Non-coherent distributed source direction of arrival estimation method based on generalized array flow pattern under color noise

Abstract

The present application relates to the non-coherent distributed source DOA estimation method based on generalized array flow pattern under color noise, and the method is: the array signal receiving model based on generalized array flow pattern under the uniform linear array is established; the sample covariance matrix of array receiving signal is calculated, and the covariance difference matrix is further obtained by using difference operation; the eigenvalue decomposition and subarray division are carried out on the covariance difference matrix, and the signal subspace corresponding to two subarrays is obtained; the non-coherent distributed source DOA estimation is obtained based on matrix reduction criterion by using the phase relationship corresponding to two signal subspaces; the present application method has very good applicability to the multipath transmission under Toeplitz structure color noise and fast fading channel, can provide higher resolution and DOA estimation accuracy, and only needs one-dimensional spectrum peak search, and the calculation efficiency is high.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of array signal processing, and particularly relates to a non-coherent distributed source DOA estimation method based on a generalized array flow pattern under color noise. BACKGROUND

[0002] The direction of arrival (DOA) estimation based on an antenna array is an important direction of array signal processing, and has wide application in the fields of radar, sonar, wireless communication, Internet of Vehicles and intelligent transmission system. At present, many methods have appeared for the DOA estimation, and representative methods include a multiple signal classification (MUSIC) algorithm of a characteristic subspace, an ESPRIT (ESPRIT) algorithm of a rotation invariant subspace, a sparse reconstruction (SR) algorithm and a deep learning (DP) algorithm. However, most of the existing algorithms are based on a point source model, and assume that the signal source signals propagate along a line of sight or a single path. However, in actual application environments, phenomena such as signal reflection, scattering and refraction will cause the actual signals to propagate along multiple paths, and under this background, the DOA estimation method based on the point source model will cause performance decline or even failure due to a model mismatch problem.

[0003] In recent years, with the development of the theory and the increasing requirements of the practical system, two kinds of signal models based on multipath transmission have been proposed. One of the signal models corresponds to the multipath transmission in slow fading channel, which is characterized as the coherent distribution (CD) source model. The other signal model corresponds to the multipath transmission in fast fading channel, which is characterized as the incoherent distribution (ID) source model.Based on the CD source model, L. Wang et al. proposed a DOA estimation method based on the reduced-dimension MUSIC technique in the literature “DOA estimation for coherently distributed sources considering circular and noncircular signals in massive MIMO systems” in 2017, Y. Tian et al. and F. Liu et al. proposed DOA estimation methods based on the perturbed SR technique and the linear programming (LP) technique in the literatures “Multi-parameters estimation for coherently distributed sources under coexistence of circular and noncircular signals” in 2020 and “LP-DSPE algorithm for angular parameter estimation of coherently distributed sources” in 2022, respectively; based on the ID source model, A. Hu et al. and Y. Tian et al. proposed DOA estimation methods based on the ESPRIT technique in the literatures “An ESPRIT-based approach for 2-D localization of incoherently distributed sources in massive MIMO systems” in 2014 and “2-D DOA estimation of incoherently distributed sources considering gain-phase perturbations in massive MIMO systems” in 2022, respectively; Z. Zheng et al. proposed a DOA estimation method based on beam space compression in the literature “Efficient beamspace-based algorithm for two-dimensional DOA estimation of incoherently distributed sources in massive MIMO systems” in 2018.

[0004] The above algorithms / schemes are beneficial attempts and explorations of the DOA estimation technology based on the multipath transmission condition, however, analysis finds that: whether the existing CD source or the ID source, the DOA estimation algorithm is based on the white noise background condition, and in some actual systems, the background noise is often colored noise. At this time, the existing distributed source DOA estimation algorithm applied to the system with colored noise as the background noise will directly lead to the estimation performance degradation or even failure. Therefore, it is necessary to explore the distributed source DOA estimation algorithm suitable for the colored noise background. SUMMARY

[0005] In order to overcome the deficiency that the prior art is not applicable to colored noise, the present application provides an ID source DOA estimation method based on generalized array flow pattern under colored noise for Hermitian Toeplitz structure colored noise and ID source model, which is used to solve the common problem that the prior art is not applicable to colored noise, and realizes efficient, high-resolution and high-precision DOA estimation under fast fading channel multipath transmission.

