阅读说明：本技术 稀疏l型阵列的二维角度分析方法、系统、设备及介质 (Two-dimensional angle analysis method, system, equipment and medium for sparse L-shaped array ) 是由 苏龙 谷绍湖 邓桂萍 李恒 于 2021-08-31 设计创作，主要内容包括：本发明涉及一种稀疏L型阵列中基于压缩感知的二维角度分析方法、系统、设备及介质,其方法包括：首先,确定入射信息的自相关协方差矩阵并进行向量化；其次,通过虚拟阵列重建得到虚拟阵元位置集合；再者,依据虚拟阵元位置集合对向量化的自相关协方差矩阵进行重排序和去冗余,得到虚拟阵列入射信息；最后,对虚拟阵列入射信息进行二维角度分析。本发明利用二级Nested阵列构建稀疏L型阵列,确定接收数据的自相关协方差矩阵并进行排序和去冗余,得到虚拟阵列入射信息。因该虚拟阵列的长度远大于实际物理阵列的长度,所以能获得更大的阵列孔径和较高的自由度。本发明能对更多的目标信号进行估计,在DOA估计精度和分辨率上具有较大的优势。(The invention relates to a two-dimensional angle analysis method, a system, equipment and a medium based on compressed sensing in a sparse L-shaped array, wherein the method comprises the following steps: firstly, determining an autocorrelation covariance matrix of incident information and vectorizing; secondly, a virtual array element position set is obtained through virtual array reconstruction; thirdly, reordering and removing redundancy of the quantized autocorrelation covariance matrix according to the virtual array element position set to obtain virtual array incident information; and finally, carrying out two-dimensional angle analysis on the incident information of the virtual array. The method utilizes a secondary Nested array to construct a sparse L-shaped array, determines an autocorrelation covariance matrix of received data, and performs sequencing and redundancy removal to obtain incident information of a virtual array. Because the length of the virtual array is much longer than that of the actual physical array, a larger array aperture and a higher degree of freedom can be obtained. The invention can estimate more target signals and has greater advantages in DOA estimation precision and resolution.)

1. A two-dimensional angle analysis method based on compressed sensing in a sparse L-shaped array is characterized by comprising the following steps:

acquiring incident information of a sparse L-shaped array, further acquiring an autocorrelation covariance matrix of the incident information, and vectorizing the autocorrelation covariance matrix;

carrying out virtual array reconstruction on the sparse L-shaped array to obtain a virtual array element position set;

reordering and removing redundancy of the self-correlation covariance matrix subjected to warp quantization according to the virtual array element position set to obtain virtual array incident information;

performing two-dimensional angle analysis on the incident information of the virtual array by adopting an orthogonal matching pursuit algorithm based on compressed sensing to obtain an azimuth angle and a pitch angle of the incident information;

the sparse L-shaped array is constructed on the basis of a two-level Nested array.

2. The two-dimensional angle analysis method based on compressed sensing in sparse L-shaped array as claimed in claim 1, wherein said sparse L-shaped array comprises: a first Nested array disposed in the x-axis and a second Nested array disposed in the y-axis;

the first Nested array comprises: the first uniform linear array and the second uniform linear array;

the second Nested array comprises: the third uniform linear array and the fourth uniform linear array;

wherein the array element spacing of the first uniform linear array and the third uniform linear array is d₁The array elements are all N; the array element spacing of the second uniform linear array and the fourth uniform linear array is d₂The array elements are all M; and satisfy d₂＝(N+1)d₁。

3. The two-dimensional angle analysis method based on compressed sensing in the sparse L-shaped array as claimed in claim 2, wherein the obtaining of the incident information of the sparse L-shaped array, and further the obtaining and vectorizing of the autocorrelation covariance matrix of the incident information comprises:

acquiring incident information X of a first Nested array and incident information Y of a second Nested array in the sparse L-shaped array;

obtaining expressions of the incident information X and the incident information Y according to the direction matrix of the first Nested array and the direction matrix of the second Nested array;

determining an autocorrelation covariance matrix of the incident information X and the incident information Y according to the expression of the incident information X and the incident information Y:

vectorizing the autocorrelation covariance matrix of the incident information X and the incident information Y to obtain a meridionally quantized autocorrelation covariance matrix;

the expressions of the incident information X and the incident information Y are:

wherein A is_xIs the direction matrix A of the first Nested array_x＝[a_x(v₁),a_x(v₂),...,a_x(v_K)]；A_yIs a direction matrix of the second Nested array, A_y＝[a_y(u₁),a_y(u₂),...,a_y(u_K)]；s＝[s₁,s₂,...,s_K]K incident signals; n is_xAnd n_yNoise signals received for the first and second Nested arrays, n_xAnd n_yAll satisfy mean value of 0 and variance of sigma²；

The autocorrelation covariance matrix of the incident information X and the incident information Y is:

wherein the content of the first and second substances, is the average power of the kth incident signal;

the meridionally quantized autocorrelation covariance matrix is:

wherein the content of the first and second substances,which represents the product of the Kronecker,representing the product of Khatri-tao,I_n＝vec(I)。

4. the two-dimensional angle analysis method based on compressed sensing in the sparse L-shaped array as claimed in claim 3, wherein the step of performing virtual array reconstruction on the sparse L-shaped array to obtain the virtual array element position set comprises:

obtaining an optimal sparse L-shaped array by adjusting array elements of the sparse L-shaped array until a first condition is met;

performing virtual reconstruction on the optimal sparse L-shaped array to obtain a virtual array element position set;

wherein the first condition is:

the virtual array element position set comprises:

5. the two-dimensional angle analysis method based on compressed sensing in the sparse L-shaped array as claimed in claim 4, wherein the virtual array incident information is:

wherein, B_xTo comprise a pairAll row vectors are sorted and redundantly removed to obtain [ (F)²-2)/2+F]Direction matrix of x-axis of virtual array of xK-dimensional vectors, B_x＝[b_x(v₁),b_x(v₂),...,b_x(v_K)](ii) a Second matrix B_yTo comprise a pairAll row vectors are sorted and redundantly removed to obtain [ (F)²-2)/2+F]Direction matrix of the y-axis of the virtual array of xK-dimensional vectors, B_y＝[b_y(u₁),b_y(u₂),...,b_y(u_K)](ii) a And B_xAnd B_yRow i of (1) corresponds to row (-F)²/4-F/2+i)d_iA virtual array element position.

