Deep learning likelihood modeling-based belief propagation passive sonar array DOA tracking method

Abstract

The invention relates to a belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling. A belief propagation framework of likelihood function learning fuses deep learning (DL) data driving and belief propagation (BP) multi-frame association capability; a data-driven convolutional neural network (CNN) efficiently maps an array sampling covariance matrix into a sparse power spectrum in a nonlinear manner; according to the likelihood function suitable for Bayes reasoning, a sparse power spectrum is converted into a likelihood function with continuous values by using Gaussian smoothing and cubic spline interpolation technologies; efficiently solving a factor graph of a multi-target tracking problem, and reasoning confidence approximation of target state edge posteriori in combination with a BP algorithm and a constructed likelihood function; the maneuvering target stable tracking and clutter suppression capability is enhanced, and a multi-model interaction algorithm and a time correlation-based target new mechanism are fused. According to the method, the DOA of a plurality of maneuvering weak targets can be stably and continuously tracked at the same time under the conditions of complexity and low signal-to-noise ratio.

Description

Technical Field

[0001] This invention relates to the fields of deep learning, belief propagation, passive sonar array signal processing, and target DOA tracking, specifically a belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling. Background Technology

[0002] Direction-of-arrival (DOA) tracking technology for passive sonar arrays has irreplaceable strategic value in key areas such as covert operations, anti-submarine reconnaissance, and multi-target identification and tracking. Although existing DOA technologies have demonstrated good performance in controlled experimental environments, their effectiveness often significantly diminishes in real-world deployments. This challenge stems primarily from two factors: First, low signal-to-noise ratio (SNR) environments have become the norm. Increased ambient noise, advancements in platform noise reduction technologies, and the inherently limited gain of small-aperture sonar arrays all contribute to target feature blurring, severely challenging DOA estimation for weak targets. Second, with the diversification of combat scenarios, the demand for algorithm generalization capabilities is increasingly urgent, requiring DOA tracking systems to maintain stable performance under complex and non-ideal conditions, including dealing with clutter interference, multipath effects, and complex propagation environments.

[0003] Traditional methods for DOA tracking employ a two-stage, separate processing approach: detection followed by tracking. Their tracking performance heavily relies on detection accuracy and threshold settings, making it difficult to meet the stable tracking requirements of weak targets under low SNR conditions. In recent years, Track Before Detection (TBD) technology has provided a more effective solution framework for weak target tracking. Within this framework, multi-target tracking algorithms based on random finite set theory have emerged, such as Probability Hypothesis Density (PHD) filtering and Labeled Multi-Bernoulli (LMB) filtering. These methods construct accurate mathematical models by analyzing the distribution characteristics of array data, and then derive the likelihood function, achieving good tracking results for weak targets in specific scenarios. However, when the actual environment mismatches with the preset model, these methods still exhibit significant tracking errors. Existing research suffers from the following key shortcomings: First, the likelihood function modeling is highly dependent on the accuracy of the mathematical model, resulting in insufficient scene generalization ability; second, the lack of a mathematical framework for dynamically fusing single-frame detection and multi-frame tracking restricts further improvements in DOA tracking performance for weak targets in low SNR scenarios. Summary of the Invention

[0004] To address the shortcomings of the aforementioned technologies, this invention aims to provide a belief propagation (BP) passive sonar array DOA tracking method based on deep learning likelihood modeling. It uses deep learning (DL) to construct a data-driven likelihood function from the array's sampled covariance matrix, and then integrates it into the belief propagation (BP) tracking inference to achieve efficient state estimation. The learned likelihood function can capture the nonlinear relationship between array measurements and target states in complex environments, exhibiting excellent azimuth resolution and generalization performance under low SNR conditions. The BP inference process further correlates array measurements in the time dimension, enhancing the detectability of weak targets through time accumulation. Furthermore, by combining an interactive multi-model algorithm and a time-correlated target epoch mechanism, the tracking accuracy of maneuvering targets is improved while effectively suppressing the generation of false trajectories.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] A belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling includes the following steps:

[0007] 1) Based on the sampling covariance matrix of the sonar array, a CNN-based neural network is constructed to map the sampling covariance matrix to a sparse power spectrum.

