Doppler direction of arrival estimation method based on linear-nonlinear branch fusion neural network

Abstract

The application relates to a linear-nonlinear branch fusion neural network-based direction of arrival estimation method, which comprises the following steps: obtaining original signals of an antenna array, calculating a reference empirical covariance matrix based on the original signals, and obtaining an input tensor based on the reference empirical covariance matrix; based on the input tensor, a residual matrix is obtained by using a double-path neural network; the double-path neural network comprises a linear branch and a nonlinear branch; an enhanced covariance matrix is obtained based on the residual matrix and the reference empirical covariance matrix; and a DOA estimation value is obtained by using a Root-MUSIC algorithm based on the enhanced covariance matrix. Compared with the prior art, the application provides a direction of arrival estimation method which can have the advantages of both a traditional subspace algorithm and a neural network participation type method.

Description

Technical Field

[0001] This invention relates to the field of array signal processing, and in particular to a direction-of-arrival estimation method based on a linear-nonlinear branch fusion neural network. Background Technology

[0002] In systems such as Multiple-Input Multiple-Output (MIMO) communication, radar detection, and sound source localization, it is often necessary to process the received array signals to estimate the direction of arrival (DOA) of the signal source to the reference array element. In this context, subspace-based methods have become widely used algorithms for DOA estimation. These methods primarily rely on the second-order statistical properties of the signal, extracting feature information from the signal subspace and noise subspace by performing eigenvalue decomposition on the covariance matrix of the received signal, thereby estimating the DOA. Among traditional subspace-based high-resolution algorithms, the Multiple Signal Classification (MUSIC) algorithm and the Rotation-Invariant Subspace (ESPRIT) algorithm are two typical examples. The former constructs a spatial spectrum function based on the noise subspace, while the latter utilizes the rotation-invariant properties of the signal subspace for angle estimation.

[0003] However, regardless of the specific subspace method used, its estimation performance is highly dependent on the accuracy of the received signal covariance matrix. In practical applications, due to factors such as limited snapshot numbers, low signal-to-noise ratio (SNR), or coherence between signal sources, the empirical covariance matrix often contains significant errors, leading to a sharp decline in the estimation accuracy of traditional subspace algorithms and affecting the DOA estimation accuracy. In recent years, with the development of neural networks, deep learning has also provided new solutions for array signal processing. Existing technical solutions can be mainly divided into two categories: 1) Neural network alternatives: This type of method abandons the traditional signal processing flow, constructs an end-to-end neural network model, and transforms the DOA estimation problem into a multi-label classification task. Its specific implementation is as follows: the array received signal or its empirical covariance matrix is ​​directly input into the neural network, which maps and outputs the estimated value of the target's direction of arrival. The advantage of this type of scheme is that it realizes an end-to-end estimation process, but its performance has inherent limitations: First, the estimation accuracy is limited by the preset angle discretization grid, and it is difficult to avoid off-grid errors; second, the constructed model is usually complex in structure and relies on large-scale labeled datasets for training, which greatly limits the application scenarios of this type of algorithm. 2) Neural network-assisted preprocessing type: In this type of scheme, the neural network is not used as a complete black box, but is partially integrated with traditional subspace algorithms to assist the model training process. Taking Chinese patent application CN117558287A as an example, it uses an autoencoder structure to generate an optimized surrogate covariance matrix, and then inputs it into classic subspace algorithms such as ESPRIT to complete DOA estimation. Although it retains some characteristics of traditional subspace algorithms to a certain extent and can achieve relatively high estimation accuracy, the training goal of its neural network is to directly generate the complete covariance matrix, rather than to locally modify or enhance the matrix based on the prior of the signal model. This may cause the network to need to learn the entire complex structure of the covariance matrix, resulting in a heavy learning burden, and may lose the effective information already in the original empirical covariance matrix during the generation process.