6. The two-dimensional angle analysis method based on compressed sensing in the sparse L-shaped array as claimed in claim 5, wherein the two-dimensional angle analysis of the incident information of the virtual array by using the orthogonal matching pursuit algorithm based on compressed sensing to obtain the two-dimensional angle of the incident information comprises:

a direction matrix B of the x axis of the virtual array based on a preset spatial synthesis angle set_xAnd a direction matrix B of the virtual array y-axis_yExpanding to obtain a complete redundant dictionary B_xΩAnd B_yΘ；

According to the complete redundant dictionary B_xΩAnd B_yΘAnd obtaining a compressed sensing expression of the incident information of the virtual array:

based on the compressed sensing expression of the incident information of the virtual array, forming an angle v to the space by an orthogonal matching pursuit algorithm_kAnd u_kPerforming estimation to obtain an estimated valueAnd

according to the estimated valueAndobtaining the azimuth angle phi of the incident information by a reverse-thrust formula_kAnd a pitch angle theta_k；

Wherein the set of spatial resultant angles comprises: q ═ v₁,v₂,...,v_h,v_H}、Θ＝{u₁,u₂,...,u_h,u_H}，H>>K；

The complete redundant dictionary B_xΩAnd B_yΘRespectively as follows:

B_xΩ＝[b_xΩ(v₁),b_xΩ(v₂),...,b_xΩ(v_h),b_xΩ(v_H)]，

B_yΘ＝[b_yΘ(u₁),b_yΘ(u₂),...,b_yΘ(u_h),b_yΘ(u_H)]，

the compressed sensing expression of the incident information of the virtual array is as follows:

P_Ωand P_ΘIs a vector of H-dimensional coefficients, P_ΩAnd P_ΘThe number of the medium non-zero elements is K;

the backstepping formula is as follows:

7. the two-dimensional angle analysis method based on compressed sensing in the sparse L-shaped array as claimed in claim 6, wherein the estimating the spatial angle sum by the orthogonal matching pursuit algorithm based on the compressed sensing expression of the incident information of the virtual array to obtain the estimated value comprises:

from complete redundant dictionaries B, respectively_xΩAnd B_yΘMiddle screening with Z_xΩAnd Z_yθThe column with the largest inner product;

respectively calculating residual errors r by a least square method_xΩAnd r_yΘFrom complete redundant dictionaries B, respectively_xΩAnd B_yΘMiddle screening and residual error r_xΩAnd r_yθThe most closely matching column(s) is (are),

continuously iterating until the iteration number is equal to the information source number K, and at the moment, determining the number of the iterations in the complete redundant dictionary B_xΩAnd B_yΘRespectively selected K columns in the space represents a spatial angle v_kAnd u_kIs located in the position of the non-zero element of (a).

8. A two-dimensional angle analysis system based on compressed sensing in a sparse L-shaped array is characterized by comprising the following components:

the incident information acquisition module is used for acquiring incident information of the sparse L-shaped array constructed based on the secondary Nested array, and further acquiring an autocorrelation covariance matrix of the incident information and vectorizing the incidence information;

the virtual array reconstruction module is used for performing virtual array reconstruction on the sparse L-shaped array to obtain a virtual array element position set;

the reordering and redundancy removing module is used for reordering and removing redundancy of the self-correlation covariance matrix quantized in the radial direction according to the virtual array element position set to obtain the incident information of the virtual array;

and the two-dimensional angle analysis module is used for performing two-dimensional angle analysis on the incident information of the virtual array by adopting an orthogonal matching pursuit algorithm based on compressed sensing to obtain an azimuth angle and a pitch angle of the incident information.

9. A two-dimensional angular analysis apparatus, comprising:

at least one processor;

and a memory communicatively coupled to the at least one processor;

wherein the memory stores instructions executable by the at least one processor to cause the at least one processor to perform the two-dimensional compressed sensing-based angle analysis method steps of any one of claims 1-7 in a sparse L-shaped array.

10. A computer-readable storage medium having stored thereon computer-executable instructions that, when executed by a processor, perform the method steps of a compressed sensing-based two-dimensional angle analysis in a sparse L-shaped array as claimed in any one of claims 1 to 7.

Technical Field

The invention relates to the technical field of direction of arrival analysis, in particular to a two-dimensional angle analysis method, a two-dimensional angle analysis system, two-dimensional angle analysis equipment and a two-dimensional angle analysis medium based on compressed sensing in a sparse L-shaped array.

Background

Direction Of Arrival (DOA) is commonly used in array signal processing, and is one Of the key technologies in radar, sonar, and radio navigation positioning. The traditional one-dimensional DOA analysis research is early, simple in structure and low in algorithm complexity, and obtains symbolic research results, such as MUSIC algorithm, ESPRIT algorithm, subspace fitting algorithm, high-order cumulative quantity algorithm and the like.

However, in practical applications, two-dimensional DOA analysis of objects in the spatial domain is more desirable. For two-dimensional DOA analysis array structures, special designs are generally required, such as double parallel arrays, L-shaped arrays, circular arrays, planar arrays and the like, and array elements of the array structures are generally uniformly and linearly distributed. N even linear arrays can detect N-1 target signals at most, so the degree of freedom is low, the array element spacing is small, the array elements are mutually coupled, the direction matrix of the array is influenced, and the actual DOA analysis result is not satisfactory.

