Off-grid two-dimensional DOA estimation method and system based on L-type co-prime array

Abstract

The invention discloses an off-grid two-dimensional DOA (Direction of Arrival) estimation method and system based on an L-shaped co-prime array. The method comprises the following steps: firstly, constructing a two-dimensional L-type co-prime array to obtain an array signal receiving model corresponding to each array element, and calculating an autocorrelation matrix of a received signal and a virtual array received signal; then setting an over-complete discrete grid, calculating signal power, and estimating a space angle between a target signal and a receiving array; and finally, mutual matching of space angles is carried out, and a pitch angle and an azimuth angle of the target signal are calculated. The system is used for realizing the off-grid two-dimensional DOA estimation method based on the L-shaped co-prime array, and comprises a model construction module, a space angle estimation module and a pitch angle and azimuth angle calculation module. According to the method, the degree of freedom and the precision of two-dimensional DOA estimation are improved, the operation complexity is reduced, and the accuracy and the calculation efficiency of two-dimensional DOA estimation are improved.

Description

Technical Field

[0001] The invention relates to the technical field of array signal processing, and in particular to an off-grid two-dimensional DOA estimation method and system based on an L-type coprime array. Background Art

[0002] Direction Of Arrival (DOA) estimation is an important branch of array signal processing, which is to receive the signal of the radiating source through the array antenna and obtain the arrival angle information of the signal after optimization processing. It is widely used in communication, sonar, radar and seismic exploration and other fields, and plays a vital role in these fields. At present, the one-dimensional DOA estimation theory has been relatively perfected, and classic algorithms such as MUSIC and ESPRIT have been widely used. However, with the continuous advancement of technology, more and more practical application scenarios require the simultaneous estimation of the horizontal and vertical directions of the signal source, so the two-dimensional DOA estimation technology has gradually attracted attention.

[0003] As a common two-dimensional array structure, the L-type array is more attractive than other array structures in practical applications because of its simple geometric structure and convenient algorithm implementation. Compared with the linear array, the L-type array can achieve 360-degree omnidirectional DOA estimation and has higher estimation accuracy. Compared with the circular array, the L-type array is easier to process data and has less computational complexity.

[0004] In recent years, sparse array technology has received extensive attention, with the main forms including minimum redundant array, nested array and coprime array. Sparse array can achieve larger array aperture and higher degree of freedom with fewer array elements, thus significantly improving the resolution and performance of DOA estimation. Coprime array is a typical sparse array, which adopts the structure of array elements arranged with non-equidistant spacing, which not only reduces the number of array elements, but also expands the effective array aperture and provides higher degree of freedom.

[0005] Traditional DOA estimation methods usually rely on fixed grids, but the direction of the actual signal source often falls inaccurately on these grid points, resulting in off-grid errors. Off-grid DOA estimation technology is designed to solve this problem by improving the accuracy of direction estimation and overcoming the limitations of traditional gridding methods.

[0006] Chinese patent CN 117949889 A discloses a gridless DOA estimation method based on an L-type coprime array. The conjugate symmetry property of the cross-correlation function of the received signals of the physical array elements at different time intervals is used to realize the conjugate augmentation of the original coprime array. The idea of ​​atomic norm minimization in the gridless method is used to interpolate the holes in the virtual conjugate augmented array. The covariance matrix of the virtual uniform linear array is obtained by solving the semi-positive definite programming problem. The matrix is ​​then unitarily transformed and the estimated values ​​of the azimuth and elevation angles are obtained by the ESPRIT method. Then, the different powers of different signals are used to design a cost function to achieve matching of the azimuth and elevation angles, thereby improving the array's degree of freedom and array aperture, converting the matrix complex value operation into a real value operation, reducing the computational complexity, and achieving matching of the azimuth and elevation angles. However, the positioning accuracy of the signal source, especially in high-resolution and multi-target scenarios, needs to be improved. Summary of the invention

[0007] The object of the present invention is to provide an off-grid two-dimensional DOA estimation method and system based on an L-type coprime array with high estimation freedom and estimation precision, low computational complexity, high computational efficiency and high accuracy.