[0004] In summary, existing methods have the following shortcomings: 1) They cannot simultaneously achieve both the simplicity of the process and the theoretical completeness and high-precision interpolation capabilities of traditional subspace algorithms; 2) They fail to fully utilize the strong prior information contained in the empirical covariance matrix, ignoring the fact that the empirical covariance matrix already contains core information such as array structure and signal waveform in signal processing theory. Therefore, providing a direction-of-arrival estimation method that combines the advantages of traditional subspace algorithms and neural network-based methods is a technical problem that needs to be solved. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a direction-of-arrival estimation method based on a linear-nonlinear branch fusion neural network. This method guides the neural network to output a residual correction term, which locally compensates and enhances the empirical covariance matrix driven by the model but with biases. Thus, while retaining the physical interpretability of the traditional method, it effectively integrates the generalization capability of data-driven methods, achieving a deep fusion of the two paradigms.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] This invention provides a direction-of-arrival estimation method based on a linear-nonlinear branch fusion neural network, the method comprising:

[0008] The original signal of the antenna array is obtained, the reference empirical covariance matrix is ​​calculated based on the original signal, and the input tensor is obtained based on the reference empirical covariance matrix.

[0009] Based on the input tensor, a residual matrix is ​​obtained by processing it using a dual-path neural network; the dual-path neural network includes a linear branch and a non-linear branch.

[0010] The enhanced covariance matrix is ​​obtained based on the residual matrix and the benchmark empirical covariance matrix.

[0011] Based on the enhanced covariance matrix, the DOA estimate is obtained using the Root-MUSIC algorithm.

[0012] As a preferred technical solution, the method for obtaining the input tensor is as follows:

[0013] The real and imaginary parts of the aforementioned benchmark empirical covariance matrix are concatenated to obtain the input tensor, which is: ,in, Let represent the baseline empirical covariance matrix, and:

[0014] ,

[0015] Represents the original signal. Indicates the number of snapshots. Indicates conjugate operation; Indicates the real part; Indicates the imaginary part.

[0016] As a preferred technical solution, the dual-path neural network further includes a shared feature encoder, a gated fusion network, and a positive definite residual matrix construction layer, and the dual-path neural network contains:

[0017] In the shared feature encoder, the input tensor is flattened into shared features;

[0018] The shared features are input into a linear branch and a nonlinear branch respectively. The linear branch is used to extract the linear physical relationships in the shared features and output linear features. The nonlinear branch is used to fit the complex distortions, noise and unmodeled effects in the shared features and output nonlinear features. The complex distortions include antenna array position errors and signal multipath effects. The unmodeled effects include ADC sampling errors.

[0019] The gated fusion network adaptively fuses linear and nonlinear features to output fused features;

[0020] Based on the aforementioned fusion characteristics, the layer is constructed using a positive definite residual matrix and converted into a residual matrix.

[0021] As a preferred technical solution, the method for obtaining the fusion features is as follows:

[0022] The shared features are processed using a fully connected layer in a gated fusion network to obtain the initial fusion weight vector, which is: , Represents the learnable weight matrix; Indicates shared features; Indicates the bias term; Indicates the activation function; This represents the initial fusion weight vector. and These represent the initial fusion weights for linear and nonlinear features, respectively;

[0023] The initial fusion weight vector is normalized to obtain the fusion weights, which are:

[0024] ,

[0025] in, and These represent the fusion weights for linear and nonlinear features, respectively; express function; Represents the natural constant;

[0026] Based on the aforementioned fusion weights, linear and nonlinear features are weighted and fused to obtain fused features.

[0027] As a preferred technical solution, the following steps are performed in the positive definite residual matrix construction layer to convert the fused features into a residual matrix:

[0028] The fused features are segmented into real and imaginary vectors, and a complex vector is constructed based on the real and imaginary vectors as follows: , Represents a vector with the real part. Represents a vector with the real part. Represents the imaginary unit;

[0029] According to row order, the complex vectors are filled to the non-zero positions of the lower triangular matrix according to the filling rules, which are as follows:

[0030] ,

[0031] in, Represents a lower triangular matrix The Middle Line 1 Column elements; Let represent the k-th element in the complex vector, and , , Indicates the number of array elements;

[0032] Based on the aforementioned triangular matrix, the residual matrix is ​​calculated as follows: , This indicates the conjugate operation. This represents the residual matrix.

[0033] As a preferred technical solution, the method for segmenting the fusion features is as follows:

[0034] ,

[0035] in, Indicates fusion characteristics; This indicates taking the first feature from the fusion features. One element; This indicates the extraction of features from the fusion process. Each element.