[0008] 2) The sparse power spectrum data is smoothed and made continuous by Gaussian smoothing method, and then the likelihood function with continuous DOA value is obtained by cubic spline interpolation method.

[0009] 3) Construct a factor graph for the passive sonar array DOA tracking problem, and use the belief propagation algorithm to derive the messages transmitted between nodes in the factor graph, in conjunction with the likelihood function.

[0010] 4) Based on the information obtained through reasoning, calculate the confidence approximation of the marginal posterior probability density function of the target state, and use the least mean square root estimator to estimate the target DOA.

[0011] Based on the multi-channel sampling data of the sonar array, the array sampling covariance matrix is ​​constructed as follows:

[0012] Assumption There are moments in the scene A single sound source target, target DOA It is stated that the array system contains a total of Each hydrophone is in Time-sharing sampling The amplitude data is then in Time, array observation data at any time Through a A 3D vector is represented as:

[0013] ;

[0014] in, express 3D array guide vector, Indicate target exist time Dimensional sound source information, This represents zero-mean Gaussian white noise;

[0015] For the collected array data Perform a Fourier transform to obtain the array frequency domain data. Construct the sampling covariance matrix in the frequency domain. :

[0016] ;

[0017] in, This indicates the effective frequency band where the target sound source is located. This indicates the total number of frequency points contained within the frequency band after the Fourier transform. This indicates the conjugate transpose operation.

[0018] Constructing a CNN-based neural network to map the sampling covariance matrix to a sparse power spectrum includes the following steps:

[0019] Based on array parameter information and compass measurement information, an array steering vector that does not include the target frequency is constructed. ,in, express The time compass measures the angle of offset from the reference azimuth of the array, based on structure The second covariance matrix at time step , and Both serve as inputs to the neural network;

[0020] Extract separately and Using the real and imaginary parts of the integer part, a four-channel matrix input is constructed, and a sparse power spectrum is output through a CNN-based neural network. The sparse power spectrum It is a 361-dimensional vector with values ​​in the range [0,1], representing the probability value of the target's existence at the corresponding azimuth angle;

[0021] Based on sparse power spectrum Design corresponding labels ,variable and The dimensions are equal, so use the same method. This indicates that, combined with multi-classification tasks, for any angle... ,in The probability of the existence of the design target from different angles An angle with a value of 1, indicating that the target does not exist. The probability value is 0.

[0022] The CNN-based neural network consists of a Convolutional Neural Network (CNN) module and a Fully Connected Network (FCN) module. The CNN module comprises three convolutional layers with 32, 64, and 64 channels respectively, and each convolutional layer uses... The FCN uses convolutional kernels and contains three linear layers with output dimensions of 2048, 2048, and 361. Except for the last layer, which uses Sigmoid as the activation function, all other layers use ReLU activation. The CNN module and the FCN module are connected through 2D adaptive average pooling layers and flattening layers.

[0023] Supervised training of a CNN-based neural network is performed using the binary cross-entropy loss function. Specifically:

[0024] .

[0025] Step 2) includes the following steps:

[0026] Based on the Gaussian smoothing method, sparse power spectrum Smoothing is performed, where any angle , The probability value It is a sparse power spectrum The weighted average of all angular probability values, i.e.:

[0027]

[0028] in, This represents the standard deviation used to control the smoothness of the curve.

[0029] The smoothed power spectrum was obtained using cubic spline interpolation mathematical tools. The probability distribution of target occurrence is mapped to a continuous range of angle values ​​and defined as the likelihood function. ,in Indicate target exist The target state at any given moment.

