Sparsity-based direction-of-arrival (DOA) methods offer a potential super-resolution way to address the aperture limitation caused by the small size of the unmanned underwater vehicle (UUV). However, the self-noise radiated from an operating UUV platform will cause the background rising and pseudo peaks appearing in the spatial spectrum estimated by the sparsity-based methods, resulting in a degradation of the DOA estimation performance. To address this issue, this paper proposes two narrowband sparsity-based DOA estimation methods, which achieve sparse representation of the platform self-noise based on the equivalent source method (ESM) and the dictionary learning method, respectively. These enable the separation of far-field target signals from the platform self-noise, effectively enhancing the capability of the DOA estimation methods in the presence of the platform self-noise. Finally, through semi-synthetic data simulations and experimental results, this paper compares the two methods with other advanced DOA estimation methods, indicating that the proposed methods achieve superior DOA accuracy and resolution under the platform self-noise.

A Toeplitz matrix reconstruction-based method for source depth estimation is proposed. The sound pressure is treated as a superposition of coherent signals arriving from different angles. The synthetic array, created by the relative motion between a hydrophone and the source, is divided into overlapping subarrays. Hermitian Toeplitz matrices are constructed using the cross-correlation coefficient between the receive data of each element and that of the reference element. A high-resolution method is then applied to estimate the grazing angles of horizontal wavenumbers. Estimations of subarrays are integrated through majority voting, which leverages truth-value consistency to reduce noise interference. The estimated wavenumbers are extracted, grouped, and subsequently substituted into the depth ambiguity function to calculate source depth. The final depth estimation is refined through majority voting, further suppressing sidelobe interference. The proposed method does not require precise acoustic environmental information but relies on the nominal sound speed and bottom profile to calculate mode depth functions. Simulations and the Monte Carlo method are used for performance comparison, with the root-mean-square error as the evaluation metric. The effects of synthetic aperture and noise on estimation performance are numerically analyzed. The proposed method is validated using 127 and 112 data from the SWellEx-96 experiment, with satisfactory results when the synthetic aperture is greater than or equal to 2km.

Objective Source localization is a key research topic in array signal processing,with applications in radar,sonar,and wireless communications.Conventional localization methods based solely on far-field or near-field models face clear limitations when separating and localizing mixed far-field and near-field sources.Existing approaches,such as subspace-based methods,often show high computational complexity,limited localization accuracy,and degraded performance under low Signal-to-Noise Ratio(SNR)conditions.In addition,many methods assume that near-field sources lie strictly within the Fresnel region,which leads to localization errors and a reduced effective array aperture.Improved algorithms,such as Multiple Sparse Bayesian Learning for Far-and Near-Field Sources(FN-MSBL),overcome part of these limitations and achieve higher localization accuracy.However,their reliance on iterative matrix inversion leads to high computational cost and restricts real-time applicability.Therefore,this study aims to address these issues by proposing a novel algorithm that develops a sparse representation model for mixed far-field and near-field sources in the covariance domain and integrates sparse reconstruction with the Generalized Approximate Message Passing(GAMP)and Variational Bayesian Inference(VBI)frameworks.The objective is to achieve high-precision localization of mixed sources while substantially reducing computational cost. Methods Two algorithms,termed Covariance-Based VBI for Far-and Near-Field Sources(FN-CVBI)and Covariance-Based GAMP-VBI for Far-and Near-Field Sources(FN-GAMP-CVBI),are developed.First,a unified sparse representation model for mixed far-field and near-field sources is constructed based on the covariance vector.This representation benefits from the improved SNR of the covariance vector relative to the original array output,which improves far-field Direction of Arrival(DOA)estimation.Second,to reduce estimation errors in the sample covariance matrix,a pre-whitening operation is applied to the covariance vector to minimize inter-element correlation and improve robustness.Third,a hierarchical Bayesian model is established to impose sparsity,and VBI is employed to estimate model parameters through iterative posterior updates.Fourth,to reduce the computational burden associated with conventional VBI,GAMP is embedded into the VBI framework to replace matrix inversion operations.The detailed implementation of GAMP is given in Algirithm1.By combining sparse reconstruction,VBI,and GAMP,the proposed approach improves localization accuracy while markedly reducing computational complexity. Results and Discussions The proposed FN-GAMP-CVBI algorithm shows clear improvements in both localization accuracy and computational efficiency.Complexity analysis indicates a substantial reduction in computational cost(Table 1).In terms of localization performance,FN-CVBI and FN-GAMP-CVBI outperform comparative methods,including LOFNS and FN-MSBL(Fig.3,Fig.4),particularly under low SNR conditions and with sufficient snapshots(Fig.5,Fig.6).The proposed methods also show strong capability in resolving closely spaced far-field sources(Fig.7).Experimental validation using lake trial data confirms these findings,as reflected by sharper spectral peaks and fewer false peaks in the background noise of the Bearing Time Recording(BTR)results(Fig.9).FN-CVBI achieves the highest accuracy in far-field DOA estimation and near-field localization.The computational time of FN-GAMP-CVBI is reduced by up to 95％compared with FN-MSBL(Table 3),demonstrating its suitability for real-time applications. Conclusions A sparse-reconstruction-based approach for mixed far-field and near-field source localization is presented by integrating sparse reconstruction with the GAMP-VBI framework.The proposed FN-GAMP-CVBI algorithm addresses the limitations of existing methods and achieves a balanced trade-off between localization accuracy and computational efficiency.Simulation results confirm superior performance,especially under low SNR conditions with sufficient snapshots,and experimental results further support the effectiveness of the approach.The low computational complexity and ability to handle mixed-source scenarios indicate that the proposed algorithm is well suited for real-time localization in complex environments.

