High-resolution speed and angle measurement method based on frequency domain dimensionality reduction sparse Bayesian algorithm

Abstract

The invention discloses a high-resolution speed and angle measurement method based on a frequency domain dimensionality reduction sparse Bayesian algorithm. The method is suitable for radar signal processing under a two-dimensional uniform rectangular array (URA) system. According to the method, the local continuous frequency domain feature matrixes are constructed in the azimuth dimension and the Doppler dimension respectively, the dimension reduction matrix is generated through feature decomposition, and bidirectional frequency domain dimension reduction of original observation data is achieved; and combining a sparse Bayesian learning (SBL) algorithm to carry out two-dimensional sparse spectrum reconstruction on the observation signal after dimension reduction so as to obtain an accurate and high-resolution angle and speed joint estimation result. According to the method, a mode of combining frequency domain dimension reduction and Bayesian sparse reconstruction is adopted, excellent super-resolution capability and anti-noise performance can be kept while the calculation complexity can be remarkably reduced, and the method is particularly suitable for speed and angle measurement scenes with dense group targets and low signal-to-noise ratio.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of radar signal processing, in particular to a high-resolution velocity and angle measurement method based on a frequency domain dimension reduction sparse Bayesian algorithm. BACKGROUND

[0002] With the rapid development of phased array radars and multi-channel receiving technology, the target detection and parameter estimation capability of radar systems in complex electromagnetic environments has been significantly improved. However, when the radar faces a dense group target scene, the angle and velocity spectrum components of multiple targets overlap with each other, and the traditional two-dimensional spectrum estimation method has significant deficiencies in resolution, robustness and computational efficiency.

[0003] Under the coherent signal model, the conventional radar angle-velocity joint estimation generally adopts a two-dimensional fast Fourier transform (2D-FFT) or a two-dimensional multiple signal classification (2D-MUSIC) algorithm. The frequency domain grid of the two-dimensional FFT is fixed, and it is difficult to obtain sub-resolution accuracy. Although the MUSIC algorithm has super-resolution performance, it needs to accurately estimate the signal and noise subspace, and when the signal-to-noise ratio is low or the number of snapshots is small, the precision of the eigenvalue decomposition of the covariance matrix decreases, which easily causes false peaks and estimation deviation. When the number of targets is large or the angle distribution is dense, the peak search complexity of MUSIC increases sharply, and the spectral leakage problem makes the spectral overlap between group targets more serious, which further leads to the fact that MUSIC cannot accurately estimate the azimuth angle and velocity of the group target scene. SUMMARY

[0004] The purpose of the present application is to provide a high-resolution velocity and angle measurement method based on a frequency domain dimension reduction sparse Bayesian algorithm to solve the problem that MUSIC cannot accurately estimate the azimuth angle and velocity of the target.

[0005] The technical scheme adopted by the present application to solve the above technical problems is:

[0006] The high-resolution velocity and angle measurement method based on the frequency domain dimension reduction sparse Bayesian algorithm comprises the following steps:

[0007] Step 1: Obtain the radar echo signal, select the strongest distance unit in the radar echo signal according to the amplitude, then obtain the array instantaneous output of the distance unit, i.e. the snapshot matrix, and finally perform bidirectional projection on the snapshot matrix to obtain the reduced dimension matrix;

[0008] Step 2: Use the reduced dimension matrix to construct an observation model, and use the observation model to obtain a sparse coefficient vector and a noise vector ;

[0009] Step 3: Based on the sparse coefficient vector and the noise vector Two-dimensional sparse estimation is obtained through the sparse Bayesian learning algorithm. That is, a local two-dimensional spectrum;

[0010] Step 4: Obtain the two-dimensional spectral power using the local two-dimensional spectrum ;

[0011] Step 5: Based on two-dimensional spectral power The global power spectrum is obtained. ;

[0012] Step 6: In the global power spectrum Non-maximum suppression and quadratic fitting are performed to obtain the target peak. Finally, based on the target peak point Obtaining the angle With speed .

