Deep Learning-Based Sound Source Localization: A Review

Abstract

As a fundamental technology in environmental perception, sound source localization (SSL) plays a critical role in public safety, marine exploration, and smart home systems. However, traditional methods such as beamforming and time-delay estimation rely on manually designed physical models and idealized assumptions, which struggle to meet practical demands in dynamic and complex scenarios. Recent advancements in deep learning have revolutionized SSL by leveraging its end-to-end feature adaptability, cross-scenario generalization capabilities, and data-driven modeling, significantly enhancing localization robustness and accuracy in challenging environments. This review systematically examines the progress of deep learning-based SSL across three critical domains: marine environments, indoor reverberant spaces, and unmanned aerial vehicle (UAV) monitoring. In marine scenarios, complex-valued convolutional networks combined with adversarial transfer learning mitigate environmental mismatch and multipath interference through phase information fusion and domain adaptation strategies. For indoor high-reverberation conditions, attention mechanisms and multimodal fusion architectures achieve precise localization under low signal-to-noise ratios by adaptively weighting critical acoustic features. In UAV surveillance, lightweight models integrated with spatiotemporal Transformers address dynamic modeling of non-stationary noise spectra and edge computing efficiency constraints. Despite these advancements, current approaches face three core challenges: the insufficient integration of physical principles, prohibitive data annotation costs, and the trade-off between real-time performance and accuracy. Future research should prioritize physics-informed modeling to embed acoustic propagation mechanisms, unsupervised domain adaptation to reduce reliance on labeled data, and sensor-algorithm co-design to optimize hardware-software synergy. These directions aim to propel SSL toward intelligent systems characterized by high precision, strong robustness, and low power consumption. This work provides both theoretical foundations and technical references for algorithm selection and practical implementation in complex real-world scenarios.

1. Introduction

Advances in Deep Learning for Sound Source Localization: Challenges and Opportunities. As a core technology for environmental sensing, sound source localization (SSL) provides indispensable capabilities across public security, marine exploration [1,2], smart home interaction [3], and airspace surveillance [4]. In security systems, precise SSL enables rapid localization of emergency events. For marine monitoring, its accuracy in underwater target detection directly impacts national security and ecological studies. In smart homes, SSL-based voice interfaces must overcome complex reverberation to enhance user experience. However, traditional methods—including beamforming [5], time-delay estimation [6], and MUSIC algorithm [7]—rely on manually designed physical models and idealized assumptions, proving inadequate for dynamic real-world scenarios. Specific challenges include spatiotemporal heterogeneity of sound speed profiles in marine environments, high reverberation with a low signal-to-noise ratio (SNR) in indoor spaces, and non-stationary UAV noise characteristics [8,9], which significantly degrade traditional localization accuracy or cause complete failure.

Recent breakthroughs in deep learning have revolutionized SSL through three key advantages: end-to-end feature adaptability, data-driven modeling scalability, and cross-scenario generalization. In marine applications, complex-valued convolutional networks achieve centimeter-level precision under a low SNR via phase information fusion. For indoor reverberant environments, attention mechanisms combined with multimodal architectures suppress multi-source interference through adaptive acoustic feature weighting. UAV monitoring systems integrate lightweight models with spatio-temporal Transformers to attain sub-meter accuracy at −10 dB SNR while addressing edge computing constraints. Nevertheless, three critical challenges persist: the insufficient integration of environmental physics limiting model generalization [10]; the prohibitive costs of data annotation hindering unsupervised/few-shot learning [11]; unresolved trade-offs between real-time processing and accuracy in edge deployments [12].

The German Aerospace Center (DLR) exemplifies cutting-edge applications through two initiatives:

Marine Systems: The DLR Institute for the Protection of Maritime Infrastructures developed Autonomous Underwater Vehicles (AUVs) equipped with dual-frequency side-scan sonars for seabed mapping and multibeam echosounders for bathymetry. Integrated with terrestrial and aerial surveillance networks, these systems enable the near-real-time detection of mobile underwater targets.

Aerial Systems: At the National Experimental Test Center for Unmanned Aircraft Systems in Cochstedt, the DLR tests UAV platforms for medical supply delivery to remote areas, disaster relief, agricultural monitoring, and industrial logistics. These applications underscore the urgent need for robust UAV detection and localization technologies (see Figure 1).

This comprehensive review structures its analysis as follows:

Section 2 categorizes technical challenges and deep learning solutions across three domains: marine [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27] (e.g., phase-sensitive networks), indoor [26,28,29,30,31,32,33,34,35] (e.g., attention-based fusion), and UAV [36,37,38,39,40,41,42,43,44] (e.g., spatiotemporal Transformers).

Section 3 elucidates fundamental SSL principles, detailing feature extraction (time–frequency transforms, phase-difference fusion) and model architectures (CNN, LSTM, GFGRU, U-Net, GAN) with mathematical formulations and schematic diagrams.

Section 4 critically evaluates method trade-offs in computational efficiency, generalization capacity, and data dependency through comparative analysis.

