Precise near-field polarization multi-parameter joint estimation method based on L-type COLD array

Abstract

The invention discloses a precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array, which is used for estimating spatial domain position parameters and polarization domain parameters of a plurality of narrow-band near-field sources in a three-dimensional near-field source positioning scene, and comprises the following steps of: receiving signals by constructing the L-shaped COLD array, dividing a linear array into a plurality of sub-arrays, and combining the sub-arrays with the L-shaped COLD array; calculating a cross covariance matrix by using the received signal vector of the subarray, performing vectorization processing, separating a manifold matrix estimated value by combining a TALS theory, and further extracting a polarization domain parameter; performing rough estimation on spatial domain position parameters by using unambiguous delay phases in sub-arrays divided by the two linear arrays, and finally obtaining an accurate estimation value; 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 a symmetrical structure, the array element spacing does not need to be limited by a quarter wavelength, and the array aperture is expanded.

Description

Technical Field

[0001] The present invention relates to a multi-target narrowband signal source localization technology, and in particular to an accurate near-field polarization multi-parameter joint estimation method based on an L-shaped COLD (Co-centered Orthogonal Loop and Dipole) array. Background Art

[0002] The problem of multi-target narrowband signal source localization is an important topic in the field of array signal processing, and it plays an important role in fields such as radar and wireless communication. Compared with far-field sources, near-field sources are located in the Fresnel zone, and their wavefronts cannot be approximated as plane wavefronts, but exist in the form of spherical wavefronts. The phase needs to be characterized by DOA (Direction Of Arrival) and distance parameters. As a key technology for mobile communication, the large-scale multiple-input multiple-output (MIMO) system has a large array aperture during base station deployment. Therefore, the target narrowband signal source is more likely to be located in the near-field region. In addition, the phase response of the spherical wavefront is a non-linear function, and the algorithm design is more complex than that of far-field sources. Therefore, the localization problem of near-field sources has attracted much attention.

[0003] Near-field source DOA estimation algorithms often rely on the Fresnel approximation, which will introduce systematic errors. To address this issue, the literature 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. (Based on partly calibrated arrays for mixed near-field and far-field localization and array calibration, IEEE Transactions on Signal Processing) combines an exact model and proposes an algorithm based on the fourth-order cumulant matrix to achieve two-dimensional parameter estimation and gain compensation. This algorithm requires a reference value obtained from the amplitude attenuation of the signal and is greatly affected by background noise and unknown path loss exponents. On this basis, 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. (Mixed Near-Field and Far-Field Source Localization Based on Exact Spatial Propagation Geometry, IEEE Transactions on Vehicular Technology) and the literature J. He, L. Li, and T. Shu, "Localization of Near-Field Sources for Exact Source-Sensor Spatial Geometry," in IEEE Signal Processing Letters, vol. 27, pp. 1040-1044, 2020. (Localization of Near-Field Sources for Exact Source-Sensor Spatial Geometry, IEEE Signal Processing Letters) propose to achieve two-dimensional direction finding by constructing a cumulant matrix pencil. This algorithm can use the phase for unambiguous coarse estimation, but requires the array to be symmetric about the reference center, and the calculation of the cumulant matrix pencil makes the algorithm complexity relatively high. The arrays in the above algorithms are all designed based on scalar sensors.

