Three-dimensional near-field source positioning method based on depth feature fusion extraction network

Abstract

The invention discloses a three-dimensional near-field source positioning method based on a depth feature fusion extraction network, and aims to improve the accuracy and robustness of near-field source positioning. According to the method, a deep feature fusion extraction network is constructed, a near-field source parameter estimation problem is converted into a multi-task learning problem, and multi-task joint estimation of a near-field source emission signal, an X-axis included angle, a Y-axis included angle and a reference array element distance is realized by using a multi-input multi-output neural network architecture; the network effectively fuses and extracts key features through feature fusion, extraction and output of branches, and optimizes network performance through training and verification; the method has the advantages that the method does not depend on a complex signal model, is suitable for the condition that the signal model is complex or uncertain, and can show good generalization ability and robustness.

Description

Technical Field

[0001] The present invention belongs to the field of wireless positioning, and relates to a source positioning technology, and in particular to a three-dimensional near-field (NF) source positioning method based on a deep feature fusion extraction network (Feature Fusion Extraction Network, FFEN). Background Art

[0002] Source localization is a key problem in array signal processing, which plays an important role in fields such as radar, wireless communications, and astronomy. Traditional high-resolution methods, such as MUSIC (Multiple Signal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques), are mainly used to estimate the direction of arrival (DOA) of far-field (FF) signals. However, when the signal source is located within the Rayleigh distance (Fresnel zone) of the array, the so-called near-field (NF) source, the wavefront curvature becomes spherical, which is significantly different from the plane wave of the far-field source. Near-field source localization requires not only estimating the DOA but also the distance of the signal source, which makes most high-resolution methods based on the far-field source assumption no longer applicable.

[0003] In order to solve the technical challenges of near-field source localization, researchers have proposed a variety of near-field source localization methods, including subspace method, cumulant method, maximum likelihood estimation method, etc. The performance of these traditional parameter estimation methods is highly dependent on the accuracy of the signal model. If there is a deviation in the prediction and construction of the signal model, the performance of these methods will decline or even fail.

[0004] In recent years, deep learning (DL) has made significant progress in computer vision, natural language processing and other fields. In the field of array signal processing, neural networks can learn and optimize network parameters through end-to-end training. This data-driven training process makes the performance of neural networks depend on the data itself rather than the signal model, thus showing better robustness and generalization ability in different environments.

[0005] Therefore, it is necessary to design a deep learning-based 3D near-field source localization method, which can take advantage of the deep learning model to improve the accuracy and robustness of near-field source localization, especially when the signal model is complex or uncertain. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a three-dimensional near-field source positioning method based on a deep feature fusion extraction network. By constructing a deep feature fusion extraction network, the near-field source parameter estimation problem is transformed into a multi-task learning problem, which can effectively improve the accuracy and robustness of near-field source positioning. Since the deep feature fusion extraction network relies on the data itself rather than the signal model, it is suitable for situations where the signal model is complex or uncertain.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: a three-dimensional near-field source positioning method based on a deep feature fusion extraction network, characterized in that it includes the following steps:

[0008] Step 1: In a three-dimensional near-field source positioning scenario, it is assumed that there are several near-field sources and a cross-symmetric cross array. The cross-symmetric cross array includes two uniform linear arrays respectively arranged on the X-axis and the Y-axis of the three-dimensional coordinate system. The uniform linear array on the X-axis and the uniform linear array on the Y-axis are in a cross-structure. The array elements in the uniform linear array on the X-axis and the uniform linear array on the Y-axis are symmetrically distributed with respect to the origin of the three-dimensional coordinate system. The signal emitted by the near-field source is incident on each array element in the two uniform linear arrays.

[0009] Step 2: By obtaining the correlation of the data received by the adjacent array elements in the uniform linear array on the X-axis, a correlation vector consisting of the correlation of the data received by all the adjacent array elements is obtained, and then the correlation vector is sampled multiple times in pseudo snapshots at uniform time intervals to obtain the virtual received data corresponding to all the adjacent array elements in the uniform linear array on the X-axis; similarly, by obtaining the correlation of the data received by the symmetric array elements in the uniform linear array on the X-axis, a correlation vector consisting of the correlation of the data received by all the symmetric array elements is obtained, and then the correlation vector is sampled multiple times in pseudo snapshots at uniform time intervals to obtain the virtual received data corresponding to all the symmetric array elements in the uniform linear array on the X-axis; by obtaining the correlation of the data received by the symmetric array elements in the uniform linear array on the Y-axis, a correlation vector consisting of the correlation of the data received by all the symmetric array elements is obtained. Correlation vector, then multiple pseudo-snapshot sampling of the correlation vector at uniform time intervals to obtain virtual received data corresponding to all symmetrical array elements in the uniform linear array on the Y axis; then cross-correlation operation is performed on the virtual received data corresponding to all adjacent array elements in the uniform linear array on the X axis and the virtual received data corresponding to all symmetrical array elements to obtain a covariance matrix related to the angle between the signal emitted by the near-field source and the X axis and the distance between the near-field source and the reference array element; and cross-correlation operation is performed on the virtual received data corresponding to all symmetrical array elements in the uniform linear array on the X axis and the virtual received data corresponding to all symmetrical array elements in the uniform linear array on the Y axis to obtain a covariance matrix related to the angle between the signal emitted by the near-field source and the X axis and the angle with the Y axis; and then the two covariance matrices are normalized to obtain the corresponding normalized covariance matrix;

[0010] Step 3: within the set angle range and distance range, randomly adjust the positions of all near-field sources or part of the near-field sources, and obtain the corresponding two normalized covariance matrices as a set of data pairs according to the process of step 2 after each adjustment; after multiple adjustments, multiple sets of data pairs are obtained, and the first true label related to the angle between the signal emitted by the near-field source and the X-axis, the second true label related to the angle between the signal emitted by the near-field source and the Y-axis, and the third true label related to the distance between the near-field source and the reference array element corresponding to each set of data pairs are obtained, and then all data pairs and their corresponding first true labels, second true labels, and third true labels constitute a data set; then divide the data set into a training set and a validation set, each set of data pairs in the training set is defined as a training data pair, and each set of data pairs in the validation set is defined as a validation data pair;

[0011] Step 4: Construct a deep feature fusion extraction network for converting the near-field source parameter estimation problem into a multi-task learning problem, which adopts a multi-input multi-output neural network architecture, including a feature fusion network, a feature extraction network, and a feature output network. The feature extraction network is divided into a first feature extraction branch for extracting features related to the angle between the signal emitted by the near-field source and the X-axis, a second feature extraction branch for extracting features related to the angle between the signal emitted by the near-field source and the Y-axis, and a third feature extraction branch for extracting features related to the distance between the near-field source and the reference array element. The feature output network is divided into a first feature output branch corresponding to the first feature extraction branch, a second feature output branch corresponding to the second feature extraction branch, and a third feature output branch corresponding to the third feature extraction branch; input the training data pair into the feature fusion network , obtain fusion features; input the fusion features into the first feature extraction branch, the second feature extraction branch, and the third feature extraction branch respectively, and obtain X-axis angle-related features, Y-axis angle-related features, and distance-related features accordingly; input the X-axis angle-related features, the Y-axis angle-related features, and the distance-related features into the first feature output branch, the second feature output branch, and the third feature output branch respectively, and obtain a first probability vector related to the angle between the signal emitted by the near-field source and the X-axis, a second probability vector related to the angle between the signal emitted by the near-field source and the Y-axis, and a third probability vector related to the distance between the near-field source and the reference array element, wherein the dimension of the first probability vector is the same as the dimension of the first true label, the dimension of the second probability vector is the same as the dimension of the second true label, and the dimension of the third probability vector is the same as the dimension of the third true label;

[0012] Step 5: Use the training set and the validation set to train the deep feature fusion extraction network to obtain a trained deep feature fusion extraction network;

[0013] Step 6: In the three-dimensional near-field source positioning scenario, the positions of all near-field sources that need to be adjusted should be tested. After adjustment, the corresponding two normalized covariance matrices are obtained as a set of test data pairs according to the process of step 2; then the test data pairs are input into the trained deep feature fusion extraction network to obtain a first probability vector related to the angle between the signal emitted by the near-field source and the X-axis, a second probability vector related to the angle between the signal emitted by the near-field source and the Y-axis, and a third probability vector related to the distance between the near-field source and the reference array element, thereby obtaining the predicted value of the angle between the signal emitted by each near-field source and the X-axis, the predicted value of the angle between the signal emitted by each near-field source and the Y-axis, and the predicted value of the distance between each near-field source and the reference array element; then, according to the spatial geometric relationship between the angle between the signal emitted by the near-field source and the X-axis, and the pitch angle and azimuth angle of the signal emitted by the near-field source, and the angle between the signal emitted by the near-field source and the Y-axis, and the pitch angle and azimuth angle of the signal emitted by the near-field source, the pitch angle and azimuth angle of the signal emitted by each near-field source are obtained.