Section 5 outlines future directions, proposing physics-informed modeling, multimodal edge intelligence, and ethical compliance frameworks to advance SSL toward high-precision, robust, and energy-efficient intelligent systems.

2. Classification of Sound Source Localization

2.1. Marine Sound Source Localization

Marine sound source localization (SSL) is crucial in various fields. Traditional methods like MFP [45,46,47] depend on precise models but face challenges from environmental uncertainties, especially mismatch issues due to ocean parameter variations. Improved methods like environment-focused MFP [48,49,50] and Bayesian MFP [51,52] address this but raise computational load problems for real-time processing.

In the domain of marine sound source localization, deep learning approaches have remarkably improved localization performance in complex environments through data-driven modeling. Van Komen et al. proposed a CNN-based algorithm for simultaneous seabed type identification and long-range deep-sea localization, achieving a distance prediction error of <0.5 km within a 5 km range [13]. Subsequently, Liu et al. integrated a CNN with beamforming, reducing localization errors by 32% in shallow-water scenarios (see Figure 2) in the South China Sea [14]. Qian et al. employed a U-Net-based multi-task learning framework to compress features, enabling multi-source localization accuracy approaching that of SBL in deep-sea environments with internal waves [15]. Qu et al. fused CNN and Transformer architectures, decreasing underwater ranging errors by 35% compared to traditional methods [16]. Ashok et al. proposed Audio Perspective Regional CNN using depthwise separable convolution, focusing on key underwater acoustic signal features via regional extraction [17].

Nie et al. adopted a two-stage “beam network” combined with data augmentation, reducing the angular root mean square error (RMSE) to 0.5° for direction-of-arrival (DOA) estimation in marine environments [18]. Liu et al. enhanced deep-sea localization robustness via unsupervised domain adaptation, maintaining errors < 200 m under 20° array tilt [19]. Wang et al. leveraged adversarial transfer learning with generative adversarial networks for horizontal line array localization, improving transfer accuracy by 18% to 92.7% [20]. Additionally, Liu et al. optimized shallow-water geoacoustic inversion using CNN-based processing of multi-range vertical array data [21], while Niu et al. employed a 50-layer residual network (ResNet50) with a two-stage training strategy, achieving localization errors < 1 km in the Yellow Sea [22]. Qu et al. demonstrated 90.5% accuracy with a 3D residual CNN under 29% sound speed mismatch [23], and Zhai et al. combined computational mechanics and deep learning for precise shallow-water source localization [24]. Wang et al. fused multi-spectral transformation with CNN, reducing deep-sea depth estimation errors to 0.8 m [25], while Long et al. outperformed traditional matched-field processing via unsupervised domain adaptation in few-shot scenarios [26]. Yang et al. further improved deep-sea low-SNR localization by leveraging phase information through complex-valued convolutional networks [27]. Liu et al. proposed a CNN-based method for processing multi-range vertical array data to estimate shallow water geoacoustic parameters [21].

Collectively, these studies address marine challenges such as sound speed mismatch and multipath interference through CNN variants, transfer learning, and multimodal fusion, achieving 15–60% reductions in localization errors compared to traditional methods (see

Table 1. Classification of deep learning methods in marine environments.

Reference	Methods	Performance	Dataset	Scenes
[13]	CNN	Seabed type prediction accurate, range error < 0.5 km (>5 km)	Simulated data + field data	Long-range deep-sea localization
[14]	U-Net + CBAM	Localization error ↓ 32%	Simulated data + South China Sea field data	Shallow-sea source localization in the South China Sea
[15]	GFGRU	Multi-source error near SBL, better than Bartlett/FNN	Simulated data + South China Sea field data	Deep-sea source localization
[16]	CNN + Transformer	Range error ↓ 35% vs. FNN/pure CNN	Field data	Underwater source ranging
[17]	APRCNN	98.4% accuracy at 0 dB SNR	Field data	Underwater acoustic target localization
[18]	CNN	Angular RMSE 0.5°, ↓ 58% vs. traditional methods	Simulated data + field data	DOA estimation in marine environments
[19]	UDA + SOO	Error < 200 m at 20° array tilt	Simulated data + South China Sea field data	Deep-sea source localization
[20]	GAN	Transfer accuracy 92.7%, ↑ 18%	Simulated data + field data	Horizontal line array source localization
[21]	MRP-CNN	Robust geoacoustic estimation, localization performance ↑	Simulated data + East China Sea field data	Shallow-water geoacoustic inversion and localization
[22]	ResNet50	Localization error < 1 km	Simulated data + Yellow Sea field data	Source localization in the Yellow Sea
[23]	3D ResCNN	Accuracy of 90.5% at 29% sound speed mismatch	Simulated data	Deep-sea source localization
[24]	ConvNeXt	Prediction MSE 0.12, localization error < 5%	Simulated data	Shallow-sea random source localization
[25]	CNN-CBF-MSTDE	Depth error 0.8 m vs. MSTDE 2.5 m	Field data	Deep-sea source depth estimation
[26]	UDA	Error ↓ in low SNR/few data, better than MFP	Simulated data + field data	Few-shot localization in complex environments
[27]	CCNN	Deep-sea accuracy ↑ vs. MFP	Simulated data	Low-SNR deep-sea localization

).

