DOA estimation method based on transfer learning under array element failure condition

Abstract

The present application relates to a kind of array element failure condition based on migration learning DOA estimation method, for the problem of deep learning DOA estimation model performance decline under array element failure scene, this method keeps millisecond level inference speed while significantly improving the estimation accuracy and cross-domain generalization ability under array element failure condition.Gradient reversal layer is used to automatically learn domain invariant features through adversarial training, without target domain labels, and without pre-defined distribution metric form, suitable for complex and variable failure modes, source domain and target domain distribution difference is larger scene.This method realizes high-precision DOA estimation in array element failure environment, and compared with traditional sparse reconstruction method, the calculation time is greatly reduced.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of array signal processing and deep learning, and relates to a DOA estimation method based on transfer learning under array element failure conditions. Specifically, when array elements of a sensor array fail, transfer learning technology is used to transfer the knowledge of a deep learning model trained in the complete array scenario to the array element failure scenario. Under the condition of no target domain labeled samples, it can achieve rapid adaptation to multiple failure modes and high-precision DOA estimation. Background Technology

[0002] Direction of Arrival (DOA) estimation is a key technology in array signal processing, widely used in radar, sonar, and wireless communication. Traditional DOA estimation methods include beamforming, subspace-based methods, and sparse reconstruction methods such as Sparse Bayesian Learning (SBL) proposed by Gerstoft et al. in "Multisnapshot Sparse Bayesian Learning for DOA". Most of these methods rely on an ideal array model and have long computation times. In practical engineering, sensor arrays are often affected by non-ideal factors such as element failure, environmental noise, and amplitude and phase errors. Element failure can be caused by various factors such as device aging, loose connections, and environmental corrosion, resulting in zero or outlier output signals for some elements. This alters the effective aperture and spatial sampling structure of the array, causing a sharp decline in the performance of deep learning DOA estimation models trained on the complete array.

[0003] With the development of deep learning technology, techniques such as Convolutional Neural Networks (CNNs) have been introduced into the field of DOA estimation. By learning the mapping from covariance matrix features to the DOA spatial spectrum through a data-driven approach, this alleviates the dependence of traditional methods on ideal array models to some extent. However, for the problem of array element failure, existing deep learning methods often require a large number of labeled samples and training a dedicated model from scratch. Since the failure combinations of sensor arrays are diverse, this method not only incurs huge costs for real-world data acquisition but also leads to extremely high computational overhead for model retraining. Furthermore, in complex engineering scenarios, it is often difficult to obtain sufficient labeled failure scenario data, severely limiting the model's engineering applicability.

[0004] Transfer learning can uncover common knowledge between a complete array (source domain) and an array with failed elements (target domain), transferring robust feature representations and model parameters learned in the source domain to the target domain. This allows the model to quickly adapt to element failure scenarios without starting from scratch, significantly reducing the overall cost of data acquisition and model training. Existing research has introduced transfer learning into the field of DOA estimation. For example, Cao et al., in "Deep Transfer Learning for Underwater Direction of Arrival Using One Vector Sensor," fine-tuned a pre-trained network in the source domain to adapt it to new observation conditions. However, such fine-tuning methods still rely on a certain number of labeled samples in the target domain. Therefore, this invention proposes a domain adversarial transfer learning-based DOA estimation method, providing a solution for robust DOA estimation under element failure conditions. Summary of the Invention

[0005] Technical problems to be solved To overcome the shortcomings of existing technologies, this invention proposes a DOA estimation method based on transfer learning under array element failure conditions. Addressing the performance degradation of deep learning DOA estimation models trained on the complete array due to array element failure, this method introduces a domain discriminator in scenarios with significant differences in the distribution of the source and target domains and complex and varied failure modes. Through adversarial training, it eliminates inter-domain feature differences, achieving high-precision DOA estimation for unlabeled samples in the target domain.

[0006] This invention aims to provide a practical and efficient DOA estimation solution for array element failure engineering scenarios with low data cost and low training overhead.