[0014] In step 1, the number of near-field sources is K, K ≥ 1, and the wavelength of the signal emitted by the near-field source is λ; the two uniform linear arrays share the array element at the origin of the three-dimensional coordinate system, and the array element at the origin is defined as the reference array element. The uniform linear array on the X-axis includes M x Array elements, M x =2M+1, M represents the number of single-side array elements in the uniform linear array on the X axis, M≥1, and the uniform linear array on the Y axis contains M y Array elements, M y =2N+1, N represents the number of single-sided array elements in the uniform linear array on the Y axis, N≥1, the distance between adjacent array elements in each of the two uniform linear arrays is d, and the angle between the signal emitted by the kth near-field source and the X axis and the Y axis is α k and β k , k = 1, 2, ..., K, the distance between the kth near-field source and the reference array element is r k , the elevation angle and azimuth angle of the signal emitted by the kth near-field source correspond to θ k and According to the knowledge of space geometry, α k and β k With θ k and The relationship is:

[0015]

[0016] The specific process of step 2 is as follows:

[0017] Step 2_1: The data x received by the element with coordinate (l,0) in the uniform linear array on the X axis at time t l,0 (t) is expressed as The data y received by the element with coordinates (0, l) in the uniform linear array on the Y axis at time t 0,l (t) is expressed as Among them, t represents the time variable, s k (t) represents the signal emitted by the kth near-field source, e represents the natural base, j represents the imaginary number, τ xl (k) represents the phase difference between the signal emitted by the kth near-field source reaching the array element with coordinates (l,0) and the signal reaching the reference array element, τ yl (k) represents the phase difference between the signal emitted by the kth near-field source reaching the array element with coordinates (0, l) and the signal reaching the reference array element, n l,0 (t) represents x l,0 (t) is the additive white Gaussian noise, n 0,l (t) represents y 0,l Additive white Gaussian noise in (t);

[0018] Step 2_2: Perform a second-order Taylor expansion on equation 2.1 to obtain: Performing a second-order Taylor expansion on Equation 2.2 yields: Among them, ω kx Defined as φ kx Defined as ω ky Defined as φ ky Defined as

[0019] Step 2_3: Based on equation 2.3, the data received by adjacent array elements in the uniform linear array on the X-axis are correlated to obtain the corresponding correlation. The correlation between the data received by the array element with coordinates (-l-1,0) and the data received by the array element with coordinates (-l,0) in the uniform linear array on the X-axis is calculated. Expressed as

[0020] Where τ represents the delay variable, E{·} represents the mathematical expectation, the superscript “*” represents the conjugate operation, and x -l,0 (t) represents the data received by the element with coordinate (-l,0) in the uniform linear array on the X axis at time t, x -l-1,0 (t) represents the data received by the element with coordinate (-l-1,0) in the uniform linear array on the X axis at time t, x -l-1,0 (t+τ) represents x -l-1,0 (t) Data obtained after a delay of τ, s k (t+τ) represents s k (t) is the signal obtained after a delay of τ, σ 2 represents the power of the additive Gaussian white noise in the data received by the array element, δ(·) represents the impulse function,

[0021] Based on equation 2.3, the data received by the symmetrical array elements in the uniform linear array on the X-axis are correlated to obtain the corresponding correlation. The correlation between the data received by the array element with coordinates (-l, 0) and the data received by the array element with coordinates (l, 0) in the uniform linear array on the X-axis is calculated as Expressed as

[0022] Among them, x -l,0 (t+τ) represents x -l,0 (t) Data obtained after a delay of τ;

[0023] Based on equation 2.4, the data received by the symmetrical array elements in the uniform linear array on the Y axis are correlated to obtain the corresponding correlation. The correlation between the data received by the array element with coordinates (0, -l) and the data received by the array element with coordinates (0, l) in the uniform linear array on the Y axis is calculated. Expressed as

[0024]

[0025] middle, y 0,-l (t+τ) represents the signal y received by the element with coordinates (0, -l) in the uniform linear array on the Y axis at time t 0,-l (t) Data obtained after a delay of τ;

[0026] Step 2_4: Based on equation 2.5, obtain the correlation vector r consisting of the correlation of the data received by all adjacent array elements in the uniform linear array on the X axis x,adj (τ), expressed as:

[0027] Among them, the superscript "T" represents the transpose operation;

[0028] Based on formula 2.6, the correlation vector r formed by the correlation of the data received by all symmetrical array elements in the uniform linear array on the X axis is obtained x,sym (τ), expressed as:

[0029]

[0030] Based on formula 2.7, the correlation vector r formed by the correlation of the data received by all symmetrical array elements in the uniform linear array on the Y axis is obtained y,sym (τ), expressed as:

[0031]

[0032] Step 2_5: x,adj (τ) at uniform time intervals T s Perform P pseudo snapshot samplings to obtain virtual received data R corresponding to all adjacent array elements in the uniform linear array on the X axis. x,adj , expressed as: in, represents the virtual steering vector corresponding to all adjacent array elements in the uniform linear array on the X axis, R s Represents a virtual signal, R s =[u s (T s ),u s (2T s ),...,us (PT s )],u s (τ)=[u s1 (τ),u s2 (τ),...,u sK (τ)] T , for u s (τ) at uniform time intervals T s Perform P pseudo snapshot sampling to obtain P sampling values, which are u s (T s ),u s (2T s ),...,u s (PT s ), Represents R x,adj Additive Gaussian white noise in ;

[0033] R x,sym (τ) at uniform time intervals T s Perform P pseudo snapshot samplings to obtain the virtual received data R corresponding to all symmetrical array elements in the uniform linear array on the X axis. x,sym , expressed as: in, represents the virtual steering vector corresponding to all symmetrical array elements in the uniform linear array on the X axis, Represents R x,sym Additive Gaussian white noise in ;

[0034] For ry,sym(τ), the s Perform P pseudo snapshot samplings to obtain the virtual received data R corresponding to all symmetrical array elements in the uniform linear array on the Y axis. y,sym , expressed as: in, represents the virtual steering vector corresponding to all symmetrical array elements in the uniform linear array on the Y axis, Represents R y,sym Additive Gaussian white noise in ;

[0035] Step 2_6: R x,adj With R x,sym Perform cross-correlation operations to obtain the covariance matrix related to the angle between the signal emitted by the near-field source and the X-axis and the distance between the near-field source and the reference array element. The superscript "H" indicates the conjugate transpose operation. Represents R s The covariance matrix of diag(·) means finding the diagonal matrix, Indicates k The power of (t), Express and The noise covariance matrix obtained by cross-correlation operation;

[0036] R x,sym With R y,sym Perform cross-correlation operations to obtain the covariance matrix related to the angle between the signal emitted by the near-field source and the X-axis and the angle between the signal and the Y-axis. in, Express and The noise covariance matrix obtained by cross-correlation operation;

[0037] Step 2_7: Normalization processing is performed to obtain the normalized covariance matrix R related to the angle between the signal emitted by the near-field source and the X-axis and the distance between the near-field source and the reference array element. xx , in, represents the real part operation, represents the operation of taking the imaginary part, ||·|| F represents the F norm of the matrix, where R xx The size is (M x -1)×M x ×2, the third dimension represents different channels, the first channel and the second channel are R xx The real and imaginary parts of

[0038] right The normalized covariance matrix R related to the angle between the signal emitted by the near-field source and the X-axis and the angle between the signal and the Y-axis is obtained by normalization processing. xy , Among them, R xy The size is M x ×M y ×2, the third dimension represents different channels, the first channel and the second channel are R xy The real and imaginary parts of .

[0039] The feature fusion network consists of a first convolution block and a first residual block, the first residual block includes a second convolution block and a third convolution block; the training data pair is input into the first convolution block, the features output by the first convolution block are input into the second convolution block, the features output by the second convolution block are input into the third convolution block, the features output by the first convolution block are added after the padding operation and the features output by the third convolution block, and the features obtained after the addition result is subjected to the maximum pooling operation as the fusion feature.

