Precise near-field polarization multi-parameter joint estimation method based on L-shaped cold array

Abstract

The application discloses a precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array, which is used for estimating the spatial position parameters and polarization domain parameters of multiple narrow-band near-field sources in a three-dimensional near-field source positioning scene. The method receives signals through the construction of the L-shaped COLD array, divides the linear array into multiple sub-arrays, calculates the cross-covariance matrix by using the received signal vectors of the sub-arrays and performs vectorization processing, separates the manifold matrix estimation value in combination with the TALS theory, and further extracts the polarization domain parameters. The non-ambiguous delay phase in the sub-arrays divided by the two linear arrays is used for the coarse estimation of the spatial position parameters, and finally, the precise estimation value is obtained. The method has the advantages that the influence of path loss and noise interference is small, the estimation precision is higher, the array does not need to be symmetrically constructed, the distance between the array elements does not need to be limited to one fourth of the wavelength, and the array aperture is expanded.

Description

Technical Field

[0001] This invention relates to a multi-target narrowband signal source localization technique, and more particularly to a precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD (Co-centered Orthogonal Loop and Dipole) array. Background Technology

[0002] The localization of multiple target narrowband signal sources is a crucial topic in array signal processing, playing a vital role in radar, wireless communication, and other fields. Compared to far-field sources, near-field sources are located within the Fresnel zone, and their wavefronts cannot be approximated as planar wavefronts but rather exist as spherical wavefronts. The phase must be characterized using the Direction of Arrival (DOA) and range parameters. Massive Multiple Input Multiple Output (MIMO) systems, as a key technology in mobile communication, utilize large array apertures in base station deployments, making target narrowband signal sources more likely to be located in the near-field region. Furthermore, the phase response of a spherical wavefront is a nonlinear function, making algorithm design more complex than for far-field sources. Therefore, the localization problem of near-field sources has attracted significant attention.

[0003] Near-field source DOA estimation algorithms are often based on the Fresnel approximation, a simplification that introduces systematic errors. To address this systematic error problem, the paper J. He, T. Shu, L. Li, and T.-K. Truong, “Mixed near-field and far-field localization and array calibration with partly calibrated arrays,” IEEE Transactions on Signal Processing, vol. 70, pp. 2105-2118, 2022, proposes an algorithm based on a fourth-order cumulant matrix, combining an accurate model to achieve two-dimensional parameter estimation and gain compensation. This algorithm requires a reference value based on signal amplitude attenuation and is significantly affected by background noise and the unknown path loss exponent. Building upon this, the literature J. He, L. Li, T. Shu and T.-K. Truong, "Mixed Near-Field and Far-Field Source Localization Based on Exact Spatial Propagation Geometry," in IEEE Transactions on Vehicular Technology, vol. 70, no. 4, pp. 3540-3551, April 2021, and J. He, L. Li and T. Shu, "Localization of Near-Field Sources for Exact Source-Sensor Spatial Geometry," in IEEE Signal Processing, further support this work. Letters, vol. 27, pp. 1040-1044, 2020 (Near-field source localization based on precise source-sensor spatial geometry, IEEE Signal Processing Letters) proposes a two-dimensional direction finding algorithm by constructing a cumulant matrix bundle. This algorithm can make an unambiguous coarse estimate using the phase, but it requires the array to be symmetric about the reference center, and the calculation of the cumulant matrix bundle makes the algorithm complex. The arrays in the above algorithms are all based on scalar sensor designs.

[0004] Besides scalar sensors, arrays can also be designed based on vector sensors. Vector arrays composed of vector sensors can observe signals from multiple dimensions, exhibiting higher performance compared to scalar arrays composed of scalar sensors. Currently, many near-field source DOA estimation algorithms based on vector arrays have been proposed. Those based on the Fresnel approximation include: J.-W. Tao, L. Liu and Z.-Y. Lin, "Joint DOA, Range, and Polarization Estimation in the Fresnel Region," in IEEE Transactions on Aerospace and Electronic Systems, vol.47, no.4, pp.2657-2672, OCTOBER 2011. (Joint DOA, Range, and Polarization estimation in the Fresnel region, IEEE Transactions on Aerospace and Electronic Systems). For the two polarization components, a rank-reduced MUSIC algorithm for the polarization domain has been proposed, but it still requires two-dimensional spectral peak search when estimating polarization parameters, resulting in high complexity. For example, the literature H. Ma, H. T. Ao. Three-Dimensional Mixed Far-Field and Near-Field Sources Localization Utilizing Cross Tripole Array. Circuits, Systems, Signal Processing 42, 4320-4342 (2023). (Using a cross-tripole array for three-dimensional mixed far-field and near-field source localization, Circuits, Systems, Signal Processing) uses a cross-tripole array of three orthogonal dipoles to achieve three-dimensional parameter estimation and array aperture expansion. However, to ensure unambiguous phase, the array element positions need to satisfy a special multiple relationship. The above-mentioned Fresnel approximation-based algorithm has the problem of systematic error.Algorithms based on precise polarization-sensitive arrays have been proposed, such as: J. He, L. Li and T. Shu, "Near-Field Parameter Estimation for Polarized Source Using Spatial Amplitude Ratio," in IEEE Communications Letters, vol. 24, no. 9, pp. 1961-1965, Sept. 2020, which proposes a second-order statistical algorithm based on received data; and K. Yin, C. Gao, and Y. Dai, "Near-field localization based on exact model with a linear COLD array," in 2022 IEEE Radar Conference (RadarConf22), 2022, which proposes near-field localization based on an exact model and a linear COLD array, and Yin, K., Dai, Y. & Gao, C., "Near-Field DOA-Range and Polarization Estimation Based on Exact Propagation Model with COLD." Arrays. Circuits. Syst. Signal Process 41, 5183-5200 (2022). (Near-field DOA-distance and polarization estimation based on precise propagation model and COLD array, *Circuits, Systems and Signal Processing*) proposes a fourth-order cumulant algorithm based on received data. The aforementioned algorithms based on precise polarization-sensitive arrays provide closed-form solutions for the joint estimation of spatial two-dimensional position and polarization parameters. However, these algorithms are based on one-dimensional COLD arrays and can only locate spatial two-dimensional positions. Furthermore, these algorithms utilize the characteristic that the signal source and array are coplanar, neglecting the influence of array element positions on DOA, thus using amplitude attenuation for coarse estimation of spatial two-dimensional position parameters. However, in three-dimensional scenes, the amplitude response is coupled with the angle parameter in the spatial position parameters, and using amplitude attenuation for coarse estimation results in significant bias. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array. It uses the overall least squares criterion to estimate polarization domain parameters, which has high estimation accuracy. It uses the unambiguous delayed phase in the subarray divided by two linear arrays to make a coarse estimate of the spatial position parameters, which has higher estimation accuracy than using amplitude attenuation for coarse estimation. Moreover, the array does not need to be symmetrically constructed, and the element spacing does not need to be limited to a quarter wavelength, thus expanding the array aperture.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a method for accurate near-field polarization multi-parameter joint estimation based on an L-type COLD array, characterized by the following steps:

[0007] Step 1: In the three-dimensional near-field source localization scenario, multiple narrowband near-field sources are assumed to exist. An L-shaped COLD array, consisting of a first linear array and a second linear array sharing the first COLD element, is designed as the receiving array. The first linear array is deployed on the x-axis of the three-dimensional coordinate system, the second linear array is deployed on the y-axis of the three-dimensional coordinate system, and the shared first COLD element is deployed at the origin of the three-dimensional coordinate system as the reference element, forming an L-shaped COLD array precise spherical wavefront model. In the model, after the receiving array receives signals transmitted from all narrowband near-field sources, the expressions of the received signal vectors of the first and second linear arrays are obtained. The expressions of the received signal vectors of the first and second linear arrays each include the spatial position parameters and polarization parameters of each narrowband near-field source. The spatial position parameters of each narrowband near-field source include the distance from each narrowband near-field source to the reference element, the elevation angle, and the azimuth angle of each narrowband near-field source.

