A method for super-resolution two-dimensional signal angle of arrival estimation based on a reconstructed subspace

Abstract

The application relates to a kind of based on reconstruction subspace's super-resolution two-dimensional signal angle of arrival estimation method, comprising the following steps: S1, covariance matrix is constructed;S2, signal subspace matrix and noise subspace matrix are established;S3, construct two-dimensional multiple signal classification algorithm spatial spectrum expression;S4, based on eigenvalue decomposition obtains multiple eigenvalues and corresponding multiple eigenvectors;S5, based on eigenvalue, eigenvector is sorted, and constitutes to be eliminated matrix;S6, reconstruction subspace matrix is constructed, and S6 is repeated to carry out iterative calculation, and reconstruction subspace matrix is obtained Reconstruction subspace matrix set is formed;S7, simultaneously reconstruction subspace matrix set and spatial spectrum expression, obtain new spatial spectrum function set;S8, to new spatial spectrum function set is jointly estimated, and signal angle of arrival is obtained.Compared with prior art, the application has the advantages of high estimation accuracy.

Description

Technical Field

[0001] This invention relates to the field of large-scale array signal processing technology, and in particular to a super-resolution two-dimensional signal angle of arrival estimation method based on reconstructed subspace. Background Technology

[0002] Array signal processing has become an important branch of signal processing, rapidly developing in both military and civilian fields such as communications, radar, and satellite positioning. The purpose of array signal processing is to suppress noise and unwanted interference, enhance useful signals, and extract the characteristics and relevant information of useful signals. The main objective of signal angle-of-arrival estimation is to estimate the wave direction of the array signal as accurately as possible.

[0003] The development of spatial spectrum estimation technology originated in the 1960s. It applies modern spectrum estimation theory, matrix theory, and corresponding mathematical operations to estimate the spatial spectrum of incoming waves, analyze their energy distribution, and determine the direction of the incoming wave. Spatial spectrum estimation direction finding technology is not limited by the Rayleigh limit, can resolve the angles of multiple signals arriving simultaneously within a beamwidth, and has no fixed requirements on the shape of the antenna array, allowing for flexible antenna placement and high direction finding accuracy, thus showing promising application prospects.

[0004] Compared to one-dimensional array signal angle of arrival (AOA) estimation, two-dimensional signal AOA estimation can more fully describe the spatial characteristics of the signal, simultaneously obtaining the azimuth and elevation angles of the spatial signal, thus providing more accurate positioning. In this case, the detection of both azimuth and elevation angles is crucial for uniform rectangular arrays.

[0005] However, traditional multiple signal classification algorithms have significant estimation biases under adverse conditions such as low signal-to-noise ratio, short beats, and low number of array elements, and their accuracy in estimating the signal angle of arrival is not high. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art by providing a high-accuracy super-resolution two-dimensional signal angle of arrival estimation method based on reconstructed subspace.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A super-resolution two-dimensional signal angle-of-arrival estimation method based on reconstructed subspace includes the following steps:

[0009] S1. Establish a mathematical model for array receiving signals based on a uniform rectangular array, use the mathematical model for array receiving signals to receive data, construct a covariance matrix, and approximate the covariance matrix. The array receiving data in the covariance matrix includes two independent parts: signal and noise. The signal part of the covariance matrix is ​​determined by the array steering vector and the incident signal vector. Assume that the uniform rectangular array receives a total of K signals.

[0010] S2. Perform eigenvalue decomposition on the approximate covariance matrix obtained in S1 to obtain multiple eigenvalues ​​and corresponding eigenvectors, and establish a signal subspace matrix and a noise subspace matrix. The noise subspace matrix is ​​orthogonal to the array steering vector.

[0011] S3. Based on the orthogonality of the array steering vector and the noise subspace matrix, construct the spatial spectrum expression of the two-dimensional multiple signal classification algorithm based on a uniform rectangular array;

[0012] S4. Based on the eigenvalue decomposition in S2, multiple eigenvalues ​​and corresponding eigenvectors are obtained. The number of eigenvalues ​​and eigenvectors is the same as the number of elements of the uniform rectangular array, M×N.

[0013] S5. Based on the eigenvalue pair, the M×N eigenvectors of S4 are sorted in descending order to form an eigenvector space matrix, which is then used as the matrix to be eliminated.

