A deep learning assisted subspace plane array DOA estimation method

Abstract

The application discloses a deep learning assisted subspace plane array DOA estimation method, relates to the technical field of satellite navigation and artificial intelligence, and realizes high-precision DOA estimation and anti-interference in a hardware resource limited scene by combining light-weight deep learning and an optimized subspace method. First, a plane array receives a signal and calculates a covariance matrix, then a light-weight CNN-Transformer network is used to perform real-time processing on the covariance matrix, and a joint probability distribution of the elevation angle and the azimuth angle is output to provide a coarse estimation; then, a dynamic weighting strategy is used to enhance the covariance matrix, a fast MUSIC algorithm is executed in a local region guided by deep learning to realize fine DOA estimation; finally, a projection method is used to generate a null in the interference direction while maintaining the gain of the navigation signal direction, and anti-interference beam forming is completed. The application solves the problems of DOA estimation and anti-interference of a small plane array under a low SNR by combining the innovation of deep learning guided subspace search and the projection method beam forming and by synergistic optimization of a hybrid architecture, and has high precision and low resource consumption.

Description

Technical Field

[0001] This invention relates to the fields of satellite navigation technology and artificial intelligence technology, and in particular to a planar array DOA estimation method for deep learning-assisted subspace. Background Technology

[0002] In satellite navigation systems, receivers are susceptible to interference from co-channel or adjacent-channel sources, leading to decreased positioning accuracy or even failure. Traditional direction-of-arrival (DOA) estimation methods (such as MUSIC, ESPRIT, and Capon) are primarily designed for linear arrays, but when applied to planar arrays (such as 2×2 planar arrays), they still face the following key challenges:

[0003] 1. High computational complexity: Linear arrays only require estimation of one-dimensional angle (azimuth φ), while planar arrays require simultaneous estimation of both azimuth φ and elevation θ. The search space changes from linear growth (O(N)) to quadratic growth (O(N)). 2 For example, a global search with a 5° interval requires 6480 computations (72×18), far exceeding the 36 computations required for a linear array (5° interval). Meanwhile, traditional subspace methods (such as MUSIC) rely on the eigenvalue decomposition of the covariance matrix (O(N...). 3 Small arrays (such as 4-element arrays) have lower computational cost, but their performance degrades sharply under low signal-to-noise ratio (SNR).

[0004] 2. Insufficient degrees of freedom in small arrays: 2×2 planar arrays have only 3 degrees of freedom, making it difficult to distinguish between multiple signals or strong interference scenarios, and traditional algorithms are prone to failure. At the same time, the nonlinear coupling of the steering vector of the planar array θ and φ leads to inaccurate null generation in traditional beamforming (such as LCMV).

[0005] 3. Limited anti-interference capability: Traditional methods rely on accurate DOA estimation to guide beamforming, but in low SNR or multipath environments, DOA estimation error will directly reduce the interference suppression effect. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, this invention provides a planar array DOA estimation method with deep learning-assisted subspace. By combining data-driven and traditional models, it achieves efficient DOA estimation and anti-interference for small planar arrays.

[0007] To achieve the above objectives, the present invention adopts the following technical solution, including:

[0008] A planar array DOA estimation method using deep learning-assisted subspaces includes the following steps:

[0009] S1. Perform array signal reception and preprocessing. Through down-conversion, filtering sampling, and space-time data processing, establish a mathematical model of the array signal and separate signal, interference, and noise components.

[0010] S2. Calculate the covariance matrix and extract the spatial statistical characteristics of the signal;

[0011] S3. Perform deep learning DOA coarse estimation, process the real and imaginary parts of the covariance matrix of the planar array through a lightweight neural network, learn the mapping relationship between the spatial features of the signal and the angle domain, and output the discrete probability distribution of the pitch and azimuth angles.

[0012] S4. Dynamically fuse the deep learning DOA coarse estimation result with the traditional subspace method to perform hybrid DOA estimation. Use the angle probability distribution output by the neural network to correct the covariance matrix, enhance the signal subspace components, and execute the MUSIC algorithm to perform fine spectral peak search within the local angle range guided by the coarse estimation. Finally, output the accurate DOA estimate through weighted joint decision.

