A fast MUSIC method for enhancing radar angular resolution

Abstract

The application provides a fast MUSIC method for enhancing radar angle resolution, comprising the following steps: step one, establishing an array model equivalent to a radar antenna, and then calculating the distance and direction between each antenna in the array; step two, constructing a spatial spectrum function, and estimating the parameters of a signal through a spectrum peak search; step three, setting one transmitting array element, transmitting chrip signals in one frame, and then the signal received by a single receiving array element in one frame is, and point sampling is conducted on the received signal to obtain the maximum likelihood estimation of a finite-length data covariance matrix. The technical scheme can effectively accelerate the estimation speed of the arrival angle of a target, and can be applied to actual point cloud acquisition.

Description

Technical Field

[0001] The present invention relates to the field of radar detection technology, in particular to a fast MUSIC method for enhancing radar angular resolution. Background Art

[0002] In recent years, with the continuous integration and miniaturization of millimeter-wave radars, they have been widely used in behavior recognition, vital sign detection, and target tracking due to their advantages in privacy protection and environmental robustness. However, the angular resolution of targets is affected by the radar aperture. As the number of monitored targets increases, the angular difference between targets decreases sharply, making it difficult for the radar to effectively distinguish between different targets. Improving angular resolution by increasing the number of antenna arrays increases the hardware size and cost. To address this problem, a series of angular super-resolution methods have been proposed. Among them, the angle acquisition method centered on the minimum variance distortionless response (MVDR) method has been successfully implemented on TI radar boards, but its actual improvement is relatively limited. MUSIC (Multiple Signal Classification) methods, or multi-signal methods with higher angular resolution, have been widely studied, such as joint estimation based on 2D-MUSIC and 3D-MUSIC and joint estimation based on FFT-MUSIC. However, the joint estimation in the angular dimension is complex, making it difficult to implement in real-time applications.

[0003] Although existing technologies can achieve super-resolution effects in acquiring target angles, their high computational complexity makes them unsuitable for practical applications. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a fast MUSIC method for enhancing radar angular resolution, effectively speeding up the target arrival angle estimation speed, and enabling it to be applied to actual point cloud acquisition.

[0005] To achieve the above object, the present invention adopts the following technical solution: a fast MUSIC method for enhancing radar angular resolution, comprising the following steps:

[0006] Step 1: Build an array model equivalent to the radar antenna, the array geometry, and then calculate the distance and direction between each antenna in the array to construct the spatial relationship of the sensor array;

[0007] Step 2: From a geometric perspective, the observation space of signal processing is decomposed into a signal subspace and a noise subspace. The signal subspace and the noise subspace are orthogonal. The signal subspace consists of the eigenvectors corresponding to the signal in the covariance matrix of the data received by the array, while the noise subspace consists of the eigenvectors corresponding to all the minimum eigenvalues ​​in the covariance matrix. The MUSIC method uses the orthogonality of the signal subspace and the noise subspace to construct a spatial spectrum function and estimate the signal parameters through spectral peak search.

[0008] Step 3: Assume that a transmitting array element transmits M chirp signals in one frame, then the signal received by a single receiving array element in one frame is [y 1 IF ij (t),y 2 IF ij (t),y 3 IF ij (t),...,y M IF ij (t)], the received signal is sampled at N points to obtain the maximum likelihood estimation of the covariance matrix of the finite length data; then the noise subspace is obtained by eigendecomposition to obtain the spectrum containing the angle, and finally the spectrum peak is searched to obtain the DOA estimation value.

[0009] In a preferred embodiment, the step 1 specifically includes: considering P narrowband far-field target signals from different incident angles θ = [θ1, θ2, ... θ p ] is incident on the following uniform linear array consisting of L receiving elements. The spacing between adjacent elements is d = λ / 2, where λ is the carrier wavelength, and the angle θ∈[-π / 2,π / 2] between the signal and the normal of the uniform linear array. The data vector received by the uniform linear array at time t is:

[0010] y(t)=[y1(t),y2(t),…yL(t)] T =x(t)+n(t)=As(t)+n(t) (1)

[0012] In formula (1), A=[a(θ1),...a(θ p )] is an L×P dimensional direction matrix, is the incident angle θ i The L×1-dimensional steering vector of the direction, which contains the angle information; s(t) = [s1(t), s2(t), ...s p (t)] T is the P×1-dimensional incident target signal vector, n(t)=[n1(t), n2(t),…n L (t)] T is an L×1-dimensional noise vector; the noise has zero mean and variance σ2 Gaussian distribution, the noise vectors are independent of each other and the signal vector; [·] T Represents the transposition operation; for multiple incident signals received by the array, the correlation degree between the incident signals is divided into three cases: uncorrelated, partially correlated and coherent according to the correlation coefficient; for two stationary signals S i (t) and S j (t), and its correlation coefficient is defined as:

[0013]

[0014] According to formula (2), the correlation coefficient satisfies |ρ ij |≤1; when ρ ij =0, S i (t) and S j (t) are not related and are independent of each other; when 0<|ρ ij When |<1, S i (t) and S j (t) Partial correlation; when |ρ ij When |=1, S i (t) and S j (t) coherent.