[0008] Step 2: Divide the first linear array into subarray 1 and subarray 2, each containing the same number of cold array elements. Subarray 1 consists of multiple consecutive cold array elements starting from the first cold array element of the first linear array, and subarray 2 consists of multiple consecutive cold array elements starting from the last cold array element of the first linear array. Similarly, divide the second linear array into subarray 3 and subarray 4, each containing the same number of cold array elements. Subarray 3 consists of multiple consecutive cold array elements starting from the first cold array element of the second linear array, and subarray 4 consists of multiple consecutive cold array elements starting from the last cold array element of the second linear array. Then, based on the received signal vector of the first linear array, obtain the received signal vectors of subarray 1 and subarray 2 respectively, and then, based on the received signal vector of the second linear array... The received signal vectors are obtained from subarrays three and four. Next, the cross-covariance matrix of the received signal vector of subarray one and the delayed received signal vector of subarray two is calculated, as well as the cross-covariance matrix of the received signal vector of subarray three and the delayed received signal vector of subarray four. Then, the vectors obtained after vectorization of the two cross-covariance matrices are sampled at equal intervals to obtain the corresponding discrete data vectors in the delay domain. Finally, the estimated values ​​of the manifold matrix of subarray one and the manifold matrix of subarray two are obtained from the discrete data vectors in the delay domain corresponding to subarrays one and two using TALS theory. Similarly, the estimated values ​​of the manifold matrix of subarray three and the manifold matrix of subarray four are obtained from the discrete data vectors in the delay domain corresponding to subarrays three and four using TALS theory.

[0009] Step 3: Obtain the horizontal and vertical components of the estimated value of the manifold matrix of subarray one, and ensure that there is rotation invariance between the horizontal and vertical components; then solve the solution of the diagonal matrix in the expression representing the rotation invariance property; then extract the estimated value of the polarization domain parameters of each narrowband near-field source from the solution of the diagonal matrix.

[0010] Step 4: Obtain the horizontal and vertical components of the estimated manifold matrix of subarray 2, subarray 3, and subarray 4 respectively; then normalize the horizontal and vertical components of the estimated manifold matrix of subarray 1, subarray 2, subarray 3, and subarray 4 to the reference array element to obtain the spatial estimated values ​​of the manifold matrix of subarray 1, subarray 2, subarray 3, and subarray 4 respectively.

[0011] Step 5: Obtain closed-form parameter solutions for the distance from each narrowband near-field source to the reference element, and closed-form parameter solutions for the angle between the incident signal emitted by each narrowband near-field source at the reference element and the x-axis, based on the spatial domain estimation values of the manifold matrices of subarray 1 and subarray 2 respectively; obtain closed-form parameter solutions for the distance from each narrowband near-field source to the reference element, and closed-form parameter solutions for the angle between the incident signal emitted by each narrowband near-field source at the reference element and the y-axis, based on the spatial domain estimation values of the manifold matrices of subarray 3 and subarray 4 respectively; then take the average of the two closed-form parameter solutions for the distance from each narrowband near-field source to the reference element as the coarse estimation value, and obtain the coarse estimation values of the elevation angle and azimuth angle of each narrowband near-field source based on the relationship between the angle between the incident signal emitted by each narrowband near-field source at the reference element and the x-axis and the elevation angle and azimuth angle of each narrowband near-field source, and the relationship between the angle between the incident signal emitted by each narrowband near-field source at the reference element and the y-axis and the elevation angle and azimuth angle of each narrowband near-field source;

[0012] Step 6: Obtain the corresponding accurate estimation values based on the coarse estimation value of the distance from each narrowband near-field source to the reference element, and the coarse estimation values of the elevation angle and azimuth angle of each narrowband near-field source.

[0013] In said step 1, the first linear array comprises M COLD elements, the second linear array comprises N COLD elements, the spacing between two adjacent COLD elements in the first linear array and the second linear array is d, wherein M≥3, N≥3, d=λ / 2, and λ represents the wavelength of the signal emitted by the narrowband near-field source.

[0014] In said step 1, the obtaining process of the expression of the received signal vector of the first linear array and the second linear array is as follows:

[0015] Step 1.1: set that the receiving array receives signals emitted from K narrowband near-field sources at time t, and set the spatial position parameter of the k-th narrowband near-field source as and the polarization domain parameter is (γ k ,η k ), wherein 1<K<min(M,N), min(·) is the minimum function, k=1,2,…,K, θ k represents the elevation angle of the k-th narrowband near-field source, represents the azimuth angle of the k-th narrowband near-field source, r k represents the distance from the k-th narrowband near-field source to the reference element, γ k represents the polarization auxiliary angle of the k-th narrowband near-field source, γ k ∈[0°, 90°], η k represents the polarization phase difference of the k-th narrowband near-field source, η k ∈[-180°, 180°];

[0016] Step 1.2: Denote the angle between the signal emitted by the k-th narrowband near-field source at time t and the x-axis and the reference element as α. k Let β be the angle between the signal emitted by the k-th narrowband near-field source at time t and the y-axis. k Then determine θ k , With α k and β k Relationship,

[0017] Step 1.3: Obtain the distances from the k-th narrowband near-field source to the m-th cold array element of the first linear array and the n-th cold array element of the second linear array, respectively, and denote them as follows: and Where m = 1, 2, ..., M, n = 1, 2, ..., N, This represents the distance from the m-th COLD element of the first linear array to the reference element. This represents the distance from the nth COLD element of the second linear array to the reference element.

[0018] Step 1.4: Based on the propagation relationship of the precise spherical wavefront, obtain the amplitude and phase factor of the response of the signal emitted by the k-th narrowband near-field source at time t incident on the m-th COLD element of the first linear array, compared to the response incident on the reference element; and obtain the amplitude and phase factor of the response of the signal emitted by the k-th narrowband near-field source at time t incident on the n-th COLD element of the second linear array, compared to the response incident on the reference element. These are denoted as follows: and

[0019] Where p represents the path loss exponent, e is the natural constant, and j is an imaginary number. This indicates that the amplitude attenuation of the signal emitted by the k-th narrowband near-field source at time t, incident on the m-th COLD element of the first linear array, is relative to that at the reference element. This indicates that the amplitude attenuation of the signal emitted by the k-th narrowband near-field source at time t, incident on the n-th COLD element of the second linear array, is relative to that at the reference element. ψ m，k This represents the phase delay of the signal emitted by the k-th narrowband near-field source at time t, incident on the m-th COLD element of the first linear array, relative to the reference element. This represents the delay phase of the signal emitted by the k-th narrowband near-field source at time t, which is incident on the n-th COLD element of the second linear array relative to the reference element.

[0020] Step 1.5: Obtain the spatial steering vector of the k-th narrowband near-field source with respect to the first linear array and the spatial steering vector of the k-th narrowband near-field source with respect to the second linear array, denoted as a. sx (α k r k ) and a sy (β k r k ), in,(·) T Indicates the transpose operation;

[0021] Step 1.6: Obtain the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to the first linear array and the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to the second linear array, denoted as a. x，k and a y，k , Where 12 represents a 2×1 vector of all 1s. This represents the Kroneckerproduct operator. This represents the Hadamard product operator, a p Indicates polarization state, 1 M Describes an M×1 vector of all 1s, where 1 N Let v represent an N×1 vector of all ones. k =[sinα] 1，k ,…,sinα m，k ,…,sinα M，k ] T w k =[sinβ] 1，k , …, sinβ n，k , …, sinβ N，k ] T α m，k Let represent the angle between the signal emitted by the k-th narrowband near-field source at time t and the m-th COLD element of the first linear array, and the x-axis. β n，k Let represent the angle between the signal emitted by the k-th narrowband near-field source at time v and the n-th COLD element of the second linear array, and the y-axis.

