A method for calculating polarization parameters of radar array signals based on vector MUSIC algorithm

Abstract

This invention discloses a method for calculating polarization parameters of radar array signals based on the vector MUSIC algorithm, relating to the field of radar array signal processing technology. First, this invention obtains the polarization signal steering vector matrix and noise subspace corresponding to the radar array signal, and performs matrix multiplication to obtain a 2×2 complex Hermitian matrix. By extracting the ratio of the imaginary to the real part of the second element in the first row of the complex Hermitian matrix, the arctangent function is directly applied to obtain the polarization phase difference, avoiding the process of solving for eigenvectors. Then, the minimum eigenvalue of the complex Hermitian matrix is ​​calculated, and combined with the trace of the complex Hermitian matrix, the arctangent value is calculated, and the polarization auxiliary angle is directly derived, eliminating the need for a complete eigenvalue decomposition process. Therefore, when calculating polarization parameters, the calculation starts from the definition of polarization parameters, i.e., directly from the definition of polarization phase difference and polarization auxiliary angle, directly avoiding the complex calculations brought about by eigenvalue decomposition, thereby reducing computational complexity and improving computational accuracy.

Description

Technical Field

[0001] This invention relates to the field of radar array signal processing technology, and in particular to a method, apparatus, device, and medium for calculating the polarization parameters of radar array signals based on the vector MUSIC algorithm. Background Technology

[0002] Direction of Arrival (DOA) estimation is a fundamental and crucial core problem in radar array signal processing. In recent years, with the development of military and civilian needs, the algorithms and engineering aspects related to DOA have progressed rapidly. Regarding DOA algorithms, the introduction of the Multiple Signal Classification (MUSIC) method has significantly improved angular resolution and angle measurement accuracy. Furthermore, many scholars have conducted research on improved MUSIC algorithms, focusing on DOA estimation for coherent signals encountered in real-world scenarios and subarray MUSIC algorithms. It is worth noting that in recent years, conformal phased array antennas have been used in spaceborne, airborne, missile-borne, and communication fields, especially in missile-borne applications. Conformal arrays are polarization-sensitive arrays, and their DOA estimation algorithm is a vector MUSIC algorithm. This algorithm can obtain not only the angular information of the external radiation source but also the polarization information, providing an important dimension of information for signal sorting, polarization anti-interference, and data processing.

[0003] Currently, scholars have conducted in-depth research on polarization-sensitive arrays. Compared with the scalar MUSIC algorithm, the processing flow of the vector MUSIC algorithm is basically similar. The main difference lies in the calculation formula of the pseudo-cepstrum. The scalar MUSIC algorithm can only obtain the angle information of the source, while the polarization MUSIC algorithm can not only obtain the angle information of the source, but also obtain the polarization auxiliary angle and polarization phase difference of the source.

[0004] In the polarization MUSIC algorithm, the current solution process for polarization parameter information, specifically the polarization auxiliary angle and polarization phase difference, involves performing matrix eigenvalue decomposition on a 2×2 complex Hermitian matrix, and then performing arctangent operation on the elements of the eigenvector corresponding to the smallest eigenvalue to obtain the polarization auxiliary angle and polarization phase difference. Commonly used methods for calculating the eigenvalue decomposition of the 2×2 complex Hermitian matrix include the QR algorithm, the Jacobi rotation method, and the solution method based on finding the roots of a quadratic equation. However, these methods are usually based on arithmetic iteration or solving a system of equations, which leads to high computational complexity and poor computational accuracy. Summary of the Invention

[0005] This invention provides a method for calculating the polarization parameters of radar array signals based on the vector MUSIC algorithm, which can solve the problems existing in the prior art.

[0006] This invention provides a method for calculating the polarization parameters of radar array signals based on the vector MUSIC algorithm, comprising the following steps:

[0007] The radar array signal data is acquired, and the spatial spectrum of the signal data is estimated using the vector multiple signal classification method MUSIC. The polarization signal steering vector matrix and covariance matrix corresponding to the signal data are obtained, and the covariance matrix is ​​decomposed into a noise subspace. The polarization signal steering vector matrix includes horizontal polarization steering vector and vertical polarization steering vector.

