Underwater acoustic signal direction of arrival estimation method based on improved Mama network

Abstract

The invention belongs to the field of underwater acoustic array signal processing, and particularly relates to an underwater acoustic signal direction-of-arrival estimation method based on an improved Mama network, which comprises the following steps of: 1, establishing a hydrophone array model, independently sampling an information source signal, calculating a covariance matrix of the signal, separating a real part and an imaginary part of the covariance matrix, and calculating a direction-of-arrival estimation model; carrying out normalization processing on the covariance matrix after splicing processing, and taking the covariance matrix as a data set training model; step 2, establishing a lightweight module based on a Mama network, compressing a covariance matrix, adjusting dimensions, obtaining relevance of information, mixing signals of all time steps, and outputting a characteristic spectrogram of the signals; 3, processing the characteristic spectrogram by using a CBMA module, and outputting an estimated value of a corresponding direction of arrival by using a Sigmoid function after adjusting dimensions through a full connection layer; and 4, cascading the models, training by using a data set, adjusting parameters, and carrying out direction-of-arrival estimation on unknown signals by using the trained models. The operation complexity is reduced, and the method is more suitable for the underwater environment.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater acoustic array signal processing, and in particular relates to an underwater acoustic signal arrival direction estimation method based on an improved Mamba network. Background Art

[0002] Underwater acoustic communication refers to a communication method that uses water as a transmission medium to transmit information through sound waves. It has the characteristics of relatively small attenuation and strong penetration ability. It is currently the only way to achieve long-distance underwater communication. It is widely used in underwater detection, marine resource development and other fields. The hydrophone array can receive and send sound information of underwater equipment, which is crucial for the communication and positioning of underwater equipment.

[0003] In order to further improve the target positioning accuracy and communication quality of underwater equipment, the direction of arrival (DOA) estimation technology is widely used. It analyzes the arrival angle of the sound source signal through the hydrophone array to achieve accurate estimation of the target position. However, due to the problems of large noise interference and significant multipath effect faced by the underwater acoustic channel, underwater nodes are mostly powered by batteries, and their energy is limited. The performance of conventional DOA estimation methods will be significantly reduced, thus affecting the accuracy of underwater target positioning.

[0004] Therefore, a DOA estimation method with low complexity and high accuracy is needed to achieve high-resolution underwater acoustic signal direction of arrival estimation. Summary of the invention

[0005] In view of the shortcomings in the prior art, the purpose of the present invention is to provide an underwater acoustic array signal direction of arrival (DOA) estimation method based on the Mamba network and CBAM module, which estimates the angle signal through regression and uses a deep learning method to perform comprehensive feature extraction on the signal angle information, thereby solving the problems of poor versatility, low accuracy and high complexity of traditional methods.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a method for estimating the direction of arrival of underwater acoustic signals based on an improved Mamba network, comprising the following steps: Step 1: Establish a hydrophone array model, sample the source signal independently, calculate the covariance matrix of the signal, separate the real and imaginary parts of the covariance matrix, concatenate it in the vertical dimension to obtain a matrix of size 2M×M, and normalize the concatenated covariance matrix as the data set training model; Step 2: Build a lightweight module based on the Mamba network, compress the normalized covariance matrix, adjust the dimension, obtain the correlation of information at different times, dynamically control the output weight through the gating mechanism, mix the signals of all time steps, capture the deep-level features of the signal, and output the characteristic spectrum of the signal; Step 3: Process the feature spectrogram using the CBMA module to capture the correlation between deep-level features, pay attention to important features, and use the Sigmoid function to output the estimated value of the corresponding direction of arrival after adjusting the dimension through the fully connected layer; Step 4: Cascade the models of steps 2 and 3, use the data set in step 1 for training, adjust the parameters during the training process, and use the trained model to estimate the direction of arrival of unknown signals after the model training is completed.