[0006] In order to achieve the above object, the technical scheme of the present application is:

[0007] A non-coherent distributed source DOA estimation method based on generalized array flow pattern under colored noise, which comprises the following steps:

[0008] S1: establishing an array signal receiving model based on generalized array flow pattern under uniform linear array, and the specific process is:

[0009] S1.1, setting L narrowband and uncorrelated ID sources to be incident on a uniform linear array composed of M array elements, and the spacing between the array elements in the uniform linear array is d;

[0010] S1.2, performing first-order Taylor approximation on the array flow pattern under small expansion angle to obtain an array signal receiving model with generalized array flow pattern, which is expressed as: wherein y(t)=[y1(t),...,y M (t)] T , x1,...,x M represent the coordinates of the 1st array element to the Mth array element along the x-axis, and they are all not equal to 0, y M (t) represents the received signal of the Mth array element, θ k represents the DOA corresponding to the kth ID source, k=1,2,...,L, s k (t) represents the k ID source signals, N k represents the number of multipath transmissions corresponding to the k ID source, γ k,i (t) represents the path gain of the kth signal along the ith path, represents the spread angle deviation of the kth signal along the ith path, i = 1, 2, ..., N k ,n(t)=[n1(t),...,n M (t)] T ,A0=[a(θ1),...,a(θ k )],A1=[d(θ1),...,d(θ k )], A=[A0 A1] represents the generalized array flow matrix, v0(t)=[v 10 (t),v 20 (t),...,v K0 (t)] T ,v1(t)=[v 11 (t),v 21 (t),...,v K1 (t)] T , t represents the time, and the superscript T represents the transposition operation;

[0011] S2: Obtain the sample covariance matrix R of the array received signal with generalized array flow type, and further obtain the covariance difference matrix R by differential operation D , the specific process is:

[0012] S2.1. Obtain the array received data Y at N moments, Y=[y(t1),...,y(t N )], according to the array received data Y obtained at N moments, its sample covariance matrix is ​​obtained as:

[0013] Among them, R V0 and R V1 denote the sample covariance matrices of the signal vectors v0(t) and v1(t) at the array receiving end after the ID source signal is transmitted through multipath, Q denotes the covariance matrix of the colored noise with a Hermitian Toeplitz structure, and the superscript H represents the conjugate transpose operation;

[0014] S2.2, from the uniform linear array, Both and Q have Hermitian Toeplitz structure and satisfy the relationship:

[0015] Using the above relationship, the covariance difference operation is performed on the sample covariance matrix R to obtain the covariance difference matrix R D , Where J is an M×M dimensional permutation matrix, expressed as: blkdiag{·} represents the block diagonalization operation, and the superscript * represents the conjugation operation;

[0016] S3: Covariance difference matrix R D Perform eigenvalue decomposition and divide the uniform linear array into two sub-arrays. According to the covariance difference matrix R D The decomposed eigenvalues ​​are used to obtain the signal subspace matrices corresponding to the two sub-matrices;

[0017] S4: Based on the matrix rank reduction criterion, the phase relationship corresponding to the two signal subspace matrices is used to obtain the ID source DOA estimation.

