A MUSIC-based three-dimensional spherical array interferometer direction finding method

Abstract

The application provides a three-dimensional spherical array interferometer direction finding method based on MUSIC, which comprises the following steps: constructing a spherical array; using the method of uniform spherical array, constructing a direction finding device with array elements distributed in a spherical form, and representing the position parameters of each array element on the array surface in a polar coordinate form; assuming wave incidence parameters, taking the center of the sphere as a reference zero phase point, and calculating the received phase data of each array element under the condition of plane wave incidence; performing fast sampling on the received phase data of each array element at a sampling rate to obtain a receiving matrix; calculating the covariance matrix of the receiving matrix to obtain an eigenvalue matrix and an eigenvector; estimating the number of signals according to the eigenvalue matrix, dividing the eigenvector into a signal subspace and a noise subspace; using the characteristic that the eigenvectors of the signal and noise subspaces are irrelevant, obtaining the spatial spectrum value in the search region, and finding the position corresponding to the maximum value. The application solves the problem that the elevation angle direction finding accuracy of a two-dimensional plane array decreases rapidly with the increase of the elevation angle.

Description

Technical Field

[0001] This application relates to the field of direction finding technology, and in particular to a direction finding method based on a three-dimensional spherical array interferometer using MUSIC. Background Technology

[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 uniform circular arrays and elliptical arrays based on circular arrays. The two-dimensional planar circular array method, with its wide range in both frequency and azimuth, can resolve the contradiction between omnidirectional coverage, wide bandwidth, high-precision direction finding, and size, making circular array-based two-dimensional direction finding technology widely used in passive direction finding techniques. For ease of arrangement, commonly used circular array direction finding devices typically employ a uniform circular array configuration. In a uniform circular array, the antenna elements are evenly distributed along a circular curve. Therefore, uniform circular arrays offer the advantages of simple antenna arrangement and uniform distribution of direction finding accuracy in all directions.

[0003] The direction-finding error of a two-dimensional planar circular array is uniformly distributed with azimuth angle, but not uniformly with elevation angle. Similar to linear arrays, the direction-finding technology of circular arrays under planar conditions suffers from the influence of the incident angle on direction-finding accuracy, 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-finding accuracy is greatly affected by the direction of arrival; when the angle of arrival coincides with the antenna baseline, the angle-finding error is very large. Summary of the Invention

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

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

[0006] Step S1: Construct a spherical array; using the method of a uniform spherical array, construct a direction-finding device with array elements distributed in a spherical form. The position parameters of each array element on the array surface are... Quantification;

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

[0008] Step S3: Quickly sample the phase data received by each array element at the sampling rate to obtain the receiving matrix X(n);

[0009] Calculate the covariance matrix of the received matrix X(n) to obtain the eigenvalue matrix U and eigenvector V; estimate the signal quantity based on the eigenvalue matrix U, and divide the eigenvector into signal subspaces V. SWith noise subspace V Noise ;

[0010] Step S4: Utilizing the property that the eigenvectors of the signal and noise subspaces are uncorrelated, obtain the spatial spectral values ​​within the search region, and find the value corresponding to the maximum value. Position, that is, the azimuth and elevation angles of the incident wave. value.

[0011] Furthermore, in step S1, the positions of each array element are represented as follows:

[0012] At a point P on a 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 point i To indicate, that is Indicates the array element parameters.

