A space-time three-dimensional near-field source positioning method based on an accurate propagation model

Abstract

The application relates to a space-time three-dimensional near-field source positioning method based on an accurate propagation model, which comprises the following steps: establishing a cross array receiving model, establishing a three-dimensional rectangular coordinate system in the cross array receiving model, wherein the cross array receiving model is composed of a uniform linear array located on an X axis and a uniform linear array located on a Y axis; setting that there are K near-field targets, a kth near-field target S k impinges on the cross array receiving model with an electric angle {alpha k , beta k} and a distance r k ; obtaining a cumulant matrix on all array elements of the X axis and the Y axis respectively, uniformly sampling the cumulant matrix with a pseudo-snapshot N to obtain two cumulant matrices, and obtaining an estimated value of the electric angle alpha and an estimated value of the electric angle beta by using a DOA matrix method; the method can obtain automatically paired near-field two-dimensional electric angles and distance parameters under the premise of a uniform cross array, improves the estimation precision of the positioning algorithm, and avoids high calculation complexity and an additional pairing process by using the DOA matrix method for positioning.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of near-field signal positioning, in particular to a space-time three-dimensional near-field source positioning method based on an accurate propagation model. BACKGROUND

[0002] The near-field signal positioning is applied to the fields of radar, sonar, wireless communication, etc. As its application is more and more extensive, it has been widely concerned. At the beginning, the positioning algorithm of the near-field is mainly improved from the far-field positioning algorithm, so as to be applied to the near-field. For example, the near-field-based MUSIC algorithm is simple to implement, but it involves multidimensional search and has huge calculation amount. In recent years, many scholars use some dimension reduction techniques to reduce the multidimensional search to one-dimensional search, so as to improve the calculation efficiency, but the high complexity inherent in the spectral peak search still exists. On the other hand, the space-time three-dimensional near-field source positioning method based on the accurate propagation model makes full use of the time domain information and the spatial information of the signal, and can obtain better performance, while the existing near-field source estimation algorithms in the three-dimensional scene rarely utilize the time domain information, resulting in a certain loss of accuracy. In addition, many existing three-dimensional near-field source estimation algorithms are not based on the accurate spatial propagation model, which is inconsistent with the actual positioning situation. The existing research shows that this kind of algorithm will have different degrees of saturation when considering the amplitude attenuation, and then lead to the failure of the algorithm. SUMMARY

[0003] The technical problem to be solved by the present application is to provide a space-time three-dimensional near-field source positioning method based on an accurate propagation model, which can obtain automatically paired near-field two-dimensional electric angles and distance parameters under the premise of a uniform cross-shaped array, and has low complexity in the whole parameter estimation process and high accuracy in parameter pairing.

[0004] The technical solution adopted by the present application is a space-time three-dimensional near-field source positioning method based on an accurate propagation model, which comprises the following steps:

[0005] S1, a cross-shaped array receiving model is established, a three-dimensional rectangular coordinate system is established in the cross-shaped array receiving model, and the cross-shaped array receiving model is composed of a uniform linear array located on the X-axis and a uniform linear array located on the Y-axis; the uniform linear array on the X-axis comprises M=2P+1 array elements, each linear array on the Y-axis comprises M=2P+1 array elements, P represents the number of single-side array elements, the array element at the coordinate origin is taken as a reference array element, and the spacing between the array elements is set as d=λ / 4, λ represents the wavelength of the incident signal;

[0006] S2, in the three-dimensional rectangular coordinate system, it is assumed that there are K near-field targets, the kth near-field target S k The electric angle {α k ,β k} and the distance rk incident on the cross-over array receiving model, where k represents the number of sources, k = 1, 2, …, K; let the distance between the kth source and the element located at (l, 0) on the X-axis be r x,l,k , where l = -m, …, 0, …, m, Then the amplitude-phase factor of the kth source arriving at the element located at (l, 0) on the X-axis is: where, γ x,l,k represents the amplitude factor of the kth source and the element located at (l, 0) on the X-axis, τ x,l,k represents the phase factor caused by the propagation time delay of the kth source and the element located at (l, 0) on the X-axis of the array, using the Fresnel approximation, τ x,l,k ≈ lω xk + l 2 μ xk , Let the distance between the kth source and the element located at (0, l) on the Y-axis be r y,l,k , where l = -m, …, 0, …, m, Then the amplitude-phase factor of the kth source arriving at the element located at (0, l) on the Y-axis is: where, γ y,l,k represents the amplitude factor of the kth source and the element located at (0, l) on the Y-axis; τ y,l,k represents the phase factor caused by the propagation time delay of the kth source and the element located at (0, l) on the Y-axis of the array, using the Fresnel approximation, τ y,l,k ≈ lω yk + l 2 μ yk ,