[0004] In addition to scalar sensors, the array can also be designed based on vector sensors. A vector array composed of vector sensors can observe signals from multiple dimensions and has higher performance compared to a scalar array 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, for example: the literature by 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. (Jointly estimating DOA (direction of arrival), range, and polarization in the Fresnel region, IEEE Transactions on Aerospace and Electronic Systems) proposed a reduced-rank MUSIC algorithm in the polarization domain for two polarization components, but still requires two-dimensional spectral peak search when estimating polarization parameters, with relatively high complexity. Another example is the literature by H. Ma, H. Tao. Three-Dimensional Mixed Far-Field and Near-Field Sources Localization Utilizing Cross Tripole Array. Circuits Syst Signal Process 42, 4320-4342 (2023). (Three-dimensional mixed far-field and near-field source localization using a cross tripole array, Circuits, Systems and Signal Processing) uses a cross array of three orthogonal dipoles to achieve three-dimensional parameter estimation and array aperture expansion, but to ensure phase ambiguity-free, the element positions need to satisfy a special multiple relationship. The above algorithms based on the Fresnel approximation have the problem of systematic error.Existing algorithms based on exact polarization-sensitive arrays have been proposed. For example, the literature "Near-Field Parameter Estimation for Polarized Source Using Spatial Amplitude Ratio" by J. He, L. Li, and T. Shu in IEEE Communications Letters, vol. 24, no. 9, pp. 1961-1965, Sept. 2020. (Near-field parameter estimation of polarized source using spatial amplitude ratio, IEEE Communications Letters) proposed an algorithm based on the second-order statistics of received data; another example is the literature "Near-field localization based on exact model with a linear COLD array" by K. Yin, C. Gao, and Y. Dai in the 2022 IEEE Radar Conference (RadarConf22), 2022. (Near-field localization based on exact model and linear COLD array, IEEE Radar Conference) and the literature "Near-Field DOA-Range and Polarization Estimation Based on Exact Propagation Model with COLD Arrays" by Yin, K., Dai, Y. & Gao, C. in Circuits Syst Signal Process 41, 5183-5200 (2022). (Near-field DOA-range and polarization estimation based on exact propagation model and COLD array, Circuits, Systems and Signal Processing) proposed an algorithm based on the fourth-order cumulant of received data. The above algorithms based on exact polarization-sensitive arrays give closed-form solutions for the joint estimation of spatial two-dimensional position parameters and polarization parameters. However, these algorithms are based on one-dimensional COLD arrays and can only locate the spatial two-dimensional position; at the same time, these algorithms utilize the characteristic that the signal source is coplanar with the array and ignore the influence of the element position on the DOA, thus using the amplitude attenuation to roughly estimate the spatial two-dimensional position parameters. However, in a three-dimensional scenario, the amplitude response is coupled with the angular parameters in the spatial domain position parameters, and there is a large deviation problem when using amplitude attenuation for rough estimation. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an accurate near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array, which uses the total least squares criterion for polarization domain parameter estimation, has high estimation accuracy, uses the unambiguous delay phase in the sub-arrays divided by two linear arrays for rough estimation of spatial position parameters, has higher estimation accuracy compared with using amplitude attenuation for rough estimation, and the array does not need to be symmetrically constructed, and the element spacing does not require a quarter-wavelength limit, expanding the array aperture.

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

[0007] Step 1: In a three-dimensional near-field source localization scenario, assume that there are multiple narrowband near-field sources, and design an L-shaped COLD array composed of a first linear array and a second linear array sharing the first COLD element as the receiving array. The first linear array is deployed on the x-axis of the three-dimensional coordinate, the second linear array is deployed on the y-axis of the three-dimensional coordinate, and the shared first COLD element is deployed at the origin of the three-dimensional coordinate as the reference element to form an accurate spherical wavefront model of the L-shaped COLD array. After the receiving array receives the signals emitted by all narrowband near-field sources in the model, obtain the expressions of the received signal vectors of the first linear array and the second linear array respectively. Among them, the expressions of the received signal vectors of the first linear array and the second linear array both contain the spatial position parameters and polarization domain 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;