[0013] S5. To achieve anti-interference beamforming, anti-interference weights are constructed by generating nulls through projection method, forming deep nulls in the interference direction while maintaining navigation signal gain. The covariance matrix is ​​reconstructed by frequency division, and the projection operation core is reused to generate independent beam weights for BeiDou B1 signal and GPS L1 signal respectively, achieving frequency domain interference isolation and finally outputting a clean navigation signal.

[0014] Preferably, step S1 is as follows:

[0015] S11. Receive array signal, the array signal is a high-frequency time-domain signal X. raw The received original high-frequency time-domain signal X is mixed with a mixer. raw Down-convert to intermediate frequency;

[0016] S12, output the intermediate frequency signal X IF [n] performs digital down-conversion to generate the baseband time-domain signal X. BB [n], and use a low-pass filter to suppress the image component;

[0017] S13, Regarding the baseband time-domain signal X BB [n] Perform spatial frequency domain transformation, divide the time domain signal into frames, add Hanning window to reduce spectral leakage, and extract the complex spectrum of the center frequency point of Beidou B1 signal and GPS L1 signal respectively. and Where, k B1 k L1 These are the FFT frequency point indices representing the center frequencies of the BeiDou B1 signal and the GPS L1 signal, respectively, used to extract the complex spectral components of the B1 and L signals; X STFT [·] denotes the complex matrix in the frequency domain after the spatial frequency domain transformation.

[0018] Preferably, step S2 is as follows:

[0019] S21. Based on the complex spectrum of the center frequency point of the BeiDou B1 signal and the GPS L1 signal. and Perform covariance matrix calculation:

[0020]

[0021] Among them, the covariance matrix of BeiDou B1 signal and GPS L1 signal The diagonal elements represent the power of each array element, and the off-diagonal elements represent the cross-correlation between array elements; T represents the number of snapshots, i.e., the number of time samples; the superscript H indicates self-conjugation;

[0022] S22, regarding the covariance matrix R xx Perform diagonal loading correction and add correction items:

[0023] R xx ←R xx +∈I

[0024] ∈=0.01∈tr(R xx )

[0025] Among them, R xx for or tr(R xx ) represents the trace of the matrix, i.e., the sum of the diagonal elements, which represents the total received power; ∈I represents a small diagonal perturbation;

[0026] S23. Perform data normalization on the corrected covariance matrix;

[0027] First, separate the real and virtual components, preserving the phase difference information:

[0028] R stack =[Re(R xx ),Im(R xx )]

[0029] Then normalize to [-1, 1] according to the channels to obtain the covariance matrix tensor R. stack The covariance matrix tensor of BeiDou B1 signal and GPS L1 signal and

[0030] Preferably, step S3 is as follows:

[0031] S31. Based on the normalized covariance matrix tensor R stackA lightweight CNN-Transformer hybrid network is employed. First, a CNN extracts spatial features; then, a Transformer encoder captures global dependencies between array elements. Finally, a fully connected layer outputs a z-dimensional azimuth probability distribution and an n-dimensional pitch probability distribution. The output layer is then normalized using Softmax to generate a discrete probability distribution.

[0032]

[0033] Among them, P θ P is a discrete probability distribution of pitch angle θ∈[0°,90°]; φ Let φ be the discrete probability distribution of the azimuth angle φ∈[0°,360°].

[0034] S32. Calculate the joint probability distribution P. joint :

[0035] P joint (θ k ,φ l ) = P θ (θ k )·P φ (φ l )

[0036] Among them, P joint Let θ be the joint probability distribution of azimuth and elevation angles. k =a·k°(k=0,1,…,n-1),φ l = a·l° (l=0,1,…,z-1); a is the angular division interval;

[0037] S33. Perform candidate DOA extraction to provide initial search points for subsequent refined estimation, and select P. joint The M angle combinations with the highest probability:

[0038] Candidates = {(θ m ,φ m )|m=1,2,3}={(θ1,φ1),(θ2,φ2),(θ3,φ3)}

[0039] Record the corresponding probability value P m =P joint (θ m ,φ m ).