[0015] In a preferred embodiment, the step 2 specifically includes: the covariance matrix R of the signal received by the uniform linear array is:

[0016] R=E[y(t)y H (t)](3)

[0017] Substituting formula (1) into formula (3), we can get

[0018] R=AR s A H +δ 2 I (4)

[0019] Where: R s =E[s(t)s H (t)] is the P×P dimensional signal covariance matrix, diag(·) represents the construction of a diagonal matrix, the diagonal line contains the power of each incident signal; I is the L×L dimensional identity matrix; δ 2 is the power of the noise; E[·] represents the expected value calculation; [·] H Indicates the conjugate transpose calculation; after obtaining the covariance matrix R, perform eigenvalue decomposition R = U∑U H , get L eigenvalues, sort the L eigenvalues ​​from large to small as follows:

[0020] λ1≥λ2≥…≥λ i ≥λ i+1 =λ L=δ 2 (5)

[0021] Eigenvalue λ i Represents the i-th largest eigenvalue, and the above formula represents the first i eigenvalues, i.e., λ1 to λ i Greater than or equal to δ 2 That is, the noise variance, and the remaining eigenvalue λ i+1 to λ L are equal to δ 2 , indicating that they correspond to the noise subspace;

[0022] The signal and noise subspaces are distinguished by the order of eigenvalue decomposition, and the direction of the incident signal is estimated in the MUSIC algorithm;

[0023] Since the signal vector and the noise vector are independent of each other, we can further obtain where ∑ s is a diagonal matrix composed of the first P larger signal eigenvalues, ∑ N is a diagonal matrix composed of the last LP smaller noise eigenvalues; U s The signal subspace spanned by the signal eigenvectors corresponding to the first P larger signal eigenvalues, U N is the noise subspace spanned by the noise eigenvectors corresponding to the last LP smaller noise eigenvalues; when the incident target signal sources are independent of each other, the steering vectors a(θ i ) and the noise subspace U N Orthogonal, we can get Then the spatial spectrum function of the MUSIC algorithm is:

[0024]

[0025] According to the spatial spectrum function obtained by formula (6), the DOA of the incident signal is estimated by searching the spectrum peak. However, in practical applications, the covariance matrix R cannot be obtained directly, so the sample covariance matrix is ​​used. To replace R for eigenvalue decomposition;

[0026]

[0027] Where V is the number of samples;

[0028] In actual situations, due to the interference of noise, the steering vector a(θ i ) and the noise subspace U N Not completely orthogonal, The result is not strictly 0, but a minimum value close to 0. At this time, the spatial spectrum function of the MUSIC algorithm is expressed as:

[0029]

[0030] The main steps of the classic MUSIC algorithm are:

[0031] Step 1: Obtain the signal covariance matrix R received by the uniform linear array using formula (4);

[0032] Step 2: Perform eigenvalue decomposition on the signal covariance matrix R and sort the obtained eigenvalues ​​from large to small;

[0033] Step 3: Extract the signal subspace U spanned by the eigenvectors corresponding to P larger eigenvalues ​​equal to the number of incident signals s , extract the noise subspace U formed by the eigenvectors corresponding to the remaining LP smaller eigenvalues N ;

[0034] Step 4: Change θ, calculate the spatial spectrum function according to formula (6) and perform spectrum peak search to obtain the DOA estimation value of the incident signal.

[0035] In a preferred embodiment, the step 3 specifically includes: fast MUSIC algorithm, assuming that a transmitting array element transmits M chirp signals in one frame, then the signal received by a single receiving array element in one frame is Sampling the received signal at N points yields the following matrix:

[0036]

[0037] Where M is a factor that affects the calculation speed; N is a factor that affects the actual ranging resolution, i.e., the number of snapshots or sampling points; M and N are set according to actual needs.