[0008] A matrix multiplication operation is performed between the polarization signal steering vector matrix and the noise subspace to obtain a 2×2 complex Hermitian matrix. The imaginary and real parts of the second element in the first row of the complex Hermitian matrix, which represents the difference in polarization phase change in the horizontal and vertical directions, are extracted. The arctangent value of the ratio of the imaginary part to the real part is obtained, and this arctangent value is used as the polarization phase difference of the radar array signal.

[0009] Obtain the smallest eigenvalue of the complex Hermitian matrix, and calculate the arctangent value by combining it with the trace of the complex Hermitian matrix. Use this arctangent value as the polarization auxiliary angle of the radar array signal.

[0010] Preferably, the 2×2 complex Hermitian matrix is ​​obtained as follows:

[0011] ;

[0012] ;

[0013] Where: B represents a 2×2 complex Hermitian matrix; Represents the polarization signal steering vector matrix; Represents the noise subspace; H Indicates transpose; and These represent the horizontal polarization steering vector and the corresponding vertical polarization steering vector corresponding to the location of the external radiation source, respectively; , , and These represent the four matrix elements of a 2×2 complex Hermitian matrix.

[0014] Preferably, the polarization phase difference is obtained in the following way:

[0015] ;

[0016] in: Indicates polarization phase difference; This represents the arctangent function.

[0017] Preferably, the polarization auxiliary angle is obtained in the following way:

[0018] ;

[0019] ;

[0020] in: Indicates the polarization auxiliary angle; Let represent the smallest eigenvalue of a 2×2 complex Hermitian matrix.

[0021] This invention also provides a device for calculating the polarization parameters of radar array signals based on the vector MUSIC algorithm, comprising:

[0022] The matrix construction module is used to acquire radar array signal data, perform spatial spectrum estimation on the signal data using the vector multi-signal classification method MUSIC, obtain the polarization signal steering vector matrix and covariance matrix corresponding to the signal data, and decompose the covariance matrix into a noise subspace; wherein, the polarization signal steering vector matrix includes horizontal polarization steering vector and vertical polarization steering vector.

[0023] Multiply the polarization signal steering vector matrix with the noise subspace to obtain a 2×2 complex Hermitian matrix.

[0024] The parameter calculation module is used to extract the imaginary and real parts of the second element in the first row of the complex Hermitian matrix, which represents the difference in polarization phase change in the horizontal and vertical directions, obtain the arctangent value of the ratio of the imaginary part to the real part, and use the arctangent value as the polarization phase difference of the radar array signal.

[0025] Obtain the smallest eigenvalue of the complex Hermitian matrix, and calculate the arctangent value by combining it with the trace of the complex Hermitian matrix. Use this arctangent value as the polarization auxiliary angle of the radar array signal.

[0026] This invention also provides an electronic device, including a memory and a processor;

[0027] The memory is used to store computer programs;

[0028] When the processor executes the computer program stored in the memory, it implements the steps of the method for calculating the polarization parameters of radar array signals based on the vector MUSIC algorithm as described above.

[0029] This invention also provides a computer-readable storage medium for storing a computer program, which, when executed by a processor, implements the steps of a method for calculating the polarization parameters of a radar array signal based on a vector MUSIC algorithm as described above.

[0030] This invention provides a method for calculating the polarization parameters of radar array signals based on the vector MUSIC algorithm. Compared with the prior art, its advantages are as follows:

[0031] This invention first acquires radar array signal data and processes it using a vector MUSIC algorithm to obtain the polarization signal steering vector matrix and noise subspace corresponding to the signal data. Then, it performs matrix multiplication on the polarization signal steering vector matrix and noise subspace to obtain a 2×2 complex Hermitian matrix. By extracting the ratio of the imaginary to real part of the second element in the first row of the complex Hermitian matrix, which represents the difference in polarization phase change in the horizontal and vertical directions, the arctangent function is directly applied to obtain the polarization phase difference, avoiding the process of solving for eigenvectors. Next, the minimum eigenvalue of the complex Hermitian matrix is ​​calculated, and combined with the trace of the complex Hermitian matrix, the arctangent value is calculated, directly deriving the polarization auxiliary angle. This eliminates the need for a complete eigenvalue decomposition process. Therefore, when calculating the polarization parameters of the radar array signal, the calculation starts directly from the definition of polarization parameters, i.e., from the definition of polarization phase difference and polarization auxiliary angle, directly avoiding the complex calculations brought about by eigenvalue decomposition, thereby reducing computational complexity and improving computational accuracy. Attached Figure Description

[0032] Figure 1 A schematic diagram of the overall process for calculating the polarization parameters of radar array signals based on the vector MUSIC algorithm, provided in an embodiment of the present invention;

[0033] Figure 2 A schematic diagram of the overlapping pseudo-cepstrum of a horizontally polarized source at 200 different angles, provided for a method of solving the polarization parameters of a radar array signal based on the vector MUSIC algorithm in an embodiment of the present invention.

