Three-dimensional spherical array interferometer direction finding method based on MUSIC

Abstract

The invention provides a three-dimensional spherical array interferometer direction finding method based on MUSIC. The method comprises the following steps: constructing a spherical array; a uniform spherical array method is adopted, a direction finding device with array elements distributed in a spherical form is constructed, and position parameters of the array elements on an array plane are represented in a polar coordinate form; assuming a wave incidence parameter, taking the center of sphere as a reference zero phase point, and calculating receiving phase data of each array element under a plane wave incidence condition; performing snapshot sampling on the receiving phase data of each array element at a sampling rate to obtain a receiving matrix; calculating a covariance matrix of the receiving matrix to obtain an eigenvalue matrix and an eigenvector; estimating the number of signals according to the eigenvalue matrix, and dividing the eigenvector into a signal subspace and a noise subspace; and solving a spatial spectrum value in a search area by utilizing the characteristic that the signal is irrelevant to the noise subspace feature vector, and finding a position corresponding to the maximum value. The problem that the elevation direction finding precision of the two-dimensional planar array is rapidly reduced along with the increase of the elevation angle is solved.

Description

Technical Field

[0001] The present application relates to the technical field of direction finding, and in particular to a three-dimensional spherical array interferometer direction finding method based on MUSIC. Background Art

[0002] Commonly used two-dimensional planar interferometers include orthogonal arrays such as L-shaped, T-shaped, and cross-shaped arrays based on uniform linear arrays, as well as various types of uniform circular arrays and elliptical arrays based on circular arrays. The two-dimensional planar circular array method is wide in frequency and azimuth, and can solve the contradiction between omnidirectional coverage, wide bandwidth, high-precision direction finding, and volume, making the two-dimensional direction finding technology based on circular arrays widely used in passive direction finding technology. Commonly used circular array direction finding devices usually use a uniform circular array for easy arrangement. In a uniform circular array, the antenna elements are evenly distributed on a circular curve. Therefore, the uniform circular array has the characteristics of simple antenna arrangement and uniform distribution of direction finding accuracy in all directions.

[0003] The direction finding error of a two-dimensional circular array is evenly distributed with the azimuth angle, but uneven with the elevation angle. The circular array direction finding technology under plane conditions is similar to the linear array. There is a situation where the direction finding accuracy is affected by the incident angle, and the problem of decreased elevation angle direction finding accuracy at large elevation angles cannot be avoided. That is, at large elevation angles, the angle measurement accuracy is greatly affected by the direction of the incoming wave. When the arrival angle is consistent with the antenna baseline, the angle measurement error is very large. Summary of the invention

[0004] The present application provides a three-dimensional spherical array interferometer direction finding method based on MUSIC, which can be used to solve the technical problem of large angle measurement error at large elevation angles.

[0005] The present application provides a three-dimensional spherical array interferometer direction finding method based on MUSIC, the method comprising:

[0006] Step S1, construct a spherical array; using the uniform spherical array method, construct a direction finding device with array elements distributed in a spherical form, and the position parameters of each array element on the array are used Quantitative representation;

[0007] Step S2: Assuming wave incident parameters Taking the center of the sphere as the reference zero phase point, calculate the received phase data X(t) of each array element under the plane wave incidence condition;

[0008] Step S3, performing snapshot sampling on the received phase data of each array element at a sampling rate to obtain a receiving matrix X(n);

[0009] Calculate the covariance matrix of the receiving matrix X(n) to obtain the eigenvalue matrix U and eigenvector V; estimate the number of signals based on the eigenvalue matrix U and divide the eigenvector into the signal subspace V SWith the noise subspace V Noise ;

[0010] Step S4: Using the uncorrelated characteristic of the signal and noise subspace eigenvectors, the spatial spectrum value in the search area is obtained, and the corresponding maximum value is found. Position, which is the azimuth and elevation angle of the incident wave value.

[0011] Furthermore, in step S1, the position of each array element is expressed as follows:

[0012] At a certain point P on the spherical array, the azimuth angle θ of array element i is used i , the pitch angle of array element i The distance r from the reference center O i To express, that is Represents array element parameters.

