Active sonar target orientation estimation method, terminal device and storage medium

By combining the MUSIC method and CNN network, a lightweight CNN network is constructed using the generated MUSIC spatial spectrum as input, which solves the problem of low DOA estimation accuracy under low signal-to-noise ratio and achieves high-resolution target orientation detection, suitable for complex marine environments.

CN121069366APending Publication Date: 2025-12-05CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY
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Patent Information

Application Number
CN202511328128.5
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-09-17
Publication Date
2025-12-05

AI Technical Summary

Technical Problem

Existing technologies have low accuracy in estimating the DOA of underwater targets in low signal-to-noise ratio environments. Traditional methods are computationally complex and unstable, and existing deep learning methods have limited feature representation capabilities in low signal-to-noise ratio environments.

Method used

By combining the MUSIC method and CNN network, the MUSIC spatial spectrum is generated by performing eigenvalue decomposition on the array signal and used as input to the CNN network. The CNN network is then used to extract features and a lightweight three-layer convolutional neural network is constructed for DOA estimation, thus integrating the high-resolution characteristics of MUSIC and the intelligent feature recognition capabilities of CNN.

Benefits of technology

It significantly improves DOA estimation accuracy in low signal-to-noise ratio environments, reduces deployment difficulty, adapts to practical engineering application scenarios, and achieves high-resolution target orientation detection.

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Abstract

The invention discloses an active sonar target orientation estimation method, terminal equipment and a storage medium, and the method comprises the steps: generating active sonar array receiving signals under different signal-to-noise ratio conditions based on BellHop, and calculating a spatial spectrum based on a MUSIC method to construct a feature data set; designing and building a CNN convolutional neural network, and training and testing a network model by using a generated data set; and finally, realizing direction-of-arrival estimation of the underwater target based on the trained CNN network. The method not only is excellent in performance in a complex marine environment, but also still has good performance under a low signal-to-noise ratio, and a new effective method is provided for underwater target orientation estimation.
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Description

Technical Field

[0001] This invention relates to the field of underwater target detection and positioning technology, and in particular to an active sonar target location estimation method, terminal equipment and storage medium. Background Technology

[0002] Underwater target direction of arrival (DOA) estimation is a key function of sonar systems. It is not only the core foundation supporting sonar's detection capabilities but also a crucial support for continuous breakthroughs in marine information research and expanding human understanding of the ocean. Achieving high-precision and efficient DOA estimation for underwater targets in the complex marine environment has always been a pressing problem in the field of underwater acoustics. Traditional DOA methods, such as conventional beamforming (CBF), are the most basic DOA estimation methods. This method calculates the output spatial spectrum in different directions by scanning the received signal from the array and then determines the signal incident direction by detecting the peak value of the spatial spectrum. However, this method has limited resolution and suffers from large sidelobe interference and poor performance at low signal-to-noise ratios. Capon's minimum variance method is an adaptive beamforming method. This method obtains a high-resolution spatial spectrum by minimizing the output power while constraining the target direction gain to 1. Its resolution is higher than CBF, but it has high computational complexity and is unstable at low snapshot numbers. The spatial spectrum estimation algorithm (Multiple Signal Classification, MUSIC) is based on the orthogonality between the signal subspace and the noise subspace. It constructs a spatial spectrum using the eigenvalue decomposition of the received signal covariance matrix and achieves super-resolution DOA estimation by searching for the orthogonality between the noise subspace and the steering vector. This method breaks through the Rayleigh limit and has extremely high theoretical resolution, making it suitable for coherent signal separation. However, this method has high computational complexity, requires a known number of signal sources, and has a large error at low signal-to-noise ratios.

[0003] The development of artificial intelligence (AI) technology has provided new ideas for improving underwater DOA estimation capabilities. In recent years, AI technology has developed rapidly and made significant progress in various industries, with widespread applications in manufacturing, service, and even the military. Deeply integrating data-driven AI methods with physics-driven sonar signal models to handle low signal-to-noise ratio (SNR) acoustic signals in complex environments is a new and promising solution. AI-based DOA estimation methods can be applied to various fields such as underwater security, unmanned underwater vehicles, and deep-sea exploration, demonstrating broad application value. DOA estimation has undergone several development stages. Initially, in the 1970s, it was the traditional subspace decomposition and beamforming stage, with DOA estimation centered on subspace decomposition and beamforming, building classic algorithms based on array signal processing theory. In the 2010s, to address the shortcomings of traditional methods, research shifted towards sparse reconstruction and novel array designs such as Sparse Iterative Covariance-based Estimation (SPICE) and weighted norm optimization methods. In the 1920s, the introduction of deep learning and neural network technologies propelled DOA estimation into an intelligent stage.