[0013] Furthermore, in step S2, assuming wave incident parameters... Using the center of the sphere as the reference zero-phase point, calculate the received phase data X(t) of each array element under plane wave incident conditions; including:

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

[0015]

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

[0017] i = 1…M; φ i It means receiving phase data X(t);

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

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

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

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

[0022] In practice, the phase measurement data are sampled data, and the covariance matrix is ​​estimated in the following form:

[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] Further, in step S3, the covariance matrix of the received matrix X(n) is calculated to obtain the eigenvalue matrix U and the eigenvector V; the signal quantity is estimated based on the eigenvalue matrix U, and the eigenvector is divided into signal subspaces V. S With noise subspace V Noise ;include:

[0026] right Eigenvalue decomposition yields eigenvalues ​​λ1 to λ2 arranged in descending order. M and the corresponding eigenvectors V = [v1...v M ];

[0027] Based on the descending sorted feature values ​​λ1~λ M Distribution, estimate the number of sources P, and divide λ1 to λ P The corresponding eigenvectors are divided into signal subspaces V. S =[v1...v P ], λ P+1 ~λ M The corresponding feature vectors are divided into a noise subspace V. Noise =[v P+ 1...v M ].

[0028] Furthermore, by utilizing the property that the eigenvectors of the signal and noise subspaces are uncorrelated, the spatial spectral values ​​within the search region are obtained, and the values ​​corresponding to the maximum values ​​are found. Position, that is, the azimuth and elevation angles of the incident wave. Values, including:

[0029] Construct the spectral function based on the MUSIC method. Determine the azimuth and elevation angles based on the target space to be searched. The range of values ​​for is determined within the space based on the required search precision. Take values ​​and calculate the corresponding spectral functions. Value, based on the spectral function Find P peak points and their corresponding azimuth and elevation angles. That is, the signal value:

[0030]

[0031] This invention proposes a spherical array (SA) interferometer direction finding method. Utilizing the characteristic that a spherical array can be distributed in both azimuth and elevation directions, it addresses the problem that the accuracy of elevation direction finding in two-dimensional planar arrays rapidly decreases with increasing elevation angle, thus achieving high-precision two-dimensional direction finding. The spherical array direction finding solution employs a multiple signal classification (MUSIC) method, which possesses both simultaneous multi-signal direction finding capability and high-precision direction finding characteristics. Attached Figure Description

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

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

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

[0035] Figure 4 Arrangement of eigenvalues ​​of the covariance matrix;

[0036] Figure 5 The final spatial spectrum and corresponding signal peak location map are obtained through calculation;

[0037] Figure 6 Eigenvalue distribution and spatial spectrum under the presence of errors. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0039] The embodiments of this application will be described below with reference to the accompanying drawings. The direction-finding method of this invention uses the phase data received by each element of a spherical array as the raw data. Using the Multiple Signal Classification (MUSIC) method, the covariance matrix of the spherical array parameters is calculated using the phase data received by the array elements. The noise subspace and signal subspace of this matrix are obtained. The DOA is obtained by utilizing the fact that the eigenvectors of the noise and signal subspaces are uncorrelated.

[0040] The method for arranging a three-dimensional spherical array is similar to that for arranging a two-dimensional planar circular array. For example... Figure 1 As shown, a spherical array is viewed as a stack of multiple two-dimensional planar arrays, with the radius of each layer determined by its position on the sphere.

[0041] Figure 1 This is a schematic diagram of a three-layer hemispherical uniform circular array, with each layer corresponding to an elevation angle of (30°, 60°, 90°). Each layer of the circular array is a uniform five-element array. The calculation of the received phase for each element is based on the method used for calculating the received phase of elements in a two-dimensional planar circular array.

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

[0043]

[0044] The receiving phase of the M array elements is thus represented as:

[0045]

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

[0047] The same method is used in spherical arrays.

[0048] Based on the above analysis, step S1 is manifested as: at a 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 point i To indicate, that is Indicates the array element parameters.

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

[0050]

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

[0052] i = 1…M; φ i It means receiving phase data X(t);

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

[0054] Next, using the received phase data as the raw data, the K-incident angle is calculated using the Multiple Signal Classification (MUSIC) method.

[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 received phase matrix, X(t) = [x1(t)x2(t)......x M (t)] T It is an M-dimensional received data vector, where M is the number of elements in the spherical array.

