Direction of arrival estimation method, device, computer equipment, medium and product based on sensor array

Abstract

This application relates to a method, apparatus, computer device, medium, and product for direction-of-arrival (DOA) estimation based on a sensor array. The method includes: establishing a signal model of the source signal and the sensor array; determining a signal subspace based on the signal model; determining a first selection matrix and a second selection matrix; dividing the signal subspace into submatrices using the first selection matrix; obtaining a reference direction cosine based on the first submatrices; dividing the signal subspace into submatrices using the second selection matrix; obtaining an ambiguity direction cosine based on the second submatrices; performing phase compensation on the ambiguity direction cosine using the reference direction cosine to obtain a target direction cosine; and determining the two-dimensional DOA of the source signal based on the target direction cosine. This method can fully utilize the spatial response and polarization response information of the array output to achieve high-precision two-dimensional DOA estimation.

Description

Technical Field

[0001] This application relates to the field of sensor array technology, and in particular to a method, apparatus, computer device, medium, and product for direction-of-arrival estimation based on a sensor array. Background Art

[0002] Direction of Arrival (DOA) estimation is a key technology in the field of array signal processing. Its core objective is to accurately determine the azimuth of the source signal relative to the receiving array. By capturing and analyzing the signal transmitted by the target, the system can use DOA estimation technology to accurately obtain key directional information such as the azimuth and elevation angles of the target relative to the receiving antenna array or sensor array, thereby achieving precise positioning and tracking of the target.

[0003] However, in the theoretical modeling process for DOA estimation, it is usually assumed that the array structure is uniform or follows a specific design, and that the element spacing is less than or equal to half a wavelength. When the element spacing in the array is small, the electromagnetic fields between the elements will have significant mutual influence, i.e., mutual coupling. The mutual coupling effect will change the actual response characteristics of the array, making it significantly different from the response under ideal conditions, thereby reducing the accuracy of DOA estimation. Summary of the Invention

[0004] Therefore, it is necessary to provide a sensor array-based direction of arrival estimation method, apparatus, computer equipment, medium, and product that can improve the accuracy of DOA estimation in response to the above-mentioned technical problems.

[0005] In a first aspect, this application provides a direction-of-arrival estimation method based on a sensor array, including:

[0006] Establish signal models for the source signal and the sensor array, and determine the signal subspace based on the signal models;

[0007] Determine the first selection matrix and the second selection matrix; the first selection matrix is ​​used to obtain the elements in the signal subspace that satisfy the rotation invariance requirement of the polarization response; the second selection matrix is ​​used to obtain the elements in the signal subspace that satisfy the space invariance requirement.

[0008] The signal subspace is divided into submatrixes using a first selection matrix, and the reference direction cosine is obtained based on the first submatrix obtained from the division.

[0009] The signal subspace is divided into submatrixes using a second selection matrix, and the fuzzy direction cosine is obtained based on the second submatrix obtained from the division.

[0010] Phase compensation is performed on the ambiguous direction cosine using the reference direction cosine to obtain the target direction cosine. Based on the target direction cosine, the two-dimensional arrival direction of the source signal is determined; the two-dimensional arrival direction includes the azimuth and elevation angles.

[0011] The expression for the signal model is: ; where matrix A characterizes the spatial response of the sensor array, and matrix B characterizes the polarization response of the sensor array. Let be the source vector of the source signal at time t. Let be the spacetime Gaussian white noise vector at time t;

[0012] Where, the expression for matrix A is: , Let B be the spatial response vector generated when the k-th source signal arrives at the M-th element in the sensor array; the expression for matrix B is: , This is the polarization response vector generated when the k-th source signal arrives at the M-th element in the sensor array.

[0013] In one embodiment, the step of establishing the signal model of the source signal and the sensor array includes:

[0014] Based on the electrical and magnetic response vectors generated when the source signal reaches each electromagnetic vector sensor in the sensor array, the polarization response expression of the sensor array is obtained.

[0015] Based on the polarization response expression and the position information of the electromagnetic vector sensors in the sensor array, the spatial response expression of the sensor array is obtained;

[0016] The signal model is obtained based on the polarization response expression and the spatial response expression.

[0017] In one embodiment, the step of obtaining the signal subspace based on the signal model includes:

[0018] Obtain the signal covariance matrix of the signal model;

[0019] Eigenvalue decomposition is performed on the signal covariance matrix to obtain multiple eigenvalues ​​and their corresponding eigenvectors;

[0020] The signal subspace is obtained by combining the feature vectors.

[0021] In one embodiment, the step of obtaining the reference direction cosine based on the first sub-matrix obtained by partitioning includes:

[0022] The first submatrix obtained by partitioning is combined, and the combined matrix is ​​subjected to eigenvalue decomposition to obtain the first factor matrix;

[0023] Based on the diagonal elements of the first factor matrix, obtain the electric field response vector and the magnetic field response vector;

[0024] The reference direction cosine is obtained by performing a normalized vector cross product on the electric field response vector and the magnetic field response vector.

[0025] In one embodiment, the step of obtaining the fuzzy direction cosine based on the second sub-matrix obtained by partitioning includes:

[0026] Obtain the second factor matrix corresponding to the second submatrix;

[0027] By taking the phase of each diagonal element of the second factor matrix, the reference phase corresponding to the source signal is obtained;

[0028] Obtain the deterministic matrix of the signal model;

[0029] The product of the reference phase and the pseudo-inverse of the deterministic matrix is ​​used as the fuzzy direction cosine.

[0030] In one embodiment, the step of performing phase compensation on the ambiguous direction cosine using a reference direction cosine to obtain the target direction cosine includes:

[0031] Based on the signal period of the source signal and the reference direction cosine, phase compensation is performed on the fuzzy direction cosine to obtain the phase compensation value;

[0032] The product of the phase compensation value and the pseudo-inverse of the deterministic matrix is ​​used as the cosine of the target direction.

