阅读说明：本技术 基于稀疏表示的双平行线阵二维doa估计方法及计算设备 (Sparse representation-based double parallel linear array two-dimensional DOA estimation method and computing equipment ) 是由 苏龙 李雪 谷绍湖 于 2020-12-30 设计创作，主要内容包括：本发明提供一种基于稀疏表示的双平行线阵二维DOA估计方法及计算设备,涉及雷达信号处理技术领域。本发明不需要特征值分解,采用的是空间复合角解耦合思想,先利用稀疏表示方法求解其中的一个空间复合角,以此作为前提条件,另一个空间复合角就可以解耦为一维DOA估计问题,利用矩阵运算可以求解出来；最后根据已求解的两个空间复合角对方位角和俯仰角进行直接配对求解信源的DOA的数值。(The invention provides a sparse representation-based double parallel linear array two-dimensional DOA estimation method and computing equipment, and relates to the technical field of radar signal processing. According to the method, eigenvalue decomposition is not needed, a spatial compound angle decoupling thought is adopted, one spatial compound angle is solved by using a sparse representation method, the spatial compound angle is used as a precondition, the other spatial compound angle can be decoupled into a one-dimensional DOA estimation problem, and matrix operation can be used for solving the DOA estimation problem; and finally, directly pairing the azimuth angle and the pitch angle according to the two solved space compound angles to solve the DOA value of the information source.)

1. A double parallel linear array two-dimensional DOA estimation method based on sparse representation is characterized in that the double parallel linear array comprises two mutually parallel sub-arrays, and the two-dimensional DOA estimation method comprises the following steps:

s1, receiving signals from at least one source by using dual parallel linear arrays and defining spatial composite angle alpha of the signals_k、β_kAnd the signal is incident to the array manifold matrix A of Y-axis direction;

s2 obtaining beta based on sparse representation method_kAn estimated value of (d);

s3 beta-based_kObtaining the estimated value of the array manifold matrix A by the estimated value of the array manifold matrix A and the array manifold matrix A;

s4 method based on array manifold matrix AEstimation value acquisition alpha_kAn estimated value of (d);

s5 beta-based_kAnd alpha is_kThe estimate estimates a value of the DOA of the source.

2. The sparse representation-based two-dimensional DOA estimation method of double parallel linear arrays according to claim 1, wherein the spatial compound angle alpha of the definition signal_k、β_kAnd an array manifold matrix A of signals incident in the Y-axis direction, comprising:

the incident direction of the kth signal of the source is described as (alpha)_k，β_k)，α_kAnd beta_kCalled the compound angle of space, alpha_kAnd beta_kRespectively defining the included angles of the incident direction with the positive directions of the X axis and the Y axis; defining the azimuth angle and the elevation angle of the kth signal asWherein:

according to the definition of the structure and angle of the array, the subarray Y can be obtained₁、Y₂The corresponding output signals are:

Y₁＝As+n₁ (2)

Y₂＝AΦs+n₂ (3)

wherein: a ═ a₁，a₂，…，a_K]For signals incident on the Y-axis direction of the array manifold matrix,s＝[s₁，…，s_K]^Tin the form of a vector of signals,n₁and n₂Respectively representArray Y₁And sub-array Y₂And assuming that the received noise is a mean of 0 and the variance isWhite gaussian noise.

3. The sparse representation-based two-dimensional DOA estimation method of the double parallel linear arrays according to claim 1, wherein the sparse representation method comprises the following steps:

and expanding the array flow pattern matrix A to construct an overcomplete basis matrix B taking the angle to be estimated as a parameter.

4. The sparse representation-based double parallel linear array two-dimensional DOA estimation method as claimed in claim 3, wherein the expanding the array flow pattern matrix to construct an overcomplete basis matrix taking the angle to be estimated as a parameter comprises:

let the angle set Ω ═ w₁，w₂，…，w_HContains all spatial angles beta_kAnd H is the number of elements of the angle set, so that the structure can be formed by w_hH1, 2, …, H being an over-complete basis matrix B of parameters,

B＝[a₁(w₁)，a₂(w₂)，…，a_h(w_h)，…，a_H(w_H)] (4)

wherein: a is_h(w_h) Called atom, because H is far larger than the target number K and the number M of antenna elements, and all possible space angles beta are considered_kAll in the angle set omega, the submatrix Y is processed by the formula₁The corresponding output signals are respectively converted into sparse representation problems:

Y₁＝Bq+n (5)

wherein: q ═ q₁，q₂，…，q_h，…，q_H]^TAnd when w is_h＝β_kWhen there is q_h＝s_kOtherwise q_hBy solving for the vector q, the complex spatial angle β can be obtained from the positions of its non-zero elements_kAn estimate of (d).