Disclosure of Invention

Technical problem to be solved

In view of the above disadvantages and shortcomings of the prior art, the present invention provides a two-dimensional angle analysis method, system, device and medium based on compressed sensing in a sparse L-shaped array, which solves the technical problems of limited number of simultaneous analysis signal sources, and low estimation accuracy and resolution in the existing DOA.

(II) technical scheme

In order to achieve the purpose, the invention adopts the main technical scheme that:

in a first aspect, an embodiment of the present invention provides a two-dimensional angle analysis method based on compressed sensing in a sparse L-shaped array, including:

acquiring incident information of a sparse L-shaped array, further acquiring an autocorrelation covariance matrix of the incident information, and vectorizing the autocorrelation covariance matrix;

carrying out virtual array reconstruction on the sparse L-shaped array to obtain a virtual array element position set;

reordering and removing redundancy of the self-correlation covariance matrix subjected to warp quantization according to the virtual array element position set to obtain virtual array incident information;

performing two-dimensional angle analysis on the incident information of the virtual array by adopting an orthogonal matching pursuit algorithm based on compressed sensing to obtain an azimuth angle and a pitch angle of the incident information;

the sparse L-shaped array is constructed on the basis of a two-level Nested array.

Optionally, the sparse L-array comprises: a first Nested array disposed in the x-axis and a second Nested array disposed in the y-axis;

the first Nested array comprises: the first uniform linear array and the second uniform linear array;

the second Nested array comprises: the third uniform linear array and the fourth uniform linear array;

wherein the array element spacing of the first uniform linear array and the third uniform linear array is d₁The array elements are all N; the array element spacing of the second uniform linear array and the fourth uniform linear array is d₂The array elements are all M; and satisfy d₂＝(N+1)d₁。

Optionally, the obtaining incident information of the sparse L-shaped array, and further obtaining and vectorizing an autocorrelation covariance matrix of the incident information includes:

acquiring incident information X of a first Nested array and incident information Y of a second Nested array in the sparse L-shaped array;

obtaining expressions of the incident information X and the incident information Y according to the direction matrix of the first Nested array and the direction matrix of the second Nested array;

determining an autocorrelation covariance matrix of the incident information X and the incident information Y according to the expression of the incident information X and the incident information Y:

vectorizing the autocorrelation covariance matrix of the incident information X and the incident information Y to obtain a meridionally quantized autocorrelation covariance matrix;

the expressions of the incident information X and the incident information Y are:

wherein A is_xIs the direction matrix A of the first Nested array_x＝[a_x(v₁),a_x(v₂),...,a_x(v_K)]；A_yIs a direction matrix of the second Nested array, A_y＝[a_y(u₁),a_y(u₂),...,a_y(u_K)]；s＝[s₁,s₂,...,s_K]K incident signals; n is_xAnd n_yNoise signals received for the first and second Nested arrays, n_xAnd n_yAll satisfy mean value of 0 and variance of sigma²；

The autocorrelation covariance matrix of the incident information X and the incident information Y is:

wherein the content of the first and second substances, is the average power of the kth incident signal;

the meridionally quantized autocorrelation covariance matrix is:

wherein the content of the first and second substances,which represents the product of the Kronecker,representing the product of Khatri-tao,

optionally, the performing virtual array reconstruction on the sparse L-shaped array to obtain a virtual array element position set includes:

obtaining an optimal sparse L-shaped array by adjusting array elements of the sparse L-shaped array until a first condition is met;

performing virtual reconstruction on the optimal sparse L-shaped array to obtain a virtual array element position set;

wherein the first condition is:

the virtual array element position set comprises:

optionally, the virtual array incident information is:

wherein, B_xTo comprise a pairAll row vectors are sorted and redundantly removed to obtain [ (F)²-2)/2+F]Direction matrix of x-axis of virtual array of xK-dimensional vectors, B_x＝[b_x(v₁),b_x(v₂),...,b_x(v_K)](ii) a Second matrix B_yTo comprise a pairAll row vectors are sorted and redundantly removed to obtain [ (F)²-2)/2+F]Virtual array of xK-dimensional vectorsDirection matrix of y-axis, B_y＝[b_y(u₁),b_y(u₂),...,b_y(u_K)](ii) a And B_xAnd B_yRow i of (1) corresponds to row (-F)²/4-F/2+i)d_iA virtual array element position.

Optionally, performing two-dimensional angle analysis on the virtual array incidence information by using an orthogonal matching pursuit algorithm based on compressed sensing, and obtaining a two-dimensional angle of the incidence information includes:

a direction matrix B of the x axis of the virtual array based on a preset spatial synthesis angle set_xAnd a direction matrix B of the virtual array y-axis_yExpanding to obtain a complete redundant dictionary B_xΩAnd B_yΘ；

According to the complete redundant dictionary B_xΩAnd B_yΘObtaining a compressed sensing expression of the incident information of the virtual array:

based on the compressed sensing expression of the incident information of the virtual array, forming an angle v to the space by an orthogonal matching pursuit algorithm_kAnd u_kPerforming estimation to obtain an estimated valueAnd

according to the estimated valueAndobtaining the azimuth angle phi of the incident information by a reverse-thrust formula_kAnd a pitch angle theta_k；

Wherein the set of spatial resultant angles comprises: q ═ v₁,v₂,...,v_h,v_H}、 Θ＝{u₁,u₂,...,u_h,u_H}，H>>K；

The complete redundancyDictionary B_xΩAnd B_yΘRespectively as follows:

B_xΩ＝[b_xΩ(v₁),b_xΩ(v₂),...,b_xΩ(v_h),b_xΩ(v_H)]，

B_yΘ＝[b_yΘ(u₁),b_yΘ(u₂),...,b_yΘ(u_h),b_yΘ(u_H)]，

the compressed sensing expression of the incident information of the virtual array is as follows:

P_Ωand P_ΘIs a vector of H-dimensional coefficients, P_ΩAnd P_ΘThe number of the medium non-zero elements is K;

the backstepping formula is as follows:

optionally, estimating the spatial angle sum by an orthogonal matching pursuit algorithm based on the compressed sensing expression of the virtual array incident information, and obtaining an estimated value includes:

from complete redundant dictionaries B, respectively_xΩAnd B_yΘMiddle screening with Z_xΩAnd Z_yθThe column with the largest inner product;

respectively calculating residual errors r by a least square method_xΩAnd r_yΘFrom complete redundant dictionaries B, respectively_xΩAnd B_yΘMiddle screening and residual error r_xΩAnd r_yθThe most closely matching column(s) is (are),

continuously iterating until the iteration number is equal to the source number K of the incident information, and at the moment, determining the number of the source numbers of the incident information in a complete redundant dictionary B_xΩAnd B_yΘRespectively selected K columns in the space represents a spatial angle v_kAnd u_kIs located in the position of the non-zero element of (a).

In a second aspect, an embodiment of the present invention provides a two-dimensional angle analysis system based on compressed sensing in a sparse L-shaped array, including:

the incident information acquisition module is used for acquiring incident information of the sparse L-shaped array constructed based on the secondary Nested array, and further acquiring an autocorrelation covariance matrix of the incident information and vectorizing the incidence information;

the virtual array reconstruction module is used for performing virtual array reconstruction on the sparse L-shaped array to obtain a virtual array element position set;

the reordering and redundancy removing module is used for reordering and removing redundancy of the self-correlation covariance matrix quantized in the radial direction according to the virtual array element position set to obtain the incident information of the virtual array;

and the two-dimensional angle analysis module is used for performing two-dimensional angle analysis on the incident information of the virtual array by adopting an orthogonal matching pursuit algorithm based on compressed sensing to obtain an azimuth angle and a depression elevation angle of the incident information.

In a third aspect, an embodiment of the present invention provides a two-dimensional angle analysis device, including:

at least one processor;

and a memory communicatively coupled to the at least one processor;

wherein said memory stores instructions executable by said at least one processor to enable said at least one processor to perform the steps of a compressed sensing based two-dimensional angular analysis method in a sparse L-shaped array as described above.

Fourth invention, an embodiment of the present invention provides a computer-readable storage medium, on which computer-executable instructions are stored, and when executed by a processor, the steps of the two-dimensional angle analysis method based on compressed sensing in a sparse L-type array as described above are implemented.

(III) advantageous effects

The invention constructs a sparse L-shaped array by utilizing a secondary Nested array, then calculates an autocorrelation covariance matrix of received data, and performs sequencing and redundancy removal to obtain incident information of a virtual array. Because the length of the virtual array is far longer than that of the actual physical array, a larger array aperture and a higher degree of freedom can be obtained compared with a uniform linear array with the same physical array elements. The method can accurately estimate the azimuth angle and the pitch angle of the incident signal, and simultaneously the number of the estimated information sources is improved compared with the number of the common uniform linear arrays of the same physical array element, thereby having more advantages in precision and resolution compared with the existing DOA estimation scheme.

Drawings

FIG. 1 is a schematic flow chart of a compressed sensing-based two-dimensional angle analysis method in a sparse L-shaped array according to the present invention;

FIG. 2 is a schematic diagram of a sparse L-shaped array in a two-dimensional angle analysis method based on compressive sensing in the sparse L-shaped array according to the present invention;

FIG. 3 is a schematic flowchart of step S1 of the compressed sensing-based two-dimensional angle analysis method for sparse L-shaped arrays according to the present invention;

FIG. 4 is a schematic diagram of a virtual array element position of a compressed sensing-based two-dimensional angle analysis method in a sparse L-shaped array according to the present invention;

FIG. 5 is a schematic flowchart of step S4 of the compressed sensing-based two-dimensional angle analysis method for sparse L-shaped arrays according to the present invention;

FIG. 6 is a schematic flowchart of step S43 of the two-dimensional angle analysis method based on compressive sensing in the sparse L-shaped array according to the present invention;

FIG. 7 is a schematic diagram of a first simulation result of a compressed sensing-based two-dimensional angle analysis method in a sparse L-shaped array according to the present invention;

FIG. 8 is a diagram illustrating a second simulation result of a compressed sensing-based two-dimensional angle analysis method in a sparse L-shaped array according to the present invention;

FIG. 9 is a schematic diagram of a third simulation result of a compressed sensing-based two-dimensional angle analysis method in a sparse L-shaped array according to the present invention;

FIG. 10 is a diagram illustrating a fourth simulation result of a compressed sensing-based two-dimensional angle analysis method in a sparse L-shaped array according to the present invention;

FIG. 11 is a diagram illustrating a fifth simulation result of a compressed sensing-based two-dimensional angle analysis method in a sparse L-shaped array according to the present invention;

FIG. 12 is a diagram illustrating a sixth simulation result of a compressed sensing-based two-dimensional angle analysis method in a sparse L-shaped array according to the present invention;

fig. 13 is a schematic composition diagram of a two-dimensional angle analysis system based on compressed sensing in a sparse L-shaped array according to the present invention.

[ description of reference ]

100: a two-dimensional angle analysis system;

101: an incident information acquisition module;

102: a virtual array reconstruction module;

103: a reordering and de-redundancy module;

104: and a two-dimensional angle analysis module.

Detailed Description

For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.