[0013] Furthermore, the dimension-reduced matrix is ​​represented as follows:

[0014] ,

[0015] in, For snapshot matrix, For a space dimension reduction matrix, This is a Doppler dimension-reduced matrix.

[0016] Furthermore, the spatial dimension reduction matrix It is obtained through the following steps:

[0017] In the spatial domain, i.e., the azimuth dimension, a local continuous frequency domain feature matrix is ​​established. :

[0018] ,

[0019] in, ;

[0020] For local continuous frequency domain characteristic matrix Performing eigenvalue decomposition yields:

[0021] ,

[0022] Pick forward Each component forms a dimensionless matrix:

[0023] ,

[0024] in, For local spatial frequency range, and These are the row and column indices in the matrix, respectively. is the normalized spatial frequency for the incident target azimuth angle , is the inter-element spacing, is the eigenvector matrix after eigen-decomposition, is the eigenvalue diagonal matrix after eigen-decomposition.

[0025] Further, the Doppler dimension reduction matrix is obtained by the following steps:

[0026] establishing an eigen-matrix in the Doppler frequency dimension :

[0027] ,

[0028] where ;

[0029] eigen-decomposing the eigen-matrix to obtain:

[0030] ,

[0031] taking the first components to form a dimension reduction matrix:

[0032] ,

[0033] where is the local frequency range, is the eigenvector matrix after eigen-decomposition, is the eigenvalue diagonal matrix after eigen-decomposition.

[0034] Further, the observation model is expressed as:

[0035] ,

[0036] ,

[0037] ,

[0038] ,

[0039] ,

[0040] In and , , ​

[0041] ,

[0042] ,

[0043] exist and middle, ,

[0044] ,

[0045] in, and These are spatial dimension and Doppler dimension global dictionaries, respectively. For the first The normalized Doppler frequency of each target. For the first Normalized spatial frequency of each target For the number of array elements, For the number of snapshots, , These are the azimuth and Doppler frequency points, respectively. For the dimensionality reduction of the orientation dimension dictionary and This is the normalized Doppler frequency dimension dictionary after dimensionality reduction. The wavelength is the signal wavelength.

[0046] Furthermore, the specific steps of step 3 are as follows:

[0047] based on and This yields a sparse Bayesian framework, represented as:

[0048] ,

[0049] ,

[0050] Initialize hyperparameters ,

[0051] , For the dictionary matrix D, the first... List, for The A quick snapshot, It is the identity matrix;

[0052] Iteration is represented as:

[0053] ,

[0054] ,

[0055] ,

[0056] ,

[0057] ,

[0058] ,

[0059] in, For the first The two-dimensional sparse estimate obtained in the second iteration It is a small constant. For noise variance, and As an intermediate variable, These are prior parameters. No. Intermediate variables obtained from the next iteration;

[0060] The convergence condition for the iteration is:

[0061] The maximum number of iterations set has been reached, or ;

[0062] =[ ],

[0063] in, It is a positive number. =0.001,

[0064] After convergence, a two-dimensional sparse estimate is obtained. That is, a local two-dimensional spectrum.

[0065] Furthermore, the two-dimensional spectral power Represented as:

[0066] ,

[0067] in, This indicates that the vector will be re-traced. The matrix.

[0068] Furthermore, the global power spectrum Represented as:

[0069] ,

[0070] ,

[0071] ,

[0072] in, To smoothly splice weights, Spatial weights, For frequency weights, For weight parameters, The azimuth length of the tile. Doppler is the tile length. To normalize the Doppler frequency, For the first Normalized spatial frequency at the center of each tile, For the first Normalized Doppler frequency at the center of each tile.

[0073] Furthermore, the angle Represented as:

[0074] ,

[0075] in, This is the predicted normalized spatial frequency.