2.2. Indoor Sound Source Localization

Traditional sound source localization methods, such as TODA [53,54] and beamforming [55], rely on multi-channel microphone arrays and wave equation propagation models. TDOA estimates source coordinates via time delay differences from generalized cross-correlation, while beamforming forms spatial spectral peaks through covariance matrix optimization. These methods excel in ideal conditions but suffer from reduced accuracy in high-reverberation or low-SNR environments due to signal distortion and high computational complexity. Their reliance on precise array geometry and environmental models also limits adaptability in dynamic scenarios (see

Table 2. Classification of deep learning methods in indoor localization.

Reference	Methods	Performances	Dataset	Scenes
[32]	GCC	Average azimuth error 4.6°, elevation error 3.1°	Simulated data	Extreme environments
[29]	RAN	Average accuracy 95.8% (far-field), 98.3% (near-field)	Simulated data + field data	Indoor reverberant environments
[28]	CNN	Accuracy 98.4% at SNR = 10 dB, T60 = 100 ms	Simulated data	Non-structured indoor environments
[30]	CNN-R	Angular accuracy > 99%	Simulated data	Indoor environments
[31]	DNN	Angular accuracy 99.85%	Simulated data + field data	Indoor reverberant environments
[33]	SSLIDE	MAE 0.39 m, DOA error 8.06°	Simulated data + field data	Dynamic reverberant environments
[34]	DNN	Average relative localization error < 3%	Simulated data	Highly reverberant environments
[35]	Data augmentation	Amplitude features outperform Mel-spectrogram and TDoA features	SoS dataset	Multi-scene indoor localization

).

Deep learning has revolutionized SSL by enabling data-driven feature learning. Architectures like deep neural networks [56], convolutional neural networks [28,57], and recurrent neural networks [29] enable end-to-end acoustic feature extraction, outperforming traditional methods in noisy/reverberant conditions. For example, Zhang et al. integrated CNN with TDOA for regional localization [28], while Liu et al. used DNN with room-specific reverberation modeling to enhance robustness [30]. Tan et al. combined CNN with regression for phase difference-based SSL (see Figure 3) [31], and Wu et al. improved accuracy via deep learning-assisted sound intensity estimation [32]. Recent breakthroughs focus on reverberation suppression and unsupervised domain adaptation, such as Wu et al.’s SSLIDE method [33], Long et al.’s unsupervised range estimation [26], and Yan et al.’s 3D localization [34]. The SoS dataset introduced by Nguyen-Vu and Lee [35] serves as a benchmark for indoor SSL research.

2.3. Unmanned Aerial Vehicle Localization

UAV technology has seen wide application, but illegal uses pose security risks. Traditional monitoring methods like RF [58], radar [59], and vision [60] have limitations in addressing these risks, while acoustic localization using UAV noise offers all-weather, anti-interference advantages for low-SNR monitoring. In the domain of unmanned aerial vehicle (UAV) acoustic localization, deep learning methods have particularly addressed critical challenges posed by non-stationary noise and real-time processing constraints (see

Table 3. Classification of deep learning methods in UAV localization.

Reference	Methods	Performance	Dataset	Scene
[36]	MUSIC + DP	Localization error ≤ 20 m at SNR = −8 dB	Simulated data + field data	Low-SNR environments
[37]	MFCC-1DCNN	Precision 96.57%, recall 92.53%	Field data	Outdoor UAV detection
[38]	Log-Mel + MFCC Fusion	Accuracy 94.5%, effective detection range ≤ 50 m	Field data	Outdoor UAV detection
[39]	Multi-scale + Attention	Accuracy 98.11%	Field data	Complex environments
[40]	LWCNN + SVM	Accuracy 95.61%	Field data	High-noise environments
[41]	GAN	Accuracy 96.38%	Synthetic data + field data	Low-SNR environments
[42]	BF + CNN	Detection range ≤ 135 m	Field data	Outdoor UAV detection
[43]	LSP	Detection accuracy improved by 15.12%	Field data	Complex background environments
[44]	STFT+CNN	Accuracy 98.87%	Field data	Outdoor UAV detection

). Wu et al. integrated the MUSIC algorithm with deep prediction to achieve localization errors ≤ 20 m at −8 dB SNR, outperforming traditional signal processing in low-SNR environments [36]. Manikandan combined mel-frequency cepstral coefficients (MFCC) with 1D CNN for UAV sound recognition, achieving 96.57% precision and 92.53% recall in outdoor detection scenarios [37]. Dong et al. proposed a feature-level fusion model using Log-Mel spectrograms and MFCC, achieving 94.5% detection accuracy within 50 m by leveraging evidential theory to integrate dual-channel CNN outputs [38].