The paper focuses on accurately measuring periodic pulse signals, such as black box beacon signals, in underwater environments. A standard beacon signal typically manifests as a periodic pulse signal with a specific frequency. To start with, a time-frequency analysis method based on the Short-Time Fourier Transform (STFT) is investigated for detecting periodic signal. Then, a novel approach named Group Pulses Coherent Integration (GPCI) with a data group alignment technique is proposed to enhance the output gain of the signal. Subsequently, the periodic characteristics of multi-pulse signals are leveraged to perform Pulse Chain Detection (PCD). Effectiveness of the proposed method is validated through both simulation and lake trial data analysis. Compared with state-of-the-art methods, the GPCI-PCD method achieves superior performance, with an SNR improvement over 4 dB and a false alarm probability (FAP) that is 30 % lower when the number of interference pulses is fewer than 150. These advantages make the GPCI-PCD method highly beneficial for practical applications.

The multi-sensor bearing-only tracking system plays an important role in underwater target localization. However, due to propagation delays, observations from multiple sensors at the same time are asynchronous, as the signals are emitted from the target at different moments, creating a time offset issue. Additionally, as the relative distance between the target and sensors changes, the time intervals between two consecutive observations by the sensors also vary. Furthermore, missed detections, false alarms, and target birth and death phenomena negatively impact state estimation. To address these issues, this paper proposes a multi-sensor bearing-only tracking algorithm that considers propagation delay. Using the Gauss-Helmert model to achieve accurate state transitions, the algorithm establishes kinematic and temporal constraints between multi-sensors. Simultaneously, it employs a loopy belief propagation method to calculate the posterior probabilities of each target and perform fusion updates. To improve tracking accuracy in complex environments, a time decay factor is proposed to reduce the covariance of sensors with higher delays, and a trajectory birth-and-death management strategy combined with delayed decisions is proposed. Simulation results show that this algorithm outperforms traditional algorithms that ignore propagation delays in state estimation accuracy and perform better than existing bias compensation algorithms in environments with false alarms and missed detections.

To effectively classify ship radiated noise signals under incomplete training data sets, this article proposes a ship radiated noise recognition method. This method consists of a feature selection method based on the Bhattacharyya distance measurement (FS-BD) and the fuzzy support vector machine (SVM) based on fuzzy support vector center (FSVM-fsv). In the feature extraction stage, FS-BD removes redundant dimensions based on the similarity of feature probability distribution, aiming to improve the separability of features. However, the complex underwater acoustic environment leads to heterogeneity between similar samples, which further causes the incompleteness of the learning feature set. In the classifier design, under the framework of SVM, the FSVM-fsv method uses the distance between samples and their respective fuzzy support vector centers to optimize the decision hyperplane's spatial division capability, thereby reducing the impact of outliers and noise on classifier performance. The experimental results show that the FS-BD method can significantly improve the difference and robustness of the target features under the condition of about 900 samples of single-class targets and containing multiple environments. At the same time, the performance of FSVM-fsv under incomplete training sets is better than other machine learning methods, such as SVM, FSVM based on class center, FSVM based on estimated hyperplane, FSVM based on actual hyperplane, and FSVM based on support vector center (FSVM-sv), and the average recognition accuracy reaches 84.65%. This recognition method provides a reliable solution for target recognition in unknown environments.