[0007] S3, according to the amplitude-phase factor a l (α k , r k ) of the kth source arriving at the element located at (l, 0) on the X-axis obtained in step S2, the receiving data model of the element located at (l, 0) on the X-axis is obtained where s k (t) represents the incident signal of the kth near-field target, n l,0 (t) represents independent complex additive Gaussian noise with mean 0 and variance σ 2 , t = 1, 2, …, T, T represents the total number of snaps; according to the amplitude-phase factor a l (β k , r k), the received data model of the element located at (0, 1) on the Y axis is: where s k (t) represents the incident signal of the kth near-field target, n 0,l (t) represents independent complex additive Gaussian noise with mean 0 and variance σ 2 ;

[0008] S4, the received data model z l,0 (t) of the element located at (l, 0) on the X axis obtained in step S3 is extended to all elements on the X axis, to obtain the received data model z x (t) of all elements on the X axis; the received data model z y (t) of the element located at (0, 1) on the Y axis obtained in step S3 is extended to all elements on the Y axis, to obtain the received data model z x (t) of all elements on the Y axis; the received data model z y (t) and the received data model z x (t) are respectively extended to matrix form by multi-block sampling, that is, Z y and Z m ;

[0009] S5, the zero-mean fourth-order cross-cumulant signal with time delay τ is set as x, x = {x n (t), x p (t), x q (t)}, where x m (t), x n (t), x p (t), x q (t) respectively represent the received data of elements located at m, n, p, q four different positions; the zero-mean fourth-order cross-cumulant signal is defined as:

[0010] S6, according to the fourth-order cross-cumulant signal defined in step S5, the received signals at {-m, 0}, {m, 0}, {0, 1}, {0, -1} on the X axis and the Y axis are selected to form the actual cross-cumulant wherein, z m,0 (t), z 0,-1 (t) respectively represent the actual received data of elements located at (-m, 0), (m, 0), (0, 1), (0, -1); according to the zero-mean fourth-order cross-cumulant signal c 4x (τ) defined in step S5, the cross-cumulant c 4m,n (τ) is obtained as: Similarly, the actual cross-cumulative amount is obtained by selecting the received signals at {-m,0}, {m,0}, {0,-1}, and {0,1} on the X and Y axes, respectively: in, This represents the fourth-order cumulant after a signal delay of τ.

[0011] S7. Based on the cross-cumulative amount c formed in step S6 4m,n (τ), obtain the cumulant matrix on all elements of the X-axis and Y-axis respectively, and get Its matrix form is: Where, A=[a(ω 1x ),...,a(ω Kx ] represents the steering vector for virtual data reception. c s (τ) represents the virtual signal vector in the cumulative domain.

[0012] S8. The cumulative matrix c obtained in step S7 x (τ) and c y (τ) Perform uniform sampling using pseudo-fastsnap N to obtain two cumulant matrices: Among them, C s =[c s (T s ),c s (2T s ),...,c s (NT s )], R s T represents the cumulative domain virtual signal matrix after N pseudo-snapshot samplings. s The sampling period;

[0013] S9. The two cumulant matrices C obtained from step S8 x and C y Since there exists a rotation invariant factor Φ, a new matrix is ​​defined using the DOA matrix method. in,[·] - Indicates a false reversal. The non-zero eigenvalues ​​of Φ are equal to the K elements on the main diagonal, and the corresponding eigenvectors are equal to the K columns of the manifold matrix A, i.e. The estimated value of the electric angle β is from The phase ω of the eigenvalues xk Obtained from, that is The estimated value of the electric angle α is from It is obtained from the feature vector, that is Furthermore, since there is a one-to-one correspondence between eigenvalues ​​and eigenvectors, electric angles α and β can be automatically paired.