[0007] Technical solution A method for estimating DOA based on transfer learning under the condition of array element failure, characterized in that: the sensor array is composed of... A uniform linear array consisting of 100 elements, with element 1 as the reference element, and the element spacing is half a wavelength. Sensor array receives The far-field narrowband signal, the first The direction of arrival of the target signal is The angle search range is ,in, The minimum angle for direction finding. The maximum angle for direction finding; the index set of the failed array elements is denoted as . The steps of the DOA estimation method are as follows: Step 1: The array receives the signal vector as follows: The estimated value of the covariance matrix is , Indicates the number of samples. This represents the conjugate transpose operation; in: For guiding matrix; for time A signal vector composed of several information sources; Zero-mean Gaussian noise; Step 2: Input data construction: For Decompose the real and imaginary parts to construct a dual-channel real-valued input tensor. ,in This indicates the operation of taking the real part. This indicates the operation of taking the imaginary part, resulting in... Dimension tensor; right Z-score standardization is performed to obtain the network input. ,in and Tensors The mean and standard deviation of all elements in the dataset; Step 3: Define the input training data based on whether the array elements are working properly: The data for a complete array where all array elements are functioning normally is the source domain data used for input training; Some array elements are faulty, resulting in incomplete array data, which serves as the target domain data for input training. Step 4: Construct classification labels for the source domain data: For the input tensor Construction and Corresponding label vector To form data-label pairs ; obtained by The training dataset consists of source domain data and label pairs. ; Step 5: The received signals of the m randomly failed array elements are 0, and the resulting target domain input tensor is... Its dimensions and Consistent; for the target domain, i.e. M Of the array elements, m elements randomly fail, generating corresponding input data, resulting in... The training dataset consists of group target domain data. This dataset does not require labels; Step 6: Training process: The base network based on the domain adversarial transfer learning method is trained in two stages; The first-stage method, based on domain adversarial transfer learning, uses a foundational network consisting of a feature extraction module and a label classifier; it utilizes only the source domain dataset. The feature extraction module and label classifier are pre-trained to enable the network to learn basic DOA classification capabilities; the label classification loss is used for this purpose. For classification cross-entropy; The second stage adds a domain discriminator after the feature extractor to the source domain dataset. and target domain dataset The data is fed into the network for simultaneous training, and in the first few rounds, the domain discrimination loss is based solely on the difference between the source and target domains. The parameters are updated to gradually establish an adversarial relationship between the domain discriminator and the feature extraction module, and then the source domain label classification loss is added. Joint training is performed; the domain discrimination loss adopts binary cross-entropy, wherein the labels of the source domain data are uniformly set to 0, and the labels of the target domain data are uniformly set to 1; During training When the gradient is passed to the feature extraction module, it is automatically reversed, so that the feature extraction module learns domain-invariant features that the domain discriminator cannot distinguish. The label classification loss is calculated only on the source domain labeled data. ;in, Indicates the batch size of the source domain. G Indicates the number of angle categories. For the source domain i The nth sample label vector g One element, For the first i The network output pseudospace spectrum of the nth sample g One element; The domain discrimination loss is calculated simultaneously on the source and target domain data. ,in These represent the batch size of the target domain. For the domain discriminator to the source domain The output probability of each sample For the domain discriminator to the target domain The output probability of each sample; The label classification loss and the domain discrimination loss constitute the total loss function; Step 7: DOA estimation process: Randomly generate signals that are not in the training dataset. and noise And construct test data according to the method described in step (2). The vector is fed into the trained network to obtain the G-dimensional pseudospace spectrum output vector. .right Perform a peak search and select the first peak. K The angle corresponding to each larger spectral peak is used as K DOA estimation results for each source .

[0008] The label vector It is constructed using the one-hot encoding principle, taking 1 at the grid position of the information source and 0 at the other positions.

[0009] The feature extraction module includes Each convolutional layer is followed by batch normalized (BN) and ReLU activation functions; the first... The output of each convolutional layer is The forward propagation process of the feature extraction module is as follows: , After L layers of convolution, the feature map is transformed into a one-dimensional feature vector through a flattening operation. .

[0010] The feature extraction module Convolutional layers, with the number of convolutional kernels as follows: The kernel sizes are as follows: .

