Method for carrying out coherent signal angle estimation by utilizing circular array rotation

Abstract

The invention belongs to the technical field of aero-engines, and particularly relates to a method for performing coherent signal angle estimation by using circular array rotation, which comprises the following steps: S1, a fixed radiation source radiates a uniform circular array with a circle center movement track as a circumference, and the uniform circular array has an output vector at each moment in the circle center movement process, the output vector at the ith moment is that the number of array elements of the uniform circular array and the number of the output vectors are both two; s2, constructing a covariance matrix by using the output vectors; s3, carrying out characteristic decomposition on the covariance matrix to obtain a noise subspace; s4, constructing a spatial spectrum function according to the noise subspace; and S5, obtaining an extreme value according to the spatial spectrum function, and determining an azimuth angle and a pitch angle of the radiation source radiation according to the position of the extreme value. According to the method, spatial transformation is not needed, extra residual errors are not introduced, and therefore accurate angle estimation can be obtained.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aero-engines, and particularly relates to a method for angle estimation of coherent signals by rotating a circular array. BACKGROUND

[0002] The angle estimation of coherent signals has always been a challenge in the field of array signal processing. Unlike independent signals, coherent signals will cause the rank deficiency of the covariance of the array output vector, thereby causing the angle estimation method based on independent signals to fail, and further increasing the processing difficulty of the angle estimation of coherent signals. Most of the existing angle estimation methods use linear arrays, and compared with linear arrays, the geometric simplicity of uniform circular arrays makes them easy to deploy and maintain, and the uniform circular array can estimate 360° and 90° for azimuth and elevation angles respectively, so that the azimuth information of the target can be obtained more accurately.

[0003] The existing angle estimation methods based on circular arrays include:

[0004] 1. The real beam space transformation method based on phase mode excitation. The real beam space transformation technology effectively maps the steering vector of the uniform circular array to the manifold of the linear array, so that the estimation method based on the linear array can be applied to the uniform circular array. After the output vector of the uniform circular array is transformed by using the beam space transformation matrix, the MUSIC method can be used for angle estimation. However, this method needs to assume the known elevation angle, and the transformation of the output of the uniform circular array by using the real beam space transformation method will introduce residual errors, thereby reducing the accuracy of the angle estimation.

[0005] 2. The singular value decomposition algorithm and the Bayesian method both need to assume that the incident signal has a fixed 90° elevation angle, so that the uniform circular array is limited to one-dimensional angle estimation, resulting in the loss of important incident signal angle information.

[0006] Main disadvantage one: the real beam space transformation method based on phase mode excitation will introduce residual errors, thereby reducing the accuracy of the angle estimation.

[0007] Main disadvantage two: the singular value decomposition algorithm and the Bayesian method need to assume that the incident signal has a fixed 90° elevation angle, so that the uniform circular array can only perform one-dimensional angle estimation, resulting in the loss of important incident signal angle information. SUMMARY

[0008] In order to solve the above problems, the application provides a method for angle estimation of coherent signals by rotating a circular array, which comprises:

[0009] Step S1: radiate a uniform circular array with a circular center motion trajectory as a circle by a fixed radiation source. The uniform circular array has an output vector at each time during the circular center motion process, and the output vector at the i th time is represented as x i, i = 1, 2, …, N, where N is the number of elements of the uniform circular array. the output vector is , the number of elements of the uniform circular array and the number of output vectors are both ;

[0010] Step S2: constructing a covariance matrix from the output vectors;

[0011] Step S3: performing eigen decomposition on the covariance matrix to obtain a noise subspace ;

[0012] Step S4: constructing a spatial spectrum function from the noise subspace ;

[0013] Step S5: obtaining extrema from the spatial spectrum function , and determining the azimuth and elevation of the radiation source according to the positions of the extrema.

[0014] Preferably, the expression of

[0015] (1)

[0016] (2)

[0017] (3)

[0018] wherein, is a steering vector, is a direction matrix of the uniform circular array, is an incident angle of the far-field coherent signal; is an incident signal, is a signal correlation coefficient vector composed of non-zero complex values, is a signal correlation coefficient, , is an additive white Gaussian noise vector independent of the incident signal, , , is a wavelength of the signal, denotes a transposition operation of a matrix or a vector; is the number of elements of the uniform circular array, is a radius of the uniform circular array, and an angle of the ( )th element relative to the axis is , is a natural constant, is a noise vector, is a direction matrix during array rotation.