[0014] S10, obtaining a spectrum peak function P of the distance from the electrical angle a obtained in step S9 MUSIC .

[0015] As a preference, in step S4, the received data model z x (t) of the whole X-axis array elements is expressed as: z x (t) = A x s(t) + n x (t), wherein A x = [a x (a1, r1),..., a x (a k , r k ),..., a x (a K , r K )] T represents an M x K dimensional flow matrix, a x (a k , r k ) = [a -m (a k , r k ),..., 1,..., a m (a k , r k )] T , a m (a k , r k ) represents the amplitude phase factor of the array element located at (m, 0), s(t) represents a K x 1 dimensional baseband signal vector, n x (t) represents an M x 1 dimensional additive noise vector of the array X; the received data model z y (t) of the whole Y-axis array elements is expressed as: z y (t) = A y s(t) + n y (t), wherein A y = [a y (b1, r1),..., a y (b k , r k ),..., a y (b K , r K )] T represents an M x K dimensional flow matrix, a y (b k , r k ) = [a -m (b k , r k ),..., 1,..., a m(β k ,r k )] T ,a m (β k ,r k ) represents the amplitude phase factor of the array element located at the array (0, m), s(t) represents a K*1 dimensional baseband signal vector, n y (t) represents an M*1 dimensional additive noise vector of the array Y, and the corresponding matrix forms are respectively Z x =A x S+N x and Z y =A y S+N y , wherein Z x and Z y respectively represent the matrix forms of the entire X-axis and Y-axis array element received data model, both of which are M*T dimensional, S represents a K*T dimensional baseband signal matrix, N x and N y respectively represent the matrix forms of the array element noise on the entire X-axis and the entire Y-axis, both of which are M*T dimensional.

[0016] As preferred, in step S10, the spectral peak function P MUSIC of the distance is obtained according to the electrical angle a obtained in step S9. The specific process is as follows: the estimated value of the electrical angle a obtained in step S9 is brought into Z x obtained in step S4, to generate a model containing only unknown parameters r k : The estimated value of the covariance matrix is: The covariance matrix is subjected to eigenvalue decomposition to obtain the noise subspace and the signal subspace, i.e. According to the orthogonality principle of the signal subspace and the noise subspace, the following is obtained: Further, the spectral peak function P of the distance is obtained.

[0017] The present application has the following beneficial effects: the above-mentioned space-time three-dimensional near-field source positioning method based on an accurate propagation model can obtain automatically paired near-field two-dimensional electrical angle and distance parameters under the premise of a uniform cross-shaped array, the estimation accuracy of the positioning algorithm is effectively improved by introducing the time delay pseudo snapshot into the near-field source three-dimensional positioning algorithm, the positioning is performed by using the DOA matrix method to avoid high calculation complexity and an additional pairing process, the parameter estimation process complexity is reduced, and the parameter pairing accuracy is improved. In addition, the near-field source three-dimensional positioning algorithm based on the accurate space propagation model is closer to the actual positioning scene. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 This is a schematic diagram of the cross-shaped array receiving model in the spatiotemporal three-dimensional near-field source localization method based on the accurate propagation model of the present invention;

[0019] Figure 2 The image shows the result of angle estimation of the near-field signal obtained in an example of a specific embodiment of the present invention.

[0020] Figure 3 This is a diagram showing the distance estimation result of the near-field signal obtained in an example of a specific embodiment of the present invention. Detailed Implementation

[0021] The invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can implement it based on the description. The scope of protection of the invention is not limited to these specific embodiments.

[0022] This invention designs a spatiotemporal three-dimensional near-field source localization method based on an accurate propagation model, the method comprising the following steps:

[0023] S1, such as Figure 1 As shown, a cross-shaped array receiving model is established, and a three-dimensional Cartesian coordinate system is established in the cross-shaped array receiving model. The cross-shaped array receiving model consists of a uniform linear array located on the X-axis and a uniform linear array located on the Y-axis. The uniform linear array on the X-axis contains M = 2P + 1 array elements, and each linear array on the Y-axis contains M = 2P + 1 array elements, where P represents the number of array elements on a single side. The array element located at the origin of the coordinate system is used as the reference array element, and the spacing between array elements is set to d = λ / 4, where λ represents the wavelength of the incident signal.