[0076] Furthermore, the speed Represented as:

[0077] ,

[0078] in, For the predicted normalized Doppler frequency, The sampling frequency.

[0079] The beneficial effects of this invention are:

[0080] This application applies to radar signal processing in a two-dimensional uniform rectangular array (URA) system. It constructs local continuous frequency domain feature matrices in both the azimuth and Doppler dimensions, and generates a dimensionality reduction matrix using eigenvalue decomposition, achieving bidirectional frequency domain dimensionality reduction of the original observation data. Then, it combines this with the Sparse Bayesian Learning (SBL) algorithm to perform two-dimensional sparse spectrum reconstruction on the dimensionality-reduced observation signal, thereby obtaining accurate and high-resolution joint angle and velocity estimation results. This application employs a combination of frequency domain dimensionality reduction and Bayesian sparse reconstruction, which can significantly reduce computational complexity while maintaining excellent super-resolution capability and noise resistance, making it particularly suitable for velocity and angle measurement scenarios with dense target groups and low signal-to-noise ratios. Attached Figure Description

[0081] Figure 1 This is a flowchart of the offline process in the embodiment;

[0082] Figure 2 This is a flowchart of the online process in the embodiment;

[0083] Figure 3 This is a diagram showing the result of the technical solution in this application. Detailed Implementation

[0084] It should be noted that, where there is no conflict, the various embodiments disclosed in this application can be combined with each other.

[0085] Specific Implementation Method 1: The high-resolution velocity and angle measurement method based on frequency domain dimensionality reduction sparse Bayesian algorithm described in this implementation method includes the following steps:

[0086] Step 1: Acquire radar echo signals and select the strongest range cell in the radar echo signals based on the amplitude. Then, acquire the instantaneous array output of the range cell, i.e., the snapshot matrix. Finally, perform bidirectional projection on the snapshot matrix to obtain the dimension-reduced matrix.

[0087] Step 2: Construct an observation model using the dimensionality reduction matrix, and obtain the sparse coefficient vector using the observation model. and noise vector ;

[0088] Step 3: Based on sparse coefficient vector and noise vector Two-dimensional sparse estimation is obtained through the sparse Bayesian learning algorithm. That is, a local two-dimensional spectrum;

[0089] Step 4: Obtain the two-dimensional spectral power using the local two-dimensional spectrum ;

[0090] Step 5: Based on two-dimensional spectral power The global power spectrum is obtained. ;

[0091] Step 6: In the global power spectrum Non-maximum suppression and quadratic fitting are performed to obtain the target peak. Finally, based on the target peak point Obtaining the angle With speed .

[0092] This application constructs a two-dimensional reduced-dimensional observation matrix by performing local continuous frequency domain dimensionality reduction on the directional dimension and Doppler dimension under a two-dimensional uniform rectangular array (URA), and then uses the sparse Bayesian learning (SBL) algorithm to achieve high-precision sparse reconstruction of the target spectrum, thereby realizing high-resolution velocity and angle measurement of group targets.

[0093] Compared with existing sparse Bayesian processing methods based on one-dimensional frequency domain dimensionality reduction, this application has the following significant innovations in algorithm system and implementation structure:

[0094] 1. Two-dimensional joint dimensionality reduction structure: This application is the first to construct locally continuous frequency feature matrices in both the spatial and Doppler frequency domains, and obtain a two-dimensional dimensionality reduction matrix through eigenvalue decomposition, achieving joint dimensionality reduction in the spatial and frequency domains. This structure significantly reduces dimensionality while preserving the main lobe energy.

[0095] 2. Local feature modeling in continuous integral form: by defining Continuous frequency integration interval (width) This method constructs a smooth local feature correlation matrix to achieve frequency domain smoothing and energy concentration. Unlike discrete sampling dimensionality reduction methods, this approach effectively suppresses spectral leakage and numerical oscillations.