[0036] As a preferred technical solution, the method for obtaining the DOA estimate using the Root-MUSIC algorithm is as follows:

[0037] The enhanced covariance matrix Eigenvalue decomposition yields: , Represents the eigenvector matrix, , Indicates the first Column vectors; Represents an eigenvalue diagonal matrix. , Indicates the first One eigenvalue; Indicates conjugate operation;

[0038] Dividing the eigenvalue decomposition results into M sources, the signal subspace is then: , Represents the first in the signal subspace If there are elements, then the noisy subspace is: , Represents the first in the noise subspace One element;

[0039] Construct the polynomial as follows:

[0040] ,

[0041] in, Represents an array manifold polynomial. Indicates the angle of arrival of the information source. Mapping representation on the complex plane, Indicates the number of array elements; Represents the noise subspace; Represents the imaginary unit;

[0042] Solve the polynomial and select the solution closest to the unit circle. One solution, based on this Each solution yields a continuous angle estimate, as follows:

[0043] ,

[0044] in, Indicates to An angle estimation of each information source; This indicates the total number of information sources.

[0045] As a preferred technical solution, the dual-path neural network has the following characteristics during training:

[0046] A multi-task loss function is constructed, and the parameters of the dual-path neural network are updated during training based on the gradient of the multi-task loss function. The multi-task loss function includes DOA angle loss and covariance matrix loss, and the gradient is calculated in the following form: ,in, and Let represent the adaptive weights of the DOA angle loss and the covariance matrix loss, respectively, and have , Let represent the i-th trainable parameter vector. Let represent the j-th trainable parameter vector. Represents the natural constant.

[0047] As a preferred technical solution, the DOA angle loss is:

[0048] ,

[0049] in, This represents the predicted DOA vector. Indicates the first The predicted DOA for each information source; This represents the angle modulo operation, expressed in angles. For example:

[0050] ;

[0051] Indicates arrangement The first in the rearranged prediction vector One source; Indicates the total number of information sources; Indicates the first The true DOA vector corresponding to each information source.

[0052] As a preferred technical solution, the covariance matrix loss is:

[0053] ,

[0054] in, Represents the enhanced covariance matrix; Let represent the ideal covariance matrix, and , Let represent the array manifold matrix, and we have:

[0055] ,

[0056] Indicates the first The steering vector of each source, and , Indicates the first The true DOA vectors of each source; Indicates the number of array elements. Represents the imaginary unit. Represents the natural constant; Let represent the covariance matrix of the source signal, and , Indicates the first The signal power of each signal source Indicates additive noise power. express An identity matrix of order 1; Represents the stability constant; This represents the Frobenius norm operation.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] 1) To address the shortcomings of existing technologies, this invention first constructs a benchmark empirical covariance matrix based on the original signal when performing direction-of-arrival estimation. This matrix is ​​then used as the input to a neural network. The invention utilizes the inherent physical prior information such as array structure, signal waveform, and number of sources, enabling the neural network to focus on correcting finite sample errors and distortions in the benchmark empirical covariance matrix, thus fully leveraging physical prior knowledge. Furthermore, in the method provided by this invention, the neural network predicts the residual matrix of the covariance matrix. During training, the neural network only needs to learn simpler error corrections. Compared to the complex end-to-end mapping process from signal to covariance matrix required for the complete empirical covariance matrix, the method provided by this invention is faster. Since the residual matrix only needs to correct errors caused by finite sample effects, noise, and non-ideal factors, the residual amplitude is smaller than that of traditional methods, and the complexity of the corresponding function mapping is also reduced to some extent.

[0059] 2) In this invention, the enhanced covariance matrix after enhancement by the residual matrix is ​​used to construct the noise subspace using the Root-MUSIC algorithm, thereby achieving continuous angle estimates. Compared with existing methods that can only output estimates of specific angles, this invention fundamentally avoids off-grid errors caused by angle discretization.

[0060] 3) This invention provides a dual-path neural network structure that includes linear and nonlinear processing. Specifically, the linear branch in the network learns signal model knowledge such as array manifolds to ensure that the output meets mathematical specifications; the nonlinear branch focuses on learning the distortion components in the covariance matrix that are difficult to model analytically. Furthermore, during training, the linear branch is responsible for the model determination part, while the nonlinear branch only needs to learn bias correction. This architectural design significantly reduces the functional complexity that the neural network needs to learn, enabling the network to converge quickly with a small number of samples. It avoids the need for existing data-driven methods to rely entirely on a large number of training samples to learn the complex mapping relationships of signal processing. By combining physical models with data-driven approaches, it avoids the problems of overfitting or insufficient performance under small sample conditions.

