Off-lattice DOA estimation method and system based on deep learning under array error

Abstract

The invention relates to the technical field of array signal processing, in particular to an out-of-lattice DOA estimation method and system based on deep learning under array errors, and the method comprises the steps: receiving a narrowband signal sent by a narrowband target through an observation array, obtaining a corresponding array receiving signal, and obtaining a covariance matrix based on the array receiving signal; and inputting the array receiving signal and the covariance matrix into a pre-trained DOA estimation model, and obtaining a DOA estimation result of the narrowband target by using the DOA estimation model, the DOA estimation model comprises a first feature extraction network used for extracting array signal features, a second feature extraction network used for extracting covariance matrix features, and a full-connection network used for fusing the array signal features and the covariance matrix features and obtaining a narrowband target DOA estimation result. According to the method, the influence of the array error on the DOA estimation performance can be effectively suppressed, and the DOA estimation effect of the narrowband target is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of array signal processing, and particularly relates to an off-grid DOA estimation method and system based on deep learning under array errors. Background Art

[0002] Direction of arrival (DOA) estimation is an important research content in array signal processing, and has wide applications in multiple fields such as radar, sonar, and wireless communication. In actual situations, the receiving array is not ideal, and it usually has amplitude-phase errors, mutual coupling errors, and element position perturbations. These array errors will have a great impact on the DOA estimation accuracy. Therefore, it is of great significance to study high-precision DOA estimation in the presence of array errors.

[0003] Traditional DOA estimation methods are mainly conventional beamforming (CBF) - type algorithms. However, this type of method is limited by the physical system of the array and cannot provide high resolution. To overcome the Rayleigh limit, many super-resolution DOA estimation algorithms have emerged. Among them, subspace - type algorithms are the most classic type of algorithms, mainly including the Multiple Signal Classification (MUSIC) algorithm and the Estimating Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm. Based on these two algorithms, many improved subspace - type algorithms have been proposed. For example, the Root - MUSIC algorithm, which is a polynomial root - finding form of the MUSIC algorithm, and its basic idea is Pisarenko decomposition; another example is the Compressive MUSIC (CS - MUSIC) algorithm, which realizes super - resolution DOA estimation through a compressive sensing recovery algorithm; and the Unitary ESPRIT algorithm, which utilizes the unitary matrix property of the phase delay between two sub - regions to further improve the estimation accuracy of the ESPRIT algorithm. For example, using the Total Least Squares (TLS) criterion for matrix estimation, the Total Least Squares ESPRIT (TLS ESPRIT) algorithm is proposed. However, these methods have high signal - to - noise ratio requirements and high computational complexity in practical applications. Summary of the Invention

[0004] Therefore, the present invention provides an off - grid DOA estimation method and system based on deep learning under array errors, so as to solve the problems of limited application of signal - to - noise ratio and high computational complexity existing in the existing DOA estimation.

[0005] According to the design solution provided by the present invention, on the one hand, a method for off-grid DOA estimation based on deep learning under array error is provided, including:

[0006] Use the observation array to receive the narrowband signal sent by the narrowband target, obtain the corresponding array received signal, and obtain the covariance matrix based on the array received signal;

[0007] Input the array received signal and the covariance matrix into the pre-trained DOA estimation model, and use the DOA estimation model to obtain the DOA estimation result of the narrowband target. The DOA estimation model includes: a first feature extraction network for extracting array signal features, a second feature extraction network for extracting covariance matrix features, and a fully connected network for fusing array signal features and covariance matrix features and obtaining the DOA estimation result of the narrowband target.

[0008] As the method for off-grid DOA estimation based on deep learning under array error of the present invention, further, using the observation array to receive the narrowband signal sent by the narrowband target includes:

[0009] Deploy an M-element uniform linear array as the observation array, and set the interval between each element to half a wavelength;

[0010] Based on amplitude-phase error, mutual coupling error and element position perturbation, establish an array reception signal model of the observation array to obtain the array received signal corresponding to the narrowband signal by using the array received signal model.