5. The sparse representation-based two-dimensional DOA estimation method of the double parallel linear arrays according to claim 4, wherein the solving the vector q comprises the following steps:

solving the vector q is equivalent to solving the problem, namely,

min||q||₀ s.t.Y₁＝Bq+n (6)

wherein: | q | non-conducting phosphor₀Representing the number of non-zero terms in the sequence q, the problem shown by equation (6) is non-convex, and equation (6) is translated to solve the problem

min||q||₁ s.t.Y₁＝Bq+n (7)

Equation (7) is very sensitive to noise and the problem can be further translated into minimizing the objective function

min||Y₁-Bq||₂+λ||q||₁ (8)

The former item in the target function reflects the mismatch degree, and the latter item reflects the sparse requirement; since q is a complex number, l thereof₁Norm is:

converting the second-order cone programming into a method adopting the second-order cone programming

min||q||₁ s.t.||Y₁-Bq||₂≤η (10)

Wherein: eta is a regularization parameter and is used for balancing the error of B in sparse representation of q and the sparsity of a vector q, after the regularization parameter eta is determined, the problem of the formula (10) is converted into a second-order cone programming problem, and the second-order cone programming problem can be solved by utilizing an interior point method to obtain a composite space angle beta_kAn estimate of (d).

6. The sparse representation-based two-dimensional linear array DOA estimation method as recited in claim 1, wherein the method comprisesAlpha is obtained based on estimated value of array manifold matrix A_kComprises:

subarray Y₁The autocorrelation matrix of (a) is:

R₁₁＝E[Y₁Y₁ ^H]＝ASA^H+σ²I (11)

wherein: e is the mathematical expectation operator, S is the covariance matrix of the source signal, I is the identity matrix, σ²Is the additive noise variance;

subarray Y₁And subarray Y₂The cross-correlation matrix of (a) is:

additive noise is uncorrelated and is a zero-mean random process independent of the source signal, so equation (12) is followed by three terms equal to zero, with:

R₁₂＝E[Y₁Y₂ ^H]＝AΦSA^H (13)

from an autocovariance matrix R₁₁And cross covariance matrix R₁₂Constructing a DOA matrix R as follows:

R＝R₁₂[R₁₁]^- (14)

wherein: [ R ]₁₁]^-Represents a pseudo-inverse;

if both a and S are full rank, and Φ has no identical diagonal elements, then the K non-zero eigenvalues of the DOA matrix R are equal to the K diagonal elements in Φ, and the eigenvectors corresponding to these eigenvalues are equal to the corresponding signal steering vectors, i.e.:

RA＝AΦ (15)

estimating an array flow pattern matrixAnd substituting the obtained matrix into the above formulaAs follows

And matrixTherein contains a space angleEstimate outThen the space angle is estimated Denotes alpha_kAn estimate of (d).

7. A computer-readable storage medium for storing program code for performing the method of any one of claims 1-6.

8. A computing device, the computing device comprising a processor and a memory:

the memory is used for storing program codes and transmitting the program codes to the processor;

the processor is configured to perform the method of any of claims 1-6 according to instructions in the program code.

Technical Field

The invention relates to the technical field of radar signal processing, in particular to a double parallel linear array two-dimensional DOA estimation method and calculation equipment based on sparse representation.

Background

Direction of arrival (DOA) estimation is of great importance in array signal processing, and has gained increasing research and application, particularly in the fields of radar, communication, and sonar. Compared with the one-dimensional DOA estimation, the two-dimensional DOA estimation has more precise space division and more specific target position positioning, so the two-dimensional DOA estimation has more practical significance.