[0030] Likelihood function obtained by combining CNN network Furthermore, based on the joint posterior probability density function pdf after factorization of the passive sonar array DOA tracking problem, a factor graph is constructed, specifically as follows:

[0031] Define the target state ,in Indicates the kinematic state of the target. and These represent the target's DOA and angular velocity, respectively. The target has decision variables. Used to indicate whether a target exists. Indicate target exist Always present This indicates that the target does not exist; the target motion model variables. Used to indicate the target motion model. This represents the total number of target motion models. time The set of target states is represented as follows: From the initial moment to The total set of states of the target at time t is represented as From the initial moment to The total set of sampling covariances of the time array is represented as: In order to estimate the target state , Based on Bayes' rule, a joint posterior PDF is constructed:

[0032] ;

[0033] in, Let represent the global likelihood function, assuming the array sampling covariance. With the target state Regarding time Conditional independence; additionally, the likelihood function is constructed based on the sparse power spectrum of the CNN network output. Also about the goal Conditionally independent, construct the factorized expression for the joint posterior pdf:

[0034] ;

[0035] in, Indicate target The prior distribution, The target state transition is represented in PDF format.

[0036] The variables in the factorized expression are extracted as variable nodes and represented by circles, while the function expression is represented by rectangles, thus constructing a factor graph for the DOA tracking problem of passive sonar arrays.

[0037] Based on the factor graph, the message is predicted using the belief propagation backpropagation algorithm, specifically as follows:

[0038] Predict messages based on factor graph message passing rules. for:

[0039] ;

[0040] in, It is a confidence approximation of the posterior pdf of the target state calculated in the previous moment;

[0041] Will Substitute into the prediction message calculation expression, when When, it indicates the target. exist The moment already exists, and from... Transmitted in real time At any given time, update the prediction of the existence of the message:

[0042] ;

[0043] in, Indicates the probability of the target's survival. In the model Target kinematic state transition under certain conditions (pdf) The model represents from Switch to The probability of;

[0044] when ,and When, it indicates that the target is at The moment does not exist, it needs to be New goals are constantly being generated, and the status of these goals is then transmitted to... At any given moment, the target state of newborns changes from the birth distribution. The sampled and updated prediction messages are as follows:

[0045] ;

[0046] Regardless of the goal exist Whether the information is always present or not, the prediction message must be guaranteed. The characteristic that the integral sum of the probability distributions is 1, i.e. Predicting the absence of messages at any time :

[0047] ;

[0048] For any target , Predicted news Includes prediction of existence message And the prediction does not exist. .

[0049] Based on the factor graph, the backpropagation (BP) algorithm for belief propagation is used to infer and update messages, specifically as follows:

[0050] Based on likelihood function nodes Update message for:

[0051] ;

[0052] when At that time, predict the message ;when At this time, the likelihood function It's meaningless; the target update message doesn't exist. Due to the state It is irrelevant, It is equivalent to a constant.

[0053] Step 4) specifically involves:

[0054] For any target , Based on predicted messages With Update Message ,calculate Always Believe :

[0055] ;

[0056] ;

[0057] in, Represents the normalization constant:

[0058] ;

[0059] Estimating the target using the least mean square root estimator (MMSE) exist state of time :

[0060] ;

[0061] in, This indicates the probability that the target exists.

[0062] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned confidence propagation passive sonar array DOA tracking method based on deep learning likelihood modeling.

[0063] The present invention has the following beneficial effects and advantages:

[0064] 1. The present invention proposes a belief propagation (BP) framework for likelihood function learning, which integrates the data-driven learning capability of deep learning (DL) with the multi-frame association characteristics of the BP algorithm, significantly improving the tracking robustness of weak targets in complex scenes.

[0065] 2. The method of this invention designs a CNN-based network structure, which nonlinearly maps the array sampling covariance matrix into a sparse power spectrum, and innovatively introduces array geometric parameters and compass measurement information as prior constraints, thereby optimizing the network feature extraction efficiency and reducing the model's dependence on label data.

[0066] 3. The method of this invention uses Gaussian smoothing and cubic spline interpolation techniques to convert the discretized sparse power spectrum into a continuous likelihood function, which can maintain stable generalization performance in different scenarios.

[0067] 4. The method of this invention constructs a Bayesian closed inference process based on the BP algorithm, and realizes dynamic estimation of the number and state of targets through message passing mechanism, which significantly improves the DOA tracking accuracy while maintaining computational efficiency.