[0011] The label classification module consists of Composed of fully connected layers, front The first layer uses the ReLU activation function, and the last layer uses the Softmax activation function, outputting a G-dimensional pseudospace spectral vector. .

[0012] The number of neurons in the fully connected layer of the classification module is as follows: .

[0013] The domain discriminator is composed of Composed of fully connected layers, outputting a probability scalar in the domain. The source domain sample domain label is defined as follows: The target domain sample domain label is defined as .

[0014] The number of neurons in the fully connected layer of the domain discriminator is as follows: Gradient reversal coefficient Using the SGD optimizer, the decay parameter , .

[0015] An electronic device, characterized in that it includes a processor and a memory, the processor being configured to execute a computer program stored in the memory to implement the steps of a DOA estimation method based on transfer learning under the condition of array element failure.

[0016] A computer program product, characterized in that it includes computer-executable instructions, which, when executed, are used to implement the DOA estimation method based on transfer learning under the condition of array element failure.

[0017] Beneficial effects This invention proposes a DOA estimation method based on transfer learning under element failure conditions. Addressing the performance degradation of deep learning DOA estimation models in element failure scenarios, this method significantly improves estimation accuracy and cross-domain generalization ability under these conditions while maintaining millisecond-level inference speed. It automatically learns domain-invariant features through adversarial training using gradient inversion, requiring no target domain label and no predefined distribution metric, making it suitable for scenarios with complex and varied failure modes and significant differences between the source and target domain distributions. This method achieves high-precision DOA estimation under element failure conditions and significantly reduces computation time compared to traditional sparse reconstruction methods. Attached Figure Description

[0018] Figure 1 Overall technical flow chart of the present invention Figure 2. Schematic diagram of the model based on the domain adversarial method Figure 3. Comparison of average test times for different methods Figure 4. RMSE curves of each model as a function of signal-to-noise ratio and snapshot number under single-element failure scenario. Figure 5. RMSE curves of various models as a function of signal-to-noise ratio and snapshot number in the dual-element failure scenario. Figure 6. Curves showing the variation of RMSE of each model with signal-to-noise ratio and number of snapshots under the three-element failure scenario. Detailed Implementation The present invention will now be further described in conjunction with the embodiments and accompanying drawings: The purpose of this invention is to provide a DOA estimation method based on transfer learning in the case of array element failure.

[0019] The present invention will be further described in conjunction with simulation embodiments thereof: Network parameter configuration: The network infrastructure used in the method of this invention consists of a feature extraction module and a classification module. The feature extraction module comprises... The system consists of multiple convolutional layers, with the number of convolutional kernels as follows: The kernel sizes are as follows: The number of neurons in the fully connected layer of the classification module is as follows: The number of neurons in the fully connected layer of the domain discriminator in the domain adversarial method is as follows: Gradient reversal coefficient Using the SGD optimizer, the decay parameter , The training consists of two phases: source domain pre-training and adversarial joint training. Since the number of training samples in the target domain is much smaller than that in the source domain, if there are too many training rounds, the network is prone to overfitting to the limited target domain samples, resulting in a decrease in generalization performance on unseen data. Therefore, an early stopping mechanism is introduced to terminate training early when the loss no longer decreases after a certain number of consecutive rounds.

[0020] The objective of this invention is achieved as follows: The array of the present invention is composed of A uniform linear array consisting of 100 elements, with element 1 as the reference element, and the element spacing is half a wavelength. Sensor array receives The far-field narrowband signal, the first The direction of arrival of the target signal is The angle search range is ,in, The minimum angle for direction finding. Let be the maximum angle for direction finding. The set of indices for the failed array elements is denoted as . .

[0021] The specific implementation steps of the method include: The array consists of Composed of individual array elements, Several far-field narrowband target signals are incident on a planar array at incident angles of respectively. The spacing between array elements is... Assuming that array element 1 is the reference array element, the first... The position of each array element relative to the reference array element is: . time The signal vector composed of n sources is Guiding matrix , It is the first The steering vector of a signal. ,in The imaginary unit, This indicates the transpose operation. Zero-mean Gaussian noise is used, and its representation is... Therefore, the array receives the signal vector as follows: In practice, the sample size is finite; therefore, a finite sample size is used to estimate the covariance matrix of the signal. The estimated value of the covariance matrix is... , Indicates the number of samples. This indicates the conjugate transpose operation.