[0004] In recent years, a comparison of invention patent applications in the field of underwater target detection and localization technology is as follows: "An Underwater Target DOA Estimation Method Based on CNN under a Ray-Sound Field Model" (Publication No.: CN119716726 A, Publication Date: 2025.03.28). This method builds a CNN network based on shallow and deep-sea ray-sound field models, and uses the trained CNN network to estimate the DOA of underwater targets, solving the algorithm robustness problem of the sharp decline in estimation performance of traditional underwater DOA estimation methods as the signal-to-noise ratio of the received signal decreases. However, its feature representation ability is limited as the signal-to-noise ratio decreases. The paper, titled "A Deep Learning-Based Method and System for Estimating Out-of-Band DOA under Array Error" (Publication No.: CN120162640A, Publication Date: 2025.06.17), utilizes an observation array to receive narrowband signals transmitted by narrowband targets, obtains the corresponding array received signals, and acquires the covariance matrix based on the array received signals. The array received signals and the covariance matrix are then input into a pre-trained DOA estimation model to obtain the DOA estimation results for the narrowband targets. This effectively suppresses the impact of array errors on DOA estimation performance and improves the DOA estimation effect for narrowband targets. However, its feature representation capability depends on the signal-to-noise ratio (SNR); when the SNR is low, the network's estimation performance is poor. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an active sonar target azimuth estimation method, terminal equipment and storage medium to improve the target echo detection capability, in order to address the shortcomings of the existing technology.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: an active sonar target location estimation method, comprising the following steps:

[0007] S1. Generate active sonar array received data;

[0008] S2. Calculate the spatial spectrum of the active sonar array received data based on the MUSIC method, and use the spatial spectrum as a feature dataset;

[0009] S3. Use the generated feature dataset as input to the neural network model to train the neural network model and obtain the estimated model.

[0010] The specific implementation process of step S1 includes:

[0011] The target echo signal y(t) is obtained by convolving the channel impulse response with the transmitted signal, where y(t) = s(t) * h(t), and s(t) is the transmitted signal and h(t) is the channel impulse response.

[0012] The signals received by each array element are represented as: x(t)=a(θ)y(t-τ) m )+n(t), where vector x(t) represents the signal received by the array element, θ is the azimuth angle, a(θ) represents the spatial steering vector, and n(t) represents the noise signal;

[0013] The array data in the discrete domain is obtained by sampling and transforming x(t), which is the active sonar array received data.

[0014] Calculation of the spatial spectrum P of active sonar array received data based on the MUSIC method MUSIC The expression for (θ) is: P MUSIC (θ)=1 / (a H (θ)U N U N H a(θ)); where a(θ) represents the spatial steering vector, H is the conjugate transpose, and U N Let N be the noise subspace matrix, and N represent the number of snapshots.

[0015] The neural network model is a CNN model.

[0016] The expression for the cross-entropy loss function Loss of the CNN model is as follows: Where, p i Let yi represent the probability that a sample belongs to the i-th class; y0, ..., yi C-1 It is the sample label, y is the label when the sample belongs to the i-th category. i =1, otherwise y i =0; C is the sample label.

[0017] As an inventive concept, the present invention also provides a terminal device, including a memory, a processor, and a computer program stored in the memory; wherein the processor executes the computer program to implement the steps of the method.

[0018] As an inventive concept, the present invention also provides a computer-readable storage medium having a computer program / instructions stored thereon; wherein the computer program / instructions, when executed by a processor, implement the steps of the method.

[0019] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention constructs the MUSIC spatial spectrum of the echo signal as the input feature of the network; it uses a CNN network to extract its features, and outputs the classification results through fully connected layers and softmax layers to obtain the detection results of the target echo. This invention effectively enhances the signal feature recognition by performing eigenvalue decomposition on the covariance matrix of traditional array signals and calculating the MUSIC spatial spectrum features of the array signals based on these eigenvalues. Even in low signal-to-noise ratio environments, CNN can still significantly improve the accuracy of DOA estimation. Simultaneously, addressing the problem of missing active sonar data samples, this invention uses the BELLHOP underwater acoustic model, incorporating key factors such as complex marine environmental conditions, underwater acoustic channel characteristics, and ocean noise to generate array received signals, significantly improving the authenticity and effectiveness of the samples and providing high-quality data support for the training of subsequent detection models. This invention employs a CNN network with only 3 convolutional layers—its greatest advantage over traditional complex networks lies in its lightweight nature, significantly reducing deployment difficulty and making it more suitable for various practical engineering applications. Current mainstream solutions often directly use the received signal matrix as network input, which is significantly limited by the signal-to-noise ratio, resulting in unsatisfactory azimuth resolution and DOA estimation accuracy. Therefore, this invention first performs deep processing on the array signal matrix: extracting the MUSIC spatial spectrum through eigenvalue decomposition. Relying on the orthogonality between the signal and noise subspaces, noise interference can be effectively filtered out, significantly improving azimuth resolution. Traditional MUSIC spatial spectra themselves lack the ability to intelligently distinguish between targets and noise. This invention deeply integrates the MUSIC spatial spectrum with the CNN network—fully utilizing the high-resolution characteristics of the MUSIC spatial spectrum while leveraging the intelligent feature recognition capabilities of CNN to compensate for the shortcomings of traditional MUSIC. The two work synergistically, ultimately achieving a significant improvement in DOA estimation accuracy. Attached Figure Description