[0068] 5. The method of this invention combines an interactive multi-model algorithm with a time-related target generation mechanism, which effectively suppresses the generation of false trajectories while maintaining high tracking accuracy for maneuvering targets. Attached Figure Description

[0069] Figure 1 This is an overall framework diagram of the method of the present invention;

[0070] Figure 2 This is a diagram of the CNN-based network structure constructed by the method of this invention;

[0071] Figure 3 It is established by the method of this invention. Time's up BP message factor graph at different times; Detailed Implementation

[0072] The present invention will be further described in detail below with reference to embodiments. The method steps will be described with reference to the accompanying drawings.

[0073] The basic idea of ​​this invention is to propose a belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling. This method combines high computational efficiency with strong environmental adaptability, achieving stable tracking of maneuvering targets even under low SNR conditions. Its innovation lies in dynamically constructing the likelihood function through deep learning, overcoming the limitation of traditional methods where the likelihood function is fixed to a specific distribution, thus possessing cross-scenario generalization capabilities. Although developed in the context of passive sonar, the core method of learning a continuous likelihood function and embedding it into Bayes inference is widely applicable to other sensing methods facing similar challenges, such as radar. Regarding clutter suppression, this invention addresses the issue from two aspects: firstly, it utilizes Fourier transform to extract only the target frequency band; secondly, it effectively suppresses the generation of false trajectories using a data-association-based target generation mechanism. To address the issue that likelihood function modeling relies on mathematical models, this invention designs a CNN-based network structure, which, through data-driven approaches, possesses generalization capabilities across different scenarios. To address the problem that existing deep learning methods output only sparse power spectra and do not satisfy the continuity of the likelihood function, this invention utilizes Gaussian smoothing and cubic spline interpolation techniques to transform the sparse power spectrum into a continuously valued likelihood function. To address the multi-target tracking problem, this invention derives a closed-form backpropagation (BP) method based on the proposed likelihood function, organically fusing single-frame detection with multi-frame correlation. This further improves the tracking capability for weak targets in low SNR scenarios while maintaining the inherent high computational efficiency of BP inference. To address the difficulty of effectively tracking maneuvering targets using a single model, this invention integrates an interactive multi-model algorithm during the tracking process, improving the ability to stably track maneuvering targets. This invention achieves superior DOA tracking stability and environmental adaptability for maneuvering targets in complex, low SNR scenarios.

[0074] like Figure 1 As shown, this embodiment designs a belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling. The input of the method is the array sampling covariance matrix. The output is the target state. The proposed framework mainly consists of two parts: a CNN-based network and a backpropagation (BP) inference process. The CNN network maps the sampling covariance to a likelihood function, while the BP algorithm uses this likelihood function to complete the message inference process and calculates the estimated target state with full confidence.

[0075] Based on the multi-channel sampling data of the sonar array, the array sampling covariance matrix is ​​constructed, assuming... There are moments in the scene A single sound source target, target DOA The array system comprises... Each hydrophone is in Time-sharing sampling Dimensional amplitude data. Taking time as an example, array observation data at any time. Through a A 3D vector is represented as:

[0076]

[0077] in, express 3D array guide vector, Indicate target exist time The sound source information is a non-Gaussian, stationary, zero-mean random process. This represents zero-mean Gaussian white noise.

[0078] To suppress noise and focus on the target frequency band of interest, the acquired array data... Perform a Fourier transform to obtain the array frequency domain data. Construct the sampling covariance matrix in the frequency domain. :

[0079]

[0080] in, This indicates the effective frequency band where the target sound source is located. This indicates the total number of frequency points contained within the frequency band after the Fourier transform. This indicates the conjugate transpose operation.

[0081] like Figure 2 As shown, a CNN-based neural network is constructed to map the sampling covariance matrix into a sparse power spectrum. First, the network's input information is constructed, including the aforementioned sampling covariance matrix. In addition, by taking into account array parameter information and compass measurement information, an array steering vector that does not include the target frequency is constructed. ,in, express The angle at which the time compass measurement array deviates from the reference azimuth. Based on ,structure The second input covariance matrix at time step .