Most of the existing two-dimensional DOA estimation methods are based on simplified area arrays (namely DOA matrix methods) with array element spacing equal to half wavelength, such as L-shaped arrays, double parallel line arrays, cross-shaped arrays and the like. The double parallel linear arrays are widely concerned and applied due to the advantages of simple structure, easy realization, strong method applicability and the like. The existing two-dimensional DOA estimation method based on double parallel linear arrays mainly adopts a DOA matrix method, the structural schematic diagram is shown in figure 1, and the double parallel linear arrays comprise an array element number of M and an array element interval of d_xTwo uniform sub-arrays X of_a、Y_aComposition with a subarray spacing of d_y。

Currently, the DOA matrix method is used to perform eigen decomposition, which results in a large amount of computation.

Disclosure of Invention

Technical problem to be solved

Aiming at the defects of the prior art, the invention provides a double parallel linear array two-dimensional DOA estimation method based on sparse representation, and solves the technical problem of large calculation amount of the existing DOA estimation method.

(II) technical scheme

In order to achieve the purpose, the invention is realized by the following technical scheme:

the invention provides a sparse representation-based double parallel linear array two-dimensional DOA estimation method, wherein the double parallel linear array comprises two mutually parallel sub-arrays, and the two-dimensional DOA estimation method comprises the following steps:

s1, receiving signals from at least one source by using dual parallel linear arrays and defining spatial composite angle alpha of the signals_k、β_kAnd the signal is incident to the array manifold matrix A of Y-axis direction;

s2 obtaining beta based on sparse representation method_kAn estimated value of (d);

s3 beta-based_kObtaining the estimated value of the array manifold matrix A by the estimated value of the array manifold matrix A and the array manifold matrix A;

s4, obtaining alpha based on the estimated value of the array manifold matrix A_kAn estimated value of (d);

s5 beta-based_kAnd alpha is_kThe estimate estimates a value of the DOA of the source.

Preferably, the spatial complex angle α of the definition signal_k、β_kAnd an array manifold matrix A of signals incident in the Y-axis direction, comprising:

the incident direction of the kth signal of the source is described as (alpha)_k，β_k)，α_kAnd beta_kCalled the compound angle of space, alpha_kAnd beta_kRespectively defining the included angles of the incident direction with the positive directions of the Y axis and the Y axis; defining the azimuth angle and the elevation angle of the kth signal asWherein:

according to the definition of the structure and angle of the array, the subarray Y can be obtained₁、Y₂The corresponding output signals are:

Y₁＝As+n₁ (2)

Y₂＝AΦs+n₂ (3)

wherein: a ═ a₁，a₂，…，a_K]For signals incident on the Y-axis direction of the array manifold matrix,s＝[s₁，…，s_K]^Tin the form of a vector of signals,n₁and n₂Respectively, denote sub-arrays Y₁And sub-array Y₂And assuming that the received noise is a mean of 0 and the variance isWhite gaussian noise.

Preferably, the sparse representation method includes:

and expanding the array flow pattern matrix A to construct an overcomplete basis matrix B taking the angle to be estimated as a parameter.

Preferably, the expanding the array flow pattern matrix to construct an overcomplete basis matrix taking the angle to be estimated as a parameter includes:

let the angle set Ω ═ w₁，w₂，…，w_HContains all spatial angles beta_kAnd H is the number of elements of the angle set, so that the structure can be formed by w_hH1, 2, …, H being an over-complete basis matrix B of parameters,

B＝[a₁(w₁)，a₂(w₂)，…，a_h(w_h)，…，a_H(w_H)] (4)

wherein: a is_h(w_h) Called atom, because H is far larger than the target number K and the number M of antenna elements, and all possible space angles beta are considered_kAll in the angle set omega, the submatrix Y is processed by the formula₁The corresponding output signals are respectively converted into sparse representation problems:

Y₁＝Bq+n (5)

wherein: q ═ q₁，q₂，…，q_h，…，q_H]^TAnd when w is_h＝β_kWhen there is q_h＝s_kOtherwise q_hBy solving for the vector q, the complex spatial angle β can be obtained from the positions of its non-zero elements_kAn estimate of (d).