The radiated noise from ships is notably characterized by their tonal properties, making tone detection essential for passive sonar systems. The fast Fourier transform plays a crucial role in this process, but Doppler shifts can significantly diminish the integration gain. To address this issue, time warping is applied to modify the time axis of the signal, stabilizing the tonal frequency to a constant value. Traditionally, the warping operator, which determines how to modify the time axis, is designed by estimating motion parameters. In contrast, this study presents a method that eliminates the estimation step by using a set of pre-designed warping operators. The designing process involves preprocessing and clustering the delay vectors corresponding to various motion scenarios. The enhanced gain of the proposed algorithm, in comparison to the existing methods, has been validated through both simulation and experimental data.

In the acoustic confrontation scenario of noncooperative localization, a ship needs to receive continuous wave (CW) pulse signals from other nodes for localization. At the same time, the ship emits broadband interference used to jam and deceive an enemy ship. The interference creates an extremely strong interference background at the hydrophone close to the ship, thus damaging subsequent localization. Therefore, to localize other nodes, the problem of CW pulse signal reconstruction under strong interference background needs to be solved on a priority basis. Focusing on the signal reconstruction problem under strong interference conditions, this article proposes a parallel convolutional neural network with skip connections. The network mainly consists of a target subnet and an interference subnet. The input to the network contains a CW pulse signal, interference, and background noise. The target subnet is designed to estimate the target component, that is, the CW pulse signal. Additionally, the interference subnet is tasked with estimating the interference component. Ultimately, the acquired target and interference components are used to reconstruct the CW pulse signal of interest. The performance of the proposed network is evaluated using the signal-to-interference ratio (SIR) gain and signal-to-distortion ratio (SDR). According to simulation results, when the input SIR and signal-to-noise ratio are in the range of -8 to 10 dB, the SIR gain and the SDR of our method surpass comparative algorithms. Experimental results show that our network outperforms other benchmark algorithms in reconstructing underwater CW pulse signals with low input SIR. The calculated SIR gain and SDR are 37.80 dB and 6.82 dB, respectively.

In acoustic target detection using an unmanned underwater vehicle (UUV), platform self-noise and ambient noise emerge as dominant constraints on detection performance. In complex acoustic environments, flow noise, propeller noise, and ambient noise exhibit distinct spectral and spatial characteristics. Their partial overlap with target signals in frequency and spatial domains leads to degradation in noise suppression performance. To address this issue, this paper investigates the characteristics of signals and noise during UUV motion. While platform self-noise and ambient noise remain relatively stable, the incidence angle of signal varies with the platform's heading angle. This paper exploits this phenomenon to achieve signal-noise separation and develop a method for suppressing complex noise. The goal is to enhance the detection performance of weak targets. Experimental results demonstrate that the proposed method requires little prior information, effectively suppresses complex noise, and does not compromise the integrity of the target signal.

In passive acoustic monitoring system, information is typically derived from radiated noise signals of targets distributed across multiple subbands. When targets are close in the node field of view, direct processing of the entire frequency band may lead to premature merging of detection results or masking of weaker targets due to differences in energy distribution among the target bands. This situation can degrade the performance of tracking algorithms because the downstream tracking processing cannot compensate for the loss of upstream measurements. This study proposes a novel wideband multitarget tracking algorithm based on belief propagation to address this challenge. Initially, a merged target model is established to simulate the mechanism of measurement generation from multiple targets. Based on this model, merged targets and each subband measurement form a cyclic association structure. This structure is processed using the loopy belief propagation algorithm to prevent the combinatorial explosion. A mixture of belief and mutual information entropy weight is established for each subband to fuse all posterior probability density functions, considering differences in subband energy distribution. Simulation and lake trial results demonstrate that this algorithm substantially improves the tracking capabilities of passive acoustic monitoring system for wideband targets, underscoring its practical application value.

