# Minimum Variance Distortionless Response--Hanbury Brown and Twiss Sound Source Localization
## 1 Introduction  
In recent years, with the continuous development of sound source localization technology and artificial intelligence, microphone array-based sound source localization technology [1] has found important applications in industrial inspection [2; 3; 4], military detection [5; 6; 7; 8], human-computer interaction [9; 10], video conferencing systems [11; 12], and other fields. However, in the face of increasingly complex real-world environments, there is a higher demand for sound source localization algorithms to accurately locate sound sources under low signal-to-noise ratios (SNRs). Sound source localization under complex acoustic conditions puts greater emphasis on the anti-interference capabilities of sound source localization algorithms, and the accuracy of sound source localization is an important indicator of the performance of such algorithms. Currently, traditional sound source localization methods under low SNR include high-resolution spectral estimation [13], time delay estimation based on time difference of arrival (TDOA) [14; 15], and controlled beamforming [16]. The high-resolution spectrum estimation method calculates the correlation matrix of each element to obtain subspaces under different parameters, thereby obtaining the orientation information of the sound source. [PERSON] [17] modified the classical MUSIC algorithm by absorbing the Jordon normalization matrix in the covariance matrix to reconstruct the data. With this modification, even coherent sources can be accurately estimated in low-SNR environments. However, due to the short duration and smoothnature of the sound signal, this method struggles to meet the high-resolution requirements for estimation accuracy and has limited practicality. The time delay difference localization method [18; 19] is computationally efficient and easy to implement, but the accuracy of the algorithm is highly dependent on the topology of the microphone array, and the accuracy of time delay estimation affects the position estimation. The controllable beamforming method [20; 21; 22; 23], with the SRP (steered response power) algorithm being the most famous example [24; 25], is based on the idea of weighting the output of each element and summing them together while directing the array beam to the same direction at the same time to give the direction where the expected signal achieves the maximum output power, thus achieving sound source localization. However, this method has a large computational cost and is not suitable for real-time localization. After considering the advantages and disadvantages of traditional positioning methods, it is clear that a single traditional algorithm is no longer suitable for complex positioning requirements. Therefore, in 2019, [PERSON] et al. [26] introduced the HBT [27] interference principle from optics into the acoustic field and proposed a positioning method based on HBT interference in the acoustic field. This method analyzes the coherence of the signal to eliminate the influence of noise on passive target positioning, and it calculates the normalized correlation function to describe the coherence of the field, thus achieving accurate positioning of weak target sound sources. This method combines the advantages of time-delay estimation and controllable beamforming, solving some of the problems associated with traditional positioning methods. However, the positioning accuracy of this method still needs to be further improved under low-SNR conditions. Based on the HBT principle and combining it with the MVDR algorithm [28; 29], this paper achieves accurate positioning of sound source targets under low-SNR conditions without changing the geometry of the array. This paper first focuses on narrowband signals and calculates the inverse of the autocorrelation matrix of the preprocessed sound signal.