A method for direction finding of unknown coherent sources based on double relaxation solution

Abstract

The application discloses a method for direction finding of unknown coherent sources based on double relaxation solution, and belongs to the technical field of array signal processing. The application calculates the covariance matrix of array receiving signals, and performs eigenvalue decomposition on the covariance matrix, then sorts the eigenvalues to obtain the eigenvectors corresponding to the maximum eigenvalue and the minimum eigenvalue, constructs a dictionary matrix of beam domain steering vectors, and realizes convex optimization solution of the linear relationship between the dictionary matrix and the maximum and minimum eigenvectors by introducing a relaxation factor, and completes accurate calculation of the signal wave direction. The application can provide a high-precision direction finding method for the passive detection field under the condition that there are related sources and the number of sources is unknown.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and in particular to a direction finding method for unknown coherent sources based on double relaxation solution. Background Technology

[0002] Spatial spectrum direction finding techniques mainly include the MUSIC algorithm and subspace fitting algorithm, but these algorithms require accurate knowledge or estimation of the number of information sources to complete the angle of arrival estimation. In practical engineering applications, the number of information sources is often unknown. Furthermore, traditional source estimation techniques, such as information theory methods and the Geisel method, are designed for incoherent source conditions. Therefore, when relevant sources exist, it is often impossible to accurately provide information on the number of sources, which severely impacts the performance of spatial spectrum algorithms and limits their engineering applications. Summary of the Invention

[0003] In view of this, this invention proposes a direction finding method for unknown coherent sources based on double relaxation. This invention provides a high-precision direction finding method for passive detection under conditions where there are correlated sources and the number of sources is unknown.

[0004] The technical solution adopted in this invention is as follows:

[0005] A direction-finding method for unknown coherent sources based on double relaxation solution includes the following steps:

[0006] Step 1: Calculate the covariance matrix R of the array signal:

[0007]

[0008] In the above formula, X is the received data matrix of M array elements, and N is the number of sampling points;

[0009] Step 2: Perform eigenvalue decomposition on R to obtain the eigenvalue sequence ∑ n ;

[0010] Step 3: For ∑ n Sort the eigenvalues ​​and denote the largest and smallest eigenvalues ​​as λ. max and λ min , where λ max The corresponding eigenvector is denoted as u. s , λ min The corresponding eigenvector is denoted as u. n ;

[0011] Step 4: Construct the guiding vector dictionary matrix A(θ) P The dictionary matrix contains P angles, where P >> K, and K is the number of unknown sources.

[0012] Step 5: Introduce the double relaxation factor εs and ε n And satisfy ε s >0, ε n If the value is greater than 0, construct convex optimization conditions for inequalities using the relaxation factor, and calculate the coefficient sequence c.

[0013] Step 6: Construct the spatial spectrum P(θ):

[0014]

[0015] Among them, P i ∈P, c i ∈c, a(θ) i ) is A(θ p The column vector of ) is given by the superscript H, which indicates the conjugate transpose. The azimuth angle of the signal can be obtained by searching for the spectral peaks in the spatial spectrum P(θ).

[0016] Furthermore, the convex optimization condition for the inequality constructed in step 5 is:

[0017] minimize||c||2

[0018] subject to

[0019] ||A(θ p )cu s ||≤ε s

[0020] ||[A(θ p )c] H ·u n ||≤ε n

[0021] or

[0022] minimize||c||1

[0023] subject to

[0024] ||A(θ p )cu s ||≤ε s

[0025] ||[A(θ p )c] H ·u n ||≤ε n .

[0026] Compared with the prior art, the present invention has the following advantages:

[0027] 1. Compared with traditional spatial spectrum direction finding algorithms, it can achieve accurate direction finding of coherent sources even when the number of sources is unknown;

[0028] 2. Compared with the traditional MUSIC algorithm, it has a higher sidelobe suppression ratio;

[0029] 3. Compared with traditional sparse reconstruction direction finding algorithms based on single snapshots, this algorithm makes full use of the array's snapshot data, resulting in higher algorithm stability and spatial resolution. Attached Figure Description

[0030] Figure 1 This is the overall flowchart of the present invention.

[0031] Figure 2 This is a comparison of the direction finding results of this invention with those of the traditional MUSIC algorithm when the number of information sources is unknown. Detailed Implementation

[0032] Reference Figure 1 This paper presents a direction-finding method for unknown coherent sources based on double relaxation. After obtaining received data from N snapshots of an array, the method calculates the covariance matrix of the received data and performs eigenvalue decomposition on the covariance matrix. The eigenvalues ​​are sorted to obtain the eigenvectors corresponding to the largest and smallest eigenvalues. A dictionary matrix and complex coefficient vector for the beam domain steering vector are constructed, ensuring that the number of azimuth angles in the dictionary matrix is ​​much greater than the actual number of incident signals. A double relaxation factor is introduced, relaxing the original equality into an inequality as a convex optimization condition. The algorithm solves for the linear relationship between the dictionary matrix and the largest and smallest eigenvectors (i.e., the complex coefficient vectors). Finally, the signal azimuth is calculated through the correspondence between the complex coefficient vectors and the azimuth angles in the dictionary matrix.