[0008] Step 2: Divide the first linear array into sub-array one and sub-array two, which contain the same number of COLD elements. Sub-array one consists of multiple consecutive COLD elements starting from the 1st COLD element of the first linear array, and sub-array two consists of multiple consecutive COLD elements starting from the last COLD element of the first linear array and moving forward. Similarly, divide the second linear array into sub-array three and sub-array four, which contain the same number of COLD elements. Sub-array three consists of multiple consecutive COLD elements starting from the 1st COLD element of the second linear array, and sub-array four consists of multiple consecutive COLD elements starting from the last COLD element of the second linear array and moving forward. Then, based on the received signal vector of the first linear array, obtain the received signal vectors of sub-array one and sub-array two respectively, and based on the received signal vector of the second linear array, obtain the received signal vectors of sub-array three and sub-array four respectively. Next, calculate the cross-covariance matrix between the received signal vector of sub-array one and the delayed received signal vector of sub-array two, and calculate the cross-covariance matrix between the received signal vector of sub-array three and the delayed received signal vector of sub-array four. Then, perform equally-spaced sampling on the vectors obtained after respectively vectorizing the two cross-covariance matrices to obtain the corresponding discrete data vectors in the delay domain. Finally, use the TALS theory to separately obtain the estimated values of the manifold matrices of sub-array one and sub-array two from the discrete data vectors in the delay domain corresponding to sub-array one and sub-array two, and use the TALS theory to separately obtain the estimated values of the manifold matrices of sub-array three and sub-array four from the discrete data vectors in the delay domain corresponding to sub-array three and sub-array four;

[0009] Step 3: Obtain the horizontal direction component and vertical direction component of the estimated value of the manifold matrix of sub-array one, and there is rotational invariance between the horizontal direction component and the vertical direction component. Then, solve the solution of the diagonal matrix in the expression representing the rotational invariance property. Next, extract the estimated values of the polarization domain parameters of each narrowband near-field source from the solution of the diagonal matrix;

[0010] Step 4: Respectively obtain the horizontal direction component and vertical direction component of the estimated value of the manifold matrix of sub-array two, sub-array three, and sub-array four. Then, respectively normalize the horizontal direction component and vertical direction component of the estimated value of the manifold matrix of sub-array one, sub-array two, sub-array three, and sub-array four to the reference element to obtain the spatial domain estimated values of the manifold matrices of sub-array one, sub-array two, sub-array three, and sub-array four;

[0011] Step 5: According to the spatial domain estimation values of the manifold matrices of Sub-array 1 and Sub-array 2 respectively, obtain the parametric closed-form solutions of the distances from each narrowband near-field source to the reference element, and the parametric closed-form solutions of the angles between the signals emitted by each narrowband near-field source incident on the reference element and the x-axis; According to the spatial domain estimation values of the manifold matrices of Sub-array 3 and Sub-array 4 respectively, obtain the parametric closed-form solutions of the distances from each narrowband near-field source to the reference element, and the parametric closed-form solutions of the angles between the signals emitted by each narrowband near-field source incident on the reference element and the y-axis; Then, take the average value of the two parametric closed-form solutions of the distances from each narrowband near-field source to the reference element as the rough estimation value, and according to the relationship between the angle between the signal emitted by each narrowband near-field source incident on the reference element and the x-axis and the elevation angle and azimuth angle of each narrowband near-field source, as well as the relationship between the angle between the signal emitted by each narrowband near-field source incident on the reference element and the y-axis and the elevation angle and azimuth angle of each narrowband near-field source, obtain the rough estimation values of the elevation angle and azimuth angle of each narrowband near-field source respectively;

[0012] Step 6: According to the rough estimation values of the distances from each narrowband near-field source to the reference element, and the rough estimation values of the elevation angle and azimuth angle of each narrowband near-field source respectively, obtain the corresponding accurate estimation values.

[0013] In Step 1, the first linear array includes M COLD elements, the second linear array includes N COLD elements, and the spacing between two adjacent COLD elements in the first linear array and the second linear array 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.

