Two-dimensional arrival direction estimation method and device based on tensor decomposition and one-dimensional optimization

Abstract

The invention provides a two-dimensional arrival direction estimation method and device based on tensor decomposition and one-dimensional optimization, and the method comprises the steps: obtaining an L-shaped array receiving signal, and constructing a tensor signal model; constructing an x-axis sub-array receiving signal model and a y-axis sub-array receiving signal model based on the tensor signal model; respectively constructing an x-axis sub-array receiving signal covariance matrix and a y-axis sub-array receiving signal covariance matrix based on the x-axis sub-array receiving signal model and the y-axis sub-array receiving signal model, and performing eigenvalue decomposition on the constructed covariance matrixes to obtain an x-axis sub-array noise subspace matrix and a y-axis sub-array noise subspace matrix; and constructing a corresponding MUSIC spatial spectrum function based on the x-axis noise subspace matrix and the y-axis noise subspace matrix, and searching a maximum spectrum peak position in parallel to obtain a direction of arrival estimation result. According to the method, the complexity of original two-dimensional search is changed into two parallel one-dimensional search, and the search efficiency is remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and in particular to a two-dimensional direction-of-arrival estimation method and apparatus based on tensor decomposition and one-dimensional optimization. Background Technology

[0002] In systems such as wireless communication and radar sonar, two-dimensional direction-of-arrival (DOA) estimation is a key technology for DOA estimation and is widely used in scenarios such as source localization, beamforming, and spatial spectrum estimation. Traditional two-dimensional MUSIC algorithms typically employ a two-dimensional spectral function and search across the entire angular space. Although the estimation accuracy is high, the computational complexity increases exponentially with angular resolution due to its two-dimensional search structure, which is not conducive to the deployment of real-time processing systems.

[0003] Due to its orthogonality, the L-shaped array structure allows the elevation and azimuth angles to be extracted from two orthogonal array directions. However, traditional methods often neglect the spatial coupling relationship of signals in the array geometry, resulting in a significant reduction in estimation performance, especially in low signal-to-noise ratio or multi-source scenarios.

[0004] Therefore, a technical solution is urgently needed to solve the above problems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a two-dimensional arrival direction estimation method and apparatus based on tensor decomposition and one-dimensional optimization.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: On the one hand, this invention provides a two-dimensional direction-of-arrival estimation method based on tensor decomposition and one-dimensional optimization, comprising the following steps: Acquire the received signal from the L-shaped array and construct a tensor signal model; Based on the tensor signal model, construct the x-axis subarray received signal model and the y-axis subarray received signal model; Based on the x-axis subarray received signal model and the y-axis subarray received signal model, the covariance matrix of the x-axis subarray received signal and the covariance matrix of the y-axis subarray received signal are constructed respectively. Then, the eigenvalue decomposition of the constructed covariance matrix is ​​performed to obtain the x-axis subarray noise subspace matrix and the y-axis subarray noise subspace matrix. Based on the x-axis noise subspace matrix and the y-axis noise subspace matrix, the corresponding MUSIC spatial spectrum function is constructed, and the position of the maximum spectral peak is searched in parallel to obtain the arrival direction estimation result.

[0007] Furthermore, a tensor signal model is constructed, including: The received signal from the L-shaped array is modeled as a third-order tensor, which is:

[0008] in, It is a third-order tensor. The number of elements in the x-axis matrix. The number of elements in the y-axis matrix. For the number of snapshots; For complex numbers; Perform CP decomposition on the third-order tensor to construct a tensor signal model, which is as follows:

[0009] in, For the first k x-axis direction array manifold vector of each source For the first k The y-axis direction array manifold vector of each source. For outer product operation, For the first k The time-domain waveform of each source. It is the additive noise tensor; This represents the total number of information sources.

[0010] Furthermore, the aforementioned and for:

[0011] in, j The imaginary unit, For the first k The projection cosine of each source in the xz plane. For the first k The projection cosine of each source in the yz plane. The antenna spacing along the x-axis of the L-shaped array. The antenna spacing along the y-axis of the L-shaped array. The wavelength of the incident signal; The and Calculate using the following formula:

[0012]

[0013] in, The cosine of the projection of the received signal onto the xz plane. The cosine of the projection of the received signal onto the yz plane. The elevation angle of the incident signal. The azimuth angle of the incident signal.