[0033] Secondly, this application also provides a direction-of-arrival estimation device based on a sensor array, comprising:

[0034] The signal model building module is used to build signal models of the source signal and the sensor array, and to determine the signal subspace based on the signal models.

[0035] The selection matrix determination module is used to determine a first selection matrix and a second selection matrix; the first selection matrix is ​​used to obtain the elements in the signal subspace that satisfy the rotation invariance requirement of the polarization response; the second selection matrix is ​​used to obtain the elements in the signal subspace that satisfy the space invariance requirement.

[0036] The reference direction acquisition module is used to divide the signal subspace into submatrixes using a first selection matrix, and to obtain the reference direction cosine based on the first submatrix obtained from the division.

[0037] The fuzzy direction acquisition module is used to divide the signal subspace into submatrixes using a second selection matrix, and to obtain the fuzzy direction cosine based on the second submatrix obtained from the division.

[0038] The direction of arrival acquisition module is used to perform phase compensation on the ambiguous direction cosine using the reference direction cosine to obtain the target direction cosine, and determine the two-dimensional direction of arrival of the source signal based on the target direction cosine; the two-dimensional direction of arrival includes azimuth and elevation angles.

[0039] The expression for the signal model is: ; where matrix A characterizes the spatial response of the sensor array, and matrix B characterizes the polarization response of the sensor array. Let be the source vector of the source signal at time t. Let be the spacetime Gaussian white noise vector at time t;

[0040] Where, the expression for matrix A is: , Let B be the spatial response vector generated when the k-th source signal arrives at the M-th element in the sensor array; the expression for matrix B is: , This is the polarization response vector generated when the k-th source signal arrives at the M-th element in the sensor array.

[0041] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method steps of any one of the first aspects.

[0042] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method steps of any one of the first aspects.

[0043] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, implements the method steps of any one of the first aspects.

[0044] The aforementioned sensor array-based direction-of-arrival (DOA) estimation method, apparatus, computer equipment, medium, and product establish a signal model of the source signal and the sensor array, determine the signal subspace based on the signal model, and obtain the elements in the subspace that satisfy the rotational invariance requirement of polarization response and the spatial invariance requirement by selecting matrices. Based on the submatrices obtained by partitioning the signal subspace, a coarse reference direction cosine and a high-precision fuzzy direction cosine are obtained. Phase compensation is performed on the fuzzy direction cosine using the reference direction cosine to obtain a high-precision, unfuzzy target direction cosine, ultimately yielding an accurate two-dimensional DOA. This method is applicable to scenarios with a limited number of array elements and a limited array space. While the array geometry is unconstrained, it reduces mutual coupling effects and can fully utilize the spatial and polarization response information output by the array to achieve high-precision two-dimensional DOA estimation. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the description of the embodiments of this application or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a flowchart illustrating a direction-of-arrival estimation method based on a sensor array in one embodiment;

[0047] Figure 2 This is a flowchart illustrating a direction-of-arrival estimation method based on a sensor array in another embodiment;

[0048] Figure 3 This is a graph showing the variation of the direction of arrival estimation in one embodiment;

[0049] Figure 4 This is a graph showing the variation of average runtime in one embodiment;

[0050] Figure 5 This is a structural block diagram of a sensor array-based direction-of-arrival estimation device in one embodiment;

[0051] Figure 6 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0053] In an exemplary embodiment, Figure 2 As shown, a direction-of-arrival (DOA) estimation method based on a sensor array is provided. The method is illustrated using an example of an array composed of multiple electromagnetic vector sensors arranged at irregular intervals, and includes steps 102 to 110. Wherein:

[0054] S102: Establish signal models of the source signal and sensor array, and determine the signal subspace based on the signal models.

[0055] Optionally, since source signals arriving at the sensor array from different directions will experience time delays or phase differences when reaching each array element, and these delays or phase differences are closely related to the direction of arrival (DOA), the geometric relationship of signal propagation needs to be considered when establishing the signal model. For example, in common cases such as the far-field plane wave assumption, the phase difference between array elements is related to the signal's angle of arrival, and this angle-related information is reflected in the signal model through mathematical expressions, becoming an important basis for subsequent DOA estimation.

[0056] Optionally, the signal model includes the array’s spatial response vector and polarization response vector, which can describe the array’s response to incident signals from different directions. Since the electromagnetic vector sensor (EMVS) array can also sense the electromagnetic field components of the output signal, the polarization response can usually be characterized by four parameters: azimuth angle, elevation angle, auxiliary polarization angle, and polarization phase difference.

[0057] The expression for the signal model is: ; where matrix A is used to characterize the spatial response of the sensor array; matrix B is used to characterize the polarization response of the sensor array; The source vector of the source signal at time t is used to characterize information such as the intensity or amplitude of the source signal at time t. Let t be the spatiotemporal Gaussian white noise vector at time t, used to simulate noise interference in the actual signal reception process.

[0058] Where, the expression for matrix A is: , Let A be the spatial response vector generated when the k-th source signal arrives at the M-th element in the sensor array. That is, each element in matrix A reflects the spatial response characteristics of different source signals on a specific element of the EMVS array. The expression for matrix B is: , Let B be the polarization response vector generated when the k-th source signal arrives at the M-th array element in the sensor array. Since different source signals have different polarization modes, the polarization information corresponding to the source signal can be represented in vector form through matrix B.

[0059] Furthermore, after constructing the signal model, a signal covariance matrix is ​​established based on the model and the collected effective signal data. This covariance matrix describes the correlation between signals, containing relevant information about the signals across different array elements or subarrays. Subsequently, by performing eigenvalue decomposition on the signal covariance matrix, estimates of the signal subspace can be obtained.

[0060] S104: Determine the first selection matrix and the second selection matrix; the first selection matrix is ​​used to obtain the elements in the signal subspace that satisfy the rotation invariance requirement of the polarization response; the second selection matrix is ​​used to obtain the elements in the signal subspace that satisfy the space invariance requirement.