[0014] S6. Remove the eigenvector corresponding to the largest eigenvalue from the matrix to be removed to obtain the first set of reconstructed subspace matrices. Then, use the first set of reconstructed subspace matrices as the new matrix to be removed and repeat S6 for iterative calculation. After S6 is executed K-1 times, K-1 sets of reconstructed subspace matrices are obtained. The K-1 sets of reconstructed subspace matrices form a set of reconstructed subspace matrices.

[0015] S7. Combine the set of reconstructed subspace matrices with the spatial spectrum expression of the two-dimensional multiple signal classification algorithm obtained in S3 to obtain a new set of spatial spectrum functions.

[0016] S8. Perform joint estimation on the new set of spatial spectral functions, and obtain the angle value corresponding to the maximum value of the spatial spectral function in the set of spatial spectral functions by searching for the peak value of the spectral function. The angle value is the signal arrival angle.

[0017] Furthermore, the mathematical model for the array receiving signal is located on the XOY plane. A uniform rectangular array is configured with M×N array elements, with the element located at the origin serving as the reference element. In the far-field scene, K narrowband signal sources with wavelength λ are incident on the uniform rectangular array. The uniform rectangular array receives a total of K signals. At this point, the vector form of the array received data is:

[0018]

[0019] Where X(t) is the array received data vector, and S(t) is the incident signal vector. Let N(t) represent the Kronecker product, N(t) be the additive white Gaussian noise vector, and a y (φ k ,θ k ) represents the direction vector along the y-axis, a x (φ k ,θ k ) represents the direction vector along the x-axis, φ k and θ k Let these represent the elevation and azimuth angles corresponding to the k-th signal, respectively, where k = 1, 2, ..., K. This represents the array steering vector.

[0020] Furthermore, the expression for the approximate covariance matrix is:

[0021]

[0022] in, Let L represent the approximate covariance matrix, L represent the number of data sampling snapshots of the array received signal vector, n represent the sequence number of the data sampling snapshots, and H represent the conjugate transpose operation.

[0023] Furthermore, after performing eigenvalue decomposition on the approximated covariance matrix in S2, the expressions for the signal subspace matrix and noise subspace matrix are as follows:

[0024]

[0025] in, Represents the signal subspace matrix. Denotes the noise subspace matrix, E s E is the signal subspace composed of the eigenvectors corresponding to eigenvalues ​​exceeding a set threshold. n D is the noise subspace formed by the eigenvectors corresponding to eigenvalues ​​that do not exceed a set threshold. s The first diagonal matrix, D, consists of eigenvalues ​​exceeding a set threshold. n It is the second diagonal matrix, consisting of eigenvalues ​​that do not exceed a set threshold.

[0026] Furthermore, the spatial spectrum expression for the two-dimensional multiple signal classification algorithm is as follows:

[0027]

[0028] Where P(φ,θ) represents the spatial spectrum of the two-dimensional multiple signal classification algorithm.

[0029] Furthermore, the M×N eigenvalues ​​of S4 satisfy the following condition:

[0030]

[0031] Where, λ1 to λ MN These represent the eigenvalues ​​from the 1st to the MNth, respectively. This represents the variance of the noise component of the data received by the array.

[0032] Furthermore, in S5, the sorted feature vector is:

[0033] E = [V1 V2 … V] K V K+1 … V MN ]

[0034] Where E is the eigenvector space matrix, V1 to V MN The first and MNth eigenvectors are sorted sequentially.

[0035] Furthermore, the expression for the K-1 group of reconstructed subspace matrices is:

[0036] E1 = [V2, V3, ..., V MN ]

[0037] E2 = [V3, V4, ..., V MN ]

[0038]

[0039] E K-1 =[V K V K+1 …,V MN ]

[0040] Among them, E1 to E K-1 The reconstructed subspace matrices are arranged sequentially from the first group to the (K-1)th group.

[0041] Furthermore, in S7, the expression for the new set of spatial spectral functions is:

[0042]

[0043] Where Ψ1(φ,θ) to Ψ K-1 (φ,θ) represent the first to the (K-1)th spatial spectral functions, respectively.

