High-resolution velocity and direction finding method based on frequency domain dimension reduction sparse bayesian algorithm
By employing a frequency-domain dimensionality reduction sparse Bayesian algorithm in radar signal processing, constructing a local continuous frequency-domain feature matrix, and combining it with a sparse Bayesian learning algorithm, the problem of accuracy in estimating azimuth angle and velocity in dense target scenarios is solved, achieving high-resolution angle and velocity estimation, reducing computational complexity, and improving estimation accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HARBIN INST OF TECH
- Filing Date
- 2025-12-11
- Publication Date
- 2026-06-30
AI Technical Summary
Traditional two-dimensional spectrum estimation methods struggle to accurately estimate the azimuth and velocity of targets in densely packed scenarios, especially at low signal-to-noise ratios or with a small number of snapshots. The MUSIC algorithm suffers from high peak search complexity and severe spectral leakage, leading to estimation shifts and overlaps.
A high-resolution velocity and angle measurement method based on frequency domain dimensionality reduction sparse Bayesian algorithm is adopted. By constructing local continuous frequency domain feature matrices in the azimuth dimension and Doppler dimension respectively, two-dimensional sparse spectrum reconstruction is performed using sparse Bayesian learning algorithm, and tile-type Gaussian weighted smooth stitching is combined to achieve high-resolution angle and velocity estimation.
While significantly reducing computational complexity, it maintains high resolution and noise resistance, and can accurately estimate the azimuth and velocity of a group of targets, making it particularly suitable for scenarios with dense groups of targets and low signal-to-noise ratio.
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Figure CN121679514B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of radar signal processing technology, specifically a high-resolution velocity and angle measurement method based on a frequency-domain dimensionality-reduced sparse Bayesian algorithm. Background Technology
[0002] With the rapid development of phased array radar and multi-channel receiving technology, the target detection and parameter estimation capabilities of radar systems in complex electromagnetic environments have been significantly improved. However, when radar faces densely packed target scenarios, the angle and velocity spectrum components of multiple targets overlap, and traditional two-dimensional spectrum estimation methods have significant shortcomings in terms of resolution, robustness, and computational efficiency.
[0003] In coherent signal models, conventional radar angle-velocity joint estimation typically employs two-dimensional Fast Fourier Transform (2D-FFT) or two-dimensional MUSIC (2D-Multiple Signal Classification) algorithms. The fixed frequency domain grid of 2D FFT makes it difficult to achieve sub-resolution accuracy. While MUSIC algorithms offer super-resolution performance, they require precise estimation of the signal and noise subspaces. Furthermore, at low signal-to-noise ratios or with a small number of snapshots, the eigenvalue decomposition accuracy of the covariance matrix decreases, easily leading to spurious peaks and estimation shifts. When the number of targets is large or the angular distribution is dense, the peak search complexity of MUSIC increases dramatically, and spectral leakage further exacerbates spectral overlap among group targets, resulting in MUSIC's inability to accurately estimate the target's azimuth and velocity in group target scenarios. Summary of the Invention
[0004] The purpose of this invention is to provide a high-resolution velocity and angle measurement method based on a frequency domain dimensionality reduction sparse Bayesian algorithm to address the problem that MUSIC cannot accurately estimate the azimuth and velocity of a target.
[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:
[0006] A high-resolution velocity and angle measurement method based on frequency domain dimensionality reduction sparse Bayesian algorithm includes the following steps:
[0007] 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.
[0008] Step 2: Construct an observation model using the dimensionality reduction matrix, and obtain the sparse coefficient vector using the observation model. and noise vector ;
[0009] 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;
[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. azimuth of the incident target Normalized spatial frequency, For the spacing between array elements, for The eigenvector matrix after eigenvalue decomposition for The diagonal matrix of eigenvalues after eigenvalue decomposition.