[0007] In the above-mentioned method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network, in step 1, a hydrophone array model is established, and independent sampling of the source signal includes: Step 1-1: vertically deploy a uniform linear hydrophone array with M array elements underwater, where each array element corresponds to a single channel and the array element spacing is d and is less than half the wavelength of the signal; Step 1-2: Calculate the delay difference based on the path difference D between the mth array element and the previous array element ,in, represents the speed of sound, ,in Represents the incident angle of all possible incoming wave directions; Step 1-3: According to the delay difference, the phase difference of the mth array element is obtained as: ,in, represents the wavelength of the carrier wave, represents the imaginary unit, represents the frequency of the signal, Indicated in The incident angle in the direction of the incoming wave, e represents a natural constant; Step 1-4: The signal received by the mth array element under the influence of underwater noise is expressed as: ,in, is the noise received by the mth array element, Indicates the current incoming wave direction. represents all possible directions of incoming waves in space, Indicates A narrowband signal source; Step 1-5: Represent the signal in step 1-4 using a matrix: ,in, represents the signal matrix, represents the noise matrix, , represents the flow matrix of the signal, and T represents the time period.

[0008] The above-mentioned underwater acoustic signal arrival direction estimation method based on the improved Mamba network calculates the formula of the covariance matrix of the signal as follows: ,in, represents the covariance matrix of the signal, represents the input matrix, It represents the conjugate transpose of the matrix. For a finite length signal, can be caused by The snapshot sampling is obtained at the moment To express it, the expression can be written as: .

[0009] In the above-mentioned method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network, step 1 further comprises: Perform min-max normalization on the spliced ​​results. ,in, represents the signal after normalization, S represents the signal before normalization, and Indicates the maximum and minimum values ​​of the signal within the carrier period.

[0010] In the above-mentioned method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network, step 2 comprises: Step 2-1: Perform a 2M×1 one-dimensional convolution operation on the data in step 1 to expand the 2M×M matrix into a 1×M sequence. The expression of the one-dimensional convolution is: ,in, represents the input of the first convolutional layer, and They represent the weight matrix and bias term of the tth convolution kernel in the first convolution layer respectively. represents the output of the tth convolution kernel in the first convolution layer, represents the activation function; Step 2-2: Use RELU as the activation function of the one-dimensional convolutional layer. The expression of the RELU function is: ,in, represents the input signal; Step 2-3: Flatten the matrix signal and input it into the Mamba model, including the state space model and the gating unit to synchronously process the signal, and dynamically control the output weight through the gating mechanism; Step 2-4: Use the Sigmoid function to normalize the gate value to the [0,1] interval. The expression of the Sigmoid function is: ; Step 2-5: After repeating the above steps for the entire sequence, the information at all moments is merged. The information at each moment contains the state information of the previous moment, and the deep-level features of the signal are extracted.

[0011] In the above-mentioned method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network, steps 2-3 include: Step a: The matrix signal is dimensionalized through a linear layer to obtain a one-dimensional sequence of length 32×M. Layer normalization is used to reduce the offset of the internal variables of the model. The expression of layer normalization is as follows: ,in, represents the normalized output of the layer, represents the normalized input of the layer, and Respectively represent the mean and standard deviation of the output of each neuron in the linear layer during the whole process, is a small constant; Step b: The output sequence is expressed through the state space model, the state update equation and the output equation as follows: , where V is the state transfer matrix, used to control the change of state over time, B is the input mapping matrix, which maps the input signal to the state space, F is the output mapping matrix, which maps the state to the output space, and G is the direct transfer matrix, which is used to map the output signal directly to the output; Step c: For each moment of information, a time mixing method is introduced. ,in represents the batch size, represents the sequence length, represents the hidden dimension, and the temporal mixing is represented as ,in, represents element-wise multiplication, represents a learnable time parameter, Represents a movement operation in time; Step d: Integrated time step The time mixing output can be expressed as: ,The time step adopts an exponential decay method, the size can be learned, and it is dynamically allocated by the optimizer to adaptively adjust each time step.

[0012] In the above-mentioned method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network, in step 3, the CBMA module includes a channel attention mechanism and a spatial attention mechanism, and extracts the input features in two stages by sequentially inferring the attention maps in the two dimensions of channel and space.

