Continuous DOA estimation method based on plural Transformers and mask reconstruction

Abstract

The invention discloses a continuous DOA (direction of arrival) estimation method based on a plurality of Transformers and mask reconstruction, and belongs to the technical field of array signal processing. Comprising the following steps: constructing a data set, constructing a plurality of Transform network structures, pre-training the plurality of Transform network structures by adopting a self-supervised learning strategy, and performing fine tuning training on the pre-trained plurality of Transform network structures based on the data set to obtain a final plurality of Transform network structures. And running a final plural Transform network structure on test data with different signal-to-noise ratios, using the RMSE as a performance evaluation index, and outputting a DOA continuous estimation result. According to the method, through the complex number Transform and mask self-supervised learning, high-precision and meshless continuous DOA estimation under a low signal-to-noise ratio is realized, and the estimation robustness and the real-time performance are remarkably improved.

Description

A continuous DOA estimation method based on complex Transformer and mask reconstruction Technical Field

[0001] This invention relates to the field of array signal processing technology, and more specifically to a continuous DOA estimation method based on complex Transformer and mask reconstruction. Background Technology

[0002] Direction of Arrival (DOA) estimation is a core technology in array signal processing, widely used in radar, sonar, wireless communication, UAV sensing, and signal monitoring. Traditional DOA methods rely on accurate mathematical models of the array signal, deriving the signal direction through priors such as the covariance matrix and array manifold. They typically assume an ideal array, independent and identically distributed white noise, and require a stable and sufficient number of snapshots. When real-world conditions deviate from these ideals, especially in scenarios with low signal-to-noise ratios or insufficient snapshots, noise significantly disrupts the covariance matrix structure, leading to a sharp degradation in estimation performance and limited robustness.

[0003] Although deep learning methods have improved their adaptability to complex environments through data-driven approaches in recent years, they still face bottlenecks such as strong data dependence, insufficient generalization ability, poor physical interpretability, and off-grid effects, making it difficult to completely replace traditional methods.

[0004] To address the aforementioned issues, there is an urgent need for a continuous DOA estimation method based on complex Transformer and mask reconstruction to solve the problems existing in traditional methods and traditional deep learning methods, thereby achieving high-precision and robust continuous DOA estimation in complex electromagnetic environments. Summary of the Invention

[0005] The purpose of this invention is to provide a continuous DOA estimation method based on complex Transformer and mask reconstruction. Through complex Transformer and mask self-supervised learning, high-precision, gridless continuous DOA estimation under low signal-to-noise ratio is achieved, which significantly improves the estimation robustness and real-time performance.

[0006] To achieve the above objectives, the technical solution adopted by this invention is as follows: A continuous DOA estimation method based on complex Transformer and mask reconstruction, comprising: Step 1: Constructing a uniform linear array received signal model, simulating and generating radiation source signal data with different signal-to-noise ratios, calculating the noisy covariance matrix and continuous angle labels, and finally generating a dataset; Step 2: Constructing a complex Transformer network structure, wherein the complex Transformer network consists of complex multi-head attention layers, multi-scale complex convolutional layers, and complex feedforward network layers; Step 3: Pre-training the complex Transformer network structure using a self-supervised learning strategy; Step 4: Fine-tuning the pre-trained complex Transformer network structure based on the dataset to obtain the final complex Transformer network structure; Step 5: Running the final complex Transformer network structure on test data with different signal-to-noise ratios, using RMSE as the performance evaluation index, and outputting the continuous DOA estimation result.

[0007] Further, in step 1, a uniform linear array receiving signal model is constructed, and radiation source signal data with different signal-to-noise ratios are simulated and generated. The noisy covariance matrix and continuous angle labels are calculated, and finally, a dataset is generated. Specifically: Step 101: Set the basic parameters of the uniform linear array, establish an array receiving model for far-field narrowband radiation source signals, construct the radiation source baseband signal using BPSK digital modulation, and achieve pulse shaping through a raised cosine filter to finally obtain the transmitted signal vector, i.e., the radiation source signal data; Step 102: Calculate the noisy sampling covariance matrix at each observation time step based on the array received signal vector; Step 103: Generate a dataset based on the radiation source signal data and the noisy covariance matrix.