[0040] Preferably, step S4 is performed as follows:

[0041] S41. Based on the deep learning DOA, coarsely estimate the candidate angles and the original / corrected covariance matrix R of the output. xx Calculate the covariance matrix to enhance the weights:

[0042]

[0043] Among them, the enhancement weight α is dynamically adjusted with network confidence and SNR; γ and β are used to adjust the SNR sensitivity; SNR is the signal-to-noise ratio of the input signal;

[0044] S42, Corrected covariance matrix:

[0045]

[0046] Where a(θ,φ) is the guiding vector, R enhanced This is the corrected covariance matrix;

[0047] S43. Perform a local music spectrum search; for R enhanced Perform eigenvalue decomposition R enhanced =UΛU H The eigenvectors corresponding to the smallest eigenvalues ​​are used to construct the noise subspace E. n ;

[0048] S44. In the candidate area Ω={(θ,φ)∣|θ-θ m |≤b,|φ-φ m Calculate the MUSIC spectrum within |≤b}:

[0049]

[0050] Where b represents the set angle range;

[0051] S45. The joint network probability and the MUSIC spectrum are enhanced and fused to generate the final spatial spectrum:

[0052] P final (θ,φ)=k1P joint (θ,φ)+k2P MUSIC (θ,φ)

[0053] Where k1 and k2 are proportionality coefficients; P final (θ,φ) represents the final spatial spectrum;

[0054] S46, By finding P final Obtain accurate DOA estimation by finding the global maximum value. If multiple peaks exist, the second peak is marked as the direction of interference for subsequent beamforming.

[0055] Preferably, the specific process of step S5 is as follows:

[0056] S51. Perform projection-based null trap generation; construct the interference subspace, and combine the steering vectors of the interference direction into matrix U. j :

[0057]

[0058] Where K is the number of interferences, usually K≤3;

[0059] S52. Calculate the orthogonal projection matrix to project the signal onto the orthogonal complement space of the interference subspace to suppress interference. The orthogonal projection matrix... for:

[0060]

[0061] S53. Generate beam weights:

[0062]

[0063] S54. Perform frequency division beamforming of BeiDou B1 signals and GPS L1 signals:

[0064]

[0065] Among them, w B1 w L1 These are the beam weights for the BeiDou B1 signal and the GPS L1 signal, respectively; a B1 (·), a L1 (·) represent the steering vectors of the BeiDou B1 signal and the GPS L1 signal, respectively; X B1 (t), X L1 (t) represents the multi-channel frequency domain signal vectors of the BeiDou B1 signal and the GPS L1 signal after spatial frequency domain transformation and frequency point extraction; through frequency division processing, mutual interference between the BeiDou B1 signal and the GPS L1 signal is avoided, and finally a clean navigation signal y is output. B1 (t) and y L1 (t).

[0066] The present invention also provides a readable storage medium having a computer program stored thereon, which, when executed, implements the aforementioned planar array DOA estimation method for deep learning-assisted subspaces.

[0067] The present invention also provides an electronic device, which includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aforementioned planar array DOA estimation method for deep learning-assisted subspace.

[0068] The present invention also provides a computer program product comprising a computer program / instructions that, when executed by a processor, implement the aforementioned planar array DOA estimation method for a deep learning-assisted subspace.

[0069] The advantages of this invention are:

[0070] (1) This invention provides a planar array DOA estimation method for deep learning-assisted subspace, which achieves efficient DOA estimation and anti-interference for small planar arrays through the collaboration of data-driven and traditional models.

[0071] (2) This invention employs a lightweight CNN-Transformer network to directly regress the joint probability distribution of θ and φ from the covariance matrix, compressing the global search of MUSIC to the Top-3 candidate regions (reducing computational cost by 90%). It also overcomes the performance collapse problem of traditional methods at low SNR (<0dB), significantly improving robustness.

[0072] (3) This invention dynamically corrects the covariance matrix through the probability distribution output by the network, thereby enhancing the signal subspace components and improving the estimation accuracy of the noise subspace. Based on the DOA estimation results, it uses the orthogonal projection method to generate nulls, avoiding the matrix inversion of traditional LCMV (reducing the computational load by 50%), and supports dual-frequency joint processing (BeiDou B1 / GPS L1 isolation). Attached Figure Description

[0073] Figure 1 This is a flowchart of a planar array DOA estimation method for a deep learning-assisted subspace according to the present invention.

