Two-dimensional direction of arrival estimation method under impulse noise

Abstract

The invention provides a two-dimensional direction of arrival estimation method under impulse noise, and the method comprises the steps: obtaining a first output matrix outputted by an augmented co-prime array and a second output matrix outputted by an augmented expanded co-prime array through a preset receiving model; the preset receiving model comprises a parallel line structure composed of an augmented co-prime array and an augmented expanded co-prime array, conjugate operation is carried out on ECA, the non-circular characteristic of signals is fully utilized, meanwhile, in order to suppress impulse noise, a correlation entropy method based on a generalized dustpan function (GVF) is utilized, and the non-circular characteristic of the signals is fully utilized. Compared with a traditional method, the method has better robustness.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and particularly to a two-dimensional direction-of-arrival estimation method under impulse noise conditions. Background Art

[0002] Direction-of-arrival (DOA) estimation is a branch of array signal processing and has become a research hotspot in fields such as radar and sonar in recent years. Traditional estimation methods are mostly based on one-dimensional arrays. However, two-dimensional arrays can describe the direction of signals more accurately. In the past few decades, scholars have proposed many DOA estimation algorithms for two-dimensional array structures, such as planar arrays, L-shaped arrays, and parallel-line arrays. However, similar to one-dimensional arrays, the degrees of freedom (DOF) and resolution of two-dimensional arrays are also limited by the number of physical array elements. Therefore, improving the DOF and resolution of array elements while saving the number of array elements is also a challenging research hotspot in two-dimensional DOA estimation.

[0003] The co-prime array (CA) is an effective method to solve this problem. Some researchers have extended the CA to a double parallel-line array and achieved good experimental results. However, most studies have ignored the non-circular (NC) characteristics of signals, which hinders the full extraction of signal features and thus wastes physical array elements. More importantly, most parallel-line arrays perform DOA estimation in a Gaussian white noise environment. However, in nature, noise often has impulse characteristics, and in this environment, the performance of traditional DOA estimation methods will decrease significantly. To overcome this difficulty, researchers have proposed many DOA estimation methods under impulse noise. For example, the mainstream method for dealing with impulse noise in the DOA matrix is based on fractional-order low-order statistics, such as fractional-order low-order moment (FLOM), phase fractional-order low-order moment (PFLOM), and robust covariance (ROC). The disadvantage of these DOA estimation methods is that they need to obtain some key information about signal noise in advance, which is difficult to achieve in practical applications. To improve the practicality of the algorithm, researchers have proposed a class of DOA estimation methods based on correlation coefficients, such as the correlation coefficient-based correlation entropy (CRCO) method and the square-based correlation coefficient operator (SCO) method. However, these algorithms usually involve Gaussian kernels in the operation process, which usually requires exponential calculations, resulting in significant computational costs, that is, the methods adopted in the prior art cannot meet the more stringent requirements of two-dimensional DOA estimation and cannot accurately calculate the DOA direction angle in an impulse noise environment. Summary of the Invention

[0004] Aiming at the problem that the methods adopted in the prior art cannot meet the more stringent requirements of two-dimensional DOA estimation and cannot accurately calculate the DOA direction angle in an impulse noise environment, this application provides a two-dimensional direction-of-arrival estimation method under impulse noise.

[0005] In a first aspect, the present invention provides a two-dimensional direction of arrival estimation method under impulse noise, comprising the following steps:

[0006] Obtain a first output matrix output by an augmented co-prime array and a second output matrix output by an augmented extended co-prime array through a preset receiving model, where the preset receiving model includes a parallel line structure composed of an augmented co-prime array and an augmented extended co-prime array;

[0007] Perform conjugate processing on the first output matrix to obtain conjugate data, and splice the first output matrix and the conjugate data to obtain a fusion matrix;

[0008] Process the fusion matrix and the second output matrix by using a correlation entropy method based on GVF to obtain a first target matrix corresponding to the fusion matrix and a second target matrix corresponding to the second output matrix;

[0009] Calculate the cross-covariance matrix of the first target matrix and the second target matrix, and perform vectorization processing on the cross-covariance matrix;

[0010] Perform decorrelation on the vectorized cross-covariance matrix by a smoothing method to construct an autocovariance matrix, perform eigenvalue decomposition on the autocovariance matrix to obtain a noise subspace;

[0011] According to the noise subspace, calculate two estimated angles of the direction of arrival through the MUSIC algorithm and the total least squares method.

