Low-redundancy high-order direction-of-arrival measurement method and system based on co-prime characteristics and computer storage medium

Abstract

The application discloses a low-redundancy high-order measurement direction method and system based on the coprime characteristic and a computer storage medium, and the method comprises the following steps: receiving signals from multiple signal sources by using a low-redundancy array improved based on a coprime array to obtain received signals; calculating a fourth-order cumulant matrix of the received signals according to the received signals; obtaining a covariance matrix according to the fourth-order cumulant matrix; calculating eigenvalues and eigenvectors of the covariance matrix according to the covariance matrix; dividing the eigenvectors into a signal subspace and a noise subspace according to the sizes of the eigenvalues; constructing a spectral function according to projections of the steering vectors on the noise subspace; searching for peak values of the spectral function in all possible directions to determine the directions of the signal sources. The low-redundancy array improved based on the coprime array can not only expand the estimated number of signal sources on the basis of reducing the number of received array elements, but also adopt the fourth-order cumulant, so that the positioning precision in a non-Gaussian noise environment can be improved.

Description

Technical Field

[0001] The present invention relates to the field of signal processing technology, and more particularly to a low-redundancy high-order direction finding method, system and computer storage medium based on coprime characteristics. Background Art

[0002] In modern communications systems, directional antenna array technology has become an essential component of radar systems. Accurately estimating the direction of arrival of a signal at the antenna is crucial. Consequently, DOA (direction of arrival) estimation has become a highly sought-after research topic in signal processing.

[0003] The MUSIC algorithm is a commonly used DOA estimation algorithm. Its core concept is to estimate the direction of arrival (DOA) of a received signal by performing spatial spectrum analysis on the received signal. The algorithm first applies spatial filtering to the signal and then calculates the spatial spectrum of the received signal. Based on the processed spatial spectrum of the signal, the angle of arrival (DOA) of the signal can be estimated. However, it should be noted that since the MUSIC algorithm is essentially a DOA estimation method based on spatial spectrum analysis, it is based on a traditional uniform linear antenna array (ULA). The number of antennas in a ULA is limited, and only the directions of L-1 signals can be estimated (where L is the number of antennas). Using coprime antenna arrays can increase the number of virtual linear antenna arrays. Although the number of arrays deployed in actual space is reduced compared to traditional uniform linear arrays (ULAs), this method can estimate more signals than the traditional MUSIC algorithm can.

[0004] However, existing coprime arrays generally have redundancy after simulation, which may increase the cost in practical applications. In addition, in the above-mentioned DOA (direction angle estimation) estimation algorithm, the noise type targeted is mainly limited to Gaussian white noise. The processing of this type of white noise depends on the second-order statistical characteristics of the received signal, specifically by analyzing the autocovariance matrix or cross-covariance matrix of the array received data. However, the noise encountered in actual application scenarios is often not all Gaussian white noise, but contains non-Gaussian signals, and because the estimated number of signal sources is relatively poor, this may cause the performance of the above-mentioned algorithm to decline significantly in practical applications. In addition, due to the existence of coprime arrays, the mutual coupling effect between antennas in the DOA estimation algorithm of coprime arrays will also be relatively high. Summary of the Invention

[0005] One of the objectives of the present invention is to provide a low-redundancy high-order direction finding method based on coprime characteristics, so as to solve the technical problem in the prior art that the algorithm performance is significantly reduced in practical applications due to the noise containing non-Gaussian signals; the second objective of the present invention is to provide a low-redundancy high-order direction finding system based on coprime characteristics; the third objective of the present invention is to provide a computer storage medium.

[0006] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0007] A first aspect of the present invention provides a low-redundancy high-order direction finding method based on coprime characteristics, comprising the following steps:

[0008] Using a low-redundancy array obtained by improving a coprime array to receive signals from multiple signal sources, thereby obtaining a received signal;

[0009] Calculating a fourth-order cumulant matrix of the received signal according to the received signal;

[0010] Obtaining a covariance matrix according to the fourth-order cumulant matrix;

[0011] Calculating the eigenvalues ​​and eigenvectors of the covariance matrix according to the covariance matrix;

[0012] Dividing the eigenvector into a signal subspace and a noise subspace according to the magnitude of the eigenvalue;

[0013] constructing a spectral function according to the projection of the steering vector on the noise subspace;

[0014] The peak of the spectrum function is searched in all possible directions to determine the direction of the signal source.