Li et al. developed a multi-scale convolutional network with global–local attention, directly processing raw audio signals to enhance UAV monitoring accuracy to 98.11% in complex environments [39]. Aydın et al. designed a lightweight CNN (LWCNN) for high-noise environments, combining mel-spectral features with SVM to achieve a 95.61% classification accuracy while reducing computational load [40]. Sun et al. improved UAV sound event detection by integrating beamforming with CNN, expanding the effective range to 135 m despite background noise [42]. Al-Emadi et al. utilized GANs to augment UAV audio datasets, improving novel UAV detection accuracy to 96.38% when combined with CNN-RNN hybrid models [41].

Yan et al. proposed a linear shrinkage–subspace projection (LSP) method to reconstruct covariance matrices (see Figure 4), suppressing interference and enhancing localization accuracy by 15.12% [43]. Seo et al. achieved 98.87% accuracy using STFT-based CNN features for outdoor UAV detection, demonstrating robust spectral-temporal feature extraction [44]. Collectively, these approaches leverage lightweight architectures, spatiotemporal Transformer fusion, and data augmentation to address UAV noise non-stationarity, enabling real-time edge deployment with detection errors reduced by 20–45% compared to traditional acoustic methods.

3. General Principles of Deep Learning-Based Sound Source Localization

3.1. Feature Extraction

Multi-channel input signals recorded by a microphone array are processed through a feature extraction module to generate input features. These features are then fed into various neural networks for direction-of-arrival DOA estimation. Signals are typically converted into time–frequency representations via generalized cross-correlation or short-time Fourier transform STFT, or by extracting features such as phase differences and cepstral differences.

$$X\left(t,f\right)=\sum _{n=0}^{N-1}x\left(n\right)w\left(n-t/∆t\right)e^{-{\displaystyle \frac{j2\pi fn}{N}}}$$

(1)

X(t,f) denotes the STFT result, representing the signal intensity at time t, and frequency. X(n) is the discrete time-domain signal, defined as a complex exponential function which converts the time-domain signal to the frequency domain. $w\left(n-t/∆t\right)$ is a window function. The core idea of STFT is to divide the signal into short segments, apply the Fourier transform to each segment, and thereby capture local time–frequency characteristics, commonly serving as input features for deep learning models.

$$\begin{array}{c}{R}_{ij}\left(\tau \right)={\displaystyle \sum _f}{\displaystyle \frac{X_i\left(f\right)X_j^{\ast }\left(f\right)}{\left|X_i\left(f\right)X_j^{\ast }\left(f\right)\right|}}{e}^{j2\pi f\tau }\end{array}$$

(2)

$R_{ij}\left(\tau \right)$ quantifies the cross-correlation between signals xi(t) and xj(t) at time delay τ. $X_i\left(f\right)$ and $X_j\left(f\right)$ are their frequency-domain representations, with $X_j^{\ast }\left(f\right)$ as the complex conjugate. The phase term $e^{j2\pi f\tau }$ models the time delay effect in the frequency domain. $\mathsf{\Delta }f=f_s/N=1/\left(N\mathsf{\Delta }t\right)$. ${\sum }_f$ sums over discrete frequency bins to ensure accurate correlation estimation, where $f_s$ is the sampling rate and $N$ is the FFT length.

3.2. Model Architectures

The neural network architectures for SSL integrate deep learning-based feature extraction with physical models from traditional signal processing, forming core frameworks such as CNN, CRNN, Transformer, GFGRU (Gated Feedback Gated Recurrent Unit), and multi-task networks. These architectures demonstrate significant advantages in complex scenarios including indoor environments, UAV monitoring, and underwater applications.

3.2.1. LSTM

Long short-term memory (LSTM) networks, a specialized type of recurrent neural network, address the gradient vanishing problem in traditional RNNs through gating mechanisms and enable efficient modeling of long-term temporal dependencies. Following the implementation in [17], the LSTM core comprises memory cells and three gating modules, operating as follows (see Figure 5):

The LSTM dynamically controls information flow through the following gates:

Forget Gate: Determines which information to discard from the cell state by outputting weights in the range [0, 1] via a Sigmoid function.

Input Gate: Regulates the degree to which current input updates the cell state, jointly governed by Sigmoid and Tanh functions.

Output Gate: Generates the current hidden state output based on the updated cell state.

The mathematical expressions for each gate are defined as:

$$\begin{array}{l}{f}_t=\sigma \left(W_f\cdot \left[h_{t-1},i_t\right]+b_f\right)\\ x_t=\sigma \left(W_x\cdot \left[h_{t-1},i_t\right]+b_x\right)\\ {\hat{g}}_t=\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left(W_g\cdot \left[h_{t-1},i_t\right]+b_g\right)& & \\ C_t=f_t\odot C_{t-1}+x_t\odot {\hat{g}}_t\\ o_t=\sigma \left(W_o\cdot \left[h_{t-1},i_t\right]+b_o\right)\\ h_t=o_t\odot \tanh \left(C_t\right)& & \end{array}$$

(3)

σ(⋅) denotes the Sigmoid function, ⊙ represents element-wise multiplication, W is the weight matrix, and b is the bias term.

