A beam domain matrix array angle estimation method based on subspace whitening processing

Abstract

The present application relates to a kind of beam domain matrix array angle estimation method based on subspace whitening processing, belong to radar, wireless communication field.The method of the present application includes: constructing rectangular array radar receiving signal mathematical model;Based on the approximate region of target existence or the space region of interest, the X-axis array and Z-axis array beam matrix are designed offline using the method of convex optimization;The spatial filtering processing is carried out to receiving signal matrix to obtain filtered matrix;The pre-whitening processing is carried out to filtered matrix, covariance matrix is constructed, and signal subspace is obtained after eigenvalue decomposition;From the signal subspace obtained, the azimuth and elevation angle information of target is extracted.The present application reconstructs spatial filter, realizes that bandwidth is dynamically adapted with detection scene;Incorporate sidelobe suppression mechanism, optimization filtering coefficient solving strategy, suppress sidelobe energy, improve main lobe concentration;By pre-whitening processing to the signal filtered in beam domain, improve angle estimation precision.

Description

Technical Field

[0001] This invention belongs to the fields of radar and wireless communication, and specifically relates to a beam domain matrix array angle estimation method based on subspace whitening processing. Background Technology

[0002] In modern electronic systems such as radar, wireless communication, and sonar detection, two-dimensional direction of arrival (DOA) estimation is a core technology for target localization, signal sorting, and resource scheduling. Rectangular arrays, with their planar element arrangement advantage, can simultaneously acquire azimuth and elevation angle information, making them the mainstream array structure for two-dimensional DOA estimation. Traditional one-dimensional arrays can only achieve single-angle measurement, failing to meet the needs of multi-target two-dimensional localization in complex scenarios. Rectangular arrays, by expanding the spatial aperture, significantly improve the resolution and degrees of freedom of angle estimation and have been widely applied in key areas such as military detection, smart antennas, and IoT positioning.

[0003] A schematic diagram of a rectangular array radar system is shown below. Figure 2 As shown. Currently, angle estimation methods for rectangular array radars are centered around subspace algorithms, with the MUSIC and ESPRIT algorithms being the most widely used classic solutions. However, there are significant differences between the two in their core computational logic and practical engineering applications. Specifically, the MUSIC algorithm requires a two-dimensional spectral peak search to calculate the angle. While it achieves basic angle estimation, the two-dimensional search process incurs enormous computational overhead, making it difficult to meet the performance standards required for engineering applications in scenarios with stringent latency requirements, such as real-time detection and dynamic tracking. In contrast, the ESPRIT algorithm, by exploiting the rotational invariance of the array antenna structure, eliminates the cumbersome spectral peak search step in traditional methods, effectively reducing overall computational complexity and better meeting the application requirements of high real-time scenarios.

[0004] In practical scenarios such as radar target tracking, the approximate spatial orientation of a target can usually be determined using prior information or previous detection data. Based on this practical characteristic, beam-domain algorithms, with their advantages of focusing on the target's spatial domain and suppressing background noise interference, have become an important technical direction for improving angle measurement accuracy. For example, in the paper "Performance analysis of closed-form, ESPRIT based 2-D angle estimator for rectangular arrays," a beam-domain ESPRIT angle estimation algorithm is proposed. This algorithm maps the original signal received in the element domain to the beam domain through a discrete Fourier transform (DFT) matrix, and optimizes the angle measurement accuracy by utilizing the spatial energy focusing effect. However, this type of traditional beam-domain ESPRIT method has a significant technical shortcoming: the spatial filter used is directly composed of multiple discrete Fourier transform beams, and the inherent frequency domain equalization characteristic of Fourier beams makes it impossible to flexibly adjust the main lobe width and side lobe level according to actual needs. When the main lobe width is too wide, it will lead to a decrease in target echo gain. Furthermore, if an orthogonal spatial filter is not used, the filtered noise will become colored noise, and the above-mentioned drawbacks will ultimately cause a significant decline in the accuracy of target angle estimation. Summary of the Invention

[0005] (a) Technical problems to be solved The technical problem to be solved by this invention is how to provide a beam domain matrix array angle estimation method based on subspace whitening processing, so as to solve the shortcomings of the existing beam domain ESPRIT algorithm in terms of spatial filtering performance and angle measurement accuracy.