[0015] Based on the use of a coprime array, the present invention can estimate the direction of a larger number of signals than the number of array elements by using fourth-order cumulants. Moreover, due to the use of fourth-order cumulants, the non-Gaussian characteristics of the signal can be better captured, thereby providing more accurate DOA estimation in a non-Gaussian noise environment. This can perfectly solve the technical problem in the prior art that the algorithm performance is significantly reduced in actual applications due to the noise containing non-Gaussian signals.

[0016] Furthermore, the low-redundancy array obtained by improving the coprime array includes:

[0017] The coprime array includes a first subarray and a second subarray arranged in parallel with each other, wherein the first subarray is a uniform subarray consisting of N elements with an element spacing of M*d, and the elements in the first subarray are numbered from 0 to N-1; the second subarray is a 2M uniform subarray with an element spacing of N*d, and the elements in the second subarray are numbered from 0 to 2M-1. Elements in the second subarray with numbers in the range of [1, (3M-4) / 2] are removed to obtain the low-redundancy array improved based on the coprime array.

[0018] Furthermore, the received signal is as follows:

[0019] K=AS+N

[0020] X=[x(1),x(2),…,x(T)]

[0021] A=[a(θ1),a(θ2),…,a(θ k )]

[0022] S=[s(1),s(2),s(3),…,s(T)]

[0023] Where X represents the received signal, x(1), x(2), …, x(T) represent the signals obtained by sampling the signals received from multiple signal sources for the 1st, 2nd, …, Tth times; A represents the direction vector matrix, θ1, θ2, …, θ k represents the incident angle of the 1st, 2nd, ..., kth signal source, a(θ1), a(θ2), ..., a(θ k ) represents the steering vector of the 1st, 2nd,…, kth signal source; S represents the signal source vector, s(1), s(2), s(3),…, s(T) represent the 1st, 2nd,…, Tth sampled signals, and N represents the array noise.

[0024] Further, calculating a fourth-order cumulant matrix of the received signal according to the received signal includes:

[0025]

[0026] Where C Y represents the fourth-order cumulant matrix, E{} represents the mathematical expectation, represents the Kronecker product, and H represents the conjugate transpose of the matrix.

[0027] Furthermore, according to the fourth-order cumulant, a covariance matrix is ​​obtained, including:

[0028] Vectorizing the fourth-order cumulant matrix to obtain a first vector;

[0029] Remove repeated signals from the first vector to obtain a second vector;

[0030] Divide the second vector into P overlapping sub-arrays Each subarray has P virtual elements, where the sensors of the i-th subarray are located at (-i+1+n)d, where n=0,1,..,P-1; the covariance matrix of the i-th subarray is then defined as After calculating the covariance matrix of each subarray, the P×P dimensional spatial smoothing covariance matrix R z Defined as the mean of all subarray covariance matrices.

[0031] Furthermore, the fourth-order cumulant matrix is ​​vectorized to obtain a first vector, including:

[0032] Z=vec(C Y )=Vu

[0033] Where Z is the first vector, vec() represents vectorization processing, V represents the equivalent direction vector matrix composed of virtual elements in the fourth-order cumulant matrix, and u represents the equivalent signal vector.

[0034] Furthermore, the P×P-dimensional spatial smoothing covariance matrix R z Defined as the mean of all subarray covariance matrices, including:

[0035]

[0036] Where, is the number of subarray covariance matrices, Λ is a K×K dimensional diagonal matrix, is the equivalent direction vector matrix of P×K dimensions.

[0037] A second aspect of the present invention provides a low-redundancy high-order direction finding system based on coprime characteristics, comprising:

[0038] A receiving module, wherein the receiving module receives signals from multiple signal sources using a low-redundancy array obtained by improving a coprime array to obtain a received signal;

[0039] A fourth-order cumulant matrix module, wherein the fourth-order cumulant matrix module calculates a fourth-order cumulant matrix of the received signal according to the received signal;

[0040] A covariance matrix module, wherein the covariance matrix module obtains a covariance matrix according to the fourth-order cumulant matrix;

[0041] An eigenvalue module, wherein the eigenvalue module calculates the eigenvalues ​​and eigenvectors of the covariance matrix according to the covariance matrix;

[0042] a partitioning module, wherein the partitioning module partitions the eigenvector into a signal subspace and a noise subspace according to the magnitude of the eigenvalue;

[0043] a spectral function construction module, wherein the spectral function construction module constructs a spectral function according to a projection of the steering vector on the noise subspace;

[0044] A direction determination module searches for the peak of the spectrum function in all possible directions to determine the direction of the signal source.