[0074] Figure 2 This is an experimental result diagram of the present invention. Detailed Implementation

[0075] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] Depend on Figure 1 and Figure 2 As shown, a planar array DOA estimation method for deep learning-assisted subspace includes the following steps:

[0077] S1. Perform array signal reception and preprocessing. Through down-conversion, filtering sampling, and space-time data processing, establish a mathematical model of the array signal, separate signal, interference, and noise components, and provide high-quality signal input for subsequent deep learning DOA coarse estimation and covariance matrix calculation.

[0078] S2. Calculate the covariance matrix and extract the spatial statistical characteristics of the signal for subsequent DOA estimation.

[0079] S3. Perform deep learning DOA coarse estimation. Process the real and imaginary parts of the covariance matrix of the planar array through a lightweight neural network, learn the complex mapping relationship from the spatial features of the signal to the angle domain, and output the discrete probability distribution of the pitch and azimuth angles; provide initial search points for subsequent fine estimation.

[0080] S4. Dynamically fuse the coarse estimation results of deep learning with the traditional subspace method to perform hybrid DOA estimation; use the angular probability distribution output by the neural network to correct the covariance matrix, enhance the signal subspace components, and execute the MUSIC algorithm within the local angular range guided by the coarse estimation to perform fine spectral peak search. Finally, output high-precision DOA through weighted joint decision.

[0081] S5. To achieve anti-interference beamforming, anti-interference weights are constructed by generating nulls through projection method, forming deep nulls in the interference direction while maintaining navigation signal gain; and by reconstructing the covariance matrix through frequency division, the projection operation core is reused to generate independent beam weights for BeiDou B1 and GPS L1 respectively, achieving frequency domain interference isolation, and finally outputting a clean navigation signal with improved signal-to-noise ratio.

[0082] Step S1 is as follows:

[0083] S11. Based on the input 4-element original time-domain signal (Including noise, interference, and target signal), the original time-domain signal X is first mixed by a mixer. raw Down-converting to intermediate frequency (IF) shifts the received high-frequency signal (such as 1561.098MHz for BeiDou B1 and 1575.42MHz for GPS L1) to the IF for output. This facilitates subsequent digital signal processing.

[0084] S12. Perform digital signal processing, digitally down-convert the output intermediate frequency signal to generate baseband I / Q signals. A low-pass filter with a cutoff frequency of 2MHz is used to suppress image components, and the baseband signal is output after being processed in frames of 1024 points each.

[0085] S13. Perform spatial-frequency transformation (STFT) on the baseband time-domain signal, divide the time-domain signal into frames (256 points per frame, 50% overlap), add a Hanning window to reduce spectral leakage, and extract the complex spectrum of the center frequency point of the BeiDou B1 signal and GPS L1 signal. and To avoid the impact of out-of-band interference on covariance matrix estimation.

[0086] Step S2 is detailed below:

[0087] S21, according to and Perform covariance matrix calculation:

[0088]

[0089] Among them, the covariance matrix of BeiDou B1 signal and GPS L1 signal The diagonal elements represent the power of each array element, and the off-diagonal elements represent the cross-correlation between array elements; T represents the number of snapshots, i.e., the number of time samples; the superscript H represents self-conjugation.

[0090] S22, regarding the covariance matrix R xx ( or Perform diagonal loading correction and add correction items:

[0091] R xx ←R xx +∈I

[0092] ∈=0.01·tr(R xx )

[0093] Where, tr(R) xx ) denotes the trace of the matrix (sum of diagonal elements), representing the total received power; ∈I denotes a small diagonal perturbation, intended to prevent matrix singularities (especially at low SNR), and the diagonally loaded corrected covariance matrix.

[0094] S23. Normalize the corrected covariance matrix by first separating the real and imaginary parts to preserve phase difference information and avoid increasing the training complexity of directly inputting complex numbers into the network.

[0095]

[0096] Normalize to [-1, 1] by channel to obtain the covariance matrix tensor.

[0097] Step S3 is as follows:

[0098] S31. Based on the normalized covariance matrix tensor ( or This study employs a lightweight CNN-Transformer hybrid network. First, three CNN layers extract spatial features. The first 3×3 convolutional layer outputs an 8-channel feature map, which is then expanded to 16 channels by a second convolutional layer after 2×2 pooling. Next, a Transformer encoder captures the global dependencies between array elements. Finally, a fully connected layer outputs a 72-dimensional azimuth probability distribution and an 18-dimensional pitch probability distribution. The output layer is then normalized using Softmax to generate a discrete probability distribution.