Preferably, the solution vector q includes:

solving the vector q is equivalent to solving the problem, namely,

min||q||₀ s.t.Y₁＝Bq+n (6)

wherein: | q | non-conducting phosphor₀Representing the number of non-zero entries in the sequence qThe problem shown by the formula (6) is non-convex, and the formula (6) is converted to solve the following problems

min||q||₁ s.t. Y₁＝Bq+n (7)

Equation (7) is very sensitive to noise and the problem can be further translated into minimizing the objective function

min||Y₁-Bq||₂+λ||q||₁ (8)

The former item in the target function reflects the mismatch degree, and the latter item reflects the sparse requirement; since q is a complex number, l thereof₁Norm is:

converting the second-order cone programming into a method adopting the second-order cone programming

min||q||₁ s.t. ||Y₁-Bq||₂≤η (10)

Wherein: eta is a regularization parameter and is used for balancing the error of B in sparse representation of q and the sparsity of a vector q, after the regularization parameter eta is determined, the problem of the formula (10) is converted into a second-order cone programming problem, and the second-order cone programming problem can be solved by utilizing an interior point method to obtain a composite space angle beta_kAn estimate of (d).

Preferably, the alpha is obtained based on the estimated value of the array manifold matrix A_kComprises:

subarray Y₁The autocorrelation matrix of (a) is:

R₁₁＝E[Y₁Y₁ ^H]＝ASA^H+σ²I (11)

wherein: e is the mathematical expectation operator, S is the covariance matrix of the source signal, I is the identity matrix, σ²Is the additive noise variance;

subarray Y₁And subarray Y₂The cross-correlation matrix of (a) is:

additive noise is uncorrelated and is a zero-mean random process independent of the source signal, so equation (12) is followed by three terms equal to zero, with:

R₁₂＝E[Y₁Y₂ ^H]＝AΦSA^H (13)

from an autocovariance matrix R₁₁And cross covariance matrix R₁₂Constructing a DOA matrix R as follows:

R＝R₁₂[R₁₁]^- (14)

wherein: [ R ]₁₁]^-Represents a pseudo-inverse;

if both a and S are full rank, and Φ has no identical diagonal elements, then the K non-zero eigenvalues of the DOA matrix R are equal to the K diagonal elements in Φ, and the eigenvectors corresponding to these eigenvalues are equal to the corresponding signal steering vectors, i.e.:

RA＝AΦ (15)

estimating an array flow pattern matrixAnd substituting the obtained matrix into the above formulaAs follows

And matrixTherein contains a space angleEstimate outThen the space angle is estimatedDenotes alpha_kAn estimate of (d).

In a second aspect, the invention provides a computer readable storage medium for storing program code for performing the method of any one of claims 1 to 6.

In a third aspect, the invention provides a computing device comprising a processor and a memory:

the memory is used for storing program codes and transmitting the program codes to the processor;

the processor is configured to perform the method of any of claims 1-6 according to instructions in the program code.

(III) advantageous effects

The invention provides a double parallel linear array two-dimensional DOA estimation method based on sparse representation. Compared with the prior art, the method has the following beneficial effects:

the invention first uses dual parallel linear arrays to receive signals from at least one source and defines the spatial compound angle alpha of the signals_k、β_kAnd the signal is incident to the array manifold matrix A of Y-axis direction; sparse representation method-based beta acquisition_kAn estimated value of (d); based on beta_kObtaining the estimated value of the array manifold matrix A by the estimated value of the array manifold matrix A and the array manifold matrix A; alpha is obtained based on estimated value of array manifold matrix A_kAn estimated value of (d); based on beta_kAnd alpha is_kThe estimate estimates a value of the DOA of the source. According to the method, eigenvalue decomposition is not needed, a spatial compound angle decoupling thought is adopted, one spatial compound angle is solved by using a sparse representation method, the spatial compound angle is used as a precondition, the other spatial compound angle can be decoupled into a one-dimensional DOA estimation problem, and matrix operation can be used for solving the DOA estimation problem; and finally, directly pairing the azimuth angle and the pitch angle according to the two solved space compound angles to solve the DOA value of the information source.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a schematic structural diagram of dual parallel linear arrays of a prior DOA matrix method;