In [17], LSTM is integrated into a denoising autoencoder DAE framework to form an LSTM-DAE network. This network employs unsupervised learning to encode and decode ship-radiated noise, effectively extracting deep temporal features from acoustic signals. The encoder progressively compresses input dimensions through stacked LSTM layers while reconstructing model parameters; the decoder leverages LSTM’s temporal modeling capability to recover key signal features and suppress noise interference. Specifically, LSTM encodes and decodes acoustic signals through unsupervised temporal feature extraction, enhancing robustness against complex acoustic variations and providing high-quality feature representations for subsequent classification and localization tasks. By capturing long-term dependencies through memory gate mechanisms, LSTM helps distinguish temporal patterns of different sound sources, indirectly aiding localization. Although primarily used for temporal feature extraction and classification, LSTM’s ability to model temporal dynamics, suppress noise, and enhance feature discriminability provides critical support for downstream SSL algorithms.

Furthermore, LSTM’s long-term dependency modeling capability is combined with DLMN to form a collaborative training architecture. Through reinforcement learning strategies, features extracted by LSTM-DAE are further optimized for target classification tasks. Experiments confirm that this synergistic mechanism significantly improves the robustness of underwater acoustic target recognition, particularly excelling in low-SNR environments.

3.2.2. CNN

The convolutional neural network (CNN), as a canonical feedforward deep neural network, excels in hierarchical feature extraction and parameter sharing mechanisms. As referenced [61] in the literature and illustrated in the figure, a CNN primarily consists of an input layer, multiple feature extraction layers, fully connected layers, and an output layer. The feature extraction phase achieves progressive spatial abstraction through cascaded convolution-pooling operations, culminating in feature integration and classification by the fully connected layers. CNN’s weight-sharing property significantly reduces model complexity and parameter count. Unlike traditional neural networks, convolutional kernels slide over local receptive fields of input data, extracting translation-invariant features through shared weight parameters. This mechanism not only mimics the local receptive characteristics of biological vision systems but also endows the model with strong robustness against geometric distortions such as translation, scaling, and tilting.

Convolutional Layer: Performs local feature extraction via trainable kernels, mathematically expressed as

$$X_j^l=f\left(\sum _{i\in M_j}{X}_j^{l-1}\times k_{ij}^l+b_j^l\right)$$

(4)

$M_j$ denotes the feature map selection set, $k_{ij}^l$ represents convolutional kernel weights, $b_j^l$ is the bias term, and $f(\cdot )$ employs the ReLU activation function to enhance nonlinear expressiveness.

Pooling Layer: Compresses feature dimensions through downsampling, serving to enhance feature spatial compactness, reduce model parameters (n × n pooling decreases parameters by n² times), and improve noise immunity.

$$X_j^l=f\left({\beta }_j^l\cdot down\left(X_j^{l-1}\right)+b_j^l\right)$$

(5)

Fully Connected Layer: Compresses high-dimensional features into 1D vectors and implements classification via Softmax cross-entropy loss.

Traditional sound source localization methods rely on manually designed features and algorithms, such as DOA estimation based on time differences or phase analysis. However, these approaches often require extensive manual tuning and optimization in complex environments. In contrast, CNNs automatically learn and extract features, eliminating laborious manual feature engineering. As demonstrated in the literature, a CNN-compatible input format is constructed by converting audio signals from an 8-microphone virtual array into spectrograms via a short-time Fourier transform (STFT). These spectrograms are then concatenated across frequency bands into a 1024-dimensional input vector preserving spatial information (see Figure 6). The first four convolutional layers extract spatial features from audio spectra through local connectivity and weight sharing, while the subsequent three fully connected layers map these features to a classification space. This transforms direction estimation into a multi-class classification problem, assigning probabilities to distinct azimuthal angles for source focusing.

3.2.3. GFGRU

The computational flow of GFGRU units is defined by the following equations, simulating SBL’s iterative optimization through gating mechanisms:

Update Gate and Reset Gate:

$$z_t^l=\sigma \left(W_z^l{h}_t^{l-1}+U_z^l{h}_{t-1}^l\right)$$

(6)

$$r_t^l=\sigma \left(W_r^l{h}_t^{l-1}+U_r^l{h}_{t-1}^l\right)$$

(7)

${\mathrm{z}}_t^l,{\mathrm{r}}_t^l\in \left[\mathrm{0,1}\right]$: Control the retention ratio of historical states and the intensity of information resetting, respectively.

Global Reset Gate:

$$g^{i\to j}=\sigma \left(W_g^{i\to j}{h}_t^{l-1}+U_g^{i\to j}{H}_{t-1}\right)$$

(8)

${\mathrm{H}}_{t-1}=[{\mathrm{h}}_{t-1}^1,{\mathrm{h}}_{t-1}^2]$: The concatenation of historical states from all stacked layers.