[0018] Furthermore, in step S3, the covariance difference matrix R D Perform eigenvalue decomposition and divide the uniform linear array into two sub-arrays. According to the covariance difference matrix R D The specific process of obtaining the signal subspace matrix corresponding to the two sub-matrices by decomposing the eigenvalues ​​includes the following steps:

[0019] S3.01, R D Perform eigenvalue decomposition to obtain its signal subspace U S , the signal subspace U S is a matrix composed of eigenvectors corresponding to the L largest eigenvalues; the L largest eigenvalues ​​refer to the D Sort the eigenvalues ​​in descending order and take the first L eigenvalues ​​as the maximum eigenvalue;

[0020] S3.02. Divide the uniform linear array into two sub-arrays, one of which contains the first M-1 array elements and the other contains the last M-1 array elements. Then, the signal subspace matrix U corresponding to the sub-array containing the first M-1 array elements is S1 is the signal subspace U S The first M-1 rows of , which contain the signal subspace matrix U corresponding to the sub-matrix of the last M-1 array elements S2 is the signal subspace U S The last M-1 rows.

[0021] Furthermore, in step S3, the covariance difference matrix R D Perform eigenvalue decomposition and divide the uniform linear array into two sub-arrays. According to the covariance difference matrix R D The specific process of obtaining the signal subspace matrix corresponding to the two sub-matrices by decomposing the eigenvalues ​​includes the following steps:

[0022] S3.11, R D Perform eigenvalue decomposition to obtain its signal subspace The signal subspace is a matrix composed of eigenvectors corresponding to the L smallest eigenvalues; the L smallest eigenvalues ​​refer to the DSort the eigenvalues ​​in ascending order and take the first L eigenvalues ​​as the minimum eigenvalue;

[0023] S3.12. Divide the uniform linear array into two sub-arrays, one of which contains the first M-1 array elements and the other contains the last M-1 array elements. Then, the signal subspace matrix corresponding to the sub-array containing the first M-1 array elements is is the signal subspace The first M-1 rows of the signal subspace matrix corresponding to the sub-matrix of the last M-1 array elements is the signal subspace The last M-1 rows.

[0024] Furthermore, in step S4, based on the matrix rank reduction criterion, the specific process of obtaining the ID source DOA estimation using the phase relationship corresponding to the two signal subspace matrices includes the following steps:

[0025] S4.01, using U S1 and U S2 Construct a new matrix Ξ, expressed as: Ξ=U S2 -Ψ(θ)U S1 ,in, θ represents all possible DOA values, diag{·} represents the diagonalization operation;

[0026] S4.02. Based on the matrix rank reduction criterion, obtain the DOA estimation of the ID source through a one-dimensional spectrum search. The expression of the one-dimensional spectrum search is: Here, det{·} represents the matrix determinant operation.

[0027] Furthermore, in step S4, based on the matrix rank reduction criterion, the specific process of obtaining the ID source DOA estimation using the phase relationship corresponding to the two signal subspace matrices includes the following steps:

[0028] S4.11. Utilization and Construct a new matrix Expressed as: in, θ represents all possible DOA values, diag{·} represents the diagonalization operation;

[0029] S4.02. Obtain DOA estimation of the ID source by one-dimensional spectrum search. The expression of the one-dimensional spectrum search is: Here, det{·} represents the matrix determinant operation.

[0030] Compared with the prior art, the method has better universality, is applicable to not only color noise with Hermitian Toeplitz structure but also white noise (which is a special case of noise with Hermitian Toeplitz structure), can provide higher resolution and estimation accuracy compared with the ESPRIT method proposed by A. Hu et al. and the beam space compression method proposed by Z. Zheng et al., and can complete DOA estimation of ID sources based on one-dimensional spectrum search, and is high in calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 is a flow chart of an ID source DOA estimation method based on generalized array flow pattern under color noise according to the present application;

[0032] Figure 2A is a spatial spectrum output graph of the method under Gaussian white noise;

[0033] Figure 2B is a spatial spectrum output graph of the method under Hermitian Toeplitz structure color noise;

[0034] Figure 3A is a comparison graph of root mean square error (RMSE) varying with the number of array elements obtained by using different DOA estimation methods in the present application;

[0035] Figure 3B is a comparison graph of RMSE varying with the number of sampling samples obtained by using different DOA estimation methods in the present application;

[0036] Figure 4A is a comparison graph of resolution success rate varying with the number of array elements obtained by using different DOA estimation methods for DOA estimation in the present application;

[0037] Figure 4B is a comparison graph of resolution success rate varying with the number of sampling samples obtained by using different DOA estimation methods for DOA estimation in the present application. DETAILED DESCRIPTION

[0038] The application will be further described in the following with reference to the accompanying drawings and in conjunction with the specific embodiments, and the protection scope of the present application is not limited to the specific embodiments.