[0034] Figure 3 A schematic diagram showing the ratio of the polarization phase difference obtained by calculating 200 sets of data to the polarization phase difference obtained by calculating 200 sets of data using MATLAB, provided in an embodiment of the present invention.

[0035] Figure 4 This diagram illustrates the ratio of the polarization auxiliary angle obtained from calculating 200 sets of data to the polarization parameter calculation method for radar array signals based on the vector MUSIC algorithm, as provided in this embodiment of the invention, to the polarization auxiliary angle obtained from calculating 200 sets of data using MATLAB. Detailed Implementation

[0036] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0037] See Figure 1 This invention provides a method for calculating the polarization parameters of radar array signals based on the vector MUSIC algorithm, comprising the following steps:

[0038] Step 1: Perform matrix multiplication on the steering vector and noise subspace corresponding to the source of the input radar array signal to obtain a 2×2 complex Hermitian matrix; specifically:

[0039] The steering vector and noise subspace corresponding to the source are respectively and Matrix multiplication yields:

[0040] .

[0041] Then, we can obtain:

[0042] .

[0043] in: and These represent the horizontal polarization steering vector and the corresponding vertical polarization steering vector corresponding to the location of the external radiation source, respectively; , , and These are the four matrix elements of a 2×2 complex Hermitian matrix.

[0044] Step 2: Solve for the arctangent function of the ratio of the imaginary to the real part of the second element in the first row of the 2×2 complex Hermitian matrix. This result is the polarization phase difference for the vector MUSIC algorithm. Specifically:

[0045] The formula for calculating the polarization phase difference is:

[0046] .

[0047] in: Indicates polarization phase difference; This represents the arctangent function.

[0048] Step 3: Directly solve for the smallest eigenvalue of the 2×2 complex Hermitian matrix, and then perform calculations. The result is the polarization auxiliary angle of the vector MUSIC algorithm; specifically:

[0049] The formula for calculating the polarization auxiliary angle is:

[0050] .

[0051] .

[0052] in: Indicates the polarization auxiliary angle; Representation matrix The smallest eigenvalue, .

[0053] In the specific experiment, this invention selected a microwave anechoic chamber to record echo data from a horizontally polarized radiation source at 200 different angles. The pseudo-cepstrum overlap of the horizontally polarized source at these 200 different angles was plotted as follows: Figure 2 As shown, the echo data is processed using the vector MUSIC algorithm, and then the polarization auxiliary angle and polarization phase difference are calculated according to the method of this invention.

[0054] First, following the programming of this invention, for 200 echo data from different angles, the calculated polarization phase difference results of this invention and the calculated polarization phase difference results of MATLAB are compared. The simulation results are as follows: Figure 3 As shown; where the X-axis coordinate represents the number of points, and the Y-axis represents the ratio of the polarization phase difference value obtained by this invention to the polarization phase difference value obtained by MATLAB.

[0055] Secondly, following the programming of this invention, for 200 echo data from different angles, the simulation results of calculating the polarization auxiliary angle using this invention and using MATLAB are compared, as shown below. Figure 4 As shown; where the X-axis coordinate represents the number of points, and the Y-axis represents the ratio of the polarization auxiliary angle value obtained by this invention to the polarization auxiliary angle value obtained by MATLAB.

[0056] Starting from the definition of polarization parameters, this invention uses matrix multiplication to obtain a 2×2 complex Hermitian matrix, and then calculates the analytical polarization parameters of the vector MUSIC algorithm according to the method of this invention, which can effectively improve the accuracy and real-time performance of the vector MUSIC algorithm in solving polarization parameters.