[0040] The structures of the first feature extraction branch, the second feature extraction branch, and the third feature extraction branch are the same, and are all composed of a fourth convolution block, a fifth convolution block, and a second residual block, and the second residual block includes a self-attention mechanism and a sixth convolution block; the fused features are input into the fourth convolution block, the features output by the fourth convolution block are input into the fifth convolution block, the features output by the fifth convolution block are input into the self-attention mechanism, the attention features output by the self-attention mechanism are input into the sixth convolution block, the features output by the sixth convolution block are added to the features output by the fifth convolution block, and the features obtained after the addition is subjected to the maximum pooling operation are used as the features output by the feature extraction branch.

[0041] The structures of the first feature output branch, the second feature output branch, and the third feature output branch are the same, and all include a Flatten layer, a first fully connected layer, a first Dropout layer, a second fully connected layer, and a second Dropout layer connected in sequence; the features output by the feature extraction branch corresponding to the feature output branch are input into the Flatten layer, the features output by the Flatten layer are input into the first fully connected layer, the features output by the first fully connected layer are input into the first Dropout layer, the features output by the first Dropout layer are input into the second fully connected layer, the features output by the second fully connected layer are input into the second Dropout layer, and the probability vector output by the second Dropout layer is used as the probability vector output by the feature output branch.

[0042] The first convolution block, the second convolution block, the third convolution block, the fourth convolution block, the fifth convolution block, and the sixth convolution block have the same structure, and all include sequentially connected convolution layers, batch normalization layers, and Leaky ReLU activation functions.

[0043] The training process of step 5 is as follows:

[0044] Step 5_1: Randomly divide all training data pairs in the training set and their corresponding first true labels, second true labels, and third true labels into multiple batches, so that each batch contains batch size groups of training data pairs and their corresponding first true labels, second true labels, and third true labels;

[0045] Step 5_2: Take one of the batches of the training set, and use all the training data pairs in this batch as the input of the deep feature fusion extraction network, and input them into the deep feature fusion extraction network for processing to obtain the first probability vector, the second probability vector, and the third probability vector corresponding to each group of training data pairs in this batch;

[0046] Step 5_3: For each training data pair in this batch, supervise the network training by calculating the training loss Loss, Loss = λ1L CEL +λ2L CEL +λ3L CEL , where λ1, λ2 and λ3 are weight coefficients, L CEL represents the cross entropy loss between the first probability vector and the first true label corresponding to each set of training data, L CEL represents the cross entropy loss between the second probability vector and the second true label corresponding to each set of training data, L CEL Represents the cross entropy loss of the third probability vector and the third true label corresponding to each set of training data;

[0047] Step 5_4: The weights and biases in the deep feature fusion extraction network are initialized using the default strategy, and the deep feature fusion extraction network is trained offline in a supervised manner using the Adam optimizer to complete the training of the deep feature fusion extraction network for this batch, and the network parameters are updated through back propagation;

[0048] Step 5_5: Repeat the process from step 5_2 to step 5_4 until all batches of the training set have trained the deep feature fusion extraction network once;

[0049] Step 5_6: Randomly divide all the verification data pairs in the verification set and their corresponding first true labels, second true labels, and third true labels into multiple batches, so that each batch contains batch size groups of verification data pairs and their corresponding first true labels, second true labels, and third true labels;

[0050] Step 5_7: Take one of the batches of the validation set; then input all the validation data pairs in this batch into the deep feature fusion extraction network trained with the training set to obtain the first probability vector, the second probability vector, and the third probability vector corresponding to each set of validation data pairs in this batch; then follow the process of step 5_3 and calculate the validation loss corresponding to each set of validation data pairs in this batch in the same way;

[0051] Step 5_8: Repeat the process of step 5_7 until all batches of the validation set have been processed once;

[0052] Step 5_9: Repeat the process from step 5_1 to step 5_8, and end the training after the set rounds to obtain a trained deep feature fusion extraction network. The warm-up learning rate strategy is adopted, and the initial learning rate is set to 0.0005. In the first 5 rounds of training, the learning rate increases linearly to 0.001, and then decays exponentially with each round.

[0053] Compared with the prior art, the advantages of the present invention are:

[0054] 1) Two normalized covariance matrices are constructed by preprocessing the data received by the array element, which realizes the decoupling of near-field source parameters, reduces the complexity of training the deep feature fusion extraction network, and improves the stability of training.

[0055] 2) A deep feature fusion extraction network is proposed, which regards the near-field source parameter estimation as a multi-task learning problem and adopts a multi-input and multi-output model structure to simultaneously process different parameter features, which can effectively improve the accuracy and robustness of near-field source positioning. The network avoids gradient vanishing through residual connections and enhances its feature extraction capability by adding an attention mechanism to each feature extraction branch. The network relies on the data itself rather than the signal model, so it is suitable for situations where the signal model is complex or uncertain.

[0056] 3) The present invention has a small estimation error for the two-dimensional angle and distance parameters of off-grid data and has strong generalization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A schematic diagram of a three-dimensional near-field source positioning scene in the method of the present invention in which only one near-field source exists;

[0058] Figure 2 A structural diagram of a deep feature fusion extraction network constructed in the method of the present invention;

[0059] Figure 3 It is a schematic diagram of the changes of three cross entropy losses related to the validation set with the training rounds (Epochs) when the deep feature fusion extraction network is trained in the method of the present invention;

[0060] Figure 4 It is a schematic diagram of the changes of three cross entropy losses related to the training set with the training rounds (Epochs) when the deep feature fusion extraction network is trained in the method of the present invention;

[0061] Figure 5This is a schematic diagram showing the change of the accuracy of α, β, and r with the training rounds (Epochs) according to the three probability vectors obtained by deep feature fusion extraction network training;

[0062] Figure 6 It is a schematic diagram showing the variation of RMSE of α with signal-to-noise ratio (SNR) obtained by using the method of the present invention for a test data set generated under the accurate model and the approximate model of the signal model;

[0063] Figure 7 It is a schematic diagram showing the variation of RMSE of β obtained by the method of the present invention with the signal-to-noise ratio (SNR) for a test data set generated under the accurate model and the approximate model of the signal model;

[0064] Figure 8 The figure is a schematic diagram showing the variation of RMSE of r with signal-to-noise ratio (SNR) obtained by using the method of the present invention for a test data set generated under the exact model and the approximate model of the signal model. DETAILED DESCRIPTION

[0065] The present invention is further described in detail below with reference to the accompanying drawings.

[0066] The present invention proposes a three-dimensional near-field source positioning method based on a deep feature fusion extraction network, which comprises the following steps:

[0067] Step 1: In a three-dimensional near-field source positioning scenario, it is assumed that there are several near-field sources and a cross-symmetric cross array. The cross-symmetric cross array includes two uniform linear arrays respectively arranged on the X-axis and Y-axis of the three-dimensional coordinate system. The uniform linear array on the X-axis and the uniform linear array on the Y-axis are in a cross-structure. The array elements in the uniform linear array on the X-axis and the uniform linear array on the Y-axis are symmetrically distributed with respect to the origin of the three-dimensional coordinate system. The signal emitted by the near-field source is incident on each array element in the two uniform linear arrays.

[0068] Further define in step 1 that the number of near-field sources is K, K ≥ 1, and the wavelength of the signal emitted by the near-field source is λ; the two uniform linear arrays share the array element at the origin of the three-dimensional coordinate system, and the array element at the origin is defined as the reference array element, and the uniform linear array on the X-axis includes M x Array elements, M x =2M+1, M represents the number of single-side array elements in the uniform linear array on the X axis, M≥1, and the uniform linear array on the Y axis contains M y Array elements, M y =2N+1, N represents the number of single-side array elements in the uniform linear array on the Y axis, N≥1, and the distance between adjacent array elements in each of the two uniform linear arrays is d. In this embodiment The angle between the signal emitted by the kth near-field source and the X-axis and Y-axis is α k and β k , k = 1, 2, ..., K, the distance between the kth near-field source and the reference array element is r k , the elevation angle and azimuth angle of the signal emitted by the kth near-field source correspond to θ k and According to the knowledge of space geometry, α k and β k With θ k and The relationship is:

[0069] Figure 1 A schematic diagram of a three-dimensional near-field source localization scenario with only one near-field source is given.