[0014] Furthermore, the signal receiving models of the x-axis subarray and the y-axis subarray are as follows:

[0015]

[0016]

[0017] in, The x-axis subarray receives the signal model. This is a model for the signal received by the y-axis subarray. The phase distribution of the received signal along the x-axis. To represent the phase distribution of the received signal along the y-axis, Let x be the noise tensor along the x-axis. Let be the noise tensor along the y-axis. This is the signal vector.

[0018] Furthermore, the covariance matrix of the received signal from the x-axis subarray and the covariance matrix of the received signal from the y-axis subarray are as follows:

[0019]

[0020] in, Let x be the covariance matrix of the received signal from the x-axis subarray. The covariance matrix of the received signal from the y-axis subarray is... For the desired processing, The x-axis subarray receives the signal model. This is a model for the signal received by the y-axis subarray. for The conjugate transpose of . for The conjugate transpose of . For noise variance, It is the identity matrix. for The covariance matrix, for The covariance matrix, Let be the steering vector matrix of all information sources in the x-direction. for The conjugate transpose of . Let be the steering vector matrix of all information sources in the y-direction. for The conjugate transpose of .

[0021] Furthermore, the constructed covariance matrix is ​​decomposed into eigenvalues ​​according to the following formula:

[0022]

[0023] in, Let be the subspace matrix of the signal received by the x-axis subarray. for The conjugate transpose of . This is the diagonal matrix for the signals received by the x-axis subarray. The x-axis subarray noise subspace matrix is... for The conjugate transpose of . The noise diagonal matrix of the x-axis subarray. Let be the subspace matrix of the signal received by the y-axis subarray. for The conjugate transpose of . This is the diagonal matrix for the signals received by the y-axis subarray. The noise subspace matrix of the y-axis subarray. for The conjugate transpose of . It is the noise diagonal matrix of the y-axis subarray.

[0024] Furthermore, the MUSIC spatial spectral function is:

[0025] in, The spatial spectral function along the x-axis. The spatial spectral function along the y-axis. The x-axis direction array manifold vector. for The conjugate transpose of . The y-axis direction array manifold vector. for The conjugate transpose of; The position of the maximum spectral peak obtained by parallel search is:

[0026]

[0027] in, For the first k The maximum spectral peak of the spatial spectral function of the x-axis of the source. For the first k The maximum spectral peak of the spatial spectral function of the y-axis of each source; Through nonlinear transformation Mapped to The arrival direction estimation result is obtained; the nonlinear transformation is performed according to the following formula:

[0028] in, For the estimated first k The azimuth angle of each signal source. For the estimated first k The pitch angle of a signal source.

[0029] Furthermore, it also includes: A local search grid is constructed within the domain of the arrival direction estimation results, and a projection error function is also constructed. The arrival direction estimation results are optimized by using the projection error function; The Newton-Raphson iteration method is used to optimize the arrival direction estimation results within the constructed local search grid.

[0030] Furthermore, the local search grid is:

[0031] in, For the first k Local search grid for each information source, For the estimated first k The azimuth angle of each signal source. For the estimated first k The elevation angle of a signal source, This represents the azimuth estimation error. The pitch angle estimation error, It is the azimuth angle. The pitch angle; and Calculate using the following formula:

[0032]

[0033] in, For the first k The estimation error of the azimuth angle of each information source. For the first k The estimation error of the elevation angle of each signal source. For the first k The maximum spectral peak of the spatial spectral function of the x-axis of the source. For the first k The maximum spectral peak of the spatial spectral function along the y-axis of each source. For the first k The estimation error of the x-axis direction cosine of each source. For the first k The estimation error of the y-axis direction cosine of each source; The projection error function Constructed based on the following formula:

[0034] in, The phase difference on the array elements caused by the horizontal and vertical angles. This is the conjugate transpose of the joint noise subspace matrix; The arrival direction estimation results are optimized through the projection error function, including: Fixed azimuth angle, optimized pitch angle:

[0035] in, The optimized pitch angle; Fixed pitch angle, optimized azimuth angle:

[0036] in, The optimized azimuth angle; The Newton iteration method is based on the following formula:

[0037] in, For the first n +1 azimuth iteration value, For the first n +1 pitch angle iteration value, For the first n The azimuth angle iteration value of the nth iteration. For the first n The pitch angle iteration value of the next iteration. for The inverse of the Hessian matrix, For the first n Subprojection error function The gradient vector.