[0045] Furthermore, the low-redundancy array obtained by improving the coprime array includes:

[0046] The coprime array includes a first subarray and a second subarray arranged in parallel with each other, wherein the first subarray is a uniform subarray consisting of N elements with an element spacing of M*d, and the elements in the first subarray are numbered from 0 to N-1; the second subarray is a 2M uniform subarray with an element spacing of N*d, and the elements in the second subarray are numbered from 0 to 2M-1. Elements in the second subarray with numbers in the range of [1, (3M-4) / 2] are removed to obtain the low-redundancy array improved based on the coprime array.

[0047] A third aspect of the present invention provides a computer storage medium storing a computer program. When the computer program is executed by a processor, the method for low-redundancy high-order direction finding based on coprime characteristics is implemented.

[0048] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0049] Traditional angle estimation methods use uniform arrays and can only estimate signal sources equal to the number of array elements minus 1 at most. However, the low-redundancy array improved based on the coprime array of the present invention can not only expand the number of estimated signal sources while reducing the number of receiving array elements, but also use fourth-order cumulants to improve positioning accuracy in non-Gaussian noise environments, thereby improving the performance of DOA estimation and reducing the mutual coupling between antennas. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A schematic diagram of a flow chart of a low-redundancy high-order direction finding method based on coprime characteristics provided by an embodiment of the present invention;

[0051] Figure 2 A schematic diagram of a conventional coprime array structure provided in an embodiment of the present invention;

[0052] Figure 3 A schematic diagram of the structure of a low-redundancy array obtained by improving a coprime array according to an embodiment of the present invention;

[0053] Figure 4 A schematic structural diagram of a low-redundancy high-order direction-finding system based on coprime characteristics provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0054] The accompanying drawings are for illustrative purposes only and are not to be construed as limiting this patent;

[0055] In order to better illustrate this embodiment, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product size;

[0056] It is understandable to those skilled in the art that some well-known structures and descriptions thereof may be omitted in the drawings.

[0057] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0058] Example 1

[0059] The embodiment of the present invention provides a low-redundancy high-order direction finding method based on coprime characteristics, such as Figure 1 As shown, the following steps are included:

[0060] Using a low-redundancy array obtained by improving a coprime array to receive signals from multiple signal sources, thereby obtaining a received signal;

[0061] Calculating a fourth-order cumulant matrix of the received signal according to the received signal;

[0062] Obtaining a covariance matrix according to the fourth-order cumulant matrix;

[0063] Calculating the eigenvalues ​​and eigenvectors of the covariance matrix according to the covariance matrix;

[0064] Dividing the eigenvector into a signal subspace and a noise subspace according to the magnitude of the eigenvalue;

[0065] constructing a spectral function according to the projection of the steering vector on the noise subspace;

[0066] The peak of the spectrum function is searched in all possible directions to determine the direction of the signal source.

[0067] In a further embodiment, the low-redundancy array obtained by improving the coprime array includes:

[0068] The coprime arrays are Figure 2As shown, it includes a first sub-array and a second sub-array arranged in parallel with each other, wherein the first sub-array is a uniform sub-array consisting of N array elements with an array element spacing of M*d, and the array elements in the first sub-array are numbered from 0 to N-1, and the second sub-array is a 2M uniform sub-array with an array element spacing of N*d, and the array elements in the second sub-array are numbered from 0 to 2M-1, and the array elements in the second sub-array whose numbers are in the range of [1, (3M-4) / 2] are removed, as shown in FIG. Figure 3 As shown, the low redundancy array obtained by improving the coprime array is obtained.

[0069] In a further embodiment, it is assumed that there are K far-field narrowband signals in space, θ1, θ2, ..., θ k The angle of incidence is a low redundancy array of a low redundancy design (such as Figure 3 As shown in FIG, after the incident signal is sampled T times by the receiving array, the output signal X of the array is:

[0070] The received signal is as follows:

[0071] X=AS+N

[0072] X=[x(1),x(2),…,x(T)]

[0073] A=[a(θ1),a(θ2),…,a(θ k )]

[0074] S=[s(1),s(2),s(3),…,s(T)]

[0075] Where X represents the received signal, x(1), x(2), …, x(T) represent the signals obtained by sampling the signals received from multiple signal sources for the 1st, 2nd, …, Tth times; A represents the direction vector matrix, θ1, θ2, …, θ k represents the incident angle of the 1st, 2nd, ..., kth signal source, a(θ1), a(θ2), ..., a(θ k ) represents the steering vector of the 1st, 2nd,…, kth signal source; S represents the signal source vector, s(1), s(2), s(3),…, s(T) represent the 1st, 2nd,…, Tth sampled signals, and N represents the array noise.