[0061] 3) In addition, this invention designs a positive definite residual construction layer in the neural network. Based on the basic principles of matrix theory, this layer ensures that the output has correct mathematical properties from the root, and strictly guarantees that the enhanced covariance matrix of the network output satisfies the positive semi-definite Hermitian property. This ensures that the enhanced covariance matrix can be directly processed by the Root-MUSIC algorithm, effectively solving the problem that the output of the data-driven method may violate mathematical norms.

[0062] 4) This invention proposes an adaptive multi-task loss function that achieves a dynamic balance between DOA angle estimation and covariance matrix reconstruction through trainable weight parameters. Compared with multi-task learning with fixed weights, this mechanism can autonomously optimize the contribution of each task, thereby improving training efficiency and generalization ability. Attached Figure Description

[0063] Figure 1 This is a flowchart of the method of the present invention;

[0064] Figure 2 This is a flowchart of the dual-path neural network workflow of the present invention;

[0065] Figure 3 This is a schematic diagram of the training results of the dual-path neural network of the present invention under a large data signal-to-noise ratio of 10dB;

[0066] Figure 4 This is a schematic diagram of the training results of the path neural network of the present invention under a small data signal-to-noise ratio of 10dB;

[0067] Figure 5 This is a performance comparison chart between the method of the present invention and existing methods. Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0069] Example 1

[0070] This invention aims to address the following prominent problems in existing DOA estimation techniques: 1) Under non-ideal conditions such as low signal-to-noise ratio, few snapshots, or coherent sources, the empirical covariance matrix relied upon by traditional subspace methods deviates significantly from ideal characteristics, leading to a significant decrease in estimation accuracy; while pure deep learning schemes avoid the limitations of traditional models, they lack prior support for signal physics, have poor interpretability, and rely on a large number of parameters and labeled data, resulting in low practicality; 2) In addition, although existing neural network-assisted methods attempt to combine the advantages of both, the coupling between the network structure and traditional algorithms is loose, and the learning objective fails to effectively focus on the local enhancement of the empirical covariance matrix, resulting in both information loss and computational redundancy.

[0071] Specifically, this invention provides a direction-of-arrival estimation method based on a linear-nonlinear branch fusion neural network, the process of which is as follows: Figure 1 As shown, it includes:

[0072] S1. Obtain the original signal of the antenna array, calculate the reference empirical covariance matrix based on the original signal, and obtain the input tensor based on the reference empirical covariance matrix.

[0073] Empirical covariance matrix It naturally contains physical prior information such as array structure, signal waveform, and number of signal sources, and satisfies the basic mathematical properties of the covariance matrix (positive semi-definite, Hermitian). Traditional deep learning methods ignore this strong prior information, forcing the network to learn the complete signal modeling process from scratch. To reduce the cost and complexity of neural network learning, this invention will... As the input benchmark for the neural network, it enables the network's learning objective to focus on correction. This reduces the finite sample error and distortion in the learning process, thereby significantly reducing learning complexity and making full use of prior physical information.

[0074] S1. Concatenate the real and imaginary parts of the benchmark empirical covariance matrix to obtain the input tensor. ,for:

[0075] ,

[0076] in, Indicates the number of array elements. Let represent the baseline empirical covariance matrix, and:

[0077] ,

[0078] Represents the original signal. Indicates the number of snapshots. Indicates conjugate operation; Indicates the real part; Indicates the imaginary part.

[0079] S2. Based on the input tensor, the residual matrix is ​​obtained by processing it using a dual-path neural network.

[0080] The dual-path neural network provided by this invention includes a shared feature encoder, linear and nonlinear branches, a gated fusion network, and a positive definite residual matrix construction layer, performing operations such as... Figure 2 The steps shown are used to obtain the residual matrix:

[0081] S21. In the shared feature encoder, the input tensor is flattened into shared features. ,for:

[0082] ,

[0083] in, This represents fully connected layers, batch normalized layers, and Layer operations consisting of activation functions; This indicates a flattening operation.

[0084] S22. Input the shared features into the linear branch and the nonlinear branch respectively, and output the linear features. and nonlinear characteristics .