As shown in fig. 1, a two-dimensional angle analysis method based on compressive sensing in a sparse L-shaped array according to an embodiment of the present invention includes: firstly, acquiring incident information of a sparse L-shaped array, further acquiring an autocorrelation covariance matrix of the incident information, and vectorizing, wherein the sparse L-shaped array is constructed on the basis of a two-stage Nested array; secondly, carrying out virtual array reconstruction on the sparse L-shaped array to obtain a virtual array element position set; thirdly, reordering and removing redundancy of the self-correlation covariance matrix quantized in the radial direction according to the position set of the virtual array element to obtain virtual array incident information (single snapshot data received by the virtual array); and finally, performing two-dimensional angle analysis on the incident information of the virtual array by adopting an orthogonal matching pursuit algorithm based on compressed sensing to obtain an azimuth angle and a pitch angle of the incident information.

The invention constructs a sparse L-shaped array by utilizing a secondary Nested array, then calculates an autocorrelation covariance matrix of received data, and performs sequencing and redundancy removal to obtain incident information of a virtual array. Because the length of the virtual array is far longer than that of the actual physical array, a larger array aperture and a higher degree of freedom can be obtained compared with a uniform linear array with the same physical array elements. The method can accurately estimate the azimuth angle and the pitch angle of the incident signal, and simultaneously the number of the estimated information sources is improved compared with the number of the common uniform linear arrays of the same physical array element, thereby having more advantages in precision and resolution compared with the existing DOA estimation scheme.

For a better understanding of the above-described technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

Specifically, the invention provides a two-dimensional angle analysis method based on compressed sensing in a sparse L-shaped array, which comprises the following steps:

and S1, acquiring incident information of the sparse L-shaped array, further acquiring an autocorrelation covariance matrix of the incident information, and vectorizing the autocorrelation covariance matrix.

As shown in fig. 2, the sparse L-type array includes: a first Nested array disposed in the x-axis and a second Nested array disposed in the y-axis; the first Nested array comprises: the first uniform linear array and the second uniform linear array; the second Nested array comprises: the third uniform linear array and the fourth uniform linear array.

Wherein, the array element spacing of the first uniform linear array and the third uniform linear array is d₁The array elements are all N; the array element spacing of the second uniform linear array and the fourth uniform linear array is d₂The array elements are all M; and satisfy d₂＝(N+1)d₁. And taking the origin of coordinates as a reference point, and the array element position coordinate set of the Nested array is as follows: l ═ nd₁|0≤n≤N-1}∪{Nd₁+m(N+1)d₁|0≤m≤M-1}。

As shown in fig. 3, step S1 specifically includes:

s11, acquiring incident information X of a first Nested array and incident information Y of a second Nested array in the sparse L-shaped array;

s12, obtaining expressions of incident information X and incident information Y according to the direction matrix of the first Nested array and the direction matrix of the second Nested array;

s13, determining an autocorrelation covariance matrix of the incident information X and the incident information Y according to the expressions of the incident information X and the incident information Y:

s14, vectorizing the autocorrelation covariance matrix of the incident information X and the incident information Y to obtain a meridionally quantized autocorrelation covariance matrix;

if K incoherent narrow-band far-field signals existIncident to the array, the incident direction of the kth signal can be described as (φ)_k,θ_k)，φ_k,θ_kRespectively the azimuth and elevation angles of the incident signal. Defining a spatial angle (v)_k,u_k)， And the wavelength of the incident signal is lambda.

The expressions of the incident information X and the incident information Y are:

A_xis a directional matrix of a first Nested array, A_x＝[a_x(v₁),a_x(v₂),...,a_x(v_K)]The concrete expression form is as follows:

A_yis a directional matrix of a second Nested array, A_y＝[a_y(u₁),a_y(u₂),...,a_y(u_K)]The concrete expression form is as follows:

wherein s ═ s₁,s₂,...,s_K]K incident signals; n is_xAnd n_yNoise signals received for the first and second Nested arrays, n_xAnd n_yAll satisfy mean value of 0 and variance of sigma²。

Based on the sparse L-shaped array, calculating an autocorrelation covariance matrix of the incident information X and the incident information Y as follows:

wherein the content of the first and second substances, is the average power of the kth incident signal.

The autocorrelation covariance matrix for the warp quantization is:

wherein the content of the first and second substances,which represents the product of the Kronecker,representing the product of Khatri-tao,

the matrix is known due to the characteristics of the Nested matrixAndthe virtual array can be regarded as a virtual array obtained after virtualization, and the array elements of the virtual array are out of order and have redundancy. If it is not, the matrixAndwhen p is taken as the incident signal vector of a single fast beat, thenAndis the data received by the virtual array, the angle of the incoming and outgoing signals can be estimated using a correlation angle estimation algorithm.

And S2, carrying out virtual array reconstruction on the sparse L-shaped array to obtain a virtual array element position set.

Further, step S2 includes:

s21, obtaining an optimal sparse L-shaped array by adjusting array elements of the sparse L-shaped array until a first condition is met;

and S22, performing virtual reconstruction on the optimal sparse L-shaped array to obtain a virtual array element position set.

In the above steps, for the secondary Nested array whose array element number is N + M, when N and M of the optimal secondary Nested array satisfy the first condition, the array element number (Degree of spatial Freedom) of the virtual array can be maximized.

Wherein the first condition is:

the position set of the virtual array elements is as follows:

and S3, reordering and removing redundancy of the vector quantized autocorrelation covariance matrix according to the virtual array element position set to obtain virtual array incident information.

The virtual array incident information is:

wherein, B_xTo comprise a pairAll row vectors are sorted and redundantly removed to obtain [ (F)²-2)/2+F]Direction matrix of x-axis of virtual array of xK-dimensional vectors, B_x＝[b_x(v₁),b_x(v₂),...,b_x(v_K)](ii) a Second matrix B_yTo comprise a pairAll row vectors are sorted and redundantly removed to obtain [ (F)²-2)/2+F]Direction matrix of the y-axis of the virtual array of xK-dimensional vectors, B_y＝[b_y(u₁),b_y(u₂),...,b_y(u_K)](ii) a And B_xAnd B_yRow i of (1) corresponds to row (-F)²/4-F/2+i)d_iA virtual array element position.