[0024] S2. In a three-dimensional rectangular coordinate system, there are K near-field targets. The k-th near-field target S k With electric angle {α k ,β k} and distance r k The signal is incident on a cross-shaped array receiving model, where k represents the number of sources, k = 1, 2, ..., K; the distance between the k-th source and the array element located at (l, 0) on the X-axis is set to r. x,l,k Where l = -m,...,0,...m, Then the amplitude phase factor of the k-th source reaching the array element located at (l,0) on the X-axis is: in, γ x,l,k τ represents the amplitude factor of the k-th source relative to the array element located at (l,0) on the X-axis. x,l,k The phase factor τ is the propagation delay between the k-th source and the array element located at (l,0) on the X-axis of the array. Using the Fresnel approximation, we obtain τ. x,l,k ≈lωxk +l 2 μ xk , Let r be the distance between the k-th source and the array element located at (0, l) on the Y-axis. y,l,k Where l = -m,...,0,...m, The amplitude phase factor of the k-th source reaching the array element located at (0, l) on the Y-axis is then obtained as follows: in, γ y,l,k Let τk represent the amplitude factor between the k-th source and the array element located at (0,l) on the Y-axis; τy,l,k represent the phase factor caused by the propagation delay between the k-th source and the array element located at (0,l) on the Y-axis. Using the Fresnel approximation, we obtain τk. y,l,k ≈lω yk +l 2 μ yk ,

[0025] S3. The amplitude phase factor a of the k-th source reaching the array element located at (l,0) on the X-axis, obtained from step S2. l (α k ,r k This yields the received data model of the array element located at (l,0) on the X-axis. Among them, s k (t) represents the incident signal of the k-th near-field target, n l,0 (t) represents a mean of 0 and a variance of σ. 2 Independent additive Gaussian noise, t = 1, 2, ..., N, N represents the Nth snapshot; the amplitude and phase factor a of the kth source arriving at the array element located at (0, l) on the Y-axis, obtained from step S2. l (β k ,r k The received data model of the array element located at (0, l) on the Y-axis is obtained as follows: Among them, s k (t) represents the incident signal of the k-th near-field target, n 0,l (t) represents a mean of 0 and a variance of σ. 2 Independent additive Gaussian noise;

[0026] S4. The received data model z of the array element located at (l,0) on the X-axis obtained in step S3. l,0 (t) is extended to the array elements along the entire X-axis to obtain the received data model z of the array elements along the entire X-axis. x (t); Extend the received data model of the array element at (0,l) on the Y-axis obtained in step S3 to the array elements along the entire Y-axis, to obtain the received data model z of the array elements along the entire Y-axis.y (t), the received data model z x (t) and the received data model z y (t) are respectively expanded into matrix form by multi-block sampling, i.e. Z x and Z y ; the expression of the received data model z x (t) of the whole X-axis array element is: z x (t) = A x s(t) + n x (t), wherein A x = [a x (α1, r1),..., a x (α k , r k ),..., a x (α K , r K )] T represents an M × K dimensional flow matrix, a x (α k , r k ) = [a -m (α k , r k ),..., 1,..., a m (α k , r k )] T , a m (α k , r k ) represents the amplitude phase factor of the array element located at (m, 0), s(t) represents a K × 1 dimensional baseband signal vector, n x (t) represents an M × 1 dimensional additive noise vector of the array X; the expression of the received data model z y (t) of the whole Y-axis array element is: z y (t) = A y s(t) + n y (t), wherein A y = [a y (β1, r1),..., a y (β k , r k ),..., a y (β K , r K )] T represents an M × K dimensional flow matrix, a y (β k , r k ) = [a -m (β k , r k),...,1,...,a m (β k ,r k )] T , a m (β k ,r k ) represents the amplitude phase factor of the array element located at the array (0, m), s(t) represents a Kx1 dimensional baseband signal vector, n y (t) represents a Mx1 dimensional additive noise vector of the array Y, and the corresponding matrix forms are respectively x = A x S + N x and y = A y S + N y , wherein Z x and Z y respectively represent the matrix forms of the entire X-axis and Y-axis array element received data models, both of which are MxT dimensional, S represents a KxT dimensional baseband signal matrix, N x and N y respectively represent the matrix forms of the array element noises on the entire X-axis and the entire Y-axis, both of which are MxT dimensional;