[0076] In a further embodiment, calculating a fourth-order cumulant matrix of the received signal according to the received signal includes:

[0077]

[0078] Where C Y represents the fourth-order cumulant matrix, E{} represents the mathematical expectation, represents the Kronecker product, and H represents the conjugate transpose of the matrix.

[0079] In a specific embodiment, the fourth-order cumulant matrix can be decomposed into:

[0080] C Y =BC S B H

[0081] B is the direction matrix expanded by using the fourth-order cumulant, and its i-th column can be expressed as C Y As shown below:

[0082]

[0083] Therefore, the original array is expanded after using the fourth-order cumulant matrix.

[0084] In a further embodiment, a covariance matrix is ​​obtained according to the fourth-order cumulant, including:

[0085] Vectorizing the fourth-order cumulant matrix to obtain a first vector;

[0086] Remove repeated signals from the first vector to obtain a second vector;

[0087] Divide the second vector into P overlapping sub-arrays Each subarray has P virtual elements, where the sensors of the i-th subarray are located at (-i+1+n)d, where n=0,1,..,P-1; the covariance matrix of the i-th subarray is then defined as After calculating the covariance matrix of each subarray, the P×P dimensional spatial smoothing covariance matrix R z Defined as the mean of all subarray covariance matrices.

[0088] In a specific embodiment, after calculating C Y Then, let x rp1 , x rp2 , x rp3 , x rp4 Indicates the signal received by the antenna at position rp1, rp2, rp3, and rp4. Y Rewritten as follows:

[0089]

[0090] in, λ is the wavelength and d is half the wavelength.

[0091] In order to further improve the estimation accuracy of DOA, the fourth-order cumulant matrix is ​​vectorized to obtain a first vector, including:

[0092] Z=vec(C Y )=Vu

[0093] Where Z is the first vector, vec() represents vectorized processing, is the equivalent direction vector matrix composed of virtual elements in the fourth-order cumulant, is the equivalent signal vector, Represents the fourth-order cumulant of the source.

[0094] Since there are repeated signals in Z, the repeated signals can be removed based on the positional relationship of the distribution array, as shown in the following formula:

[0095]

[0096] The specific removal method is as follows: Assume that D is a 3×3 matrix, C Y After vectorization, Z is obtained and stretched into a 9×1 matrix. The specific form after vectorization is B=[b 11 ,b 12 ,b 13 ,b 21 ,b 22 ,b 23 ,b 31 ,b 32 ,b 33 ] T , and make the difference between its two elements:

[0097] D + =[B 11 ,B 12 ,B 13 ,B 21 ,B 22 ,B 23 ,B 31 ,B 32 ,B 33 ] T

[0098] D - =[-B 11 ,-B 12 ,-B 13 ,-B 21 ,-B 22 ,-B 23 ,-B 31 ,-B 32 ,-B 33 ] T

[0099] D=D + ∪D -

[0100] When the elements in D are added and the results are obtained by taking the difference between them, there are redundant elements in the fourth-order cumulant matrix. The corresponding element of the virtual array element with array element position u is r. u , the redundancy is p(r u ), the virtual array element receiving data can be obtained by adding and averaging all redundant elements, that is, Where p is the array element position, u is the redundancy number, r ui represents the i-th element corresponding to the array element at position u. Therefore, Z is deduplicated and sorted to construct a new vector Z1. For example, if the array element positions are [0, 2d4d6d9d], there are 35 virtual continuous arrays, and the array element coordinates can be recorded as: U = [-17, -16, ..., -1, 0, 1, ..., 16, 17].

[0101] Z1 is a fourth-order continuous virtual array of coprime arrays, and the common coprime arrays (such as Figure 2 ), the dimension of Z1 is 6MN+2M-2N-1, and the array of the present invention (such as Figure 3 ), reduced antenna ([] represents rounding up), that is, the original coprime array is rounded up to The antennas at the position are removed, and the number of Z1 is still 6MN+2M-2N-1. That is to say, for the same M and N, the array of the present invention can reduce antennas, so the distance between antennas becomes larger and the mutual coupling effect between signals is reduced.