Further, B_xThe specific expression form of (A) is as follows:

further, B_yThe specific expression form of (A) is as follows:

in a specific embodiment, as shown in fig. 4, under the condition that N is 4 and M is 4, F is 8 according to the first condition, and based on the sparse L-type array, the array element position coordinate set of the secondary Nested array is known as: {0,1,2,3,4,9,14,19}, so the optimal virtual array element position set obtained after 8-array element two-stage Nested virtualization is { -19, -18, … …, -1, 0,1, … …, -18, -19 }.

And S4, performing two-dimensional angle analysis on the incident information of the virtual array by adopting an orthogonal matching pursuit algorithm based on compressed sensing to obtain an azimuth angle and a pitch angle of the incident information.

It should be noted that p in the virtual array incident information is an incident signal vector of a single snapshot and the rank of p is 1, so that the uncorrelated condition is no longer satisfied, and therefore the angle estimation algorithm using the covariance matrix eigenvalue decomposition fails. Analysis shows that the number of incident signals needing to be estimated is limited, so that angles needing to be estimated are sparse relative to the whole spatial domain range, and compressed sensing is a set of theory about sparse signal acquisition and recovery, so that the solution of an angle estimation problem can be converted into the solution of a compressed sensing problem. Therefore, the following method of compressed sensing is used to estimate the incident signal.

As shown in fig. 5, step S4 specifically includes:

s41, based on the preset space synthetic angle set, the direction matrix B of the virtual array x axis_xAnd a direction matrix B of the virtual array y-axis_yExpanding to obtain a complete redundant dictionary B_xΩAnd B_yΘ。

S42, according to the complete redundant dictionary B_xΩAnd B_yΘAnd obtaining a compressed sensing expression of the incident information of the virtual array:

s43, based on the compressed sensing expression of the incident information of the virtual array, forming an angle v to the space through an orthogonal matching pursuit algorithm_kAnd u_kPerforming estimation to obtain an estimated valueAnd

s44, estimating value according toAndobtaining the azimuth angle phi of the incident information by a reverse-thrust formula_kAnd a pitch angle theta_k。

In the above step, the spatially combining angle set includes: q ═ v₁,v₂,...,v_h,v_HContains all possible incident resultant angles v_k；Θ＝{u₁,u₂,...,u_h,u_H}，H>>K also contains all possible resultant angles of incidence u_k. Therefore, a complete redundant dictionary B can be constructed according to omega and theta_xΩAnd B_yΘComplete redundant dictionary B_xΩAnd B_yΘRespectively as follows:

B_xΩ＝[b_xΩ(v₁),b_xΩ(v₂),...,b_xΩ(v_h),b_xΩ(v_H)]，

B_yΘ＝[b_yΘ(u₁),b_yΘ(u₂),...,b_yΘ(u_h),b_yΘ(u_H)]，

wherein, b_xΩ(v_h) And b_yΘ(u_h) Is an atom.

Since H is far greater than the target number K, and the spatial synthesis angle sets Ω and Θ include all possible spatial synthesis angles, the complete redundant dictionary B can be utilized_xΩAnd B_yΘConverting the virtual array incident information into a compressed sensing problem, wherein if the compressed sensing expression of the virtual array incident information is as follows:

wherein, P_ΩAnd P_ΘIs a vector of H-dimensional coefficients, P_ΩAnd P_ΘThe number of the medium non-zero elements is K.

According to the compressed sensing theory, the compressed sensing expression of the incident information of the virtual array is an underdetermined equation, namely infinite groups of solutions exist. But from the previous analysis one can know P_ΩAnd P_ΘIs sparse, then P_ΩAnd P_ΘIs equivalent to solving the following problem:

wherein | p | purple₀Represents the number of non-zero terms in the sequence p, and the expression is non-convex as known from the theory of compressed sensing₀The solution of norm is an NP problem, on one hand, direct solution is difficult to carry out, on the other hand, the anti-noise capability is poor, and the requirement of signal recovery is difficult to meet, so that l is generally adopted₁Norm instead of l₀Norm, such that the non-convex problem is transformed into a convex optimization problem. The following formula:

the solving algorithm of the signals of the above formula usually adopts a greedy algorithm, the invention utilizes a common greedy avaricious algorithm to solve, namely, an Orthogonal Matching Pursuit (OMP) algorithm is adopted to solve the spatial synthetic angle v_kAnd u_k。

As shown in fig. 6, the spatial resultant angle v is solved_kAnd u_kThe basic idea is as follows:

s431, respectively selecting complete redundant dictionary B_xΩAnd B_yΘMiddle screening with Z_xΩAnd Z_yθThe column with the largest inner product.

S432, respectively calculating residual errors r by a least square method_xΩAnd r_yΘFrom the complete redundant dictionary B, respectively_xΩAnd B_yΘMiddle screening and residual error r_xΩAnd r_yθThe most matched column.

S433, continuously iterating until the iteration number is equal to the source number K of the incident information, and stopping the iteration process at the moment when a complete redundant dictionary B_xΩAnd B_yΘRespectively selected K columns in the space represents a spatial angle v_kAnd u_kIs located in the position of the non-zero element of (a).