[0013] In the above-mentioned method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network, step 3 comprises: Step 3-1: The signal passes through the channel attention module, and the channel relationship between features is used to generate a channel attention map to capture the correlation between different channels, expressed as: ,in, represents the sigmoid activation function, and Represent the dimensionality reduction convolution and dimensionality increase convolution operations respectively, and Represent average pooling and maximum pooling operations respectively; Step 3-2: The signal passes through the spatial attention module, which uses the spatial relationship between features to capture the importance information of different spatial positions in the features, thereby extracting features in a targeted manner, expressed as: ,in, Indicates that a convolution operation is performed using a convolution kernel of size 7×7. Indicates that the results of average pooling and maximum pooling are concatenated in the channel dimension; Step 3-3: Process the signal through three fully connected layers. The expression of the fully connected layer is: ,in, represents the input of the fully connected layer, represents the output of the fully connected layer, represents the weight matrix between two hidden layers, represents the weight matrix between the second hidden layer and the output layer, and represents the bias term, and represents the activation function; Step 3-4: Use the Sigmoid function as the output layer to convert the arrival angle into a continuous distribution between [0,1], and then obtain the arrival direction estimation result through denormalization.

[0014] In the above-mentioned method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network, step 4 comprises: Step 4-1: Label the signal according to different angles and use it as a training set to train the network model; Step 4-2: During the training process, the mini-batch gradient descent method is used to train the neural network. The training set is divided into several groups of data. The neural network learns information from one group of data in each iteration. Step 4-3: Select mean square error as the loss function and minimize the loss function as the training goal. The expression of mean square error MSE is: ,in represents the number of samples, and Represent the true value and estimated value of the sample respectively; Step 4-4: Iterate the network model multiple times, optimize the network model parameters with the training objectives in step 4-3, save the model parameters as model weights, input the unlabeled signal received by the hydrophone array, and the model outputs the angle information of the wave to accurately estimate the direction of arrival.

[0015] Compared with the traditional method, the method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network of the present invention has the following beneficial effects: the traditional signal subspace-based method and beamforming method require a long time of spectrum peak search, the algorithm operation complexity is high, and it is difficult to apply to the underwater energy-constrained environment. The method of the present invention uses a deep learning method to extract signal context features through the Mamba network, uses the attention mechanism of the CBAM module to pay attention to important features, reduces the computational complexity, and the trained model only occupies a small amount of computing resources during reasoning, which is more suitable for underwater environments.

[0016] The accuracy of the traditional DOA estimation method based on compressed sensing depends on the grid resolution, and it is difficult to achieve super-resolution DOA estimation. The present invention uses a neural network to construct a regression model, and the DOA estimation result output by the network is continuous and has a higher resolution.

[0017] There is strong noise interference in the underwater environment. The traditional method is easily interfered by noise under high signal-to-noise ratio conditions, and the estimation result deviates greatly from the true value. The method proposed in the present invention relies on the powerful feature extraction capability of neural network and Mamba architecture, and can accurately extract signal angle features under strong interference conditions with stronger robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a scene graph implemented in an embodiment of the present invention; Figure 2 is a schematic diagram of a hydrophone array receiving a signal in an embodiment of the present invention; Figure 3 It is a schematic diagram of the network structure in an embodiment of the present invention. DETAILED DESCRIPTION

[0019] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is described below in conjunction with specific implementation methods and drawings.

[0020] In underwater wireless sensor networks, a linear hydrophone array is used to receive water acoustic signals, the array received signals are modeled, the covariance matrix of the array signals is calculated, and they are used as network input after splicing and preprocessing. An improved deep learning model based on the Mamba network is designed to process signal samples. The network consists of multiple improved Mamba blocks, which extract the correlation between data with the help of Mamba's powerful feature extraction capabilities and low complexity. The state space model and gating mechanism are used to process the signal and extract the multi-dimensional features of the signal. Then, the CBAM module is used to capture the key features using the channel attention mechanism and the spatial attention mechanism, and the computational complexity is reduced. The DOA estimation problem is transformed into a regression problem, and the Sigmoid function is used to output the continuous estimated value of the corresponding angle to improve the network resolution.