[0020] Figure 1 A flowchart illustrating the process of generating a feature dataset;

[0021] Figure 2 The impulse response of the channel under weak negative sound velocity conditions in a fine sand environment;

[0022] Figure 3 Echo signal under weak negative sound velocity conditions in a fine sand environment;

[0023] Figure 4 MUSIC spectrum diagram

[0024] Figure 5 A schematic diagram of the network structure used;

[0025] Figure 6 To estimate the relationship between DOA accuracy and SNR;

[0026] Figure 7 Estimate the relationship between RMSE and SNR for DOA;

[0027] Figure 8 To estimate the relationship between DOA accuracy and the number of snapshots;

[0028] Figure 9 Estimate the relationship between RMSE and the number of snapshots for DOA. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] Example 1

[0031] This invention provides an artificial intelligence-based active sonar target location estimation method, the process of which is as follows: Figure 1 As shown, the specific steps include:

[0032] Step 1: Use BellHop to generate simulation data samples for various scenarios.

[0033] The BellHop tool was used to generate underwater acoustic channel impulse responses for complex marine scenarios, including nine typical seabed sediments such as coarse sand, fine sand, very fine sand, silt, sand-mud, sand-mud-clay, clay, and muddy clay, and four typical acoustic velocity profiles: isoacoustic velocity, weak negative gradient, strong transition layer, and positive gradient. The dataset generation process is consistent across all scenarios, differing only in the input environmental parameters. The following section describes the dataset generation process using a very fine sand environment and a weak negative gradient condition as examples. The feature dataset generation process is as follows: Figure 1 As shown.

[0034] First, use BellHop to generate a weak negative sound velocity profile. Input the depth array / m: "0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200", and the sound velocity / m / s: "1530 1529.5 1529 1528.5 1528 1527.5 1527 1526.5 1526 1525.5 1525 1524.5 1524 1523.5 1523 1522.5 1522 1521.5 1521 1520.5 1520".

[0035] The parameters were then simulated to generate a weak negative sound velocity profile.

[0036] BellHop is then used to generate the underwater acoustic channel environment file.

[0037] Sea surface parameters: The sea surface sound velocity interpolation method is N2 linear interpolation, and the sea surface boundary type is vacuum.

[0038] Seabed parameters: Seabed boundary type is acoustic elastic half-space; seabed density is 1.697 g / cm³. 3 The sound velocity is 1866 m / s and the longitudinal wave attenuation coefficient is 0.5.

[0039] Array parameters: sound source depth is 30m, vertical direct receiving array number is 1, horizontal receiving array number is 201 and evenly distributed in the range of 0-20km.

[0040] Simulation parameters: 10 simulated sound rays, sound ray emission angle range of -10° to 10°, maximum simulation depth of 201m, and maximum simulation distance of 20km.

[0041] The above parameter configuration generates a simulation 2D environment file for a fine sand environment.

[0042] Based on the generated 2D sound velocity file and environment file, the impulse response of the channel under conditions of extremely fine sand and weak negative sound velocity is generated, such as... Figure 2 As shown.

[0043] According to signal and system theory, the convolution of a system's input and its impulse response yields the system's output under that input signal. Convolving the channel impulse response with the transmitted signal yields the target echo signal y(t), where y(t) = h(t) * s(t), and h(t) is the channel impulse response, and s(t) is the transmitted signal. Taking a CW signal transmission as an example, a CW signal with a transmission frequency of 500Hz and a pulse width of 1s is used as the channel input. Convolving this signal with the channel impulse response generates an echo signal with an azimuth angle of -60° to 60°. Figure 3 As shown.