[0061] Optionally, since the signal subspace contains many elements related to the polarization response, and the polarization response exhibits rotational invariance, the first selection matrix can be used to filter out elements from the complex signal subspace that satisfy the rotational invariance requirement of the polarization response. Rotational invariance means that when the polarization state of the source signal rotates within a certain range, certain characteristics of the polarization response remain unchanged. This eliminates the need for the algorithm to calculate and process each possible polarization rotation angle individually; instead, it can utilize this invariance to extract key polarization information. Therefore, by filtering elements that satisfy the rotational invariance requirement of the polarization response, the computational load and the difficulty of algorithm implementation can be reduced.

[0062] Similarly, in the signal subspace, the array's response to incident signals from different directions exhibits spatial invariance. The second selection matrix allows for the precise acquisition of elements that satisfy this spatial invariance requirement. Spatial invariance refers to the fact that when signals are incident on the sensor array from different directions, the relative spatial relationships between different array elements (such as element spacing and geometric layout) result in fixed signal phase differences, which are only related to the direction of signal arrival.

[0063] S106: Divide the signal subspace into submatrices using the first selection matrix, and obtain the reference direction cosine based on the first submatrix obtained from the division.

[0064] Optionally, the entire signal subspace is partitioned using a first selection matrix. The resulting first submatrix contains elements that satisfy the rotation invariance requirement of the polarization response. Therefore, the partitioned submatrices can be transformed into each other by multiplying by a specific diagonal factor matrix. Based on this, by performing eigenvalue decomposition on the results of specific combinations of different submatrices, a specific factor matrix can be obtained, whose diagonal elements are the ratios of different elements in the polarization response. Finally, the elements in the factor matrix are used to construct the specific vector required by the normalization (VCP) technique, and VCP is performed on the vector to obtain a coarse direction cosine.

[0065] S108: Divide the signal subspace into submatrices using the second selection matrix, and obtain the fuzzy direction cosine based on the second submatrix obtained from the division.

[0066] Alternatively, similar to the first submatrix, the second submatrixes divided by the second selection matrix can also be transformed into each other through a specific diagonal matrix. Furthermore, the diagonal elements in the second submatrix consist of the ratios of different spatial responses. By constructing a factor matrix, a specific vector required by the normalization (VCP) technique is constructed through the elements in the factor matrix, and VCP operations are performed on the vector to obtain the fuzzy direction cosine.

[0067] S110: Phase compensation is performed on the ambiguous direction cosine by the reference direction cosine to obtain the target direction cosine. Based on the target direction cosine, the two-dimensional arrival direction of the source signal is determined; the two-dimensional arrival direction includes the azimuth angle and the elevation angle.

[0068] Optionally, when the element spacing is greater than half a wavelength, since the exponential mapping form of the spatial response is periodic, the phase result of taking the phase of the diagonal elements of the matrix may be an incorrect phase value, that is, the fuzzy direction cosine is an incorrect phase value. Since the reference direction cosine is obtained independently of the spatial response, that is, it is unfuzzy, phase compensation recovery of the fuzzy direction cosine obtained through spatial rotation invariance can yield a high-precision, unfuzzy direction cosine estimate, that is, the target direction cosine, ultimately achieving high-precision two-dimensional direction of arrival (2D-DOA) estimation.

[0069] In the aforementioned sensor array-based direction-of-arrival (DOA) estimation method, a signal model of the source signal and the sensor array is established. Based on the signal model, a signal subspace is determined. By selecting matrices, elements in the subspace that satisfy the rotational invariance requirement of polarization response and the spatial invariance requirement are obtained. Based on the submatrix obtained by partitioning the signal subspace, a coarse reference direction cosine and a high-precision fuzzy direction cosine are obtained. The fuzzy direction cosine is phase-compensated using the reference direction cosine to obtain a high-precision, unfuzzy target direction cosine. Finally, an accurate two-dimensional DOA is obtained. This method is applicable to scenarios with a limited number of array elements and a limited array space. While the array geometry is unconstrained, it reduces mutual coupling effects and can fully utilize the spatial and polarization response information output by the array to achieve high-precision two-dimensional DOA estimation.

[0070] In an exemplary embodiment, the step of establishing a signal model of the source signal and the sensor array includes: obtaining a polarization response expression of the sensor array based on the electrical response vector and magnetic response vector generated when the source signal reaches each electromagnetic vector sensor in the sensor array; obtaining a spatial response expression of the sensor array based on the polarization response expression and the position information of the electromagnetic vector sensors in the sensor array; and obtaining a signal model based on the polarization response expression and the spatial response expression.

[0071] Optionally, when the source signal arrives at each electromagnetic vector sensor in the sensor array, it generates corresponding electrical and magnetic response vectors. These vectors contain the polarization information of the source signal at the sensor, such as the strength and direction of the electric and magnetic fields. By analyzing and processing these electrical and magnetic response vectors, the polarization response expression of the sensor array can be obtained, which can quantitatively describe the response characteristics of the sensor array to source signals with different polarization states.

[0072] Furthermore, after obtaining the polarization response expression, the position information of the electromagnetic vector sensors in the sensor array is also considered. The sensor position information is crucial for determining the signal propagation path in space and the time delay and phase difference at different sensors. Since the source signals received by sensors at different locations differ spatially, these differences are closely related to the sensor positions and the direction of arrival (DOA). By combining the polarization response expression with the sensor position information, the spatial response expression of the sensor array can be derived, reflecting characteristics such as the spatial phase relationship between the sensors when the source signal arrives from different directions.

[0073] Furthermore, based on the obtained polarization response expression and spatial response expression, the two are combined to construct a complete signal model. The signal model can comprehensively describe the interaction between the source signal and the sensor array, including the polarization characteristics of the source signal, its propagation in space, and the sensor array's reception and response to these signals.

[0074] For example, a co-located EMVS consists of six components (three electric dipoles and three magnetic rings) located at a point in space, which can measure electric and magnetic fields respectively. For a scenario where k fully polarized transverse electromagnetic (TEM) plane waves impact the EMVS, the noise-free output vector corresponding to the k-th (k=1, 2, ..., k) TEM wave is... (That is, the k-th polarization response vector) can be expressed as:

[0075]

[0076] in, , , and These represent the elevation angle, azimuth angle, auxiliary polarization angle, and polarization phase difference, respectively.