FIG. 2 is a block diagram of a sparse representation-based two-dimensional DOA estimation method for dual parallel linear arrays according to an embodiment of the present invention;

FIG. 3 is a schematic structural diagram of a bilinear parallel array according to an embodiment of the present invention;

FIG. 4 is an angle estimation diagram of the experimental results of simulation 1;

FIG. 5 is a schematic of the variation of the RMSE with SNR for each algorithm of simulation 2;

FIG. 6 is a schematic diagram of the variation of the algorithm goniometers RMSE with fast beat number for simulation 3;

FIG. 7 is a schematic diagram of the variation of the RMSE with azimuth angle for each algorithm of simulation 4;

FIG. 8 is a schematic diagram of the variation of each algorithm angle measurement RMSE with pitch angle of simulation 4;

fig. 9 is a schematic diagram of the variation of the algorithm goniometric RMSE with azimuth and pitch angles of simulation 4.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described, and it is obvious that the described embodiments are a part of the embodiments of the present invention, but not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The embodiment of the application solves the technical problem of large calculation amount of the existing DOA estimation method by providing the double parallel linear arrays two-dimensional DOA estimation method based on sparse representation, and realizes reduction of calculation amount.

In order to solve the technical problems, the general idea of the embodiment of the application is as follows:

at present, the sparse representation technology is widely researched in the DOA estimation field, and a better result is obtained. Most DOA algorithms are researched aiming at one dimension at present, and two-dimension DOA estimation is often needed more times. In order to solve the problem, a feasible method is to directly extend the existing one-dimensional DOA method to two-dimensional DOA estimation, and although angle information can also be estimated, the method needs to extend the array elements from a one-dimensional structure to a two-dimensional plane, such as an area array, a circular array and the like, when the two-dimensional DOA estimation is performed, so that the number of the array elements is greatly increased, and correspondingly, the algorithm complexity is also increased. Another possible approach is to convert the two-dimensional DOA estimation problem into two one-dimensional DOA estimates, which can make use of already mature one-dimensional DOA estimation algorithms. The embodiment of the invention is based on the second thought, adopts the bilinear parallel array, can utilize the sparse representation technology on the premise of less array elements, does not need to perform spectral peak search and characteristic value decomposition, and automatically pairs the estimation angle parameters, thereby ensuring the estimation performance of the algorithm, reducing the calculation complexity and improving the applicability of the method.

In order to better understand the technical solution, the technical solution will be described in detail with reference to the drawings and the specific embodiments.

The embodiment of the invention provides a sparse representation-based dual parallel linear array two-dimensional DOA estimation method, wherein the dual parallel linear array comprises two mutually parallel sub-arrays. As shown in fig. 2, the method includes:

s1, receiving signals from at least one source by using dual parallel linear arrays and defining spatial composite angle alpha of the signals_k、β_kAnd the signal is incident to the array manifold matrix A of Y-axis direction;

s2 obtaining beta based on sparse representation method_kAn estimated value of (d);

s3 beta-based_kObtaining the estimated value of the array manifold matrix A by the estimated value of the array manifold matrix A and the array manifold matrix A;

s4, obtaining estimated value based on array manifold matrix Aα_kAn estimated value of (d);

s5 beta-based_kAnd alpha is_kThe estimate estimates a value of the DOA of the source.

According to the embodiment of the invention, eigenvalue decomposition is not needed, a spatial compound angle decoupling thought is adopted, one spatial compound angle is solved by using a sparse representation method, the spatial compound angle is used as a precondition, the other spatial compound angle can be decoupled into a one-dimensional DOA estimation problem, and the DOA estimation problem can be solved by using matrix operation; and finally, directly pairing the azimuth angle and the pitch angle according to the two solved space compound angles to solve the DOA value of the information source.