[0008] Furthermore, in step 2, the Transformer network structure is composed of six stacked layers with the same structure. Each layer includes three core sub-layers, a residual connection layer, and a layer normalization layer. The three core sub-layers are a complex multi-head attention layer, a multi-scale complex convolutional layer, and a complex feedforward network layer, respectively.

[0009] Furthermore, the complex feedforward network layer includes two complex linear transformation layers and a ReLU activation layer.

[0010] Furthermore, the complex multi-head attention layer is provided with eight attention heads.

[0011] Furthermore, in step 3, a self-supervised learning strategy is used to pre-train the complex Transformer network structure, specifically: Step 301: Perform a random masking operation on the noisy covariance matrix; Step 302: Input the noisy covariance matrix after the random masking operation into the complex Transformer network structure for mask reconstruction; Step 303: After training is completed, extract and save the weights of the complex Transformer network structure with the lowest verification loss as the pre-trained model.

[0012] Further, in step 4, the pre-trained complex Transformer network structure is fine-tuned based on the dataset to obtain the final complex Transformer network structure. Specifically: Step 401: Extract the weights of the complex Transformer network structure based on the pre-trained model, and remove the output layer weights from the complex Transformer network structure weights; Step 402: Reconstruct the complex Transformer network structure based on the removed complex Transformer network structure weights, wherein a DOA regression head is constructed and the output layer of the original network structure is replaced by the DOA regression head; Step 403: Fine-tune the replaced complex Transformer network structure based on the dataset to obtain the final complex Transformer network structure.

[0013] Furthermore, the DOA regression head comprises two fully connected layers.

[0014] In summary, this invention possesses four core advantages: high precision without mesh, strong robustness, full utilization of complex domain information, and high computational efficiency. These advantages directly correspond to the technical problems it addresses: 1. For the off-mesh constraint problem, by reconstructing DOA estimation into a continuous regression task to directly output continuous angle values, it fundamentally eliminates discrete mesh mismatch errors and achieves super-resolution angle estimation; 2. For the accuracy degradation problem under low signal-to-noise ratio and limited snapshots, a two-stage pre-training-fine-tuning strategy is adopted. In the pre-training stage, robust structural features are extracted from noisy data through masked self-supervised learning. In the fine-tuning stage, the focus is on the angle regression task, enabling the model to maintain excellent direction-finding performance even under low signal-to-noise ratio; 3. For the problems of insufficient information utilization in traditional methods and loss of phase features in deep learning, a fully complex Transformer encoder is constructed. Its core operations, such as complex convolution and complex attention, fully mine the dual information of covariance matrix amplitude and phase; 4. For real-time requirements, model inference does not require eigenvalue decomposition or spectral peak search, significantly improving computational efficiency and providing strong support for practical radiation source tracking applications. Attached Figure Description

[0015] Figure 1 is a schematic diagram of the method of the present invention; Figure 2 is a schematic diagram of the complex multi-head attention layer; Figure 3 is a schematic diagram of the multi-scale complex convolutional layer; Figure 4 is a diagram of the DOA estimation network architecture; Figure 5 is a schematic diagram of the pre-training process; Figure 6 is a schematic diagram of the prediction process. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0017] As shown in Figure 1, this invention provides a continuous DOA estimation method based on complex Transformer and mask reconstruction, comprising: Step 1: Constructing a uniform linear array received signal model, simulating and generating radiation source signal data with different signal-to-noise ratios, calculating the noisy covariance matrix and continuous angle labels, and finally generating a dataset; Step 2: Constructing a complex Transformer network structure, wherein the complex Transformer network consists of complex multi-head attention layers, multi-scale complex convolutional layers, and complex feedforward network layers; Step 3: Pre-training the complex Transformer network structure using a self-supervised learning strategy; Step 4: Fine-tuning the pre-trained complex Transformer network structure based on the dataset to obtain the final complex Transformer network structure; Step 5: Running the final complex Transformer network structure on test data with different signal-to-noise ratios, using RMSE as the performance evaluation index, and outputting the continuous DOA estimation results.