[0014] In Step 1, the process of obtaining the expressions of the received signal vectors of the first linear array and the second linear array respectively is as follows:

[0015] Step 1.1: Assume that at time t, the receiving array receives signals emitted by K narrowband near-field sources, and assume that the spatial domain position parameters of the k-th narrowband near-field source are and the polarization domain parameters are (γ k , η k ), where 1 < K < min(M, N), min(·) is the minimum value 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 \(t\) incident on the reference element and the \(x\)-axis as \(\alpha\). k Denote the angle between the signal emitted by the \(k\)-th narrowband near-field source at time \(t\) incident on the reference element and the \(y\)-axis as \(\beta\). k Then determine \(\theta\). k , and the relationship between \(\theta\) k and \(\alpha\) k and \(\beta\).

[0017] 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 to the \(n\)-th COLD element of the second linear array, denoted as and respectively, where \(m = 1, 2, \cdots, M\), \(n = 1, 2, \cdots, N\). denotes the distance from the \(m\)-th COLD element of the first linear array to the reference element. denotes the distance from the \(n\)-th COLD element of the second linear array to the reference element.

[0018] Step 1.4: According to the propagation relationship of the accurate spherical wavefront, obtain the amplitude-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 that incident on the reference element, and the amplitude-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 that incident on the reference element, denoted as and

[0019] where \(p\) represents the path loss exponent, \(e\) is the natural constant, and \(j\) is the imaginary unit. denotes 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 relative to the reference element. denotes 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 relative to the reference element. \(\psi\) m，k denotes the delay phase 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. Denote the delay phase of the signal emitted by the \(k\)-th narrowband near-field source at time \(t\) when 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 \(\mathbf{a}\) sx (\alpha k , r k ) and \(\mathbf{a}\) sy (\beta k , r k ), where, \((\cdot)^\mathrm{T}\) T represents 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 \(\mathbf{a}\) x，k and \(\mathbf{a}\) y，k , where, \(\mathbf{1}_{2}\) represents a \(2\times1\) all-ones vector, \(\otimes\) represents the Kronecker product operator, \(\odot\) represents the Hadamard product operator, \(\mathbf{a}\) p represents the polarization state, \(\mathbf{1}_{M}\) M represents an \(M\times1\) all-ones vector, \(\mathbf{1}_{N}\) N represents an \(N\times1\) all-ones vector, \(\mathbf{v}\) k = [\(\sin\alpha\) 1，k , …, \(\sin\alpha\) m，k , …, \(\sin\alpha\) M，k ^\mathrm{T} T , \(\mathbf{w}\) k = [\(\sin\beta\) 1，k , …, \(\sin\beta\) n，k , …, \(\sin\beta\) N，k ^\mathrm{T} T , \(\alpha\) m，k represents the angle between the signal emitted by the \(k\)-th narrowband near-field source at time \(t\) when incident on the \(m\)-th COLD element of the first linear array and the \(x\)-axis, \(\beta\) n，k represents the angle between the signal emitted by the \(k\)-th narrowband near-field source at time \(v\) when incident on 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 \(\mathbf{X}(t)\) and \(\mathbf{Y}(t)\) respectively,

[0023] Among them, s k (t) represents the signal emitted by the k-th narrowband near-field source at time t, w x (t) represents the zero-mean additive Gaussian white noise vector on the first linear array at time t, w y (t) represents the zero-mean additive Gaussian white noise vector on the second linear array at time t, A x represents the manifold matrix of the first linear array, A x = [a x，1 ,..., a x，K , A y represents the manifold matrix of the second linear array, A 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, sub-array one is composed of the first M - 1 COLD array elements of the first linear array, and sub-array two is composed of the last M - 1 COLD array elements of the first linear array; sub-array three is composed of the first N - 1 COLD array elements of the second linear array, and sub-array four is composed of the last N - 1 COLD array elements of the second linear array.