[0011] As the method for off-grid DOA estimation based on deep learning under array error of the present invention, further, the DOA estimation model training process includes:

[0012] Use narrowband signal sources with known incoming wave direction angles to construct network model training samples;

[0013] Discretize the angle region by specifying an angle interval to obtain an angle set, and set the DOA category label of the corresponding narrowband signal source according to the rounded integer value of the incoming wave direction angle;

[0014] Based on the binary cross-entropy function, use a regularization function and a weighting coefficient to construct a loss function for model training;

[0015] Based on the loss function and using the network model training samples to train the DOA estimation model.

[0016] As the method for off-grid DOA estimation based on deep learning under array error of the present invention, further, using narrowband signal sources with known incoming wave direction angles to construct network model training samples includes:

[0017] Set up several narrowband signal sources with known incoming wave direction angles, use the observation array to receive the narrowband signals of several known narrowband signal sources, and obtain the array received signal sample data corresponding to the narrowband signal sources;

[0018] Obtain the covariance matrix sample data based on the array received signal sample data, splice the covariance matrix sample data with the array received signal sample data to obtain the network model training samples.

[0019] As the off-grid DOA estimation method based on deep learning under array errors of the present invention, further, the process of setting the DOA category label corresponding to the narrowband signal source according to the rounded integer value of the incoming wave direction angle is expressed as:

[0020] where p i represents the i-th DOA category label element, θ k represents the incoming wave direction angle corresponding to the k-th narrowband signal source, represents rounding θ k to the nearest integer, represents the existence of θ k the rounded value is equal to Θ i Θ i represents the integer part corresponding to the target DOA. P is a constant, representing the label value when there is no corresponding DOA..

[0021] As the off-grid DOA estimation method based on deep learning under array errors of the present invention, further, the loss function is expressed as: where z represents the network predicted category output vector, p represents the label vector, and Q is the number of label categories, g(z q ) represents the regularization function, and w represents the weight coefficient, and Top K (·) represents the number of categories corresponding to the subscript indices of the top K larger elements in the vector. ε is a constant, and ε = 1 can be set. Its function is to prevent the denominator from being 0.

[0022] As the off-grid DOA estimation method based on deep learning under array errors of the present invention, further, the first feature extraction network includes: a batch normalization layer, a position encoding layer, a Transformer encoder, a connection layer, and a Dropout layer. The second feature extraction network includes: a batch normalization layer, a fully connected layer with residual connections, and an output fully connected layer. The fully connected network includes a fully connected layer and a Dropout layer.

[0023] On the other hand, the present invention also provides an off-grid DOA estimation system based on deep learning under array error, comprising: a signal receiving module and a signal estimation module, wherein,

[0024] The signal receiving module is used to receive the narrowband signal sent by the narrowband target by using the observation array, obtain the corresponding array received signal, and obtain the covariance matrix based on the array received signal;

[0025] The signal estimation module is used to input the array received signal and the covariance matrix into the pre-trained DOA estimation model, and use the DOA estimation model to obtain the DOA estimation result of the narrowband target. The DOA estimation model includes: a first feature extraction network for extracting array signal features, a second feature extraction network for extracting covariance matrix features, and a fully connected network for fusing array signal features and covariance matrix features and obtaining the DOA estimation result of the narrowband target.

[0026] Advantages of the present invention:

[0027] Based on the signal data and covariance matrix received by the uniform linear array, the present invention uses a deep learning network to estimate the direction-of-arrival angles of multiple signals. Among them, in the deep learning network, the Transformer encoder is used to extract time series features from the array output signal, the covariance matrix is estimated by using the received finite number of snapshots of the signal, its Toeplitz structure possessed by the theoretical covariance matrix is used to enhance it, and the fully connected residual network is used to extract the covariance matrix features. The extracted time series features and covariance matrix features are fused by using a neural network and finally the DOA estimation results of multiple targets are obtained. Due to the fusion of the time series features in the array output signal and the enhancement of the covariance matrix features, the influence of array error on the DOA estimation performance can be effectively suppressed, and the DOA estimation effect of the narrowband target can be improved. Description of the Drawings

[0028] Figure 1 Schematic diagram of the off-grid DOA estimation process based on deep learning under array error in the embodiment;

[0029] Figure 2 Schematic diagram of the DOA estimation model structure in the embodiment;

[0030] Figure 3 Schematic diagram of the IQ-Net structure of the first feature extraction network in the embodiment;

[0031] Figure 4 Schematic diagram of the ENSCM-Net structure of the second feature extraction network in the embodiment;