[0096] 3. Two-dimensional sparse Bayesian reconstruction: Utilizing a joint dictionary with a two-dimensional Kronecker structure, an improved multi-observation vector fast sparse Bayesian (NFSBL-MMV) algorithm is employed to directly reconstruct the target spectrum in the two-dimensional parameter space. This avoids the problem that the peak search complexity of MUSIC increases sharply when the number of targets is large or the angle distribution is dense, and that the spectral leakage problem makes the spectral overlap between group targets more severe. This achieves higher accuracy in azimuth and velocity estimation.

[0097] 4. Tile-based Gaussian weighted smooth stitching: To ensure the continuity and stability of the global spectrum, this invention proposes a tile-based smooth stitching method based on two-dimensional Gaussian weights. The weighting function is taken as... The center weight is approximately 0.78, and the edge weight decays to 0.002. This mechanism eliminates spurious peaks at tile boundaries, ensuring the continuity of the group target spectrum.

[0098] In its implementation, the method described in this application consists of offline and online steps.

[0099] The offline steps are as follows, and the flowchart is shown below. Figure 1 As shown:

[0100] Step 1: Establish the URA array signal receiving model;

[0101] Let the array be Two-dimensional uniform rectangle (URA) with element spacing of 1. The signal wavelength is Then the first The normalized spatial location of the element is:

[0102] (1)

[0103] Define the azimuth angle of the incident target. Its normalized spatial frequency is:

[0104] (2)

[0105] For the The target has the following normalized Doppler frequencies:

[0106] (3)

[0107] in This is the actual Doppler frequency. The sampling frequency is equal to the pulse repetition frequency (PRF), which is set to 1000Hz in the simulation.

[0108] Then the target The space-time steering vector is:

[0109] (4)

[0110] in:

[0111] ,

[0112] (5)

[0113] This is the Kronecker product.

[0114] Step 2: Establishing the spatial domain feature matrix;

[0115] To achieve dimensionality compression without losing key spectral features, a local continuous frequency domain feature matrix is ​​established in the spatial domain (azimuth dimension):

[0116] (6)

[0117] in For local spatial frequency range, .

[0118] Step 3: Establishing the velocity dimension feature matrix;

[0119] Similarly, establish the characteristic matrix in the Doppler frequency dimension:

[0120] (7)

[0121] Step 4: Eigenvalue decomposition and dimensionality reduction matrix generation;

[0122] Perform eigenvalue decomposition on equations (6) and (7) respectively:

[0123] (8)

[0124] Take the first corresponding feature vector One portion, This forms a dimension-reduced matrix:

[0125] (9)

[0126] This dimensionality reduction matrix satisfies energy concentration and orthogonality, and can preserve the target main lobe energy while reducing dimensionality.

[0127] Step 5: Generate the global dictionary matrix;

[0128] Uniform sampling across the entire spatial and velocity domains yields the original dictionary:

[0129] (10)

[0130] The online steps are as follows, and the flowchart is shown below. Figure 2 As shown:

[0131] Step 1: Tensorization and dimensionality reduction projection of the received signal;

[0132] The radar echo signal is acquired, and the range cell with the strongest echo is selected based on the amplitude. The instantaneous array output of this range cell is then acquired, i.e., the snapshot matrix. The dimension-reduced matrix is ​​obtained by bidirectional projection through left and right multiplication of the dimension-reducing matrix:

[0133] (11)

[0134] This formula is equivalent to projecting the spatial and velocity dimensions onto a lower-dimensional energy subspace, respectively.

[0135] Step 2: Two-dimensional sparse observation model;

[0136] Based on the dimensionality reduction matrix The observation model is constructed as follows:

[0137] (12)

[0138] in:

[0139] (13)

[0140] is a sparse coefficient vector, representing the sparse distribution of the azimuth-velocity two-dimensional spectrum.

[0141] Step 3: Solve using the Sparse Bayesian Learning (SBL) algorithm;

[0142] Based on s and Employing a sparse Bayesian framework:

[0143] (14)

[0144] in Initialize hyperparameters:

[0145] .