[0006] (II) Technical Solution To address the aforementioned technical problems, this invention proposes a beam domain matrix array angle estimation method based on subspace whitening processing. This method includes the following steps: S1. Construct a mathematical model for the received signals of a rectangular array radar; S2. Based on the approximate region where the target exists or the spatial region of interest, the X-axis and Z-axis array beam matrices are designed offline using convex optimization methods. as well as This ensures that the virtual steering vector has a rotation-invariant structure, and that the sidelobe level of the spatial filter is as low as possible. S3, For the received signal matrix Spatial domain filtering is performed to obtain the filtered matrix. ; S4, to Pre-whitening is performed, the covariance matrix is ​​constructed, and the signal subspace is obtained after eigenvalue decomposition. , It is the eigenvalue matrix formed by the eigenvalues ​​corresponding to the signal covariance matrix; S5. From the obtained signal subspace The azimuth and elevation angle information of the target are extracted.

[0007] (III) Beneficial Effects This invention proposes a beam domain matrix array angle estimation method based on subspace whitening processing. Compared with existing technologies, this invention has the following advantages: (1) This invention innovatively adopts the convex optimization method for the design of spatial filters, which breaks through the limitation of fixed filter bandwidth in traditional technology. The filter bandwidth parameters can be flexibly adjusted according to the specific needs of actual detection tasks, thereby achieving efficient adaptation to different application scenarios. (2) After completing the beam domain conversion operation, the present invention can effectively control the sidelobe level of the spatial filter while retaining the key rotation invariant structure, thereby avoiding interference caused by the sidelobe and ensuring the effectiveness of signal processing. (3) By pre-whitening the signal after beam domain filtering, the present invention can significantly improve the accuracy of angle estimation. Attached Figure Description

[0008] Figure 1 This is a flowchart provided for an embodiment of the present invention; Figure 2 This is a schematic diagram of a rectangular array radar structure; Figure 3 The graph shows the root mean square error as a function of the signal-to-noise ratio when the pulse number is fixed at 50. Figure 4 The graph shows the root mean square error as a function of the number of pulses when the signal-to-noise ratio of a single pulse is fixed at 0dB. Detailed Implementation

[0009] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0010] To address the aforementioned shortcomings, the present invention aims to propose a beam domain rectangular array angle estimation method based on subspace whitening processing, which can effectively improve the target angle measurement accuracy.

[0011] To address the shortcomings of existing beam-domain ESPRIT algorithms in spatial filtering performance and angle measurement accuracy, this invention proposes the following: First, it reconstructs the spatial filter by introducing an adjustable parameterized model, overcoming the limitation of fixed Fourier beam bandwidth and achieving dynamic bandwidth adaptation to the detection scenario. Second, it incorporates a sidelobe suppression mechanism, optimizes the filter coefficient solution strategy, suppresses sidelobe energy, and improves main lobe concentration. Third, it improves angle estimation accuracy by pre-whitening the signal after beam-domain filtering.

[0012] To achieve the above objectives, the present invention employs the following technical solution.

[0013] A beam domain matrix array angle estimation method based on subspace whitening processing specifically includes the following steps: S1. Constructing a mathematical model for the received signal of a rectangular array radar. ; S2. Based on the approximate region where the target exists or the spatial region of interest, the X-axis and Z-axis array beam matrices are designed offline using convex optimization methods. as well as This ensures that the virtual steering vector has a rotation-invariant structure, and that the sidelobe level of the spatial filter is as low as possible. S3, For the received signal matrix Spatial domain filtering is performed to obtain the filtered matrix. ; S4, to Pre-whitening is performed, the covariance matrix is ​​constructed, and the signal subspace is obtained after eigenvalue decomposition. , It is the eigenvalue matrix formed by the eigenvalues ​​corresponding to the signal covariance matrix; S5. From the obtained signal subspace The azimuth and elevation angle information of the target are extracted.

[0014] Example 1: Reference Figure 1 The specific implementation steps of this invention are as follows: Step S1: Construct a mathematical model for the received signals of a rectangular array radar.

[0015] Figure 2 This is a schematic diagram of a rectangular array radar, with the array elements located in the XOZ plane. The number of array elements along the X and Z axes are respectively... M and N The total number of units in the rectangular array is MN All are half-wavelength, equally spaced, uniform linear arrays, i.e., the element spacing is... , This represents the signal wavelength. Assume the number of incoherent targets in the far field is... , No. The azimuth and elevation angles of each target are respectively used as... and In this case, under single-shot conditions, the signal received by the rectangular array can be represented as... vector (1) Among them, the guiding matrix (2) Among them, matrix , ,symbol Represents the Khatri-Rao product, symbol It represents the Kronecker product.