[0022] In the embodiment, the sensor array is A uniform linear array of array elements, with an incident signal wavelength of... The element spacing is half a wavelength, and the number of sources is... Quick shot number .

[0023] Training dataset construction: The source domain data comes from a complete array where all elements are functioning normally. For the target domain (array with failed elements) data, the set of failed element indices is used. Set the received data of all array elements to zero. Calculate the values ​​for the source and target domains respectively. The covariance matrix corresponding to the failed matrix element has zero rows and zero columns, and the matrix dimension is preserved. The input dimensions of the source and target domains remain unchanged, ensuring consistency. The real and imaginary parts of the covariance matrix are decomposed to construct a dual-channel real-valued input tensor. ,in This indicates the operation of taking the real part. This represents the imaginary part operation, with dimension 1. .right Z-score standardization is performed to obtain the network input. ,in and Tensors The mean and standard deviation of all elements in the dataset.

[0024] The source and target domain data use the same label construction rules, and the angle search range is evenly divided into... There are 1 grid, with a grid spacing of 1. For the first There are 10 incident information sources on the array, and their grid indices are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 ... ,in Indicates rounding down. Label vector The input tensor is constructed using one-hot encoding, assigning a 1 to the grid position corresponding to the information source and a 0 to all other positions. and its corresponding label vector To form data-label pairs Ultimately, it was obtained from The training dataset consists of group data and label pairs. .

[0025] In this embodiment: the source domain data comes from a complete array where all elements are functioning normally, and the target domain training data comes from an array with randomly selected two elements that have failed. The angle search range is... The grid spacing is 1°, and the total number of grids is 1°. Categories. Signal-to-noise ratio , For the target signal power, Given noise power, training data is generated under zero-mean Gaussian noise conditions. The source domain signal-to-noise ratio set is... dB, traversing the angular range in steps of 0.2° and repeating 5 times; the target domain signal-to-noise ratio set is The data is traversed in dB with a step size of 0.5° and repeated twice, resulting in a source domain to target domain training data ratio of approximately 175:12. Following the input data and label construction method described above, corresponding data-label pairs are generated for the source and target domain data, ultimately forming the source domain training dataset and the target domain training dataset.

[0026] Network Structure The basic network architecture based on domain adversarial transfer learning consists of a feature extraction module and a classification module. The feature extraction module includes... Each convolutional layer is followed by batch normalization (BN) and ReLU activation. The output of each convolutional layer is The forward propagation process of the feature extraction module is as follows: , After L layers of convolution, the feature map is transformed into a one-dimensional feature vector through a flattening operation. The classification module consists of... Composed of fully connected layers, front The first layer uses the ReLU activation function, and the last layer uses the Softmax activation function, outputting a G-dimensional pseudospace spectral vector. .

[0027] The basic network training process based on domain adversarial transfer learning: A domain discriminator is introduced during training, so the network consists of three parts: a feature extraction module, a label classifier, and a domain discriminator. The label classifier structure is the same as the classification module in step (3); the domain discriminator consists of... Composed of fully connected layers, outputting a probability scalar in the domain. The source domain sample domain label is defined as follows: The target domain sample domain label is defined as eigenvectors Before entering the domain discriminator, the sample first passes through a gradient inversion layer (GRL). The GRL performs an identity transformation during forward propagation and multiplies the gradient by a coefficient during backward propagation. ,Right now The total loss function consists of two parts: label classification loss and domain discrimination loss. The label classification loss... Calculated only on the source domain labeled data Domain-based loss discrimination Simultaneous computation on source and target domain data ,in and These are the batch sizes for the source and destination domains, respectively. For the domain discriminator to the source domain The output probability of each sample For the domain discriminator to the target domain The output probability of each sample. GRL makes... When the gradient is passed to the feature extraction module, it is automatically reversed, so that the feature extraction module learns domain-invariant features that the domain discriminator cannot distinguish.