[0008] The technical solution to achieve the purpose of the present invention is: an off-grid two-dimensional DOA estimation method based on an L-type coprime array, comprising the following steps:

[0009] Step 1: construct a two-dimensional L-shaped coprime array, obtain an array signal receiving model corresponding to each array element, and calculate the autocorrelation matrix of the received signal and the virtual array received signal;

[0010] Step 2: Set up an overcomplete discrete grid, calculate the signal power, and estimate the spatial angle between the target signal and the receiving array;

[0011] Step 3: Match the spatial angles and calculate the pitch angle and azimuth angle of the target signal.

[0012] An off-grid two-dimensional DOA estimation system based on an L-type mutually prime array, the system is used to implement the off-grid two-dimensional DOA estimation method based on an L-type mutually prime array, the system comprises a model building module, a space angle estimation module and a pitch angle and azimuth angle calculation module, wherein:

[0013] A model building module is used to build a two-dimensional L-shaped coprime array, obtain an array signal receiving model corresponding to each array element, and calculate the autocorrelation matrix of the received signal and the virtual array received signal;

[0014] The spatial angle estimation module is used to set up an overcomplete discrete grid, calculate the signal power, and estimate the spatial angle between the target signal and the receiving array;

[0015] The pitch angle and azimuth angle calculation module is used to match the spatial angles and calculate the pitch angle and azimuth angle of the target signal.

[0016] A mobile terminal comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the off-grid two-dimensional DOA estimation method based on an L-type coprime array is implemented.

[0017] A computer-readable storage medium having a computer program stored thereon, characterized in that when the program is executed by a processor, the steps in the off-grid two-dimensional DOA estimation method based on an L-type coprime array are implemented.

[0018] Compared with the prior art, the present invention has the following significant advantages: (1) It adopts an L-type coprime array, combining the advantages of the L-type array's all-round coverage and simple calculation. It adopts an array element structure with non-equidistant spacing, which reduces the number of array elements, expands the effective array aperture, and improves the accuracy and degree of freedom of two-dimensional DOA estimation; (2) It adopts an off-grid DOA estimation method to improve the positioning accuracy of the signal source in high-resolution and multi-target scenarios; (3) It has low computational complexity and improves the computational efficiency of two-dimensional DOA estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 The present invention is a flowchart of an off-grid two-dimensional DOA estimation method based on an L-type mutually prime array.

[0020] Figure 2 Schematic diagram of the structure of an L-type coprime array signal receiving model in an embodiment of the present invention.

[0021] Figure 3 This is a diagram of measurement results when there are three signal sources in an embodiment of the present invention.

[0022] Figure 4 The figure is a performance comparison diagram of the method of the present invention and the traditional DOA estimation method under different signal-to-noise ratios in the embodiment of the present invention. DETAILED DESCRIPTION

[0023] It is easy to understand that according to the technical solution of the present invention, without changing the essential spirit of the present invention, a person skilled in the art can imagine various implementation methods of the present invention. Therefore, the following specific implementation methods and drawings are only exemplary descriptions of the technical solution of the present invention, and should not be regarded as the whole of the present invention or as a limitation or restriction of the technical solution of the present invention.

[0024] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that the relative arrangement of components and steps, numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present invention unless otherwise specifically stated.

[0025] The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses.

[0026] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0027] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0028] The present invention provides an off-grid two-dimensional DOA estimation method based on an L-type coprime array, comprising the following steps:

[0029] Step 1: construct a two-dimensional L-shaped coprime array, obtain an array signal receiving model corresponding to each array element, and calculate the autocorrelation matrix of the received signal and the virtual array received signal;

[0030] Step 2: Set up an overcomplete discrete grid, calculate the signal power, and estimate the spatial angle between the target signal and the receiving array;

[0031] Step 3: Match the spatial angles and calculate the pitch angle and azimuth angle of the target signal.

