# Deep Learning-Based Low-Frequency Passive Acoustic Source Localization
###### Abstract  
This paper develops benchmark cases for low- and very-low-frequency passive acoustic source localization (ASL) using synthetic data. These cases can be potentially applied to the detection of turbulence-generated low-frequency acoustic emissions in the atmosphere. A deep learning approach is used as an alternative to conventional beamforming, which performs poorly under these conditions. The cases, which include two- and three-dimensional ASL, use a shallow and inexpensive convolutional neural network (CNN) with an appropriate input feature to optimize the source localization. CNNs are trained on a limited dataset to highlight the computational tractability and viability of the low-frequency ASL approach. Despite the modest training sets and computational expense, detection accuracies of at least 80% and far superior performance compared with beamforming are achieved--a result that can be improved with more data, training, and deeper networks. These benchmark cases offer well-defined and repeatable representative problems for comparison and further development of deep learning-based low-frequency ASL. a pacs: 42.30. Machine learning (ML), and deep learning (DL) in particular, have shown great promise in the field of acoustics [20; 21; 22]. Deep learning algorithms involve the use of neural networks that process data in multiple layers to perform regression, classification, and many other such tasks. Despite the limitations of these methods, such as requiring large numbers of data and not being physically intuitive, the ability of deep learning algorithms to extract features from data in any shape or form provides much scope for their application in ASL. Thus, the goal of this paper is to build deep learning models for low-frequency ASL as an alternative to beamforming. A general study of the literature on deep learning-based ASL offers insights into the different kinds of input features and network architectures used, which can then be applied to low-frequency source localization. Most research in deep learning-based ASL is focused on the localization of speech signals. While most works process the acoustic data before feeding them to a network, [PERSON] et al. [23] were the first to use raw audio signals as input to a convolutional neural network (CNN) [24] to predict the position of the three-dimensional source. [PERSON] and [PERSON] [25] and [PERSON] et al. [26] used the phase component of the short-time Fourier transform (STFT) and Generalized Cross-Correlation with Phase Transform (GCC-PHAT), respectively, as input for estimating the direction of arrival (DoA) of speech signals. Studies focusing on a source frequency range such as [PERSON] and [PERSON] [27] simulated a phased microphone array and monopole sources at high frequencies (3000-8000 Hz) on a scanning plane, and used the cross-spectral matrix (CSM) as input to a CNN for localization of these sources. They were able to demonstrate excellent spatial resolution, comparable to that of DAMAS, and much better than conventional beamforming. However, they did not address the challenges at lower source frequencies. [PERSON] et al. [18] employed a similar setup and methodology, but focused on a wider source frequency range of 200-20,000 Hz and were able to predict the source distribution, even for low frequencies. However, they used a densely connected convolutional network (DenseNet) [28] that required large numbers of data and a large amount of memory for training. [PERSON] et al. [29] carried out ocean source localization in the frequency range of 100-200 Hz using a single hydrophone and the discrete Fourier transform of the raw pressure data. Fifty-layer residual networks (ResNet-50), which also needed a significant number of training data, were separately trained to determine the range and depth of the source. The literature has broadly explored the viability of deep learning techniques for low-frequency acoustic source localization. Most of it, however, does not focus exclusively on low-frequency sound, and infrasound (below 20 Hz).