[0038] On the other hand, the present invention provides a two-dimensional direction-of-arrival estimation device based on tensor decomposition and one-dimensional optimization, comprising: The first module is used to acquire the received signal from the L-shaped array and construct a tensor signal model. The second module is used to construct the x-axis subarray received signal model and the y-axis subarray received signal model based on the tensor signal model; The third module is used to construct the covariance matrix of the x-axis subarray received signal and the covariance matrix of the y-axis subarray received signal based on the x-axis subarray received signal model and the y-axis subarray received signal model, respectively, and to perform eigenvalue decomposition on the constructed covariance matrix to obtain the x-axis subarray noise subspace matrix and the y-axis subarray noise subspace matrix. The fourth module is used to construct the corresponding MUSIC spatial spectrum function based on the x-axis noise subspace matrix and the y-axis noise subspace matrix, and to search for the position of the maximum spectral peak in parallel to obtain the arrival direction estimation result.

[0039] Compared with the prior art, the beneficial technical effects of the present invention are as follows: The present invention provides a two-dimensional direction-of-arrival estimation method and apparatus based on tensor decomposition and one-dimensional optimization. It constructs a tensor signal model by using an L-shaped array to receive signals, and further constructs x-axis and y-axis subarray signal models. Utilizing the orthogonality of the L-shaped array, the pitch and azimuth angles are extracted from the x-axis and y-axis subarray signal models. The covariance matrices corresponding to the x-axis and y-axis subarray signal models are then constructed and eigenvalue decomposition is performed to obtain the corresponding noise subspace matrix. The maximum spectral peak position is searched in parallel using the MUSIC algorithm to obtain the direction-of-arrival estimation result. By performing parallel search estimation in the x-axis and y-axis directions, the complexity of the original two-dimensional search is reduced to two parallel one-dimensional searches, significantly improving search efficiency. Furthermore, the step-by-step search and parallel computation are easy to implement on platforms such as FPGAs and embedded systems, facilitating the deployment of real-time processing systems. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0041] Figure 1 A flowchart of a two-dimensional arrival direction estimation method based on tensor decomposition and one-dimensional optimization is provided as an embodiment. Figure 2 This is a comparison chart showing the results of measuring the direction of arrival using different methods in different scenarios provided in one embodiment. Figure 2 (a) is a comparison chart of the results obtained by the two-dimensional direction of arrival estimation method based on tensor decomposition and one-dimensional optimization and the results obtained by the subspace estimation method in scenario 1. Figure 2 (b) is a comparison chart of the results obtained by the two-dimensional direction of arrival estimation method based on tensor decomposition and one-dimensional optimization and the results obtained by the subspace estimation method in scenario 2. Figure 2 (c) is a comparison of the results obtained by the two-dimensional arrival direction estimation method based on tensor decomposition and one-dimensional optimization and the results obtained by the subspace estimation method in scenario 3. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0043] Reference Figure 1 One embodiment provides a two-dimensional direction-of-arrival estimation method based on tensor decomposition and one-dimensional optimization, including the following steps: Acquire the received signal from the L-shaped array and construct a tensor signal model; Based on the tensor signal model, construct the x-axis subarray received signal model and the y-axis subarray received signal model; Based on the x-axis subarray received signal model and the y-axis subarray received signal model, the covariance matrix of the x-axis subarray received signal and the covariance matrix of the y-axis subarray received signal are constructed respectively. Then, the eigenvalue decomposition of the constructed covariance matrix is ​​performed to obtain the x-axis subarray noise subspace matrix and the y-axis subarray noise subspace matrix. Based on the x-axis noise subspace matrix and the y-axis noise subspace matrix, the corresponding MUSIC spatial spectrum function is constructed, and the position of the maximum spectral peak is searched in parallel to obtain the arrival direction estimation result.

[0044] By using an L-shaped array to receive signals, a tensor signal model is constructed, and further, x-axis and y-axis subarray signal models are built. Utilizing the orthogonality of the L-shaped array, elevation and azimuth angles are extracted from these x-axis and y-axis subarray signal models. The covariance matrices corresponding to the x-axis and y-axis subarray signal models are then constructed and eigenvalue decomposition is performed to obtain the corresponding noise subspace matrix. The maximum spectral peak position is searched in parallel using the MUSIC algorithm to obtain the direction of arrival estimation result. By performing parallel search estimations along the x-axis and y-axis, the complexity of the original two-dimensional search is reduced to two parallel one-dimensional searches, significantly improving search efficiency.