[0012] Optionally, the expressions of the first output matrix output by the augmented co-prime array and the second output matrix output by the augmented extended co-prime array are:

[0013]

[0014] where, x AUCA (t) and x ECA (t) respectively represent the first output matrix output by the augmented co-prime array and the second output matrix output by the augmented extended co-prime array, s(t) represents a signal matrix, and s(t) = [s1(t), …, s K (t)] T , n1(t) and n2(t) are impulse noises with symmetric alpha-stable distributions, where A1 and A2 are array manifold matrices, containing array position information and information of angle θ, and for convenience of processing, the information of angle α is separated into a diagonal matrix Φ.

[0015] Optionally, the mathematical representation of the fusion matrix is:

[0016]

[0017] Among them is the conjugate form of x ECA (t), x CECA (t) is the fusion matrix, and is the conjugate form of A2 and n2(t).

[0018] Optionally, the step of processing the fusion matrix and the second output matrix by using the GVF-based correlation entropy method includes:

[0019] Construct a preset function based on the generalized odd-symmetric function, and the mathematical representation of the preset function is:

[0020]

[0021] where f(x) is a function based on the generalized odd-symmetric function, and u, τ, p are hyperparameters, and the degree of suppression of impulse noise is controlled by adjusting their magnitudes;

[0022] Process the fusion matrix and the second output matrix based on the preset function.

[0023] Optionally, the mathematical representation of the cross-covariance matrix is:

[0024]

[0025] where E(·) represents the mathematical expectation, and R (i,j) represents the element in the i-th row and j-th column of the covariance matrix, and x AUCA (t) and x CECA (t) represent the i-th and j-th elements of x AUCA (t), x CECA (t).

[0026] Optionally, the step of vectorizing the cross-covariance matrix includes:

[0027] Perform a vectorization operation on the estimated cross-covariance matrix through a preset vectorization function, and the mathematical representation of the preset vectorization function is:

[0028] r = vec(R) = vec(A1ΦR s (A 22 ) H ) = ((A 22 ) * ⊙A1)u = Au

[0029] where A = (A 22 ) *⊙A1, where ⊙ represents the Kronecker product, is the signal covariance matrix, indicating the power of the k-th signal.

[0030] Optionally, the steps of decorrelating the vectorized cross-covariance matrix by a smoothing method to construct an auto-covariance matrix and performing eigenvalue decomposition on the auto-covariance matrix to obtain a noise subspace include:

[0031] Performing a redundancy removal operation on the vectorized cross-covariance matrix to obtain a target cross-covariance matrix;

[0032] Selecting continuous arrays in the virtual array of the target cross-covariance matrix to obtain an array to be processed;

[0033] Decorrelating the array to be processed by a smoothing method to construct an auto-covariance matrix and performing eigenvalue decomposition on the auto-covariance matrix to obtain a noise subspace.

[0034] Optionally, the steps of calculating two estimated angles of the direction of arrival according to the noise subspace by the MUSIC algorithm and the total least squares method include:

[0035] Based on the noise subspace, calculating a spatial spectrum function according to the MUSIC algorithm, and the mathematical representation of the spatial spectrum function is:

[0036]

[0037] Solving for α using the total least squares method:

[0038]

[0039] Obtaining two estimated angles of the direction of arrival.