[0033] Specifically, the following steps are included:

[0034] Step 1: Calculate the covariance matrix R of the array signal:

[0035]

[0036] Where X is the received data matrix of the M array elements, N is the number of sampling points, and R is the estimated value of the array received signal covariance matrix;

[0037] Step 2: Perform eigenvalue decomposition on R to obtain the eigenvalue sequence ∑ n ;

[0038] Step 3: For ∑ n Sort the data so that when the number of incident sources is K, ∑ n Median value λ k (k∈K) has the following relation:

[0039] λ1≥λ2≥…≥λ K >λ K+1 =…λ M

[0040] In the above formula, M represents the number of array elements, and the maximum and minimum eigenvalues ​​are denoted as λ. max and λ min , where λ max The corresponding eigenvector is denoted as u. s , λ min The corresponding eigenvector is denoted as u. n When the number of information sources is unknown and they are coherent sources, u s It contains all source information, u n This includes noise information;

[0041] Step 4: Construct the guiding vector dictionary matrix A(θ) P The dictionary matrix contains P angles, where P >> K, and K is the number of unknown sources.

[0042] Step 5: Given the steering vector matrix A formed by the azimuth angle of the incident source. d The space spanned by the source feature vectors is consistent with the space spanned by the source feature vectors and perpendicular to the space spanned by the noise feature vectors. Therefore, u s Can be derived from A d The column vectors in the vector representation are linear, while u n Then with A d The column vectors in the equation are perpendicular. However, due to noise, the above equality and perpendicularity relationships cannot be strictly maintained, leading to an infeasible solution for the convex optimization condition under the equation. Therefore, a double relaxation factor ε is introduced. s and ε n And satisfy ε s >0, ε n >0, using the relaxation factor, construct the convex optimization conditions of the inequality:

[0043] minimize||c||2

[0044] subject to

[0045] ||A(θ p )cu s ||≤ε s

[0046] ||[A(θ p )c] H ·u n ||≤ε n

[0047] Calculating the above formula yields the coefficient sequence c;

[0048] Step 6: Construct the spatial spectrum P(θ):

[0049]

[0050] Where P i ∈P, c i ∈c, a(θ) i ) is A(θ p The azimuth angle of the signal can be obtained by searching for the spectral peaks in the spatial spectrum P(θ) of the column vector of θ.

[0051] The double relaxation factor ε in step 5 s and ε n All of these are local minima close to 0. The values ​​can be adjusted according to the convergence of the solution to improve the spatial resolution of the direction finding while ensuring the existence of a feasible solution.

[0052] Furthermore, in step 5, ||c||2 in the convex optimization objective function can also be changed to ||c||1.

[0053] Simulation verification:

[0054] Figure 2 The simulation conditions are as follows: the number of array elements M is 16, the center frequency of the signal source is 800MHz, the array is a uniform linear array with an array spacing of half a wavelength, the number of snapshots N is 1024, the signal-to-noise ratio is 15dB, the number of signal sources K is 2, and the azimuths of the incoming waves are 50° and 85° respectively.

[0055] When the number of information sources is unknown, let the noise subspace of MUSIC be u n Zhang Cheng obtained the direction finding results of the conventional beamforming algorithm and the high-precision direction finding algorithm proposed in this invention, respectively. Figure 2 As shown. (Through) Figure 2 As can be seen, in the traditional MUSIC algorithm, due to the unknown number of information sources, the noise subspace leaks into the information source subspace, and the direction finding spatial spectrum shows a high spurious peak at 130°, causing the algorithm to fail. However, the unknown coherent information source direction finding algorithm based on double relaxation solution in this invention can accurately complete the direction finding of two incident information sources and has a higher sidelobe suppression ratio.

[0056] The above analysis leads to the following conclusions: This invention can perform direction finding even when there are coherent sources and the number of sources is unknown. Therefore, compared with traditional spatial spectrum direction finding techniques, this invention has wider algorithm adaptability and higher algorithm stability.

Claims

1. A direction-finding method for an unknown coherent source based on double relaxation solution, characterized in that, Includes the following steps: Step 1: Calculate the covariance matrix R of the array signal: In the above formula, X is the received data matrix of M array elements, and N is the number of sampling points; Step 2: Perform eigenvalue decomposition on R to obtain the eigenvalue sequence ∑ n ; Step 3: For ∑ n Sort the eigenvalues ​​and denote the largest and smallest eigenvalues ​​as λ. max and λ min , where λ max The corresponding eigenvector is denoted as u. s , λ min The corresponding eigenvector is denoted as u. n ; Step 4: Construct the guide vector dictionary matrix A(θ) P ) and complex coefficient sequence c, the dictionary matrix contains P angles, P >> K, where K is the number of unknown sources; Step 5: Introduce the double relaxation factor ε s and ε n And satisfy ε s >0, ε n If the value is greater than 0, construct convex optimization conditions for inequalities using the relaxation factor, and calculate the coefficient sequence c. Step 6: Construct the spatial spectrum P(θ): Among them, P i ∈P, c i ∈c, a(θ) i ) is A(θ p The column vector of ) with superscript H denotes conjugate transpose, and the signal azimuth angle is obtained by searching for spectral peaks in the spatial spectrum P(θ).

2. The method for direction finding of an unknown coherent source based on double relaxation solution according to claim 1, characterized in that, The convex optimization conditions for the inequalities constructed in step 5 are: minimize||c||2 subject to ||A(θ p ) c -u s ||≤e s ||[A(θ p )c] H ·u n ||≤ε n or minimize||c||1 subject to ||A(θ p ) c -u s ||≤e s ||[A(θ p )c] H ·u n ||≤ε n 。

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