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

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

[0060] The array manifold matrix of dimension M×P is represented as:

[0061]

[0062] Wherein, 2πf0τ MP This represents 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] The phase data 2πf0τ in the array manifold matrix constructed in the form of a spherical array MP Represented as:

[0066]

[0067] Where k p Let r represent the wave number of the p-th signal. m θ m and This represents the position parameter of the m-th array element.

[0068] The signal S(t) uses a narrowband point frequency signal, representing S p (t)=exp(j2πf p t), f p This represents the signal frequency. After obtaining X(t), calculate the covariance matrix of X(t) using the following method:

[0069] R = APA H +σ 2 I

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

[0071] The covariance matrix P of the S(t) vector is a non-singular matrix with rank equal to the number of signals P. When the manifold matrix A satisfies full column rank, i.e., the column vectors of A are uncorrelated, step S31 is executed as follows:

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

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

[0074] In practice, the phase measurement data are sampled data, and the covariance matrix is ​​estimated in the following form:

[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 range of values ​​for is such that, since the signal and noise subspaces are uncorrelated, their cross-correlation coefficient is 0. In real-world scenarios, due to the presence of noise, the cross-correlation coefficient is a very small value. Therefore, we use the reciprocal to find the maxima of the spectral function. The spatial spectrum of the MUSIC method is then calculated using the following formula:

[0078]

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

[0080] Based on the element design of a uniform spherical array, each element in the spherical array is used... Represented in the form of .

[0081] Simultaneously, the antenna receives phase data X(t) and samples it according to the sampling rate, obtaining array element received phase data X(n) with N samples. According to... Calculate the covariance matrix R of the received phase data.

[0082] Step S32: For Eigenvalue decomposition yields eigenvalues ​​λ1 to λ2 arranged in descending order. M and the corresponding eigenvectors V = [v1...vM ];

[0083] Based on the descending sorted feature values ​​λ1~λ M Distribution, estimate the number of sources P, and divide λ1 to λ P The corresponding eigenvectors are divided into signal subspaces V. S =[v1...v P ], λ P+1 ~λ M The corresponding feature vectors are divided into a noise subspace V. Noise =[v P+ 1...v M ].

[0084] Step S4: Construct the spectral function according to the MUSIC method. Determine the azimuth and elevation angles based on the target space to be searched. The range of values ​​for is determined within the space based on the required search precision. Take values ​​and calculate the corresponding spectral functions. Value, based on the spectral function Find P peak points and their corresponding azimuth and elevation angles. That is, the signal value:

[0085]

[0086] The following example will be used to explain the direction finding method of the spherical array interferometer in detail.

[0087] spherical array adopts Figure 1 The diagram shows a three-layer uniform five-element array with a spherical array radius of 250 mm. It assumes that, under ideal conditions, each element is independent and the element radiation patterns are isotropic.

[0088] Signal parameter settings: Two independent narrowband signals are incident, both with a signal-to-noise ratio of 15dB, and carrier frequencies of 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] Based on step 3, calculate the eigenvalues ​​and sort them in ascending order, from smallest to largest, to obtain the eigenvalue distribution as follows: Figure 4 As shown.

[0090] Eigenvalues ​​λ1~λ 13 The largest eigenvalue is 0.048. 14 =5.63,λ 15 =24.47, two values ​​significantly larger than the previous ones, so we can consider λ to be... 14 With λ15 Let λ1 be a signal characteristic value, and the number of signal sources be 2. 13 These are the eigenvalues ​​of the noise vector.

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

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

[0093] In reality, due to factors such as manufacturing precision, the amplitude and phase received by the array elements will inevitably have random deviations. We simulated the spatial spectrum under the condition that each array element has amplitude and phase errors. The amplitude error is taken as 1, and the error follows a normal distribution with a mean of 0 and a standard deviation of 0.2. The phase deviation also follows a normal distribution with a mean of 0 and a standard deviation of 30°.