[0028] In the example: During the testing phase, test samples are fed into the trained network to obtain a G-dimensional pseudo-space spectral output vector. Spectral peak search is performed on this vector, and the angle grid corresponding to the spectral peak with the highest energy is selected as the DOA estimation result of the information source. The performance metrics for DOA estimation are the root mean square error (RMSE) and the average MC test time across 100 Monte Carlo (MC) experiments. Comparison methods include CNN models trained on source domain data (source domain CNN), CNN models trained from scratch on target domain data (target domain CNN), fine-tuning methods, and sparse reconstruction (SBL) methods.

[0029] The training process is divided into two stages: the first stage uses only source domain data to pre-train the feature extraction module and the label classifier, allowing the network to learn basic DOA classification capabilities; the second stage adds a domain discriminator, feeding source domain data and target domain data into the network for simultaneous training. In the first few rounds, the parameters are updated only with domain discriminator loss, allowing the domain discriminator and the feature extraction module to gradually establish an adversarial relationship. Then, the source domain classification loss is added for joint training.

[0030] During the testing phase, the test samples are constructed into dual-channel standardized inputs according to the method described in step (2), and then fed into the trained network to obtain the G-dimensional pseudo-space spectrum output vector. .right A spectral peak search is performed, and the angles corresponding to the top K largest spectral peaks are selected as the DOA estimation results for the K sources. .

[0031] The experiment examines the algorithm's performance. DOA estimation performance at time, unless otherwise specified, is based on the number of samples. Signal-to-noise ratio The actual DOA is ( ).

[0032] The above experimental results show the effectiveness of the method of the present invention under different experimental conditions: Average MC test time Figure 3 As shown, the average test time of the network model method is around 5ms, which is on the same order of magnitude and can meet the engineering application scenarios with high time requirements. In contrast, the traditional SBL method has a high time cost due to repeated iterations.

[0033] Figure 4 shows the RMSE variation curve of DOA estimation under single element failure. Figure 4(a) shows the array element. The curve of RMSE of DOA estimation as a function of signal-to-noise ratio under failure conditions. Source domain CNN models in The RMSE is close to 5°. Performance improves with increasing signal-to-noise ratio (SNR), but fluctuates significantly, consistently outperforming domain adversarial methods across the entire SNR range. This is because the model is trained only on complete array data, and the learned feature mappings differ fundamentally from the covariance matrix structure of the failed array. Directly applying this to failure scenarios results in the model output deviating from the true DOA. The RMSE of the method is stable below 0.5°. During training, this method simultaneously utilizes source and target domain data for feature alignment, enabling the network to learn feature representations invariant to inter-domain differences. Even when low signal-to-noise ratios lead to a decrease in feature quality, the aligned features still maintain good classification discriminative power. The fine-tuned model is relatively stable within the signal-to-noise ratio range, but its performance is lower than domain adversarial methods, and its training relies on labeled target domain samples. Although the SBL method has high estimation accuracy at medium to high signal-to-noise ratios, its performance is highly dependent on the signal-to-noise ratio, exhibiting significant performance degradation at low signal-to-noise ratios. Furthermore, its testing time is much longer than that of deep learning methods, making it difficult to balance estimation accuracy, robustness, and real-time performance. Figure 4(b) shows the array elements. The curve showing the change of RMSE of DOA estimation with the number of snapshots under failure conditions. As the number of snapshots increases, the RMSE of the source domain CNN model is approximately 1°–2°, showing no significant improvement, while the RMSE of the target domain CNN model and the fine-tuned model almost overlap. The domain adversarial model maintains a low RMSE level with almost no fluctuation under all snapshot count conditions, demonstrating good stability.