[0018] In step 1, a uniform linear array receiving signal model is constructed, and radiation source signal data with different signal-to-noise ratios are simulated and generated. The noisy covariance matrix and continuous angle labels are calculated, and finally, a dataset is generated. Specifically, step 101: Set the basic parameters of the uniform linear array, establish an array receiving model for far-field narrowband radiation source signals, construct the radiation source baseband signal using BPSK digital modulation, and achieve pulse shaping through a raised cosine filter to finally obtain the transmitted signal vector, i.e., the radiation source signal data. Specifically, 1. Set the basic parameters of the uniform linear array: number of array elements M=8, array element spacing d is set to half wavelength, i.e. ,in For the signal wavelength, this spacing setting ensures that the array is free from grating lobe interference within a ±90° spatial range, while guaranteeing the orthogonality of the steering vector. The array geometry satisfies the far-field narrowband signal reception conditions, and the mutual coupling effect between array elements is negligible. 2. Establish an array reception model for far-field narrowband radiation source signals. For a single radiation source with an incident angle of θ, the array received signal at time t... Represented as: ,in, Let be the baseband signal vector emitted by the radiation source. Let be the additive white Gaussian noise matrix received by each array element, whose elements follow an independent and identically distributed complex Gaussian distribution, and the noise power is . ; Guide vector Characterizing array for incoming wave direction The spatial response of is expressed mathematically as follows: The steering vector precisely describes the phase difference relationship of the signal between each array element and is the physical basis for subsequent geometric modeling of the covariance matrix. 3. A BPSK digital modulation method is used to construct the baseband signal of the radiation source, and a raised cosine filter is used to achieve pulse shaping to simulate the spectral characteristics of a real communication radiation source. The specific generation process is as follows: Assume the oversampling factor is 8, the filter roll-off factor is 0.5, and the filter time span is 6 symbol periods. Based on the snapshot number of 200 and the above parameters, calculate the required number of bits, generate a random binary bit sequence, and map it to BPSK symbols to obtain a modulation symbol stream with values ​​in {-1, +1}. A square root raised cosine filter is used to pulse shape the symbol sequence. Through upsampling and filtering operations, a continuous baseband signal is generated, and the first 200 sampling points are extracted to form the final transmitted signal vector. That is, radiation source signal data.

[0019] Step 102: Based on the array received signal vector, calculate the noisy sampling covariance matrix for each observation time step. Specifically: Define the number of snapshots L=T=200, then the noisy covariance matrix... It is obtained through maximum likelihood estimation. The superscript H denotes the conjugate transpose operation, and the resulting covariance matrix possesses Hermite positive definiteness and conjugate symmetry, i.e. Furthermore, all eigenvalues ​​are non-negative real numbers, fully preserving the array manifold structure and noise statistics, providing physically interpretable training inputs for subsequent mask reconstruction tasks.

[0020] Step 103: Based on the radiation source signal data and the noisy covariance matrix, generate a dataset. Specifically, to simulate the continuous motion characteristics of the radiation source in the spatial domain, construct a full-coverage angle trajectory dataset, set the trajectory segment length to 10, and the starting angle set to cover the entire observation spatial domain. For the starting angle, generate a continuous angle trajectory of length 10. This design ensures that the dataset contains all possible local angle change patterns. Organize the simulation data hierarchically according to the signal-to-noise ratio, construct a structure array, and finally generate the dataset.

[0021] As shown in Figures 2, 3, and 4, in step 2, a complex Transformer network structure is constructed. Specifically, the Transformer network structure consists of six stacked layers with identical structures. Each layer includes three core sub-layers, a residual connection layer, and a layer normalization layer. The three core sub-layers are a complex multi-head attention layer, a multi-scale complex convolutional layer, and a complex feedforward network layer, respectively. In Figure 2, R and I represent the real and imaginary parts of the input signal, respectively. MH(Q, K, V) represents the multi-head attention operation, and the three parameters in parentheses correspond to Query, Key, and Value, respectively. R' and I' are the real and imaginary parts of the module's output, which are formed by cross-addition and subtraction of four components: real output R' = MH(R,R,R) + MH(R,I,I) − MH(I,R,I) − MH(I,I,R), imaginary output I' = MH(R,R,I) + MH(R,I,R) − MH(I,R,R) − MH(I,I,I).