[0025] Furthermore, the Doppler dimension reduction matrix It is obtained through the following steps:
[0026] Establish the characteristic matrix in the Doppler frequency dimension. :
[0027] ,
[0028] in, ;
[0029] For the characteristic matrix Performing eigenvalue decomposition yields:
[0030] ,
[0031] Pick forward Each component forms a dimensionless matrix:
[0032] ,
[0033] in, For local frequency range, for The eigenvector matrix after eigenvalue decomposition for The diagonal matrix of eigenvalues after eigenvalue decomposition.
[0034] Furthermore, the observation model is expressed as:
[0035] ,
[0036] ,
[0037] ,
[0038] ,
[0039] ,
[0040] exist and middle, ,
[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 next 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 reception 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 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 Speed resolution (normalized) FFT 5° 1.6 MUSIC 3° 0.1 The proposed method 0.8° 0.02
[0168] Table 1 Comparison of resolution of different algorithms
[0169] method Average estimated runtime (s) SBL 2586.156 The 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 angle measurement method based on frequency domain dimensionality reduction sparse Bayesian algorithm, characterized in that... Includes the following steps: 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. Step 2: Construct an observation model using the dimensionality reduction matrix, and obtain the sparse coefficient vector using the observation model. and noise vector ; 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; Step 4: Obtain the two-dimensional spectral power using the local two-dimensional spectrum ; Step 5: Based on two-dimensional spectral power The global power spectrum is obtained. ; 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 ; The reduced-dimensional matrix is represented as follows: ， in, For snapshot matrix, For a space dimension reduction matrix, The dimension reduction matrix is the Doppler dimension. The spatial dimension reduction matrix It is obtained through the following steps: In the spatial domain, i.e., the azimuth dimension, a local continuous frequency domain feature matrix is established. : ， in, ; For local continuous frequency domain characteristic matrix Performing eigenvalue decomposition yields: ， Pick forward Each component forms a dimensionless matrix: ， in, For local spatial frequency range, and These are the row and column indices in the matrix, respectively. azimuth of the incident target Normalized spatial frequency, For the spacing between array elements, for The eigenvector matrix after eigenvalue decomposition for The eigenvalue diagonal matrix after eigenvalue decomposition; The Doppler dimension reduction matrix It is obtained through the following steps: Establish the characteristic matrix in the Doppler frequency dimension. : ， in, ; For the characteristic matrix Performing eigenvalue decomposition yields: ， Pick forward Each component forms a dimensionless matrix: ， in, For local frequency range, for The eigenvector matrix after eigenvalue decomposition for The eigenvalue diagonal matrix after eigenvalue decomposition; The observation model is expressed as follows: ， ， ， ， ， present sum Inside, , ， ， present sum Inside, , ， 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 of the signal; The specific steps of step 3 are as follows: based on and This yields a sparse Bayesian framework, represented as: ， ， Initialize hyperparameters , , For the dictionary matrix D, the first... List, for The A quick snapshot, It is the identity matrix; Iteration is represented as: ， ， ， ， ， ， in, For the first The two-dimensional sparse estimate obtained in the next 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; The convergence condition for the iteration is: The maximum number of iterations set has been reached, or ; =[ ]， in, It is a positive number. =0.001, After convergence, a two-dimensional sparse estimate is obtained. That is, a local two-dimensional spectrum; The two-dimensional spectral power Represented as: ， in, This indicates that the vector will be re-traced. Matrix; The global power spectrum Represented as: ， ， ， 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.
2. The high-resolution velocity and angle measurement method based on frequency domain dimensionality reduction sparse Bayesian algorithm according to claim 1, characterized in that... The angle Represented as: ， in, This represents the predicted normalized spatial frequency.
3. The high-resolution velocity and angle measurement method based on frequency domain dimensionality reduction sparse Bayesian algorithm according to claim 2, characterized in that... The speed Represented as: ， in, For the predicted normalized Doppler frequency, The sampling frequency.
Citation Information
Patent Citations
CN111610502A
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