[0044] In real-world environments, the complex underwater acoustic environment causes the signals received by the receiving array to be mixed with a large amount of environmental noise. Therefore, in simulation, it is necessary to superimpose noise of various signal-to-noise ratios onto the echo signals to make the dataset more closely resemble the echo signals in real-world environments.

[0045] Finally, Gaussian white noise was added to the echo signal to generate noisy echo signals under signal-to-noise ratio conditions of -10dB, -5dB, 0dB, 5dB, and 10dB.

[0046] Step 2: Process the array received signals in the dataset and perform MUSIC estimation to obtain the feature dataset.

[0047] The noisy echo signal is the final generated echo signal dataset. The parameters are set as follows: the number of hydrophone array elements is 16, and the number of snapshots are 10, 20, 50, 100, and 150 respectively. Assume the time delay of the target echo arriving at this array element is τ. m, The signals received by each array element can then be expressed as: x(t)=a(θ)y(t-τ) m )+n(t), where vector x(t) represents the signal received by the array element, θ is the azimuth angle, a(θ) represents the spatial steering vector, and n(t) represents the noise signal. Sampling and transforming x(t) yields the discrete-domain array data as x(n). Performing MUSIC spatial spectrum calculations on the received array signal, the resulting signal number multiplied by 181 dimensions yields the generated feature dataset. One example of the feature data is as follows: Figure 4 As shown.

[0048] The main idea of ​​the MUSIC algorithm is to first perform eigenvalue decomposition on the covariance matrix of the array received data, and then use the separated noise subspaces and the orthogonality between the subspaces to form a spatial scanning spectrum.

[0049] First, calculate the covariance matrix of the received signal. Then, obtain the estimated value R of the covariance matrix based on the received signal vector.

[0050]

[0051] Eigenvalue decomposition of the covariance matrix yields:

[0052] R=USU H (1-2)

[0053] Finally, calculate the spatial spectrum P of the signal received by the array. MUSIC (θ):

[0054] P MUSIC (θ)=1 / (a H (θ)U N U NH a(θ)) (1-3)

[0055] Step 3: Use the input features as input to the CNN network, configure the designed network parameters, and obtain the DOA estimation result through the trained network.

[0056] A three-layer convolutional neural network was built using Keras in Python. The model expects a one-dimensional sequence of length 181 with one channel as input, which represents the signal's MUSIC spatial spectrum. The three-layer convolutional structure is used to progressively extract signal features, as shown in the structure below. Figure 5 As shown, the kernel size decreases by 25, 15, and 5 layer by layer, and the temporal length of the kernel also decreases by 12, 6, and 3 layer by layer, forming a pyramid structure with three one-dimensional convolutional layers. The ReLU activation function is used to introduce non-linear characteristics, which helps the model learn complex features of the spatial spectrum in this design. Same padding is used to ensure that the length of the output sequence is consistent with the input, facilitating data processing by the network. A flattening layer follows the convolutional layers, preparing for the fully connected layer. Finally, a fully connected layer serves as the output layer, with an output dimension of 181, corresponding to 181 angles from -90° to 90°. The Softmax activation function is used to convert the output into a probability distribution, representing the probability of the signal originating from each direction. The network updates the weights based on the cross-entropy loss function, the expression for which is: Where, p i Let yi represent the probability that a sample belongs to the i-th class; y0, ..., yi C-1 It is the sample label, y is the label when the sample belongs to the i-th category. i =1, otherwise y i =0; C is the sample label.

[0057] The CNN network was trained using Adam as the optimizer, cross-entropy as the loss function, an initial learning rate of 0.001, a batch size of 128, and 20 training epochs. The SVM algorithm was trained using Gaussian radial basis functions as the kernel function, with kernel parameters set to auto and a penalty factor of 1, for 20 training epochs. The BP algorithm was trained using tansig and logsig as activation functions, traingdx as the training function, an initial learning rate of 0.0001, 60 hidden layer nodes, and 20 training epochs.

[0058] To compare the advantages of the method proposed in this invention with traditional methods, various traditional DOA estimation methods (including CBF, Capon, MUSIC) and traditional neural networks (SVM, BP) were also designed for DOA estimation experiments.