The following describes each step in detail:

in step S1, a dual-parallel linear array is used to receive a signal from at least one source and define a spatial composite angle α of the signal_k、β_kAnd the signals are incident on the array manifold matrix A in the Y-axis direction. The specific implementation process is as follows:

the dual parallel linear arrays adopted in the embodiment of the invention are shown in fig. 3 and comprise two sub-arrays Y₁And Y₂The number of the array elements of the subarray is M, and the array element spacing of the subarray is d_Y"submatrix" Y₁And subarray Y₂At a distance d from each other_X. Assuming K incoherent narrow-band signalsIncident to the dual parallel linear arrays, the incident direction of the k-th signal can be described as (alpha)_k，β_k)，α_kAnd beta_kThe angle is defined as the angle between the incident direction and the positive direction of the X axis and the positive direction of the Y axis. Defining the azimuth angle and the elevation angle of the k signal asThen, as can be seen from the geometric relationship in fig. 3:

according to the definition of the structure and angle of the array, the sub-array Y can be obtained₁、Y₂Corresponding output signals are respectively

Y₁＝As+n₁ (2)

Y₂＝AΦs+n₂ (3)

Wherein: a ═ a₁，a₂，…，a_K]For signals incident on the Y-axis direction of the array manifold matrix,s＝[s₁，…，s_K]^Tin the form of a vector of signals,n₁and n₂Respectively, denote sub-arrays Y₁And sub-array Y₂And assuming that the received noise is a mean of 0 and the variance isWhite gaussian noise.

In step S2, β is acquired based on the sparse representation method_kAn estimate of (d). The specific implementation process is as follows:

to use a sparse representation method to correct the space angle beta_kFor estimation, the array flow pattern matrix a is usually expanded to form an overcomplete basis matrix B, and thus an overcomplete basis matrix with the angle to be estimated as a parameter needs to be constructed. Assume angle set Ω ═ w₁，w₂，…，w_HContains all spatial angles beta_kAnd has H > K, H > M. H is the number of elements of the angle set, and thus, the angle set can be constructed with w_hH1, 2, …, H, is an over-complete basis matrix B of parameters.

B＝[a₁(w₁)，a₂(w₂)，…，a_h(w_h)，…，a_H(w_H)] (4)

Wherein: a is_h(w_h) Referred to as atoms. Due to the fact thatH is far greater than the target number K and the number M of antenna elements, and all possible space angles beta are considered_kAll in the angle set Ω, equation (2) can be converted into a sparse representation problem by using equation (4):

Y₁＝Bq+n (5)

wherein: q ═ q₁，q₂，…，q_h，…，q_H]^TAnd when ω is_h＝β_kWhen there is q_h＝s_kOtherwise q_hBy solving for the vector q, the complex spatial angle β can be obtained from the positions of its non-zero elements_kAn estimate of (d).

The process of solving for vector q is as follows:

because H is far greater than the target number K and the number M of the antenna elements, q in the formula (5) is solved into an underdetermined problem, namely infinite groups of solutions exist. But it can be known from the previous analysis that the vector q is sparse, the vector q is equivalent to solving the problem that,

min||q||₀ s.t. Y₁＝Bq+n (6)

wherein: | q | non-conducting phosphor₀The number of non-zero terms in the sequence q is expressed, and the problem shown in the formula (6) is non-convex and is difficult to directly solve as known from the sparse representation basic theory. To solve this difficulty, it is converted to solve the following problems:

min||q||₁ s.t. Y₁＝Bq+n (7)

equation (7) is very sensitive to noise, and a slight amount of noise may cause a great change in the optimal solution of the problem, which may further be converted into minimizing the objective function:

min||Y₁-Bq||₂+λ||q||₁ (8)

the former term in the objective function reflects the degree of mismatch, and the latter term reflects the sparsity requirement. Since q is a complex number, l thereof₁Norm is:

since the square root term still cannot be eliminated by the square of the above equation, it directly results in that the objective function cannot be minimized by means of quadratic programming. In order to solve the problem, a second-order cone programming method is adopted, and the method is converted into the following steps:

min||q||₁ s.t. ||Y₁-Bq||₂≤η (10)

wherein: η is a regularization parameter that balances the error when B sparsely represents q and the sparsity of the vector q. After the regularization parameter eta is determined, the problem of the formula (10) is converted into a second-order cone programming problem, the second-order cone programming problem can be solved by utilizing an interior point method, and beta is solved_kAn estimate of (d).