[0094] The eigenvalue distribution and spatial spectrum were calculated as follows: Figure 6 As shown: It can be seen that compared to the ideal situation, the eigenvalues ​​of the noise vector are larger due to the presence of error. However, in this case, the eigenvalues ​​of the signal vector and the noise vector still maintain a significant difference. The calculated spatial spectrum is as follows... Figure 6 The MUSIC spatial spectrum direction finding method employed has high resolution. Even with errors, it can still distinguish two targets with similar incident angles quite well.

[0095] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

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

Claims

1. A direction-finding method for a three-dimensional spherical interferometer based on MUSIC, characterized in that, The method includes: Step S1: Construct a spherical array; using the method of a uniform spherical array, construct a direction-finding device with array elements distributed in a spherical form. The position parameters of each array element on the array surface are... Quantification; Step S2: Assume wave incident parameters Using the center of the sphere as the reference zero-phase point, calculate the received phase data X(t) of each array element under plane wave incident conditions; Step S3: Quickly sample the phase data received by each array element at the sampling rate to obtain the receiving matrix X(n); Calculate the covariance matrix of the received matrix X(n) to obtain the eigenvalue matrix U and eigenvector V; estimate the signal quantity based on the eigenvalue matrix U, and divide the eigenvector into signal subspaces V. S With noise subspace V Noise ; Step S4: Utilizing the property that the eigenvectors of the signal and noise subspaces are uncorrelated, obtain the spatial spectral values ​​within the search region, and find the value corresponding to the maximum value. Position, that is, the azimuth and elevation angles of the incident wave. value.

2. The method according to claim 1, characterized in that, In step S1, the positions of each array element are represented as follows: At a point P on a 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 point i To indicate, that is Indicates the array element parameters.

3. The method according to claim 2, characterized in that, Step S2: Assume wave incident parameters Using the center of the sphere as the reference zero-phase point, calculate the received phase data X(t) of each array element under plane wave incident conditions; including: Taking the center O of the sphere as the phase reference zero, the received phase of any point P on the spherical array can be understood as: the phase change corresponding to the distance from point P to the plane passing through point O and with normal vector K; the distance can be expressed using the vector method as: The receiving phase of each array element is represented as follows: φ i It means 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 quickly at a sampling rate to obtain the receiving matrix X(n); including: After sorting the eigenvalues ​​of the covariance matrix R of X(t) from largest to smallest: λ1≥λ2≥....≥λ P >l P+1 =...=l M =s 2 The phase measurement data are sampled data, and the covariance matrix is ​​estimated in the following form: 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 received matrix X(n) is calculated to obtain the eigenvalue matrix U and the eigenvector V; the signal quantity is estimated based on the eigenvalue matrix U, and the eigenvector is divided into signal subspaces V. S With noise subspace V Noise ; include: right Eigenvalue decomposition yields eigenvalues ​​λ1 to λ2 arranged in descending order. M and the corresponding eigenvectors V = [v1...v M ]; Based on the descending sorted feature values ​​λ1~λ M Distribution, estimate the number of sources P, and divide λ1 to λ P The corresponding eigenvectors are divided into signal subspaces V. S =[v1...v P ], λ P+1 ~λ M The corresponding feature vectors are divided into a noise subspace V. Noise =[v P+1 ...v M ].

6. The method according to claim 4, characterized in that, By utilizing the property that the eigenvectors of the signal and noise subspaces are uncorrelated, the spatial spectral values ​​within the search region are obtained, and the values ​​corresponding to the maximum values ​​are found. Position, that is, the azimuth and elevation angles of the incident wave. Values, including: Construct the spectral function based on the MUSIC method. Determine the azimuth and elevation angles based on the target space to be searched. The range of values ​​for is determined within the space based on the required search precision. Take values ​​and calculate the corresponding spectral functions. Value, based on the spectral function Find P peak points and their corresponding azimuth and elevation angles. That is, the signal value:

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