[0040] Advantageous effects: Compared with the existing technical means, the present invention has the following advantages:

[0041] By presetting a receiving model, a first output matrix output by an augmented co-prime array and a second output matrix output by an augmented expanded co-prime array are obtained. The preset receiving model includes a parallel line structure composed of an augmented co-prime array and an augmented expanded co-prime array; conjugate processing is performed on the first output matrix to obtain conjugate data, and the first output matrix and the conjugate data are spliced to obtain a fusion matrix; the fusion matrix and the second output matrix are processed by using a GVF-based correlation entropy method to obtain a first target matrix corresponding to the fusion matrix and a second target matrix corresponding to the second output matrix; the cross-covariance matrix of the first target matrix and the second target matrix is calculated, and the cross-covariance matrix is vectorized; the vectorized cross-covariance matrix is decorrelated by a smoothing method to construct an auto-covariance matrix, and the auto-covariance matrix is eigen-decomposed to obtain a noise subspace; according to the noise subspace, two estimated angles of the direction of arrival are calculated by using the MUSIC algorithm and the total least squares method. The GVF function is adopted to avoid the loss of computing resources and improve the accuracy of DOA estimation. At the same time, the co-prime array is introduced to make full use of the non-circular characteristics of the signal. By conjugating the signal, the overall degree of freedom of the array is improved, enabling the array to estimate more signal sources. Description of the Drawings

[0042] Figure 1 It is a flowchart of a two-dimensional direction-of-arrival estimation method under impulse noise in an embodiment;

[0043] Figure 2 It is a two-dimensional array model diagram of a two-dimensional direction-of-arrival estimation method under impulse noise in an embodiment;

[0044] Figure 3 It is a conjugate principle diagram of an internal array of a two-dimensional direction-of-arrival estimation method under impulse noise in an embodiment;

[0045] Figure 4 It is a result comparison diagram of a two-dimensional direction-of-arrival estimation method under impulse noise and an existing method in an embodiment;

[0046] Figure 5 It is a result comparison diagram of a two-dimensional direction-of-arrival estimation method under impulse noise and an existing method in an embodiment;

[0047] Figure 6 It is a structural block diagram of a two-dimensional direction-of-arrival estimation device under impulse noise in an embodiment;

[0048] Figure 7 It is a structural block diagram of a computer device in an embodiment;

[0049] Figure 8It is a structural block diagram of a computer device in another embodiment. Detailed implementation manners

[0050] In order to make the objectives, technical solutions and advantages of the present application clearer, the present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0051] As Figure 1 shown, the present invention provides a two-dimensional direction-of-arrival estimation method under impulse noise, including the following steps:

[0052] S101. Obtain a first output matrix output by an augmented co-prime array and a second output matrix output by an augmented extended co-prime array through a preset reception model, where the preset reception model includes a parallel line structure composed of an augmented co-prime array and an augmented extended co-prime array;

[0053] Exemplarily, as Figure 2 shown, assume that there are K far-field signals incident on the array at an angle of (θ i , α i ). The output signals of the two sub-arrays at time t are:

[0054]

[0055] where n1(t) and n2(t) are additive impulse noise vectors of the two sub-arrays, independent of the signal s(t). Their expressions are respectively x AUCA (t) = [x1(t),..., x (2M+N) (t)] T , x CECA (t) = [x c1 (t),..., x c(2M+N) (t)] T , s(t) = [s1(t),..., s k (t)], A1 = [a1(θ1), …, a1(θ K ), A2 = [a2(θ1), …, a2(θ K )] and there is

[0056]

[0057]

[0058] where p i and q i are the coordinate information of the two arrays.

[0059] S102. Conjugate the first output matrix to obtain conjugate data, and splice the first output matrix and the conjugate data to obtain a fusion matrix;

[0060] Exemplarily, in combination with Figure 3 , conjugate the received data of ECA to generate virtual array elements based on real array elements. The specific formula is:

[0061]

[0062] Benefiting from the non-circularity and realness of s(t), a new received data matrix x CECA (t) is calculated and used as the new sub-array output signal (conjugate data).