[0022] Step 1.7: Obtain the received signal vector of the first linear array at time t and the received signal vector of the second linear array at time t, denoted as X(t) and Y(t) respectively.

[0023] Among them, s k (t) represents the signal emitted by the k-th narrowband near-field source at time t, w x w(t) represents the zero-mean additive white Gaussian noise vector on the first linear array at time t. y (t) represents the zero-mean additive white Gaussian noise vector on the second linear array at time t. x Let A be the manifold matrix of the first linear array. x =[a x，1 , ..., a x，K A y Let A be the manifold matrix of the second linear array. y =[a y，1 , ..., a y，K ], s(t) represents the signal source vector, s(t) = [s1(t), ..., s k (t), …s K (t) ] .

[0024] In step 2, subarray one consists of the first M-1 COLD array elements of the first linear array, subarray two consists of the last M-1 COLD array elements of the first linear array, subarray three consists of the first N-1 COLD array elements of the second linear array, and subarray four consists of the last N-1 COLD array elements of the second linear array.

[0025] In step 2, the process of obtaining the estimated values ​​of the manifold matrices of subarray one and subarray two, as well as the estimated values ​​of the manifold matrices of subarray three and subarray four, is as follows:

[0026] Step 2.1: Denote the received signal vectors of subarray one and subarray two as X1(t) and X2(t), respectively. The received signal vectors of subarray three and subarray four are denoted as Y1(t) and Y2(t) respectively. in, The selection matrix for submatrix one. This represents the selection matrix for submatrix two. I2 represents a 2×2 identity matrix, I M-1 This represents an identity matrix of dimension (M-1)×(M-1), where 0 M-1，1 This represents the zero vector of dimension (M-1)×1. This represents the selection matrix for submatrix three. The selection matrix for subarray four, IN-1 This represents an identity matrix of dimension (N-1)×(N-1), where 0 N-1，1 This represents the zero vector of dimension (N-1)×1. Describes the manifold matrix of submatrix one. Describes a manifold matrix with submatrix 2. This represents the zero-mean additive white Gaussian noise vector on the submatrix at time t. This represents the zero-mean additive white Gaussian noise vector on submatrix 2 at time t. Describes the manifold matrix of submatrix three. The matrix representing the manifold of subarray four, This represents the zero-mean additive white Gaussian noise vector over the three submatrices at time t. This represents the zero-mean additive white Gaussian noise vector over the submatrix at time t.

[0027] Step 2.2: Calculate the cross-covariance matrix of the received signal vector X1(t) of subarray one and the received signal vector X2(t+τ) of subarray two after a delay of τ, denoted as R. x (τ),

[0028] Calculate the cross-covariance matrix of the received signal vector Y1(t) of subarray three and the received signal vector Y2(t+τ) of subarray four after a delay of τ, denoted as R. y (τ),

[0029] Where E[·] represents the statistical expectation, (·) H This represents the conjugate transpose operation, (· ) * indicates the conjugate operation. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray 1. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray 2. s k (t+τ) represents the signal emitted by the k-th narrowband near-field source at time t+τ. R represents the zero-mean additive white Gaussian noise vector on submatrix 2 at time t+τ. s (τ) is a diagonal matrix, R s (τ)=diag[r s，1 (τ), ..., r s，k (τ), ..., r s，K[(τ)], diag[·] denotes the construction of a diagonal matrix. R w (τ) is a diagonal matrix whose diagonal elements are σ. 2 δ(τ) and δ(·) denote the Dirac function, σ 2 Indicates noise power. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray 3. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray four. This represents the zero-mean additive white Gaussian noise vector on the submatrix at time t+τ;

[0030] Step 2.3: For R x (τ) is vectorized to obtain a vector. And thus obtain Similarly, for R y (τ) is vectorized to obtain a vector. And thus obtain Where vec{·} denotes the vectorization operation, ⊙ denotes the Khatri-Rao product operator, and ρ(τ)=[r s，1 (τ), r s，k (τ), ..., r s，K (τ)] T ;

[0031] Step 2.4: For Perform equal-interval sampling to obtain discrete data vectors in the delay domain. Similarly, for Perform equal-interval sampling to obtain discrete data vectors in the delay domain. Among them, T s N represents the pseudo-snapshot sampling interval. p Represents the number of pseudo-snapshots, Γ=[ρ(T s ), ρ(2T s ), …, ρ(N) p T s );

[0032] Step 2.5: Applying TALS theory from Separation from and Their respective estimates are denoted as: and Similarly, applying TALS theory from Separation from and Their respective estimates are denoted as: and

[0033] The specific process of step 3 is as follows:

[0034] Step 3.1: Obtain the estimated value of the manifold matrix of submatrix one. The horizontal and vertical components are denoted as follows: and Among them, J hx This represents the selection matrix for the horizontal direction of the first linear array. J vx This represents the selection matrix with respect to the vertical direction of the first linear array. e1 and e2 are both row vectors with a dimension of 1×2. The first element of e1 is 1 and the rest are 0, and the second element of e2 is 1 and the rest are 0.

[0035] Step 3.2: and There exists rotational invariance, therefore: Where, Φ p It is a diagonal matrix; then for and Each adds a perturbation, according to get in, express The disturbance express The disturbance; Step 3.3: Let and Let the rank of be K, and let Then to Perform generalized feature decomposition to obtain in, This represents a diagonal matrix constructed from eigenvalues. This represents a matrix constructed from the eigenvectors corresponding to the eigenvalues; then... Decomposed into in, for Four submatrices of the same dimension;

[0036] Step 3.4: Let Then according to Sure and Orthogonal; then construct the optimization equation, described as: Among them, ||·|| F Denotes the Frobenius norm;

[0037] Step 3.5: Solve the optimization equation using the overall least squares criterion to obtain Φ. p The solution is denoted as and satisfy in, Indicates y k The estimated value, Indicates η k The estimated value;

[0038] Step 3.6: From Extract and Where |·| represents the modulo operator, and [·] k This indicates taking the k-th element of the diagonal matrix, and angle(·) indicates taking the phase angle of a complex number.

[0039] The specific process of step 4 is as follows:

[0040] Step 4.1: Obtain the estimated value of the manifold matrix of submatrix 2. The horizontal and vertical components are denoted as follows: and Similarly, obtain the estimate of the manifold matrix of submatrix three. The horizontal and vertical components are denoted as follows: and Obtain the estimate of the manifold matrix of subarray four. The horizontal and vertical components are denoted as follows: and Among them, J hy This represents the selection matrix for the horizontal direction of the second linear array. J vy This represents the selection matrix with respect to the vertical direction of the second linear array.

[0041] Step 4.2: Obtain the spatial domain estimates of the manifold matrices of subarrays 1, 2, 3, and 4, respectively, denoted as [reference needed]. Where i = 1, 2, express The horizontal component obtained after normalization to the reference array element express The vertical component obtained after normalization to the reference array elements express The horizontal component obtained after normalization to the reference array element express The vertical component obtained after normalization to the reference array element.

