Deep learning (DL) approaches in underwater acoustic localization (UAL) have gained a great deal of popularity. While numerous works are devoted to improving the localization precision, they neglect another critical challenge inherent in the DL-based UAL problem, i.e., the model's practicality. Advanced DL models generally exhibit extremely high complexity, requiring a large amount of computational resources and resulting in slow inference time. Unfortunately, the limited processing power and real-time demands in oceanic applications make the deployment of complex DL models exceedingly challenging. To address this challenge, this article proposes a lightweight UAL framework based on knowledge distillation (KD) techniques, which effectively reduces the size of a deep UAL model while maintaining competitive performance. Specifically, a dedicated teacher network is designed using attention mechanisms and convolutional neural networks (CNNs). Then, the KD is performed to distill the knowledge from the teacher network into a lightweight student model, such as a three-layer CNN. In practical deployment, only the lightweight student model will be utilized. With the proposed lightweight framework, the student model has 98.68% fewer model parameters and is 87.4% faster in inference time compared to the teacher network, while the prediction accuracy drops to only 1.07% (97.55% $\rightarrow$ 96.48%). In addition, the generalization ability of the student model is examined through transfer learning, where the model is transferred between two different ocean environments. The student model demonstrates a stronger generalization ability compared to the model without the KD process, as it can quickly adapt itself to a new application environment using just 10% of the data.

Purpose: The existing dimensionality reduction algorithms suffer serious performance degradation under low signal-to-noise ratio (SNR) owing to the presence of noise. To address these problems, an enhanced spatial smoothing scheme is proposed that exploits the subarray time-space correlation matrices to reconstruct the data matrix to overcome this weakness. This method uses the strong correlation of signal and the weak correlation of noise in time and space domains, which improves the noise suppression ability.Design/methodology/approach: In this paper, an enhanced spatial smoothing method is proposed. By using the strong correlation of signal and the weak correlation of noise, the time-space smoothed array covariance matrix based on the subarray time-space correlation matrices is constructed to improve the noise suppression ability. Compared with the existing Toeplitz matrix reconstruction and spatial smoothing methods, the proposed method improves the DOA estimation performance at low SNR.Findings: Theoretical analysis and simulation results show that compared with the existing dimensionality reduction processing algorithms, the proposed method improves the DOA estimation performance in cases with a low SNR. Furthermore, in cases where the DOAs between the coherent sources are closely spaced and the snapshot number is low, our proposed method significantly improves the performance of the DOA estimation performance.Originality/value: The proposed method improves the DOA estimation performance at low SNR. In particular, for the cases with a low SNR, the proposed method provides a better RMSE. The convergence of the proposed method is also faster than other methods for the low number of snapshots. Our analysis also confirms that in cases where the DOAs between the coherent sources are closely spaced, the proposed method achieves a much higher angular resolution than that of the other methods.

Purpose: The purpose of this paper is to exploit the multiple-Toeplitz matrices reconstruction method combined with quadratic spatial smoothing processing to improve the direction-of-arrival (DOA) estimation performance of coherent signals at low signal-to-noise ratio (SNRs).Design/methodology/approach: An improved multiple-Toeplitz matrices reconstruction method is proposed via quadratic spatial smoothing processing. Our proposed method takes advantage of the available information contained in the auto-covariance matrices of individual Toeplitz matrices and the cross-covariance matrices of different Toeplitz matrices, which results in a higher noise suppression ability.Findings: Theoretical analysis and simulation results show that, compared with the existing Toeplitz matrix processing methods, the proposed method improves the DOA estimation performance in cases with a low SNR. Especially for the cases with a low SNR and small snapshot number as well as with closely spaced sources, the proposed method can achieve much better performance on estimation accuracy and resolution probability.Research limitations/implications: The study investigates the possibility of reusing pre-existing designs for the DOA estimation of the coherent signals. The proposed technique enables achieve good estimation performance at low SNRs.Practical implications: The paper includes implications for the DOA problem at low SNRs in communication systems.Originality/value: The proposed method proved to be useful for the DOA estimation at low SNR.

The Toeplitz matrix reconstruction methods are capable of resolving coherent signals, playing a crucial role in the direction-of-arrival (DOA) estimation of acoustic sources. However, the decoherence processing sacrifices the array aperture and further results in a reduced resolution capability for the number of identifiable sources. To solve this issue, we propose an enhanced method using the Khatri–Rao subspace to resolve more coherent sources than that of the existing Toeplitz matrix reconstruction methods. Firstly, a full set of Toeplitz matrices with full rank is obtained. Then, the virtual array aperture can be obtained using the Khatri–Rao product of the array response, and the degree of freedom provided inherently in the virtual array structure is about twice the size of that of the existing Toeplitz methods. Next, linear processing is further used to achieve complexity reduction without losing the effective degree of freedom. Finally, the DOA estimation for more coherent sources can be achieved by combining it with conventional methods. Numerical simulations verify the superiority of the proposed method.