[0045] In a preferred embodiment, constructing a tensor signal model includes: The received signal from the L-shaped array is modeled as a third-order tensor, which is:

[0046] in, It is a third-order tensor. The number of elements in the x-axis matrix. The number of elements in the y-axis matrix. For the number of snapshots; For complex numbers; Perform CP decomposition on the third-order tensor to construct a tensor signal model, which is as follows:

[0047] in, For the first k x-axis direction array manifold vector of each source For the first k The y-axis direction array manifold vector of each source. For outer product operation, For the first k The time-domain waveform of each source. For additive noise tensor, This represents the total number of information sources.

[0048] The and for:

[0049] in, j The imaginary unit, For the first k The projection cosine of each source in the xz plane. For the first k The projection cosine of each source in the yz plane. The antenna spacing along the x-axis of the L-shaped array. The antenna spacing along the y-axis of the L-shaped array. The wavelength of the incident signal; The and Calculate using the following formula:

[0050]

[0051] in, The cosine of the projection of the received signal onto the xz plane. The cosine of the projection of the received signal onto the yz plane. The elevation angle of the incident signal. The azimuth angle of the incident signal.

[0052] By modeling the L-shaped array structure signal as a third-order tensor and constructing the tensor signal model using CP decomposition, the multidimensional spatial coupling is maintained, effectively separating the influence of azimuth and elevation angles.

[0053] The signal receiving models for the x-axis subarray and the y-axis subarray are as follows:

[0054]

[0055]

[0056] in, The x-axis subarray receives the signal model. This is a model for the signal received by the y-axis subarray. The phase distribution of the received signal along the x-axis. To represent the phase distribution of the received signal along the y-axis, Let x be the noise tensor along the x-axis. Let be the noise tensor along the y-axis. This is the signal vector.

[0057] In one embodiment, the covariance matrix of the received signal from the x-axis subarray and the covariance matrix of the received signal from the y-axis subarray are:

[0058]

[0059] in, Let x be the covariance matrix of the received signal from the x-axis subarray. The covariance matrix of the received signal from the y-axis subarray is... For the desired processing, The x-axis subarray receives the signal model. This is a model for the signal received by the y-axis subarray. for The conjugate transpose of . for The conjugate transpose of . For noise variance, It is the identity matrix. for The covariance matrix, for The covariance matrix, Let be the steering vector matrix of all information sources in the x-direction. for The conjugate transpose of . Let be the steering vector matrix of all information sources in the y-direction. for The conjugate transpose of .

[0060] The eigenvalue decomposition of the constructed covariance matrix is ​​performed according to the following formula:

[0061]

[0062] in, Let be the subspace matrix of the signal received by the x-axis subarray. for The conjugate transpose of . This is the diagonal matrix for the signals received by the x-axis subarray. The x-axis subarray noise subspace matrix is... for The conjugate transpose of . The x-axis subarray noise diagonal matrix, Let be the subspace matrix of the signal received by the y-axis subarray. for The conjugate transpose of . This is the diagonal matrix for receiving signals from the y-axis subarray. The noise subspace matrix of the y-axis subarray. for The conjugate transpose of . It is the noise diagonal matrix of the y-axis subarray.

[0063] The MUSIC spatial spectral function is:

[0064] in, The spatial spectral function along the x-axis. The spatial spectrum function along the y-axis. The x-axis direction array manifold vector. for The conjugate transpose of . The y-axis direction array manifold vector. for The conjugate transpose of; The position of the maximum spectral peak obtained by parallel search is:

[0065]

[0066] in, For the first k The maximum spectral peak of the spatial spectral function of the x-axis of the source. For the first k The maximum spectral peak of the spatial spectral function of the y-axis of each source; Through nonlinear transformation Mapped to The arrival direction estimation result is obtained; the nonlinear transformation is performed according to the following formula:

[0067] in, For the estimated first k The azimuth angle of each signal source. For the estimated first k The pitch angle of a signal source.