[0070] Step 2: By obtaining the correlation of the data received by the adjacent array elements in the uniform linear array on the X-axis, a correlation vector consisting of the correlation of the data received by all the adjacent array elements is obtained, and then the correlation vector is sampled multiple times in pseudo snapshots at uniform time intervals to obtain the virtual received data corresponding to all the adjacent array elements in the uniform linear array on the X-axis; similarly, by obtaining the correlation of the data received by the symmetric array elements in the uniform linear array on the X-axis, a correlation vector consisting of the correlation of the data received by all the symmetric array elements is obtained, and then the correlation vector is sampled multiple times in pseudo snapshots at uniform time intervals to obtain the virtual received data corresponding to all the symmetric array elements in the uniform linear array on the X-axis; by obtaining the correlation of the data received by the symmetric array elements in the uniform linear array on the Y-axis, a correlation vector consisting of the correlation of the data received by all the symmetric array elements is obtained. The correlation vector is then pseudo-snapshot sampled multiple times at uniform time intervals to obtain virtual received data corresponding to all symmetrical array elements in the uniform linear array on the Y axis; then the virtual received data corresponding to all adjacent array elements in the uniform linear array on the X axis and the virtual received data corresponding to all symmetrical array elements are cross-correlated to obtain a covariance matrix related to the angle between the signal emitted by the near-field source and the X axis and the distance between the near-field source and the reference array element; and the virtual received data corresponding to all symmetrical array elements in the uniform linear array on the X axis and the virtual received data corresponding to all symmetrical array elements in the uniform linear array on the Y axis are cross-correlated to obtain a covariance matrix related to the angle between the signal emitted by the near-field source and the X axis and the angle with the Y axis; and the two covariance matrices are normalized to obtain a corresponding normalized covariance matrix.

[0071] The specific process of step 2 is further defined as follows:

[0072] Step 2_1: The data x received by the element with coordinate (l,0) in the uniform linear array on the X axis at time t l,0(t) is expressed as The data y received by the element with coordinates (0, l) in the uniform linear array on the Y axis at time t 0,l (t) is expressed as Among them, t represents the time variable, s k (t) represents the signal emitted by the kth near-field source, e represents the natural base, e = 2.71…, j represents the imaginary number, τ xl (k) represents the phase difference between the signal emitted by the kth near-field source reaching the array element with coordinates (l,0) and the signal reaching the reference array element, τ yl (k) represents the phase difference between the signal emitted by the kth near-field source reaching the array element with coordinates (0, l) and the signal reaching the reference array element, n l,0 (t) represents x l,0 (t) is the additive white Gaussian noise, n0,l(t) represents y 0,l Additive white Gaussian noise in (t).

[0073] Step 2_2: Perform a second-order Taylor expansion on equation 2.1 to obtain:

[0074] Performing a second-order Taylor expansion on Equation 2.2 yields: Among them, ω kx Defined as φ kx Defined as ω ky Defined as φ ky Defined as

[0075] Step 2_3: Based on equation 2.3, the data received by adjacent array elements in the uniform linear array on the X-axis are correlated to obtain the corresponding correlation. The correlation between the data received by the array element with coordinates (-l-1,0) and the data received by the array element with coordinates (-l,0) in the uniform linear array on the X-axis is calculated. Expressed as

[0076] (Equation 2.5), where τ represents the delay variable, E{·} represents the mathematical expectation, the superscript “*” represents the conjugate operation, and x -l,0 (t) represents the data received by the element with coordinate (-l,0) in the uniform linear array on the X axis at time t, x -l-1,0 (t) represents the data received by the element with coordinate (-l-1,0) in the uniform linear array on the X axis at time t, x -l-1,0 (t+τ) represents x -l-1,0 (t) Data obtained after a delay of τ, s k (t+τ) represents sk (t) is the signal obtained after a delay of τ, σ 2 represents the power of the additive Gaussian white noise in the data received by the array element, δ(·) represents the impulse function, To define symbols.

[0077] Based on equation 2.3, the data received by the symmetrical array elements in the uniform linear array on the X-axis are correlated to obtain the corresponding correlation. The correlation between the data received by the array element with coordinates (-l, 0) and the data received by the array element with coordinates (l, 0) in the uniform linear array on the X-axis is calculated as Expressed as Among them, x -l,0 (t+τ) represents x -l,0 (t) Data obtained after a delay of τ.

[0078] Based on equation 2.4, the data received by the symmetrical array elements in the uniform linear array on the Y axis are correlated to obtain the corresponding correlation. The correlation between the data received by the array element with coordinates (0, -l) and the data received by the array element with coordinates (0, l) in the uniform linear array on the Y axis is calculated. Expressed as Among them, y 0,-l (t+τ) represents the signal y received by the element with coordinates (0, -l) in the uniform linear array on the Y axis at time t 0,-l (t) Data obtained after a delay of τ.

[0079] Step 2_4: Based on equation 2.5, obtain the correlation vector r consisting of the correlation of the data received by all adjacent array elements in the uniform linear array on the X axis x,adj (τ), expressed as: in, Correspondingly, in the uniform linear array on the X-axis, it represents the correlation between the array element with coordinates (M-1,0) and the array element with coordinates (M,0), the correlation between the array element with coordinates (0,0) and the array element with coordinates (1,0), the correlation between the array element with coordinates (-1,0) and the array element with coordinates (0,0), the correlation between the array element with coordinates (-2,0) and the array element with coordinates (-1,0), and the correlation between the array element with coordinates (-M,0) and the array element with coordinates (-M+1,0). The superscript "T" represents the transposition operation.

[0080] Based on formula 2.6, the correlation vector r formed by the correlation of the data received by all symmetrical array elements in the uniform linear array on the X axis is obtained x,sym (τ), expressed as: in, Correspondingly, in the uniform linear array on the X-axis, the correlation between the array element with coordinate (M, 0) and the array element with coordinate (-M, 0), the correlation between the array element with coordinate (1, 0) and the array element with coordinate (-1, 0), the correlation between the array element with coordinate (0, 0) and the array element with coordinate (0, 0), the correlation between the array element with coordinate (-1, 0) and the array element with coordinate (1, 0), and the correlation between the array element with coordinate (-M, 0) and the array element with coordinate (M, 0).

[0081] Based on formula 2.7, the correlation vector r formed by the correlation of the data received by all symmetrical array elements in the uniform linear array on the Y axis is obtained y,sym (τ), expressed as: in, Correspondingly, in the uniform linear array on the Y-axis, the correlation between the array element with coordinate (N, 0) and the array element with coordinate (-N, 0), the correlation between the array element with coordinate (1, 0) and the array element with coordinate (-1, 0), the correlation between the array element with coordinate (0, 0) and the array element with coordinate (0, 0), the correlation between the array element with coordinate (-1, 0) and the array element with coordinate (1, 0), and the correlation between the array element with coordinate (-N, 0) and the array element with coordinate (N, 0).

[0082] Step 2_5: x,adj (τ) at uniform time intervals T s Perform P pseudo snapshot samplings to obtain virtual received data R corresponding to all adjacent array elements in the uniform linear array on the X axis. x,adj , expressed as: Among them, r x,adj (T s ),r x,adj (2T s ),r x,adj (PT s ) corresponds to r x,adj (τ) is the first sampling value, the second sampling value, and the Pth sampling value obtained by pseudo-snapshot sampling, represents the virtual steering vector corresponding to all adjacent array elements in the uniform linear array on the X axis,

[0083] R s Represents a virtual signal, R s =[u s (T s ),u s (2T s ),...,u s (PT s )],u s (τ)=[u s1 (τ),us2 (τ),...,u sK (τ)] T , for u s (τ) at uniform time intervals T s Perform P pseudo snapshot sampling to obtain P sampling values, which are u s (T s ),u s (2T s ),...,u s (PT s ), Represents R x,adj Additive white Gaussian noise in .

[0084] R x,sym (τ) at uniform time intervals T s Perform P pseudo snapshot samplings to obtain the virtual received data R corresponding to all symmetrical array elements in the uniform linear array on the X axis. x,sym , expressed as: Among them, r x,sym (T s ),r x,sym (2T s ),r x,sym (PT s ) corresponds to r x,sym (τ) is the first sampling value, the second sampling value, and the Pth sampling value obtained by pseudo-snapshot sampling, represents the virtual steering vector corresponding to all symmetrical array elements in the uniform linear array on the X axis,

[0085] Represents R x,sym Additive white Gaussian noise in .

[0086] For ry,sym(τ), the s Perform P pseudo snapshot samplings to obtain the virtual received data R corresponding to all symmetrical array elements in the uniform linear array on the Y axis. y,sym , expressed as: Among them, r y,sym (T s ),r y,sym (2T s ),r y,sym (PT s ) corresponds to r y,sym (τ) is the first sampling value, the second sampling value, and the Pth sampling value obtained by pseudo-snapshot sampling, represents the virtual steering vector corresponding to all symmetrical array elements in the uniform linear array on the Y axis, Represents R y,sym Additive white Gaussian noise in .