[0082] Extract separately and The real and imaginary parts of the matrix are used to construct a four-channel input matrix, which is then processed by a CNN-based neural network to output a sparse power spectrum. The sparse power spectrum It is a 361-dimensional vector with values ​​in the range [0,1], representing the probability value of the target's existence at the corresponding azimuth angle.

[0083] Based on sparse power spectrum Design corresponding labels ,variable and The dimensions are equal, so use the same method. This indicates that, combined with multi-classification tasks, for any angle... ,in The probability of the existence of the design target from different angles An angle with a value of 1, indicating that the target does not exist. The probability value is 0.

[0084] The CNN-based neural network consists of a Convolutional Neural Network (CNN) module and a Fully Connected Network (FCN) module. The CNN comprises three convolutional layers with 32, 64, and 64 channels respectively, all using... The convolutional kernels are used. These layers are followed by 2D adaptive average pooling layers and flattening layers, which connect the CNN and FCN modules. The FCN contains three linear layers with output dimensions of 2048, 2048, and 361. Except for the last layer, which uses the Sigmoid activation function, all other layers use the ReLU activation function. The CNN and FCN modules are connected via 2D adaptive average pooling layers and flattening layers.

[0085] Supervised training of a CNN-based neural network is performed using the binary cross-entropy loss function. Specifically:

[0086]

[0087] Note the power spectral density obtained from the CNN network output Having probabilistic values ​​only at discrete angles does not satisfy the requirement that the likelihood function be continuously distributed in Bayesian tracking inference.

[0088] Based on the obtained sparse power spectrum First, the smoothed power spectrum is obtained using Gaussian smoothing technique. Then, using cubic spline interpolation, a continuous likelihood function of the target occurrence probability within an arbitrary angle range is obtained. Based on the Gaussian smoothing method, the sparse power spectrum is processed. Smoothing is performed, where any angle , The probability value It is a sparse power spectrum The weighted average of all angular probability values, i.e.:

[0089]

[0090] in, This represents the standard deviation used to control the smoothness of the curve. A larger standard deviation indicates a lower standard deviation. This will produce a smoother output curve, while a smaller one This will produce a steeper output curve.

[0091] Then, cubic spline interpolation was used to smooth the power spectrum. The probability distribution of target occurrence is mapped to a continuous range of angle values ​​and defined as the likelihood function. ,in Indicate target exist The target state at time t is used as the likelihood function, which will serve as a key factor node in subsequent backpropagation inference.

[0092] Define the target state ,in Indicates the kinematic state of the target. and These represent the target's DOA and angular velocity, respectively. The target has decision variables. Used to indicate whether a target exists. Indicate target exist Always present This indicates that the target does not exist; the target motion model variables. Used to indicate the target motion model. This represents the total number of target motion models. time The set of target states is represented as follows: From the initial moment to The total set of states of the target at time t is represented as From the initial moment to The total set of sampling covariances of the time array is represented as: In order to estimate the target state , Based on Bayes' rule, a joint posterior PDF is constructed:

[0093]

[0094] in, This represents the global likelihood function. Assume the array sampling covariance... With the target state Regarding time Conditional independence. Furthermore, the likelihood function is constructed based on the sparse power spectrum of the CNN network output. Also about the goal Conditionally independent, construct the factorized expression for the joint posterior pdf:

[0095]

[0096] in, Indicate target The prior distribution, The target state transition is represented in PDF format.

[0097] like Figure 3 As shown, the likelihood function obtained by combining the CNN network Based on the above factorized joint posterior PDF, a model is constructed from... Time's up The factor graph at time step. Variables in the factorized expression are extracted as variable nodes, represented by circles, and the function expression is represented as factor nodes, represented by rectangles. This factor graph contains two messages to be solved, defined as the predicted messages. and update messages .

[0098] Predict messages based on factor graph message passing rules. for:

[0099]

[0100] in, It is a confidence approximation of the posterior pdf of the target state calculated in the previous moment.

[0101] Will Substitute the predicted message into the calculation expression. When When, it indicates the target. exist The moment already exists, and from... Transmitted in real time At any given time, update the prediction of the existence of the message:

[0102]

[0103]

[0104] in, Indicates the probability of the target's survival. In the model Target kinematic state transition under certain conditions (pdf) The model represents from Switch to The probability of.