[0016] vector and For the X-axis array and Z-axis array about the first The guidance vectors of the targets are respectively represented as: (3) (4) in, , .symbol Represents the transpose of a matrix or vector.

[0017] This represents the received signal vector. ,in L This represents the total number of snapshots.

[0018] Let represent the noise vector of the rectangular array, where each element follows a zero-mean Gaussian distribution. For convenience, equation (1) can be reformulated as a received signal matrix. (5) Among them, matrix , as well as .

[0019] Step S2: Based on the approximate spatial domain of the target or the spatial region requiring special attention, use convex optimization methods to design the beam matrices of the X-axis and Z-axis arrays offline. as well as .

[0020] First, construct the virtual guide vector of the X-axis array. ,in , This is called the dimension of the X-axis array beam domain. The core design goal is to construct a... beam matrix Make in the desired airspace As close as possible Due to the virtual guide vector It possesses a rotation-invariant structure, thus avoiding the need for angle estimation using search algorithms. (Symbol) This represents the conjugate transpose of a matrix or vector. Simultaneously, the sidelobe level of the spatial filter should be as low as possible to improve the main-to-sidelobe ratio. Based on this, the X-axis array beam matrix... This is obtained by solving the following convex optimization problem.

[0021] (6) in, This indicates the sinusoidal spatial region of interest. yes The complement of the spatial filter is the sidelobe region. and They are in and Number of sampling points in the two regions. Positive parameter. Limited to middle and The maximum permissible error.

[0022] For Z-axis arrays, the design logic remains the same, and the beam matrix is ​​designed using the same method.

[0023] (7) in This indicates the pitch sine space region of interest. yes The complement of the spatial filter is the sidelobe region. This is called the Z-axis array virtual guide vector, where This is called the Z-axis array beam domain dimension, and it exists. Similarly, positive parameters Limited to middle and The maximum permissible error.

[0024] Thus, the normalized amplitude-frequency response functions in the azimuth and elevation dimensions are respectively... (8) (9) Step S3: Calculate the beam matrix based on the beam matrix obtained in step S2. as well as and the received signal matrix Spatial filtering is performed, specifically as follows: (10) Among them, symbols Represent the Kronecker product. In equation (5), ... Substituting the expression into the above formula yields...

[0025]

[0026]

[0027]

[0028] (11) in, Affected by beam domain filtering, The noise is no longer Gaussian white noise, but colored noise, which will affect the accuracy of angle measurement. Note that, without considering interpolation errors, there is an equation. and .matrix and It has the following forms (12) (13) Under this premise, the above formula can be transformed into (14) Step S4: For the matrix Pre-whitening is performed, a covariance matrix is ​​constructed, and eigenvalue decomposition is performed to obtain the signal subspace.

[0029] Step S4 specifically includes the following sub-steps: S41. Define the prewhitening matrix. (15) (16) right Pre-whitening treatment is performed, and the specific method is as follows: (17) in (18) As can be seen from the above equation, the noise matrix It is an identity matrix, which has eliminated the effects of beam domain transformation.

[0030] S42. The signal model obtained now It is The matrix, by constructing covariance matrix Based on well-known techniques in the field, the matrix Eigenvalue decomposition yields the signal subspace ,in It is by The feature matrix is ​​composed of the principal eigenvalues, and the number of columns is the same as the number of targets.

[0031] Step S5: From the obtained signal subspace The azimuth and elevation angle information of the target are extracted.

[0032] Step S5 specifically includes the following sub-steps: S51. From (17), we can see that the signal subspace and The resulting subspaces are identical. This yields the signal subspace. Then, it was processed as follows. (19) S52. Angle information can be extracted based on the following two formulas: (20) (twenty one) in, , , as well as This is called the selection matrix. and It has the following forms of expression. and , in It is non-singular matrices, , The above. express The identity matrix of order above express An identity matrix of order 1, for example Intuitively represented as:

[0033] S53. Obtained using the least squares algorithm and ,get (twenty two) (twenty three) in, This indicates finding the pseudo-inverse of a matrix.