[0087] Step 2_6: R x,adj With R x,sym Perform cross-correlation operations to obtain the covariance matrix related to the angle between the signal emitted by the near-field source and the X-axis and the distance between the near-field source and the reference array element. Only with parameter α k 、r k The superscript "H" indicates the conjugate transpose operation. Represents R s The covariance matrix of diag(·) means finding the diagonal matrix, Indicates k The power of (t), Express and The noise covariance matrix obtained by performing cross-correlation operations.

[0088] R x,sym With R y,sym Perform cross-correlation operations to obtain the covariance matrix related to the angle between the signal emitted by the near-field source and the X-axis and the angle between the signal and the Y-axis. Only with parameter α k , β k It can be regarded as the virtual output in the far-field scenario, where Express and The noise covariance matrix obtained by performing cross-correlation operations.

[0089] Step 2_7: To prevent neuron inactivation and better adapt and train the deep learning model, Normalization processing is performed to obtain the normalized covariance matrix R related to the angle between the signal emitted by the near-field source and the X-axis and the distance between the near-field source and the reference array element. xx , in, represents the real part operation, represents the operation of taking the imaginary part, ||·|| F represents the F norm of the matrix, where R xx The size is (M x -1)×M x ×2, the third dimension represents different channels, the first channel and the second channel are the real part and the imaginary part of Rxx respectively.

[0090] right The normalized covariance matrix R related to the angle between the signal emitted by the near-field source and the X-axis and the angle between the signal and the Y-axis is obtained by normalization processing. xy , Among them, R xy The size is M x ×M y ×2, the third dimension represents different channels, the first channel and the second channel are R xy The real and imaginary parts of .

[0091] Due to parameter coupling, it is challenging to directly apply neural networks to near-field source parameter estimation, mainly because the coupling of parameters makes learning difficult. Therefore, it is proposed to preprocess the data received by the array element to achieve estimated parameter decoupling and finally obtain two normalized covariance matrices. In this way, the parameter feature coupling can be reduced and the learning of parameter features by the neural network can be simplified.

[0092] Step 3: Within the set angle range and distance range, randomly adjust the positions of all near-field sources or part of the near-field sources, and obtain the corresponding two normalized covariance matrices as a set of data pairs according to the process of step 2 after each adjustment; after multiple adjustments, multiple sets of data pairs are obtained, and the first true label related to the angle between the signal emitted by the near-field source and the X-axis, the second true label related to the angle between the signal emitted by the near-field source and the Y-axis, and the third true label related to the distance between the near-field source and the reference array element corresponding to each set of data pairs are obtained, and then all data pairs and their corresponding first true labels, second true labels, and third true labels constitute a data set; then divide the data set into a training set and a validation set, randomly shuffle the data pairs in the data set, 80% of which are used for training to constitute a training set, and 20% of which are used for validation to constitute a validation set, each set of data pairs in the training set is defined as a training data pair, and each set of data pairs in the validation set is defined as a validation data pair.

[0093] The set angle range is 30 to 149 degrees, and the set distance range is 1.2 to 4.5 meters, that is, the angle between the signal emitted by the near-field source and the X-axis, the angle between the signal emitted by the near-field source and the Y-axis are required to be within the set angle range, and the distance between the near-field source and the reference array element is within the set distance range.

[0094] The dimension of the first true label is determined by the range of the angle between the signal emitted by the near-field source and the X-axis. The range of the angle between the signal emitted by the near-field source and the X-axis is 30 to 149 degrees. When the precision is 1 degree, there are 120 possible values, so the dimension of the first true label is 120. For any near-field source, if the angle between the signal emitted by the near-field source and the X-axis is 90 degrees, the index of 90 degrees in the range of 30 to 149 degrees is 60, then the value of the 60th element in the first true label is set to 1. If there are K near-field sources, the indexes are determined in the range of 30 to 149 degrees in the order of the angle between the signal emitted by the K near-field sources and the X-axis from small to large, and the values ​​of the corresponding K indexed elements in the first true label are set to 1, and the values ​​of the remaining elements are set to 0.

[0095] The dimension of the second true label is determined by the range of the angle between the signal emitted by the near-field source and the Y-axis. The range of the angle between the signal emitted by the near-field source and the Y-axis is 30 to 149 degrees. When the precision is 1 degree, there are 120 possible values, so the dimension of the second true label is 120. If there are K near-field sources, the second true label is obtained according to the acquisition process of the first true label. The value of K elements in the second true label is 1, and the values ​​of the remaining elements are set to 0.

[0096] The dimension of the third real label is determined by the range of the distance between the near-field source and the reference array element. The range of the distance between the near-field source and the reference array element is 1.2 to 4.5 meters. When the accuracy is 0.1 meters, there are 34 possible values, so the dimension of the third real label is 34. The acquisition process of the third real label is the same as the acquisition process of the first real label.

[0097] Step 4: Construct a deep feature fusion extraction network (FFEN) to transform the near-field source parameter estimation problem into a multi-task learning problem, which adopts a multiple-input multiple-output (MIMO) neural network architecture, such as Figure 2As shown, it includes a feature fusion network (Feature Fusion Net, FFN), a feature extraction network (Feature Extraction Net, FEN), and a feature output network (Feature Output Net, FON). The feature extraction network is divided into a first feature extraction branch for extracting features related to the angle between the signal emitted by the near-field source and the X-axis, a second feature extraction branch for extracting features related to the angle between the signal emitted by the near-field source and the Y-axis, and a third feature extraction branch for extracting features related to the distance between the near-field source and the reference array element. The feature output network is divided into a first feature output branch corresponding to the first feature extraction branch, a second feature output branch corresponding to the second feature extraction branch, and a third feature output branch corresponding to the third feature extraction branch; the training data pair is input into the feature fusion network to obtain fused features; the fused features are respectively input into the first feature extraction branch, the second feature extraction branch, In the third feature extraction branch, corresponding features related to the X-axis angle, features related to the Y-axis angle, and features related to the distance are obtained; the X-axis angle related features, the Y-axis angle related features, and the distance related features are input into the first feature output branch, the second feature output branch, and the third feature output branch respectively, and a first probability vector related to the angle between the signal emitted by the near-field source and the X-axis, a second probability vector related to the angle between the signal emitted by the near-field source and the Y-axis, and a third probability vector related to the distance between the near-field source and the reference array element are correspondingly obtained, wherein the dimension of the first probability vector is the same as the dimension of the first true label, the dimension of the second probability vector is the same as the dimension of the second true label, and the dimension of the third probability vector is the same as the dimension of the third true label.

[0098] If there are K near-field sources, the angle values ​​corresponding to the indices corresponding to the largest K probability values ​​in the first probability vector are used as the predicted values ​​of the angles between the signals emitted by the K near-field sources and the X-axis. Similarly, the angle values ​​corresponding to the indices corresponding to the largest K probability values ​​in the second probability vector are used as the predicted values ​​of the angles between the signals emitted by the K near-field sources and the Y-axis. The distance values ​​corresponding to the indices corresponding to the largest K probability values ​​in the third probability vector are used as the predicted values ​​of the distances between the K near-field sources and the reference array element.

[0099] Further limiting, such as Figure 2 As shown in the figure, the feature fusion network consists of a first convolution block and a first residual block, and the first residual block includes a second convolution block and a third convolution block; the training data pair is input into the first convolution block, the features output by the first convolution block are input into the second convolution block, the features output by the second convolution block are input into the third convolution block, the features output by the first convolution block are added to the features output by the third convolution block through the padding operation, and the features obtained by the addition result after the maximum pooling operation are used as the fusion feature.

[0100] The first convolution block extracts and abstracts features of the training data pairs in the feature fusion network, so that the feature fusion network can automatically learn useful features in the training data pairs; because the traditional convolution layer will cause problems such as information loss and loss during information transmission, and the network depth is too large, it may cause problems such as gradient explosion or disappearance. The first residual block introduces jump connections, so that information can be directly transmitted from one layer to the subsequent layer, thereby alleviating the gradient disappearance problem. The first residual block can help the feature fusion network learn deeper features and improve the performance of the feature fusion network.