[0057] Starting from the definition of polarization parameters, this invention first performs matrix multiplication on the steering vector and noise subspace corresponding to the input source to obtain a 2×2 complex Hermitian matrix. The arctangent function of the ratio of the imaginary part to the real part of the second element in the first row of the 2×2 complex Hermitian matrix is ​​then calculated, and the result is the polarization phase difference. The minimum eigenvalue of the 2×2 complex Hermitian matrix is ​​then directly calculated. The arctangent function of the minimum eigenvalue is then calculated according to the formula listed in this invention, and the result is the polarization auxiliary angle. This can effectively reduce the computational complexity of the vector MUSIC algorithm in calculating polarization parameters, which is beneficial for its hardware implementation.

[0058] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for calculating the polarization parameters of radar array signals based on the vector MUSIC algorithm, characterized in that, Includes the following steps: The radar array signal data is acquired, and the spatial spectrum of the signal data is estimated using the vector multiple signal classification method MUSIC. The polarization signal steering vector matrix and covariance matrix corresponding to the signal data are obtained, and the covariance matrix is ​​decomposed into a noise subspace. The polarization signal steering vector matrix includes horizontal polarization steering vector and vertical polarization steering vector. A matrix multiplication operation is performed between the polarization signal steering vector matrix and the noise subspace to obtain a 2×2 complex Hermitian matrix. The imaginary and real parts of the second element in the first row of the complex Hermitian matrix, which represents the difference in polarization phase change in the horizontal and vertical directions, are extracted. The arctangent value of the ratio of the imaginary part to the real part is obtained, and this arctangent value is used as the polarization phase difference of the radar array signal. Obtain the smallest eigenvalue of the complex Hermitian matrix, and calculate the arctangent value by combining it with the trace of the complex Hermitian matrix. Use this arctangent value as the polarization auxiliary angle of the radar array signal. The 2×2 complex Hermitian matrix is ​​obtained as follows: ； ； Where: B represents a 2×2 complex Hermitian matrix; Represents the polarization signal steering vector matrix; Represents the noise subspace; H Indicates transpose; and These represent the horizontal polarization steering vector and the corresponding vertical polarization steering vector corresponding to the location of the external radiation source, respectively; , , and These represent the four matrix elements of a 2×2 complex Hermitian matrix; The polarization phase difference is obtained as follows: ； in: Indicates polarization phase difference; Represents the arctangent function; The polarization auxiliary angle is obtained as follows: ； ； in: Indicates the polarization auxiliary angle; Let represent the smallest eigenvalue of a 2×2 complex Hermitian matrix.

2. A device for calculating the polarization parameters of radar array signals based on a vector MUSIC algorithm, comprising the steps of the method for calculating the polarization parameters of radar array signals based on a vector MUSIC algorithm as described in claim 1, characterized in that, include: The matrix construction module is used to acquire radar array signal data, perform spatial spectrum estimation on the signal data using the vector multi-signal classification method MUSIC, obtain the polarization signal steering vector matrix and covariance matrix corresponding to the signal data, and decompose the covariance matrix into a noise subspace; wherein, the polarization signal steering vector matrix includes horizontal polarization steering vector and vertical polarization steering vector. Multiply the polarization signal steering vector matrix with the noise subspace to obtain a 2×2 complex Hermitian matrix. The parameter calculation module is used to extract the imaginary and real parts of the second element in the first row of the complex Hermitian matrix, which represents the difference in polarization phase change in the horizontal and vertical directions, obtain the arctangent value of the ratio of the imaginary part to the real part, and use the arctangent value as the polarization phase difference of the radar array signal. Obtain the smallest eigenvalue of the complex Hermitian matrix, and calculate the arctangent value by combining it with the trace of the complex Hermitian matrix. Use this arctangent value as the polarization auxiliary angle of the radar array signal.

3. An electronic device, characterized in that, include: Memory and processor; The memory is used to store computer programs; When the processor executes the computer program stored in the memory, it implements the steps of the method for calculating the polarization parameters of radar array signals based on the vector MUSIC algorithm as described in claim 1.

4. A computer-readable storage medium, characterized in that, Used to store a computer program, which, when executed by a processor, implements the steps of a method for calculating the polarization parameters of radar array signals based on a vector MUSIC algorithm as described in claim 1.

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