[0063] S103. Process the fusion matrix and the second output matrix by using the GVF-based correlation entropy method to obtain a first target matrix corresponding to the fusion matrix and a second target matrix corresponding to the second output matrix;

[0064] In a possible implementation manner, the mathematical representation of the cross-covariance matrix is:

[0065]

[0066] where E(·) represents the mathematical expectation, and R (i,j) represents the element in the i-th row and j-th column of the covariance matrix, and x AUCA (t) and x CECA (t) represent the i-th and j-th elements in x AUCA (t), x CECA (t).

[0067] S104. Calculate the cross-covariance matrix of the first target matrix and the second target matrix, and perform vectorization processing on the cross-covariance matrix;

[0068] Exemplarily, construct the cross-covariance matrix of two sub-array output signals as:

[0069]

[0070] where a i (t) and are respectively the i-th row and j-th column of x AUCA (t) and x ECA (t), and the values of the hyperparameters are 0 < u ≤ 1, τ = 1, p = 0.5 respectively. So the complete R is:

[0071]

[0072] Exemplarily, the vectorization operation is as follows:

[0073] r = vec(R) = vec(A1ΦR s (A 22 ) H )

[0074] = ((A 22 ) * ⊙ A1)u = Au

[0075] After redundancy removal, the continuous virtual ULA is taken as:

[0076]

[0077] S105. Decorrelate the cross-covariance matrix after vectorization processing through a smoothing method to construct an auto-covariance matrix, and perform eigen-decomposition on the auto-covariance matrix to obtain a noise subspace;

[0078] Exemplarily, the smoothing to construct the auto-covariance matrix is as follows:

[0079]

[0080] S106. According to the noise subspace, calculate two estimated angles of the direction of arrival through the MUSIC algorithm and the total least squares method;

[0081] Exemplarily, perform eigen-decomposition on R rr to separate the noise subspace Un, and use the spectral function to obtain θ:

[0082]

[0083] Based on the above formula, use the total least squares method to obtain α:

[0084]

[0085] Optionally, the expressions of the first output matrix output by the augmented co-prime array and the second output matrix output by the augmented expanded co-prime array are:

[0086]

[0087] where, x AUCA (t) and x ECA (t) respectively represent the first output matrix output by the augmented co-prime array and the second output matrix output by the augmented expanded co-prime array, s(t) represents the signal matrix, and s(t) = [s1(t), …, s K (t)] T, n1(t) and n2(t) are impulsive noises with symmetric alpha-stable distributions, where A1 and A2 are array manifold matrices that contain array position information and information about the angle θ. For convenience of processing, the information about the angle α is separated into the diagonal matrix Φ.

[0088] Optionally, the mathematical representation of the fusion matrix is:

[0089]

[0090] where is the conjugate form of x ECA (t), x CECA (t) is the fusion matrix, and are the conjugate forms of A2 and n2(t).

[0091] Optionally, the step of processing the fusion matrix and the second output matrix using the GVF-based correlation entropy method includes:

[0092] Constructing a preset function based on the generalized Gabor function, and the mathematical representation of the preset function is:

[0093]

[0094] where f(x) is a function based on the generalized Gabor function, and u, τ, p are hyperparameters, and the degree of suppression of impulsive noise is controlled by adjusting their magnitudes;

[0095] Processing the fusion matrix and the second output matrix based on the preset function.

[0096] Optionally, the mathematical representation of the cross-covariance matrix is:

[0097]

[0098] where E(·) represents the mathematical expectation, and R (i,j) represents the element in the i-th row and j-th column of the covariance matrix, and x AUCA (t) and x CECA (t) represent the i-th and j-th elements in x AUCA (t), x CECA (t).