[0099]

[0100] Among them, P θ P represents the discrete probability distribution (5° interval) for pitch angles θ ∈ [0°, 90°]. φ Let φ be the discrete probability distribution of the azimuth angle φ∈[0°,360°] (5° interval).

[0101] S32. Calculate the joint probability distribution P. joint :

[0102] P joint (P k ,φ l ) = P θ (θ k )·P φ (φ l )

[0103] Among them, P joint Let θ be the joint probability distribution of azimuth and elevation angles. k =5k° (k=0,1,…,17),φ l =5l° (l=0,1,…,71).

[0104] S33. Perform candidate DOA extraction to provide initial search points for subsequent refined estimation, and select P. joint The M angle combinations with the highest probability (usually M=3):

[0105] Candidates = {(θ m ,φ m )|m=1,2,3}={(θ1,φ1),(θ2,φ2),(θ3,φ3)}

[0106] Record the corresponding probability value P m =P joint (θ m ,φ m ).

[0107] The specific process of step S4 is as follows:

[0108] S41. Based on deep learning, coarsely estimate the candidate angles and the original / corrected covariance matrix R of the output. xx Calculate the covariance matrix to enhance the weights:

[0109]

[0110] Among them, the enhancement weight α is dynamically adjusted with network confidence and SNR, α max=0.3 is the upper limit of the weight; γ=0.5 and β=5 are used to adjust the SNR sensitivity. SNR is the signal-to-noise ratio of the input signal (high SNR reduces prior influence).

[0111] S42, Corrected covariance matrix:

[0112]

[0113] Where a(θ,φ) is the guiding vector.

[0114] S43. Perform a local music spectrum search. First, search R... enhanced Perform eigenvalue decomposition R enhanced =UΛU H The eigenvectors corresponding to the smallest eigenvalues ​​are used to construct the noise subspace E. n =U[:,K:].

[0115] S44. In the candidate area Ω={(θ,φ)∣|θ-θ m |≤10°,|φ-φ m Calculate the MUSIC spectrum within |≤10°}:

[0116]

[0117] S45. The joint network probability and the MUSIC spectrum are enhanced and fused to generate the final spatial spectrum:

[0118] P final (θ,φ)=0.3P joint (θ,φ)+0.7P MUSIC (θ,φ)

[0119] S46, By finding P final Obtain accurate DOA estimation by global maximum value If multiple peaks exist, the second peak is marked as the direction of interference for subsequent beamforming.

[0120] Step S5 is as follows:

[0121] S51. Perform projection-based null trap generation; first, construct the interference subspace, and combine the steering vectors of the interference direction into a matrix:

[0122]

[0123] Where K is the number of interferences, usually K≤3.

[0124] S52. Calculate the orthogonal projection matrix to project the signal onto the orthogonal complement space of the interference subspace to suppress interference. The orthogonal projection matrix is:

[0125]

[0126] S53. Generate beam weights:

[0127]

[0128] The goal is to achieve zero gain in the interference direction (zero-hole depth ≤ -30dB) and maintain unity gain in the signal direction.

[0129] S54. Perform frequency division beamforming of BeiDou B1 signals and GPS L1 signals:

[0130]

[0131] Among them, w B1 w L1 These are the beam weights for the BeiDou B1 signal and the GPS L1 signal, respectively; a B1 (·), a L1 (·) represent the steering vectors of the BeiDou B1 signal and the GPS L1 signal, respectively; X B1 (t), X L1 (t) represents the multi-channel frequency domain signal vectors of the BeiDou B1 signal and the GPS L1 signal after spatial frequency domain transformation and frequency point extraction; through frequency division processing, mutual interference between the BeiDou B1 signal and the GPS L1 signal is avoided, and finally a clean navigation signal y is output. B1 (t), y L1 (t).

[0132] This invention combines lightweight deep learning with optimized subspace methods to achieve high-precision DOA estimation and anti-interference in hardware-restricted scenarios. First, a planar array receives the signal and calculates the covariance matrix. Then, a lightweight CNN-Transformer network is used to process the covariance matrix in real time, outputting the joint probability distribution of pitch and azimuth angles to provide a coarse estimate. Next, a dynamic weighting strategy is employed to enhance the covariance matrix, and a fast MUSIC algorithm is executed within a deep learning-guided local region to achieve refined DOA estimation. Finally, nulls are generated in the interference direction using a projection method while maintaining the gain in the navigation signal direction, completing anti-interference beamforming. This invention innovatively combines deep learning-guided subspace search with projection beamforming, and through hybrid architecture collaborative optimization, solves the challenge of DOA estimation and anti-interference for small planar arrays with low SNR, achieving both high accuracy and low resource consumption.