[0102] When using the second-order covariance matrix, the coprime array becomes redundant, which can be seen from the [Thinned CoprimeArray for Second-Order Difference Co-Array Generation with Reduced MutualCoupling] document. The contribution of antenna d to DOA is 0, and the fourth-order cumulant matrix is ​​used here. As we know from the previous text, the fourth-order cumulant is differentiated twice, because after one difference, we can know The antenna at d can be removed, so the two differentials must include one differential, so this part can be removed. Combined with the above content, when two differentials are performed, the redundant antennas will become more. The embodiment of the present invention mainly increases Because the contribution of this part of the array elements will be replaced by other array elements, the first The antenna is redundant.

[0103] The array arrangement of the present invention is as follows Figure 3 As shown, the first The antenna is a redundant antenna, which means that its contribution to DOA is 0 and it will also increase the mutual coupling effect between antennas, so this part is removed.

[0104] Therefore, with the same number of antennas, the arrangement of the present invention can estimate more DOAs than the traditional coprime arrangement, and increases the spacing between antennas, reducing the mutual coupling effect of signals.

[0105] In a further embodiment, the P×P dimensional spatial smoothing covariance matrix R z Defined as the mean of all subarray covariance matrices, including:

[0106]

[0107] Where, is the number of subarray covariance matrices, Λ is a K×K dimensional diagonal matrix, is the equivalent direction vector matrix of P×K dimensions.

[0108] Example 2

[0109] This embodiment provides a low-redundancy high-order direction finding system based on the coprime property on the basis of embodiment 1, such as Figure 4 Shown, including:

[0110] A receiving module, wherein the receiving module receives signals from multiple signal sources using a low-redundancy array obtained by improving a coprime array to obtain a received signal;

[0111] A fourth-order cumulant matrix module, wherein the fourth-order cumulant matrix module calculates a fourth-order cumulant matrix of the received signal according to the received signal;

[0112] A covariance matrix module, wherein the covariance matrix module obtains a covariance matrix according to the fourth-order cumulant matrix;

[0113] An eigenvalue module, wherein the eigenvalue module calculates the eigenvalues ​​and eigenvectors of the covariance matrix according to the covariance matrix;

[0114] a partitioning module, wherein the partitioning module partitions the eigenvector into a signal subspace and a noise subspace according to the magnitude of the eigenvalue;

[0115] a spectral function construction module, wherein the spectral function construction module constructs a spectral function according to a projection of the steering vector on the noise subspace;

[0116] A direction determination module searches for the peak of the spectrum function in all possible directions to determine the direction of the signal source.

[0117] In a further embodiment, the low-redundancy array obtained by improving the coprime array includes:

[0118] The coprime array includes a first subarray and a second subarray arranged in parallel with each other, wherein the first subarray is a uniform subarray consisting of N elements with an element spacing of M*d, and the elements in the first subarray are numbered from 0 to N-1; the second subarray is a 2M uniform subarray with an element spacing of N*d, and the elements in the second subarray are numbered from 0 to 2M-1. Elements in the second subarray with numbers in the range of [1, (3M-4) / 2] are removed to obtain the low-redundancy array improved based on the coprime array.

[0119] Example 3

[0120] This embodiment provides a computer storage medium storing a computer program. When the computer program is executed by a processor, the low-redundancy high-order direction finding method based on coprime characteristics described in Embodiment 1 is implemented.

[0121] The same or similar reference numerals correspond to the same or similar components;

[0122] The terms used in the drawings to describe positional relationships are for illustrative purposes only and should not be construed as limiting this patent;

[0123] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A low-redundancy high-order direction finding method based on coprime characteristics, characterized in that: The following steps are involved: Using a low-redundancy array obtained by improving a coprime array to receive signals from multiple signal sources, thereby obtaining a received signal; Calculating a fourth-order cumulant matrix of the received signal according to the received signal; Obtaining a covariance matrix according to the fourth-order cumulant matrix; Calculating the eigenvalues ​​and eigenvectors of the covariance matrix according to the covariance matrix; Dividing the eigenvector into a signal subspace and a noise subspace according to the magnitude of the eigenvalue; constructing a spectral function according to the projection of the steering vector on the noise subspace; Searching for the peak of the spectrum function in all possible directions to determine the direction of the signal source; The low-redundancy array obtained by improving the coprime array includes: The coprime array includes a first subarray and a second subarray arranged in parallel with each other, wherein the first subarray is a uniform subarray consisting of N elements with an element spacing of M*d, and the elements in the first subarray are numbered from 0 to N-1; the second subarray is a 2M uniform subarray with an element spacing of N*d, and the elements in the second subarray are numbered from 0 to 2M-1. Elements in the second subarray with numbers in the range of [1, (3M-4) / 2] are removed to obtain the low-redundancy array obtained by improving the coprime array.