[0068] In a preferred embodiment, the two-dimensional direction-of-arrival estimation method based on tensor decomposition and one-dimensional optimization further includes: A local search grid is constructed within the domain of the arrival direction estimation results, and a projection error function is also constructed. The arrival direction estimation results are optimized by using the projection error function; The Newton-Raphson iteration method is used to optimize the arrival direction estimation results within the constructed local search grid.

[0069] The local search grid is:

[0070] in, For the first k Local search grid for each information source, For the estimated first k The azimuth angle of each signal source. For the estimated first k The elevation angle of a signal source, This represents the azimuth estimation error. The pitch angle estimation error, It is the azimuth angle. The pitch angle; and Calculate using the following formula:

[0071]

[0072] in, For the first k The estimation error of the azimuth angle of each information source. For the first k The estimation error of the elevation angle of each signal source. For the first k The maximum spectral peak of the spatial spectral function of the x-axis of the source. For the first k The maximum spectral peak of the spatial spectral function along the y-axis of each source. For the first k The estimation error of the x-axis direction cosine of each source. For the first k The estimation error of the y-axis direction cosine of each source; The projection error function Constructed based on the following formula:

[0073] in, The phase difference on the array elements caused by the horizontal and vertical angles. This is the conjugate transpose of the joint noise subspace matrix; The arrival direction estimation results are optimized through the projection error function, including: Fixed azimuth angle, optimized pitch angle:

[0074] in, The optimized pitch angle; Fixed pitch angle, optimized azimuth angle:

[0075] in, The optimized azimuth angle; The Newton iteration method is based on the following formula:

[0076] in, For the first n +1 azimuth iteration value, For the first n +1 pitch angle iteration value, For the first n The azimuth angle iteration value of the nth iteration. For the first n The pitch angle iteration value of the next iteration. for The inverse of the Hessian matrix, For the first n Subprojection error function The gradient vector.

[0077] First, the arrival direction estimation result is optimized by using a projection error function, effectively reducing noise interference and improving the accuracy of arrival direction estimation in low signal-to-noise ratio environments, making the optimized arrival direction estimation result more accurate and reliable. Then, by further refining the optimized arrival direction estimation result within the constructed local search grid using Newton's iteration method, the error can be significantly reduced, estimation accuracy improved, and the estimation capability of the method enhanced in low channel ratio environments. Specifically, by employing Newton's iteration method, a local quadratic approximation is constructed using the first derivative and the second reciprocal, resulting in rapid convergence near the optimal solution. Newton's iteration method utilizes the function curvature information in the local space, more accurately capturing the shape of the error surface, avoiding full-space search, improving computational efficiency, and facilitating convergence. This avoids misjudgment due to excessively large search or loss of the true direction due to excessively small search.

[0078] To verify the effectiveness and practicality of this invention, three different transmission and reception scenarios were set up for indoor angle estimation experiments, in which the position of the receiver changed in each scenario; after each data acquisition, a two-dimensional direction of arrival (DOA) was estimated based on the new receiver position. The scenario settings and corresponding angle calculations are shown in the table below: Table 1 Scene Settings and Corresponding Angles

[0079] Reference Figure 2 ,from Figure 2 As can be seen in (a), in scenario 1, the method of this invention (a two-dimensional arrival direction estimation method based on tensor decomposition and one-dimensional optimization) measures a horizontal direction angle of 0.35° and a pitch angle of -0.05°; the subspace estimation method measures a horizontal direction angle of -6.29° and a pitch angle of -1.54°; from Figure 2 As can be seen in (b), in scenario 2, the method of this invention measures a horizontal angle of -44.55° and a pitch angle of 0.66°; the subspace estimation method measures a horizontal angle of 53.59° and a pitch angle of -0.90°; from Figure 2 As shown in (c), in scenario 3, the method of this invention measures a horizontal angle of 45.26° and a pitch angle of 8.63°; the subspace estimation method measures a horizontal angle of 38.93° and a pitch angle of 7.04°. It is clear from these results that the angle estimation result obtained by the method of this invention is significantly closer to the theoretical value, and the accuracy of the obtained estimation result is higher than that of the subspace estimation method. This demonstrates that the method of this invention can efficiently and accurately estimate the direction of arrival.