[0042] The specific process of step 5 is as follows:

[0043] Step 5.1: From Extract an unambiguous delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as from Extract an unambiguous delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as in, express The element in the 2nd row and kth column, i = 1, 2, Indicates r k The estimated value, express The estimated value, express The estimated value;

[0044] Step 5.2: Establish and respectively with r k and α k The relationship is as follows: Solve the relation again to obtain r. k and a k Their respective closed-form solutions are denoted as follows: and

[0045] Step 5.3: From Extract a delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as from Extract a delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as in, express The element in the 2nd row and kth column, i = 1, 2, express The estimated value, express The estimated value;

[0046] Step 5.4: Establish and respectively with r k and β k The relationship is as follows: Solve the relation again to obtain r. k and β k Their respective closed-form solutions are denoted as follows: and

[0047] Step 5.5: Calculation Get r k rough estimate Will and Substitute them separately and In the middle, we get θ k and Their respective rough estimates are denoted as: and

[0048] Compared with the prior art, the advantages of the present invention are as follows:

[0049] 1) The problem of estimating pitch, azimuth and distance parameters in the airspace is transformed into a two-dimensional parameter estimation problem of x-axis and y-axis angle and distance by using an L-shaped COLD array. Compared with the cross array structure, it is simpler and can locate the three-dimensional position in space.

[0050] 2) Due to phase ambiguity in the steering vector under the precise spherical wavefront model, a coarse estimate is needed for deambiguation. This invention divides the first linear array into subarray one and subarray two, and the second linear array into subarray three and subarray four. A time-delay-related cross-covariance matrix is ​​constructed using the received signal vectors of two subarrays belonging to the same linear array. The estimated values ​​of the manifold matrix of the subarrays are obtained using the parallel factorization method. Since each of these subarray manifold matrices contains an unambiguous phase, these unambiguous phases can be used to coarsely estimate the spatial position parameters. Compared to using amplitude attenuation for coarse estimation, this coarse estimate is less affected by path loss and noise interference, has higher accuracy, and overcomes the limitations of near-field DOA estimation requiring array symmetry about the reference element and a quarter-wavelength spacing between elements, thus expanding the array aperture. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the precise spherical wavefront model of the L-shaped COLD array in the method of the present invention;

[0052] Figure 2 A three-dimensional joint scatter plot of the precise estimates of the angles of the signals emitted by each narrowband near-field source onto the reference array element with respect to the x-axis and the y-axis, as well as the distances from each narrowband near-field source to the reference array element, under 500 Monte Carlo simulations.

[0053] Figure 3 This is a three-dimensional joint scatter plot of the estimated values ​​of polarization auxiliary angle and polarization phase difference for each narrowband near-field source under 500 Monte Carlo simulations. Detailed Implementation

[0054] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0055] This invention proposes a method for accurate near-field polarization joint estimation based on an L-shaped COLD array, which includes the following steps:

[0056] Step 1: As Figure 1 As shown, in a three-dimensional near-field source localization scenario, multiple narrowband near-field sources are assumed to exist. An L-shaped COLD array, consisting of a first linear array and a second linear array sharing a common first COLD element, is designed as the receiving array. The first linear array is deployed on the x-axis of the three-dimensional coordinate system, the second linear array is deployed on the y-axis of the three-dimensional coordinate system, and the common first COLD element is deployed at the origin of the three-dimensional coordinate system as a reference element, forming an L-shaped COLD array precise spherical wavefront model. In the model, after the receiving array receives signals transmitted from all narrowband near-field sources, it obtains the expressions for the received signal vectors of the first and second linear arrays. The expressions for the received signal vectors of the first and second linear arrays each include the spatial position parameters and polarization parameters of each narrowband near-field source. The spatial position parameters of each narrowband near-field source include the distance from each narrowband near-field source to the reference element, the elevation angle, and the azimuth angle of each narrowband near-field source.

[0057] In step 1, the first linear array contains M COLD elements, the second linear array contains N COLD elements, and the spacing between two adjacent COLD elements in the first and second linear arrays is d. The receiving array contains a total of M+N-1 COLD elements, where M≥3, N≥3, and d=λ / 2, where λ represents the wavelength of the signal emitted by the narrowband near-field source.

[0058] Furthermore, in step 1, the process of obtaining the expressions for the received signal vectors of the first linear array and the second linear array is as follows:

[0059] Step 1.1: Set the receiving array to receive signals from K narrowband near-field sources at time t, and set the spatial position parameter of the k-th narrowband near-field source as follows. And the polarization domain parameter is (γ k,η k ), where 1 < K < min(M, N), min(·) is the minimum function, k = 1, 2, ..., K, θ k This represents the pitch angle of the k-th narrowband near-field source. This represents the azimuth angle of the k-th narrowband near-field source. r k γ represents the distance from the k-th narrowband near-field source to the reference array element. k γ represents the polarization auxiliary angle of the k-th narrowband near-field source. k ∈[0°,90°],η k η represents the polarization phase difference of the k-th narrowband near-field source. k ∈[-180°, 180°].

[0060] Step 1.2: Denote the angle between the signal emitted by the k-th narrowband near-field source at time t and the x-axis and the reference element as α. k Let β be the angle between the signal emitted by the k-th narrowband near-field source at time t and the y-axis. k Then by Figure 1 The solid geometric relationship shown, θ k , It can be mapped to α k and β k θ can then be determined. k , With α k and β k Relationship,

[0061] Step 1.3: Obtain the distances from the k-th narrowband near-field source to the m-th COLD element of the first linear array and the n-th COLD element of the second linear array using trigonometric relationships, denoted as follows: and Where m = 1, 2, ..., M, n = 1, 2, ..., N, This represents the distance from the m-th COLD element of the first linear array to the reference element. This represents the distance from the nth COLD element of the second linear array to the reference element.

[0062] Step 1.4: Based on the propagation relationship of the precise spherical wavefront, obtain the amplitude and phase factor of the response of the signal emitted by the k-th narrowband near-field source at time t incident on the m-th COLD element of the first linear array, compared to the response incident on the reference element; and obtain the amplitude and phase factor of the response of the signal emitted by the k-th narrowband near-field source at time t incident on the n-th COLD element of the second linear array, compared to the response incident on the reference element. These are denoted as follows: and

[0063] Where p represents the path loss exponent, e is the natural constant, and j is an imaginary number. This indicates that the amplitude attenuation of the signal emitted by the k-th narrowband near-field source at time t, incident on the m-th COLD element of the first linear array, is relative to that at the reference element. This indicates that the amplitude attenuation of the signal emitted by the k-th narrowband near-field source at time t, incident on the n-th COLD element of the second linear array, is relative to that at the reference element. ψ m,k This represents the phase delay of the signal emitted by the k-th narrowband near-field source at time t, incident on the m-th COLD element of the first linear array, relative to the reference element. This represents the delay phase of the signal emitted by the k-th narrowband near-field source at time t, incident on the n-th COLD element of the second linear array, relative to the reference element.

[0064] Step 1.5: Obtain the spatial steering vector of the k-th narrowband near-field source with respect to the first linear array and the spatial steering vector of the k-th narrowband near-field source with respect to the second linear array, denoted as a. sx (α k ,r k ) and a sy (β k ,r k ), in,(·) T This indicates the transpose operation.

[0065] Step 1.6: Obtain the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to the first linear array and the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to the second linear array, denoted as a. x，k and a y，k ,

[0066] Where 12 represents a 2×1 vector of all 1s. This represents the Kroneckerproduct operator. This represents the Hadamard product operator, a p Indicates polarization state, 1 M Describes an M×1 vector of all 1s, where 1 N Let v represent an N×1 vector of all ones. k =[sinα] 1，k ,…,sinα m，k ,…,sinα M，k ] T W k =[sinβ] 1，k , …, sinβ n，k , …, sinβ N,k ] T α m，k Let represent the angle between the signal emitted by the k-th narrowband near-field source at time t and the m-th COLD element of the first linear array, and the x-axis. β n,k Let represent the angle between the signal emitted by the k-th narrowband near-field source at time v and the n-th COLD element of the second linear array, and the y-axis.