[0099] Optionally, the step of vectorizing the cross-covariance matrix includes:

[0100] Performing a vectorization operation on the estimated cross-covariance matrix through a preset vectorization function, and the mathematical representation of the preset vectorization function is:

[0101] r = vec(R) = vec(A1ΦR s (A 22 ) H ) = ((A 22 ) * ⊙A1)u = Au

[0102] Optionally, the steps of decorrelating the cross-covariance matrix after vectorization processing by a smoothing method, constructing an auto-covariance matrix, and performing eigen-decomposition on the auto-covariance matrix to obtain a noise subspace include:

[0103] Performing a redundancy removal operation on the cross-covariance matrix after vectorization processing to obtain a target cross-covariance matrix;

[0104] Selecting consecutive arrays in the virtual array of the target cross-covariance matrix to obtain an array to be processed;

[0105] Decorrelating the array to be processed by a smoothing method, constructing an auto-covariance matrix, and performing eigen-decomposition on the auto-covariance matrix to obtain a noise subspace.

[0106] Optionally, the steps of calculating two estimated angles of the direction of arrival by the MUSIC algorithm and the total least squares method according to the noise subspace include:

[0107] Based on the noise subspace, calculating a spatial spectrum function according to the MUSIC algorithm, and the mathematical representation of the spatial spectrum function is:

[0108]

[0109] Solving for α using the total least squares method:

[0110]

[0111] Obtaining two estimated angles of the direction of arrival.

[0112] Experiment 1: In this example, M = 4 and N = 5 are set in the two-dimensional array. The angles of 5 far-field incident signals are (40°, 40°), (45°, 50°), (50°, 60°), (60°, 70°), (70°, 80°), and the number of snapshots is set to 500. In the experiment, common two-dimensional arrays such as the sum-difference combined parallel array (S-CPPA), the double-augmented co-prime parallel array (NCA), and the three-parallel-line array (TPCA) are compared, as well as the comparison array of the present invention without using the ECA conjugate (SAS). Taking the root mean square error sum of two angles as the evaluation criterion, the performance under different generalized signal-to-noise ratios (GSNR) is compared, and the experimental results are as Figure 4 shown. From Figure 4It can be seen that the result of the method for two-dimensional direction of arrival estimation under impulse noise of the present invention can estimate the incident angle more accurately than other arrays.

[0113] Experiment 2: On the basis of Experiment 1, using the present invention in an impulse noise environment, different methods for suppressing noise are compared, such as FLOM, ROC, infinite norm normalization (IN), and CRCO. The performance under different impulse noise intensities (α) is compared, and the experimental results are as Figure 5 shown. It can be seen from the figure that under different intensities of impulse noise, the present invention can show excellent effects compared with other methods.

[0114] On the other hand, as shown in / 6, the present application provides a device for two-dimensional direction of arrival estimation under impulse noise, and the device includes:

[0115] A data acquisition module 201, configured to obtain a first output matrix output by an augmented co-prime array and a second output matrix output by an augmented expanded co-prime array through a preset reception model, where the preset reception model includes a parallel line structure composed of an augmented co-prime array and an augmented expanded co-prime array;

[0116] A splicing module 202, configured to perform conjugate processing on the first output matrix to obtain conjugate data, and splice the first output matrix and the conjugate data to obtain a fusion matrix;

[0117] A GVF module 203, configured to process the fusion matrix and the second output matrix by using a GVF-based correlation entropy method to obtain a first target matrix corresponding to the fusion matrix and a second target matrix corresponding to the second output matrix;

[0118] A vectorization module 204, configured to calculate the cross-covariance matrix of the first target matrix and the second target matrix, and perform vectorization processing on the cross-covariance matrix;

[0119] A construction module 205, configured to decorrelate the vectorized cross-covariance matrix by a smoothing method, construct an autocovariance matrix, and perform eigenvalue decomposition on the autocovariance matrix to obtain a noise subspace;

[0120] A calculation module 206, configured to calculate two estimated angles of the direction of arrival according to the noise subspace through the MUSIC algorithm and the total least squares method.

[0121] In one embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as Figure 7As shown in the figure. The computer device includes a processor, a memory, a network interface, and a database connected via a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile and / or volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external client via a network connection. When the computer program is executed by the processor, it realizes the functions or steps on the server side of a data encryption method.