[0039] Embodiment one:

[0040] Embodiment one of the present application provides a non-coherent distributed source DOA estimation method based on generalized array flow pattern under color noise, as shown in Figure 1 The method comprises the following steps:

[0041] S1: considering the color noise with Hermitian Toeplitz structure and ID source incidence, an array signal receiving model based on generalized array flow pattern is established under the uniform linear array, and the specific process is as follows:

[0042] S1.1, the signals of L narrowband and uncorrelated ID sources are incident on the uniform linear array composed of M array elements, and the spacing between the array elements in the uniform linear array is d;

[0043] S1.2, the first-order Taylor approximation is performed on the array flow pattern under small spread angle, and the array signal receiving model with generalized array flow pattern is obtained, which is expressed as:

[0044] wherein, y(t) = [y1(t),..., y M (t)] T , x1,...,x M represent the coordinates of the first to the Mth array elements along the x-axis, and none of them is equal to 0, y M (t) represents the received signal of the Mth array element, θ k represents the DOA corresponding to the kth ID source, k = 1, 2,..., L, s k (t) represents the k ID source signals, N k represents the number of multipath transmissions corresponding to the k ID sources, γ k,i (t) represents the path gain of the kth signal along the ith path, represents the spread angle deviation of the kth signal along the ith path, i = 1, 2,..., N k , n(t) = [n1(t),..., n M (t)] T , A0 = [a(θ1),..., a(θ k )], A1 = [d(θ1),..., d(θ k )], A = [A0 A1] represents the generalized array flow pattern matrix, v0(t) = [v 10 (t), v 20 (t),..., v K0 (t)] T , v1(t) = [v 11 (t), v 21 (t),..., v K1 (t)] T , t represents the time, and the superscript T represents the transposition operation;

[0045] S2: Obtain the sample covariance matrix R of the array received signal with a generalized array stream pattern, and further obtain the covariance difference matrix R by using a difference operation D , and the specific process is as follows:

[0046] S2.1, obtain the array received data Y of N time points, Y = [y (t1),..., y (tN)], and obtain the sample covariance matrix R of the array received data Y of N time points: N

[0047] wherein, R V0 and R V1 respectively represent the sample covariance matrix of the signal vectors v0 (t) and v1 (t) of the ID source signal after multipath transmission at the array receiving end, Q represents the color noise covariance matrix with Hermitian Toeplitz structure, and the superscript H represents the conjugate transpose operation;

[0048] S2.2, under the uniform linear array, and Q both have the Hermitian Toeplitz structure and satisfy the relationship:

[0049] By using the relationship, the covariance difference matrix R D is obtained by performing the covariance difference operation on the sample covariance matrix R wherein, J is an MxM permutation matrix, and is represented as: blkdiag{·} represents the block diagonalization operation, and the superscript * represents the conjugate operation;

[0050] S3: Perform eigenvalue decomposition on the covariance difference matrix R D , divide the uniform linear array into two subarrays, and obtain the signal subspace matrix corresponding to the two subarrays according to the eigenvalues of the covariance difference matrix R D decomposition.

[0051] S4: Obtain the ID source DOA estimation based on the phase relationship corresponding to the two signal subspace matrices according to the matrix rank reduction criterion.