[0067] Step 1.7: Obtain the received signal vector of the first linear array at time t and the received signal vector of the second linear array at time t, denoted as X(t) and Y(t) respectively.

[0068] Among them, s k (t) represents the signal emitted by the k-th narrowband near-field source at time t, w x w(t) represents the zero-mean additive white Gaussian noise vector on the first linear array at time t. x The dimension of (t) is 2M×1, w y (t) represents the zero-mean additive white Gaussian noise vector on the second linear array at time t, w y The dimension of (t) is 2N×1, A x Let A be the manifold matrix of the first linear array. x =[a x，1 , ..., a x，K A x The dimension is 2M×K, A y Let A be the manifold matrix of the second linear array. y =[a y，1 , ..., a y，K A y The dimension is 2N×K, s(t) represents the signal source vector, s(t)=[s1(t),…,s k(t), ..., s K (t)] T The dimension of s(t) is K×1.

[0069] Step 2: Divide the first linear array into subarray 1 and subarray 2, each containing the same number of cold array elements. Subarray 1 consists of multiple consecutive cold array elements starting from the first cold array element of the first linear array, and subarray 2 consists of multiple consecutive cold array elements starting from the last cold array element of the first linear array. Similarly, divide the second linear array into subarray 3 and subarray 4, each containing the same number of cold array elements. Subarray 3 consists of multiple consecutive cold array elements starting from the first cold array element of the second linear array, and subarray 4 consists of multiple consecutive cold array elements starting from the last cold array element of the second linear array. Then, based on the received signal vector of the first linear array, obtain the received signal vectors of subarray 1 and subarray 2 respectively, and then, based on the received signal vector of the second linear array... The received signal vectors are obtained from subarrays three and four. Then, the cross-covariance matrix of the received signal vector of subarray one and the delayed received signal vector of subarray two is calculated, as well as the cross-covariance matrix of the received signal vector of subarray three and the delayed received signal vector of subarray four. The vectors obtained after vectorization of the two cross-covariance matrices are then sampled at equal intervals to obtain the corresponding discrete data vectors in the delay domain. Finally, the estimated values ​​of the manifold matrix of subarray one and the manifold matrix of subarray two are obtained from the discrete data vectors in the delay domain corresponding to subarrays one and two using TALS theory. Similarly, the estimated values ​​of the manifold matrix of subarray three and the manifold matrix of subarray four are obtained from the discrete data vectors in the delay domain corresponding to subarrays three and four using TALS theory.

[0070] In step 2, subarray one consists of the first M-1 COLD array elements of the first linear array, subarray two consists of the last M-1 COLD array elements of the first linear array, subarray three consists of the first N-1 COLD array elements of the second linear array, and subarray four consists of the last N-1 COLD array elements of the second linear array.

[0071] Further specifying, in step 2, the process of obtaining the estimated values ​​of the manifold matrices of subarray one and subarray two, as well as the estimated values ​​of the manifold matrices of subarray three and subarray four, is as follows:

[0072] Step 2.1: Denote the received signal vectors of subarray one and subarray two as X1(t) and X2(t), respectively. The received signal vectors of subarray three and subarray four are denoted as Y1(t) and Y2(t) respectively. in, The selection matrix for submatrix one. This represents the selection matrix for submatrix two. I2 represents a 2×2 identity matrix, I M-1 This represents an identity matrix of dimension (M-1)×(M-1), where 0 M-1，1 This represents the zero vector of dimension (M-1)×1. This represents the selection matrix for submatrix three. The selection matrix for subarray four, I N-1 This represents an identity matrix of dimension (N-1)×(N-1), where 0 N-1，1 This represents the zero vector of dimension (N-1)×1. Describes the manifold matrix of submatrix one. Describes a manifold matrix with submatrix 2. This represents the zero-mean additive white Gaussian noise vector on the submatrix at time t. This represents the zero-mean additive white Gaussian noise vector on submatrix 2 at time t. Describes the manifold matrix of submatrix three. The matrix representing the manifold of subarray four, This represents the zero-mean additive white Gaussian noise vector over the three submatrices at time t. w y2 (t) represents the zero-mean additive white Gaussian noise vector on the submatrix at time t.

[0073] Step 2.2: Calculate the cross-covariance matrix of the received signal vector X1(t) of subarray one and the received signal vector X2(t+τ) of subarray two after a delay of τ, denoted as R. x (τ),

[0074] Calculate the cross-covariance matrix of the received signal vector Y1(t) of subarray three and the received signal vector Y2(t+τ) of subarray four after a delay of τ, denoted as R. y (τ),

[0075] Where E[·] represents the statistical expectation, (·) H The conjugate transpose operation is represented by (·). * This indicates the conjugate operation. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray 1. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray 2. s k (t+τ) represents the signal emitted by the k-th narrowband near-field source at time t+τ. R represents the zero-mean additive white Gaussian noise vector on submatrix 2 at time t+τ. s (τ) is a diagonal matrix, R s (τ)=diag[r s，1 (τ), ..., r s，k (τ), ..., r s，K [(τ)], diag[·] denotes the construction of a diagonal matrix. R w (τ) is a diagonal matrix whose diagonal elements are σ. 2 δ(τ) and δ(·) denote the Dirac function, σ 2 Indicates noise power. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray 3. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray four. Let represent the zero-mean additive white Gaussian noise vector on submatrix 4 at time t+τ.

[0076] Step 2.3: For R x (τ) is vectorized to obtain a vector. And thus obtain Similarly, for R y (τ) is vectorized to obtain a vector. And thus obtain Where vec{·} denotes the vectorization operation, ⊙ denotes the Khatri-Rao product operator, and ρ(τ)=[r s，1 (τ), ..., r s，k (τ), ..., r s，K (τ)] T .

[0077] Step 2.4: For Perform equal-interval sampling to obtain discrete data vectors in the delay domain. Similarly, for Perform equal-interval sampling to obtain discrete data vectors in the delay domain. Among them, T s N represents the pseudo-snapshot sampling interval. p Represents the number of pseudo-snapshots, Γ=[ρ(Ts ),ρ(2T s ),…,ρ(N p T s )).

[0078] Step 2.5: and The expression satisfies the standard form of Parallel Factorization (PARAFAC), and TALS theory is used to... Separation from and Their respective estimates are denoted as: and Similarly, applying TALS theory from Separation from and Their respective estimates are denoted as: and

[0079] Step 3: Obtain the horizontal and vertical components of the estimated value of the manifold matrix of subarray one, and ensure that there is rotation invariance between the horizontal and vertical components; then solve the solution of the diagonal matrix in the expression representing the rotation invariance property; and then extract the estimated value of the polarization domain parameters of each narrowband near-field source from the solution of the diagonal matrix.

[0080] To further specify, the specific process of step 3 is as follows:

[0081] Step 3.1: Obtain the estimated value of the manifold matrix of submatrix one. The horizontal and vertical components are denoted as follows: and Among them, J hx This represents the selection matrix for the horizontal direction of the first linear array. J vx This represents the selection matrix with respect to the vertical direction of the first linear array. Both e1 and e2 are row vectors of dimension 1×2. The first element of e1 is 1 and the rest are 0, and the second element of e2 is 1 and the rest are 0.

[0082] Step 3.2: Due to and There exists a fixed amplitude-phase factor, therefore and There exists rotational invariance, therefore: Where, Φ p It is a diagonal matrix; then for and Each adds a perturbation, according to get in, express The disturbance express The disturbance.