[0027] S5, set the zero mean fourth order cross-cumulant signal with a time delay τ as x, x = {x m (t), x n (t), x p (t), x q (t)}, wherein x m (t), x n (t), x p (t), x q (t) respectively represent the received data of the array elements located at m, n, p, q four different positions; the zero mean fourth order cross-cumulant signal is defined as:

[0028] S6, according to the fourth order cross-cumulant signal defined in step S5, the received signals at {-m, 0}, {m, 0}, {0, 1}, {0, -1} on the X-axis and the Y-axis are selected to form the actual cross-cumulant wherein, z m,0 (t), z 0,-1 (t) respectively represent the actual received data of the array elements located at (-m, 0), (m, 0), (0, 1), (0, -1), which indicates that the signal has a time delay of τ; according to the zero mean fourth order cross-cumulant signal c 4x (τ) defined in step S5, the cross-cumulant c4m,n (τ) is: Similarly, the actual cross-cumulant composed of the received signals at the points {-m, 0}, {m, 0}, {0, -1}, {0, 1} on the X-axis and Y-axis respectively is obtained: wherein, represents the fourth-order cumulant after signal delay τ,

[0029] S7, the cross-cumulant c 4m,n (τ) composed according to step S6 is obtained, and the cumulant matrix is obtained at all elements on the X-axis and Y respectively, and its matrix form is: wherein, A = [a(ω 1x ),...,a(ω Kx )] represents the steering vector of the virtual received data, wherein, c s (τ) represents the virtual signal vector of the cumulant domain,

[0030] S8, the cumulant matrix c x (τ) obtained in step S7 and the cumulant matrix c y (τ) are uniformly sampled with pseudo-snapshot N respectively, and two cumulant matrices can be obtained: wherein, C s = [c s (T s ), c s (2T s ),...,c s (NT s )], R s represents the virtual signal matrix of the cumulant domain after N times of pseudo-snapshot sampling, T s represents the sampling period; sampling refers to observing the same signal according to a fixed time interval T s ;

[0031] S9, there is a rotation invariant factor Φ between the two cumulant matrices C x and C y obtained in step S8, and the DOA matrix method is adopted to define a new matrix wherein, [·] - represents pseudo-inverse, the non-zero eigenvalues of the new matrix are equal to the K elements on the main diagonal of Φ, and the corresponding eigenvectors are equal to the K columns of the flow matrix A, i.e. the estimated value of the electric angle β is obtained from the phase ω xk of the eigenvalue of the new matrix, i.e. the estimated value of the electric angle α is obtained from the phase ω MUSIC of the eigenvalue of the new matrix, i.e. The features are obtained from the eigenvectors, based on the preceding discussion. The result of dividing the first and second rows of the feature vector is: Then the electric angle α can pass: The solution is obtained by using this method, and since the eigenvalues ​​and eigenvectors are in one-to-one correspondence, the electric angles α and β can be automatically paired.

[0032] S10. Obtain the spectral peak function P of the distance based on the electric angle α obtained in step S9. MUSIC The specific process is as follows: Substitute the estimated value of the electric angle α obtained in step S9 into the Z value obtained in step S4. x In (t), a function containing only the unknown parameter r is generated. k model The estimated value of its covariance matrix is: For the one containing only the unknown parameter r k Model Z x (t) is used for eigenvalue decomposition to obtain the noise subspace and the signal subspace, i.e. Based on the orthogonality principle of the signal subspace and the noise subspace, we obtain: This leads to the spectral peak function of the distance.

[0033] The effectiveness of the proposed method for estimating three-dimensional parameters of a spatiotemporal near-field source based on parallel factor decomposition is demonstrated through the following examples.