[0077] Furthermore, It can be broken down into:

[0078]

[0079] in:

[0080]

[0081]

[0082] in, It is a matrix that is only related to direction. It is a vector that is only related to polarization. Therefore, It can be divided into two parts, where the first three entities correspond to the electrical response vector. The remaining part corresponds to the magnetic response vector. ,Right now:

[0083]

[0084]

[0085] Where b(k) represents the k-th element in vector b, This indicates transpose.

[0086] For the EMVS matrix and The VCP between them satisfies:

[0087]

[0088] in, This represents the vector cross product operation. Indicates conjugate. This represents the Frobenius norm.

[0089] Furthermore, for irregularly spaced EMVS arrays, the irregularity of the EMVS positions necessitates considering the coordinates of each element in the reference coordinate system when determining the DOA expression for the source signal. Based on this, for an M-element EMVS array with arbitrary array geometry, This represents the position of the m-th EMVS.

[0090] For example, at time t, the array response (i.e., signal model) of k far-field, incoherent, narrowband (carrier wavelength denoted by λ) TEM sources can be expressed as:

[0091]

[0092] in, This represents the source vector at time t. Represents the spacetime Gaussian white noise vector. And there are:

[0093] ; ; ; ; ;

[0094] in, The time delay when the k-th source signal reaches the M-th array element. This is the position information of the Mth array element. Let be the direction cosine of the k-th source signal.

[0095] In this embodiment, by combining the polarization response sensed and output by the electromagnetic vector sensor array in the signal model, the polarization response information can be fully utilized to more finely characterize the source signals arriving from different directions, so that the signal model can more accurately reflect the propagation characteristics and response modes of the signal in the sensor array.

[0096] In an exemplary embodiment, the step of obtaining a signal subspace based on a signal model includes: obtaining the signal covariance matrix of the signal model; performing eigenvalue decomposition on the signal covariance matrix to obtain multiple eigenvalues ​​and corresponding eigenvectors; and obtaining the signal subspace based on the combination of eigenvectors.

[0097] Optionally, based on the signal model, the effective signal information actually received by the sensor array is obtained. Based on the effective signal, the signal covariance matrix of the signal model is obtained. The signal covariance matrix describes the correlation between signals, reflecting the degree of correlation between signals received at different times or by different array elements. Then, eigenvalue decomposition is performed on the signal covariance matrix. Eigenvalue decomposition is a method of decomposing a matrix into eigenvalues ​​and eigenvectors. For the signal covariance matrix, eigenvalue decomposition can reveal its inherent structure and characteristics. Specifically, after eigenvalue decomposition, a set of eigenvalues ​​and corresponding eigenvectors are obtained. The eigenvalues ​​reflect the importance or "weight" of the "component" represented by the corresponding eigenvector in the entire signal covariance matrix, while the eigenvectors constitute a special vector space. They have specific linear relationships with each other, and these eigenvectors carry different modes and characteristic information of the signal.

[0098] Furthermore, the signal subspace is obtained by combining eigenvectors. Typically, eigenvectors corresponding to larger eigenvalues ​​are used to span the signal subspace because these eigenvectors represent components that constitute a larger proportion of the signal and better reflect its main features and information. Eigenvectors corresponding to smaller eigenvalues ​​are often considered noise-related and are excluded from the signal subspace construction. By selecting and combining appropriate eigenvectors, the signal subspace can be constructed, containing the core information of the signal.

[0099] For example, in conjunction with the above embodiments, if and If unrelated, then The covariance matrix is:

[0100]

[0101] in, This indicates the conjugate transpose. Represents the covariance matrix of the source. The power representing the noise. This represents a 6M×6M identity matrix.

[0102] In the form of eigenvalue decomposition (EVD), It can be represented as:

[0103]

[0104] in, and Let m represent the m-th eigenvalue and the m-th eigenvector, respectively, where the eigenvalue satisfies:

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] in, This represents the operation of constructing a diagonal matrix. and These are the signal subspace and the noise subspace, respectively. Because... and Spanning the same subspace, that is:

[0113]

[0114] in, It is a non-singular matrix. When L (L > 1) snapshots are available, It can be estimated in the following ways:

[0115]

[0116] Therefore, its EVD is represented as:

[0117]

[0118] in, , , , , , , and They represent respectively to , , , , , , and The estimated value.

[0119] In this embodiment, by obtaining the signal covariance matrix of the signal model, eigenvalues ​​are decomposed into multiple eigenvalues ​​and corresponding eigenvectors. Based on the combination of eigenvectors, the signal subspace is obtained, which can separate the feature information and noise influence in the signal subspace and improve the accuracy of the signal space.

[0120] In an exemplary embodiment, the step of obtaining the reference direction cosine based on the first sub-matrix obtained by partitioning includes: combining the first sub-matrix obtained by partitioning; performing eigenvalue decomposition on the combined matrix to obtain a first factor matrix; obtaining the electric field response vector and the magnetic field response vector based on the diagonal elements of the first factor matrix; and performing normalized vector cross product processing on the electric field response vector and the magnetic field response vector to obtain the reference direction cosine.

[0121] Optionally, during signal processing, based on the rotational invariance of the polarization response in the signal subspace, a first sub-matrix is ​​obtained by partitioning the signal subspace using a specific selection matrix. Each of the first sub-matrices contains specific information related to the polarization response. Through a specific combination method, these dispersed sub-matrices are integrated to comprehensively reflect the characteristic relationship of the signal in terms of polarization. Subsequently, eigenvalue decomposition is performed on the combined matrix. The first factor matrix obtained after eigenvalue decomposition carries the key characteristics contained in the combined matrix.