[0022] In Figure 4, Real and Imag are the two channels representing the real and imaginary parts of the input signal after separation. Real With X Imag These are the real and imaginary features output after processing through N stacked blocks.

[0023] After the output of the complex multi-head attention layer is added to the input residual, layer normalization is performed on the real and imaginary parts respectively. The multi-scale complex convolutional layer further refines local features, and the output is added to the input residual and normalized. The complex feedforward network layer includes two complex linear transformation layers and a ReLU activation layer to realize nonlinear feature transformation. The output is then connected and normalized again. The layer normalization operation acts independently on the real and imaginary flows to ensure numerical stability and accelerate model convergence. After processing by 6 layers of encoder, the original noisy covariance matrix is ​​converted into a high-dimensional complex feature representation, which fully preserves the spatial structure information of the array manifold and effectively suppresses noise interference. The encoder is a complex Transformer network structure, and the decoder is the last two fully connected layers.

[0024] The complex Transformer network structure is described in detail below: 1. The model receives a sequence of noisy covariance matrices with a dimension of 10×8×8. First, each matrix is ​​flattened into a 64-dimensional vector. The input vector is divided into two independent channels: a real part and an imaginary part, corresponding to the real and imaginary values ​​of the covariance matrix elements, respectively. These two data streams are input to a complex convolutional layer. This layer contains two sets of convolutional kernels: one for real part weights and one for imaginary part weights. The real and imaginary inputs are processed in parallel, and the convolutional output follows the complex multiplication rule. This operation is performed in the early stages of feature extraction. 1. **Preserving the interaction relationships of phase information and mapping the original data to a high-dimensional complex feature space:** 2. **Multi-scale complex convolution feature extraction:** Multi-scale complex convolution modules are embedded in each layer of the complex Transformer network structure to capture the local and global correlations of the covariance matrix sequence. This module deploys three convolution kernel sizes in parallel: 1, 3, and 5. Each size is equipped with independent real and imaginary convolution parameters. After the input complex features are convolved in three parallel paths, they are concatenated along the channel dimension to restore the original embedding dimension. The branch with a kernel size of 1 focuses on the fine structure of single-step features, the branch with a kernel size of 3 captures short-range dependencies between adjacent time steps, and the branch with a kernel size of 5 perceives the global trend of trajectory changes. The multi-scale design enables the model to extract spatial features under different receptive fields simultaneously, significantly improving the modeling ability of the dynamic characteristics of the array manifold; 3. **Complex multi-head self-attention mechanism:** The core of the encoder is a complex multi-head self-attention mechanism with eight attention heads, each with a dimension one-eighth of the embedding dimension. The query, key, and value vectors are all generated from complex embedding features. The attention score calculation comprehensively considers the real-real and imaginary-imaginary interactions between the query and key, as well as cross-interaction terms, fully utilizing the geometric properties of the complex inner product. To enhance the model's ability to perceive temporal relationships within a sequence, a learnable relative position bias is introduced. This mechanism dynamically retrieves bias values ​​from a pre-defined encoding table based on the relative distance between the query and key positions and adds them to the attention score, enabling the model to display the relative dependencies between different moments in the modeling trajectory. The attention weights are applied to the value vector after softmax normalization, achieving adaptive fusion of the sequence context, maintaining consistency between the output and input dimensions. The attention score calculation comprehensively considers the interaction between the real and imaginary parts; for the h-th head, its attention weight... The calculation formula is: ; where Q h and K h K represents the query and key vector of the h-th head, respectively. h H d represents the conjugate transpose of the key vector. k R is the dimension of the head. h This is a relative position bias matrix that dynamically adjusts the attention score based on the relative position between the query and the key. In this way, the model can more flexibly capture the complex relationships between elements in a sequence.