[0019] Preferably, the direction matrix is expressed as:

[0020] (4)

[0021] where, is a steering vector during array rotation.

[0022] Preferably, the covariance matrix is constructed as:

[0023] When is even, and when (i.e. ), the element in the th row and th column of the matrix is:

[0024] (5)

[0025] where, , denotes taking the expectation, denotes taking the row of a matrix, denotes the conjugate of a matrix, denotes the conjugate transpose of a matrix, denotes the noise energy, , , denotes the diagonal function, , denotes the signal energy, , , is written as:

[0026] (6)

[0027] From equation (5), when varies from 1 to in , there are independent elements. By stacking these elements together, a vector is formed, and as varies from 1 to in , there are vectors, and by arranging these vectors in the following manner, a matrix :

[0028] (7)

[0029] When , i.e. , the th element of the matrix is:

[0030] (8)

[0031] When , in , changes from 1 to , and changes from to , the following covariance matrix can be obtained:

[0032] (9)

[0033] By combining equation (7) and equation (9), the covariance matrix when is even is:

[0034] (10)

[0035] where denotes the noise power, is the identity matrix of , is full rank, is full rank;

[0036] When is odd, and when , i.e. , denotes the floor function, there is:

[0037] (11)

[0038] When changes from 1 to , and changes from 1 to , there is

[0039] (12)

[0040] When , i.e. , there is (13)

[0041] When from 1 to , and from to , there are

[0042] (14)

[0043] By combining equation (12) and equation (14), the covariance matrix when n is even is obtained is:

[0044] (15)

[0045] Preferably, step S3 specifically comprises: performing eigenvalue decomposition on the covariance matrix to obtain n small eigenvalues corresponding to eigenvectors , wherein , and the eigenvectors constitute the noise subspace . , .

[0046] Preferably, the spatial spectrum function is:

[0047] (16)

[0048] wherein, .

[0049] Preferably, step S5 specifically comprises: setting the elevation angle search range , the azimuth angle search range , obtaining the values of each point in the elevation angle search range and the azimuth angle search range , and the values contain n maximum values, the position corresponding to the mth maximum value is the estimated value of the elevation angle of the mth incident signal , and the estimated value of the azimuth angle of the mth incident signal , and further obtaining the azimuth angle and the elevation angle of the radiation source.

[0050] ​​​​This invention implements a novel two-dimensional angle estimation algorithm for coherent signals by rotating a circular array. It primarily addresses the problem that in real-world scenarios, signals incident on the array often exhibit correlation or complete coherence due to refraction, reflection, and diffraction, leading to inaccurate target angle estimation. Unlike real-beam spatial transformation methods based on phase mode excitation, which introduce residual errors and reduce angle estimation accuracy, and methods such as singular value decomposition and sparse Bayesian methods, which require assuming a 90° elevation angle for the incident signal and limit the uniform circular array to one-dimensional angle estimation, resulting in the loss of crucial incident signal information, this invention does not require a 90° elevation angle assumption and can simultaneously estimate both the azimuth and elevation angles of the coherent signal.

[0051] The advantages of this application are:

[0052] (1) Unlike the real beam spatial transformation method based on phase mode excitation, which introduces residual errors and reduces the accuracy of angle estimation, this invention can obtain accurate angle estimation without spatial transformation and without introducing additional residuals.

[0053] (2) Unlike singular value decomposition algorithms and sparse Bayesian methods, which require assuming the elevation angle of the incident signal is 90°, limiting the uniform circular array to one-dimensional angle estimation and resulting in the loss of elevation information of the incident signal, this invention does not require assuming the elevation angle is 90° and can simultaneously estimate the azimuth and elevation angles.

[0054] Improved angle estimation accuracy allows for more precise location of target radiation sources, enabling more accurate target search, rescue, or strike missions. Attached Figure Description

[0055] Figure 1 This is a flowchart illustrating a method for estimating the angle of a coherent signal using circular array rotation, as provided in Example 1.