[0080] In one embodiment, a two-dimensional direction-of-arrival estimation device based on tensor decomposition and one-dimensional optimization is provided, comprising: The first module is used to acquire the received signal from the L-shaped array and construct a tensor signal model. The second module is used to construct the x-axis subarray received signal model and the y-axis subarray received signal model based on the tensor signal model; The third module is used to construct the covariance matrix of the x-axis subarray received signal and the covariance matrix of the y-axis subarray received signal based on the x-axis subarray received signal model and the y-axis subarray received signal model, respectively, and to perform eigenvalue decomposition on the constructed covariance matrix to obtain the x-axis subarray noise subspace matrix and the y-axis subarray noise subspace matrix. The fourth module is used to construct the corresponding MUSIC spatial spectrum function based on the x-axis noise subspace matrix and the y-axis noise subspace matrix, and to search for the position of the maximum spectral peak in parallel to obtain the arrival direction estimation result.

[0081] Matters not covered in this invention are common knowledge.

[0082] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0083] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application.

[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A two-dimensional direction-of-arrival estimation method based on tensor decomposition and one-dimensional optimization, characterized in that, Includes the following steps: Acquire the received signal from the L-shaped array and construct a tensor signal model; Based on the tensor signal model, construct the x-axis subarray received signal model and the y-axis subarray received signal model; Based on the x-axis subarray received signal model and the y-axis subarray received signal model, the covariance matrix of the x-axis subarray received signal and the covariance matrix of the y-axis subarray received signal are constructed respectively. Then, the eigenvalue decomposition of the constructed covariance matrix is ​​performed to obtain the x-axis subarray noise subspace matrix and the y-axis subarray noise subspace matrix. Based on the x-axis noise subspace matrix and the y-axis noise subspace matrix, the corresponding MUSIC spatial spectrum function is constructed, and the position of the maximum spectral peak is searched in parallel to obtain the arrival direction estimation result.

2. The two-dimensional arrival direction estimation method based on tensor decomposition and one-dimensional optimization as described in claim 1, characterized in that, Constructing a tensor signal model includes: The received signal from the L-shaped array is modeled as a third-order tensor, which is: in, It is a third-order tensor. The number of elements in the x-axis matrix. The number of elements in the y-axis matrix. For the number of snapshots; For complex numbers; Perform CP decomposition on the third-order tensor to construct a tensor signal model, which is as follows: in, For the first k x-axis direction array manifold vector of each source For the first k The y-axis direction array manifold vector of each source. For outer product operation, For the first k The time-domain waveform of each source. It is the additive noise tensor; This represents the total number of information sources.

3. The two-dimensional arrival direction estimation method based on tensor decomposition and one-dimensional optimization as described in claim 2, characterized in that, The and for: in, j The imaginary unit, For the first k The projection cosine of each source in the xz plane. For the first k The projection cosine of each source in the yz plane. The antenna spacing along the x-axis of the L-shaped array. The antenna spacing along the y-axis of the L-shaped array. The wavelength of the incident signal; and Calculate using the following formula: in, The cosine of the projection of the received signal onto the xz plane. The cosine of the projection of the received signal onto the yz plane. The elevation angle of the incident signal. The azimuth angle of the incident signal.

4. The two-dimensional arrival direction estimation method based on tensor decomposition and one-dimensional optimization as described in claim 3, characterized in that, The signal receiving models for the x-axis subarray and the y-axis subarray are as follows: in, The x-axis subarray receives the signal model. This is a model for the signal received by the y-axis subarray. The phase distribution of the received signal along the x-axis. To represent the phase distribution of the received signal along the y-axis, Let x be the noise tensor along the x-axis. Let be the noise tensor along the y-axis. This is the signal vector.

5. The two-dimensional arrival direction estimation method based on tensor decomposition and one-dimensional optimization as described in claim 1, characterized in that, The covariance matrix of the received signal from the x-axis subarray and the covariance matrix of the received signal from the y-axis subarray are as follows: in, Let x be the covariance matrix of the received signal from the x-axis subarray. The covariance matrix of the received signal from the y-axis subarray is... For the desired processing, The x-axis subarray receives the signal model. This is a model for the signal received by the y-axis subarray. for The conjugate transpose of . for The conjugate transpose of . For noise variance, It is the identity matrix. for The covariance matrix, for The covariance matrix, Let be the steering vector matrix of all information sources in the x-direction. for The conjugate transpose of . Let be the steering vector matrix of all information sources in the y-direction. for The conjugate transpose of .