[0083] Step 3.3: Due to and Zhang Cheng's subspace is the same subspace, so let and Let the rank of be K, and let Then to Perform generalized feature decomposition to obtain in, This represents a diagonal matrix constructed from eigenvalues. This represents a matrix constructed from the eigenvectors corresponding to the eigenvalues; then... Decomposed into in, for The four submatrices of the same dimension in the matrix. The dimension is 2K×2K. The dimensions are all K×K.

[0084] Step 3.4: Let Then according to Sure and Orthogonal; then construct the optimization equation, described as: Among them, ||·|| F denoted by Frobenius norm, and st means "bound to...".

[0085] Step 3.5: Solve the optimization equation using the overall least squares criterion to obtain Φ. p The solution is denoted as and satisfy in, Indicates γ k The estimated value, Indicates η k The estimated value.

[0086] Step 3.6: From Extract and Where |·| represents the modulo operator, and [·] k This indicates taking the k-th element of the diagonal matrix, and angle(·) indicates taking the phase angle of a complex number.

[0087] Step 4: Obtain the horizontal and vertical components of the estimated manifold matrix of subarray 2, subarray 3, and subarray 4 respectively; then normalize the horizontal and vertical components of the estimated manifold matrix of subarray 1, subarray 2, subarray 3, and subarray 4 to the reference element to eliminate the influence of polarization components, and obtain the spatial estimated values ​​of the manifold matrix of subarray 1, subarray 2, subarray 3, and subarray 4 respectively.

[0088] To further specify, the specific process of step 4 is as follows:

[0089] Step 4.1: Obtain the estimated value of the manifold matrix of submatrix 2. The horizontal and vertical components are denoted as follows: and Similarly, obtain the estimate of the manifold matrix of submatrix three. The horizontal and vertical components are denoted as follows: and Obtain the estimate of the manifold matrix of subarray four. The horizontal and vertical components are denoted as follows: and Among them, J hy This represents the selection matrix for the horizontal direction of the second linear array. J vy This represents the selection matrix with respect to the vertical direction of the second linear array.

[0090] Step 4.2: Obtain the spatial domain estimates of the manifold matrices of subarrays 1, 2, 3, and 4, respectively, denoted as [reference needed]. Where i = 1, 2, express The horizontal component obtained after normalization to the reference array element express The vertical component obtained after normalization to the reference array elements express The horizontal component obtained after normalization to the reference array element express The vertical component obtained after normalization to the reference array element.

[0091] Step 5: Based on the spatial domain estimates of the manifold matrices of subarrays one and two, obtain the parametric closed-form solution for the distance from each narrowband near-field source to the reference element, and the parametric closed-form solution for the angle between the incident signal from each narrowband near-field source and the reference element and the x-axis; based on the spatial domain estimates of the manifold matrices of subarrays three and four, obtain the parametric closed-form solution for the distance from each narrowband near-field source to the reference element, and the parametric closed-form solution for the angle between the incident signal from each narrowband near-field source and the reference element and the y-axis. The closed-form solution is obtained; then the average value of the two parameters of the closed-form solution for the distance from each narrowband near-field source to the reference array element is used as a coarse estimate. Based on the relationship between the angle of the signal emitted by each narrowband near-field source incident on the reference array element with respect to the x-axis and the elevation and azimuth angles of each narrowband near-field source, and the relationship between the angle of the signal emitted by each narrowband near-field source incident on the reference array element with respect to the y-axis and the elevation and azimuth angles of each narrowband near-field source, the coarse estimates of the elevation and azimuth angles of each narrowband near-field source are obtained.

[0092] To further specify, the specific process of step 5 is as follows:

[0093] Step 5.1: For the phase ambiguity problem of an L-shaped COLD array with an element spacing of λ / 2, the manifold matrix of the separated subarrays will each contain a set of unambiguous delayed phases. Using... and For the unambiguous delayed phase, perform coarse parameter estimation. The reference element is the first COLD element in subarray one. The second row of elements does not have phase ambiguity; for The reference element is the second COLD element in subarray two. The elements in the second row correspond to the response of the third COLD element in the manifold matrix of the first linear array; therefore, there is no phase ambiguity. From Extract an unambiguous delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as from Extract an unambiguous delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as in, express The element in the 2nd row and kth column, i = 1, 2, Indicates r k The estimated value, express The estimated value, express The estimated value.

[0094] Step 5.2: Establish and respectively with r k and α k The relationship is as follows: Solve the relation again to obtain r. k and α k Their respective closed-form solutions are denoted as follows: and

[0095] Step 5.3: From Extract a delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as from Extract a delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as in, express The element in the 2nd row and kth column, i = 1, 2, express The estimated value, express The estimated value.

[0096] Step 5.4: Establish and respectively with r k and β k The relationship is as follows: Solve the relation again to obtain r. k and β k Their respective closed-form solutions are denoted as follows: and

[0097] Step 5.5: Calculation Get r k rough estimate Will and Substitute them separately and In the middle, we get θ k and Their respective rough estimates are denoted as: and

[0098] Step 6: Based on the coarse estimates of the distance from each narrowband near-field source to the reference array element, and the coarse estimates of the elevation and azimuth angles of each narrowband near-field source, obtain the corresponding precise estimates. Here, obtaining the precise estimates is achieved directly using existing technology.

[0099] To further illustrate the feasibility and effectiveness of the method of the present invention, a simulation experiment was conducted on the method of the present invention.

[0100] Three incoherent narrowband near-field sources are incident on an L-shaped COLD array in three-dimensional space. The signal-to-noise ratio (SNR) is 25 dB. The spatial position parameters of the three narrowband near-field sources are (60°, 50°, 3.5λ), (80°, 70°, 5λ), and (30°, 100°, 6.5λ), respectively. The polarization parameters of the three narrowband near-field sources are (10°, 20°), (35°, -40°), and (45°, 30°), respectively. The number of array elements on the x-axis is M = 7, the number of array elements on the y-axis is N = 7, the element spacing is λ / 2, the number of snapshots is 1950, and the number of pseudo-snapshots is N. p =50.

[0101] Figure 2 A three-dimensional joint scatter plot is presented, showing the precise estimates of the angles between the signals emitted by each narrowband near-field source and the x-axis, the angles between the signals and the y-axis incident on the reference array element, and the distances from each narrowband near-field source to the reference array element under 500 Monte Carlo simulations. Figure 3 A three-dimensional joint scatter plot of the estimated values ​​of polarization auxiliary angle and polarization phase difference for each narrowband near-field source under 500 Monte Carlo simulations is presented. Simulation results show that the method of this invention provides high accuracy in estimating the spatial position parameters and polarization parameters of the narrowband near-field source and can automatically pair them.