[0032] As a specific example, the construction of a two-dimensional L-shaped coprime array described in step 1 is as follows:

[0033] A two-dimensional L-shaped coprime array is constructed, including subarray 1 and subarray 2. Subarray 1 is unfolded along the X-axis, and subarray 2 is unfolded along the Y-axis. Subarray 1 and subarray 2 have the same number of array elements and array structure, and share an array element at the origin of the coordinate system. Subarray 1 and subarray 2 are non-uniform linear arrays, each consisting of two coprime uniform linear arrays nested in each other. The number of array elements of the first uniform linear array is M, and the array element spacing is Nd, where d = λ / 2, λ is the signal wavelength, and the position of all array elements on the X-axis or Y-axis is miNd, where m i ∈(0,1,…,M-1), i represents the i-th array element; the number of array elements in the second uniform linear array is N, the array element spacing is Md, and the position of all array elements on the X-axis or Y-axis is n i Md, where n i∈(0,1,…,N-1); M and N are prime numbers to each other; the first uniform linear array and the second uniform linear array share the array element at the origin of the coordinate system, and the remaining array elements are nested to form a non-uniform linear array arranged on the X-axis and the Y-axis, and the total number of array elements is M+N-1; the total number of array elements in the entire L-shaped array is 2M+2N-3; θ k are the azimuth and elevation angles of the kth signal source in free space, α k , β k are the spatial angles between the kth signal source and sub-array 1 and sub-array 2 respectively.

[0034] As a specific example, the array signal receiving model corresponding to each array element is obtained in step 1, and the autocorrelation matrix of the received signal and the virtual array received signal are calculated as follows:

[0035] Step 1.1: The array signal receiving model corresponding to each array element is:

[0036]

[0037] Among them, x X (t), x Y (t) represents the received signals of the two sub-arrays located on the X-axis and the Y-axis respectively, K represents the number of signal sources, and a X (α k ), a Y (β k ) represent the steering vectors of the kth signal on subarray 1 and subarray 2, respectively, k = 1, 2, ..., K, as follows:

[0038]

[0039] Among them, α k , β k denote the spatial angles between the kth incident signal and subarray 1 and subarray 2, respectively, d i represents the distance from each array element to the origin of the coordinate system, and i=1,2,…,N+M-1; s k (t) represents the incident signal component, n X (t), n Y (t) represents the signal noise of the received signal on subarray 1 and subarray 2, respectively. X , A Y They represent the steering vector matrices of the received signal on subarray 1 and subarray 2 respectively, as follows:

[0040] A X =[a X (α1),…,a X (α K )]

[0041] A Y =[a Y (β1),…,a Y (β K )]

[0042] Step 1.2: The autocorrelation matrices of the received signal on subarray 1 and subarray 2 are:

[0043]

[0044] Among them, E[…] represents the expected value, and P represents the diagonal matrix composed of the power of the signal.

[0045] Step 1.3: Autocorrelation matrix R xx , R yy Vectorize to get a single snapshot matrix:

[0046]

[0047] Among them, vec(…) indicates vectorization processing, B1 and B2 represent the steering vector matrix A respectively. X , A Y The Kronecker product, represents the noise vector, and e represents the vectorized unit vector;

[0048] Extract the continuous linear virtual array elements in z1 and z2, remove the repeated elements, and rearrange the continuous parts to obtain the equivalent virtual array single snapshot receiving data y x (t), y y (t), where the equivalent array element position is the difference between the actual positions of any two array elements, and the corresponding steering vector is:

[0049]

[0050] Where Di represents the distance between the virtual array element and the coordinate origin, i = 1, 2, ..., M D -1;M D Indicates the total number of equivalent virtual array elements;

[0051] Step 1.4: Calculate the signal component sk(t) of the array receiving data of the corresponding virtual array of subarray 1 and subarray 2. For subarray 1, the spatial angle is α k The signal components are:

[0052]

[0053] For subarray 2, the spatial angle is β k The signal components are:

[0054]

[0055] As a specific example, the overcomplete discrete grid is set in step 2, the signal power is calculated, and the spatial angle between the target signal and the receiving array is estimated as follows:

[0056] Step 2.1: In subarray 1, based on the principle of equal cosine values, an overcomplete discrete grid is set in the spatial domain to obtain the corresponding steering vector a(γ i ), where i = 1, 2, ..., n, and n is the number of discrete grids;

[0057] Step 2.2, calculate the initial power component corresponding to each grid point:

[0058]

[0059] Step 2.3: Dynamically adjust the grid size according to the density of power distribution, iterate in sequence, improve the local grid density, and optimize the power component p(γ i ), autocorrelation matrix Until the weighted least squares cost function converges, the initial estimate of the space angle α is obtained according to the power value of each grid point of the overcomplete grid;

[0060] Step 2.4, calculate the loss function based on the minimum mean square error:

[0061]

[0062] in, represents the initial estimated azimuth and signal power components obtained in step 2.3;

[0063] Step 2.5: Solve the loss function for The first derivative of :

[0064]

[0065] The iterative formula for the estimated value is:

[0066]

[0067] in, represents the estimated value of the spatial angle α of the kth incident signal at the lth iteration, μ represents the estimated parameter, and L l Represents the loss function value of the lth iteration. l+1 >L l Or when the maximum number of iterations is exceeded, the iteration is terminated to obtain the final estimation result.

[0068] Step 2.6: Calculate subarray 2 according to steps 2.1 to 2.5 to obtain the final estimation result of spatial angle β.

[0069] As a specific example, in step 2.3, the grid size is dynamically adjusted according to the density of the power distribution, and the local grid density is improved by iteration, as follows:

[0070] In areas where signal power is densely distributed, the grid density is changed to twice the initial value within the range of ±3°, with the degree corresponding to the point with the maximum power value as the center; in areas where signal power is sparsely distributed, the grid density is changed to 1 / 2 of the initial value within the range of ±3°.

[0071] As a specific example, the power component p(γ i ), as follows:

[0072] An adaptive weight mechanism is introduced to weight different signal sources according to the signal source strength and signal noise level.

[0073] As a specific example, the spatial angles are matched with each other in step 3 to calculate the pitch angle and azimuth angle of the target signal, as follows:

[0074] Step 3.1: Assume that there are K signal sources in the space, then there are K ways to pair the spatial angles. For each spatial angle combination by As the center, respectively is the step size, take the paired subgrid Matching is performed, where j represents the number of subgrid points, j = 1, 2, ..., 10; the steering vector of the real pairing angle is orthogonal to the noise subspace, and the real pairing space angle (α, β) is obtained;

[0075] Step 3.2: Calculate the azimuth of the signal source in free space and pitch angle θ, the formula is:

[0076]

[0077] The present invention also provides an off-grid two-dimensional DOA estimation system based on an L-type coprime array, which is used to implement the off-grid two-dimensional DOA estimation method based on an L-type coprime array, and the system includes a model building module, a space angle estimation module, and a pitch angle and azimuth angle calculation module, wherein:

[0078] A model building module is used to build a two-dimensional L-shaped coprime array, obtain an array signal receiving model corresponding to each array element, and calculate the autocorrelation matrix of the received signal and the virtual array received signal;

[0079] The spatial angle estimation module is used to set up an overcomplete discrete grid, calculate the signal power, and estimate the spatial angle between the target signal and the receiving array;

[0080] The pitch angle and azimuth angle calculation module is used to match the spatial angles and calculate the pitch angle and azimuth angle of the target signal.

[0081] The present invention also provides a mobile terminal, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that when the processor executes the program, the off-grid two-dimensional DOA estimation method based on an L-type coprime array is implemented.

[0082] The present invention also provides a computer-readable storage medium having a computer program stored thereon, characterized in that when the program is executed by a processor, the steps in the off-grid two-dimensional DOA estimation method based on an L-type coprime array are implemented.