[0105] when ,and When, it indicates that the target is at The moment does not exist, it needs to be New goals are constantly being generated, and the status of these goals is then transmitted to... Moment. Newborn target state from birth distribution The sampled and updated prediction messages are as follows:

[0106]

[0107]

[0108] It is noted that the mechanism of generating a new target state by associating the previous moment with the current moment can effectively suppress the generation of false trajectories compared to generating a new target directly from the current moment.

[0109] Regardless of the goal exist Whether the information is always present or not, the prediction message must be guaranteed. The characteristic that the integral sum of the probability distributions is 1, i.e. Predicting the absence of messages at any time :

[0110]

[0111] For any target , Predicted news Includes prediction of existence message And the prediction does not exist. .

[0112] Based on likelihood function nodes Update message for:

[0113]

[0114] when At that time, predict the message ;when At this time, the likelihood function It's meaningless; the target update message doesn't exist. Because of the state Irrelevant It is equivalent to a constant.

[0115] For any target , Based on predicted messages With Update Message ,calculate Always Believe :

[0116]

[0117] in, Represents the normalization constant:

[0118]

[0119] Estimating the target using the least mean square root estimator (MMSE) exist state of time :

[0120]

[0121] in, This indicates the probability that the target exists.

Claims

1. A belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling, characterized in that, Includes the following steps: 1) Based on the sampling covariance matrix of the sonar array, a CNN-based neural network is constructed to map the sampling covariance matrix to a sparse power spectrum. 2) The sparse power spectrum data is smoothed and made continuous by Gaussian smoothing method, and then the likelihood function with continuous DOA value is obtained by cubic spline interpolation method. 3) Construct a factor graph for the passive sonar array DOA tracking problem, and use the belief propagation algorithm to derive the messages transmitted between nodes in the factor graph, in conjunction with the likelihood function. 4) Based on the information obtained through reasoning, calculate the confidence approximation of the marginal posterior probability density function of the target state, and use the least mean square root estimator to estimate the target DOA.

2. The belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling according to claim 1, characterized in that, Based on the multi-channel sampling data of the sonar array, the array sampling covariance matrix is ​​constructed as follows: Assumption There are moments in the scene A single sound source target, target DOA It is stated that the array system contains a total of Each hydrophone is in Time-sharing sampling The amplitude data, then in Time, array observation data at any time Through a A 3D vector is represented as: ； in, express 3D array guide vector, Indicate target exist time Dimensional sound source information, This represents zero-mean Gaussian white noise; For the collected array data Perform a Fourier transform to obtain the array frequency domain data. Construct the sampling covariance matrix in the frequency domain. : ； in, This indicates the effective frequency band where the target sound source is located. This indicates the total number of frequency points contained within the frequency band after the Fourier transform. This indicates the conjugate transpose operation.

3. The belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling according to claim 1, characterized in that, Constructing a CNN-based neural network to map the sampling covariance matrix to a sparse power spectrum includes the following steps: Based on array parameter information and compass measurement information, an array steering vector that does not include the target frequency is constructed. ,in, express The time compass measures the angle of offset from the reference azimuth of the array, based on structure The second covariance matrix at time step , and Both serve as inputs to the neural network; Extract separately and Using the real and imaginary parts of the integer part, a four-channel matrix input is constructed, and a sparse power spectrum is output through a CNN-based neural network. The sparse power spectrum It is a 361-dimensional vector with values ​​in the range [0,1], representing the probability value of the target's existence at the corresponding azimuth angle; Based on sparse power spectrum Design corresponding labels ,variable and The dimensions are equal, so use the same method. This indicates that, combined with multi-classification tasks, for any angle... ,in The probability of the existence of the design target from different angles An angle with a value of 1, indicating that the target does not exist. The probability value is 0.