[0025] As shown in Figure 5, in step 3, a self-supervised learning strategy is used to pre-train the complex Transformer network structure. Specifically, step 301: a random masking operation is performed on the noisy covariance matrix. Specifically, for the input noisy covariance matrix sequence, elements are randomly selected and zeroed at a ratio of p=30% to generate a mask matrix. The masked missing regions force the model to infer reasonable values ​​using contextual information, thus mining the global correlation, Hermite symmetry, and array manifold constraints of the covariance matrix. The masking operation simulates the scenario of data loss or corruption in the actual system, enhancing the robustness and generalization ability of the model. Step 302: the noisy covariance matrix after random masking is input into the complex Transformer network structure for mask reconstruction. Specifically, the noisy covariance matrix after random masking is input into the complex Transformer network structure, whose encoder utilizes... Using unmasked elements as context, deep feature representations are extracted through multi-layer complex convolution and attention mechanisms. The decoder performs cross-attention computation based on the encoder output, focusing on inferring the latent values ​​of the masked regions. The model needs to complete the mask positions based on physical laws, thereby learning robust representations of the signal subspace. Step 303: After training, extract and save the complex Transformer network structure weights with the lowest verification loss as a pre-trained model. Specifically, after training, extract and save the encoder weights with the lowest verification loss as a pre-trained model. These weights have fully learned the complex geometric properties of the array manifold, the noise distribution law across signal-to-noise ratios, and the temporal evolution mode of the angle trajectory. The saved pre-trained model is stripped of the decoder and output head, retaining only the encoder part to form a general feature extractor, which can be directly loaded into the subsequent fine-tuning stage to provide high-quality initialization for the angle regression task.

[0026] In step 4, the pre-trained complex Transformer network structure is fine-tuned based on the dataset to obtain the final complex Transformer network structure. Specifically, step 401: Extract the weights of the complex Transformer network structure based on the pre-trained model, and remove the output layer weights from the complex Transformer network structure weights. Specifically, load the pre-trained model file obtained in step 3, extract the encoder weight parameters. Since the pre-training task is covariance matrix reconstruction, its output layer weights are incompatible with the DOA regression task. Therefore, during transfer learning, all parameters related to the output head are removed, and only the weights of the complex embedding layer, multi-scale convolutional layer, multi-head attention layer, and layer normalization layer are retained. The model structure is adjusted as follows: the input layer receives the complete, unmasked noisy covariance matrix, and the encoder extracts high-dimensional complex features, where T=10 is the trajectory step size. After the encoder parameters are initialized, either freezing or open fine-tuning can be selected. If the freezing strategy is adopted, the gradient calculation of all encoder parameters is turned off, and only the newly added regression head is trained. If open fine-tuning is adopted, the encoder and the regression head jointly participate in gradient updates to make the deep features more suitable for the angle regression task. Step 402: Reconstruct the complex Transformer network structure based on the weights of the removed complex Transformer network structure. Specifically, a DOA regression head is constructed, and the output layer of the original network structure is replaced by the DOA regression head. Specifically, the DOA regression head is constructed by removing the reconstructed output layer in the pre-training stage and replacing it with a lightweight DOA regression prediction head. This regression head consists of two fully connected network layers. The first layer maps the spliced ​​features output by the encoder to the hidden dimension of 1024 and introduces non-linearity through the ReLU activation function. The second layer maps the hidden features to the final output dimension, corresponding to the continuous angle values ​​of a single radiation source. The predicted angle sequence is consistent with the dimension of the true label. The regression head has few parameters and is computationally efficient, avoiding the introduction of too many redundant parameters that could lead to overfitting. Step 403: Fine-tuning the replaced complex Transformer network structure based on the dataset to obtain the final complex Transformer network structure. Specifically, during the fine-tuning stage, the noisy covariance matrix generated in step 1 and the corresponding angle trajectory are used as supervision signals. Each training sample is a triple (noisy covariance matrix, true incident angle sequence, signal-to-noise ratio label). Unlike pre-training, no masking operation is applied during fine-tuning. The input is the complete covariance matrix, ensuring that the model learns the angle mapping relationship on real data without missing data. When loading data, the covariance matrix is ​​flattened into a real vector column-wise. The real and imaginary parts are separated and then input into the network. The angle labels are normalized to [ The range of 90°, 90° is used to match the output scale.