Candidate State and Final State Update:

$${\hat{\mathit{h}}}_t^l=\mathit{tanh}\left(\begin{array}{c}{\mathit{W}}^{l-1}{\mathit{h}}_t^{l-1}+{\mathit{r}}_t^l\odot \\ {\displaystyle \sum _{i=1}^{N_L}}{\mathit{g}}^{i\to j}{\mathit{U}}^{i\to j}{\mathit{h}}_{t-1}^i\end{array}\right)$$

(9)

$${\mathit{h}}_t^l=\left(1-{\mathit{z}}_t^l\right){\mathit{h}}_{t-1}^l+{\mathit{z}}_t^l{\hat{\mathit{h}}}_t^l$$

(10)

Element-wise multiplication achieves selective information fusion. The hidden states are concatenated through horizontal unrolling steps:

${\mathbf{q}}^{all}=[{\mathbf{q}}_1,\dots ,{\mathbf{q}}_T]$, generating the final ambiguity surface:

$$P_{\mathit{GFGRU}}\left({\theta }_m\right)=softmax\left({\mathit{W}}_{\mathit{pred}}{\mathit{q}}^{all}+{\mathit{b}}_{\mathit{pred}}\right)$$

(11)

GFGRU comprises multiple stacked GRU layers [14], with identical input features at each timestep to simulate SBL’s iterative optimization. By regulating hidden state flow via gating mechanisms and global reset gates for inter-layer interactions, GFGRU effectively suppresses sidelobes and enhances localization accuracy (see Figure 7). As demonstrated in the literature, GFGRU takes frequency-domain signals obtained from vertical array acoustic pressure measurements via short-time Fourier transform (STFT) as input. The localization problem is formulated as a sparse estimation task, where input signals are preprocessed by computing normalized covariance matrices or applying singular value decomposition (SVD). The real and imaginary upper-triangular parts of the spatial covariance matrix (SCM) are flattened into vectors as input features, which are then concatenated across frequencies. The resulting ambiguity surface outputs probability values for candidate locations through a Softmax layer, forming a probability distribution. In summary, GFGRU integrates gating mechanisms with feedback connections to mimic sparse estimation algorithms’ iterative optimization, effectively addressing deep-sea multi-source localization challenges.

3.2.4. U-Net

The MTL-UNET-CBAM model described in [15] extends the classical U-Net architecture by integrating feature compression mechanisms and a multi-task learning framework for joint estimation of distance and depth in shallow-water underwater source localization. The network structure adopts a symmetrical encoder–decoder design, as depicted in the accompanying figure (see Figure 8).

Encoder (Entry Flow): Each stage of the encoder employs cascaded feature compression modules with three key components:

Dual Convolutional Layers: Utilize 3 × 3 convolutional kernels for local feature extraction, augmented by batch normalization and parametric activation functions to strengthen nonlinear mapping capabilities.

Attention Mechanism: Incorporates the Convolutional Block Attention Module (CBAM), which dynamically reweights critical feature channels and spatial regions through channel-wise and spatial attention mechanisms.

Downsampling Layer: Reduces feature map spatial dimensions using 2 × 2 max-pooling with stride 2. This operation is mathematically expressed as

$$F_{out}={\mathrm{MaxPool}}_{2\times 2}\left(\mathrm{CBAM}\left(\mathrm{ConvBlock}({\mathrm{F}}_{\mathrm{i}\mathrm{n}})\right)\right)$$

(12)

This design reduces input dimensions from 2F × L × L to 1 × F × L², addressing the dimensional imbalance in traditional MTL-CNN.

The U-Net framework leverages its signature encoder–decoder structure with skip connections, enhanced through multi-task learning and transfer learning strategies to achieve precise and efficient localization in challenging marine environments. Following the methodology in [15], input signals are first transformed via Fast Fourier Transform (FFT) to compute normalized covariance matrices. These matrices undergo progressive spatial reduction through two convolutional layers and 2 × 2 max-pooling operations, preserving essential abstract features. The decoder branch subsequently processes distance and depth estimation tasks independently, with final predictions generated through fully connected layers. A key innovation lies in the integration of CBAM attention mechanisms and multi-task learning: CBAM selectively amplifies discriminative features through adaptive channel and spatial attention. Multi-task learning employs trainable weight parameters to harmonize optimization objectives across tasks.

$$\mathcal{L}={\displaystyle \frac{1}{2{\sigma }_r^2}}\left||\left|y_r-{\hat{y}}_r\right|{|}^2+{\displaystyle \frac{1}{2{\sigma }_d^2}}\right||\left|y_d-{\hat{y}}_d\right|{|}^2+\mathit{log}{\sigma }_r{\sigma }_d$$

(13)

where ${\sigma }_r^2$ and ${\sigma }_d^2$ are adaptive task weights learned via backpropagation, balancing scale differences between km-level range and m-level depth estimations.