[0025] In step 2, the processes of obtaining the respective estimated values of the manifold matrix of sub-array one and the manifold matrix of sub-array two, and the respective estimated values of the manifold matrix of sub-array three and the manifold matrix of sub-array four are as follows:

[0026] Step 2.1: Denote the received signal vectors of sub-array one and sub-array two as X1(t) and X2(t) respectively, Denote the received signal vectors of sub-array three and sub-array four as Y1(t) and Y2(t) respectively, Among them, represents the selection matrix of sub-array one, represents the selection matrix of sub-array two, I2 represents the 2×2 identity matrix, I M-1 represents the (M - 1)×(M - 1) identity matrix, 0 M-1，1 represents the (M - 1)×1 zero vector, represents the selection matrix of sub-array three, represents the selection matrix of sub-array four, IN-1 represents an identity matrix of dimension (N - 1)×(N - 1), 0 N-1，1 represents a zero vector of dimension (N - 1)×1, represents the manifold matrix of sub - array one, represents the manifold matrix of sub - array two, represents an additive white Gaussian noise vector with zero mean on sub - array one at time t, represents an additive white Gaussian noise vector with zero mean on sub - array two at time t, represents the manifold matrix of sub - array three, represents the manifold matrix of sub - array four, represents an additive white Gaussian noise vector with zero mean on sub - array three at time t, represents an additive white Gaussian noise vector with zero mean on sub - array four at time t,

[0027] Step 2.2: Calculate the cross - covariance matrix of the received signal vector X1(t) of sub - array one and the received signal vector X2(t + τ) of sub - array 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 sub - array three and the received signal vector Y2(t + τ) of sub - array four after a delay of τ, denoted as R y (τ),

[0029] where E[·] represents statistical expectation, (·) H represents the conjugate transpose operation, (· ) * represents the conjugate operation, represents the spatial - polarization domain steering vector of the k - th narrow - band near - field source with respect to sub - array one, represents the spatial - polarization domain steering vector of the k - th narrow - band near - field source with respect to sub - array two, s k (t + τ) represents the signal emitted by the k - th narrow - band near - field source at time t + τ, represents an additive white Gaussian noise vector with zero mean on sub - array two at time t + τ, R s (τ) is a diagonal matrix, R s (τ)=diag[r s，1 (τ),…,r s，k (τ),…,r s，K(τ)], diag[·] represents constructing a diagonal matrix, R w (τ) is a diagonal matrix, and its diagonal elements are σ 2 δ(τ), δ(·) represents the Dirac function, σ 2 represents the noise power, represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray three, represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to subarray four, represents the zero-mean additive Gaussian white noise vector on subarray four at time t + τ;

[0030] Step 2.3: Vectorize R x (τ) to obtain the vector and then obtain Similarly, vectorize R y (τ) to obtain the vector and then obtain where, vec{·} represents the vectorization operation, ⊙ represents the Khatri-Rao product operator, ρ(τ) = [r s，1 (τ), r s，k (τ), …, r s，K (τ)] T ;

[0031] Step 2.4: Perform equally spaced sampling on to obtain the discrete data vector in the delay domain Similarly, perform equally spaced sampling on to obtain the discrete data vector in the delay domain where, T s represents the pseudo-snapshot sampling interval, N p represents the number of pseudo-snapshots, Γ = [ρ(T s ), ρ(2T s ), …, ρ(N p T s );

[0032] Step 2.5: Use the TALS theory to separate and obtain from and their respective estimated values, denoted as and Similarly, use the TALS theory to separate and obtain from and Their respective estimated values, denoted correspondingly 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 subarray 1 The horizontal direction component and the vertical direction component of, denoted correspondingly as and where J hx represents the horizontal direction selection matrix with respect to the first linear array, J vx represents the vertical direction selection matrix with respect to the first linear array, Both e1 and e2 are row vectors with a dimension of 1×2. The first element in e1 is 1 and the remaining elements are 0. The second element in e2 is 1 and the remaining elements are 0;