[0034] Example: Suppose four independent near-field signals are incident on a cross-shaped array receiver model at four azimuths: (49°, 97°, 0.43λ), (157°, 36°, 0.51λ), (84°, 117°, 0.27λ), and (119°, 63°, 0.32λ). The cross-shaped array has 5 elements on both the X and Y axes, i.e., 2 elements per side and a total of 9 elements. Setting the signal-to-noise ratio (SNR) and snapshot number to 15dB and 5000 respectively, and using pseudo-snapshots, the angle estimation results of the near-field signals are as follows: Figure 2 As shown, from Figure 2 As can be seen, the estimated parameters of the four near-field sources can be correctly estimated and paired; the distance estimation results of the near-field signals are as follows: Figure 3 As shown, the distance values ​​corresponding to the locations of the peaks are from... Figure 3 It can also be seen that the distance estimate is accurate. Therefore, the method proposed in this invention is effective.

Claims

1. A method for locating a three-dimensional near-field source based on an accurate propagation model, characterized in that: The method comprises the following steps: S1, establishing a cross array receiving model, establishing a three-dimensional rectangular coordinate system in the cross array receiving model, the cross array receiving model is composed of a uniform linear array located on the X axis and a uniform linear array located on the Y axis; the uniform linear array on the X axis contains M=2m+1 elements, each linear array on the Y axis contains M=2m+1 elements, m represents the number of single-side elements, the element at the coordinate origin is used as a reference element, and the spacing between elements is set as d=λ / 4, λ represents the wavelength of the incident signal; S2, in a three-dimensional rectangular coordinate system, set to exist K near-field targets, the kth near-field target S k in the electric angle {α k ,β k} and distance r k incident on the cross array receiving model, wherein k represents the number of sources, k=1,2,…,K; set the distance between the kth source and the array element located at (l,0) on the X axis r x,l,k , wherein l=-m,…,0,…m, The amplitude phase factor of the kth source arriving at the array element located at (l,0) on the X axis is: wherein, γ x,l,k represents the amplitude factor of the kth source and the array element located at (l,0) on the X axis, τ x,l,k represents the phase factor caused by the propagation delay of the kth source and the array element located at (l,0) on the X axis, using the Fresnel approximation, τ x,l,k ≈lω xk +l 2 μ xk , Set the distance between the kth source and the array element located at (0,l) on the Y axis r y,l,k , wherein l=-m,…,0,…m, The amplitude phase factor of the kth source arriving at the array element located at (0,l) on the Y axis is: wherein, γ y,l,k represents the amplitude factor of the kth source and the array element located at (0,l) on the Y axis; τ y,l,k represents the phase factor caused by the propagation delay of the kth source and the array element located at (0,l) on the Y axis, using the Fresnel approximation, τ y,l,k ≈lω yk +l 2 μ yk , S3, the amplitude-phase factor a of the kth source reaching the element located at (l, 0) on the X-axis obtained according to step S2 l (α k , r k ), a received data model of the element located at (l, 0) on the X-axis is obtained wherein s k (t) represents an incident signal of the kth near-field target, n l,0 (t) represents independent complex additive Gaussian noise with a mean of 0 and a variance of σ 2 , t = 1, 2,..., N, N represents the Nth fast snap; the amplitude-phase factor a of the kth source reaching the element located at (0, l) on the Y-axis obtained according to step S2 l (β k , r k ), a received data model of the element located at (0, l) on the Y-axis is obtained wherein s k (t) represents an incident signal of the kth near-field target, n 0,l (t) represents independent complex additive Gaussian noise with a mean of 0 and a variance of σ 2 ​ S4, extending the received data model z of the element located at (1, 0) of the X axis obtained in step S3 to all elements of the X axis to obtain a received data model z of all elements of the X axis l,0 (t) of all elements of the X axis x (t); extending the received data model z of the element located at (0, 1) of the Y axis obtained in step S3 to all elements of the Y axis to obtain a received data model z of all elements of the Y axis y (t) of all elements of the Y axis x (t) and the received data model z y (t) are respectively extended into matrix form by multi-block sampling, i.e. Z x and Z y ; S5, set the zero-mean fourth-order cross-cumulant signal with time delay τ as x, x = {x m (t), x n (t), x p (t), x q (t)} where x m (t), x n (t), x p (t), x q (t) respectively represent the received data of the elements located at m, n, p, q four different positions; the zero-mean fourth-order cross-cumulant signal is defined as: S6, selecting the received signals at {-m, 0}, {m, 0}, {0, 1}, {0, -1} on the X-axis and Y-axis respectively to form the actual cross-cumulant according to the fourth-order cross-cumulant signal defined in step S5 wherein, z m,0 (t), z 0,-1 (t) respectively represent the actual received data of the elements located at (-m, 0), (m, 0), (0, 1), (0, -1); the zero-mean fourth-order cross-cumulant signal c 4x (τ) defined in step S5, the cross-cumulant c 4m,n (τ) is represented as: Similarly, the actual cross-cumulant formed by the received signals at the points {-m, 0}, {m, 0}, {0, -1}, {0, 1} on the X and Y axes, respectively, is obtained: where, denotes the fourth-order cumulant after signal delay τ, S7. Cross-correlation c constructed according to step S6 4m,n (τ), respectively, on all elements of the X and Y axes to obtain The matrix form is: Where A = [a(ω 1x ),...,a(ω Kx )] represents the steering vector of the virtual received data, c s (τ) represents the virtual signal vector of the cross-correlation domain, S8, accumulating the matrix c obtained in step S7 x (τ) and c y (τ) are uniformly sampled with pseudo-samples N to obtain two accumulation matrices: where C s = [c s (T s ), c s (2T s ),..., c s (NT s )], R s represents a virtual signal matrix in the accumulation domain after N pseudo-samples, and T s is a sampling period. S9, two cumulant matrices C obtained from step S8 x and C y exist a rotation invariant factor Φ, using DOA matrix method, define a new matrix where [·] - denotes pseudo-inverse, The non-zero eigenvalues of equal to K elements on the main diagonal of Φ, the corresponding eigenvectors equal to K columns of flow pattern matrix A, that is The estimated value of the electrical angle β is obtained from the phase ω of the eigenvalues of xk , that is The estimated value of the electrical angle α is obtained from the eigenvectors of , that is And since the eigenvalues and eigenvectors are one-to-one correspondence, the electrical angles α and β can be automatically paired; S10. Obtain the spectral peak function P of the distance from the electrical angle a obtained in step S9 MUSIC .