[0021] like Figure 1-3 As shown, a method for estimating the direction of arrival of underwater acoustic signals based on an improved Mamba network comprises the following steps: Step 1: Establish a hydrophone array model, sample the source signal independently, calculate the covariance matrix of the signal, separate the real and imaginary parts of the covariance matrix, concatenate it in the vertical dimension to obtain a matrix of size 2M×M, and normalize the processed covariance matrix to obtain a data training model; Step 2: Build a lightweight module based on the Mamba network to compress the signal matrix, adjust the dimension, obtain the correlation of information at different times, dynamically control the output weight through the gating mechanism, mix the signals of all time steps, and capture the deep-level characteristics of the signal; Step 3: Use the CBMA module to process the output of step 2 to capture the correlation between features, pay attention to important features, adjust the dimension through the fully connected layer, and use the Sigmoid function to output the estimated value of the corresponding direction of arrival; Step 4: Adjust the parameters to train the data training model in step 1, and use the trained model to estimate the direction of arrival of the unknown signal.

[0022] Specifically, a method for estimating the direction of arrival of underwater acoustic signals based on an improved Mamba network is described in detail. Figure 1 The application scenario of the present invention is to use a hydrophone array to receive signals sent by a target device in an underwater wireless sensor network, and estimate the direction of arrival based on the angle of the incoming wave.

[0023] Reference Figure 2 , the embodiment process of the array receiving signal in the present invention is as follows: Step 1: Establish a hydrophone array model and obtain array reception data.

[0024] In underwater application scenarios, for ease of deployment, a uniform linear hydrophone array model is often used to receive the signal sent by the signal source. The number of array elements used is The hydrophone array has each array element corresponding to a single channel and the array element spacing is and is smaller than half the wavelength of the signal. We assume that , ,…… direction, in the far field there is Individual and An irrelevant narrowband signal source is incident on the array element. There is a path difference between the array element and the previous array element , which can be expressed as: , in Represents the incident angle of all possible incoming wave directions.

[0025] Based on this, the delay difference can be calculated: ,in Indicates the speed of sound.

[0026] The first The phase difference of each array element can be expressed as: , in, represents the wavelength of the carrier wave, represents the imaginary unit, represents the frequency of the signal, Indicated in The incident angle in the direction of the incoming wave, e represents a natural constant. Considering the influence of underwater noise, such as Figure 2 As shown, yes The sub-element in represents the Mth array element in the array, then the The signal received by each array element can be expressed as: , in, Indicates the current incoming wave direction. represents all possible directions of incoming waves in space, Indicates A narrowband signal source, For the The receiving noise of each array element. Usually, for intuitive expression, the above formula is expressed in the form of a matrix: , in, represents the signal matrix, represents the noise matrix, Represents the flow matrix of the signal. In the actual process, it is necessary to collect The sampling snapshot within a period of time, at which time the received signal Receive signal Contains original information such as signal waveform, modulation method, frequency, bandwidth, angle, etc.

[0027] Step 2: Calculate the covariance matrix of the array received signal and preprocess the covariance matrix.

[0028] For the received signal in step 1 , calculate its covariance matrix, the covariance matrix can be expressed as: , in, represents the covariance matrix of the signal, represents the input matrix, It represents the conjugate transpose of the matrix. In practical applications, since the received signal is of finite length, can be caused by The snapshot sampling is obtained at the moment To express it, the expression can be written as: , The above formula obtains This is the complex covariance matrix. Compared with the original signal, it contains fewer information dimensions and is easier to process. is a complex matrix. In order to avoid feature loss and preserve signal integrity, Separate into real part and the imaginary part , whose expression is: , , For an array of M elements, we have The real matrix of and the imaginary matrix , concatenate them in the vertical dimension to obtain a matrix of size 2M×M. The matrix is ​​normalized and the calculation method is: , in, represents the normalized signal. represents the signal before normalization, and Represents the maximum and minimum values ​​of the carrier signal, and the data obtained is used to train the network model.

[0029] Reference Figure 3The embodiment process of Mamba network construction and training in the present invention is as follows: Step 1: Build a network model and input the signal.