[0013] Further, step S2, assuming that the wave incident parameters Taking the center of the sphere as the reference zero phase point, calculate the received phase data X(t) of each array element under the plane wave incidence condition; including:

[0014] Taking the sphere center position O as the phase reference zero point, the received phase of any point P on the spherical array is understood as: the distance from point P to the plane passing through point O and with a normal vector K corresponds to the phase change; the distance is expressed by the vector method as:

[0015]

[0016] The receiving phase of each array element is expressed as:

[0017] i=1…M;φ i That is, receiving phase data X(t);

[0018] Where k represents the wave number, k = 2π / λ, and λ is the signal wavelength.

[0019] Further, in step S3, the phase data received by each array element is sampled at a sampling rate to obtain a receiving matrix X(n); including:

[0020] After sorting the eigenvalues ​​of the covariance matrix R of X(t) from large to small:

[0021] λ1≥λ2≥....≥λ P ≥λ P+1 =... =λ M =σ 2

[0022] In actual situations, the phase measurement data is sampled data, and the covariance matrix estimation is calculated as follows:

[0023]

[0024] Where N represents the number of sampling snapshots, and X(n) represents the discrete data of X(t) after sampling at the sampling rate.

[0025] Furthermore, in step S3, the covariance matrix of the receiving matrix X(n) is calculated to obtain the eigenvalue matrix U and the eigenvector V; the number of signals is estimated according to the eigenvalue matrix U, and the eigenvector is divided into the signal subspace V S With the noise subspace V Noise ;include:

[0026] right Perform eigenvalue decomposition and obtain the eigenvalues ​​λ1~λ in descending order M And the corresponding eigenvector V = [v1...v M ];

[0027] According to the descending order of eigenvalues ​​λ1~λ M distribution, estimate the number of information sources P, and set λ1~λ P The corresponding eigenvector is divided into the signal subspace V S =[v1...v P ],λ P+1 ~λ M The corresponding eigenvector is divided into the noise subspace V Noise =[v P+ 1...v M ].

[0028] Furthermore, by using the uncorrelated characteristic of the signal and noise subspace eigenvectors, the spatial spectrum value in the search area is obtained and the value corresponding to the maximum value is found. Position, which is the azimuth and elevation angle of the incident wave Values, including:

[0029] According to the MUSIC method, construct the spectral function Determine the azimuth and elevation angles according to the target space to be searched The value range of Take values ​​and calculate the corresponding spectral function Value, according to the spectral function Find P peak points, corresponding to the azimuth and elevation angles Signal value:

[0030]

[0031] The present invention proposes a spherical array (SA) interferometer direction finding method, which uses the characteristics of the spherical array that can be distributed in azimuth and elevation to solve the problem that the elevation direction finding accuracy of a two-dimensional plane array decreases rapidly with the increase of the elevation angle, so as to achieve two-dimensional high-precision direction finding. The spherical array direction finding solution method adopts the multiple signal classification (MUSIC) method with simultaneous multi-signal direction finding capability and high-precision direction finding characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 A schematic diagram (hemisphere) showing the distribution of array elements in a uniformly distributed spherical array;

[0033] Figure 2 Schematic diagram of a plane wave incident on a two-dimensional planar circular array;

[0034] Figure 3 Schematic diagram of a plane wave incident on a three-dimensional spherical array;

[0035] Figure 4 Covariance matrix eigenvalue arrangement plot;

[0036] Figure 5 The final spatial spectrum and the corresponding signal peak position map are calculated;

[0037] Figure 6 Eigenvalue distribution and spatial spectrum in the presence of errors. DETAILED DESCRIPTION

[0038] In order to make the objectives, technical solutions and advantages of the present application clearer, the implementation methods of the present application will be further described in detail below with reference to the accompanying drawings.

[0039] The following first introduces the embodiments of the present application in conjunction with the accompanying drawings. The direction finding method of the present invention uses the phase data received by each array element of the spherical array as the original data. The multiple signal classification (MUSIC) method is used to calculate the spherical array parameter covariance matrix using the array element received phase data, and the noise subspace and signal subspace of the matrix are obtained. The DOA is obtained by using the characteristics that the eigenvectors of the noise and signal subspaces are uncorrelated.