[0038] The maximum likelihood estimate of the covariance matrix of finite length data is obtained by formula (9), which is expressed as:

[0039]

[0040] In the formula, x is the snapshot signal, i.e. the echo signal, and N is the number of snapshots, i.e. the number of sampling points;

[0041] R c After eigendecomposition, the noise subspace U composed of noise vectors is obtained N , finally, the spectrum expression including the angle is:

[0042]

[0043] Where a(θ i ) is the signal steering vector; for a(θ i), find the θ value that makes P appear at the peak, calculate the spatial spectrum function according to formula (11) and perform spectrum peak search to obtain the DOA estimation value of the incident signal; in this way, through N θ times of calculation and N θ Search again to get the horizontal angle of the target.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The present invention relates to the arrangement characteristics and echo signal model of the radar antenna array. By analyzing the arrangement characteristics and echo signal model of the radar antenna array, the search strategy of the MUSIC algorithm in the angle dimension is optimized, achieving a lower amount of calculation; the improved algorithm is successfully applied to the actual radar point cloud acquisition, and the multi-target point cloud is separated faster and better. Compared with the traditional method MUSIC algorithm, the algorithm of the present invention has a faster measurement speed and can more accurately record the angle information of the target without much loss of accuracy. The 3D-FFT and TI (MVDR) methods are not suitable for practical applications due to their high computational complexity in target angle acquisition. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A schematic diagram of a fast MUSIC algorithm according to a preferred embodiment of the present invention;

[0047] Figure 2 Schematic diagram of an L receiving antenna array according to a preferred embodiment of the present invention;

[0048] Figure 3 Schematic diagram of a 3-transmit 4-receive radar antenna according to a preferred embodiment of the present invention;

[0049] Figure 4 A schematic diagram of a radar array model according to a preferred embodiment of the present invention;

[0050] Figure 5 This is a spectrum obtained by setting three targets in front of the radar in the preferred embodiment of the present invention, where: Figure 5 (a) is sinθcosφ, Figure 5 (b) is φ, Figure 5 (c) is θ;

[0051] Figure 6 This is a point cloud distribution diagram of a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0053] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present application belongs.

[0054] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form, and it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations.

[0055] In order to verify the fast MUSIC algorithm proposed in this invention to enhance the radar angular resolution, refer to Figure 1-6 The present invention will be further described below with reference to specific implementation methods. The following is an example of an embodiment.

[0056] This embodiment of the present invention proposes a fast MUSIC algorithm for enhancing radar angular resolution. The so-called fast MUSIC algorithm achieves super-resolution in target angle acquisition and applies it to real-time point cloud acquisition, achieving faster processing speed and better multi-target point cloud separation capabilities.

[0057] The effectiveness of the algorithm is tested using a three-transmit four-receive antenna radar as an example. The radar antenna model is shown in the figure.

[0058] A. Radar Array Structure and Signal Model

[0059] The radar array model used in this embodiment is equivalent to: Figure 4 The structure shown is a 3-transmit 4-receive antenna with a horizontal angle θ and a pitch angle Assume that the position matrix of 12 array elements in space is r = [r 11 ,...r ij ,...,r 34 ]∈R 3×12 , where i represents the i-th transmitting antenna, j represents the j-th receiving antenna, and r ij is the 3D coordinate of the corresponding virtual array element.

[0060] The emission signal expression is:

[0061]

[0062] Among them A T is the signal amplitude, f c is the starting frequency, and S is the frequency modulation slope. The echo signal expression obtained by the electromagnetic wave reflected by g targets in space is:

[0063]

[0064] where R q is the distance between the qth target and the radar, c is the electromagnetic wave propagation speed, is the unit direction vector of the target, r ij is the 3D coordinate of the equivalent virtual element. Assuming that one transmitting element transmits M chirp signals in a frame, the signal received by a single receiving element in a frame is N-point sampling of the received signal can obtain the following matrix:

[0065]

[0066] B. Fast MUSIC algorithm

[0067] From equation (2) and Figure 4 it can be seen that the signal steering vector composed of horizontal elements T1R1-T2R4 is where L represents the number of horizontal virtual elements, and L=8 in the 3-transmitting 4-receiving antenna. The signal steering vector composed of all elements is where K represents the number of vertical virtual elements, and K=4 in the 3-transmitting 4-receiving antenna, i.e., T3R1-T3R4.

