# Fast Sound Source Localization Based on SRP-PHAT Using Density Peaks Clustering
## 1 Introduction  
Sound source localization is a technology to determine the position of the objective sound source by analyzing sound signals and has been applied in many areas, such as speaker localization in teleconferencing, the noise testing of wind turbines, sound discrimination of robots, car whistle identification, etc. [1, 2, 3, 4, 5, 6]. The existing sound source localization methods can be divided into three categories [7, 8, 9, 10, 11]: Time delay estimation (TDE)-based two-step localization methods, methods based on high-resolution spectral estimation, and beamforming methods based on the maximum steered response power. The TDE based two-step location methods first evaluate the time difference of the sound arrival at different elements of the microphone array and then identify the sound source according to the geometry configuration of the microphone array. These methods have simple principles and high efficiency; however, the TDE performance drops markedly under relatively heavy noise or reverberation. Therefore, these methods are not applicable in scenarios with a low signal-to-noise ratio (SNR) or high reverberation. In the methods based on high-resolution spectral estimation, a covariance matrix derived from the received signals is needed, which is estimated under the assumption that the signal and noise are stationary. However, such a condition can be hardly satisfied for non-stationary sound signals. In 2000, [PERSON] proposed a new approach of sound source localization, i.e., steered response power-phase transform (SRP-PHAT) [12]. The new approach combines the robustness and short-time analysis characteristics of the steered response power methodwith the advantage of the phase transformation method in time delay estimation. Hence, SRP-PHAT features robustness against noise and reverberation. However, SRP-PHAT has heavy computation due to the grid search scheme, which limits its application in real-time situations. Since the SRP-PHAT algorithm was proposed, various improved algorithms have been published to reduce the computational load. Based on the fact that the time difference of arrival (TDOA) of two close candidates in space may be the same in the discrete-time domain, [PERSON] et al. [13] proposed the classification of points with the same TDOA into one class, to store them in an offline table, and then to search only the representative points of all classes to determine the global maximum value. [PERSON] et al. [14] proposed a two-level search space clustering sound source localization method (TL-SSC) based on the characteristic that the output powers at the searched grid points are close when the phase difference is within \(2\pi/5\). [PERSON] et al. [15] took advantage of the similarity of the TDOA vectors in adjacent regions and developed a fast SRP-PHAT sound source localization algorithm based on a cluster search. [PERSON] et al. [16], [PERSON] et al. [17; 18], [PERSON] et al. [19], [PERSON] et al. [20], and [PERSON] et al. [21] did similar work. Although these suggested methods do improve SRP-PHAT for specific situations, they ask for either strict conditions or complicated computation. Evidently, it is still a problem for SRP-PHAT to simplify the computation while maintaining the robustness. An improved procedure called ODB-SRP-PHAT was put forward by the authors to reduce the heavy computational load of SRP-PHAT. Considering the different probability of each candidate sound source in the space to be searched, all positions of possible sound sources were located to build an ODB in advance. Based on the ODB, a real-time search scheme was laid down for the search space. This paper is divided into seven sections. In the second and third sections, the preprocessing of sound signal and the principle of SRP-PHAT were introduced respectively. The fourth section proposed the improved procedure, i.e., ODB-SRP-PHAT. Simulations were implemented to verify the efficiency of ODB-SRP-PHAT as shown in the fifth section.