[0122] In one embodiment, a computer device is provided. The computer device can be a client, and its internal structure diagram can be as Figure 8 shown in the figure. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected via a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external server via a network connection. When the computer program is executed by the processor, it realizes the functions or steps on the client side of a data encryption method.

[0123] In one embodiment, a computer device is proposed, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the following steps are implemented: obtaining a first output matrix output by an augmented co-prime array and a second output matrix output by an augmented unfolded co-prime array through a preset reception model, where the preset reception model includes a parallel line structure composed of an augmented co-prime array and an augmented unfolded co-prime array;

[0124] Performing conjugate processing on the first output matrix to obtain conjugate data, and splicing the first output matrix and the conjugate data to obtain a fusion matrix;

[0125] Processing the fusion matrix and the second output matrix by using a GVF-based correlation entropy method to obtain a first target matrix corresponding to the fusion matrix and a second target matrix corresponding to the second output matrix;

[0126] Calculating the cross-covariance matrix of the first target matrix and the second target matrix, and performing vectorization processing on the cross-covariance matrix;

[0127] Decorrelate the cross-covariance matrix after vectorization processing by a smoothing method to construct an auto-covariance matrix, and perform eigen-decomposition on the auto-covariance matrix to obtain a noise subspace;

[0128] According to the noise subspace, calculate two estimated angles of the direction of arrival through the MUSIC algorithm and the total least squares method.

[0129] In one embodiment, a computer-readable storage medium is proposed. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the following steps are implemented: obtain a first output matrix output by an augmented co-prime array and a second output matrix output by an augmented expanded co-prime array through a preset reception model, and the preset reception model includes a parallel line structure composed of an augmented co-prime array and an augmented expanded co-prime array;

[0130] Perform conjugate processing on the first output matrix to obtain conjugate data, and splice the first output matrix and the conjugate data to obtain a fusion matrix;

[0131] Process the fusion matrix and the second output matrix by using the GVF-based correlation entropy method to obtain a first target matrix corresponding to the fusion matrix and a second target matrix corresponding to the second output matrix;

[0132] Calculate the cross-covariance matrix of the first target matrix and the second target matrix, and perform vectorization processing on the cross-covariance matrix;

[0133] Decorrelate the cross-covariance matrix after vectorization processing by a smoothing method to construct an auto-covariance matrix, and perform eigen-decomposition on the auto-covariance matrix to obtain a noise subspace;

[0134] According to the noise subspace, calculate two estimated angles of the direction of arrival through the MUSIC algorithm and the total least squares method.

[0135] It should be noted that the functions or steps that can be realized by the above computer-readable storage medium or computer device can refer to the relevant descriptions on the server side and the client side in the foregoing method embodiments. To avoid repetition, they will not be described one by one here.

[0136] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided in the present application can include non-volatile and / or volatile memories. Non-volatile memories can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memories can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0137] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the above division of each functional unit and module is used as an example. In actual applications, the above functions can be allocated to different functional units and modules according to needs, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above.

[0138] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included in the protection scope of the present invention.

Claims

1. A two-dimensional direction of arrival estimation method under impulse noise, characterized in that, Including the following steps: Obtain a first output matrix output by an augmented co-prime array and a second output matrix output by an augmented expanded co-prime array through a preset receiving model, where the preset receiving model includes a parallel line structure composed of an augmented co-prime array and an augmented expanded co-prime array; Perform conjugate processing on the first output matrix to obtain conjugate data, and splice the first output matrix and the conjugate data to obtain a fusion matrix; Process the fusion matrix and the second output matrix by using a correlation entropy method based on GVF to obtain a first target matrix corresponding to the fusion matrix and a second target matrix corresponding to the second output matrix; Calculate the cross-covariance matrix of the first target matrix and the second target matrix, and perform vectorization processing on the cross-covariance matrix; Perform decorrelation on the vectorized cross-covariance matrix by a smoothing method to construct an auto-covariance matrix, perform eigenvalue decomposition on the auto-covariance matrix to obtain a noise subspace; According to the noise subspace, calculate two estimated angles of the direction of arrival through the MUSIC algorithm and the total least squares method.