[0101] Further limiting, such as Figure 2 As shown in the figure, the structures of the first feature extraction branch, the second feature extraction branch, and the third feature extraction branch are the same, and are all composed of the fourth convolution block, the fifth convolution block, and the second residual block. The second residual block includes a self-attention mechanism and a sixth convolution block; the fusion feature is input into the fourth convolution block, the feature output by the fourth convolution block is input into the fifth convolution block, the feature output by the fifth convolution block is input into the self-attention mechanism, the attention feature output by the self-attention mechanism is input into the sixth convolution block, the feature output by the sixth convolution block is added to the feature output by the fifth convolution block, and the feature obtained by the maximum pooling operation is used as the feature output by the feature extraction branch. The self-attention mechanism is introduced into the three feature extraction branches to realize the learning and extraction of parameter features. The core idea is to realize the modeling of sequence relationships and the association of key features by allocating feature weights at different sequence positions. The three self-attention mechanisms realize the extraction of features corresponding to different parameters by adjusting the attention weights of the input features corresponding to different parameters.

[0102] Further limiting, such as Figure 2As shown, the structures of the first feature output branch, the second feature output branch, and the third feature output branch are the same, and all include a Flatten layer, a first fully connected layer, a first Dropout layer, a second fully connected layer, and a second Dropout layer connected in sequence; the features output by the feature extraction branch corresponding to the feature output branch are input into the Flatten layer, the features output by the Flatten layer are input into the first fully connected layer, the features output by the first fully connected layer are input into the first Dropout layer, the features output by the first Dropout layer are input into the second fully connected layer, the features output by the second fully connected layer are input into the second Dropout layer, and the probability vector output by the second Dropout layer is used as the probability vector output by the feature output branch. The Flatten layer converts the multi-dimensional feature map into a one-dimensional vector, which improves the flexibility of the network; the Dropout layer uses regularization technology to reduce the overfitting problem by randomly disabling the output of neurons, thereby improving the generalization ability of the network.

[0103] Further limiting, such as Figure 2 As shown in the figure, the first convolution block, the second convolution block, the third convolution block, the fourth convolution block, the fifth convolution block, and the sixth convolution block have the same structure, and all include sequentially connected convolution layers (Conv2D), batch normalization layers (BatchNormalization, BN), and Leaky ReLU activation functions. The batch normalization layer can standardize the input data, provide regularization effects, and improve gradient propagation, making the network easier to train; the Leaky ReLU activation function can ensure that the gradient does not completely disappear during the back propagation process, thereby preventing neurons from "dying", which helps solve the gradient disappearance problem.

[0104] Step 5: Use the training set and the validation set to train the deep feature fusion extraction network to obtain a trained deep feature fusion extraction network.

[0105] The training process of step 5 is further defined as:

[0106] Step 5_1: Randomly divide all training data pairs in the training set and their corresponding first true labels, second true labels, and third true labels into multiple batches, so that each batch contains batch size groups of training data pairs and their corresponding first true labels, second true labels, and third true labels. In this embodiment, the batch size is set to 64.

[0107] In actual processing, if the number of training data pairs in the training set is divisible by batchsize, it is divided into Num batches, where Num = number of training data pairs / batch size; if the number of training data pairs in the training set is not divisible by batchsize, the excess part is discarded to obtain int(Num) batches, where int() represents the rounding function.

[0108] Step 5_2: Take one of the batches of the training set, and use all the training data pairs in this batch as the input of the deep feature fusion extraction network, and input them into the deep feature fusion extraction network for processing to obtain the first probability vector, the second probability vector, and the third probability vector corresponding to each group of training data pairs in this batch.

[0109] Step 5_3: For each training data pair in this batch, supervise the network training by calculating the training loss Loss, Loss = λ1L CEL +λ2L CEL +λ3L CEL , where λ1, λ2 and λ3 are weight coefficients. In this embodiment, λ1=λ2=λ3=1 / 3, L CEL represents the cross entropy loss between the first probability vector and the first true label corresponding to each set of training data, L CEL represents the cross entropy loss between the second probability vector and the second true label corresponding to each set of training data, L CEL Represents the cross entropy loss between the third probability vector and the third true label corresponding to each set of training data pairs.

[0110] Step 5_4: The weights and biases in the deep feature fusion extraction network use the default initialization strategy, and use the Adam optimizer to train the deep feature fusion extraction network offline in a supervised manner to complete the training of the deep feature fusion extraction network for this batch, and update the network parameters through back propagation.

[0111] Step 5_5: Repeat the process from step 5_2 to step 5_4 until all batches of the training set have trained the deep feature fusion extraction network once.

[0112] Step 5_6: Randomly divide all the verification data pairs in the verification set and their corresponding first true labels, second true labels, and third true labels into multiple batches, so that each batch contains batch size groups of verification data pairs and their corresponding first true labels, second true labels, and third true labels.

[0113] Step 5_7: Take one of the batches of the validation set; then input all the validation data pairs in this batch into the deep feature fusion extraction network trained with the training set to obtain the first probability vector, the second probability vector, and the third probability vector corresponding to each group of validation data pairs in this batch; then follow the process of step 5_3 and calculate the validation loss corresponding to each group of validation data pairs in this batch in the same way.

[0114] Step 5_8: Repeat the process of step 5_7 until all batches of the validation set have been processed once.

[0115] Step 5_9: Repeat the process from step 5_1 to step 5_8, and end the training after the set rounds to obtain a trained deep feature fusion extraction network. The warm-up learning rate strategy is adopted, and the initial learning rate is set to 0.0005. In the first 5 rounds of training, the learning rate increases linearly to 0.001, and then decays exponentially with each round.

[0116] In this embodiment, the number of rounds is set to 80. Through experiments, it is found that after 80 epochs of training, Figure 3 , Figure 4 and 5 As shown in the figure, both the training loss and the validation loss tend to be stable, and the validation loss is less than the training loss, indicating that the deep feature fusion extraction network is not overfitting and has a high accuracy. Since the training data pairs are obtained from the approximate model, learning the distance parameter features is more challenging than learning the DOA parameter features, resulting in a higher cross entropy loss related to the distance parameter and a relatively low accuracy of the distance parameter.

[0117] Step 6: In the three-dimensional near-field source positioning scenario, the positions of all near-field sources that need to be adjusted should be tested. After adjustment, the corresponding two normalized covariance matrices are obtained as a set of test data pairs according to the process of step 2; then the test data pairs are input into the trained deep feature fusion extraction network to obtain a first probability vector related to the angle between the signal emitted by the near-field source and the X-axis, a second probability vector related to the angle between the signal emitted by the near-field source and the Y-axis, and a third probability vector related to the distance between the near-field source and the reference array element, thereby obtaining the predicted value of the angle between the signal emitted by each near-field source and the X-axis, the predicted value of the angle between the signal emitted by each near-field source and the Y-axis, and the predicted value of the distance between each near-field source and the reference array element; then, according to the spatial geometric relationship between the angle between the signal emitted by the near-field source and the X-axis, and the pitch angle and azimuth angle of the signal emitted by the near-field source, and the angle between the signal emitted by the near-field source and the Y-axis, and the pitch angle and azimuth angle of the signal emitted by the near-field source, the pitch angle and azimuth angle of the signal emitted by each near-field source are obtained.

[0118] In order to further illustrate the feasibility and effectiveness of the method of the present invention, a simulation experiment was carried out on the method of the present invention.

[0119] In the simulation experiment, a cross-symmetric array with M=N=3 is considered, the array element spacing d=λ / 4, the DOA resolution is set to 1°, and the distance resolution is set to 0.1λ. The 2-D angle of the signal emitted by the near-field source (i.e., the angle between the signal emitted by the near-field source and the X-axis, and the angle between the signal emitted by the near-field source and the Y-axis) and the distance r between the near-field source and the reference array element are 73.04°, 123.12°, and 4.31λ respectively. The number of snapshots is 250, and the number of Monte Carlo is 500.

[0120] Figure 6 A schematic diagram showing the variation of the RMSE of α obtained by the method of the present invention with the signal-to-noise ratio (SNR) for a test data set generated under the exact model and the approximate model of the signal model is given. Figure 7 A schematic diagram showing the variation of the RMSE of β obtained by the method of the present invention with the signal-to-noise ratio (SNR) for the test data set generated under the exact model and the approximate model of the signal model is given. Figure 8 A schematic diagram showing the variation of the RMSE of r obtained by the method of the present invention with the signal-to-noise ratio (SNR) for a test data set generated under the exact model and the approximate model of the signal model is given. Figures 6 to 8 It can be seen that even if the relevant features under the precise model are not introduced during training, they can be well estimated during testing. The RMSE curves of the two are roughly fitted and both decrease with the increase of SNR. This result further proves the robustness and generalization of the method of the present invention.