[0146] The iterative update formula is:

[0147] (15)

[0148] (16)

[0149] in , Small constants (e.g.) ), =[ The convergence condition of the algorithm is:

[0150] The maximum number of iterations set (maxiter) has been reached.

[0151] , It is a very small positive number, usually set to 0.001.

[0152] Finally, a two-dimensional sparse estimate is obtained. That is, a local two-dimensional spectrum. These are the azimuth and Doppler frequency points, respectively. .

[0153] Step 4: Two-dimensional spectrum generation and splicing;

[0154] Obtain the posterior mean Then, calculate the two-dimensional spectral power:

[0155] (17)

[0156] To ensure continuity across the entire domain, the azimuth and velocity dimensions are tiled with a fixed step size and Gaussian weights are applied. Average the splicing of each tile:

[0157] (18)

[0158] in Indicates the weight for smooth splicing:

[0159] (19)

[0160] in These are the weighted parameters, azimuth dimension and Doppler tile length, respectively, and the subscripts are... To indicate different types of tiles.

[0161] .

[0162] Step 5: Peak detection and subpixel interpolation;

[0163] In the global power spectrum Perform non-maximum suppression (NMS) and quadratic fitting to obtain the target peak. And convert them into angle and velocity:

[0164] (20)

[0165] 1. Significantly improved resolution: In near-neighbor scenarios with group targets, the algorithm proposed in this invention can separate targets with an azimuth difference of 0.8° and a velocity difference of 0.02. The resolution is improved by approximately 8dB compared to 2D-FFT and approximately 5dB compared to 2D-MUSIC.

[0166] 2. High computational efficiency: The projection matrix constructed by the local continuous frequency domain feature matrix compresses the original spatial / temporal dimension data into the principal energy subspace, with a computational cost of only about 0.3% of the original SBL.

[0167] Method Azimuth resolution Velocity resolution (normalized) FFT 5° 1.6 MUSIC 3° 0.1 Proposed method 0.8° 0.02

[0168] Table 1 Comparison of resolution of different algorithms

[0169] Method Average per estimation run time (s) SBL 2586.156 Proposed method 7.758

[0170] Table 2 Comparison of actual algorithm running time

[0171] It should be noted that the specific embodiments are merely explanations and illustrations of the technical solution of the present invention and should not be used to limit the scope of protection. Any modifications made in accordance with the claims and specification of the present invention that are only partial should still fall within the protection scope of the present invention.

Claims

1. A high-resolution velocity and direction finding method based on frequency domain dimensionality reduction sparse Bayesian algorithm, characterized in that The method comprises the following steps: Step 1: obtaining a radar echo signal, selecting a strongest distance unit in the radar echo signal according to an amplitude, obtaining an array instantaneous output of the distance unit, i.e., a snapshot matrix, and performing bidirectional projection on the snapshot matrix to obtain a reduced-dimension matrix; Step 2: Construct the observation model using the dimension reduction matrix, and obtain the sparse coefficient vector using the observation model and the noise vector ; Step 3: Based on the sparse coefficient vector and the noise vector , obtain a two-dimensional sparse estimate , i.e., a local two-dimensional spectrum; Step 4: Obtain 2D spectrum power using local 2D spectrum ; Step 5: Two-dimensional spectrum-based power , resulting in a global power spectrum ; Step 6: Non-maximum suppression and quadratic fitting are performed on the global power spectrum to obtain the target peak point to obtain the angleand the speed.​ 2. The high resolution RATA method based on frequency domain dimensionality reduction sparse Bayesian algorithm according to claim 1, characterized in that The reduced-dimension matrix is represented as: ， wherein, is a fast-scan matrix, is a spatial dimension reduction matrix, is a Doppler dimension reduction matrix.