In step S3, based on β_kAnd the array manifold matrix a obtains an estimate of the array manifold matrix a. The specific implementation process is as follows:

by the above-mentioned formula A ═ a₁，a₂，…，a_K]For signals incident on the Y-axis direction of the array manifold matrix,will beta_kAnd substituting the estimated value to obtain the estimated value of the array manifold matrix A.

In step S4, α is acquired based on the estimated value of the array manifold matrix a_kAn estimate of (d). The specific implementation process is as follows:

subarray Y₁The autocorrelation matrix of (a) is:

R₁₁＝E[Y₁Y₁ ^H]＝ASA^H+σ²I (11)

wherein: e is the mathematical expectation operator, S is the covariance matrix of the source signal, I is the identity matrix, σ²Is the additive noise variance.

Subarray Y₁And sub-array Y₂The cross-correlation matrix of (a) is:

from the previous assumption, additive noise is uncorrelated and is a zero-mean random process independent of the source signal, so the three terms behind equation (12) are equal to zero. Comprises the following steps:

R₁₂＝E[Y₁Y₂ ^H]＝AΦSA^H (13)

from an autocovariance matrix R₁₁And cross covariance matrix R₁₂Constructing a DOA matrix R of

R＝R₁₂[R₁₁]^- (14)

Wherein: [ R ]₁₁]^-The pseudo-inverse is represented.

Theorem 1 if both a and S are full rank, and Φ has no identical diagonal elements, then the K non-zero eigenvalues of the DOA matrix R are equal to the K diagonal elements in Φ, and the eigenvectors corresponding to these eigenvalues are equal to the corresponding signal steering vectors, i.e.:

RA＝AΦ (15)

it is assumed that the array flow pattern matrix can be estimated(An estimated value representing the array manifold matrix a), and substituting the estimated value into the above equation, a matrix can be obtainedThe following were used:

and matrixTherein contains a space angleEstimate outThen the space angle is estimated

In step S5, based on β_kAnd alpha is_kThe estimate estimates a value of the DOA of the source. The specific implementation process is as follows:

when the method of dimension division is used for estimating the azimuth angle and the pitch angle, the problem of pairing the azimuth angle and the pitch angle is a difficult problem. For example, when the algorithm needs to perform eigenvalue decomposition, the ordering of the eigenvectors may be different, so that the estimated azimuth angle and pitch angle cannot be directly paired. The embodiment of the invention solves two spatial compound angles alpha in sequence_kAnd beta_kThen, the azimuth angle θ and the pitch angle Φ may be reversely deduced according to equation (1):

to verify the effectiveness of the embodiments of the present invention, a comparative description is made below through simulation experiments.

And simultaneously giving out experimental results of the DOA matrix algorithm, the ESPRIT algorithm and the MEMP algorithm under the same experimental conditions.

In the experiment, the assumed subarray Y₁And subarray Y₂The number M of the array elements is 10, and the distance d between the array elements of the two sub-arrays along the Y-axis direction_YEqual to half wavelength, sub-array to sub-array spacing d_XEqual to half a wavelength. Assuming that the power of each target incident signal is equal, the estimated Root Mean Square Error (RMSE) of each algorithm is defined as

WhereinThe estimated values of the azimuth angle and the pitch angle of the jth experiment to the kth target are respectively shown, J represents the number of Monte Carlo experiments, and the value of J is set to be 500 in each subsequent simulation experiment.

Simulation 1: the following first analyzes the estimation angle situation of the proposed method (i.e., the method of the embodiment of the present invention). Suppose that two incoherent far-field narrow-band signals are incident on a bilinear parallel array, and the incident azimuth angle and the incident elevation angle of the two incident signals are respectivelyAndthe received snapshot number is set to 500 and the SNR is 15 dB. The simulation experiment result is shown in fig. 4, and it can be known from the figure that the proposed method can accurately distinguish the azimuth angle and the pitch angle of the two signals.

Simulation 2: the variation of the estimated angle RMSE of each algorithm with the signal-to-noise ratio is analyzed. In the simulation experiment, the incident azimuth angle and the pitch angle of two incident signals are set to be the same as those of the simulation experiment 1, the received fast beat number is 500, the signal-to-noise ratio of a signal received by a single array element is changed from 0dB to 20dB, and the change condition of the estimated angle RMSE of each algorithm along with the signal-to-noise ratio is shown in FIG. 5.