[0034] S54, Obtain the matrix and Then, they are subjected to feature decomposition, and their first... Each eigenvalue is used as follows: and This indicates that the calculation of the first... Estimated pitch and azimuth angles for each target.

[0035] No. The pitch angle estimate of a target can be expressed in the following form: (twenty four) in, This indicates a phase take operation.

[0036] No. The estimated azimuth angles of the targets are: (25) Example 2: The effectiveness of this invention can be further illustrated by the following computer simulation results: I. Simulation Conditions Simulation condition 1, reference Figure 2 Rectangular array radar X array element number Z array element number The azimuth and pitch dimensions of interest are respectively in the spatial region. and Suppose two unrelated far-field targets. and The accuracy of angle measurement is evaluated using the root mean square error, which is defined as follows: (26) in, and They represent the first Estimates of the azimuth and elevation angles of the k-th target in the Monte Carlo test. This represents the total number of Monte Carlo experiments. Based on the above conditions, a comparative analysis is conducted on the angle measurement accuracy of the improved method of this patent and the traditional two-dimensional beam domain ESPRIT.

[0037] II. Simulation Content Simulation 1 compares the angle measurement accuracy of this patented method with that of the traditional beam-domain ESPRIT method, where CRB is the theoretical value of the Cramer-Rao boundary. The traditional and improved methods have the same transmit and receive spatial dimensions. and Set optimization parameters as well as . Figure 3 The results show the variation of root mean square error with signal-to-noise ratio when the pulse number is fixed at 50. Figure 4 This demonstrates how the root mean square error varies with the number of pulses when the signal-to-noise ratio of a single pulse is fixed at 0dB.

[0038] like Figure 3 , 4 As shown, compared to the traditional beam-domain ESPRIT method, the angle measurement accuracy of the method in this invention is significantly improved. Two key factors contribute to this advantage: first, the designed spatial filter possesses excellent characteristics; and second, the signal after spatial filtering undergoes pre-whitening processing to eliminate the adverse effects of colored noise.

[0039] Compared with the prior art, the present invention has the following advantages: (1) This invention innovatively adopts the convex optimization method for the design of spatial filters, which breaks through the limitation of fixed filter bandwidth in traditional technology. The filter bandwidth parameters can be flexibly adjusted according to the specific needs of actual detection tasks, thereby achieving efficient adaptation to different application scenarios. (2) After completing the beam domain conversion operation, the present invention can effectively control the sidelobe level of the spatial filter while retaining the key rotation invariant structure, thereby avoiding interference caused by the sidelobe and ensuring the effectiveness of signal processing. (3) By pre-whitening the signal after beam domain filtering, the present invention can significantly improve the accuracy of angle estimation.

[0040] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A beam domain matrix array angle estimation method based on subspace whitening processing, characterized in that, The method includes the following steps: S1. Construct a mathematical model for the received signals of a rectangular array radar; S2. Based on the approximate region where the target exists or the spatial region of interest, the X-axis and Z-axis array beam matrices are designed offline using convex optimization methods. as well as This ensures that the virtual steering vector has a rotation-invariant structure, and that the sidelobe level of the spatial filter is as low as possible. S3, For the received signal matrix Spatial domain filtering is performed to obtain the filtered matrix. ; S4, to Pre-whitening is performed, the covariance matrix is ​​constructed, and the signal subspace is obtained after eigenvalue decomposition. , It is the eigenvalue matrix formed by the eigenvalues ​​corresponding to the signal covariance matrix; S5. From the obtained signal subspace The azimuth and elevation angle information of the target are extracted.

2. The beam domain matrix array angle estimation method based on subspace whitening processing as described in claim 1, characterized in that, S1 includes: The array elements are located in the XOZ plane of the coordinate system; the number of array elements along the X-axis and Z-axis are respectively... M and N The total number of units in the rectangular array is MN All are half-wavelength, equally spaced, uniform linear arrays, i.e., the element spacing is... , Indicates the signal wavelength; Assume the number of incoherent targets in the far field is , No. The azimuth and elevation angles of each target are respectively used as... and This indicates that, under single-shot conditions, the signal received by the rectangular array is represented as follows: vector （1） in, Guiding Matrix （2） Among them, matrix , ,symbol Represents the Khatri-Rao product, symbol Indicates the Kronecker product; vector and For the X-axis array and Z-axis array about the first The guidance vectors of the targets are respectively represented as: （3） （4） in, , ;symbol Represents the transpose of a matrix or vector; This represents the received signal vector. ,in L This represents the total number of snapshots. The noise vector of the rectangular array is represented by each element following a zero-mean Gaussian distribution; Equation (1) is rewritten as the received signal matrix. （5） Among them, matrix , as well as .