3. The high resolution RATA method based on frequency domain dimensionality reduction sparse Bayesian algorithm according to claim 2, characterized in that the spatial dimension reduction matrix by the following steps: In the spatial domain, i.e. azimuth dimension, a locally continuous frequency domain feature matrix is established : ， wherein ; Local continuous frequency domain feature matrix Eigen decomposition is performed to obtain: ， Take The components, forming a dimension reduction matrix: ， wherein, is the local spatial frequency range, and are the row and column indices in the matrix, respectively, is the incident target azimuth angle is the normalized spatial frequency, is the inter-element spacing, is is the eigenvector matrix after eigen-decomposition, is is the diagonal matrix of eigenvalues after eigen-decomposition.

4. The high resolution RATA method based on frequency domain dimensionality reduction sparse Bayesian algorithm according to claim 3, characterized in that The Doppler dimension reduction matrix was obtained by the following steps: Establishing a feature matrix in the doppler frequency dimension : ， wherein ; Eigenmatrix The eigenmatrix is obtained by performing an eigen decomposition ， Take The components, forming a reduced dimension matrix: ， wherein, is a local frequency range, is is a matrix of eigenvectors after eigen decomposition, is is a diagonal matrix of eigenvalues after eigen decomposition.

5. The high resolution RATA method based on frequency domain dimensionality reduction sparse Bayesian algorithm according to claim 4, characterized in that The observation model is represented as: ， ， ， ， ， In and , , ， ， In and , , ， wherein, and are spatial and Doppler domain dictionaries, respectively, is the normalized Doppler frequency of the th target, is the normalized spatial frequency of the th target, is the number of array elements, is the number of snapshots, , are azimuth and Doppler frequency points, respectively, is the azimuth domain dictionary after dimension reduction and is the normalized Doppler frequency domain dictionary after dimension reduction, is the signal wavelength.

6. The high resolution direction finding method based on frequency domain dimensionality reduction sparse Bayesian algorithm according to claim 5, characterized in that The specific steps of the step 3 are: Based on and , the sparse Bayesian framework is obtained, denoted as: ， ， Initializing hyperparameters , , is the jth column of the dictionary matrix D, is the jth column of the dictionary matrix D, is the jth column of the dictionary matrix D, is the jth column of the dictionary matrix D,​​ The iteration is represented as: ， ， ， ， ， ， wherein is the first iteration of the two-dimensional sparse estimate, is the second iteration of the two-dimensional sparse estimate, is a small constant, is the noise variance, and is an intermediate variable, is a prior parameter, is the first iteration of the intermediate variable, is the second iteration of the intermediate variable; The iteration convergence condition is: reaching a set maximum number of iterations, or ; =[ ]， wherein is positive, = 0.001, After convergence, we obtain a two-dimensional sparse estimate i.e., a local two-dimensional spectrum.

7. The high resolution RATA method based on frequency domain dimensionality reduction sparse Bayesian algorithm according to claim 6, characterized in that The two-dimensional spectrum power is represented as: ， wherein, represents a reshaping of the vector into a matrix.

8. The high resolution RATA method based on frequency domain dimensionality reduction sparse Bayesian algorithm according to claim 7, characterized in that The global power spectrum is represented as: ， ， ， wherein, is a smoothing stitching weight, is a spatial weight, is a frequency weight, is a weight parameter, is an azimuthal dimension tile length, is a Doppler dimension tile length, is a normalized Doppler frequency, is a normalized spatial frequency for a center position of a th tile, is a normalized Doppler frequency for a center position of a th tile.

9. The high resolution direction finding method based on frequency domain dimensionality reduction sparse Bayesian algorithm according to claim 8, characterized in that The angle is represented as: ， wherein, is the predicted normalized spatial frequency.

10. The high resolution direction finding method based on frequency domain dimensionality reduction sparse Bayesian algorithm according to claim 9, characterized in that The speed is expressed as: ， wherein, is the normalized Doppler frequency, is the sampling frequency.

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