Claims

1. A method for accurate near-field polarization joint estimation based on an L-shaped COLD array, characterized in that... Includes the following steps: Step 1: In the three-dimensional near-field source localization scenario, multiple narrowband near-field sources are assumed to exist. An L-shaped COLD array consisting of a first linear array and a second linear array sharing the first COLD element is designed as the receiving array. The first linear array is deployed on the three-dimensional coordinate axis, the second linear array is deployed on the three-dimensional coordinate axis, and the shared first COLD element is deployed at the origin of the three-dimensional coordinate as the reference element, forming an L-shaped COLD array precise spherical wavefront model. In the model, after the receiving array receives the signals emitted from all narrowband near-field sources, the expressions of the received signal vectors of the first and second linear arrays are obtained. The expressions of the received signal vectors of the first and second linear arrays each include the spatial position parameters and polarization parameters of each narrowband near-field source. The spatial position parameters of each narrowband near-field source include the distance from each narrowband near-field source to the reference element, the elevation angle and azimuth angle of each narrowband near-field source. Step 2: Divide the first linear array into subarray 1 and subarray 2, each containing the same number of cold array elements. Subarray 1 consists of multiple consecutive cold array elements starting from the first cold array element of the first linear array, and subarray 2 consists of multiple consecutive cold array elements starting from the last cold array element of the first linear array. Similarly, divide the second linear array into subarray 3 and subarray 4, each containing the same number of cold array elements. Subarray 3 consists of multiple consecutive cold array elements starting from the first cold array element of the second linear array, and subarray 4 consists of multiple consecutive cold array elements starting from the last cold array element of the second linear array. Then, based on the received signal vector of the first linear array, obtain the received signal vectors of subarray 1 and subarray 2 respectively, and then, based on the received signal vector of the second linear array... The received signal vectors are obtained from subarrays three and four. Next, the cross-covariance matrix of the received signal vector of subarray one and the delayed received signal vector of subarray two is calculated, as well as the cross-covariance matrix of the received signal vector of subarray three and the delayed received signal vector of subarray four. Then, the vectors obtained after vectorization of the two cross-covariance matrices are sampled at equal intervals to obtain the corresponding discrete data vectors in the delay domain. Finally, the estimated values ​​of the manifold matrix of subarray one and the manifold matrix of subarray two are obtained from the discrete data vectors in the delay domain corresponding to subarrays one and two using TALS theory. Similarly, the estimated values ​​of the manifold matrix of subarray three and the manifold matrix of subarray four are obtained from the discrete data vectors in the delay domain corresponding to subarrays three and four using TALS theory. Step 3: Obtain the horizontal and vertical components of the estimated value of the manifold matrix of subarray one, and ensure that there is rotation invariance between the horizontal and vertical components; then solve the solution of the diagonal matrix in the expression representing the rotation invariance property; then extract the estimated value of the polarization domain parameters of each narrowband near-field source from the solution of the diagonal matrix. Step 4: Obtain the horizontal and vertical components of the estimated manifold matrix of subarray 2, subarray 3, and subarray 4 respectively; then normalize the horizontal and vertical components of the estimated manifold matrix of subarray 1, subarray 2, subarray 3, and subarray 4 to the reference array element to obtain the spatial estimated values ​​of the manifold matrix of subarray 1, subarray 2, subarray 3, and subarray 4 respectively. Step 5: Based on the spatial domain estimates of the manifold matrices of subarrays one and two, obtain the parametric closed-form solution for the distance from each narrowband near-field source to the reference element, and the parametric closed-form solution for the angle between the incident signal from each narrowband near-field source and the reference element and the x-axis; based on the spatial domain estimates of the manifold matrices of subarrays three and four, obtain the parametric closed-form solution for the distance from each narrowband near-field source to the reference element, and the parametric closed-form solution for the angle between the incident signal from each narrowband near-field source and the reference element and the y-axis. The closed-form solution is obtained; then the average value of the two parameters of the closed-form solution of the distance from each narrowband near-field source to the reference array element is used as the coarse estimate. Based on the relationship between the angle of the signal emitted by each narrowband near-field source incident on the reference array element with the x-axis and the elevation and azimuth angles of each narrowband near-field source, and the relationship between the angle of the signal emitted by each narrowband near-field source incident on the reference array element with the y-axis and the elevation and azimuth angles of each narrowband near-field source, the coarse estimates of the elevation and azimuth angles of each narrowband near-field source are obtained. Step 6: Based on the coarse estimate of the distance from each narrowband near-field source to the reference array element, and the coarse estimates of the elevation and azimuth angles of each narrowband near-field source, obtain the corresponding precise estimates.

2. The precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array according to claim 1, characterized in that... In step 1, the first linear array contains M COLD elements, the second linear array contains N COLD elements, and the spacing between two adjacent COLD elements in the first and second linear arrays is d, where M≥3, N≥3, d=λ / 2, and λ represents the wavelength of the signal emitted by the narrowband near-field source.

3. The precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array according to claim 2, characterized in that... In step 1, the process of obtaining the expressions for the received signal vectors of the first linear array and the second linear array is as follows: Step 1.1: Set the signal transmitted from K narrowband near-field sources received by the receiving array at time t, and set the spatial domain position parameter of the k-th narrowband near-field source as and the polarization domain parameter is (γ k , η k ), where 1<K<min(M, N), min(·) is the minimum function, k=1, 2, …, K, θ k represents the elevation angle of the k-th narrowband near-field source, represents the azimuth angle of the k-th narrowband near-field source, r k represents the distance from the k-th narrowband near-field source to the reference array element, γ k represents the polarization auxiliary angle of the k-th narrowband near-field source, γ k ∈[0°, 90°], η k represents the polarization phase difference of the k-th narrowband near-field source, η k ∈[-180°, 180°]; Step 1.2: Denote the angle between the signal emitted by the k-th narrowband near-field source at time t and the x-axis and the reference element as α. k Let β be the angle between the signal emitted by the k-th narrowband near-field source at time t and the y-axis. k Then determine With α k and β k Relationship, Step 1.3: Obtain the distances from the k-th narrowband near-field source to the m-th cold array element of the first linear array and the n-th cold array element of the second linear array, respectively, and denote them as follows: and Where m = 1, 2, ..., M, n = 1, 2, ..., N, This represents the distance from the m-th COLD element of the first linear array to the reference element. This represents the distance from the nth COLD element of the second linear array to the reference element. Step 1.4: Based on the propagation relationship of the precise spherical wavefront, obtain the amplitude and phase factor of the response of the signal emitted by the k-th narrowband near-field source at time t incident on the m-th COLD element of the first linear array, compared to the response incident on the reference element; and obtain the amplitude and phase factor of the response of the signal emitted by the k-th narrowband near-field source at time t incident on the n-th COLD element of the second linear array, compared to the response incident on the reference element. These are denoted as follows: and Where p represents the path loss exponent, e is the natural constant, and j is an imaginary number. This indicates that the amplitude attenuation of the signal emitted by the k-th narrowband near-field source at time t, incident on the m-th COLD element of the first linear array, is relative to that at the reference element. This indicates that the amplitude attenuation of the signal emitted by the k-th narrowband near-field source at time t, incident on the n-th COLD element of the second linear array, is relative to that at the reference element. ψ m，k This represents the phase delay of the signal emitted by the k-th narrowband near-field source at time t, incident on the m-th COLD element of the first linear array, relative to the reference element. θ n，k This represents the delay phase of the signal emitted by the k-th narrowband near-field source at time t, which is incident on the n-th COLD element of the second linear array relative to the reference element. Step 1.5: Obtain the spatial steering vector of the k-th narrowband near-field source with respect to the first linear array and the spatial steering vector of the k-th narrowband near-field source with respect to the second linear array, denoted as a. sx (α k r k ) and a sy (β k r k ), in,(·) T Indicates the transpose operation; Step 1.6: Obtain the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to the first linear array and the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to the second linear array, denoted as a. x，k and a y,k , Where 12 represents a 2×1 vector of all 1s. This represents the Kroneckerproduct operator. This represents the Hadamard product operator, a p Indicates polarization state, 1 M Describes an M×1 vector of all 1s, where 1 N V represents an N×1 vector of all 1s. k =[sinα] 1，k ,…,sinα m，k ,…,sinα M，k ] T W k =[sinβ] 1，k , …, sinβ n，k , …, sinβ N，k ] T α m,k Let represent the angle between the signal emitted by the k-th narrowband near-field source at time t and the m-th COLD element of the first linear array, and the x-axis. β n，k Let represent the angle between the signal emitted by the k-th narrowband near-field source at time t and the n-th COLD element of the second linear array, and the y-axis. Step 1.7: Obtain the received signal vector of the first linear array at time t and the received signal vector of the second linear array at time t, denoted as X(t) and Y(t) respectively. Among them, s k (t) represents the signal emitted by the k-th narrowband near-field source at time t, w x w(t) represents the zero-mean additive white Gaussian noise vector on the first linear array at time t. y (t) represents the zero-mean additive white Gaussian noise vector on the second linear array at time t. x Let A be the manifold matrix of the first linear array. x =[a x，1 , ..., a x，K A y Let A be the manifold matrix of the second linear array. y =[a y，1 , ..., a y，K ], s(t) represents the signal source vector, s(t) = [s1(t), ..., s k (t), ..., s K (t)] T .