[0122] Optionally, the diagonal elements of the first factor matrix contain key information closely related to the polarization response. Necessary information for constructing the electric field response vector and the magnetic field response vector can be extracted from them. The electric field response vector and the magnetic field response vector are important mathematical representations for describing the polarization characteristics of a signal, and can comprehensively characterize the polarization state, direction and other key features of the signal in the electromagnetic field.

[0123] Optionally, the Normalized Vector Cross Product (VCP) technique is a processing method unique to EMVS. It normalizes the acquired electric and magnetic field response vectors, eliminating the influence of factors such as vector amplitude differences on the results, allowing subsequent cross product operations to focus more on the directional characteristics of the vectors. The final reference direction cosine is an important intermediate result, representing the angular information of the signal in a certain dimension, and is the data basis for 2D-DOA estimation.

[0124] For example, It can be rewritten as:

[0125]

[0126] in, .

[0127] Furthermore, we can obtain:

[0128]

[0129] definition , .

[0130] because If is a constant, then:

[0131]

[0132] Therefore, the direction cosine can be estimated from the normalized polarization response vector, for example, by using a signal processing algorithm (ESPRIT-Like) to determine the direction cosine from the signal subspace. , that is:

[0133]

[0134] in, Indicates taking The qth row, i.e. Define the first choice matrix as:

[0135]

[0136] in, Represents the identity matrix In the v-th row, then:

[0137]

[0138] Will Substituting, we get:

[0139]

[0140] in, and These represent the operations of taking the matrix inverse and taking the pseudo-inverse, respectively.

[0141] Therefore, the left side of the formula matches the EVD expression, that is... EVD can be obtained and Therefore, for EVD can be obtained and The estimated values ​​are denoted as follows: and Then, the residual factor matrix can be represented as:

[0142]

[0143] make for The k-th diagonal element. Construction and The reference direction cosine can be obtained using the following formula:

[0144]

[0145] Furthermore, the 2D-DOA calculation method is as follows:

[0146]

[0147]

[0148] in, of The sign is determined by the sign of the symbol. Because... The resulting displacement effect has been The calculation process is compensated for, therefore the estimated 2D-DOA is automatically matched. It should be noted that... It is independent of the spatial response moment A, which includes the geometry of the EMVS array. Therefore, It is unambiguous.

[0149] In this embodiment, by constructing a specific selection matrix, the signal subspace is divided into submatrixes. Based on the rotation invariance between different submatrixes, they can be transformed into each other through factor matrices in a specific diagonal matrix form. By decomposing the eigenvalues ​​of different combinations of submatrices, factor matrices are obtained, which can accurately obtain the reference direction cosine.

[0150] In an exemplary embodiment, the step of obtaining the fuzzy direction cosine based on the second sub-matrix obtained by partitioning includes: obtaining the second factor matrix corresponding to the second sub-matrix; taking the phase of the diagonal elements of the second factor matrix respectively to obtain the reference phase corresponding to the source signal; obtaining the deterministic matrix of the signal model; and using the product of the reference phase and the pseudo-inverse of the deterministic matrix as the fuzzy direction cosine.

[0151] Optionally, in signal processing, based on the inherent spatial rotation invariance of the signal subspace, a selection matrix is ​​used to partition the signal subspace into a second submatrix, which contains information related to spatial rotation invariance. Similar to the processing of the first submatrix, a second factor matrix corresponding to the second submatrix is ​​obtained, where the diagonal elements of the second factor matrix typically contain information related to the spatial response.

[0152] Furthermore, considering the spatial rotation invariance, the phase of the diagonal elements of the second factor matrix is ​​taken, and this information is converted into more intuitive phase information. The phase information can reflect the relative phase relationship of the signal source on different array elements. Because in array signal processing, the arrival direction of the signal source is closely related to the phase difference between array elements, the phase of these diagonal elements can be used as the reference phase of the source signal, providing a basis for subsequent calculation of fuzzy direction cosine.

[0153] Optionally, the reference phase is a key intermediate quantity for calculating the fuzzy direction cosine. It reflects the phase change of the signal during its propagation in space due to the different array element positions and the direction of arrival of the signal source. Although what we get at this time is a preliminary phase information that may be ambiguous, it provides an important foundation for subsequent compensation processing. By further processing these reference phases, we can get closer to the final accurate direction cosine.

[0154] For example, for any array geometry, the following condition is met:

[0155]

[0156] in, , .

[0157] Define the selection matrix as follows:

[0158]

[0159] Then, rotation invariance can be expressed as:

[0160]

[0161] Similarly, using replace We can obtain:

[0162]

[0163] Therefore, EVD on the right side of the formula provides... and The estimate. Assumptions and All have been estimated using the ESPRIT-Like algorithm, then It can be estimated using the following formula:

[0164]

[0165] If the space between array elements satisfies Then we have:

[0166]

[0167] in, This represents the phase take operation. It can be represented in matrix form as follows:

[0168]

[0169] in:

[0170]

[0171] Since F is deterministic, the fuzzy direction cosine can be obtained through spatial rotation invariance:

[0172]

[0173] in, , express The kth diagonal element.

[0174] In this embodiment, the signal subspace is divided into submatrixes by selecting a matrix, and the combination result of specific submatrixes is decomposed by spatial rotation invariance to obtain a factor matrix whose diagonal elements are spatial response ratios. The phase of the diagonal elements of the factor matrix is ​​taken and multiplied by the pseudo-inverse of the deterministic matrix to obtain a high-precision fuzzy direction cosine.

[0175] In an exemplary embodiment, the step of performing phase compensation on the fuzzy direction cosine using a reference direction cosine to obtain the target direction cosine includes: performing phase compensation on the fuzzy direction cosine based on the signal period of the source signal and the reference direction cosine to obtain a phase compensation value; and using the product between the phase compensation value and the pseudo-inverse matrix of the deterministic matrix as the target direction cosine.

[0176] Optionally, the signal period of the source signal reflects the repetitive pattern of the signal in time. Due to the influence of factors such as spatial response, there is phase ambiguity in the fuzzy direction cosine. The time periodic information contained in the signal period can be used to judge and correct the phase deviation based on the pattern of the signal itself.