Claims

1. A three-dimensional near-field source localization method based on a deep feature fusion extraction network, characterized in that The following steps are involved: Step 1: In a three-dimensional near-field source positioning scenario, it is assumed that there are several near-field sources and a cross-symmetric cross array. The cross-symmetric cross array includes two uniform linear arrays respectively arranged on the X-axis and Y-axis of the three-dimensional coordinate system. The signal emitted by the near-field source is incident on each array element in the two uniform linear arrays. Step 2: By obtaining the correlation of the data received by the adjacent array elements in the uniform linear array on the X-axis, a correlation vector consisting of the correlation of the data received by all the adjacent array elements is obtained, and then the correlation vector is sampled multiple times in pseudo snapshots at uniform time intervals to obtain the virtual received data corresponding to all the adjacent array elements in the uniform linear array on the X-axis; similarly, by obtaining the correlation of the data received by the symmetric array elements in the uniform linear array on the X-axis, a correlation vector consisting of the correlation of the data received by all the symmetric array elements is obtained, and then the correlation vector is sampled multiple times in pseudo snapshots at uniform time intervals to obtain the virtual received data corresponding to all the symmetric array elements in the uniform linear array on the X-axis; by obtaining the correlation of the data received by the symmetric array elements in the uniform linear array on the Y-axis, a correlation vector consisting of the correlation of the data received by all the symmetric array elements is obtained. Correlation vector, then multiple pseudo-snapshot sampling of the correlation vector at uniform time intervals to obtain virtual received data corresponding to all symmetrical array elements in the uniform linear array on the Y axis; then cross-correlation operation is performed on the virtual received data corresponding to all adjacent array elements in the uniform linear array on the X axis and the virtual received data corresponding to all symmetrical array elements to obtain a covariance matrix related to the angle between the signal emitted by the near-field source and the X axis and the distance between the near-field source and the reference array element; and cross-correlation operation is performed on the virtual received data corresponding to all symmetrical array elements in the uniform linear array on the X axis and the virtual received data corresponding to all symmetrical array elements in the uniform linear array on the Y axis to obtain a covariance matrix related to the angle between the signal emitted by the near-field source and the X axis and the angle with the Y axis; and then the two covariance matrices are normalized to obtain the corresponding normalized covariance matrix; Step 3: within the set angle range and distance range, randomly adjust the positions of all near-field sources or part of the near-field sources, and obtain the corresponding two normalized covariance matrices as a set of data pairs according to the process of step 2 after each adjustment; after multiple adjustments, multiple sets of data pairs are obtained, and the first true label related to the angle between the signal emitted by the near-field source and the X-axis, the second true label related to the angle between the signal emitted by the near-field source and the Y-axis, and the third true label related to the distance between the near-field source and the reference array element corresponding to each set of data pairs are obtained, and then all data pairs and their corresponding first true labels, second true labels, and third true labels constitute a data set; then divide the data set into a training set and a validation set, each set of data pairs in the training set is defined as a training data pair, and each set of data pairs in the validation set is defined as a validation data pair; Step 4: Construct a deep feature fusion extraction network for converting the near-field source parameter estimation problem into a multi-task learning problem, which adopts a multi-input multi-output neural network architecture, including a feature fusion network, a feature extraction network, and a feature output network. The feature extraction network is divided into a first feature extraction branch for extracting features related to the angle between the signal emitted by the near-field source and the X-axis, a second feature extraction branch for extracting features related to the angle between the signal emitted by the near-field source and the Y-axis, and a third feature extraction branch for extracting features related to the distance between the near-field source and the reference array element. The feature output network is divided into a first feature output branch corresponding to the first feature extraction branch, a second feature output branch corresponding to the second feature extraction branch, and a third feature extraction branch corresponding to the third feature extraction branch. The third feature output branch corresponding to the feature extraction branch; input the training data pair into the feature fusion network to obtain fused features; input the fused features into the first feature extraction branch, the second feature extraction branch, and the third feature extraction branch respectively, and correspondingly obtain X-axis angle related features, Y-axis angle related features, and distance related features; input the X-axis angle related features, Y-axis angle related features, and distance related features into the first feature output branch, the second feature output branch, and the third feature output branch respectively, and correspondingly obtain a first probability vector related to the angle between the signal emitted by the near-field source and the X-axis, a second probability vector related to the angle between the signal emitted by the near-field source and the Y-axis, and a third probability vector related to the distance between the near-field source and the reference array element; Step 5: Use the training set and the validation set to train the deep feature fusion extraction network to obtain a trained deep feature fusion extraction network; Step 6: In the three-dimensional near-field source positioning scenario, the positions of all near-field sources that need to be adjusted should be tested. After adjustment, the corresponding two normalized covariance matrices are obtained according to the process of step 2 as a set of test data pairs; then the test data pairs are input into the trained deep feature fusion extraction network to obtain the first probability vector related to the angle between the signal emitted by the near-field source and the X-axis, the second probability vector related to the angle between the signal emitted by the near-field source and the Y-axis, and the third probability vector related to the distance between the near-field source and the reference array element, thereby obtaining the predicted value of the angle between the signal emitted by each near-field source and the X-axis, the predicted value of the angle between the signal emitted by each near-field source and the Y-axis, and the predicted value of the distance between each near-field source and the reference array element.

2. The three-dimensional near-field source localization method based on deep feature fusion extraction network according to claim 1 is characterized in that In step 1, the number of near-field sources is K, K ≥ 1, and the wavelength of the signal emitted by the near-field source is λ; the two uniform linear arrays share the array element at the origin of the three-dimensional coordinate system, and the array element at the origin is defined as the reference array element. The uniform linear array on the X-axis includes M x Array elements, M x =2M+1, M represents the number of single-side array elements in the uniform linear array on the X axis, M≥1, and the uniform linear array on the Y axis contains M y Array elements, M y =2N+1, N represents the number of single-sided array elements in the uniform linear array on the Y axis, N≥1, the distance between adjacent array elements in each of the two uniform linear arrays is d, and the angle between the signal emitted by the kth near-field source and the X axis and the Y axis is α k and β k , k = 1, 2, ..., K, the distance between the kth near-field source and the reference array element is r k .