[0044] Furthermore, in S8, the expression for the new spatial spectral function after joint estimation of the new set of spatial spectral functions is:

[0045]

[0046] Where Ψ(φ,θ) is the new spatial spectral function after joint estimation.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] This invention utilizes a uniform rectangular array to receive signal sources in space and constructs a sampling covariance matrix. This sampling covariance matrix contains the angular information of the spatial signal sources. After reconstructing the subspace by improving the eigenvalue decomposition covariance matrix, it is then combined with the spatial spectrum function of the multiple signal decomposition algorithm to obtain high-precision two-dimensional orientation information. Compared with existing technologies, this reduces estimation bias under adverse conditions such as low signal-to-noise ratio, small beats, and low array element number, and improves angular resolution performance. Attached Figure Description

[0049] Figure 1 This is a flowchart of the present invention;

[0050] Figure 2 This is a schematic diagram of the array structure of the two-dimensional uniform rectangular array of the present invention. Detailed Implementation

[0051] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0052] This invention proposes a super-resolution two-dimensional signal angle-of-arrival estimation method based on a reconstructed subspace. It processes received signal data using a uniform rectangular array model, fully utilizing signal feature vectors and successively eliminating larger signal feature vectors to obtain a reconstructed subspace. A new spatial spectrum function is then obtained by combining this subspace with the spatial spectrum function of a multi-signal classification algorithm. Peak search is performed on this new spatial spectrum function, thereby effectively estimating the signal's direction of arrival and improving the accuracy of two-dimensional signal angle-of-arrival estimation.

[0053] The flowchart of the method of the present invention is as follows Figure 1 As shown. The method of the present invention includes the following steps:

[0054] Step 1: Establish a mathematical model of the array received signal based on a uniform rectangular array, and construct the covariance matrix using the array received data. For example... Figure 2 As shown, the array model is located on the XOY plane. The array element located at the origin is used as the reference element. A uniform rectangular array is configured with M×N array elements, where the spacing between adjacent elements along the X and Y axes is d. Assume that there are K narrowband signal sources with wavelength λ incident on the uniform rectangular array in the far-field scene, and φ... k and θ kLet represent the elevation angle and azimuth angle corresponding to the k-th signal, respectively, where k = 1, 2, ..., K.

[0055] Using the array element at the origin as the reference array element, the array received signal matrix vector form can be expressed as follows:

[0056]

[0057] Where X(t) is the received data vector and S(t) is the incident signal vector. It represents the Kronecker product.

[0058] N(t)=[n1(t) T n2(t) T … n N (t) T ] T It is an additive white Gaussian noise vector.

[0059]

[0060]

[0061] Assume the received additive noise is stationary, zero-mean Gaussian white noise with variance . Furthermore, it is uncorrelated with the signal. Therefore, performing autocorrelation on the array-received data X(t) yields the array-received covariance matrix:

[0062] R = E[XX] H ]

[0063] Here, H represents the conjugate transpose operation.

[0064] In step 1, the obtained covariance matrix is ​​approximated using the data sampling covariance matrix of the array received data. The data sampling covariance matrix is ​​as follows:

[0065]

[0066] Where L represents the number of data sampling snapshots of the array received signal vector.

[0067] Step 2: Perform eigenvalue decomposition on the approximate covariance matrix obtained in Step 1. Since the signal and noise are independent of each other, the data covariance matrix can be decomposed into two parts: signal and noise, resulting in the signal subspace matrix and the noise subspace matrix.

[0068] Eigenvalues ​​are obtained by performing eigenvalue decomposition on the data sampling covariance matrix. Among them, based on the number of target signal sources K, E s It is the signal subspace composed of the signal eigenvectors corresponding to the K largest signal eigenvalues, E nIt is the noise subspace formed by the noise eigenvectors corresponding to the remaining M×NK smaller noise eigenvalues. (Diagonal matrix D) s It consists of K large eigenvalues, D n It consists of M×NK smaller eigenvalues.

[0069] Step 3: Utilize array guide vector Based on the orthogonality between the noise subspace matrix obtained in step 2, a spatial spectrum expression for a two-dimensional multiple signal classification algorithm based on a uniform rectangular array is constructed.

[0070] The spatial spectrum expression of the two-dimensional multiple signal classification algorithm based on a uniform rectangular array is:

[0071]

[0072] Step 4: Since multiple eigenvalues ​​and corresponding eigenvectors are obtained during eigenvalue decomposition in Step 2, Step 4 uses the obtained M×N eigenvalues ​​and corresponding M×N eigenvectors.