[0032] Figure 5 Schematic diagram of the Weight-Net structure of the fully connected network in the embodiment;

[0033] Figure 6 Schematic diagram of the comparison between the estimation accuracy of a single network and that of a fusion network when the target number is 2 in the embodiment;

[0034] Figure 7 Schematic diagram of the variation of DOA estimation accuracy with the signal-to-noise ratio when the target number is 2 in the embodiment;

[0035] Figure 8 Schematic diagram of the variation of DOA estimation accuracy with the signal-to-noise ratio when the target number is 3 in the embodiment;

[0036] Figure 9 Schematic diagram of the variation of DOA estimation accuracy with the signal-to-noise ratio when the target number is 4 in the embodiment;

[0037] Figure 10 Schematic diagram of the variation of DOA estimation accuracy with the number of targets when the signal-to-noise ratio is 0 dB in the embodiment;

[0038] Figure 11 Schematic diagram of the variation of DOA estimation accuracy with the angular separation when the target number is 3 in the embodiment. Detailed implementation manners

[0039] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and technical solutions.

[0040] With the rapid development of deep learning, many data-based DOA estimation methods have been proposed, and these methods have achieved better performance than traditional model-based methods. The data-driven DOA estimation methods based on deep learning can be mainly divided into two categories: classification models and regression models. Compared with the methods relying on accurate models, the data-driven methods can achieve better estimation performance. Therefore, in the embodiments of the present invention, referring to Figure 1 as shown, a method for off-grid DOA estimation based on deep learning under array errors is provided, including:

[0041] S101. Use an observation array to receive narrowband signals sent by narrowband targets, obtain corresponding array received signals, and obtain a covariance matrix based on the array received signals.

[0042] Specifically, using an observation array to receive narrowband signals sent by narrowband targets can be designed to include:

[0043] Deploy an M-element uniform linear array as the observation array, and set the interval between each element to half a wavelength;

[0044] Based on amplitude-phase errors, mutual coupling errors and element position perturbations, establish an array reception signal model of the observation array, so as to obtain the array received signals corresponding to the narrowband signals by using the array reception signal model.

[0045] Deploy an M-element uniform linear array with an element spacing of half a wavelength. The observation array is a non-ideal array with various array errors. Use the observation array to receive K narrowband signals. The observation array is a uniform linear array with M antennas. The array has amplitude-phase errors, mutual coupling errors, and element position perturbation errors. Use this receiving array to collect L snapshots and establish a corresponding array signal model.

[0046] S102: Input the array received signal and covariance matrix into a pre-trained DOA estimation model, and use the DOA estimation model to obtain the DOA estimation result of the narrowband target. The DOA estimation model includes: a first feature extraction network for extracting array signal features, a second feature extraction network for extracting covariance matrix features, and a fully connected network for fusing array signal features and covariance matrix features and obtaining the DOA estimation result of the narrowband target.

[0047] Among them, as Figure 2 shown, the first feature extraction network can be designed to include: a batch normalization layer, a position encoding layer, a Transformer encoder, a connection layer, and a Dropout layer. The second feature extraction network can be designed to include: a batch normalization layer, a fully connected layer with residual connections, and an output fully connected layer. The fully connected network includes a fully connected layer and a Dropout layer.

[0048] Figure 3 shown, in the first feature extraction network IQ-Net, the batch normalization layer can reduce data bias and thus accelerate the network training process. The position encoding layer embeds the position-encoded signal sequence into the original signal sequence to provide position information in the sequence. The Transformer encoder is used to extract sequence features.

[0049] Figure 4 shown, residual connections are adopted in the second feature extraction network ENSCM-Net. This can better retain the original features of the covariance data and effectively avoid gradient vanishing.

[0050] Figure 5 shown, all layers in the fully connected network Weight-Net are fully connected layers. Using multiple fully connected layers can effectively fuse the two proposed features to further obtain a high-precision DOA estimation result.

[0051] Specifically, the DOA estimation model training process can be designed to include:

[0052] Construct network model training samples using narrowband signal sources with known incoming wave direction angles;

[0053] The angular region is discretized by specifying an angular interval to obtain an angular set, and the DOA category label of the corresponding narrowband signal source is set according to the rounded integer value of the incoming wave direction angle.