4. The belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling according to claim 3, characterized in that, The CNN-based neural network consists of a Convolutional Neural Network (CNN) module and a Fully Connected Network (FCN) module. The CNN module comprises three convolutional layers with 32, 64, and 64 channels respectively, and each convolutional layer uses... The FCN uses convolutional kernels and contains three linear layers with output dimensions of 2048, 2048, and 361. Except for the last layer, which uses Sigmoid as the activation function, all other layers use ReLU activation. The CNN module and the FCN module are connected through 2D adaptive average pooling layers and flattening layers. Supervised training of a CNN-based neural network is performed using the binary cross-entropy loss function. Specifically: 。 5. The belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling according to claim 1, characterized in that, Step 2) includes the following steps: Based on the Gaussian smoothing method, sparse power spectrum Smoothing is performed, where any angle , The probability value It is a sparse power spectrum The weighted average of all angular probability values, i.e.: ； in, This represents the standard deviation used to control the smoothness of the curve. The smoothed power spectrum was obtained using cubic spline interpolation mathematical tools. The probability distribution of target occurrence is mapped to a continuous range of angle values ​​and defined as the likelihood function. ,in Indicate target exist The target state at any given moment.

6. The belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling according to claim 1, characterized in that, Likelihood function obtained by combining CNN network Furthermore, based on the joint posterior probability density function pdf after factorization of the passive sonar array DOA tracking problem, a factor graph is constructed, specifically as follows: Define the target state ,in Indicates the kinematic state of the target. and These represent the target's DOA and angular velocity, respectively. The target has decision variables. Used to indicate whether a target exists. Indicate target exist Always present This indicates that the target does not exist; the target motion model variables. Used to indicate the target motion model. This represents the total number of target motion models. time The set of target states is represented as follows: From the initial moment to The total set of states of the target at time t is represented as From the initial moment to The total set of sampling covariances of the time array is represented as: In order to estimate the target state , Based on Bayes' rule, a joint posterior PDF is constructed: ； in, Let represent the global likelihood function, assuming the array sampling covariance. With the target state Regarding time Conditional independence; additionally, the likelihood function is constructed based on the sparse power spectrum of the CNN network output. Also about the goal Conditionally independent, construct the factorized expression for the joint posterior pdf: ； in, Indicate target The prior distribution, The target state transition is represented in PDF format. The variables in the factorized expression are extracted as variable nodes and represented by circles, while the function expression is represented by rectangles, thus constructing a factor graph for the DOA tracking problem of passive sonar arrays.

7. The belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling according to claim 1, characterized in that, Based on the factor graph, the message is predicted using the belief propagation backpropagation algorithm, specifically as follows: Predict messages based on factor graph message passing rules. for: ； in, It is a confidence approximation of the posterior pdf of the target state calculated in the previous moment; Will Substitute into the prediction message calculation expression, when When, it indicates the target. exist The moment already exists, and from... Transmitted in real time At any given time, update the predicted existence of the message: ； in, Indicates the probability of the target's survival. In the model Target kinematic state transition under certain conditions (pdf) The model represents from Switch to The probability of; when ,and When, it indicates that the target is at The moment does not exist, it needs to be New goals are constantly being generated, and the status of these goals is then transmitted to... At any given moment, the target state of newborns changes from the birth distribution. The sampled and updated prediction messages are as follows: ； Regardless of the goal exist Whether the information is always present or not, the prediction message must be guaranteed. The characteristic that the integral sum of the probability distributions is 1, i.e. Predicting the absence of messages at any time : ； For any target , Predicted news Includes prediction of existence message And the prediction does not exist. .

8. The belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling according to claim 1, characterized in that, Based on the factor graph, the backpropagation (BP) algorithm for belief propagation is used to infer and update messages, specifically as follows: Based on likelihood function nodes Update message for: ； when At that time, predict the message ;when At this time, the likelihood function It's meaningless; the target update message doesn't exist. Due to the state It is irrelevant, It is equivalent to a constant.

9. The belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling according to claim 1, characterized in that, Step 4) specifically involves: For any target , Based on predicted messages With Update Message ,calculate Always Believe : ； ； in, Represents the normalization constant: ； Estimating the target using the least mean square root estimator (MMSE) exist state of time : ； in, This indicates the probability that the target exists.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements a belief propagation passive sonar array DOA tracking method based on deep learning likelihood modeling as described in any one of claims 1-9.

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