[0073] The M×N eigenvalues ​​are: {λ1 λ2 … λ K λ K+1 … λ MN}

[0074] M×N eigenvalues ​​have the following characteristics:

[0075] The M×N eigenvectors corresponding to the eigenvalues ​​are: {V1 V2 … V K V K+1 … V MN}

[0076] Step 5: Sort the M×N eigenvectors obtained in Step 4 according to their corresponding eigenvalues ​​from largest to smallest to form an eigenvector space matrix. The eigenvector space matrix is ​​used as the matrix to be eliminated.

[0077] After sorting from largest to smallest, the eigenvector space matrix is: E = [V1 V2 … V K V K+1 … V MN ]

[0078] Step 6: Remove the eigenvector corresponding to the largest eigenvalue from the matrix to be removed to obtain the first set of reconstructed subspace matrices. Then, use the first set of reconstructed subspace matrices as the new matrix to be removed and repeat step 6 for iterative calculation. After step 6 is executed K-1 times, K-1 sets of reconstructed subspace matrices are obtained. The K-1 sets of reconstructed subspace matrices form a set of reconstructed subspace matrices.

[0079] The set of K-1 reconstructed subspace matrices is:

[0080] E1 = [V2, V3, ..., V MN ]

[0081] E2 = [V3, V4, ..., V MN ]

[0082]

[0083] E K-1 =[V K V K+1 …,V MN ]

[0084] Step 7: Combine the set of reconstructed subspace matrices from Step 6 with the spatial spectrum of the two-dimensional multiple signal classification algorithm obtained in Step 3 to obtain a new set of spatial spectrum functions.

[0085] Combining the reconstructed subspace matrix set with the spatial spectrum of the two-dimensional multiple signal classification algorithm, we obtain a new set of spatial spectral functions as follows:

[0086]

[0087] Step 8: Jointly estimate the set of spatial spectral functions obtained in Step 7, and obtain the angle value corresponding to the maximum value of the spatial spectral function by searching for the peak value of the spectral function. This angle value is the signal arrival angle.

[0088] The new spatial spectral function obtained by joint estimation of the obtained set of spatial spectral functions is:

[0089]

[0090] By searching for the peak of the spectral function, the coordinates corresponding to the maxima of the spatial spectral function are further obtained as {(φ1,θ1)(φ2,θ2) … (φ K ,θ K The coordinate is the signal arrival angle.

[0091] This invention applies a super-resolution two-dimensional signal angle of arrival estimation method based on reconstructed subspace to the field of array signal processing, which significantly improves the accuracy of signal angle of arrival estimation compared to traditional multi-signal decomposition algorithms. First, a uniform rectangular array is used to receive signal sources in space, and a sampling covariance matrix is ​​constructed. This sampling covariance matrix contains the angular information of the spatial signal sources. After improving the eigenvalue decomposition covariance matrix, the subspace is reconstructed. Then, it is combined with the spatial spectrum function of the multi-signal decomposition algorithm, enabling this invention to obtain high-precision two-dimensional orientation information, while also significantly improving the angular resolution performance of the algorithm.

[0092] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A super-resolution two-dimensional signal angle-of-arrival estimation method based on reconstructed subspace, characterized in that, Includes the following steps: S1. Establish a mathematical model for the array receiving signal based on a uniform rectangular array. Receive data using this model, construct a covariance matrix, and approximate the covariance matrix. The array receiving data in the covariance matrix includes two independent parts: signal and noise. The signal part of the covariance matrix is ​​determined by the array steering vector and the incident signal vector. Assume the uniform rectangular array receives a total of... K One signal; S2. Perform eigenvalue decomposition on the approximate covariance matrix obtained in S1 to obtain multiple eigenvalues ​​and corresponding eigenvectors, and establish a signal subspace matrix and a noise subspace matrix. The noise subspace matrix is ​​orthogonal to the array steering vector. S3. Based on the orthogonality of the array steering vector and the noise subspace matrix, construct the spatial spectrum expression of the two-dimensional multiple signal classification algorithm based on a uniform rectangular array; S4. Based on the eigenvalue decomposition in S2, multiple eigenvalues ​​and corresponding eigenvectors are obtained. The number of eigenvalues ​​and eigenvectors is equal to the number of elements in a uniform rectangular array. ; S5, based on eigenvalue pairs S4 The eigenvectors are sorted in descending order to form an eigenvector space matrix, which is then used as the matrix to be eliminated. S6. Remove the eigenvector corresponding to the largest eigenvalue from the matrix to be removed, obtaining the first set of reconstructed subspace matrices. Then, use the first set of reconstructed subspace matrices as the new matrix to be removed, and repeat S6 iteratively. S6 is executed. K-1 After that, I got K-1 Group reconstruct subspace matrix, K-1 The reconstructed subspace matrices form a set of reconstructed subspace matrices; S7. Combine the set of reconstructed subspace matrices with the spatial spectrum expression of the two-dimensional multiple signal classification algorithm obtained in S3 to obtain a new set of spatial spectrum functions. S8. Perform joint estimation on the new set of spatial spectral functions. Obtain the angle value corresponding to the maximum value of the spatial spectral function in the set by searching for the peak value of the spectral function. This angle value is the signal angle of arrival. , and They represent the first The elevation and azimuth angles corresponding to each signal; In S8, the expression for the new spatial spectral function after joint estimation of the new set of spatial spectral functions is: in, The new spatial spectral function after joint estimation. arrive The spatial spectral functions are listed sequentially from the first spatial spectral function to the (K-1)th spatial spectral function.

