-arrival signal. To predict the angular and radial coordinates of the sound source relative to the diffraction point, a new magnitude delay frequency profile is proposed. The profile can be estimated by applying the uniform geometrical theory of diffraction and be extracted from measured signals using a derived formulation. Similar to the first technique, the second proposed technique estimates the measured delay of the first-arrival signal for computing the radial coordinate. The angular coordinate is then obtained by matching the estimated and measured profiles at the measured delay. A key achievement of the second proposed technique is enabling NLoS localisation using only one microphone without any time-consuming pre-measurement. This technique is implemented into a localisation system of a controlled sound source and validated experimentally with three different sound sources and under two background noise levels.