[0030] Specifically, the input data must first undergo a 2M×1 one-dimensional convolution operation to convert the size The matrix of is expanded into a 1×M sequence. The expression of one-dimensional convolution is: , in, represents the input of the first convolutional layer, and Respectively represent the weight matrix and bias term of the tth convolution kernel in the first convolution layer, Represents the output of the tth convolution kernel in the first convolution layer, Represents the activation function. For the one-dimensional convolution layer, RELU is used as the activation function to reduce the computational overhead. The expression of the RELU function is: , in, Indicates the input signal.

[0031] After flattening the matrix signals, they are input into the Mamba model, which contains the state space model (SSM) and the gating unit to process the signals synchronously. The Mamba model provides an efficient method for processing sequence data by utilizing selective state space and structured state space components.

[0032] Specifically, the matrix signal is dimensionalized through a linear layer to obtain a one-dimensional sequence of length 32×M, and layer normalization is used to reduce the offset of the internal variables of the model. The expression of layer normalization is as follows: , in represents the normalized output of the layer, represents the normalized input of the layer, and Respectively represent the mean and standard deviation of the output of each neuron in the linear layer during the whole process, is a small constant used to prevent the denominator from being zero.

[0033] The normalized output is processed using the Dropout layer to discard the output of some neurons to prevent the network from overfitting. The Dropout expression can be expressed as: , Among them, x represents the signal received by the dropout layer, It is a binary mask, which has only two expressions: 0 and 1. 0 means discarding, and 1 means keeping. represents the drop probability of each neuron.

[0034] The output sequence is passed through the state space model, and its basic table form can be represented by the following state update equation and output equation: , Among them, V is the state transfer matrix, which is used to control the change of state over time. B is the input mapping matrix, which maps the input signal to the state space. F is the output mapping matrix, which maps the state to the output space. G is the direct transfer matrix, which is used to directly map the output signal to the output. Parameters A, B, and F are learnable and are updated in real time by the network. The direct transfer matrix G is cancelled to reduce the computational complexity and the number of parameters.

[0035] For the information at each moment, a time mixing method is introduced. ,in represents the batch size, represents the sequence length, represents the hidden dimension, and the time mixture can be expressed as , represents element-wise multiplication, represents a learnable time parameter, represents the movement operation in time. Considering the time step The time mixing output can be expressed as: , e represents the natural number base, which is the natural number base e commonly used in mathematics, not a symbol; The time step size is exponentially decayed. The size is learnable and dynamically allocated by the optimizer to adaptively adjust each time step.

[0036] In each time step, the output weight is dynamically controlled by the gating mechanism. The gate value is normalized to the [0,1] interval using the Sigmoid function. The expression of the Sigmoid function is: , Where e represents a natural constant. After repeating the above steps for the entire sequence, the information at all moments is merged. The information at each moment contains the state information at the previous moment, and the deep-level features of the signal are extracted. SiLU is introduced as an activation function to enhance the nonlinear representation ability of the model. The expression of SiLU is: , After that, the signal is input into the CBAM module. The CBAM module mainly consists of a channel attention mechanism and a spatial attention mechanism. Through the channel attention module, the channel attention map is generated by utilizing the channel relationship between features and capturing the correlation between different channels. It can be expressed as: , in, represents the sigmoid activation function, and Represent the dimensionality reduction convolution and dimensionality increase convolution operations respectively, and Represent average pooling and maximum pooling operations respectively.

[0037] After that, the spatial attention module uses the spatial relationship between features to capture the importance information of different spatial positions in the features, so as to extract features in a targeted manner. This module can be expressed as: , in, Indicates that a convolution operation is performed using a convolution kernel of size 7×7. It means concatenating the results of average pooling and maximum pooling in the channel dimension. It can extract deep features of the signal without introducing additional calculations, which helps to reduce the computational complexity.

[0038] Finally, the signal is processed through three fully connected layers. The expression of the fully connected layer is as follows , in, represents the input of the fully connected layer, represents the output of the fully connected layer, represents the weight matrix between two hidden layers, represents the weight matrix between the second hidden layer and the output layer, and represents the bias term, and Represents the activation function.

[0039] The Sigmoid function is used as the output layer to convert the arrival angle into a continuous distribution between [0, 1] to improve the network resolution. The arrival direction estimation result is then obtained through denormalization.