2. The super-resolution two-dimensional signal angle of arrival estimation method based on reconstructed subspace according to claim 1, characterized in that, The mathematical model for the array's received signal is located in the XOY plane, with a uniform rectangular array configuration. There are several array elements, with the element located at the origin serving as the reference element. In the far-field scene, there are... Each wavelength is A narrowband signal source is incident on a uniform rectangular array, and the uniform rectangular array receives a total of K There are one signal. At this time, the vector form of the data received by the array is: in, For array receiving data vectors, The incident signal vector, Indicates the Kronecker product. It is an additive white Gaussian noise vector. This represents the direction vector along the y-axis. This represents the direction vector along the x-axis. and They represent the first The elevation and azimuth angles corresponding to each signal , This represents the array steering vector.

3. The super-resolution two-dimensional signal angle of arrival estimation method based on reconstructed subspace according to claim 2, characterized in that, The expression for the approximate covariance matrix is: in, This represents the approximate covariance matrix. L This represents the number of data sampling snapshots of the array received signal vector. n Indicates the sequence number of the data sampling snapshot. H This represents the conjugate transpose operation.

4. The super-resolution two-dimensional signal angle of arrival estimation method based on reconstructed subspace according to claim 1, characterized in that, After performing eigenvalue decomposition on the approximated covariance matrix in S2, the expressions for the signal subspace matrix and noise subspace matrix are as follows: in, Represents the signal subspace matrix. Represents the noise subspace matrix. It is the signal subspace composed of the feature vectors corresponding to feature values ​​that exceed a set threshold. It is the noise subspace composed of the feature vectors corresponding to feature values ​​that do not exceed a set threshold. This is the first diagonal matrix, composed of eigenvalues ​​exceeding a set threshold. It is the second diagonal matrix, consisting of eigenvalues ​​that do not exceed a set threshold.

5. The super-resolution two-dimensional signal angle of arrival estimation method based on reconstructed subspace according to claim 4, characterized in that, The spatial spectrum expression for the two-dimensional multiple signal classification algorithm is: in, This represents the spatial spectrum of a two-dimensional multiple signal classification algorithm.

6. The super-resolution two-dimensional signal angle of arrival estimation method based on reconstructed subspace according to claim 1, characterized in that, S4 The eigenvalues ​​satisfy the following condition: in, arrive These represent the eigenvalues ​​from the 1st to the MNth, respectively. This represents the variance of the noise component of the data received by the array.

7. The super-resolution two-dimensional signal angle of arrival estimation method based on reconstructed subspace according to claim 1, characterized in that, In S5, the sorted feature vectors are: in, The eigenvector space matrix, arrive The first and MNth eigenvectors are sorted sequentially.

8. The super-resolution two-dimensional signal angle of arrival estimation method based on reconstructed subspace according to claim 7, characterized in that, K-1 The expression for the group reconstructed subspace matrix is: in, arrive The reconstructed subspace matrices are arranged sequentially from the first group to the (K-1)th group.

9. The super-resolution two-dimensional signal angle of arrival estimation method based on reconstructed subspace according to claim 8, characterized in that, In S7, the expression for the new set of spatial spectral functions is: in, arrive The spatial spectral functions are listed sequentially from the first spatial spectral function to the (K-1)th spatial spectral function.

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