Water currents affect circular vector sensor arrays (CVSAs) suspended from a moored platform, causing them to rotate underwater. This rotation alters the direction of sources within the array coordinate system over time. Traditional methods that rely on numerous snapshots often yield inaccurate results, particularly for faint sources. To improve the accuracy, we introduce a direction-finding technique for CVSAs that employs low-rank rotation matrices (RM). The low-rank RM are constructed using the heading information of the CVSAs and the subregion array manifold vector matrices to achieve spatial focusing. When these matrices are applied to the measurement data, the resulting covariance matrix displays subspace characteristics similar to that of a stationary CVSA. Our performance analysis revealed that low-rank RM offer higher focusing gains than conventional RM. The method proposed in this study effectively improves the direction estimation performance for weak targets and extends the practical applicability of measurement techniques for rotating platforms. Both simulations and experiments confirm that our approach outperforms the modified traditional beamforming and other spatial focusing techniques in terms of resolution and precision. Notably, when the signal-to-noise ratio is below -4 dB, the resolution for distinguishing between the two sources increases by more than 50%

In non-cooperative DSSS signal reception, the accurate estimation of the pseudo-noise (PN) sequence period is essential for successful despreading and information recovery. In this paper, we propose an average second-order-moment autocorrelation method based on the accumulated code difference function to enhance the estimation accuracy under low-signal-to-noise-ratio (SNR) conditions. The proposed approach involves three key aspects: First, a quadrature receiver is employed to mitigate the impact of the random initial phase on demodulation, enabling the full utilization of the signal energy. Second, a code difference function is constructed using transition information between adjacent spreading codes, and by leveraging the strong correlation between these functions, accumulated processing effectively suppresses the noise influence. Third, the autocorrelation result of the accumulated code difference function displays periodic peaks separated by intervals equal to the PN sequence period, allowing for period estimation through peak interval extraction. In addition, the introduced average-second-order-moment technique addresses the peak loss caused by information code randomness while further smoothing noise. Simulation and experimental results verify the effectiveness and practicality of the proposed method, which outperformed the average-second-order-moment method by about 1.5 dB and the accumulated-power-spectrum-reprocessing method by about 2 dB.

In underwater multi-sensor systems for bearing-only tracking, propagation delays cause uncertainty in the state transition intervals. These intervals vary even for the same target observed by different sensors. Additionally, time offsets between sensors also exist, even when they receive signals simultaneously. As a result, directly applying the common Gaussian Markov model for state transitions introduces significant systematic errors. To address this problem, we propose a new tracking algorithm. It establishes motion and time delay constraints between multiple sensors. For state transitions, the Gauss-Helmert model is adopted instead of the conventional one. In underwater target tracking, environmental noise interference often leads to outliers in observational data, significantly affecting tracking accuracy. To address this issue, we propose a backtracking fusion method that merges backtracking reconstructed estimates with current estimates. Simulation results demonstrate that the proposed algorithm outperforms existing methods in estimation accuracy, significantly enhancing system performance.

To address the performance degradation of traditional underwater target localization algorithms in high-speed motion scenarios, this paper proposes a vertically moving localization method based on interference feature matching using a single hydrophone. Due to the overlapping of interference fringes in the time–frequency domain, the method first employs a two-dimensional homomorphic filter to separate different types of interference fringes while removing line-spectrum interference. Then, a theoretical interference period database is constructed, and feature matching is performed on the interference fringes to achieve localization of the vertically moving target. Simulation results show that, under conditions of strong broadband noise and line-spectrum interference, the proposed method effectively separates and restores the interference fringes of high-speed vertically moving targets and successfully locates the moving target under large Doppler conditions. Further validation using field data from Qiandao Lake confirms that the actual measurements align with theoretical analysis, validating the effectiveness of the proposed method.

It is a complex task to remove noise from underwater pulse signals without prior information. Benefiting from the advancements in neural networks, self-supervised learning methods like blind spot network (BSN) have been increasingly utilized for signal denoising due to their ability to operate without labeled data. However, BSN overlooks blind spot information and assumes noise independence, thereby limiting its performance in dealing with real underwater noise. This paper proposes a self-supervised learning method specifically designed to address the challenge of removing correlated noise. The method begins with the implementation of an improved pixel shuffle downsampling (PD) procedure to downsample the original data in the spatial and time domain, thereby reducing the influence of spatio-temporal correlation of underwater ambient noise on the denoising performance. Subsequently, a switch blind spot network (SBSN) is developed. By utilizing switch variables to control the network uses or ignores blind spot information, the method ensures network training convergence while enhancing the denoising performance. Lastly, a signal refinement method suitable for underwater acoustic signals is proposed to improve the ability to restore signal details. The results of simulations and processing of lake experimental data illustrate that the proposed method effectively eliminates spatial and temporal correlated noise and delivers impressive denoising performance. Crucially, this method does not depend on prior knowledge or manually annotated data, rendering it highly practical and valuable for promotion.