3.2.5. GAN

Reference [26] proposes an unsupervised adversarial domain adaptation (UDA) algorithm that addresses the distribution shift between simulated and measured data through a modified generative adversarial network (GAN) framework. Unlike conventional GANs focused on data synthesis, this methodology eliminates domain discrepancy by aligning latent space representations across domains. The architecture employs a feature generator (G) and domain discriminator (D) in an adversarial learning paradigm (see Figure 9).

The generator, implemented as a deep neural network, maps both simulated and measured acoustic pressure signals into a shared latent space through multi-band normalized covariance matrix inputs. To enhance frequency-specific feature extraction, the generator incorporates a modified ResNet architecture with grouped convolutional layers that independently process distinct frequency bands of acoustic field data. Simultaneously, the discriminator learns to classify feature origins (source vs. target domain) using binary cross-entropy loss. A gradient reversal layer inverts discriminator gradients during backpropagation, enforcing adversarial optimization where the generator minimizes domain discriminability while the discriminator maximizes classification accuracy. The optimization objective combines source domain classification error minimization with domain discrepancy reduction, measured as follows:

$${\epsilon }_{\mathcal{T}}\left(h\right)\le {\epsilon }_{\mathcal{S}}\left(h\right)+{\displaystyle \frac{1}{2}}{d}_{\mathcal{H}\Delta \mathcal{H}}\left(\mathcal{S},\mathcal{T}\right)$$

(14)

where ${\epsilon }_{\mathcal{T}}\left(h\right)$ and ${\epsilon }_{\mathcal{S}}\left(h\right)$ denote target/source domain errors, respectively. The adversarial training dynamically estimates and optimizes the distributional distance $d_{\mathcal{H}\mathsf{\Delta }\mathcal{H}}$. For practical implementation, continuous source distance estimation is discretized into 93 equidistant intervals, transforming the regression task into a multi-class classification problem. The final classifier produces a 93-dimensional probability vector, with the maximum probability interval selected as the predicted distance. This domain-invariant feature learning enables robust cross-domain generalization, allowing the classifier trained on labeled simulated data to achieve accurate source localization in unlabeled measured environments without explicit target domain annotations.

4. Strengths and Limitations of Deep Learning Methods

CNNs have demonstrated remarkable efficacy in indoor single-source localization and drone-based acoustic detection due to their localized feature extraction capabilities and computational efficiency. For instance, multi-scale convolutional kernels enable high-precision azimuth estimation in low-reverberation environments by capturing spectral features. However, CNNs exhibit limitations in modeling multi-source overlapping signals and long-term temporal dependencies, rendering them less adaptable to dynamic noise scenarios. In contrast, U-Net’s encoder–decoder architecture supports multi-task outputs, such as joint estimation of distance and depth in marine environments. Despite its ability to process complex acoustic field data, U-Net’s substantial parameter count and computational overhead restrict real-time performance, making it more suitable for offline applications. To address non-stationary interference in drone noise and indoor reverberant environments, GFGRU leverage temporal feature fusion through gating mechanisms and cross-layer feedback. Yet, their reliance on high-quality annotated data and convergence instability hinder practical deployment efficiency.

Lightweight CNNs, employing depthwise separable convolutions and parameter compression techniques, enable low-power real-time monitoring on edge devices like oceanic buoys and drones. However, these models suffer from significant accuracy degradation, particularly under low signal-to-noise ratio (SNR) conditions. Conversely, complex-valued convolutional networks achieve a 20–30% reduction in localization errors in deep-sea low-SNR environments by integrating acoustic phase information through complex-domain operations. Nevertheless, their heightened hardware requirements and model complexity necessitate high-performance computing platforms, limiting their edge deployment. Transformers, while exhibiting strong robustness in complex noise environments via global self-attention mechanisms, face challenges in small-scale labeled scenarios due to prohibitive computational complexity and data demands.

Current methodologies are constrained by three core limitations: Inadequate integration of physical principles: Traditional CNNs lack explicit modeling of acoustic wave propagation equations, restricting generalization in dynamic marine environments. Data dependency trade-offs: Although GANs alleviate annotation scarcity through domain adaptation, their performance is hindered by adversarial training instability and synthetic data quality issues. Real-time-precision imbalance: Architectures like residual CNNs, despite enabling deep acoustic field modeling, struggle with edge deployment due to excessive parameter counts and computational loads.

Future research should prioritize physics-informed architectures that embed domain-specific knowledge (e.g., differentiable wave equation solvers), unsupervised domain adaptation techniques to bridge simulation-to-reality gaps, and hardware–algorithm co-design for resource-constrained platforms. For instance, integrating neural architecture search with model compression could optimize edge-device efficiency, while hybrid approaches combining CNNs with spectral graph theory may enhance multi-source separation. These advancements will drive acoustic localization technologies toward intelligent systems characterized by high precision, robustness, and energy efficiency, enabling transformative applications in underwater exploration, autonomous drones, and adaptive smart environments (see

Table 4. Analysis of strengths and limitations.