[0085] The linear branch structure is relatively simple and is used to extract linear physical relationships in shared features; the nonlinear branch structure is deeper, including nonlinear activation functions and dropout layers, and is used to fit complex distortions, noise and unmodeled effects in shared features. Complex distortions include antenna array position errors and signal multipath effects, while unmodeled effects include ADC sampling errors.

[0086] S23. The gated fusion network adaptively fuses linear and nonlinear features to output fused features.

[0087] S231. The shared features are processed using the fully connected layer in the gated fusion network to obtain the initial fusion weight vector, which is: , Represents the learnable weight matrix. For shared features The dimension; Indicates shared features; Indicates the bias term; The activation function is represented by the hyperbolic tangent function, which is selected in this embodiment. ; This represents the initial fusion weight vector. and These represent the initial fusion weights for linear and nonlinear features, respectively.

[0088] S232. Normalize the initial fusion weight vector to obtain the fusion weights, as follows:

[0089] ,

[0090] in, and Let represent the fusion weights for linear and nonlinear features, respectively, and the fusion weights must satisfy . ; express function; Represents the natural constant.

[0091] S233. Based on the fusion weight, the linear and nonlinear features are weighted and fused to obtain the fused features as follows: .

[0092] S24. Based on the fusion features, the layer is converted into a residual matrix using the positive definite residual matrix.

[0093] This is a key step in the invention, used to ensure that the network output is a valid covariance matrix. Specifically, this layer converts the fused features into a residual matrix, and the steps are as follows:

[0094] S241. Divide the fused features into real vectors and imaginary vectors, and construct complex vectors based on the real vectors and imaginary vectors.

[0095] The method for segmenting and fusing features is as follows:

[0096] ,

[0097] in, Indicates fusion characteristics; This indicates taking the first feature from the fusion features. One element; This indicates the extraction of features from the fusion process. Each element.

[0098] Complex vectors are: , Represents a vector with the real part. Represents a vector with the real part. It represents the imaginary unit.

[0099] S242. According to row precedence, fill the complex vectors to the non-zero positions of the lower triangular matrix according to the filling rules. Assume the matrix index starts from 0. This represents the row index of the matrix, corresponding to the row number from top to bottom. OK. This represents the column index of the matrix, corresponding to the first column from left to right. The column, i.e., the fill rule, is:

[0100] ,

[0101] in, Represents a lower triangular matrix The Middle Line 1 Column elements; Let represent the k-th element in the complex vector, and , , Indicates the number of array elements.

[0102] S243. Based on the triangular matrix, calculate the residual matrix as follows: , This indicates the conjugate operation. This represents the residual matrix.

[0103] This operation is based on a mathematical property: any matrix Conjugate with product It must be a positive semi-definite Hermitian matrix, thus guaranteeing the residual matrix. and enhanced covariance matrix The semi-definite Hermitian matrix structure required to have the covariance matrix satisfies: , Represents any non-zero complex test vector used to test the positive semidefiniteness of a matrix.

[0104] S3. Obtain the enhanced covariance matrix based on the residual matrix and the benchmark empirical covariance matrix.

[0105] In detail, the enhanced covariance matrix is ​​as follows: .

[0106] Steps S2 and S3 ultimately output the estimated residual matrix, enabling the neural network to learn the residual matrix rather than an incomplete covariance matrix. This significantly reduces learning complexity for the following reasons:

[0107] 1) Reduced complexity of function mapping: The complete covariance matrix contains Complex elements, need to be learned Complex mapping relationships of magnitude; and the residual matrix Only representing the ideal covariance matrix With the empirical covariance matrix Deviation between:

[0108] ,

[0109] The benchmark covariance matrix It can be calculated using simple methods based on the original signal.

[0110] 2) Residual amplitude is relatively small: In practical systems, the empirical covariance matrix... It already contains the main information of the signal, residuals Only errors caused by finite sample effects, noise, and non-ideal factors need to be corrected:

[0111] .

[0112] 3) Clear learning objectives: Neural networks only need to learn relatively simple error correction, i.e. Rather than a complex end-to-end mapping of signals to covariance matrices. Furthermore, the following must be satisfied during the learning error correction process:

[0113] .

[0114] 4) Faster convergence speed: Assuming the ideal covariance matrix is... The enhanced covariance matrix can then be expressed as: Initial settings Neural network output As training progresses, the network gradually learns the biases. This design results in a smaller initial error, a clear gradient update direction, and significantly faster convergence.