[0034] The RMSE change curve of DOA estimation under dual-element failure condition is as follows: Figure 5 As shown. Figure 5 (a) Displaying the array elements The curve of RMSE of DOA estimation as a function of signal-to-noise ratio under failure conditions. As can be seen from the figure, the RMSE of the source domain CNN model remains high across the entire signal-to-noise ratio range, making it unable to effectively adapt to this failure scenario. The domain adversarial model performs the best, in... At that time, RMSE dropped to approximately 0.1°. The gradient then stabilizes at around 0.3°, mainly because the gradient reversal mechanism of GRL allows the feature extraction module to actively eliminate the distribution differences between the source and target domains. The time-fine-tuned model outperforms the target domain CNN model. Figure 5 (b) Displaying the array elements The curve showing the change of RMSE of DOA estimation with the number of snapshots under failure conditions. The source domain CNN model has an RMSE of approximately 1.5° under all snapshot count conditions, with no significant improvement as the number of snapshots increases. The domain adversarial model performs best, maintaining the lowest RMSE level; the RMSE of the other three methods does not change significantly with the number of snapshots, but all are significantly better than the source domain CNN model.

[0035] The RMSE change curve of DOA estimation under the condition of three-element failure is as follows: Figure 6 As shown. Figure 6 (a) Displaying the array elements The curve of RMSE of DOA estimation as a function of signal-to-noise ratio under failure conditions. As can be seen from the figure, due to the failure of 3 out of 8 array elements (a failure rate of 37.5%), the effective degrees of freedom of the array decrease significantly, and the overall RMSE of all methods increases compared to the single-element and double-element failure scenarios. The source domain CNN model in... The RMSE reaches approximately 10°, decreasing slightly with increasing signal-to-noise ratio (SNR), making it the most unstable performance. The target domain CNN model achieves an RMSE of approximately 2° in the medium-to-high SNR range, and training from scratch with only limited target domain data is insufficient to handle severe element failure scenarios. In contrast, domain adversarial transfer learning methods demonstrate significant advantages over the two baseline models. The RMSE was approximately 2.5° at that time. It then drops below 1° and performs best in the high signal-to-noise ratio range. Figure 6 (b) Displaying the array elements The curve showing the change of RMSE of DOA estimation with the number of snapshots under failure conditions. The RMSE of the source domain CNN model is approximately 3° across the entire test range, the highest under all snapshot count conditions. The RMSE of the target domain CNN model and the fine-tuned model is approximately 2°, showing similar performance. The RMSE of the domain adversarial model is approximately between 0.7° and 1.5°, outperforming other methods overall, further validating the effectiveness of adversarial training in automatically learning domain-invariant features under severe failure scenarios.