4. The precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array according to claim 3, characterized in that... In step 2, subarray one consists of the first M-1 COLD array elements of the first linear array, subarray two consists of the last M-1 COLD array elements of the first linear array, subarray three consists of the first N-1 COLD array elements of the second linear array, and subarray four consists of the last N-1 COLD array elements of the second linear array.

5. The precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array according to claim 4, characterized in that... In step 2, the process of obtaining the estimated values ​​of the manifold matrices of subarray one and subarray two, as well as the estimated values ​​of the manifold matrices of subarray three and subarray four, is as follows: Step 2.1: Denote the received signal vectors of subarray one and subarray two as X1(t) and X2(t), respectively. The received signal vectors of subarray three and subarray four are denoted as Y1(t) and Y2(t) respectively. in, The selection matrix for submatrix one. This represents the selection matrix for submatrix two. I2 represents a 2×2 identity matrix, I M-1 This represents an identity matrix of dimension (M-1)×(M-1), where 0 M-1，1 This represents the zero vector of dimension (M-1)×1. This represents the selection matrix for submatrix three. The selection matrix for subarray four, I N-1 This represents an identity matrix of dimension (N-1)×(N-1), where 0 N-1，1 This represents the zero vector of dimension (N-1)×1. Describes the manifold matrix of submatrix one. Describes a manifold matrix with submatrix 2. This represents the zero-mean additive white Gaussian noise vector on the submatrix at time t. This represents the zero-mean additive white Gaussian noise vector on submatrix 2 at time t. Describes the manifold matrix of submatrix three. The matrix representing the manifold of subarray four, This represents the zero-mean additive white Gaussian noise vector over the three submatrices at time t. This represents the zero-mean additive white Gaussian noise vector over the submatrix at time t. Step 2.2: Calculate the cross-covariance matrix of the received signal vector X1(t) of subarray one and the received signal vector X2(t+τ) of subarray two after a delay of τ, denoted as R. x (τ), Calculate the cross-covariance matrix of the received signal vector Y1(t) of subarray three and the received signal vector Y2(t+τ) of subarray four after a delay of τ, denoted as R. y (τ), Where E[·] represents the statistical expectation, (·) H The conjugate transpose operation is represented by (·). * This indicates the conjugate operation. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray 1. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray 2. s k (t+τ) represents the signal emitted by the k-th narrowband near-field source at time t+τ. R represents the zero-mean additive white Gaussian noise vector on submatrix 2 at time t+τ. s (τ) is a diagonal matrix, R s (τ)=diag[r s，1 (τ), ..., r s，k (τ), ..., r s，K [(τ)], diag[·] denotes the construction of a diagonal matrix. R w (τ) is a diagonal matrix whose diagonal elements are σ. 2 δ(τ) and δ(·) denote the Dirac function, σ 2 Indicates noise power. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray 3. This represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray four. This represents the zero-mean additive white Gaussian noise vector on the submatrix at time t+τ; Step 2.3: For R x (τ) is vectorized to obtain a vector. And thus obtain Similarly, for R y (τ) is vectorized to obtain a vector. And thus obtain Where vec{·> represents the vectorization operation, ⊙ represents the Khatri-Rao product operator, and ρ(τ)=[r s，1 (τ), ..., r s，k (τ), ..., r s，K (τ)] T ; Step 2.4: For Perform equal-interval sampling to obtain discrete data vectors in the delay domain. Similarly, for Perform equal-interval sampling to obtain discrete data vectors in the delay domain. Among them, T s N represents the pseudo-snapshot sampling interval. p Represents the number of pseudo-snapshots, Γ=[ρ(T s ), ρ(2T s ), …, ρ(N) p T s )]; Step 2.5: Applying TALS theory from Separation from and Their respective estimates are denoted as: and Similarly, applying TALS theory from Separation from and Their respective estimates are denoted as: and 6. The precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array according to claim 5, characterized in that... The specific process of step 3 is as follows: Step 3.1: Obtain the estimated value of the manifold matrix of submatrix one. The horizontal and vertical components are denoted as follows: and Among them, J hx This represents the selection matrix for the horizontal direction of the first linear array. J vx This represents the selection matrix with respect to the vertical direction of the first linear array. e1 and e2 are both row vectors with a dimension of 1×2. The first element of e1 is 1 and the rest are 0, and the second element of e2 is 1 and the rest are 0. Step 3.2: and There exists rotational invariance, therefore: Where, φ p It is a diagonal matrix; then for and Each adds a perturbation, according to get in, express The disturbance express The disturbance; Step 3.3: Let and Let the rank of be K, and let Then to Perform generalized feature decomposition to obtain in, This represents a diagonal matrix constructed from eigenvalues. This represents a matrix constructed from the eigenvectors corresponding to the eigenvalues; then... Decomposed into in, for Four submatrices of the same dimension; Step 3.4: Let Then according to Sure and Orthogonal; then construct the optimization equation, described as: Among them, ||·|| F Denotes the Frobenius norm; Step 3.5: Solve the optimization equation using the overall least squares criterion to obtain Φ. p The solution is denoted as and satisfy in, Indicates γ k The estimated value, Indicates η k The estimated value; Step 3.6: From Extract and Where |·| represents the modulo operator, and [·] k This indicates taking the k-th element of the diagonal matrix, and angle(·) indicates taking the phase angle of a complex number.

7. The precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array according to claim 6, characterized in that... The specific process of step 4 is as follows: Step 4.1: Obtain the estimated value of the manifold matrix of submatrix 2. The horizontal and vertical components are denoted as follows: and Similarly, obtain the estimate of the manifold matrix of submatrix three. The horizontal and vertical components are denoted as follows: and Obtain the estimate of the manifold matrix of subarray four. The horizontal and vertical components are denoted as follows: and Among them, J hy This represents the selection matrix for the horizontal direction of the second linear array. J vy This represents the selection matrix with respect to the vertical direction of the second linear array. Step 4.2: Obtain the spatial domain estimates of the manifold matrices of subarrays 1, 2, 3, and 4, respectively, denoted as [reference needed]. Where i = 1, 2, express The horizontal component obtained after normalization to the reference array element express The vertical component obtained after normalization to the reference array elements express The horizontal component obtained after normalization to the reference array element express The vertical component obtained after normalization to the reference array element.

8. The precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array according to claim 7, characterized in that... The specific process of step 5 is as follows: Step 5.1: From Extract an unambiguous delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as from Extract an unambiguous delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as in, express The element in the 2nd row and kth column, i = 1, 2, Indicates r k The estimated value, express The estimated value, express The estimated value; Step 5.2: Establish and respectively with r k and a k The relationship is as follows: Solve the relation again to obtain r. k and a k Their respective closed-form solutions are denoted as follows: and Step 5.3: From Extract a delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as from Extract a delayed phase estimate from the element in the 2nd row and kth column, denoted as . And Represented as in, express The element in the 2nd row and kth column, i = 1, 2, express The estimated value, express The estimated value; Step 5.4: Establish and respectively with r k and β k The relationship is as follows: Solve the relation again to obtain r. k and β k Their respective closed-form solutions are denoted as follows: and Step 5.5: Calculation Get r k rough estimate Will and Substitute them separately and In the middle, we get θ k and Their respective rough estimates are denoted as: and

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