[0052] In step S3, the eigenvalue decomposition is performed on the covariance difference matrix R D , the uniform linear array is divided into two subarrays, and the specific process of obtaining the signal subspace matrix corresponding to the two subarrays according to the eigenvalues of the covariance difference matrix R D decomposition includes the following steps:

[0053] S3.01, perform eigenvalue decomposition on R D to obtain the signal subspace U S , and the signal subspace U​S is a matrix composed of L eigenvectors corresponding to L largest eigenvalues; the L largest eigenvalues refer to the first L eigenvalues in descending order of eigenvalues of R D ; and M is the total number of array elements.

[0054] R D is decomposed into the following expression: where Λ S is a diagonal matrix composed of L largest eigenvalues, U S is a matrix composed of eigenvectors corresponding to Λ S , Λ Q is a diagonal matrix composed of M-L smallest eigenvalues, and U Q is a matrix composed of eigenvectors corresponding to Λ Q .

[0055] S3.02, divide the uniform linear array into two sub-arrays, one of which contains the first M-1 array elements, and the other contains the last M-1 array elements, then the signal subspace matrix U S1 corresponding to the sub-array containing the first M-1 array elements is the first M-1 rows of the signal subspace U S , and the signal subspace matrix U S2 corresponding to the sub-array containing the last M-1 array elements is the last M-1 rows of the signal subspace U S .

[0056] In step S4, based on the matrix rank reduction criterion, the specific process of obtaining the ID source DOA estimation using the phase relationship corresponding to the two signal subspace matrices includes the following steps:

[0057] S4.01, construct a new matrix Ξ using U S1 and U S2 , denoted as Ξ = U S2 - Ψ(θ)U S1 , where θ is all possible DOA values, and diag{·} represents diagonalization operation.

[0058] S4.02, when θ in Ψ(θ) is the true DOA of the ID source, Ξ is a non-full rank matrix (i.e. a rank reduction matrix), therefore, based on the matrix rank reduction criterion, the DOA estimation of the ID source is obtained by one-dimensional spectrum search, and the expression of the one-dimensional spectrum search is: where det{·} represents the matrix determinant operation; in the specific implementation process, the DOA estimation is completed by finding the L θ values that make f(θ) take the minimum value. The finding process is a one-dimensional spectrum search process, which is well known to experts in the same field, and thus its description is omitted here.

[0059] Embodiment Two: ​

[0060] A non-coherent distributed source (DOA) estimation method based on generalized array flow pattern in colored noise, comprising the following steps:

[0061] S1: considering the case of colored noise with Hermitian Toeplitz structure and ID source incidence, an array signal receiving model based on generalized array flow pattern in uniform linear array is established, and the specific process is as follows:

[0062] S1.1, set L narrowband and uncorrelated ID sources to be incident on a uniform linear array composed of M array elements, and the spacing between the array elements in the uniform linear array is d;

[0063] S1.2, under small spread angle, first-order Taylor approximation is performed on the array flow pattern to obtain an array signal receiving model with generalized array flow pattern, which is represented as: wherein y(t)=[y1(t),...,y M (t)] T , x1,...,x M represent the coordinates of the first to the Mth array elements along the x-axis, and none of them is equal to 0, y M (t) represents the received signal of the Mth array element, θ k represents the DOA corresponding to the kth ID source, k=1,2,...,L, s k (t) represents the k ID source signals, N k represents the number of multipath transmissions corresponding to the k ID sources, γ k,i (t) represents the path gain of the kth signal along the ith path, represents the spread angle deviation of the kth signal along the ith path, i=1,2,...,N k , n(t)=[n1(t),...,n M (t)] T , A0=[a(θ1),...,a(θ k )], A1=[d(θ1),...,d(θ k )], A=[A0 A1] represents the generalized array flow pattern matrix, v0(t)=[v 10 (t), v 20 (t),...,v K0 (t)] T , v1(t)=[v 11 (t), v 21 (t),...,v K1 (t)] T , t represents the time, and the superscript T represents the transpose operation;

[0064] S2: Obtain the sample covariance matrix R of the array received signal with a generalized array flow pattern, and further obtain the covariance difference matrix R by using a difference operation D , and the specific process is as follows:

[0065] S2.1, Obtain the array received data Y of N time points, Y = [y (t1),..., y (tN)], and obtain the sample covariance matrix R of the array received data Y of N time points as follows: N

[0066] Wherein, R V0 and R V1 respectively represent the sample covariance matrix of the signal vector v0 (t) and v1 (t) of the ID source signal after multipath transmission at the array receiving end, Q represents the color noise covariance matrix with Hermitian Toeplitz structure, and the superscript H represents the conjugate transpose operation;

[0067] S2.2, under the uniform linear array, and Q both have Hermitian Toeplitz structure and satisfy the relationship:

[0068] Using the relationship, the sample covariance matrix R is subjected to a covariance difference operation to obtain the covariance difference matrix R D , Wherein, J is an MxM permutation matrix, and is represented as: blkdiag{·} represents the block diagonalization operation, and the superscript * represents the conjugate operation;

[0069] S3: Eigenvalue decomposition is performed on the covariance difference matrix R D , the uniform linear array is divided into two subarrays, and the signal subspace matrix corresponding to the two subarrays is obtained according to the eigenvalues of the covariance difference matrix R D decomposition;

[0070] S4: Based on the matrix rank reduction criterion, the ID source DOA estimation is obtained by using the phase relationship corresponding to the two signal subspace matrices.

[0071] In step S3, eigenvalue decomposition is performed on the covariance difference matrix R D , the uniform linear array is divided into two subarrays, and the signal subspace matrix corresponding to the two subarrays is obtained according to the eigenvalues of the covariance difference matrix R D decomposition, and the specific process includes the following steps:

[0072] S3.11, eigenvalue decomposition is performed on R D to obtain the signal subspace​ the signal subspace is a matrix composed of eigenvectors corresponding to L smallest eigenvalues; the L smallest eigenvalues refer to the first L eigenvalues in ascending order of eigenvalues of R D ; the first L eigenvalues are regarded as the smallest eigenvalues;

[0073] R D The expression for eigenvalue decomposition is: wherein, is a diagonal matrix composed of L smallest eigenvalues, is an eigenvector matrix corresponding to Λ S , is a diagonal matrix composed of remaining M-L largest eigenvalues, is an eigenvector matrix corresponding to .

[0074] S3.12, divide the uniform linear array into two sub-arrays, one of which contains the first M-1 array elements and the other contains the last M-1 array elements, then the signal subspace matrix corresponding to the sub-array containing the first M-1 array elements is the first M-1 rows of the signal subspace corresponding to the sub-array containing the last M-1 array elements is the last M-1 rows of the signal subspace .

[0075] In step S4, based on the matrix rank reduction criterion, the specific process of obtaining the ID source DOA estimate using the phase relationship corresponding to the two signal subspace matrices includes the following steps:

[0076] S4.11, construct a new matrix and is expressed as: wherein, θ is all possible DOA values, and diag{·} represents diagonalization operation;

[0077] S4.02, when θ in is the true DOA of the ID source, is a non-full-rank matrix (i.e. a rank-reduced matrix), based on the matrix rank reduction criterion, the DOA estimate of the ID source is obtained by one-dimensional spectrum search, and the expression of the one-dimensional spectrum search is: wherein, det{·} represents matrix determinant operation; in the specific implementation process, the DOA estimate is completed by finding L θ values that make f(θ) take the minimum value. The finding process is the one-dimensional spectrum search process, which is well known to experts in the same field, and thus its description is omitted here.

[0078] ​The performance of the ID source DOA estimation method based on generalized array flow pattern under colored noise proposed in the present invention is analyzed through simulation experiments below, and the simulation process is carried out using MATLAB software.