[0027] As shown in Figure 6, in step 5, the final complex Transformer network structure is run on test data with different signal-to-noise ratios, and the root mean square error is used as the performance evaluation index to output continuous DOA estimation results.

[0028] Embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0029] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in one or more blocks of the flowchart illustrations and / or one or more blocks of the block diagrams.

[0030] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowcharts and / or one or more block diagrams.

[0031] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more block diagrams.

[0032] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A continuous DOA estimation method based on complex Transformer and mask reconstruction, characterized in that, include: Step 1: Construct a uniform linear array signal receiving model, simulate and generate radiation source signal data with different signal-to-noise ratios, calculate the noisy covariance matrix and continuous angle labels, and finally generate a dataset; Step 2: Construct a complex Transformer network structure, which consists of complex multi-head attention layers, multi-scale complex convolutional layers, and complex feedforward network layers; Step 3: Pre-train the complex Transformer network structure using a self-supervised learning strategy; Step 4: Fine-tune the pre-trained complex Transformer network structure based on the dataset to obtain the final complex Transformer network structure; Step 5: Run the final complex Transformer network structure on test data with different signal-to-noise ratios, use RMSE as the performance evaluation metric, and output the continuous DOA estimation results.

2. The continuous DOA estimation method based on complex Transformer and mask reconstruction according to claim 1, characterized in that, In step 1, a uniform linear array receiving signal model is constructed, and radiation source signal data with different signal-to-noise ratios are simulated and generated. The noisy covariance matrix and continuous angle labels are calculated, and finally, a dataset is generated. Specifically: Step 101: Set the basic parameters of the uniform linear array, establish an array receiving model for far-field narrowband radiation source signals, construct the radiation source baseband signal using BPSK digital modulation, and achieve pulse shaping through a raised cosine filter to finally obtain the transmitted signal vector, i.e., the radiation source signal data; Step 102: Calculate the noisy sampling covariance matrix at each observation time step based on the array received signal vector; Step 103: Generate a dataset based on the radiation source signal data and the noisy covariance matrix.

3. The continuous DOA estimation method based on complex Transformer and mask reconstruction according to claim 2, characterized in that, In step 2, the Transformer network structure is composed of six identical layers stacked together. Each layer includes three core sub-layers, a residual connection layer, and a layer normalization layer. The three core sub-layers are a complex multi-head attention layer, a multi-scale complex convolutional layer, and a complex feedforward network layer, respectively.

4. The continuous DOA estimation method based on complex Transformer and mask reconstruction according to claim 3, characterized in that, The complex feedforward network layer includes two complex linear transformation layers and a ReLU activation layer.

5. The continuous DOA estimation method based on complex Transformer and mask reconstruction according to claim 3, characterized in that, The complex multi-head attention layer is configured with eight attention heads.

6. The continuous DOA estimation method based on complex Transformer and mask reconstruction according to claim 3, characterized in that, In step 3, a self-supervised learning strategy is used to pre-train the complex Transformer network structure, specifically: Step 301: Perform a random masking operation on the noisy covariance matrix; Step 302: Input the noisy covariance matrix after the random masking operation into the complex Transformer network structure for mask reconstruction; Step 303: After training is completed, extract and save the weights of the complex Transformer network structure with the lowest verification loss as the pre-trained model.

7. The continuous DOA estimation method based on complex Transformer and mask reconstruction according to claim 6, characterized in that, In step 4, the pre-trained complex Transformer network structure is fine-tuned based on the dataset to obtain the final complex Transformer network structure. Specifically: Step 401: Extract the weights of the complex Transformer network structure based on the pre-trained model, and remove the output layer weights from the complex Transformer network structure weights; Step 402: Reconstruct the complex Transformer network structure based on the removed complex Transformer network structure weights, wherein a DOA regression head is constructed and the output layer of the original network structure is replaced by the DOA regression head; Step 403: Fine-tune the replaced complex Transformer network structure based on the dataset to obtain the final complex Transformer network structure.

8. The continuous DOA estimation method based on complex Transformer and mask reconstruction according to claim 7, characterized in that, The DOA regression head consists of two fully connected layers.

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