[0115] In summary, residual learning enables neural networks to learn effective covariance matrix enhancement functions with fewer parameters and faster convergence, especially under small sample conditions.

[0116] Furthermore, in this invention, an adaptive multi-task loss function is constructed for training and optimizing the neural network. During training, the Adam optimizer is used with an initial learning rate of 1e-3 and weight decay of 1e-9. A cosine annealing learning rate scheduler is employed, with a period equal to half the total number of training epochs to dynamically adjust the learning rate. The training epochs are set to 80, and the batch size is 128. The optimization targets are the main neural network model parameters and the learnable vectors in the adaptive loss. and Finally, monitor the RMSE loss on the validation set and save the best-performing model weights for final testing and deployment.

[0117] Specifically, the loss function calculates adaptive weights in each training iteration by introducing k to train the parameter vector: , Let represent the i-th trainable parameter vector. Let represent the j-th trainable parameter vector. Represents the natural constant; and These represent the adaptive weights for the DOA angle loss and the covariance matrix loss, respectively; and it should be noted that... and Instead of being a fixed preset, it is updated along with the neural network parameters through backpropagation as model parameters in order to find the optimal task balance point.

[0118] During training, the parameters of the dual-path neural network are updated based on the gradient of the multi-task loss function. The multi-task loss function includes the DOA angle loss and the covariance matrix loss. The gradient is calculated as follows:

[0119] ,

[0120] in, This represents the loss due to multiple tasks, and includes:

[0121] ,

[0122] Indicates DOA angle loss Or covariance matrix loss Among them, the DOA angle loss is:

[0123] ,

[0124] in, This represents the predicted DOA vector. Indicates the first The predicted DOA for each information source; This represents the angle modulo operation, expressed in angles. For example:

[0125] ;

[0126] Indicates arrangement The first in the rearranged prediction vector One source; Indicates the total number of information sources; Indicates the first The true DOA vector corresponding to each information source.

[0127] The covariance matrix loss is:

[0128] ,

[0129] in, Represents the enhanced covariance matrix; Let represent the ideal covariance matrix, and , Let represent the array manifold matrix, and we have:

[0130] ,

[0131] Indicates the first The steering vector of each source, and , Indicates the first The true DOA vectors of each source; Indicates the number of array elements. Represents the imaginary unit. Represents the natural constant; Let represent the covariance matrix of the source signal, and , Indicates the first The signal power of each signal source Indicates additive noise power. express An identity matrix of order 1; Represents the stability constant; This represents the Frobenius norm operation.

[0132] To verify that the method provided in this invention performs excellently regardless of whether the sample size is large or small, it was trained on both large and small datasets with a signal-to-noise ratio of 10 dB. The results are as follows: Figure 3 and 4 As shown, the horizontal axis represents the number of training epochs (80 epochs in total), and the vertical axis represents the root mean square error (RMSE) loss value. Figure 3 The training process monitoring curves of the dual-path neural network on a large-scale training dataset are shown. Both the training loss curve and the validation loss curve show a significant decrease and then tend to stabilize during 80 training rounds, indicating that the dual-path neural network has good learning ability and convergence on large-scale datasets. Figure 4 The training process monitoring curves of the neural network on a small training dataset are shown. Both the training loss curve and the validation loss curve show a decreasing trend during the 10 training rounds, indicating that the neural network model has good generalization ability on a small dataset.

[0133] S4. Based on the enhanced covariance matrix, the DOA estimate is obtained using the Root-MUSIC algorithm.

[0134] The Root-MUSIC algorithm, a classic subspace algorithm, has been widely validated in engineering practice. This invention enhances its input covariance matrix through a neural network, maintaining the theoretical rigor and engineering reliability of the Root-MUSIC algorithm while improving its performance in challenging scenarios such as low signal-to-noise ratio and small sample sizes through a data-driven approach. In this embodiment, the Root-MUSIC algorithm estimates the DOA by constructing signal and noise subspaces and solving for the phase of the polynomial roots. The neural network of this invention is designed to directly predict continuous DOA angle values, requiring an angle measurement algorithm as backend processing to receive the enhanced covariance matrix output by the neural network. and output continuous The Root-MUSIC algorithm naturally outputs continuous angle values, which meets the requirements for backend processing, and is therefore fully compatible with the output format of the neural network of this invention.