[0040] The arrangement method of the three-dimensional spherical array refers to the arrangement method of the two-dimensional plane circular array. Figure 1 The spherical array is regarded as a stack of multiple layers of two-dimensional plane arrays, and the radius of the corresponding circular array is determined by the position of each layer on the spherical surface.

[0041] Figure 1 This is a schematic diagram of a three-layer hemispherical uniform circular array, with the corresponding pitch angles of each layer being (30°60°90°). Each layer of the circular array is in the form of a uniform five-element array. In the process of calculating the receiving phase of each element, the calculation method of the receiving phase of each element in the two-dimensional plane circular array is referred to.

[0042] like Figure 2 As shown in Figure 1, a plane wave K is incident on a two-dimensional plane circular array. The parameters of the plane wave K are expressed by the corresponding azimuth and elevation angles: The center position O of the circular array is taken as the zero phase reference position, and the positions of all array elements in the two-dimensional circular array use the azimuth angle θ of a certain array element i. i , and the distance r from the reference center O i The path difference is the distance from point P to the plane passing through point O and with a normal vector of K, expressed as:

[0043]

[0044] The receiving phase of M array elements is expressed as:

[0045]

[0046] Where k represents the wave number, k = 2π / λ, and λ is the signal wavelength.

[0047] The same approach is used for spherical arrays.

[0048] Based on the above analysis, step S1 is as follows: at a certain point P on the spherical array, the azimuth angle θ of the array element i is used. i , the pitch angle of array element i The distance r from the reference center O i To express, that is Represents array element parameters.

[0049] Step S2, taking the sphere center position O as the phase reference zero point, the received phase of any point P on the spherical array is understood as: the distance from point P to the plane passing through point O and with a normal vector K corresponds to the phase change; the distance is expressed by the vector method as:

[0050]

[0051] The receiving phase of each array element is expressed as:

[0052] i=1…M;φ i That is, receiving phase data X(t);

[0053] Where k represents the wave number, k = 2π / λ, and λ is the signal wavelength.

[0054] Next, the received phase data is used as the original data, and the multiple signal classification method (MUSIC) is used to calculate the K incident angle.

[0055] The MUSIC direction finding method is a high-resolution direction finding method. The calculation process is as follows:

[0056]

[0057] Where X(t) represents the receiving phase matrix, X(t) = [x1(t)x2(t)......x M (t)] T is the M-dimensional received data vector, and M is the number of array elements in the spherical array.

[0058] S(t)=[S1(t)S2(t)......S P (t)] T is a P-dimensional signal vector, where P represents P incoherent radar signals.

[0059] N(t)=[N1(t)N2(t)......N M (t)] T is the noise vector received by M array elements, and these noises are independent of each other.

[0060] is an M×P dimensional array flow matrix, expressed as:

[0061]

[0062] Among them, 2πf0τ MP Indicates the phase data of the Pth incident signal received by the Mth array element.

[0063] In the case of a spherical array, based on the above analysis, the receiving phase of array element i is:

[0064]

[0065] Then the phase data 2πf0τ in the array flow matrix constructed in the form of a spherical array MP It is expressed as:

[0066]

[0067] where k p Indicates the wave number of the pth signal. m ,θ m and Represents the position parameter of the mth array element.

[0068] The signal S(t) uses a narrowband frequency signal, indicating S p (t) = exp(j2πf p t), f p Represents the signal frequency. After obtaining X(t), calculate the covariance matrix of X(t) as follows:

[0069] R=APA H +σ 2 I

[0070] Where P = E{S(t)S(t) H} is the covariance matrix of the signal S(t), E is the mathematical expectation, and I is the M×M dimensional identity matrix vector.