Model	Tech	Use	Pros	Cons
CNN	Spectral conv	Indoor/UAV	Efficient local features	Multi-source overlap
U-Net	Encoder–decoder	Marine/Indoor	Multi-task output	Heavy computation
GFGRU	GRU + feature fusion	UAV noise/Indoor	Dynamic noise filtering	Data-dependent, unstable
CRNN	CNN + RNN	UAV audio	Spectral–temporal fusion	Slow inference
Transformer	Self-attention	Low SNR	Global context	High resource demand
Lightweight CNN	Depthwise conv	Edge devices	Real-time, low power	Accuracy trade-off
Complex CNN	Complex conv	Underwater	Low-SNR robustness	Hardware-intensive
GAN	Adversarial nets	Data scarcity	Reduces labeling	Training instability
ResCNN	Residual CNN	Marine fields	Deep modeling	High computational needs
LSTM	Long-term memory	UAV tracking	Temporal patterns	Sensitive to noise bursts

).

5. Conclusions

The rapid advancement of deep learning has catalyzed a paradigm shift in acoustic source localization, offering transformative solutions through end-to-end adaptive feature learning, data-driven modeling, and cross-domain generalization. In marine environments, convolutional neural networks (CNNs) and U-Net architectures address multipath interference and environmental mismatch by adaptively extracting spectral–temporal features from acoustic signals. Complex-valued CNNs further enhance precision in low-SNR deep-sea conditions by explicitly encoding acoustic phase information, achieving centimeter-level localization accuracy. While adversarial domain adaptation techniques improve robustness to dynamic sound speed profiles, challenges persist in acquiring large-scale annotated datasets and ensuring real-time inference in fluctuating underwater environments. Future advancements may integrate physics-informed neural architectures that embed differentiable wave propagation equations, coupled with hybrid frameworks combining GAN and simulation-to-reality data co-optimization to mitigate domain gaps.

Indoor localization systems face unique challenges in high-reverberation and multi-source overlapping scenarios. Attention mechanisms dynamically prioritize critical acoustic features to suppress reverberation artifacts, while lightweight CNN with depthwise separable convolutions enable edge deployment on smart devices. However, performance degradation in complex multi-source environments remains unresolved. Emerging solutions explore acoustic–visual–infrared multimodal fusion to exploit complementary sensory data, alongside spatiotemporal Transformer networks that model long-range dependencies for robust source separation. Hardware-accelerated architectures leveraging FPGA or ASIC platforms show promise for achieving millisecond-level inference speeds, essential for real-time applications in dynamic indoor settings.

Drone-based acoustic monitoring benefits from spatiotemporal Transformers and GNN, which capture non-stationary noise characteristics through spectral–temporal analysis. Distributed micro-microphone arrays paired with lightweight models facilitate low-power edge deployment, yet background noise interference and sensor layout generalization limit practical efficacy. Meta-learning frameworks aim to bridge simulation-to-reality knowledge transfer, while differential privacy techniques anonymize sensitive frequency bands to address ethical concerns in surveillance applications.

Despite the fact that current research on UAV acoustic localization has achieved sub-meter accuracy at a −10 dB signal-to-noise ratio by means of lightweight CNN and spatio-temporal Transformer models, it still faces three core challenges: the mid-high frequency tonal components are susceptible to environmental noise interference, and the time-varying characteristics of noise spectra lead to insufficient model generalization; single-modal acoustic methods have difficulty in distinguishing co-frequency interference sources, and there is ambiguity in out-of-sight localization; the inference delay and computational power consumption of high-performance models on edge devices fail to meet the real-time tracking requirements. Multi-source data fusion represents a significant trend in UAVs. will comprehensively utilize multi-sensor data from satellite navigation, inertial navigation, vision, lidar, and acoustics. Through the mutual complementation and validation of multi-source data, the accuracy, stability, and anti-jamming capabilities of localization will be enhanced to adapt to more complex and diverse environments. For example, in areas with disturbed satellite signals such as indoor spaces or urban canyons, the combination of visual positioning and inertial navigation ensures stable UAV flight; in forest monitoring, fusing lidar data to construct 3D terrain models assists satellite navigation in achieving precise positioning.

Underpinning these domain-specific advancements are three systemic challenges: the insufficient integration of wave physics in data-driven models, the reliance on costly annotated datasets, and unresolved trade-offs between algorithmic complexity and edge-device efficiency. To address these limitations, interdisciplinary efforts are converging on physics-guided architectures that couple neural operators with computational acoustic models, self-supervised learning paradigms utilizing contrastive learning and synthetic data augmentation, and hardware–algorithm co-design strategies incorporating NAS and adaptive model compression. The development of standardized datasets, open-source frameworks, and privacy-preserving protocols will be critical for fostering an ethical ecosystem to support scalable deployments in marine exploration, autonomous drones, and smart cities. By synergizing multimodal sensor fusion, computational physics, and energy-efficient edge computing, next-generation systems could achieve sub-centimeter precision with millisecond latency, ultimately advancing toward intelligent, sustainable, and socially responsible acoustic localization technologies.