[0054] A loss function for model training is constructed using a regularization function and a binary cross-entropy function.

[0055] Based on the loss function and using the network model training samples, the DOA estimation model is trained.

[0056] Among them, network model training samples are constructed using narrowband signal sources with known incoming wave direction angles, which may include:

[0057] Several narrowband signal sources with known incoming wave direction angles are set, and the narrowband signals of several known narrowband signal sources are received by the observation array to obtain the array received signal sample data corresponding to the narrowband signal sources.

[0058] According to the array received signal sample data, covariance matrix sample data is obtained, and the covariance matrix sample data and the array received signal sample data are spliced to obtain the network model training samples.

[0059] The incoming wave direction angles of K narrowband signals are θ1, θ2,..., θ K . After receiving L snapshots, the array output signal with array errors can be expressed as:

[0060]

[0061] Among them, G and C represent amplitude-phase errors and mutual coupling errors. represents the array manifold matrix with array element position perturbations. The sampling covariance matrix is obtained by estimating it using multiple snapshot numbers:

[0062]

[0063] The corresponding covariance matrix can be further enhanced using linear compression. Based on the linear shrinkage estimation, the following optimization problem is established:

[0064]

[0065] R T is a Toeplitz matrix, which can be expressed as:

[0066]

[0067] Let the derivative of the objective function with respect to α be 0, and we can get:

[0068]

[0069] Where:

[0070]

[0071] Thus, the finally enhanced covariance matrix is obtained.

[0072] The real part and the imaginary part of the array output data are extracted to obtain:

[0073]

[0074] Since the covariance matrix is a Hermitian matrix, the upper triangular or lower triangular elements in R can represent the entire matrix. The input vector of the covariance matrix can be obtained as:

[0075]

[0076] (7) and (8) are two inputs for the subsequent network model.

[0077] With an angular interval δ θ The angular region is discretized to obtain an angular set, which is expressed as: The angular region for DOA estimation refers to the range of all directions where the signal may arrive. This range is usually jointly determined by the physical characteristics of the antenna array and the algorithm design, and the specific range depends on multiple factors, including the layout of the antenna array, the number of array elements, the element spacing, the signal wavelength, and the estimation algorithm used, etc.

[0078] θ = [Θ1, Θ2,..., Θ Q = [θ min ,...,-δ θ , 0, δ θ ,..., θ max T (9)

[0079] The number of its categories is Q. The label is defined as where the calculation method of the i-th element p i is as follows:

[0080]

[0081] The label p can be further obtained as Therefore, the angle estimation result can be expressed as:

[0082]

[0083] where Max i (·) represents the subscript index of the i-th largest element in the vector, that is, the integer part of the corresponding angle. p i is the amplitude of the corresponding index, that is, the fractional part of the corresponding angle. ​

[0084] Combine the l1 regularization function with the Binary Cross Entropy (BCE) function to enable the network to achieve DOA estimation. The loss function can be expressed as:

[0085]

[0086] Denote the network output vector. [p q = P], [p q ≠ P] respectively represent the conditions required for the calculation. w represents the estimation weighting coefficient, which represents the gap between the estimated category and the true category. Its calculation method is as follows:

[0087]

[0088] Where Top K (·) represents the subscript index of the top K larger elements in the vector, that is, the corresponding number of categories. g(z q ) represents the regularization function, and its definition is as follows:

[0089]

[0090] For the narrowband target signal to be estimated, input its array signal data and covariance matrix into the trained network model. Through the network model, select the category with the highest confidence and the corresponding amplitude in the output categories, and use them as the final DOA estimation result.

[0091] Furthermore, based on the above method, an off-grid DOA estimation system based on deep learning under array error provided by an embodiment of the present invention includes: a signal receiving module and a signal estimation module, wherein,

[0092] The signal receiving module is used to receive the narrowband signal sent by the narrowband target using the observation array, obtain the corresponding array received signal, and obtain the covariance matrix based on the array received signal;

[0093] The signal estimation module is used to input the array received signal and the covariance matrix into the pre-trained DOA estimation model, and use the DOA estimation model to obtain the DOA estimation result of the narrowband target. The DOA estimation model includes: a first feature extraction network for extracting array signal features, a second feature extraction network for extracting covariance matrix features, and a fully connected network for fusing array signal features and covariance matrix features and obtaining the DOA category label of the narrowband target. The DOA category label is used to represent the DOA estimation result after the angle region is discretized.