6. The two-dimensional arrival direction estimation method based on tensor decomposition and one-dimensional optimization as described in claim 5, characterized in that, The eigenvalue decomposition of the constructed covariance matrix is ​​performed according to the following formula: in, Let be the subspace matrix of the signal received by the x-axis subarray. for The conjugate transpose of . This is the diagonal matrix for the signals received by the x-axis subarray. The x-axis subarray noise subspace matrix is... for The conjugate transpose of . The x-axis subarray noise diagonal matrix, Let be the subspace matrix of the signal received by the y-axis subarray. for The conjugate transpose of . This is the diagonal matrix for receiving signals from the y-axis subarray. The noise subspace matrix of the y-axis subarray. for The conjugate transpose of . It is the noise diagonal matrix of the y-axis subarray.

7. The two-dimensional arrival direction estimation method based on tensor decomposition and one-dimensional optimization as described in claim 6, characterized in that, The MUSIC spatial spectral function is: in, The spatial spectral function along the x-axis. The spatial spectrum function along the y-axis. The x-axis direction array manifold vector. for The conjugate transpose of . The y-axis direction array manifold vector. for The conjugate transpose of; The position of the maximum spectral peak obtained by parallel search is: in, For the first k The maximum spectral peak of the spatial spectral function of the x-axis of the source. For the first k The maximum spectral peak of the spatial spectral function of the y-axis of each source; Through nonlinear transformation Mapped to The arrival direction estimation result is obtained; the nonlinear transformation is performed according to the following formula: in, For the estimated first k The azimuth angle of each signal source. For the estimated first k The pitch angle of a signal source.

8. The two-dimensional arrival direction estimation method based on tensor decomposition and one-dimensional optimization as described in claim 1, characterized in that, Also includes: A local search grid is constructed within the domain of the arrival direction estimation results, and a projection error function is also constructed. The arrival direction estimation results are optimized by using the projection error function; The Newton-Raphson iteration method is used to optimize the arrival direction estimation results within the constructed local search grid.

9. The two-dimensional arrival direction estimation method based on tensor decomposition and one-dimensional optimization as described in claim 8, characterized in that, The local search grid is: in, For the first k Local search grid for each information source, For the estimated first k The azimuth angle of each signal source. For the estimated first k The elevation angle of a signal source, This represents the azimuth estimation error. The pitch angle estimation error, It is the azimuth angle. The pitch angle; and Calculate using the following formula: in, For the first k The estimation error of the azimuth angle of each information source. For the first k The estimation error of the elevation angle of each signal source. For the first k The maximum spectral peak of the spatial spectral function of the x-axis of the source. For the first k The maximum spectral peak of the spatial spectral function along the y-axis of each source. For the first k The estimation error of the x-axis direction cosine of each source. For the first k The estimation error of the y-axis direction cosine of each source; The projection error function Constructed based on the following formula: in, The phase difference on the array elements caused by the horizontal and vertical angles. This is the conjugate transpose of the joint noise subspace matrix; The arrival direction estimation results are optimized through the projection error function, including: Fixed azimuth angle, optimized pitch angle: in, The optimized pitch angle; Fixed pitch angle, optimized azimuth angle: in, The optimized azimuth angle; The Newton iteration method is based on the following formula: in, For the first n +1 azimuth iteration value, For the first n +1 pitch angle iteration value, For the first n The azimuth angle iteration value of the nth iteration. For the first n The pitch angle iteration value of the next iteration. for The inverse of the Hessian matrix, For the first n Subprojection error function The gradient vector.

10. A two-dimensional direction-of-arrival estimation device based on tensor decomposition and one-dimensional optimization, characterized in that, include: The first module is used to acquire the received signal from the L-shaped array and construct a tensor signal model. The second module is used to construct the x-axis subarray received signal model and the y-axis subarray received signal model based on the tensor signal model; The third module is used to construct the covariance matrix of the x-axis subarray received signal and the covariance matrix of the y-axis subarray received signal based on the x-axis subarray received signal model and the y-axis subarray received signal model, respectively, and to perform eigenvalue decomposition on the constructed covariance matrix to obtain the x-axis subarray noise subspace matrix and the y-axis subarray noise subspace matrix. The fourth module is used to construct the corresponding MUSIC spatial spectrum function based on the x-axis noise subspace matrix and the y-axis noise subspace matrix, and to search for the position of the maximum spectral peak in parallel to obtain the arrival direction estimation result.

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