[0177] Furthermore, the reference direction cosine is the relatively accurate and unambiguous direction cosine information that has already been acquired. Since the reference direction cosine correctly reflects the angular relationship of the signal in a certain dimension, by utilizing the phase difference between it and the ambiguous direction cosine, combined with the periodic constraint provided by the signal period, the specific phase difference value that needs to be compensated for in the ambiguous direction cosine can be calculated, i.e., the phase compensation value. This allows the phase of the ambiguous direction cosine to approach the accurate phase of the reference direction cosine, eliminating the ambiguity in the ambiguous direction cosine. Multiplying the phase compensation value by the pseudo-inverse matrix of the deterministic matrix yields the target direction cosine. The target direction cosine is the result after phase compensation; it eliminates the ambiguity present in the previous ambiguous direction cosine and accurately reflects the direction cosine information of the source signal. Finally, based on the established relationship between the target direction cosine and the 2D-DOA, the 2D-DOA of the source signal can be accurately determined, achieving a high-precision estimation of the source signal's direction of arrival.

[0178] For example, due to exponential mapping It is periodic and repeats at intervals of 2π, therefore once ,formula This may be invalid. Therefore, it should be modified to:

[0179]

[0180] in, If it is an integer, then:

[0181]

[0182] in, It is a vector of real-valued integers.

[0183] To accurately estimate the direction cosine from the spatial response vector, it is necessary to first determine ,because The direction cosine has been estimated using the normalized VCP technique; therefore, the constructed direction cosine is... It should be:

[0184]

[0185] therefore, It can be determined as follows:

[0186]

[0187] Afterwards, it can be restored in the following ways. True phase:

[0188]

[0189] Then, the cosine of the target direction is determined in the following way:

[0190]

[0191] Finally, the 2D-DOA estimate is:

[0192]

[0193]

[0194] In this embodiment, phase compensation is performed on the fuzzy direction cosine by using the reference direction cosine, which enables unfuzzy high-precision direction cosine estimation, thereby obtaining high-precision two-dimensional direction of arrival estimation.

[0195] In an exemplary embodiment, Figure 2 As shown, a direction-of-arrival estimation method based on a sensor array is provided, which includes the following steps:

[0196] Based on the electrical and magnetic response vectors generated when the source signal reaches each electromagnetic vector sensor in the sensor array, the polarization response expression of the sensor array is obtained; based on the polarization response expression and the position information of the electromagnetic vector sensors in the sensor array, the spatial response expression of the sensor array is obtained; based on the polarization response expression and the spatial response expression, the signal model is obtained.

[0197] The expression for the signal model is: ; where matrix A characterizes the spatial response of the sensor array, and matrix B characterizes the polarization response of the sensor array. Let be the source vector of the source signal at time t. Let be the spacetime Gaussian white noise vector at time t;

[0198] Where, the expression for matrix A is: , Let B be the spatial response vector generated when the k-th source signal arrives at the M-th element in the sensor array; the expression for matrix B is: , This is the polarization response vector generated when the k-th source signal arrives at the M-th element in the sensor array.

[0199] Obtain the signal covariance matrix of the signal model; perform eigenvalue decomposition on the signal covariance matrix to obtain multiple eigenvalues ​​and their corresponding eigenvectors; obtain the signal subspace based on the combination of eigenvectors.

[0200] Determine the first selection matrix and the second selection matrix; the first selection matrix is ​​used to obtain the elements in the signal subspace that satisfy the rotation invariance requirement of the polarization response; the second selection matrix is ​​used to obtain the elements in the signal subspace that satisfy the space invariance requirement.

[0201] The signal subspace is divided into submatrices using a first selection matrix. The first submatrices are then combined, and the combined matrix is ​​subjected to eigenvalue decomposition to obtain a first factor matrix. The electric field response vector and magnetic field response vector are obtained based on the diagonal elements of the first factor matrix. The electric field response vector and magnetic field response vector are then subjected to normalized vector cross product processing to obtain the reference direction cosine.

[0202] The signal subspace is divided into submatrices using the second selection matrix to obtain the second factor matrix corresponding to the second submatrix; the phase of the diagonal elements of the second factor matrix is ​​taken to obtain the reference phase corresponding to the source signal; the deterministic matrix of the signal model is obtained; and the product of the reference phase and the pseudo-inverse of the deterministic matrix is ​​used as the fuzzy direction cosine.

[0203] Based on the signal period of the source signal and the reference direction cosine, phase compensation is performed on the fuzzy direction cosine to obtain the phase compensation value; the product between the phase compensation value and the pseudo-inverse matrix of the deterministic matrix is ​​used as the target direction cosine.

[0204] The two-dimensional arrival direction of the source signal is determined based on the cosine of the target direction; the two-dimensional arrival direction includes the azimuth and elevation angles.

[0205] For example, extensive simulations using Monte Carlo experiments were conducted to evaluate the performance of the proposed method for 2D-DOA estimation in the embodiments of this application. Assuming a signal-to-noise ratio (SNR) of SNR = 10 dB, a snapshot number L = 200, and k = 3 far-field, incoherent, narrowband TEM sources impacting the EMVS array, the source signal parameters are as follows: , , , The root mean square error (RMSE) is used as the evaluation metric, and the calculation formula is as follows:

[0206]

[0207] in, Indicates the time of the j-th Monte Carlo experiment The estimate, Same thing.

[0208] Furthermore, the experimental results are as follows: Figure 3 and Figure 4 As shown. Figure 3 The curves showing the RMSE of the DOA estimate as a function of M when the elements of an irregularly spaced EMVS array are randomly distributed in three-dimensional space. Figure 3 The curve corresponding to the legend 'Proposed' in the figure represents the method provided in the embodiments of this application, and is compared with the theoretical lower bound of the estimation accuracy of the Beam-MUSIC algorithm, the ESPRIT-Like algorithm, and the Cramer-Rao bound (CRB). Figure 3 It is known that as the array aperture increases (M becomes larger), the RMSE of the method in this application gradually decreases. However, the comparison algorithms Beam-MUSIC and ESPRIT-Like are not sensitive to large array apertures. Therefore, the direction of arrival estimation method based on sensor array provided in this application can improve the accuracy of DOA estimation.