[0133] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements 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 planar array DOA estimation method for deep learning-assisted subspaces, characterized in that, Includes the following steps: S1. Perform array signal reception and preprocessing. Through down-conversion, filtering sampling, and space-time data processing, establish a mathematical model of the array signal and separate signal, interference, and noise components. S2. Calculate the covariance matrix and extract the spatial statistical characteristics of the signal; S3. Perform deep learning DOA coarse estimation, process the real and imaginary parts of the covariance matrix of the planar array through a lightweight neural network, learn the mapping relationship between the spatial features of the signal and the angle domain, and output the discrete probability distribution of the pitch and azimuth angles. S4. Dynamically fuse the deep learning DOA coarse estimation result with the traditional subspace method to perform hybrid DOA estimation. Use the angle probability distribution output by the neural network to correct the covariance matrix, enhance the signal subspace components, and execute the MUSIC algorithm to perform fine spectral peak search within the local angle range guided by the coarse estimation. Finally, output the accurate DOA estimate through weighted joint decision. S5. To achieve anti-interference beamforming, anti-interference weights are constructed by generating nulls through projection method, forming deep nulls in the interference direction while maintaining navigation signal gain. The covariance matrix is ​​reconstructed by frequency division, and the projection operation core is reused to generate independent beam weights for BeiDou B1 signal and GPS L1 signal respectively, achieving frequency domain interference isolation and finally outputting a clean navigation signal.

2. The planar array DOA estimation method for deep learning auxiliary subspace according to claim 1, characterized in that, Step S1 is as follows: S11. Receive array signal, the array signal is a high-frequency time-domain signal X. raw The received original high-frequency time-domain signal X is mixed with a mixer. raw Down-convert to intermediate frequency; S12, output the intermediate frequency signal X IF [n] performs digital down-conversion to generate the baseband time-domain signal X. BB [n], and use a low-pass filter to suppress the image component; S13, Regarding the baseband time-domain signal X BB [n] Perform spatial frequency domain transformation, divide the time domain signal into frames, add Hanning window to reduce spectral leakage, and extract the complex spectrum of the center frequency point of Beidou B1 signal and GPS L1 signal respectively. and Where, k B1 k L1 These are the FFT frequency point indices representing the center frequencies of the BeiDou B1 signal and the GPS L1 signal, respectively, used to extract the complex spectral components of the B1 and L signals; X STFT [·] denotes the complex matrix in the frequency domain after the spatial frequency domain transformation.

3. The planar array DOA estimation method for deep learning auxiliary subspace according to claim 2, characterized in that, Step S2 is detailed below: S21. Based on the complex spectrum of the center frequency point of the BeiDou B1 signal and the GPS L1 signal. and Perform covariance matrix calculation: Among them, the covariance matrix of BeiDou B1 signal and GPS L1 signal The diagonal elements represent the power of each array element, and the off-diagonal elements represent the cross-correlation between array elements; T represents the number of snapshots, i.e., the number of time samples; the superscript H indicates self-conjugation; S22, regarding the covariance matrix R xx Perform diagonal loading correction and add correction items: R xx ←R xx +∈I ∈=0.01·tr(R xx ) Among them, R xx for or tr(R xx ) represents the trace of the matrix, i.e., the sum of the diagonal elements, which represents the total received power; ∈I represents a small diagonal perturbation; S23. Perform data normalization on the corrected covariance matrix; First, separate the real and virtual components, preserving the phase difference information: R stack =[Re(R xx ),Im(R xx )] Then normalize to [-1, 1] according to the channels to obtain the covariance matrix tensor R. stack The covariance matrix tensor of BeiDou B1 signal and GPS L1 signal and 4. The planar array DOA estimation method for deep learning auxiliary subspace according to claim 3, characterized in that, Step S3 is detailed below: S31. Based on the normalized covariance matrix tensor R stack A lightweight CNN-Transformer hybrid network is used, first extracting spatial features through a CNN; then... The Transformer encoder captures the global dependencies between array elements, and the fully connected layer outputs the z-dimensional azimuth probability distribution and the n-dimensional pitch probability distribution. After Softmax normalization, the output layer generates a discrete probability distribution. Among them, P θ P is a discrete probability distribution of pitch angle θ∈[0°,90°]; φ Let φ be the discrete probability distribution of the azimuth angle φ∈[0°,360°]. S32. Calculate the joint probability distribution P. joint : P joint (i k ,f l )=P θ (i k )·P φ (f l ) Among them, P joint Let θ be the joint probability distribution of azimuth and elevation angles. k =a·k°(k=0,1,…,n-1),φ l = a·l° (l=0,1,…,z-1); a is the angular interval; S33. Perform candidate DOA extraction to provide initial search points for subsequent refined estimation, and select P. joint The M angle combinations with the highest probability: Candidates={(θ m ,f m )|m=1,2,3}={(θ1,φ1),(θ2,φ2),(θ3,φ3)} Record the corresponding probability value P m =P joint (θ m ,φ m ).