[0068] The maximum likelihood estimate of the finite-length data covariance matrix is obtained by equation (3), and its expression is:

[0069]

[0070] where x is the snapshot signal (i.e., the echo signal), and N is the number of snapshots (i.e., the number of sampling points). After performing eigenvalue decomposition on R c , the noise subspace U N composed of noise vectors is obtained, and finally, the spectrum expression containing the angle is:

[0071]

[0072] where a is the signal steering vector. For a1 and a2, the horizontal angle θ and the pitch angle corresponding to the peak of P are consistent, so we first bring a1 into equation (5) to obtain the value of corresponding to the peak of P. Then, bring a2 into equation (5), and at the same time, bring the value of obtained in the previous step into a2 to obtain the value of corresponding to the peak of P at this time. The value of θ can be obtained from the value of in the previous step and the value of in this step. In this way, through times of calculation and Sub-search, we get the target level angle and pitch angle.

[0073] So in this experiment, we set three targets in front of the radar, the azimuth angle is set to After calculation, we get the spectrum as Figure 5 shown in the figure:

[0074] In Figure 5 (b) and Figure 5 (c), we can clearly see the azimuth angle of the three targets. In order to further prove the time advantage of the method, we compared it with the traditional MUSIC algorithm, and conducted 100 Monte Carlo experiments, and the results are shown in Table 1 and Table 2:

[0075] Table 1 Angle accuracy comparison of the algorithm and the original algorithm

[0076]

[0077] Table 2 Time consumption comparison of the algorithm and the original algorithm

[0078]

[0079] The proposed fast MUSIC algorithm improves the azimuth angle acquisition speed by 100 times without losing too much accuracy, and has good robustness. We applied the improved algorithm to actual point cloud acquisition, and compared it with the popular 3D-FFT and TI method. When the targets are adjacent, the point cloud is as shown in Figure 6 , and the time consumption is shown in Table 3:

[0080] Table 3 Time consumption of different methods per frame

[0081]

[0082] As shown in Table 3, in different number of people scenarios, the single frame processing time of the method is maintained within 30ms. Compared with the popular 3D-FFT and TI method processing time, the average per frame processing time is increased by 82.9% and 36.9% respectively in multi-target scenarios. Our method not only meets the real-time requirement, but also realizes faster processing time, and at the same time, the adjacent target point cloud separation effect is better.

[0083] The application analyzes the arrangement characteristics of the radar antenna array and the echo signal model, and proposes a fast MUSIC algorithm based on dimension reduction search. Compared with the traditional MUSIC algorithm, the speed is improved by 100 times, and the accuracy is not greatly lost, so that the algorithm can meet the real-time requirements. In the actual target point cloud acquisition, compared with the popular 3D-FFT and TI methods, the time consumption is reduced by 82.9% and 36.9% respectively, and the point cloud separation effect is better.

Claims

1. A fast MUSIC method for enhancing radar angular resolution, characterized by The following steps are involved: Step 1: Build an array model equivalent to the radar antenna, the array geometry, and then calculate the distance and direction between each antenna in the array to construct the spatial relationship of the sensor array; Step 2: From a geometric perspective, the observation space of signal processing is decomposed into a signal subspace and a noise subspace. The signal subspace and the noise subspace are orthogonal. The signal subspace consists of the eigenvectors corresponding to the signal in the covariance matrix of the data received by the array, while the noise subspace consists of the eigenvectors corresponding to all the minimum eigenvalues ​​in the covariance matrix. The MUSIC method uses the orthogonality of the signal subspace and the noise subspace to construct a spatial spectrum function and estimate the signal parameters through spectral peak search. Step 3: Assume that a transmitting array element transmits M chirp signals in one frame, then the signal received by a single receiving array element in one frame is The received signal is sampled at N points to obtain the maximum likelihood estimate of the finite-length data covariance matrix; then its eigenvalues ​​are decomposed to obtain the noise subspace and thus the spectrum containing the angle, and finally the spectrum peak is searched to obtain the DOA estimate.