[0209] Furthermore, Figure 4 When the array elements of an irregularly spaced EMVS array are randomly distributed in a three-dimensional space, the method and comparison algorithm provided in this application present an average running time (ART) curve as a function of M. Figure 4 It is known that the ART of all algorithms increases with the increase of M. However, the DOA estimation method based on sensor array provided in this application has lower complexity while improving the accuracy of DOA estimation.

[0210] In this embodiment, a signal model of the source signal and the sensor array is established, and a signal subspace is determined based on the signal model. By selecting matrices, elements in the subspace that satisfy the rotation invariance requirement of polarization response and the spatial invariance requirement are obtained respectively. Based on the submatrix obtained by dividing the signal subspace, a coarse reference direction cosine and a high-precision fuzzy direction cosine are obtained. The fuzzy direction cosine is phase-compensated by the reference direction cosine to obtain a high-precision, unfuzzy target direction cosine. Finally, an accurate two-dimensional arrival direction is obtained. This method is applicable to scenarios with a limited number of array elements and a limited array space. While the array geometry is unconstrained, it reduces mutual coupling effects and can fully utilize the spatial response and polarization response information output by the array to achieve high-precision two-dimensional arrival direction estimation.

[0211] It should be understood that although the steps in the flowcharts of the above embodiments are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the above embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0212] Based on the same inventive concept, this application also provides a sensor array-based direction-of-arrival estimation device for implementing the sensor array-based direction-of-arrival estimation method described above. The solution provided by this device is similar to the implementation described in the above method; therefore, the specific limitations of one or more sensor array-based direction-of-arrival estimation device embodiments provided below can be found in the limitations of the sensor array-based direction-of-arrival estimation method described above, and will not be repeated here.

[0213] In an exemplary embodiment, Figure 5 As shown, a direction-of-arrival estimation device based on a sensor array is provided, including: a signal model establishment module 10, a selection matrix determination module 20, a reference direction acquisition module 30, a fuzzy direction acquisition module 40, and an arrival direction acquisition module 50, wherein:

[0214] The signal model establishment module 10 is used to establish the signal model of the source signal and the sensor array, and to determine the signal subspace based on the signal model.

[0215] The selection matrix determination module 20 is used to determine a first selection matrix and a second selection matrix; the first selection matrix is ​​used to obtain elements in the signal subspace that satisfy the rotation invariance requirement of the polarization response; the second selection matrix is ​​used to obtain elements in the signal subspace that satisfy the space invariance requirement.

[0216] The reference direction acquisition module 30 is used to divide the signal subspace into submatrices using a first selection matrix, and to obtain the reference direction cosine based on the first submatrices obtained from the division.

[0217] The fuzzy direction acquisition module 40 is used to divide the signal subspace into submatrixes using a second selection matrix, and to obtain the fuzzy direction cosine based on the second submatrix obtained from the division.

[0218] The direction of arrival acquisition module 50 is used to perform phase compensation on the ambiguous direction cosine by using the reference direction cosine to obtain the target direction cosine, and determine the two-dimensional direction of arrival of the source signal based on the target direction cosine; the two-dimensional direction of arrival includes azimuth and elevation angles.

[0219] The expression for the signal model is: ; where matrix A characterizes the spatial response of the sensor array, and matrix B characterizes the polarization response of the sensor array. Let be the source vector of the source signal at time t. Let be the spacetime Gaussian white noise vector at time t;

[0220] Where, the expression for matrix A is: , Let B be the spatial response vector generated when the k-th source signal arrives at the M-th element in the sensor array; the expression for matrix B is: , This is the polarization response vector generated when the k-th source signal arrives at the M-th element in the sensor array.

[0221] In an exemplary embodiment, the signal model building module 10 is further configured to obtain the polarization response expression of the sensor array based on the electrical response vector and magnetic response vector generated when the source signal reaches each electromagnetic vector sensor in the sensor array; obtain the spatial response expression of the sensor array based on the polarization response expression and the position information of the electromagnetic vector sensors in the sensor array; and obtain the signal model based on the polarization response expression and the spatial response expression.

[0222] In an exemplary embodiment, the signal model building module 10 is further configured to obtain the signal covariance matrix of the signal model; perform eigenvalue decomposition on the signal covariance matrix to obtain multiple eigenvalues ​​and corresponding eigenvectors; and obtain the signal subspace based on the combination of eigenvectors.

[0223] In an exemplary embodiment, the reference direction acquisition module 30 is further configured to combine the first sub-matrices obtained by partitioning, perform eigenvalue decomposition on the combined matrix to obtain a first factor matrix; obtain the electric field response vector and the magnetic field response vector based on the diagonal elements of the first factor matrix; and perform normalized vector cross product processing on the electric field response vector and the magnetic field response vector to obtain the reference direction cosine.

[0224] In an exemplary embodiment, the fuzzy direction acquisition module 40 is further configured to acquire the second factor matrix corresponding to the second sub-matrix; take the phase of the diagonal elements of the second factor matrix respectively to obtain the reference phase corresponding to the source signal; acquire the deterministic matrix of the signal model; and use the product of the reference phase and the pseudo-inverse of the deterministic matrix as the fuzzy direction cosine.

[0225] In an exemplary embodiment, the direction acquisition module 50 is further configured to perform phase compensation on the fuzzy direction cosine based on the signal period of the source signal and the reference direction cosine to obtain a phase compensation value; and to use the product between the phase compensation value and the pseudo-inverse matrix of the deterministic matrix as the target direction cosine.