[0083] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0084] Example

[0085] Combination Figure 1 The present invention provides an off-grid two-dimensional DOA estimation method based on an L-type coprime array, comprising the following steps:

[0086] Step 1: construct a two-dimensional L-shaped coprime array, obtain an array signal receiving model corresponding to each array element, and calculate the autocorrelation matrix of the received signal and the virtual array received signal;

[0087] As a specific example, the construction of a two-dimensional L-shaped coprime array described in step 1 is as follows:

[0088] like Figure 2 As shown, a two-dimensional L-type coprime array is constructed, including subarray 1 and subarray 2. Subarray 1 is unfolded along the X-axis, and subarray 2 is unfolded along the Y-axis. The number of array elements and array structure of subarray 1 and subarray 2 are the same, and they share an array element at the origin of the coordinate system. Subarray 1 and subarray 2 are non-uniform linear arrays, which are composed of two coprime uniform linear arrays nested with each other. The number of array elements of the first uniform linear array is M, and the array element spacing is Nd, where d = λ / 2, λ is the signal wavelength, and the position of all array elements on the X-axis or Y-axis is miNd, where m i ∈(0,1,…,M-1), i represents the i-th array element; the number of array elements in the second uniform linear array is N, the array element spacing is Md, and the position of all array elements on the X-axis or Y-axis is n i Md, where n i∈(0,1,…,N-1); M and N are prime numbers to each other; the first uniform linear array and the second uniform linear array share the array element at the origin of the coordinate system, and the remaining array elements are nested to form a non-uniform linear array arranged on the X-axis and the Y-axis, and the total number of array elements is M+N-1; the total number of array elements in the entire L-shaped array is 2M+2N-3; θ k are the azimuth and elevation angles of the kth signal source in free space, α k , β k are the spatial angles between the kth signal source and sub-array 1 and sub-array 2 respectively.

[0089] In this embodiment, the two-dimensional L-shaped coprime array described in step 1 is constructed to obtain the array signal receiving model corresponding to each array element, and the autocorrelation matrix of the received signal and the virtual array received signal are calculated as follows:

[0090]

[0091] Among them, x X (t), x Y (t) represents the received signals of the two sub-arrays located on the X-axis and the Y-axis respectively, K represents the number of signal sources, and a X (α k ), a Y (β k ) represent the steering vectors of the kth signal on subarray 1 and subarray 2, respectively, k = 1, 2, ..., K, as follows:

[0092]

[0093] Among them, α k , β k denote the spatial angles between the kth incident signal and subarray 1 and subarray 2, respectively, d i represents the distance from each array element to the origin of the coordinate system, and i=1,2,…,N+M-1; s k (t) represents the incident signal component, n X (t), n Y (t) represents the signal noise of the received signal on subarray 1 and subarray 2, respectively. X , A Y They represent the steering vector matrices of the received signal on subarray 1 and subarray 2 respectively, as follows:

[0094] A X =[a X (α1),…,a X (α K )]

[0095] A Y =[a Y (β1),…,aY (β K )];

[0096] Step 1.2: The autocorrelation matrices of the received signal on subarray 1 and subarray 2 are:

[0097]

[0098] Among them, E[…] represents the expected value, and P represents the diagonal matrix composed of the power of the signal;

[0099] Step 1.3: Autocorrelation matrix R xx , R yy Vectorize to get a single snapshot matrix:

[0100]

[0101]

[0102] Among them, vec(…) indicates vectorization processing, B1 and B2 represent the steering vector matrix A respectively. X , A Y The Kronecker product, represents the noise vector, and e represents the vectorized unit vector.

[0103] Extract the continuous linear virtual array elements in z1 and z2, remove the repeated elements, and rearrange the continuous parts to obtain the equivalent virtual array single snapshot receiving data y x (t), y y (t), where the equivalent array element position is the difference between the actual positions of any two array elements, and the corresponding steering vector is:

[0104]

[0105] Where Di(i=1,2,…,M D -1) represents the distance between the virtual array element and the coordinate origin, M D Indicates the total number of equivalent virtual array elements.