It should be noted that the desired angle v is included in the space_kAnd u_kThe azimuth angle and the pitch angle are not in the traditional sense, so the azimuth angle and the pitch angle need to be reversely deduced by means of a reverse-deducing formula. The formula of the reverse thrust is as follows:

in a specific embodiment, a microphone array sound source positioning system is widely used in the fields of audio/video conference systems, vehicle-mounted systems and smart speakers. The microphone array enhances the voice in the sound source direction, which requires that the position of the signal relative to the microphone array is known, and the sparse L-shaped array provides support for the two-dimensional angle estimation method based on compressed sensing. In many array structures, the sparse L-shaped array has a larger array aperture and a higher degree of freedom than the conventional L-shaped array, and thus has advantages in estimation accuracy and resolution. Compressed sensing is applied to sound source localization due to the spatial sparsity of sound sources. Aiming at the problem of microphone sound source positioning, a plurality of microphones can be adopted to form a sparse L-shaped array shown in figure 2, the sound source positioning problem is converted into a sparse signal joint reconstruction problem, then autocorrelation covariance matrixes of data received by a first Nested array and a second Nested array are calculated, then sequencing and redundancy removal are carried out, single snapshot data received by a virtual array are obtained, the length of the virtual array is far greater than that of an actual physical array, therefore, compared with a uniform linear array of the same physical array element, the array can obtain larger array aperture and higher degree of freedom, and finally, an Orthogonal Matching Pursuit (OMP) algorithm is adopted to estimate the sound source position.

In order to verify the feasibility, the invention adopts a computer simulation mode to carry out detailed analysis and description. For comparison, experimental results of an SS-MUSIC method, an augmented matrix beam method, a uniform L-array sparse representation method, a JVD method and a CCM method are given under the same computer simulation environment. The array model adopted by the SS-MUSIC method in simulation is the same as that shown in figure 2, and other methods adopt L arrays consisting of uniform linear arrays, and each sub-array comprises 8 array elements.

In the simulation experiment, the number of array elements N of the first-stage uniform linear array is set to be 4, the number of array elements M of the second-stage uniform linear array is set to be 4, and the number of array elements d of the first-stage uniform linear array is set to be 4₁Equal to half wavelength, second level uniform linear array element spacing distance d₂＝(N+1)d₁＝5d₁. Assuming that the power of the incident signal is all equal, the estimated Root Mean Square Error (RMSE) of the algorithm is defined as follows

Wherein the content of the first and second substances,respectively representing the estimated values of the azimuth angle and the pitch angle of the jth experiment to the kth source target, wherein j represents the number of Monte Carlo experiments, and the value of j is set as 100 in the subsequent simulation.

As shown in fig. 7, the estimated angle condition of the proposed algorithm is first simulated and analyzed. Suppose there are three incoherent far-field narrow-band signals incidentOn the sparse L-shaped array shown in FIG. 2, and assuming three incident signals with azimuth and pitch [ φ [ ]₁，θ₁]＝[10°，15°]、[φ₂，θ₂]＝[45°，80°]And [ phi ]₃，θ₃]＝[70°，60°]The snapshot number is set to 500, and the SNR is 10 dB. Experiments show that the method can accurately distinguish azimuth angles and pitch angles of three different signals, and the estimated angle values of the three signals are respectively [10.02 degrees ] and 14.94 degrees °],[45.05°,80.52°]And [69.83 °,59.92 °]The estimated value and the true value almost coincide.

As shown in fig. 8, the variation of the estimated angle RMSE of each algorithm with the signal-to-noise ratio is analyzed. In the simulation experiment, the azimuth angles and the pitch angles of three incident signals are set to be the same as those of the first simulation experiment shown in fig. 7, the snapshot number is still 500, the signal-to-noise ratio of the signal received by a single array element is changed from-12 dB to 12dB, and the change condition of the estimated angle RMSE of each algorithm along with the signal-to-noise ratio is provided with reference to fig. 8. From the simulation results of fig. 8, it can be known that the estimation performance of the proposed algorithm increases with the increase of the signal-to-noise ratio, and particularly when the signal-to-noise ratio is low, the estimation result of the proposed method has a significant advantage compared with the existing method. The reason is researched, on one hand, the aperture of the array is expanded by the method by using two Nested arrays, and the influence of noise is reduced by using covariance; and on the other hand, the OMP algorithm calculates the residual error by using a least square method, finds the most matched column, and iterates repeatedly until the angle estimation of the information source is obtained, so that the influence of noise on data is greatly reduced.

As shown in fig. 9, the variation of the estimated angle of each algorithm with the number of fast beats was analyzed. In this simulation experiment, the incidence azimuth angle and the pitch angle of the three incident signals are set to be the same as those in the first simulation experiment shown in fig. 7, and the SNR of the incident signals is set to be 5dB, so that the received snapshot number is changed from 20 to 1000, thereby providing the relationship between the estimated angle of each algorithm and the change of the snapshot number. As can be seen from fig. 9, the larger the snapshot number is, the smaller the estimated angle RMSE of the proposed method is. When the number of snapshots is large, the performance of the algorithm is slightly influenced by the number of the snapshots, and particularly when the number of the snapshots is small, the method has obvious advantages. The reason for this is that an overcomplete redundant dictionary is constructed, containing all possible angles of incidence, the more complete the redundant dictionary, the better the estimated angle RMSE. In addition, the compressed sensing carries out random sampling on the signals by using the sampling frequency far lower than the Nyquist sampling rate, and then the signals are reconstructed by using the nonlinear algorithm, so that the burden of the system on data storage and processing is greatly reduced, and the estimation performance of the algorithm provided by the invention under the condition of low snapshot number is better than that of a comparison algorithm.

As shown in fig. 10, the present simulation experiment analyzed the effect of the spatial angular separation of the incident signal on the performance of each algorithm. In the experiment, the interval of the azimuth angle and the interval of the pitch angle of two incident signals are changed from small to large simultaneously, so that the change condition of the performance of each method along with the interval of the azimuth angle and the pitch angle is examined, and [ phi ] is set at the moment₁，θ₁]＝[35°，75°]，[φ₂，θ₂]＝[φ₁+Δ，θ₁-Δ]. Where Δ varies from 2 ° to 18 °. This set the SNR of the incident signal to 5dB, and the received snapshot count to 500. Under the above conditions, the variation of the estimated angle RMSE with the angle interval Δ of each method is obtained with reference to fig. 10. As can be seen from the simulation result of fig. 10, the estimated angle RMSE of each method decreases with the increase of the angle interval, which indicates that each method has better performance and more accurate estimation result when the angle interval is larger. The method provided by the invention has higher angular precision resolution ratio for the information source with smaller angular interval, but when the angular interval is larger, the simulation result is more general. The reason for this may be that a parameter is determined in the OMP algorithm and will not be changed later, and if it is found that some determined parameters are not good choices as the iteration proceeds, the OMP algorithm does not discard the previous selected parameters, resulting in a deviation of the result.