[0079] Simulation experiment 1: The number of array elements is 30, the number of samples is 200, the signal-to-noise ratio (SNR) is 10 decibels (dB), the DOAs of the two ID sources are -20° and 30°, and the angular spread deviation is The standard deviation is 1°, k=1,2,i=1,2,…,N k , multipath number N k =50, the colored noise is generated by the AR(1) model with a correlation coefficient of 0.9, the array element spacing is 1 / 2 of the carrier wavelength, and the incident ID source signal is a BPSK modulated signal. The spatial spectrum output results under the white noise and colored noise models are as follows: Figure 2A and Figure 2B As shown, it can be seen that the method of the present invention can obtain accurate DOA estimation results regardless of white noise or colored noise background.

[0080] Simulation experiment 2: The root mean square error (RMSE) of DOA estimation of the method of the present invention is compared with the ESPRIT method proposed by A. Hu et al. and the beam space compression method proposed by Z. Zheng et al., and the Cramer-Rao bound (CRB) is used as the theoretical RMSE reference lower bound. Figure 3A In the example, the number of samples is 200, SNR = 0dB, and the number of array elements varies from 10 to 40; Figure 3B In the experiment, the number of array elements is 30, SNR = 0dB, and the number of samples varies from 50 to 500. The color noise is generated by the AR(1) model with a correlation coefficient of 0.92. Other simulation conditions are the same as those of the simulation experiment 1. Figure 3A and 3B It can be seen that the performance of the method of the present invention is significantly better than that of the comparison method and is closer to CRB.

[0081] Simulation experiment three: Compare the resolution success rates of DOA estimation of the method of the present invention, the ESPRIT method proposed by A. Hu et al., and the beam space compression method proposed by Z. Zheng et al. Figure 4A The simulation conditions and Figure 3A same, Figure 4B The simulation conditions and Figure 3B The same. In the simulation process, it is agreed that when the deviation of the two DOAs is less than 1°, it is considered a successful resolution. Figure 4A and Figure 4B It can be seen from the simulation results that the method of the present invention can provide a higher resolution success rate.

Claims

1. A non-coherent distributed source (DOA) estimation method based on generalized array flow pattern in colored noise, characterized in that: The method comprises the following steps: S1: establishing an array signal receiving model based on a generalized array flow pattern under a uniform linear array, and the specific process is as follows: S1.1, setting that the signals of L narrow-band and uncorrelated ID sources are incident on a uniform linear array composed of M array elements, and the interval between the array elements in the uniform linear array is d; S1.2, the first-order Taylor approximation is made to the array flow pattern under a small expansion angle, and an array signal receiving model with a generalized array flow pattern is obtained, denoted as: Where y(t)=[y1(t),...,y M (t)] T , x1,...,x M Indicates the coordinates of the 1st to Mth array elements along the x-axis, and none of them are equal to 0, y M (t) represents the received signal of the Mth array element, θ k represents the DOA corresponding to the kth ID source, k=1,2,…,L, s k (t) represents k ID source signals, N k represents the number of multipath transmissions corresponding to k ID sources, γ k,i (t) represents the path gain of the kth signal along the i-th path, represents the spread angle deviation of the kth signal along the ith path, i = 1, 2, ..., N k ,n(t)=[n1(t),...,n M (t)] T ,A0=[a(θ1),...,a(θ k )],A1=[d(θ1),...,d(θ k )], A=[A0 A1] represents the generalized array flow matrix, v0(t) = [v 10 (t), v 20 (t),..., v K0 (t)] T v1(t) = [v 11 (t), v 21 (t),..., v K1 (t)] T , t denotes time, and the superscript T denotes transposition. S2: obtain the sample covariance matrix R of the array receiving signal with generalized array stream pattern, and further obtain the covariance difference matrix R by using difference operation D The specific process is as follows: S2.