[0094] To verify the effectiveness of the solution of this case, the following is a further explanation in combination with experimental data:

[0095] In the simulation experiment, the array is a 12-element uniform linear array, the element spacing is half a wavelength, the number of signal snapshots is 256, and the number of targets K = 2, 3, 4. The angle range is [θ min , θ max = [-60°, 60°], and the angle division interval is δ θ = 1°, so the total number of categories is Q = 121. To reduce the data volume and further focus on the case where the angles of different targets are close, the interval between different target angles is set to σ θ ∈ [2°, 10°]. The array error parameters are set as: σ gmax = 1dB, σ φmax = 5°, σ cmax = 0.15, σ dmax = 0.15λ.

[0096] For different numbers of targets, 10,000 samples are randomly generated at each signal-to-noise ratio. The signal-to-noise ratio range is from -10dB to 15dB, and the step size is 5dB. Therefore, a total of 3×6×10,000 = 180,000 training samples are generated. The validation set is generated in the same way as the training samples. Based on the generated dataset, the Adam (adaptive moment estimation, Adam) optimizer is used for optimization, with β1 = 0.9, β1 = 0.999, the initial learning rate is set to 0.001, and the batch size is set to 128. A total of 100 epochs are trained, and the model with the highest validation set accuracy is used as the final network model. Figure 6 Curves of the DOA estimation accuracy of IQ-Net, ENSCM-Net, and the proposed fusion estimation network versus the signal-to-noise ratio when the number of targets is 2. It can be seen from the figure that compared with a single network, the proposed fusion network has higher DOA estimation accuracy.

[0097] Figure 7 、 Figure 8 and Figure 9 are curves of the DOA estimation accuracy versus the signal-to-noise ratio when the number of targets is 2, 3, and 4 respectively. It can be seen from the figure that as the signal-to-noise ratio increases, the DOA estimation error gradually increases. The proposed scheme in this case can maintain the highest estimation accuracy.

[0098] Figure 10 Curve of the DOA estimation accuracy versus the number of targets when the signal-to-noise ratio is 0dB. As the number of targets increases, the DOA estimation error gradually increases. The proposed scheme in this case still maintains the highest accuracy.

[0099] Figure 11When the target number is 3, it is the curve of the DOA estimation accuracy varying with the target angle interval. As the angle interval increases, the estimation error of the classical algorithm gradually decreases, while the method proposed in the solution of this case has stronger robustness.

[0100] The above experimental results show that the solution of this case has better performance than the methods of only inputting array signals and only inputting covariance matrices. In addition, the solution of this case has stronger robustness for DOA estimation of array errors and can adapt to various scenarios.

[0101] Unless otherwise specifically stated, the relative steps, numerical expressions and values of the components and steps described in these embodiments do not limit the scope of the present invention.

[0102] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0103] The units and method steps of each example described in combination with the embodiments disclosed in this article can be implemented by electronic hardware, computer software, or a combination of the two. To clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described according to functions in the above description. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Those of ordinary skill in the art can use different methods to implement the described functions for each specific application, but such implementation is not considered to exceed the scope of the present invention.

[0104] Those of ordinary skill in the art can understand that all or part of the steps in the above method can be completed by instructing relevant hardware through a program. The program can be stored in a computer-readable storage medium, such as a read-only memory, a magnetic disk, or an optical disc, etc. Optionally, all or part of the steps of the above embodiments can also be implemented using one or more integrated circuits. Correspondingly, each module / unit in the above embodiments can be implemented in the form of hardware or in the form of a software functional module. The present invention is not limited to any specific form of the combination of hardware and software.

[0105] Finally, it should be noted that the above-described embodiments are only specific embodiments of the present invention, used to illustrate the technical solutions of the present invention, rather than limiting it. The protection scope of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that any technician familiar with the technical field of the present invention can still modify the technical solutions described in the foregoing embodiments, or can easily think of changes, or perform equivalent replacements on some of the technical features; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for estimating off-grid DOA based on deep learning under array error, characterized in that: Include: Using an observation array to receive a narrowband signal sent by a narrowband target, obtaining a corresponding array receiving signal, and obtaining a covariance matrix based on the array receiving signal; The array received signal and the covariance matrix are input into a pre-trained DOA estimation model, and the DOA estimation result of the narrowband target is obtained using the DOA estimation model. The DOA estimation model includes: a first feature extraction network for extracting array signal features, a second feature extraction network for extracting covariance matrix features, and a fully connected network for fusing array signal features and covariance matrix features to obtain the DOA estimation result of the narrowband target.