Claims

1. A DOA estimation method based on transfer learning under the condition of array element failure, characterized in that: The sensor array is composed of A uniform linear array consisting of 100 elements, with element 1 as the reference element, and the element spacing is half a wavelength. Sensor array receives The far-field narrowband signal, the first The direction of arrival of the target signal is The angle search range is ,in, The minimum angle for direction finding. The maximum angle for direction finding; the index set of the failed array elements is denoted as . The steps of the DOA estimation method are as follows: Step 1: The array receives the signal vector as follows: The estimated value of the covariance matrix is , Indicates the number of samples. This represents the conjugate transpose operation; in: For guiding matrix; for time A signal vector composed of several information sources; Zero-mean Gaussian noise; Step 2: Input data construction: For Decompose the real and imaginary parts to construct a dual-channel real-valued input tensor. ,in This indicates the operation of taking the real part. This indicates the operation of taking the imaginary part, resulting in... Dimension tensor; right Z-score standardization is performed to obtain the network input. ,in and Tensors The mean and standard deviation of all elements in the dataset; Step 3: Define the input training data based on whether the array elements are working properly: The data for a complete array where all array elements are functioning normally is the source domain data used for input training; Some array elements are faulty, resulting in incomplete array data, which serves as the target domain data for input training. Step 4: Construct classification labels for the source domain data: For the input tensor Construction and Corresponding label vector To form data-label pairs ; obtained by The training dataset consists of source domain data and label pairs. ; Step 5: The received signals of the m randomly failed array elements are 0, and the resulting target domain input tensor is... Its dimensions and Consistent; for the target domain, i.e. M Of the array elements, m elements randomly fail, generating corresponding input data, resulting in... The training dataset consists of group target domain data. This dataset does not require labels; Step 6: Training process: The base network based on the domain adversarial transfer learning method is trained in two stages; The first stage, based on domain adversarial transfer learning, uses a foundational network consisting of a feature extraction module and a label classifier; it only uses the source domain dataset. The feature extraction module and label classifier are pre-trained to enable the network to learn basic DOA classification capabilities; the label classification loss is used for this purpose. For classification cross-entropy; The second stage adds a domain discriminator after the feature extractor to the source domain dataset. and target domain dataset The data is fed into the network for simultaneous training, and in the first few rounds, the domain discrimination loss is based solely on the difference between the source and target domains. The parameters are updated to gradually establish an adversarial relationship between the domain discriminator and the feature extraction module, and then the source domain label classification loss is added. Joint training is performed; the domain discrimination loss adopts binary cross-entropy, wherein the labels of the source domain data are uniformly set to 0, and the labels of the target domain data are uniformly set to 1; During training When the gradient is passed to the feature extraction module, it is automatically reversed, so that the feature extraction module learns domain-invariant features that the domain discriminator cannot distinguish. The label classification loss is calculated only on the source domain labeled data. ;in, Indicates the batch size of the source domain. G Indicates the number of angle categories. For the source domain i The nth sample label vector g One element, For the first i The network output pseudospace spectrum of the nth sample g One element; The domain discrimination loss is calculated simultaneously on the source and target domain data. ,in These represent the batch size of the target domain. For the domain discriminator to the source domain The output probability of each sample For the domain discriminator to the target domain The output probability of each sample; The label classification loss and the domain discrimination loss constitute the total loss function; Step 7: DOA estimation process: Randomly generate signals that are not in the training dataset. and noise And construct test data according to the method described in step (2). The vector is fed into the trained network to obtain the G-dimensional pseudospace spectrum output vector. .right Perform a peak search and select the first peak. K The angle corresponding to each larger spectral peak is used as K DOA estimation results for each source .

2. The DOA estimation method based on transfer learning under the condition of array element failure as described in claim 1, characterized in that: The label vector It is constructed using the one-hot encoding principle, taking 1 at the grid position of the information source and 0 at the other positions.

3. The DOA estimation method based on transfer learning under element failure conditions according to claim 1, characterized in that: The feature extraction module includes Each convolutional layer is followed by batch normalized (BN) and ReLU activation functions; the first... The output of each convolutional layer is The forward propagation process of the feature extraction module is as follows: , After L layers of convolution, the feature map is transformed into a one-dimensional feature vector through a flattening operation. .

4. The DOA estimation method based on transfer learning under element failure conditions according to claim 3, characterized in that: The feature extraction module Convolutional layers, with the number of convolutional kernels as follows: The kernel sizes are as follows: .

5. The DOA estimation method based on transfer learning under element failure conditions according to claim 1, characterized in that: The label classification module consists of Composed of fully connected layers, front The first layer uses the ReLU activation function, and the last layer uses the Softmax activation function, outputting a G-dimensional pseudospace spectral vector. .

6. The DOA estimation method based on transfer learning under element failure conditions according to claim 5, characterized in that: The number of neurons in the fully connected layer of the classification module is as follows: .

7. The DOA estimation method based on transfer learning under element failure conditions according to claim 1, characterized in that: The domain discriminator is composed of Composed of fully connected layers, outputting a probability scalar in the domain. The source domain sample domain label is defined as follows: The target domain sample domain label is defined as .

8. The DOA estimation method based on transfer learning under element failure conditions according to claim 7, characterized in that: The number of neurons in the fully connected layer of the domain discriminator is as follows: Gradient reversal coefficient Using the SGD optimizer, the attenuation parameter , .

9. An electronic device, characterized in that, It includes a processor and a memory, wherein the processor is configured to execute a computer program stored in the memory to implement the steps of the transfer learning-based DOA estimation method under element failure conditions as described in any one of claims 1 to 8.

10. A computer program product, characterized in that... It includes computer-executable instructions, which, when executed, are used to implement the DOA estimation method based on transfer learning under the array element failure condition as described in claims 1 to 8.

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