Spectral Correlation (SC) has become a critical analytical instrument for assessing the second-order cyclostationarity (CS) in signals, especially for mechanical vibration signals. Nonetheless, the computational demand for computing SC is considerable. Built upon the Smoothed Cyclic Periodogram (SCP), a consistent estimator named Fast Smoothed Cyclic Periodogram (FastSCP) is proposed to address this issue. FastSCP represents the computational process of SCP through the convolution of spectral components and incorporates the Overlap-Save algorithm for accelerating. Comparison results with other fast SC estimators, including Fast Spectral Correlation (FastSC) and Faster Spectral Correlation (FasterSC), indicate that the proposed method is competitive in terms of both computational cost and memory usage, particularly when dealing with wide cyclic frequency ranges.

For the sonar arrays mounted on an unmanned underwater vehicle (UUV), the direction-of-arrival (DOA) estimation of the far-field (FF) weak sources is influenced by the near-field (NF) interferences generated from the radiated self-noise of the UUV and the FF interferences simultaneously. To address the problem, a sparsity-based DOA estimation method resistant to the NF and FF interferences is proposed in this paper. This method isolates the FF signals from the NF signals by sparse reconstruction. Additionally, subspace projection is applied to address the masking problem of the weak target signal by the strong interferences in the spatial domain, effectively enhancing the capacity of estimating the DOA of the weak target signal in the presence of strong interferences. Numerical simulations and experimental results demonstrate the effectiveness of the proposed method. Compared to other advanced DOA estimation methods, the proposed method exhibits better DOA estimation performance in the presence of strong NF and FF interferences.

Data association is critical for resolving multisensor and multitarget tracking challenge. As the number of sensors and targets grows, the complexity of linking measurements to specific targets also grows. The question of efficiently associating ideal measurements for each target, particularly in multipassive sensor systems, remains unresolved. Inspired by least squares estimation, a cost function is determined that considers angle deviation and distance cost, the original objective function, and a set of constraints. The original objective function is then changed into a submodular function with the property of diminishing marginal benefits after an analysis of the problem's practical importance. Finally, based on the submodular optimization theory, an effective multisensor trajectory-measurement association algorithm is proposed. The simulation results show that using the proposed algorithm, each target only needs to be associated with a small number of high-accuracy measurement azimuths to achieve tracking performance comparable with the previous algorithm.

To enhance the stability of modulation spectrum structure, in this study, a novel adaptive feature purification method called variational mode decomposition (VMD) combined with feature energy entropy (FEE) is proposed. First, to decompose the noise interference envelope into simple intrinsic mode functions (IMFs), the VMD algorithm is employed. Subsequently, to compute the weight space of the IMFs, the FEE algorithm is utilized. Finally, using the respective weights, the envelope signal is reconstructed, which leads to a further enhancement in the stability of the modulation spectrum. Both simulation and real data confirm the effectiveness of the VMD-FEE algorithm in feature purification of the modulation spectrum.

The Detection of Envelope Modulation on Noise (DEMON) has been widely used in passive sonar target identification for determining the operational status and propeller structure characteristics of ships. However, the traditional DEMON spectrum is susceptible to environmental noise, which increases the difficulty of feature extraction. To address this issue, this paper investigates an adaptive feature enhancement method that combines Variational Mode Decomposition (VMD) and Singular Value Decomposition (SVD). The VMD algorithm utilizes variational equations to achieve adaptive modal decomposition of multiple feature components, while SVD utilizes the uncorrelated nature of signal and noise to achieve background noise reduction. Simulation results demonstrate that the feature strength and output signal-to-noise ratio of the VMD-SVD algorithm are higher than those of the traditional DEMON algorithm under both uniform and non-uniform modulation modes. Furthermore, processing of actual data validates the superiority of the VMD-SVD algorithm over the traditional DEMON algorithm, with the feature strength and output signal-to-noise ratio being maximally increased by 3 dB and 3.8 dB, respectively, compared to the traditional algorithm.