2. The off-grid DOA estimation method based on deep learning under array error according to claim 1, characterized in that: Utilizing an observation array to receive narrowband signals sent by narrowband targets, including: Deploy an M-element uniform linear array as the observation array, and the interval between each array element is set to half a wavelength; An array receiving signal model of the observation array is established based on amplitude and phase errors, mutual coupling errors and array element position disturbances, so as to obtain the array receiving signal corresponding to the narrowband signal using the array receiving signal model.

3. The off-grid DOA estimation method based on deep learning under array error according to claim 1, characterized in that: The DOA estimation model training process includes: Use narrowband signal sources with known incoming wave direction angles to build network model training samples; The angle region is discretized by specifying an angle interval to obtain an angle set, and the DOA category label corresponding to the narrowband signal source is set according to the rounded value of the incoming wave direction angle; Based on the binary cross entropy function, the loss function used for model training is constructed using the regularization function and weighting coefficient; The DOA estimation model is trained based on the loss function and using the network model training samples.

4. The off-grid DOA estimation method based on deep learning under array error according to claim 3, characterized in that: The network model training samples are constructed using a narrowband signal source with a known wave direction angle, including: Setting a number of narrowband signal sources with known wave direction angles, using an observation array to receive narrowband signals from the known narrowband signal sources and obtaining array received signal sample data corresponding to the narrowband signal sources; The covariance matrix sample data is obtained according to the array received signal sample data, and the covariance matrix sample data is spliced ​​with the array received signal sample data to obtain the network model training sample.

5. The off-grid DOA estimation method based on deep learning under array error according to claim 3, characterized in that: The process of setting the DOA category label corresponding to the narrowband signal source according to the rounded value of the incoming wave direction angle is expressed as: Among them, p i represents the i-th DOA category label element, θ k represents the incoming wave direction angle corresponding to the k-th narrowband signal source, Represents the k Round to the nearest integer. Indicates that there is θ k The rounded value is equal to Θ i Equal, θ i It represents the integer part corresponding to the target DOA, and P represents the label value constant when there is no corresponding DOA.

6. The off-grid DOA estimation method based on deep learning under array error according to claim 3, characterized in that: The loss function is expressed as: Among them, z represents the network output vector, p represents the label vector, and Q is the number of label categories, g(z q ) represents the regularization function of the qth vector element in the network output vector z, and w represents the weight coefficient, and Top K (·) represents the number of categories corresponding to the subscript index of the first K largest elements of the vector, and ε is a constant.

7. The off-grid DOA estimation method based on deep learning under array error according to claim 1, characterized in that: The first feature extraction network includes: a batch normalization layer, a position encoding layer, a Transformer encoder, a fully connected layer and a Dropout layer; the second feature extraction network includes: a batch normalization layer, a residual connected fully connected layer and an output fully connected layer; the fully connected network includes a fully connected layer and a Dropout layer.

8. A deep learning based off-grid DOA estimation system under array error, characterized in that: It includes: a signal receiving module and a signal estimation module, wherein: A signal receiving module is used to use an observation array to receive a narrowband signal sent by a narrowband target, obtain a corresponding array receiving signal, and obtain a covariance matrix based on the array receiving signal; The signal estimation module is used to input the array received signal and the covariance matrix into a pre-trained DOA estimation model, and use the DOA estimation model to obtain the DOA estimation result of the narrowband target. The DOA estimation model includes: a first feature extraction network for extracting array signal features, a second feature extraction network for extracting covariance matrix features, and a fully connected network for fusing array signal features and covariance matrix features and obtaining the DOA estimation result of the narrowband target.

9. An electronic device, characterized in that: include: at least one processor, and a memory coupled to the at least one processor; The memory stores a computer program, and the computer program can be executed by the at least one processor to implement the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed, the method according to any one of claims 1 to 7 can be implemented.

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