[0135] S41. Enhance the covariance matrix Eigenvalue decomposition yields: , Represents the eigenvector matrix, , Indicates the first Column vectors; Represents an eigenvalue diagonal matrix. , Indicates the first One eigenvalue; This indicates the conjugate operation.

[0136] S42. Dividing the result of eigenvalue decomposition into M sources, the signal subspace is then: , Represents the first in the signal subspace If there are elements, then the noisy subspace is: , Represents the first in the noise subspace Each element.

[0137] S43. Construct the polynomial as follows:

[0138] ,

[0139] in, Represents an array manifold polynomial. Indicates the angle of arrival of the information source. Mapping representation on the complex plane, Indicates the number of array elements; Represents the noise subspace; It represents the imaginary unit.

[0140] S44. Solve the polynomial and select the solution closest to the unit circle. One solution, based on this Each solution yields a continuous angle estimate, as follows:

[0141] ,

[0142] in, Indicates to An angle estimation of each information source; This indicates the total number of information sources.

[0143] The above process generates continuous angle output naturally without any discretization.

[0144] Traditional deep learning-based DOA estimation methods typically discretize the angle space into... fixed grid points This approach treats DOA estimation as a classification task. However, it suffers from an inherent off-grid error problem: when the true source direction... Not located at the preset grid point When it is above, that is This will produce systematic errors. ,in The nearest grid point; the theoretical lower bound for the resulting off-grid error is:

[0145] ,

[0146] in, This indicates the grid spacing. To avoid the aforementioned problems, this invention directly outputs continuous angle values ​​through a regression framework. This completely eliminated this source of error.

[0147] Example 2

[0148] This embodiment verifies the performance of the method described in this invention under test scenarios with signal-to-noise ratios of 0dB, 5dB, 10dB, and 20dB, a snapshot count of 100, and the presence of a coherent signal source. Figure 5 As shown, the present invention is compared with the classic MUSIC algorithm, the Root-MUSIC algorithm, the ESPRIT algorithm, and a neural network method in a certain existing method.

[0149] exist Figure 5 The horizontal axis represents the signal-to-noise ratio (SNR), and the vertical axis represents the root mean square (RMS) phase error. It can be seen that the present invention achieves the best estimation performance under different SNR conditions. Its RMS phase error reaches -24.95dB, -26.97dB, -28.58dB, and -31.73dB at 0dB, 5dB, 10dB, and 20dB, respectively, which is significantly better than other comparison algorithms, demonstrating excellent estimation accuracy and robustness.

[0150] And from Figure 5 It can also be observed that as the signal-to-noise ratio increases, the performance of traditional auxiliary neural networks and various subspace algorithms tends to converge to the same limit. This phenomenon is limited by the theoretical characteristics of the subspace algorithm itself. However, the method proposed in this invention can effectively break through this limitation and achieve an RMSPE (root mean square percentage error) of less than -30dB under a signal-to-noise ratio of 20dB, demonstrating an estimation ability superior to that of traditional theoretical boundaries. In other words, the method provided by this invention has superiority.

Claims

1. A method for direction of arrival estimation based on linear-nonlinear branch fusion neural network, characterized in that, The method comprises: Obtaining an original signal of an antenna array, calculating a reference empirical covariance matrix based on the original signal, and obtaining an input tensor based on the reference empirical covariance matrix; Based on the input tensor, a residual matrix is obtained by using a double-path neural network; the double-path neural network comprises a linear branch and a nonlinear branch; the double-path neural network further comprises a shared feature encoder, a gated fusion network, and a positive definite residual matrix construction layer, and in the double-path neural network, the input tensor is flattened into shared features in the shared feature encoder; the shared features are input into the linear branch and the nonlinear branch respectively, the linear branch is used to extract linear physical relationships in the shared features and output linear features, and the nonlinear branch is used to fit complex distortions, noises, and unmodeled effects in the shared features and output nonlinear features; the complex distortions comprise antenna array position errors and signal multipath effects, and the unmodeled effects comprise ADC sampling errors; the gated fusion network adaptively fuses the linear features and the nonlinear features and outputs fused features; based on the fused features, the positive definite residual matrix construction layer is used to convert the fused features into the residual matrix; Based on the residual matrix and the reference empirical covariance matrix, an enhanced covariance matrix is obtained; Based on the enhanced covariance matrix, a DOA estimation value is obtained by using a Root-MUSIC algorithm.