[0106] Step 1.4: Calculate the signal component sk(t) of the array receiving data of the corresponding virtual array of subarray 1 and subarray 2. For subarray 1, the spatial angle is α k The signal components are:

[0107]

[0108] For subarray 2, the spatial angle is β k The signal components are:

[0109]

[0110] In this embodiment, step 2 sets an overcomplete discrete grid, calculates the signal power, and estimates the spatial angle between the target signal and the receiving array, as follows:

[0111] Step 2.1: In subarray 1, based on the principle of equal cosine values, an overcomplete discrete grid is set in the spatial domain to obtain the corresponding steering vector a(γ i ), where i = 1, 2, ..., n, and n is the number of discrete grids;

[0112] Step 2.2, calculate the initial power component corresponding to each grid point:

[0113]

[0114] Step 2.3: Dynamically adjust the grid size according to the density of power distribution, iterate in sequence, improve the local grid density, and optimize the power component p(γ i ), autocorrelation matrix Until the weighted least squares cost function converges, the initial estimate of the space angle α is obtained according to the power value of each grid point of the overcomplete grid;

[0115] Step 2.4, calculate the loss function based on the minimum mean square error:

[0116]

[0117] in, represents the initial estimated azimuth and signal power components obtained in step 2.3;

[0118] Step 2.5: Solve the loss function for The first derivative of :

[0119]

[0120] The iterative formula for the estimated value is:

[0121]

[0122] in, represents the estimated value of the spatial angle α of the kth incident signal at the lth iteration, μ represents the estimated parameter, and L l Represents the loss function value of the lth iteration. l+1 >L l Or when the maximum number of iterations is exceeded, the iteration is terminated to obtain the final estimation result.

[0123] Step 2.6: Calculate subarray 2 according to steps 2.1 to 2.5 to obtain the final estimation result of spatial angle β.

[0124] In this embodiment, the grid size is dynamically adjusted according to the density of the power distribution as described in step 2.3, and the local grid density is improved by iteration, as follows:

[0125] In areas where signal power is densely distributed, the grid density is changed to twice the initial value within the range of ±3°, with the degree corresponding to the point with the maximum power value as the center; in areas where signal power is sparsely distributed, the grid density is changed to 1 / 2 of the initial value within the range of ±3°.

[0126] In this embodiment, the power component p(γ i ), specifically as follows: an adaptive weight mechanism is introduced to weight different signal sources according to the signal source strength and signal noise level to improve the robustness of DOA estimation.

[0127] In this embodiment, the value of the estimated parameter μ described in step 2.5 is μ=0.4.

[0128] In this embodiment, step 3 performs mutual matching of spatial angles to calculate the pitch angle and azimuth angle of the target signal, as follows:

[0129] Step 3.1: Assume that there are K signal sources in the space, then there are K ways to pair the spatial angles. For each spatial angle combination by As the center, respectively is the step size, take the paired subgrid Matching is performed, where j represents the number of subgrid points, j = 1, 2, ..., 10; since the steering vector of the real pairing angle is orthogonal to the noise subspace, the real pairing space angle (α, β) can be obtained;

[0130] Step 3.2: Calculate the azimuth of the signal source in free space and pitch angle θ, the formula is:

[0131]

[0132] In this embodiment, the step length described in step 3.1 is The value of

[0133] This embodiment uses the method of the present invention to estimate the DOA of three signal sources. The estimation results are as follows: Figure 3 As shown; Figure 4 The performance comparison diagram of the method of the present invention and the traditional DOA estimation method under different signal-to-noise ratios is shown in FIG. Figure 3 It can be seen that the measured angle and the actual angle are basically consistent; Figure 4 It can be seen that the estimation performance of the method of the present invention under different signal-to-noise ratios is higher than that of the traditional DOA estimation method, which proves that the method of the present invention improves the accuracy and degree of freedom of two-dimensional DOA estimation, improves the positioning accuracy of the signal source in high-resolution and multi-target scenarios, and improves the computational efficiency of two-dimensional DOA estimation.