[0071] The covariance matrix P of the S(t) vector is a non-singular matrix with a rank equal to the number of signals P. When the flow matrix A satisfies the column full rank, that is, the column vectors of A are independent of each other, step S31 is performed as follows:

[0072] After sorting the eigenvalues ​​of the covariance matrix R of X(t) from large to small:

[0073] λ1≥λ2≥....≥λ P >λ P+1 =... =λ M =σ 2

[0074] In actual situations, the phase measurement data is sampled data, and the covariance matrix estimation is calculated as follows:

[0075]

[0076] Where N represents the number of sampling snapshots, and X(n) represents the discrete data of X(t) after sampling at the sampling rate.

[0077] Determine the azimuth and elevation angles based on the search area The value range of , because the signal and noise subspaces are not correlated, the mutual correlation coefficient between the two is 0. In actual scenarios, due to the presence of noise, the mutual correlation coefficient is a very small value, and the inverse method is used to convert it into finding the maximum value of the spectrum function. Then the spatial spectrum of the MUSIC method is calculated according to the following formula:

[0078]

[0079] In summary, the specific implementation steps of the three-dimensional spherical array interferometer direction finding are summarized as follows:

[0080] According to the design of the uniform spherical array elements, each element in the spherical array is used expressed in the form of .

[0081] At the same time, the antenna receives the phase data X(t) and samples it according to the sampling rate to obtain the array element receiving phase data X(n) with a sampling number of N. Calculate the covariance matrix R of the received phase data.

[0082] Step S32: Perform eigenvalue decomposition and obtain the eigenvalues ​​λ1~λ in descending order M And the corresponding eigenvector V = [v1...vM ];

[0083] According to the descending order of eigenvalues ​​λ1~λ M distribution, estimate the number of information sources P, and set λ1~λ P The corresponding eigenvector is divided into the signal subspace V S =[v1...v P ],λ P+1 ~λ M The corresponding eigenvector is divided into the noise subspace V Noise =[v P+ 1...v M ].

[0084] Step S4: Construct spectral function according to MUSIC method Determine the azimuth and elevation angles according to the target space to be searched The value range of Take values ​​and calculate the corresponding spectral function Value, according to the spectral function Find P peak points, corresponding to the azimuth and elevation angles Signal value:

[0085]

[0086] The above spherical array interferometer direction finding method is described in detail using an example below.

[0087] Spherical array uses Figure 1 The three-layer uniform five-element array shown in the figure has a spherical array radius of 250 mm. It is assumed that the array elements are independent of each other and the array element directivity diagram is isotropic.

[0088] Signal parameter settings: Two independent narrowband signals are incident, the signal-to-noise ratio of the two signals is 15dB, and the signal carrier frequencies are 3GHz and 3.2GHz respectively. The azimuth and elevation angles of the two plane waves with similar angles are (37°65°) and (37°70°) respectively. The receiving sampling rate is 10GHz, and the number of sampling snapshots is 200.

[0089] According to step 3, calculate the eigenvalues ​​and sort them in ascending order, from small to large, to get the eigenvalue distribution as follows Figure 4 shown.

[0090] Eigenvalue λ1~λ 13 , the maximum eigenvalue is 0.048. 14 =5.63,λ 15 =24.47, both of which are significantly larger than the previous values, so it can be considered that λ 14 With λ15 is the signal characteristic value, and the number of information sources is 2. 13 is the eigenvalue of the noise vector.

[0091] Determine the azimuth search range as θ∈[0 360); the elevation search range is According to the spatial spectrum formula The spatial spectrum is obtained, such as Figure 5 As shown (the figure has been converted to logarithmic representation).

[0092] It can be seen that the peak positions are (37° 65°) and (37° 70°), which are completely consistent with the azimuth and elevation angle data of the signal.

[0093] In actual situations, due to reasons such as processing accuracy, there must be random deviations in the amplitude and phase received by the array element. We simulated the spatial spectrum when each array element has amplitude and phase errors. The amplitude error is based on 1, and the error is normally distributed with a mean of 0 and a standard deviation of 0.2. The phase deviation is also normally distributed with a mean of 0 and a standard deviation of 30°.