2. The method of claim 1, wherein the method is based on an exact propagation model. The received data model z of the elements of the entire X-axis x The expression of z (t) is: x z (t) = A x s (t) + n x (t), where A x = [a x (α1, r1),..., a x (α k , r k ),..., a x (α K , r K )] T represents an M x K dimensional flow matrix, a x (α k , r k ) = [a -m (α k , r k ),..., 1,..., a m (α k , r k )] T , a m (α k , r k ) represents the amplitude phase factor of the element located at the array (m, 0), s (t) represents a K x 1 dimensional baseband signal vector, n x (t) represents an M x 1 dimensional additive noise vector of the array X; The received data model z of the elements of the entire Y-axis y The expression of z (t) is: y z (t) = A y s (t) + n y (t), where A y = [a y (β1, r1),..., a y (β k , r k ),..., a y (β K , r K )] T represents an M x K dimensional flow matrix, a y (β k , r k ) = [a -m (β k , r k ),..., 1,..., a m (β k , r k )] T , a m (β k , r k ) represents the amplitude phase factor of the array element located at the array (0, m), s(t) represents the Kxl dimensional baseband signal vector, n y (t) represents the Mxl dimensional additive noise vector of the array Y, which corresponds to the matrix form respectively x = A x S+N x and Z y = A y S+N y , wherein Z x and Z y represent the matrix form of the entire X-axis and Y-axis array element receiving data model respectively, both of which are MxT dimensional, S represents the KxT dimensional baseband signal matrix, N x and N y represent the matrix form of the array element noise on the entire X-axis and the entire Y-axis respectively, both of which are MxT dimensional.

3. The method of claim 1, wherein the method is based on an exact propagation model. In step S10, the spectral peak function P of distance is obtained according to the electric angle a obtained in step S9 MUSIC The specific process is: the estimated value of the electric angle a obtained in step S9 is brought into Z x (t) obtained in step S4, to generate a model containing only unknown parameters r k The estimated value of the covariance matrix is: The model Z k (t) containing only unknown parameters r x is subjected to eigenvalue decomposition to obtain a noise subspace and a signal subspace, i.e. According to the orthogonality principle of the signal subspace and the noise subspace, the following is obtained: Further, the spectral peak function P of distance is obtained ​

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