[0226] The modules in the aforementioned sensor array-based direction-of-arrival estimation device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0227] In one exemplary embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 6 As shown, the computer device includes a processor, memory, input / output interfaces, a communication interface, a display unit, and an input device. The processor, memory, and input / output interfaces are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The input / output interfaces are used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, Near Field Communication (NFC), or other technologies. When executed by the processor, the computer program implements a direction-of-arrival estimation method based on a sensor array. The display unit is used to form a visually visible image and can be a display screen, a projection device, or a virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads set on the casing of the computer device, or external keyboards, touchpads, or mice, etc.

[0228] Those skilled in the art will understand that Figure 6 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0229] In one exemplary embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0230] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0231] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0232] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, artificial intelligence (AI) processors, etc., and are not limited to these.

[0233] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this application.

[0234] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A direction-of-arrival estimation method based on a sensor array, characterized in that, The method is applied to a sensor array consisting of multiple electromagnetic vector sensors arranged at irregular intervals; the method includes: Establish a signal model for the source signal and the sensor array, and determine the signal subspace based on the signal model; A first selection matrix and a second selection matrix are determined; the first selection matrix is ​​used to obtain the elements in the signal subspace that satisfy the rotation invariance requirement of the polarization response; the second selection matrix is ​​used to obtain the elements in the signal subspace that satisfy the space invariance requirement. The signal subspace is divided into submatrixes using the first selection matrix, and the reference direction cosine is obtained based on the first submatrix obtained from the division. The signal subspace is divided into submatrixes using the second selection matrix, and the fuzzy direction cosine is obtained based on the second submatrix obtained from the division. Phase compensation is performed on the ambiguous direction cosine using the reference direction cosine to obtain the target direction cosine. Based on the target direction cosine, the two-dimensional arrival direction of the source signal is determined. The two-dimensional arrival direction includes azimuth and elevation angles. The expression for the signal model is as follows: ; where matrix A characterizes the spatial response of the sensor array, and matrix B characterizes the polarization response of the sensor array. Let be the source vector of the source signal at time t. Let be the spacetime Gaussian white noise vector at time t; The expression for matrix A is as follows: , Let B be the spatial response vector generated when the k-th source signal arrives at the M-th element in the sensor array; the expression for matrix B is: , It is the polarization response vector generated when the k-th source signal arrives at the M-th array element in the sensor array.

2. The method according to claim 1, characterized in that, The establishment of the signal model between the source signal and the sensor array includes: Based on the electrical and magnetic response vectors generated when the source signal reaches each electromagnetic vector sensor in the sensor array, the polarization response expression of the sensor array is obtained. Based on the polarization response expression and the position information of the electromagnetic vector sensors in the sensor array, the spatial response expression of the sensor array is obtained; The signal model is obtained based on the polarization response expression and the spatial response expression.

3. The method according to claim 1, characterized in that, The step of obtaining the signal subspace based on the signal model includes: Obtain the signal covariance matrix of the signal model; The signal covariance matrix is ​​subjected to eigenvalue decomposition to obtain multiple eigenvalues ​​and eigenvectors corresponding to the eigenvalues; The signal subspace is obtained based on the combination of the feature vectors.

4. The method according to claim 1, characterized in that, The step of obtaining the reference direction cosine based on the first sub-matrix obtained by partitioning includes: The first submatrix obtained by partitioning is combined, and the combined matrix is ​​subjected to eigenvalue decomposition to obtain the first factor matrix; Based on the diagonal elements of the first factor matrix, obtain the electric field response vector and the magnetic field response vector; The electric field response vector and the magnetic field response vector are subjected to normalized vector cross product processing to obtain the reference direction cosine.

5. The method according to claim 1, characterized in that, The step of obtaining the fuzzy direction cosine based on the second sub-matrix obtained from the partitioning includes: Obtain the second factor matrix corresponding to the second submatrix; The reference phase corresponding to the source signal is obtained by taking the phase of each diagonal element of the second factor matrix; Obtain the deterministic matrix of the signal model; The product of the reference phase and the pseudo-inverse of the deterministic matrix is ​​used as the fuzzy direction cosine.

6. The method according to claim 5, characterized in that, The step of performing phase compensation on the ambiguous direction cosine using the reference direction cosine to obtain the target direction cosine includes: Based on the signal period of the source signal and the reference direction cosine, phase compensation is performed on the fuzzy direction cosine to obtain a phase compensation value; The product of the phase compensation value and the pseudo-inverse of the deterministic matrix is ​​taken as the cosine of the target direction.

7. A direction-of-arrival estimation device based on a sensor array, characterized in that, The device includes: The signal model building module is used to build a signal model of the source signal and the sensor array, and to determine the signal subspace based on the signal model. The selection matrix determination module is used to determine a first selection matrix and a second selection matrix; the first selection matrix is ​​used to obtain elements in the signal subspace that satisfy the rotation invariance requirement of the polarization response; the second selection matrix is ​​used to obtain elements in the signal subspace that satisfy the space invariance requirement. The reference direction acquisition module is used to divide the signal subspace into sub-matrixes using the first selection matrix, and to obtain the reference direction cosine based on the first sub-matrix obtained from the division. The fuzzy direction acquisition module is used to divide the signal subspace into submatrixes using the second selection matrix, and to obtain the fuzzy direction cosine based on the second submatrix obtained from the division. The direction of arrival acquisition module is used to perform phase compensation on the fuzzy direction cosine using the reference direction cosine to obtain the target direction cosine, and determine the two-dimensional direction of arrival of the source signal based on the target direction cosine; the two-dimensional direction of arrival includes azimuth and pitch angle. The expression for the signal model is as follows: ; where matrix A characterizes the spatial response of the sensor array, and matrix B characterizes the polarization response of the sensor array. Let be the source vector of the source signal at time t. Let be the spacetime Gaussian white noise vector at time t; The expression for matrix A is as follows: , Let B be the spatial response vector generated when the k-th source signal arrives at the M-th element in the sensor array; the expression for matrix B is: , It is the polarization response vector generated when the k-th source signal arrives at the M-th array element in the sensor array.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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