1. Obtain the array received data Y at N moments, Y=[y(t1),...,y(t N )], according to the array received data Y obtained at N moments, its sample covariance matrix is ​​obtained as: where R V0 and R V1 respectively represent the sample covariance matrices of the signal vectors v0(t) and v1(t) at the array receiving end after multipath transmission of the ID source signal, Q represents the covariance matrix of the color noise with Hermitian Toeplitz structure, and the superscript H represents the conjugate transpose operation. S2.2, from under the uniform linear array, and Q both have Hermitian Toeplitz structure and satisfy the relation: Q = JQ T J, Using the relationship, covariance difference operation is performed on the sample covariance matrix R to obtain a covariance difference matrix R D , wherein J is an M x M permutation matrix, and is represented as: blkdiag{·} represents a block diagonalization operation, and the superscript * represents a conjugate operation. S3: Covariance difference matrix R D Perform eigenvalue decomposition and divide the uniform linear array into two sub-arrays. According to the covariance difference matrix R D The decomposed eigenvalues ​​are used to obtain the signal subspace matrices corresponding to the two sub-matrices; Wherein, the specific process of one of the ways of executing step S3 is as follows: S3.11、to R D performing eigenvalue decomposition to obtain a signal subspace the signal subspace a matrix composed of eigenvectors corresponding to L smallest eigenvalues; the L smallest eigenvalues refer to the smallest L eigenvalues in ascending order of eigenvalues of R D performing ascending order sorting on the eigenvalues of R, and taking the first L eigenvalues as the smallest eigenvalues S3.12, dividing the uniform linear array into two sub-arrays, one of which contains the first M-1 elements and the other contains the last M-1 elements, then the signal subspace matrix corresponding to the sub-array containing the first M-1 elements is the first M-1 rows of the signal subspace and the signal subspace matrix corresponding to the sub-array containing the last M-1 elements is the last M-1 rows of the signal subspace . S4: obtaining ID source DOA estimation based on a matrix rank reduction criterion and using the phase relationship corresponding to the two signal subspace matrices; Wherein, the specific process of step S4 is as follows: S4.11, exploiting and constructing a new matrix is denoted as: where, Θ is the set of all possible DOA values, diag{·} represents the diagonalization operation; S4.02, based on the matrix rank reduction criterion, obtaining the DOA estimation of the ID source by one-dimensional spectrum search, the expression of the one-dimensional spectrum search is: wherein, det{·} represents the matrix determinant operation.

2. The method of claim 1, wherein the method is a non-coherent distributed source (DOA) estimation method based on generalized array flow pattern in colored noise. Wherein, The specific process of another way of executing step S3 is as follows: S3.01, R D Eigenvalue decomposition to obtain its signal subspace U S , the signal subspace U S is composed of the matrix of the eigenvectors corresponding to the L largest eigenvalues; the L largest eigenvalues refer to the descending order of eigenvalues of R D , taking the first L eigenvalues as the largest eigenvalues; S3.02, dividing the uniform linear array into two sub-arrays, one of which contains the first M-1 elements and the other of which contains the last M-1 elements, then the signal subspace matrix U corresponding to the sub-array containing the first M-1 elements is the first M-1 rows of the signal subspace U S1 and the signal subspace matrix U corresponding to the sub-array containing the last M-1 elements is the last M-1 rows of the signal subspace U S . S2 and the signal subspace matrix U corresponding to the sub-array containing the last M-1 elements is the last M-1 rows of the signal subspace U S .

3. The method of claim 2, wherein the method is based on generalized array flow pattern for non-coherent distributed source (DOA) estimation in colored noise. In step S4, the specific process of obtaining ID source DOA estimation based on a matrix rank reduction criterion and using the phase relationship corresponding to the two signal subspace matrices comprises the following steps: S4.01, with U S1 and U S2 A new matrix Ξ is constructed, denoted as: Ξ = U S2 - Ψ(θ)U S1 where, θ represents all possible DOA values, diag{·} represents diagonalization operation; S4.02, based on the matrix rank reduction criterion, obtaining the DOA estimation of the ID source by one-dimensional spectrum search, the expression of the one-dimensional spectrum search is: wherein, det{·} represents the matrix determinant operation.

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