2. The low-redundancy high-order direction finding method based on coprime characteristics according to claim 1, characterized in that: The received signal is as follows: X=AS+N X=[x(1),x(2),…,x(T)] A=[a(θ1),a(θ2),…,a(θ k )] S=[s(1),s(2),s(3),…,s(T)] Where X represents the received signal, x(1), x(2), …, x(T) represent the signals obtained by sampling the signals received from multiple signal sources for the 1st, 2nd, …, Tth times; A represents the direction vector matrix, θ1, θ2, …, θ k represents the incident angle of the 1st, 2nd, ..., kth signal source, a(θ1), a(θ2), ..., a(θ k ) represents the steering vector of the 1st, 2nd,…, kth signal source; S represents the signal source vector, s(1), s(2), s(3),…, s(T) represent the 1st, 2nd,…, Tth sampled signals, and N represents the array noise.

3. The low-redundancy high-order direction finding method based on coprime characteristics according to claim 2, characterized in that: Calculating a fourth-order cumulant matrix of the received signal according to the received signal includes: Where C Y represents the fourth-order cumulant matrix, E{} represents the mathematical expectation, represents the Kronecker product, and H represents the conjugate transpose of the matrix.

4. The low-redundancy high-order direction finding method based on coprime characteristics according to claim 3, characterized in that: According to the fourth-order cumulants, the covariance matrix is ​​obtained, including: Vectorizing the fourth-order cumulant matrix to obtain a first vector; Remove repeated signals from the first vector to obtain a second vector; Divide the second vector into P overlapping sub-arrays Each subarray has P virtual elements, where the sensors of the i-th subarray are located at (-i+1+n)d, where n=0,1,..,P-1; the covariance matrix of the i-th subarray is then defined as After calculating the covariance matrix of each subarray, the P×P dimensional spatial smoothing covariance matrix R z Defined as the mean of all subarray covariance matrices.

5. The low-redundancy high-order direction finding method based on coprime characteristics according to claim 4, characterized in that: The fourth-order cumulant matrix is ​​vectorized to obtain a first vector, including: Z=vec(CY)=Vu Where Z is the first vector, vec() represents vectorization processing, V represents the equivalent direction vector matrix composed of virtual elements in the fourth-order cumulant matrix, and u represents the equivalent signal vector.

6. The low-redundancy high-order direction finding method based on coprime characteristics according to claim 5, characterized in that: P×P dimensional spatial smoothing covariance matrix R z Defined as the mean of all subarray covariance matrices, including: Where, is the number of subarray covariance matrices, A is a K×K dimensional diagonal matrix, is the equivalent direction vector matrix of P×K dimensions.

7. A low-redundancy high-order direction-finding system based on coprime characteristics, characterized in that: include: A receiving module, wherein the receiving module receives signals from multiple signal sources using a low-redundancy array obtained by improving a coprime array to obtain a received signal; A fourth-order cumulant matrix module, wherein the fourth-order cumulant matrix module calculates a fourth-order cumulant matrix of the received signal according to the received signal; A covariance matrix module, wherein the covariance matrix module obtains a covariance matrix according to the fourth-order cumulant matrix; An eigenvalue module, wherein the eigenvalue module calculates the eigenvalues ​​and eigenvectors of the covariance matrix according to the covariance matrix; a partitioning module, wherein the partitioning module partitions the eigenvector into a signal subspace and a noise subspace according to the magnitude of the eigenvalue; a spectral function construction module, wherein the spectral function construction module constructs a spectral function according to a projection of the steering vector on the noise subspace; a direction determination module, wherein the direction determination module searches for a peak value of the spectral function in all possible directions to determine the direction of the signal source; The low-redundancy array obtained by improving the coprime array includes: The coprime array includes a first subarray and a second subarray arranged in parallel with each other, wherein the first subarray is a uniform subarray consisting of N elements with an element spacing of M*d, and the elements in the first subarray are numbered from 0 to N-1; the second subarray is a 2M uniform subarray with an element spacing of N*d, and the elements in the second subarray are numbered from 0 to 2M-1. Elements in the second subarray with numbers in the range of [1, (3M-4) / 2] are removed to obtain the low-redundancy array obtained by improving the coprime array.

8. A computer storage medium, characterized in that The computer storage medium stores a computer program, and when the computer program is executed by the processor, the low-redundancy high-order direction finding method based on coprime characteristics according to any one of claims 1 to 6 is implemented.

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