5. The planar array DOA estimation method for a deep learning-assisted subspace according to claim 4, characterized in that, The specific process of step S4 is as follows: S41. Based on the deep learning DOA, coarsely estimate the candidate angles and the original / corrected covariance matrix R of the output. xx Calculate the covariance matrix to enhance the weights: Among them, the enhancement weight α is dynamically adjusted with network confidence and SNR; γ and β are used to adjust the SNR sensitivity; SNR is the signal-to-noise ratio of the input signal; S42, Corrected covariance matrix: Where a(θ,φ) is the guiding vector, R enhanced This is the corrected covariance matrix; S43. Perform a local music spectrum search; for R enhanced Perform eigenvalue decomposition R enhanced =UΛU H The eigenvectors corresponding to the smallest eigenvalues ​​are used to construct the noise subspace E. n ; S44. In the candidate area Ω={(θ,φ)∣|θ-θ m |≤b,|φ-φ m Calculate the MUSIC spectrum within |≤b}: Where b represents the set angle range; S45. The joint network probability and the MUSIC spectrum are enhanced and fused to generate the final spatial spectrum: P final (θ,φ)=k1P joint (θ,φ)+k2P MUSIC (i,f) Where k1 and k2 are proportionality coefficients; P final (θ,φ) represents the final spatial spectrum; S46, By finding P final Obtain accurate DOA estimation by finding the global maximum value. If multiple peaks exist, the second peak is marked as the direction of interference for subsequent beamforming.

6. The planar array DOA estimation method for a deep learning-assisted subspace according to claim 5, characterized in that, The specific process of step S5 is as follows: S51. Perform projection-based null trap generation; construct the interference subspace, and combine the steering vectors of the interference direction into matrix U. j : Where K is the number of interferences, usually K≤3; S52. Calculate the orthogonal projection matrix to project the signal onto the orthogonal complement space of the interference subspace to suppress interference. The orthogonal projection matrix... for: S53. Generate beam weights: S54. Perform frequency division beamforming of BeiDou B1 signals and GPS L1 signals: Among them, w B1 w L1 These are the beam weights for the BeiDou B1 signal and the GPS L1 signal, respectively; a B1 (·), a L1 (·) represent the steering vectors of the BeiDou B1 signal and the GPS L1 signal, respectively; X B1 (t), X L1 (t) represents the multi-channel frequency domain signal vectors of the BeiDou B1 signal and the GPS L1 signal after spatial frequency domain transformation and frequency point extraction; through frequency division processing, mutual interference between the BeiDou B1 signal and the GPS L1 signal is avoided, and finally a clean navigation signal y is output. B1 (t) and y L1 (t).

7. A readable storage medium, characterized in that, It stores a computer program, which, when executed, implements a planar array DOA estimation method for a deep learning auxiliary subspace as described in any one of claims 1 to 6.

8. An electronic device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a planar array DOA estimation method for a deep learning auxiliary subspace as described in any one of claims 1 to 6.

9. A computer program product, characterized in that, It includes a computer program / instruction that, when executed by a processor, implements a planar array DOA estimation method for a deep learning-assisted subspace as described in any one of claims 1 to 6.

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