3. The beam domain matrix array angle estimation method based on subspace whitening processing as described in claim 2, characterized in that, In S2, Constructing a virtual guide vector for the X-axis array ,in , The dimension referred to as the X-axis array beam domain; the core design objective is to construct a beam matrix Make in the desired airspace As close as possible ;symbol Represents the conjugate transpose of a matrix or vector; virtual guided vector It possesses a rotationally invariant structure, and the sidelobe level of the spatial filter should be as low as possible to improve the main-to-sidelobe ratio; accordingly, the X-axis array beam matrix... This is obtained by solving the following convex optimization problem. （6） in, This indicates the sinusoidal spatial region of interest. yes The complement of the spatial filter, i.e., the sidelobe region of the spatial filter; and They are in and Number of sampling points in two regions; positive parameter Limited to middle and The maximum permissible error.

4. The beam domain matrix array angle estimation method based on subspace whitening processing as described in claim 3, characterized in that, In S2, For Z-axis arrays, the design logic remains the same, and the beam matrix is ​​designed using the same method. （7） in This indicates the pitch sine space region of interest. yes The complement of the spatial filter, i.e., the sidelobe region of the spatial filter; This is called the Z-axis array virtual guide vector, where This is called the Z-axis array beam domain dimension, and it exists. ; Similarly, positive parameters Limited to middle and The maximum permissible error.

5. The beam domain matrix array angle estimation method based on subspace whitening processing as described in claim 4, characterized in that, S2 further includes: The normalized amplitude-frequency response functions for azimuth and elevation dimensions are calculated as follows: （8） （9）。 6. The beam domain matrix array angle estimation method based on subspace whitening processing as described in claim 4, characterized in that, S3 includes: The beam matrix calculated in step S2 as well as and the received signal matrix Spatial filtering is performed, specifically as follows: （10） Among them, symbols Represent the Kronecker product; in equation (5)(5) Substituting the expression into the above formula yields... （11） in, Affected by beam domain filtering, It is no longer Gaussian white noise, but colored noise, which will affect the accuracy of angle measurement; Without considering interpolation errors, there exists an equation. and ;matrix and It has the following forms （12） （13） Under this premise, the above formula is then transformed into （14）。 7. The beam domain matrix array angle estimation method based on subspace whitening processing as described in claim 6, characterized in that, S4 includes: S41. Define the prewhitening matrix. （15） （16） right Pre-whitening treatment is performed, and the specific method is as follows: （17） in （18） From the above equation, we can see that the noise matrix It is an identity matrix, which has eliminated the effects of beam domain transformation; S42, Signal Model It is The matrix is ​​constructed by covariance matrix For the matrix Eigenvalue decomposition yields the signal subspace ,in It is by The feature matrix is ​​composed of the principal eigenvalues, and the number of columns is the same as the number of targets.

8. The beam domain matrix array angle estimation method based on subspace whitening processing as described in claim 7, characterized in that, S5 includes: S51. From (17), we can see that the signal subspace and The constructed subspaces are identical; thus, the signal subspace is obtained. Then, it was processed as follows. （19） S52. Angle information extraction is based on the following two formulas: （20） （21） in, , , as well as This is called the selection matrix; matrix and It has the following forms of expression. and ,in It is non-singular matrices, , The above express The identity matrix of order above express An identity matrix of order 1; S53. Obtained using the least squares algorithm and ,get （22） （23） in, This indicates finding the pseudo-inverse of a matrix; S54, Obtain the matrix and Then it is subjected to feature decomposition, the first Each eigenvalue is used as follows: and This indicates that the calculation of the first... Estimates of the pitch and azimuth angles of each target.

9. The beam domain matrix array angle estimation method based on subspace whitening processing as described in claim 8, characterized in that, No. The pitch angle estimate of a target can be expressed in the following form: （24） in, This indicates a phase take operation.

10. The beam domain matrix array angle estimation method based on subspace whitening processing as described in claim 9, characterized in that, No. The estimated azimuth angles of the targets are: （25）。

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