[0059] Datasets with different signal-to-noise ratios were constructed with a fixed number of snapshots. The CNN network model method designed in this invention, along with CBF, Capon, MUSIC, SVM, and BP neural networks, were used to estimate the DOA of the same test set data. A spectral peak search was performed on the estimated spatial spectrum, and the angle corresponding to the highest peak was taken as the estimated angle. Figure 6 , Figure 7 The experimental results for DOA estimation accuracy and RMSE as a function of signal-to-noise ratio (SNR) are presented for various methods at 50 snapshots. It is evident that as the SNR increases, the DOA estimation accuracy of all methods gradually increases, while the root mean square error (RMSE) gradually decreases. Among the traditional methods, CBF and MUSIC methods perform well, while the Capon method performs poorly. The SVM method's performance falls between CBF and MUSIC methods, and the BP neural network performs the worst. The method proposed in this embodiment outperforms the other five methods under various SNR conditions, especially at -10dB and -5dB, where its accuracy can be improved by more than 30%.

[0060] Under a fixed signal-to-noise ratio (SNR), datasets with different snapshot numbers are constructed. The CNN network model method designed in this invention, along with CBF, Capon, MUSIC, SVM, and BP neural networks, are used to estimate the DOA of the same test set data. The estimated spatial spectrum is then subjected to spectral peak search; the angle corresponding to the highest peak is the estimated angle. Figure 8 , Figure 9 Experimental results for DOA estimation accuracy and RMSE as a function of snapshot number are presented for various methods at a signal-to-noise ratio of -5 dB. As the number of snapshots increases, the DOA estimation accuracy gradually increases, while the root mean square error gradually decreases. Among the traditional methods, CBF and MUSIC methods perform better, while the Capon method performs worse. Classical machine learning methods do not show a significant advantage; in fact, BP neural networks perform poorly. The method proposed in this embodiment outperforms the other five methods under various snapshot number conditions.

[0061] Example 2

[0062] Embodiment 2 of the present invention provides a terminal device corresponding to Embodiment 1 above. The terminal device can be a processing device for a client, such as a mobile phone, a laptop, a tablet computer, a desktop computer, etc., to execute the method of the above embodiments.

[0063] The terminal device in this embodiment includes a memory, a processor, and a computer program stored in the memory; the processor executes the computer program in the memory to implement the steps of the method in Embodiment 1 described above.

[0064] In some implementations, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.

[0065] In other implementations, the processor can be any type of general-purpose processor, such as a central processing unit (CPU) or a digital signal processor (DSP), and there is no limitation here.

[0066] Example 3

[0067] Embodiment 3 of the present invention provides a computer-readable storage medium corresponding to Embodiment 1 above, on which a computer program / instructions are stored. When the computer program / instructions are executed by a processor, they implement the steps of the method of Embodiment 1 above.

[0068] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof.

[0069] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0070] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0071] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0072] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0073] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method of target bearing estimation for a active sonar, characterized in that, The method comprises the following steps: S1, generating active sonar array receiving data; S2, calculating the spatial spectrum of the active sonar array receiving data based on the MUSIC method, and taking the spatial spectrum as a feature data set; S3, taking the generated feature data set as an input of a neural network model, training the neural network model, and obtaining an estimation model.

2. The active sonar target bearing estimation method of claim 1, wherein, The specific implementation process of step S1 comprises: convolving the channel impulse response with the transmitted signal to obtain a target echo signal y(t), y(t) = s(t) * h(t), wherein s(t) is the transmitted signal and h(t) is the channel impulse response; The signals received by each array element are represented as: x(t) = a(θ)y(t-τ m )+n(t), where the vector x(t) represents the signals received by the array elements, θ is the azimuth angle, a(θ) represents the spatial steering vector, and n(t) represents the noise signal. sampling and converting x(t) to obtain array data in the discrete domain, i.e., to obtain the active sonar array receiving data.

3. The method of claim 1, wherein, The spatial spectrum P of the active sonar array receiving data is calculated based on the MUSIC method MUSIC The expression of P(θ) is as follows: MUSIC P(θ) = 1 / (a H (θ)U N U N H a(θ)); wherein a(θ) represents a spatial direction vector, H is a conjugate transpose, U N is a noise subspace matrix, and N represents a number of snapshots.

4. The active sonar target bearing estimation method of claim 1, wherein, The neural network model is a CNN model, and the CNN model comprises three convolution layers connected in sequence.

5. The method of claim 4, wherein, The expression of the cross-entropy loss function Loss of the CNN model is: Wherein, p i represents the probability that the sample belongs to the i-th class; y0,..., y C-1 is a sample label, y i = 1 when the sample belongs to the i-th class, otherwise y i = 0; C is a sample label.

6. A terminal device comprising a memory, a processor, and a computer program stored on the memory; characterized in that, The processor executes the computer program to implement the steps of the method of any one of claims 1-5.

7. A computer readable storage medium having stored thereon computer programs / instructions; characterized in that, The computer program / instruction is executed by the processor to implement the steps of the method of any one of claims 1-5.

Citation Information

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