2. A fast MUSIC method for enhancing radar angular resolution according to claim 1, characterized in that: The step 1 specifically includes: considering P narrowband far-field target signals from different incident angles θ=[θ1, θ2, ... θ p ] is incident on the following uniform linear array consisting of L receiving elements. The spacing between adjacent elements is d = λ / 2, where λ is the carrier wavelength, and the angle θ∈[-π / 2,π / 2] between the signal and the normal of the uniform linear array. The data vector received by the uniform linear array at time t is: y(t)=[y1(t),y2(t),…y L (t)] T =x(t)+n(t)=As(t)+n(t) (1) In formula (1), A=[a(θ1),…a(θ p )] is an L×P dimensional direction matrix, is the incident angle θ i The L×1-dimensional steering vector of the direction, which contains the angle information; s(t)=[s1(t),s2(t),…s p (t)] T is the P×1-dimensional incident target signal vector, n(t)=[n1(t),n2(t),…n L (t)] T is an L×1-dimensional noise vector; the noise has zero mean and variance σ 2 Gaussian distribution, the noise vectors are independent of each other and the signal vector; [·] T Represents the transposition operation; for multiple incident signals received by the array, the correlation degree between the incident signals is divided into three cases: uncorrelated, partially correlated and coherent according to the correlation coefficient; for two stationary signals S i (t) and S j (t), and its correlation coefficient is defined as: According to formula (2), the correlation coefficient satisfies |ρ ij |≤1; when ρ ij =0, S i (t) and S j (t) are not related and are independent of each other; when 0<|ρ ij When |<1, S i (t) and S j (t) Partial correlation; when |ρ ij When |=1, S i (t) and S j (t) coherent.

3. The fast MUSIC method for enhancing radar angular resolution according to claim 2, characterized in that: The second step specifically includes: the covariance matrix R of the signal received by the uniform linear array is: R=E[y(t)y H (t)] (3) Substituting formula (1) into formula (3), we can get R=AR s A H +δ 2 I (4) Where: R s =E[s(t)s H (t)] is the P×P dimensional signal covariance matrix, diag(·) represents the construction of a diagonal matrix, the diagonal line contains the power of each incident signal; I is the L×L dimensional identity matrix; δ 2 is the power of the noise; E[·] represents the expected value calculation; [·] H Indicates the conjugate transpose calculation; after obtaining the covariance matrix R, perform eigenvalue decomposition R=UΣU H , get L eigenvalues, sort the L eigenvalues ​​from large to small as follows: λ1≥λ2≥…≥λ i ≥λ i+1 =λ L =d 2 (5) Eigenvalue λ i Represents the i-th largest eigenvalue, and the above formula represents the first i eigenvalues, i.e., λ1 to λ i Greater than or equal to δ 2 That is, the noise variance, and the remaining eigenvalue λ i+1 to λ L are equal to δ 2 , indicating that they correspond to the noise subspace; The signal and noise subspaces are distinguished by the order of eigenvalue decomposition, and the direction of the incident signal is estimated in the MUSIC algorithm; Since the signal vector and the noise vector are independent of each other, we can further obtain where Σ s is a diagonal matrix composed of the first P larger signal eigenvalues, Σ N is a diagonal matrix composed of the last LP smaller noise eigenvalues; U s The signal subspace spanned by the signal eigenvectors corresponding to the first P larger signal eigenvalues, U N is the noise subspace spanned by the noise eigenvectors corresponding to the last LP smaller noise eigenvalues; when the incident target signal sources are independent of each other, the steering vectors a(θ i ) and the noise subspace U N Orthogonal, we can get Then the spatial spectrum function of the MUSIC algorithm is: According to the spatial spectrum function obtained by formula (6), the DOA of the incident signal is estimated by searching the spectrum peak. However, in practical applications, the covariance matrix R cannot be obtained directly, so the sample covariance matrix is ​​used. To replace R for eigenvalue decomposition; Where V is the number of samples; In actual situations, due to the interference of noise, the steering vector a(θ i ) and the noise subspace U N Not completely orthogonal, The result is not strictly 0, but a minimum value close to 0. At this time, the spatial spectrum function of the MUSIC algorithm is expressed as:

4. The fast MUSIC method for enhancing radar angular resolution according to claim 3, characterized in that: The step 3 specifically includes: fast MUSIC algorithm, assuming that a transmitting array element transmits M chirp signals in one frame, then the signal received by a single receiving array element in one frame is Sampling the received signal at N points yields the following matrix: Where M is a factor that affects the calculation speed; N is a factor that affects the actual ranging resolution, i.e., the number of snapshots or sampling points; M and N are set according to actual needs. The maximum likelihood estimate of the covariance matrix of finite length data is obtained by formula (9), which is expressed as: In the formula, x is the snapshot signal, i.e. the echo signal, and N is the number of snapshots, i.e. the number of sampling points; R c After eigendecomposition, the noise subspace U composed of noise vectors is obtained N , finally, the spectrum expression including the angle is: Where a(θ i ) is the signal steering vector; for a(θ i ), find the θ value that makes P appear at the peak, calculate the spatial spectrum function according to formula (11) and perform spectrum peak search to obtain the DOA estimation value of the incident signal; in this way, through N θ times of calculation and N θ Search again to get the horizontal angle of the target.

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