[0056] Figure 2 This is a schematic diagram of the azimuth and elevation angles of the incident signal in a method for estimating the angle of a coherent signal using circular array rotation, as provided in Example 1.

[0057] Figure 3 This is a schematic diagram of the rotation of the circular array used in the method for coherent signal angle estimation using circular array rotation provided in Example 1.

[0058] Figure 4 The azimuth angle is an azimuth angle provided in Example 1 for a method of coherent signal angle estimation using circular array rotation. The root mean square error (RMSE) curve of the signal-to-noise ratio is shown, where the number of snapshots is set to 300.

[0059] Figure 5 The azimuth angle is an azimuth angle provided in Example 1 for a method of coherent signal angle estimation using circular array rotation. The root mean square error (RMSE) of the image is shown as a function of the number of snapshots, with the signal-to-noise ratio set to 10 dB.

[0060] Figure 6 The elevation angle is provided in Example 1 as a method for estimating coherent signal angles using circular array rotation. The root mean square error (RMSE) curve of the signal-to-noise ratio is shown, where the number of snapshots is set to 200.

[0061] Figure 7 The elevation angle is provided in Example 1 as a method for estimating coherent signal angles using circular array rotation. The root mean square error (RMSE) curve of the number of snapshots is shown, where the signal-to-noise ratio is set to 15dB. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some embodiments of this application, not all embodiments. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without creative effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings. Example 1

[0063] See Figures 1-7 This embodiment provides a method for estimating the angle of coherent signals using circular array rotation. The method specifically includes the following steps:

[0064] Step 1: Assume a uniform circular array consisting of 8 elements, with a radius of... Meters, the ( ) array elements relative to The angle of the axis is .like Figure 3 As shown, the center of this uniform circular array revolves around The axis rotates counterclockwise in a circular motion with an angular velocity of . rad / s (radian per second), and the circular array itself does not rotate. Assuming that there is a signal radiated by a radiation source and the signal is incident on the array through reflection, refraction, etc., and the total number of incident signals is 3, the angles of the three incident signals are , , where is the pitch angle, is the azimuth angle, and a schematic diagram of the azimuth angle and the pitch angle is shown in Figure 2 .

[0065] The origin is set as the phase reference center, and at the time , the output vector of the uniform circular array is:

[0066] (1)

[0067] where is the incident signal, , is a signal correlation coefficient vector composed of three non-zero complex values, is a signal correlation coefficient, , is an additive white Gaussian noise vector independent of the incident signal, is a steering vector, is a direction matrix of the uniform circular array, where

[0068] (2)

[0069] , , is the wavelength of the signal, denotes the transpose operation of a matrix or a vector, is a natural constant, is a direction matrix in the array rotation process, and is expressed as:

[0070] (3)

[0071] where is a steering vector in the array rotation process.

[0072] Step 2: by using the output of the array at the time in the rotation process, where , . When the array rotates one revolution, 8 outputs of the array rotated to an angle are obtained.

[0073] Step 3: Construct the covariance matrix using the output data of equation (1) . Using to denote the angle between the line connecting the center of the circular array and the coordinate origin and the axis of the circular array. Due to the symmetry of the uniform circular array, the following discussion will be divided into two parts.

[0074] When (i.e. ), the th element of matrix is:

[0075] (4)

[0076] where , denotes the expectation, denotes taking the th row of the matrix, denotes the conjugate of the matrix, denotes the conjugate transpose of the matrix, denotes the noise energy, , denotes the diagonal function, , denotes the signal energy, , , and can be written as:

[0077] (5)

[0078] From equation (4), when varies from 1 to 8 in , 8 independent elements are obtained. By stacking these 8 elements together, a vector is formed. As varies from 1 to 4 in , 4 vectors are obtained. Arranging these 4 vectors in the following manner, matrix is obtained:

[0079] (6)

[0080] When (i.e. ), the th element of matrix is: (7)

[0081] When varies from 1 to 8 in , and​ From to , the following covariance matrix :

[0082] (8)

[0083] By combining (6) and (8), the covariance matrix for even is:

[0084] (9)

[0085] where denotes the noise power, is the identity matrix of . It can be seen that is full rank, which means is also full rank.

[0086] Step 4: By performing eigenvalue decomposition on , we can obtain 5 small eigenvalues corresponding to eigenvectors , which constitute the noise subspace , .