[0094] The calculated eigenvalue distribution and spatial spectrum are as follows Figure 6 As shown: It can be seen that compared with the ideal case, the eigenvalue of the noise vector becomes larger due to the existence of errors. However, in this case, the eigenvalue of the signal vector is still very different from the eigenvalue of the noise vector. The calculated spatial spectrum is as follows Figure 6 The MUSIC spatial spectrum direction finding method used has a high resolution. Even in the presence of errors, it can still distinguish two targets with similar incident angles.

[0095] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0096] The above-described embodiments of the present application do not constitute a limitation on the protection scope of the present application.

Claims

1. A three-dimensional spherical array interferometer direction finding method based on MUSIC, characterized in that: The method comprises: Step S1, construct a spherical array; using the uniform spherical array method, construct a direction finding device with array elements distributed in a spherical form, and the position parameters of each array element on the array are used Quantitative representation; Step S2: Assuming wave incident parameters Taking the center of the sphere as the reference zero phase point, calculate the received phase data X(t) of each array element under the plane wave incidence condition; Step S3, performing snapshot sampling on the received phase data of each array element at a sampling rate to obtain a receiving matrix X(n); Calculate the covariance matrix of the receiving matrix X(n) to obtain the eigenvalue matrix U and eigenvector V; estimate the number of signals based on the eigenvalue matrix U and divide the eigenvector into the signal subspace V S With the noise subspace V Noise ; Step S4: Using the uncorrelated characteristic of the signal and noise subspace eigenvectors, the spatial spectrum value in the search area is obtained, and the corresponding maximum value is found. Position, which is the azimuth and elevation angle of the incident wave value.

2. The method according to claim 1, characterized in that In step S1, the position of each array element is expressed as follows: At a certain point P on the spherical array, the azimuth angle θ of array element i is used i , the pitch angle of array element i The distance r from the reference center O i To express, that is Represents array element parameters.

3. The method according to claim 2, characterized in that Step S2: Assuming wave incident parameters Taking the center of the sphere as the reference zero phase point, calculate the received phase data X(t) of each array element under the plane wave incidence condition; including: Taking the sphere center position O as the phase reference zero point, the received phase of any point P on the spherical array is understood as: the distance from point P to the plane passing through point O and with a normal vector K corresponds to the phase change; the distance is expressed by the vector method as: The receiving phase of each array element is expressed as: φ i That is, receiving phase data X(t); Where k represents the wave number, k = 2π / λ, and λ is the signal wavelength.

4. The method according to claim 3, characterized in that In step S3, the phase data received by each array element is sampled at a sampling rate to obtain a receiving matrix X(n); including: After sorting the eigenvalues ​​of the covariance matrix R of X(t) from large to small: λ1≥λ2≥....≥λ P >l P+1 =...=l M =s 2 The phase measurement data is sampled data, and the covariance matrix estimation is calculated as follows: Where N represents the number of sampling snapshots, and X(n) represents the discrete data of X(t) after sampling at the sampling rate.

5. The method according to claim 4, characterized in that In step S3, the covariance matrix of the receiving matrix X(n) is calculated to obtain the eigenvalue matrix U and the eigenvector V; the number of signals is estimated according to the eigenvalue matrix U, and the eigenvector is divided into the signal subspace V S With the noise subspace V Noise ; include: right Perform eigenvalue decomposition and obtain the eigenvalues ​​λ1~λ in descending order M And the corresponding eigenvector V = [v1...v M ]; According to the descending order of eigenvalues ​​λ1~λ M distribution, estimate the number of information sources P, and set λ1~λ P The corresponding eigenvector is divided into the signal subspace V S =[v1...v P ],λ P+1 ~λ M The corresponding eigenvector is divided into the noise subspace V Noise =[v P+1 ...v M ].

6. The method according to claim 4, characterized in that Using the uncorrelated characteristic of the signal and noise subspace eigenvectors, we can obtain the spatial spectrum value in the search area and find the value corresponding to the maximum value. Position, which is the azimuth and elevation angle of the incident wave Values, including: According to the MUSIC method, construct the spectral function Determine the azimuth and elevation angles according to the target space to be searched The value range of Take values ​​and calculate the corresponding spectral function Value, according to the spectral function Find P peak points, corresponding to the azimuth and elevation angles Signal value:

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