2. The method of claim 1, wherein, The method for obtaining the input tensor is: The real part and the imaginary part of the reference empirical covariance matrix are spliced to obtain an input tensor, which is: wherein, represents the reference empirical covariance matrix, and: ， represents an original signal, represents a number of taps, represents a conjugate operation; represents a real part; represents an imaginary part.

3. The method of claim 1, wherein, The method for obtaining the fused features is: The shared features are processed by a full connection layer in the gating fusion network to obtain an initial fusion weight vector, which is: , represents a learnable weight matrix; represents shared features; represents a bias term; represents an activation function; represents an initial fusion weight vector, and represent initial fusion weights of linear features and nonlinear features, respectively. The initial fused weight vector is normalized to obtain a fused weight, that is, ， wherein, and denote the fusion weight of linear and nonlinear features, respectively; denotes function; denotes natural constant; Based on the fused weight, the linear features and the nonlinear features are weighted and fused to obtain the fused features.

4. The method of claim 1, wherein, In the positive definite residual matrix construction layer, the following steps are performed to convert the fused features into the residual matrix: The fusion feature is divided into a real part vector and an imaginary part vector, and a complex number vector is constructed based on the real part vector and the imaginary part vector as follows: , represents the real part vector, represents the real part vector, represents the imaginary unit; According to a row priority order, the complex vector is filled into non-zero positions of a lower triangular matrix according to a filling rule, and the filling rule is: ， wherein denotes a lower triangular matrix the element in the row and the column; denotes the k-th element in the complex vector and , , denotes the number of array elements; Based on the described triangular matrix, a residual matrix is calculated, which is: , denotes a conjugate operation, denotes a residual matrix.

5. The method of claim 4, wherein, The method for splitting the fused features is: ， wherein, represents a fusion feature; represents the first elements of the fusion feature; represents the last elements of the fusion feature.

6. The method of claim 1, wherein, The method for obtaining the DOA estimation value by using the Root-MUSIC algorithm is: The enhanced covariance matrix Eigenvalue decomposition is performed to yield: , denotes the eigenvector matrix, , denotes the kth column vector; denotes the eigenvalue diagonal matrix, , denotes the kth eigenvalue; denotes the conjugate operation;​​ Dividing the eigenvalue decomposition results into M sources, the signal subspace is then: , Represents the first in the signal subspace If there are elements, then the noisy subspace is: , Represents the first in the noise subspace One element; The polynomial is constructed as: ， wherein, represents an array flow pattern polynomial, represents a source angle of arrival represents a mapping on the complex plane, represents the number of array elements; represents a noise subspace; represents the imaginary unit; Solve the polynomial and select the solution closest to the unit circle. One solution, based on this Each solution yields a continuous angle estimate, as follows: ， wherein denotes an angle estimate for sources; denotes the total number of sources.

7. The method of claim 1, wherein, For the double-path neural network, during training, the following steps are performed: A multi-task loss function is constructed, and parameters of the dual-path neural network are updated based on gradients of the multi-task loss function during training, the multi-task loss function includes a DOA angle loss and a covariance matrix loss, and the gradients are calculated in the form of: wherein, and respectively represent adaptive weights of the DOA angle loss and the covariance matrix loss, and have , represents an i-th trainable parameter vector, represents a j-th trainable parameter vector, represents a natural constant.

8. The method of claim 7, wherein, The DOA angle loss is: ， wherein, represents a predicted DOA vector, represents a predicted DOA corresponding to the represents an angle modulo operation, taking angle as an example:​ ； denotes an arrangement the first source; denotes the total number of sources denotes the real DOA vector corresponding to the first source.

9. The method of claim 7, wherein, The covariance matrix loss is: ， wherein denotes the enhanced covariance matrix; denotes the ideal covariance matrix, and , denotes the array flow pattern matrix, and has: ， Indicates the first The steering vector of each source, and , Indicates the first The true DOA vectors of each source; Indicates the number of array elements. Represents the imaginary unit. Represents the natural constant; Let represent the covariance matrix of the source signal, and , Indicates the first The signal power of each signal source; Indicates additive noise power. express An identity matrix of order 1; Represents the stability constant; This represents the Frobenius norm operation.

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