[0134] The above are only preferred embodiments of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A two-dimensional off-grid DOA estimation method based on an L-type coprime array, characterized in that: The following steps are involved: Step 1: construct a two-dimensional L-shaped coprime array, obtain an array signal receiving model corresponding to each array element, and calculate the autocorrelation matrix of the received signal and the virtual array received signal; Step 2: Set up an overcomplete discrete grid, calculate the signal power, and estimate the spatial angle between the target signal and the receiving array; Step 3: Match the spatial angles and calculate the pitch angle and azimuth angle of the target signal.

2. The off-grid two-dimensional DOA estimation method based on L-type coprime array according to claim 1, characterized in that: The construction of the two-dimensional L-type coprime array described in step 1 is as follows: A two-dimensional L-shaped coprime array is constructed, including subarray 1 and subarray 2. Subarray 1 is unfolded along the X-axis, and subarray 2 is unfolded along the Y-axis. Subarray 1 and subarray 2 have the same number of array elements and array structure, and share an array element at the origin of the coordinate system. Subarray 1 and subarray 2 are non-uniform linear arrays, each consisting of two coprime uniform linear arrays nested in each other. The number of array elements of the first uniform linear array is M, and the array element spacing is Nd, where d = λ / 2, λ is the signal wavelength, and the position of all array elements on the X-axis or Y-axis is miNd, where m i ∈(0,1,…,M-1), i represents the i-th array element; the number of array elements in the second uniform linear array is N, the array element spacing is Md, and the position of all array elements on the X-axis or Y-axis is n i Md, where n i ∈(0,1,…,N-1); M and N are prime numbers to each other; the first uniform linear array and the second uniform linear array share the array element at the origin of the coordinate system, and the remaining array elements are nested to form a non-uniform linear array arranged on the X-axis and the Y-axis, and the total number of array elements is M+N-1; the total number of array elements in the entire L-shaped array is 2M+2N-3; θ k are the azimuth and elevation angles of the kth signal source in free space, α k , β k are the spatial angles between the kth signal source and sub-array 1 and sub-array 2 respectively.

3. The off-grid two-dimensional DOA estimation method based on L-type coprime array according to claim 2, characterized in that: The array signal receiving model corresponding to each array element is obtained in step 1, and the autocorrelation matrix of the received signal and the virtual array received signal are calculated, as follows: Step 1.1: The array signal receiving model corresponding to each array element is: Among them, x X (t), x Y (t) represents the received signals of the two sub-arrays located on the X-axis and the Y-axis respectively, K represents the number of signal sources, and a X (α k ), a Y (β k ) represent the steering vectors of the kth signal on subarray 1 and subarray 2, respectively, k = 1, 2, ..., K, as follows: Among them, α k , β k denote the spatial angles between the kth incident signal and subarray 1 and subarray 2, respectively, d i represents the distance from each array element to the origin of the coordinate system, and i=1,2,…,N+M-1; s k (t) represents the incident signal component, n X (t), n Y (t) represents the signal noise of the received signal on subarray 1 and subarray 2, respectively. X , A Y They represent the steering vector matrices of the received signal on subarray 1 and subarray 2 respectively, as follows: A X =[a X (a1),…,a X (a K )] A Y =[a Y (β1),…,a Y (b K )] Step 1.2: The autocorrelation matrices of the received signal on subarray 1 and subarray 2 are: Among them, E[…] represents the expected value, and P represents the diagonal matrix composed of the power of the signal. Step 1.3: Autocorrelation matrix R xx , R yy Vectorize to get a single snapshot matrix: Among them, vec(…) indicates vectorization processing, B1 and B2 represent the steering vector matrix A respectively. X , A Y The Kronecker product, represents the noise vector, and e represents the vectorized unit vector; Extract the continuous linear virtual array elements in z1 and z2, remove the repeated elements, and rearrange the continuous parts to obtain the equivalent virtual array single snapshot receiving data y x (t), y y (t), where the equivalent array element position is the difference between the actual positions of any two array elements, and the corresponding steering vector is: Where Di represents the distance between the virtual array element and the coordinate origin, i = 1, 2, ..., M D -1;M D Indicates the total number of equivalent virtual array elements; Step 1.4: Calculate the signal component sk(t) of the array receiving data of the corresponding virtual array of subarray 1 and subarray 2. For subarray 1, the spatial angle is α k The signal components are: For subarray 2, the spatial angle is β k The signal components are:

4. The off-grid two-dimensional DOA estimation method based on L-type coprime array according to claim 3, characterized in that: The overcomplete discrete grid described in step 2 is set up, the signal power is calculated, and the spatial angle between the target signal and the receiving array is estimated as follows: Step 2.1: In subarray 1, based on the principle of equal cosine values, an overcomplete discrete grid is set in the spatial domain to obtain the corresponding steering vector a(γ i ), where i = 1, 2, ..., n, and n is the number of discrete grids; Step 2.2, calculate the initial power component corresponding to each grid point: Step 2.3: Dynamically adjust the grid size according to the density of power distribution, iterate in sequence, improve the local grid density, and optimize the power component p(γ i ), autocorrelation matrix Until the weighted least squares cost function converges, the initial estimate of the space angle α is obtained according to the power value of each grid point of the overcomplete grid; Step 2.4, calculate the loss function based on the minimum mean square error: in, represents the initial estimated azimuth and signal power components obtained in step 2.3; Step 2.5: Solve the loss function for The first derivative of : The iterative formula for the estimated value is: in, represents the estimated value of the spatial angle α of the kth incident signal at the lth iteration, μ represents the estimated parameter, and L l Represents the loss function value of the lth iteration. l+1 >L l Or when the maximum number of iterations is exceeded, the iteration is terminated to obtain the final estimation result. Step 2.6: Calculate subarray 2 according to steps 2.1 to 2.5 to obtain the final estimation result of spatial angle β.

5. The off-grid two-dimensional DOA estimation method based on L-type coprime array according to claim 4, characterized in that: In step 2.3, the grid size is dynamically adjusted according to the density of the power distribution, and the local grid density is improved by iteration, as follows: In areas where signal power is densely distributed, the grid density is changed to twice the initial value within the range of ±3°, with the degree corresponding to the point with the maximum power value as the center; in areas where signal power is sparsely distributed, the grid density is changed to 1 / 2 of the initial value within the range of ±3°.

6. The off-grid two-dimensional DOA estimation method based on L-type coprime array according to claim 5, characterized in that: The power component p(γ i ), as follows: An adaptive weight mechanism is introduced to weight different signal sources according to the signal source strength and signal noise level.

7. The off-grid two-dimensional DOA estimation method based on L-type coprime array according to claim 6, characterized in that: The spatial angles are matched in step 3 to calculate the pitch angle and azimuth angle of the target signal, as follows: Step 3.1: Assume that there are K signal sources in the space, then there are K ways to pair the spatial angles. For each spatial angle combination by As the center, respectively is the step size, take the paired subgrid Matching is performed, where j represents the number of subgrid points, j = 1, 2, ..., 10; the steering vector of the real pairing angle is orthogonal to the noise subspace, and the real pairing space angle (α, β) is obtained; Step 3.2: Calculate the azimuth of the signal source in free space and pitch angle θ, the formula is:

8. An off-grid two-dimensional DOA estimation system based on an L-type coprime array, characterized in that: The system is used to implement the off-grid two-dimensional DOA estimation method based on an L-type coprime array according to any one of claims 1 to 7, and the system includes a model building module, a space angle estimation module, and a pitch angle and azimuth angle calculation module, wherein: A model building module is used to build a two-dimensional L-shaped coprime array, obtain an array signal receiving model corresponding to each array element, and calculate the autocorrelation matrix of the received signal and the virtual array received signal; The spatial angle estimation module is used to set up an overcomplete discrete grid, calculate the signal power, and estimate the spatial angle between the target signal and the receiving array; The pitch angle and azimuth angle calculation module is used to match the spatial angles and calculate the pitch angle and azimuth angle of the target signal.

9. A mobile terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the off-grid two-dimensional DOA estimation method based on an L-type coprime array is implemented as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in the off-grid two-dimensional DOA estimation method based on an L-type coprime array are implemented as described in any one of claims 1 to 7.

Images