As shown in fig. 11, the present simulation analyzes multiple incident signals. It is assumed that 7 incoherent far-field narrow-band signals are incident on the array of fig. 1, the signal-to-noise ratio SNR of the incident signals is set to 10dB, the snapshot number is 500, and the azimuth angle of the 7 incident signals is 5 °: 12 degrees: 77 DEG, the pitch angle is 10 DEG: 10 degrees: as can be seen from fig. 7, the proposed method can accurately distinguish the azimuth angle and the elevation angle of 7 different signals, whereas the conventional method cannot accurately distinguish each incident signal. The reason is that the proposed algorithm breaks through the constraint of the physical aperture, generates continuous virtual array elements, obviously increases the virtual aperture, improves the degree of freedom of the array, and accordingly increases the number of the information source estimation.

As shown in fig. 12, to further illustrate the relationship between the performance of the proposed algorithm and the number of the sources, the simulation experiment sets the number of the sources received by the array of fig. 1 to be changed from 1 to 7, the SNR of the incident signal is 10dB, the fast beat number is 500, and the incident angle of the 1 st source is [ phi ],₁，θ₁]＝[5°，10°]the 2 nd source has an incident angle of [ phi ]₂，θ₂]＝[17°，20°]The 3 rd source has an incident angle of [ phi ]₃，θ₃]＝[29°，30°]And the incident angles of the rear information sources are analogized in turn. As can be seen from fig. 7, the performance of the proposed method increases as the number of sources decreases, so it is necessary to control the number of sources well in order to estimate the sources with high accuracy. In addition, it is also noted that the virtual array elements are not completely equivalent to the physical array elements, and when the virtual array elements are used for estimating the source angles, a certain degree of freedom is lost in the number of the sources.

On the other hand, as shown in fig. 13, the present invention further provides a two-dimensional angle analysis system 100 based on compressed sensing in a sparse L-shaped array, including:

the incident information acquisition module 101 is used for acquiring incident information of a sparse L-shaped array constructed based on a secondary Nested array, further acquiring an autocorrelation covariance matrix of the incident information and performing vectorization;

the virtual array reconstruction module 102 is configured to perform virtual array reconstruction on the sparse L-type array to obtain a virtual array element position set;

the reordering and redundancy removing module 103 is used for reordering and removing redundancy of the meridional quantized autocorrelation covariance matrix according to the virtual array element position set to obtain the incident information of the virtual array;

and the two-dimensional angle analysis module 104 is configured to perform two-dimensional angle analysis on the virtual array incident information by using an orthogonal matching pursuit algorithm based on compressed sensing to obtain an azimuth angle and a pitch angle of the incident information.

Since the system/apparatus described in the above embodiments of the present invention is a system/apparatus used for implementing the method of the above embodiments of the present invention, a person skilled in the art can understand the specific structure and modification of the system/apparatus based on the method described in the above embodiments of the present invention, and thus the detailed description is omitted here. All systems/devices adopted by the methods of the above embodiments of the present invention are within the scope of the present invention.

In addition, the present invention also provides a two-dimensional angle analyzing apparatus, comprising: at least one processor; and a memory communicatively coupled to the at least one processor; wherein the memory stores instructions executable by the at least one processor to cause the at least one processor to perform the method steps of a compressed sensing based two-dimensional angle analysis in a sparse L-shaped array as described above.

The invention also provides a computer-readable storage medium, on which computer-executable instructions are stored, and when executed by a processor, the steps of the two-dimensional angle analysis method based on compressed sensing in the sparse L-shaped array are realized.

In summary, the invention discloses a two-dimensional angle analysis method, a two-dimensional angle analysis system, two-dimensional angle analysis equipment and a two-dimensional angle analysis medium based on compressed sensing in a sparse L-shaped array. The method obtains single snapshot data received by a virtual array by calculating an autocorrelation covariance matrix of received data and then performing sequencing and redundancy removal, wherein the length of the virtual array is far longer than that of an actual physical array, so that the array can obtain larger array aperture and higher degree of freedom compared with a uniform linear array of the same physical array element. However, the array data after sorting and redundancy removal do not meet irrelevant conditions, so that an angle estimation algorithm utilizing covariance matrix eigenvalue decomposition fails, and the two-dimensional angle estimation of the incident information is carried out by adopting an Orthogonal Matching Pursuit (OMP) algorithm in compressed sensing. Simulation results show that the method can accurately estimate the azimuth angle and the pitch angle of the incident signal, and meanwhile, the estimated number of the signal sources is improved compared with that of the common uniform linear arrays of the same physical array elements.

As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.

The present invention has been described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions.

It should be noted that in the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word "comprising" does not exclude the presence of elements or steps not listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the claims enumerating several means, several of these means may be embodied by one and the same item of hardware. The use of the terms first, second, third and the like are for convenience only and do not denote any order. These words may be understood as part of the name of the component.

Furthermore, it should be noted that in the description of the present specification, the description of the term "one embodiment", "some embodiments", "examples", "specific examples" or "some examples", etc., means that a specific feature, structure, material or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Moreover, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.

While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, the claims should be construed to include preferred embodiments and all changes and modifications that fall within the scope of the invention.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention should also include such modifications and variations.