2. The two-dimensional direction of arrival estimation method under impulse noise according to claim 1, wherein, The expressions of the first output matrix output by the augmented co-prime array and the second output matrix output by the augmented expanded co-prime array are: where x AUCA (t) and x ECA (t) represent the first output matrix output by the augmented co-prime array and the second output matrix output by the augmented expanded co-prime array respectively, s(t) represents the signal matrix, and s(t) = [s1(t), …, s K (t)] T , n1(t) and n2(t) are impulsive noises with symmetric alpha-stable distributions, where A1 and A2 are array manifold matrices, containing array position information and information about the angle θ, and for convenience of processing, the information about the angle α is separated into the diagonal matrix Φ.

3. A two-dimensional direction-of-arrival estimation method under impulse noise according to claim 1, wherein The mathematical representation of the fusion matrix is: wherein is x ECA (t) in conjugate form, x CECA (t) is the fusion matrix, and are the conjugate forms of A2 and n2(t).

4. A two-dimensional direction-of-arrival estimation method under impulse noise according to claim 1, characterized in that, The step of processing the fusion matrix and the second output matrix by using a correlation entropy method based on GVF includes: Construct a preset function based on a generalized lopsided function, and the mathematical representation of the preset function is: where f(x) is a function based on a generalized lopsided function, and u, τ, p are hyperparameters, and the degree of suppression of impulse noise is controlled by adjusting their magnitudes; Process the fusion matrix and the second output matrix based on the preset function.

5. A two-dimensional direction-of-arrival estimation method under impulse noise according to claim 1, characterized in that, The mathematical representation of the cross-covariance matrix is: where E(·) represents the mathematical expectation, and R (i,j) represents the element in the i-th row and j-th column of the covariance matrix, and x AUCA (t) and x CECA (t) represent the i-th and j-th elements of x AUCA (t), x CECA (t).

6. A two-dimensional direction of arrival estimation method under impulse noise according to claim 1, characterized in that The step of performing vectorization processing on the cross-covariance matrix includes: Perform vectorization operation on the estimated cross-covariance matrix through a preset vectorization function, and the mathematical representation of the preset vectorization function is: r = vec(R) = vec(A1ΦR s (A 22 ) H ) = ((A 22 ) * ⊙A1)u = Au where \(A=(A 22 ) * \odot A_1\), and \(\odot\) represents the Kronecker product, is the signal covariance matrix, represents the power of the \(k\)th signal, where \(u\) is a vector and there is information about the angle \(\alpha\).

7. A two-dimensional direction of arrival estimation method under impulse noise according to claim 1, characterized in that The step of performing decorrelation on the vectorized cross-covariance matrix by a smoothing method to construct an auto-covariance matrix, perform eigenvalue decomposition on the auto-covariance matrix to obtain a noise subspace includes: Perform a redundancy removal operation on the vectorized cross-covariance matrix to obtain a target cross-covariance matrix; Select continuous arrays in the virtual array of the target cross-covariance matrix to obtain an array to be processed; Perform decorrelation on the array to be processed by a smoothing method to construct an auto-covariance matrix, perform eigenvalue decomposition on the auto-covariance matrix to obtain a noise subspace.

8. A two-dimensional direction-of-arrival estimation method under impulse noise according to claim 1, characterized in that The step of calculating two estimated angles of the direction of arrival through the MUSIC algorithm and the total least squares method according to the noise subspace includes: Based on the noise subspace, calculate a spatial spectrum function according to the MUSIC algorithm, and the mathematical representation of the spatial spectrum function is: Solve for α by using the total least squares method; Among them represents the estimated vector of u. Taking the angle θ as known information, an estimate is constructed where is the signal vector of the continuous virtual array after redundancy removal of the vector r Two estimated angles of the direction of arrival are obtained, where arcos(·) is the inverse cosine function and angle(·) represents taking the argument inside. Obviously, the angle α is paired with the estimated angle θ.

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