From the simulation results shown in fig. 5, it can be seen that the estimated angle RMSE of the proposed method has a better result when the signal-to-noise ratio is high, and the estimated angle RMSE of the proposed method varies greatly and the performance is degraded when the signal-to-noise ratio is low. The reason for this is that when the signal-to-noise ratio is low, the values of the regularization parameters deviate, resulting in degraded algorithm performance.

Simulation 3: the variation of the estimated angle RMSE of each algorithm with fast beat number is analyzed below. In the simulation experiment, the incident azimuth angle and the pitch angle of two incident signals are set to be the same as those in the simulation experiment 1, the signal-to-noise ratio SNR of the incident signals is 15dB, the received snapshot number is changed from 50 to 1000, and the change of the estimated angle RMSE of each algorithm along with the snapshot number is shown in fig. 6.

As can be seen from fig. 6, the performance of the proposed method is less affected by the number of snapshots than the comparative method, and thus the advantage is more apparent when the number of snapshots is smaller. In addition, the DOA matrix method and the MEMP algorithm can estimate the target angle with high precision when the number of snapshots is large, and the estimated deviation is large when the number of snapshots is small. The method has better robustness, which benefits from the utilization of the cross-correlation information of the two sub-array receiving signals and the application of the sparse representation technology.

And (4) simulation: the experiment analyzes the performance influence of the spatial domain angle interval of the incident signal on each algorithm. The following three cases were simulated in the experiment: (1) the pitch angle interval of two incident signals is large and constant, the change condition of each algorithm performance along with the azimuth angle interval is examined, and the setting is carried out at the moment(2) The interval of the azimuth angles of the two incident signals is large and constant, the change condition of the performance of each algorithm along with the interval of the pitch angle is examined, and the setting is carried out at the moment(3) The interval between the azimuth angle and the pitch angle of the two incident signals is simultaneously changed from small to large, and then the interval is setWherein Delta theta,Δ each vary from 2 ° to 20 °. The SNR of the incident signal is 15dB, and the received snapshot count is 500. Under the conditions, the estimated angle RMSE of each algorithm is obtained along with the interval delta theta of the azimuth angle and the interval of the pitch angleAnd the change in the azimuth and pitch angle intervals delta are shown in fig. 7, 8, and 9, respectively.

The simulation results of fig. 7 to 9 show that the performance of each algorithm is greatly influenced by the pitch angle interval and is less influenced by the azimuth angle interval. The reason is that when each algorithm measures the angle, the target pitch angle is measured first, and then the azimuth angle is calculated according to the pitch angle measurement result. Therefore, when the pitch angle interval is sufficiently large, the target pitch angle interval can be accurately estimated, so that the azimuth angle measurement performance is hardly affected by the azimuth angle interval.

Based on the same inventive concept, the embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium is used for storing program codes, and the program codes are used for executing the method claimed in any one of the claims.

Based on the same inventive concept, an embodiment of the present application further provides a computing device, where the computing device includes a processor and a memory:

the memory is used for storing program codes and transmitting the program codes to the processor;

a processor is configured to perform the method of any of the claims in accordance with instructions in the program code.

In summary, compared with the prior art, the method has the following beneficial effects:

1. according to the method, eigenvalue decomposition is not needed, the idea of decoupling space compound angles is adopted, one space compound angle is solved by using a sparse representation method, the space compound angle is used as a precondition, the other space compound angle can be decoupled into a one-dimensional DOA estimation problem, and matrix operation can be used for solving the problem; and finally, directly pairing the azimuth angle and the pitch angle according to the two solved space compound angles to solve the DOA value of the information source.

2. Compared with the existing algorithm, the method provided by the embodiment of the invention is less influenced by the snapshot number, and has good performance under the conditions of higher signal-to-noise ratio and larger angle interval.

3. The method provided by the embodiment of the invention is suitable for other arrays, such as T-shaped arrays and L-shaped arrays, and has strong applicability.

It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.

The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.