[0087] Step 5, construct the spatial spectrum function , its expression is

[0088] (10)

[0089] where .

[0090] Step 6: Set the elevation angle search range , the azimuth angle search range , get the value of each point in the elevation angle and azimuth angle search range. These values contain 3 maximum values, and the positions corresponding to the 3 maximum values are the elevation angle estimate and the azimuth angle estimate .

[0091] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited to this. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for estimating the angle of a coherent signal using circular array rotation, characterized in that, include: Step S1: Radiate a uniform circular array with a fixed radiation source and a circular trajectory. During the movement of the uniform circular array around the center, it has an output vector at each moment. At the i-th moment... The output vector is The number of elements and the number of output vectors of a uniform circular array are both indivual; Step S2: Construct the covariance matrix from the output vectors ; Step S3: Adjust the covariance matrix Perform eigenvalue decomposition to obtain the noise subspace. ; Step S4: Based on the noise subspace Constructing the spatial spectral function ; Step S5: Based on the spatial spectrum function get Each extreme value, according to The location of each extreme value determines the azimuth and elevation angles of the radiation source.

2. The method for coherent signal angle estimation using circular array rotation as described in claim 1, characterized in that, The expression is: ； (1) ； (2) (3) in, As the guide vector, It is the direction matrix of a uniform circular array. For have The incident angle of a far-field coherent signal; It is the incident signal. It is by A vector of signal correlation coefficients composed of non-zero complex values The correlation coefficient is the signal correlation coefficient. , It is an additive white Gaussian noise vector independent of the incident signal. , , It is the wavelength of the signal. Represents the transpose operation of a matrix or vector; The number of elements in a uniform circular array. Let be the radius of a uniform circular array, and be the... ( ) array elements relative to The angle of the axis is , It is a natural constant. For noise vectors, This is the direction matrix during the array rotation process.

3. The method for coherent signal angle estimation using circular array rotation as described in claim 1, characterized in that, Direction matrix The expression is: ； (4) in, This is the guide vector during the array rotation process.

4. The method for coherent signal angle estimation using circular array rotation as described in claim 1, characterized in that: covariance matrix The specific construction method is as follows: when It is even, and when (Right now When ), the matrix The The elements are: （5） in, , Indicates the expectation. Indicates taking the first matrix. OK, Represents the conjugate of a matrix. This represents the conjugate transpose of a matrix. Represents noise energy. , Represents a diagonal function. , Indicates signal energy. , , Written as: （6） From formula (5), it can be seen that when exist From 1 to At that time, you will receive Each is an independent element. By using this The elements are stacked together to form a vector. ,along with exist From 1 to ,get a vector, this The vectors are arranged as follows to obtain the matrix. : （7） when ,Right now At that time, matrix The The elements are: （8） when exist From 1 to ,and from Change to When this is done, the following comatrix can be obtained. : （9） By combining formulas (7) and (9), we obtain Covariance matrix when it is even for: （10） in, Indicates noise power. for The identity matrix, To be full rank, For full rank; when When it is an odd number, and when ,Right now , When rounding down, we have （11） when From 1 to ,and From 1 to Sometimes, （12） when ,Right now Sometimes, （13） when From 1 to ,and from Change to Sometimes, （14） By combining formula (12) and formula (14), we obtain Covariance matrix when it is even for: （15）。 5. The method for coherent signal angle estimation using circular array rotation as described in claim 1, characterized in that: Step S3 specifically includes: adjusting the covariance matrix Perform eigenvalue decomposition to obtain Each small eigenvalue corresponds to an eigenvector. ,in Then it constitutes the noise subspace. , .

6. The method for coherent signal angle estimation using circular array rotation as described in claim 1, characterized in that: Spatial spectral function The formula is: (16) in, .

7. The method for coherent signal angle estimation using circular array rotation as described in claim 1, characterized in that: Step S5 specifically includes: setting the pitch angle search range. Azimuth search range ,get The values ​​at each point within the pitch and azimuth search range; these values ​​include The maximum value, the th ? The position corresponding to the i-th maximum value Estimated elevation angle of each incident signal and azimuth estimate This allows us to obtain the azimuth and elevation angles of the radiation source.

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