[0040] Step 2: Train the network and fine-tune it, saving the best model weights.

[0041] Specifically, the signals are labeled according to different angles and used as training sets to train the network model. During the training process, the mini-batch gradient descent method is used to train the neural network. The training set is divided into several groups of data. The neural network learns information from one group of data in each iteration. The mean square error (MSE) is selected as the loss function, and the minimization of the loss function is the training goal. The expression of MSE is as follows: , in, represents the number of samples, and represent the true value and estimated value of the sample respectively.

[0042] Iterate the network model multiple times and save the most accurate weight for the DOA estimation result as the best model weight. After saving the trained model, input the unlabeled signal received by the hydrophone array, and the model outputs the angle information of the wave to accurately estimate the DOA.

[0043] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for a person skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to replace some of the technical features therein by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions claimed to be protected by the present invention.

Claims

1. A method for estimating the direction of arrival of underwater acoustic signals based on an improved Mamba network, characterized in that: The following steps are involved: Step 1: Establish a hydrophone array model, sample the source signal independently, calculate the covariance matrix of the signal, separate the real and imaginary parts of the covariance matrix, concatenate it in the vertical dimension to obtain a matrix of size 2M×M, and normalize the concatenated covariance matrix as the data set training model; Step 2: Build a lightweight module based on the Mamba network, compress the normalized covariance matrix, adjust the dimension, obtain the correlation of information at different times, dynamically control the output weight through the gating mechanism, mix the signals of all time steps, capture the deep-level features of the signal, and output the characteristic spectrum of the signal; Step 3: Process the feature spectrogram using the CBMA module to capture the correlation between deep-level features, pay attention to important features, and use the Sigmoid function to output the estimated value of the corresponding direction of arrival after adjusting the dimension through the fully connected layer; Step 4: Cascade the models of steps 2 and 3, use the data set in step 1 for training, adjust the parameters during the training process, and use the trained model to estimate the direction of arrival of unknown signals after the model training is completed.

2. The method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network according to claim 1 is characterized in that: In step 1, a hydrophone array model is established, and independent sampling of source signals includes: Step 1-1: vertically deploy a uniform linear hydrophone array with M array elements underwater, where each array element corresponds to a single channel and the array element spacing is d and is less than half the wavelength of the signal; Step 1-2: Calculate the delay difference based on the path difference D between the mth array element and the previous array element ,in, represents the speed of sound, ,in Represents the incident angle of all possible incoming wave directions; Step 1-3: According to the delay difference, the phase difference of the mth array element is obtained as: ,in, represents the wavelength of the carrier wave, represents the imaginary unit, represents the frequency of the signal, Indicated in The incident angle in the direction of the incoming wave, e represents a natural constant; Step 1-4: The signal received by the mth array element under the influence of underwater noise is expressed as: ,in, is the noise received by the mth array element, Indicates the current incoming wave direction. represents all possible directions of incoming waves in space, Indicates A narrowband signal source; Step 1-5: Represent the signal in step 1-4 using a matrix: ,in, represents the signal matrix, represents the noise matrix, , represents the flow matrix of the signal, and T represents the time period.

3. The method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network according to claim 2 is characterized in that: The formula for calculating the covariance matrix of a signal is: ,in, represents the covariance matrix of the signal, represents the input matrix, It represents the conjugate transpose of the matrix. For a finite length signal, can be caused by The snapshot sampling is obtained at the moment To express it, the expression can be written as: 。 4. The method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network according to claim 3 is characterized in that: The step 1 also includes: Perform min-max normalization on the spliced ​​results. ,in, represents the signal after normalization, S represents the signal before normalization, and Indicates the maximum and minimum values ​​of the signal within the carrier period.