3. The three-dimensional near-field source localization method based on deep feature fusion extraction network according to claim 2 is characterized in that The specific process of step 2 is as follows: Step 2_1: The data x received by the element with coordinate (l,0) in the uniform linear array on the X axis at time t l,0 (t) is expressed as The data y received by the element with coordinates (0, l) in the uniform linear array on the Y axis at time t 0,l (t) is expressed as Among them, t represents the time variable, s k (t) represents the signal emitted by the kth near-field source, e represents the natural base, j represents the imaginary number, τ xl (k) represents the phase difference between the signal emitted by the kth near-field source reaching the array element with coordinates (l,0) and the signal reaching the reference array element, τ yl (k) represents the phase difference between the signal emitted by the kth near-field source reaching the array element with coordinates (0, l) and the signal reaching the reference array element, n l,0 (t) represents x l,0 (t) is the additive white Gaussian noise, n 0,l (t) represents y 0,l Additive white Gaussian noise in (t); Step 2_2: Perform a second-order Taylor expansion on equation 2.1 to obtain: Performing a second-order Taylor expansion on Equation 2.2 yields: Among them, ω kx Defined as φ kx Defined as ω ky Defined as φ ky Defined as Step 2_3: Based on equation 2.3, the data received by adjacent array elements in the uniform linear array on the X-axis are correlated to obtain the corresponding correlation. The correlation between the data received by the array element with coordinates (-l-1,0) and the data received by the array element with coordinates (-l,0) in the uniform linear array on the X-axis is calculated. Expressed as (Equation 2.5), where τ represents the delay variable, E{·} represents the mathematical expectation, the superscript "*" represents the conjugate operation, and x -l,0 (t) represents the data received by the element with coordinate (-l,0) in the uniform linear array on the X axis at time t, x -l-1,0 (t) represents the data received by the element with coordinate (-l-1,0) in the uniform linear array on the X axis at time t, x -l-1,0 (t+τ) represents x -l-1,0 (t) Data obtained after a delay of τ, s k (t+τ) represents s k (t) is the signal obtained after a delay of τ, σ 2 represents the power of the additive Gaussian white noise in the data received by the array element, δ(·) represents the impulse function, Based on equation 2.3, the data received by the symmetrical array elements in the uniform linear array on the X-axis are correlated to obtain the corresponding correlation. The correlation between the data received by the array element with coordinates (-l, 0) and the data received by the array element with coordinates (l, 0) in the uniform linear array on the X-axis is calculated as Expressed as Among them, x -l,0 (t+τ) represents x -l,0 (t) Data obtained after a delay of τ; Based on equation 2.4, the data received by the symmetrical array elements in the uniform linear array on the Y axis are correlated to obtain the corresponding correlation. The correlation between the data received by the array element with coordinates (0, -l) and the data received by the array element with coordinates (0, l) in the uniform linear array on the Y axis is calculated. Expressed as Among them, y 0,-l (t+τ) represents the signal y received by the element with coordinates (0, -l) in the uniform linear array on the Y axis at time t 0,-l (t) Data obtained after a delay of τ; Step 2_4: Based on equation 2.5, obtain the correlation vector r consisting of the correlation of the data received by all adjacent array elements in the uniform linear array on the X axis x,adj (τ), expressed as: Among them, the superscript "T" represents the transpose operation; Based on formula 2.6, the correlation vector r formed by the correlation of the data received by all symmetrical array elements in the uniform linear array on the X axis is obtained x,sym (τ), expressed as: Based on formula 2.7, the correlation vector r formed by the correlation of the data received by all symmetrical array elements in the uniform linear array on the Y axis is obtained y,sym (τ), expressed as: Step 2_5: x,adj (τ) at uniform time intervals T s Perform P pseudo snapshot samplings to obtain virtual received data R corresponding to all adjacent array elements in the uniform linear array on the X axis. x,adj , expressed as: in, represents the virtual steering vector corresponding to all adjacent array elements in the uniform linear array on the X axis, R s Represents a virtual signal, R s =[u s (T s ),u s (2T s ),...,u s (PT s )],u s (τ)=[u s1 (τ),u s2 (τ),...,u sK (τ)] T , for u s (τ) at uniform time intervals T s Perform P pseudo snapshot sampling to obtain P sampling values, which are u s (T s ),u s (2T s ),...,u s (PT s ), Represents R x,adj Additive Gaussian white noise in ; R x,sym (τ) at uniform time intervals T s Perform P pseudo snapshot samplings to obtain the virtual received data R corresponding to all symmetrical array elements in the uniform linear array on the X axis. x,sym , expressed as: in, represents the virtual steering vector corresponding to all symmetrical array elements in the uniform linear array on the X axis, Represents R x,sym Additive Gaussian white noise in ; For ry,sym(τ), the s Perform P pseudo snapshot samplings to obtain the virtual received data R corresponding to all symmetrical array elements in the uniform linear array on the Y axis. y,sym , expressed as: in, represents the virtual steering vector corresponding to all symmetrical array elements in the uniform linear array on the Y axis, Represents R y,sym Additive Gaussian white noise in ; Step 2_6: R x,adj With R x,sym Perform cross-correlation operations to obtain the covariance matrix related to the angle between the signal emitted by the near-field source and the X-axis and the distance between the near-field source and the reference array element. The superscript "H" indicates the conjugate transpose operation. Represents R s The covariance matrix of diag(·) means finding the diagonal matrix, Indicates k The power of (t), Express and The noise covariance matrix obtained by performing cross-correlation operation; R x,sym With R y,sym Perform cross-correlation operations to obtain the covariance matrix related to the angle between the signal emitted by the near-field source and the X-axis and the angle between the signal and the Y-axis. in, Express and The noise covariance matrix obtained by performing cross-correlation operation; Step 2_7: Right Normalization processing is performed to obtain the normalized covariance matrix R related to the angle between the signal emitted by the near-field source and the X-axis and the distance between the near-field source and the reference array element. xx , in, represents the real part operation, represents the operation of taking the imaginary part, ||·|| F represents the F norm of the matrix, where R xx The size is (M x -1)×M x ×2, the third dimension represents different channels, the first channel and the second channel are R xx The real and imaginary parts of right Normalization processing is performed to obtain the normalized covariance matrix R related to the angle between the signal emitted by the near-field source and the X-axis and the angle between the signal and the Y-axis. xy , Among them, R xy The size is M x ×M y ×2, the third dimension represents different channels, the first channel and the second channel are R xy The real and imaginary parts of .

4. The three-dimensional near-field source localization method based on a deep feature fusion extraction network according to any one of claims 1 to 3, characterized in that The feature fusion network consists of a first convolution block and a first residual block, the first residual block includes a second convolution block and a third convolution block; the training data pair is input into the first convolution block, the features output by the first convolution block are input into the second convolution block, the features output by the second convolution block are input into the third convolution block, the features output by the first convolution block are added after the padding operation and the features output by the third convolution block, and the features obtained after the addition result is subjected to the maximum pooling operation as the fusion feature.

5. The three-dimensional near-field source localization method based on deep feature fusion extraction network according to claim 4 is characterized in that The structures of the first feature extraction branch, the second feature extraction branch, and the third feature extraction branch are the same, and are all composed of a fourth convolution block, a fifth convolution block, and a second residual block, and the second residual block includes a self-attention mechanism and a sixth convolution block; the fused features are input into the fourth convolution block, the features output by the fourth convolution block are input into the fifth convolution block, the features output by the fifth convolution block are input into the self-attention mechanism, the attention features output by the self-attention mechanism are input into the sixth convolution block, the features output by the sixth convolution block are added to the features output by the fifth convolution block, and the features obtained after the addition is subjected to the maximum pooling operation are used as the features output by the feature extraction branch.

6. The three-dimensional near-field source localization method based on deep feature fusion extraction network according to claim 5 is characterized in that The structures of the first feature output branch, the second feature output branch, and the third feature output branch are the same, and all include a Flatten layer, a first fully connected layer, a first Dropout layer, a second fully connected layer, and a second Dropout layer connected in sequence; the features output by the feature extraction branch corresponding to the feature output branch are input into the Flatten layer, the features output by the Flatten layer are input into the first fully connected layer, the features output by the first fully connected layer are input into the first Dropout layer, the features output by the first Dropout layer are input into the second fully connected layer, the features output by the second fully connected layer are input into the second Dropout layer, and the probability vector output by the second Dropout layer is used as the probability vector output by the feature output branch.

7. The three-dimensional near-field source localization method based on deep feature fusion extraction network according to claim 6 is characterized in that The first convolution block, the second convolution block, the third convolution block, the fourth convolution block, the fifth convolution block, and the sixth convolution block have the same structure, and all include sequentially connected convolution layers, batch normalization layers, and Leaky ReLU activation functions.

8. The three-dimensional near-field source localization method based on deep feature fusion extraction network according to claim 1 is characterized in that The training process of step 5 is as follows: Step 5_1: Randomly divide all training data pairs in the training set and their corresponding first true labels, second true labels, and third true labels into multiple batches, so that each batch contains batch size groups of training data pairs and their corresponding first true labels, second true labels, and third true labels; Step 5_2: Take one of the batches of the training set, and use all the training data pairs in this batch as the input of the deep feature fusion extraction network, and input them into the deep feature fusion extraction network for processing to obtain the first probability vector, the second probability vector, and the third probability vector corresponding to each group of training data pairs in this batch; Step 5_3: For each training data pair in this batch, supervise the network training by calculating the training loss Loss, Loss = λ1L CEL +λ2L CEL +λ3L CEL , where λ1, λ2 and λ3 are weight coefficients, L CEL represents the cross entropy loss between the first probability vector and the first true label corresponding to each set of training data, L CEL represents the cross entropy loss between the second probability vector and the second true label corresponding to each set of training data, L CEL Represents the cross entropy loss of the third probability vector and the third true label corresponding to each set of training data; Step 5_4: The weights and biases in the deep feature fusion extraction network are initialized using the default strategy, and the deep feature fusion extraction network is trained offline in a supervised manner using the Adam optimizer to complete the training of the deep feature fusion extraction network for this batch, and the network parameters are updated through back propagation; Step 5_5: Repeat the process from step 5_2 to step 5_4 until all batches of the training set have trained the deep feature fusion extraction network once; Step 5_6: Randomly divide all the verification data pairs in the verification set and their corresponding first true labels, second true labels, and third true labels into multiple batches, so that each batch contains batch size groups of verification data pairs and their corresponding first true labels, second true labels, and third true labels; Step 5_7: Take one of the batches of the validation set; then input all the validation data pairs in this batch into the deep feature fusion extraction network trained with the training set to obtain the first probability vector, the second probability vector, and the third probability vector corresponding to each set of validation data pairs in this batch; then follow the process of step 5_3 and calculate the validation loss corresponding to each set of validation data pairs in this batch in the same way; Step 5_8: Repeat the process of step 5_7 until all batches of the validation set have been processed once; Step 5_9: Repeat the process from step 5_1 to step 5_8, and end the training after the set rounds to obtain a trained deep feature fusion extraction network. The warm-up learning rate strategy is adopted, and the initial learning rate is set to 0.0005. In the first 5 rounds of training, the learning rate increases linearly to 0.001, and then decays exponentially with each round.

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