5. The method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network according to claim 1 is characterized in that: The step 2 comprises: Step 2-1: Perform a 2M×1 one-dimensional convolution operation on the data in step 1 to expand the 2M×M matrix into a 1×M sequence. The expression of the one-dimensional convolution is: ,in, represents the input of the first convolutional layer, and They represent the weight matrix and bias term of the tth convolution kernel in the first convolution layer respectively. represents the output of the tth convolution kernel in the first convolution layer, represents the activation function; Step 2-2: Use RELU as the activation function of the one-dimensional convolutional layer. The expression of the RELU function is: ,in, represents the input signal; Step 2-3: Flatten the matrix signal and input it into the Mamba model, including the state space model and the gating unit to synchronously process the signal, and dynamically control the output weight through the gating mechanism; Step 2-4: Use the Sigmoid function to normalize the gate value to the [0,1] interval. The expression of the Sigmoid function is: , e represents the natural number base constant; Step 2-5: After repeating the above steps for the entire sequence, the information at all moments is merged. The information at each moment contains the state information of the previous moment, and the deep-level features of the signal are extracted.

6. The method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network according to claim 5 is characterized in that: The steps 2-3 include: Step a: The matrix signal is dimensionalized through a linear layer to obtain a one-dimensional sequence of length 32×M. Layer normalization is used to reduce the offset of the internal variables of the model. The expression of layer normalization is as follows: ,in, represents the normalized output of the layer, represents the normalized input of the layer, and Respectively represent the mean and standard deviation of the output of each neuron in the linear layer during the whole process, is a small constant; Step b: The output sequence is expressed through the state space model, the state update equation and the output equation as follows: , where V is the state transfer matrix, used to control the change of state over time, B is the input mapping matrix, which maps the input signal to the state space, F is the output mapping matrix, which maps the state to the output space, and G is the direct transfer matrix, which is used to map the output signal directly to the output; Step c: For each moment of information, a time mixing method is introduced. ,in represents the batch size, represents the sequence length, represents the hidden dimension, and the temporal mixing is represented as ,in, represents element-wise multiplication, represents a learnable time parameter, Represents a movement operation in time; Step d: Integrated time step The time mixing output can be expressed as: ,The time step adopts an exponential decay method, the size can be learned, and it is dynamically allocated by the optimizer to adaptively adjust each time step.

7. The method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network according to claim 1 is characterized in that: In step 3, the CBMA module includes a channel attention mechanism and a spatial attention mechanism, and extracts input features in two stages by sequentially inferring attention maps in the channel and space dimensions.

8. The method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network according to claim 7 is characterized in that: The step 3 comprises: Step 3-1: The signal passes through the channel attention module, and the channel relationship between features is used to generate a channel attention map to capture the correlation between different channels, expressed as: ,in, represents the sigmoid activation function, and Represent the dimensionality reduction convolution and dimensionality increase convolution operations respectively, and Represent average pooling and maximum pooling operations respectively; Step 3-2: The signal passes through the spatial attention module, which uses the spatial relationship between features to capture the importance information of different spatial positions in the features, thereby extracting features in a targeted manner, expressed as: ,in, Indicates that a convolution operation is performed using a convolution kernel of size 7×7. Indicates that the results of average pooling and maximum pooling are concatenated in the channel dimension; Step 3-3: Process the signal through three fully connected layers. The expression of the fully connected layer is: ,in, represents the input of the fully connected layer, represents the output of the fully connected layer, represents the weight matrix between two hidden layers, represents the weight matrix between the second hidden layer and the output layer, and represents the bias term, and represents the activation function; Step 3-4: Use the Sigmoid function as the output layer to convert the arrival angle into a continuous distribution between [0,1], and then obtain the arrival direction estimation result through denormalization.

9. The method for estimating the direction of arrival of underwater acoustic signals based on the improved Mamba network according to claim 1, characterized in that: The step 4 comprises: Step 4-1: Label the signal according to different angles and use it as a training set to train the network model; Step 4-2: During the training process, the mini-batch gradient descent method is used to train the neural network. The training set is divided into several groups of data. The neural network learns information from one group of data in each iteration. Step 4-3: Select mean square error as the loss function and minimize the loss function as the training goal. The expression of mean square error MSE is: ,in represents the number of samples, and Represent the true value and estimated value of the sample respectively; Step 4-4: Iterate the network model multiple times, optimize the network model parameters with the training objectives in step 4-3, save the model parameters, input the unlabeled signal received by the hydrophone array, and output the angle information of the model wave to accurately estimate the direction of arrival.

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