[0035] Step 3.2: and There is rotational invariance between them, and there is: where Φ p is a diagonal matrix; then add perturbations to and respectively. According to obtain where represents 's perturbation, represents 's perturbation; Step 3.3: Let and 's rank be K, and let Then perform a generalized eigenvalue decomposition on to obtain where represents the diagonal matrix constructed by the eigenvalues, represents the matrix constructed by the eigenvectors corresponding to the eigenvalues; then decompose into where is 's four submatrices with the same dimension;

[0036] Step 3.4: Let Then determine according to that is orthogonal to ; then construct an optimization equation, described as: where ||·|| F represents the Frobenius norm;

[0037] Step 3.5: Solve the optimization equation using the total least squares criterion to obtain the solution of Φ p , denoted as and satisfies wherein represents the estimated value of y k , represents the estimated value of η k ;

[0038] Step 3.6: Extract from and and where |·| represents the modulus operation symbol, [·] k represents the k-th element of the diagonal matrix, and angle(·) represents the phase angle of the complex number.

[0039] The specific process of the said Step 4 is as follows:

[0040] Step 4.1: Obtain the estimated values of the horizontal and vertical direction components of the manifold matrix of sub-array two, correspondingly denoted as and and Similarly, obtain the estimated values of the horizontal and vertical direction components of the manifold matrix of sub-array three , correspondingly denoted as and Obtain the estimated values of the horizontal and vertical direction components of the manifold matrix of sub-array four , correspondingly denoted as and where J hy represents the horizontal direction selection matrix with respect to the second linear array, J vy represents the vertical direction selection matrix with respect to the second linear array,

[0041] Step 4.2: Obtain the spatial domain estimated values of the manifold matrices of sub-array one, sub-array two, sub-array three, and sub-array four respectively, correspondingly denoted as where i = 1, 2, represents the horizontal direction component obtained by normalizing to the reference array element, represents the vertical direction component obtained by normalizing to the reference array element, represents The horizontal direction component obtained after normalizing to the reference element, denotes the vertical direction component obtained after normalizing to the reference element.

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

[0043] Step 5.1: Extract an unambiguous delay phase estimation value from the element in the second row and the k-th column of , denoted as and express as Extract an unambiguous delay phase estimation value from the element in the second row and the k-th column of , denoted as and express as where denotes the element in the second row and the k-th column of , i = 1, 2, denotes the estimated value of r k , denotes the estimated value of denotes the estimated value of ;

[0044] Step 5.2: Establish the relationships between and with r k and α k respectively. The relationships are as follows: Then solve the relationships to obtain the closed-form solutions of the respective parameters of r k and a k , denoted as and

[0045] Step 5.3: Extract a delay phase estimation value from the element in the second row and the k-th column of , denoted as and express as Extract a delay phase estimation value from the element in the second row and the k-th column of , denoted as and express as where denotes the element in the second row and the k-th column of , i = 1, 2, denotes The estimated value of express An estimated value of

[0046] Step 5.4: Establish and Respectively with r k and β k The relationship is as follows: Solve the relationship again and get r k and β k The closed-form solutions of their respective parameters are recorded as and

[0047] Step 5.5: Calculation Get r k A rough estimate of Will and Substitute and In the k and Their respective rough estimates are recorded as and

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

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

[0050] 2) Since the steering vector under the precise spherical wavefront model has phase ambiguity, a rough estimate for deambiguation is required. The method of the present invention divides the first linear array into subarray 1 and subarray 2, and the second linear array into subarray 3 and subarray 4. The received signal vectors of the two subarrays belonging to the same linear array are used to construct the delay-related mutual covariance matrix, and the parallel factor decomposition method is used to obtain the estimated value of the manifold matrix of the subarray. Since the manifold matrices of these subarrays each contain an unambiguous phase, these unambiguous phases can be used to make a rough estimate of the spatial position parameters. Compared with the rough estimate using amplitude attenuation, the rough estimate obtained in this way is less affected by path loss and noise interference, has high estimation accuracy, and breaks through the restrictions of near-field DOA estimation that the array requires symmetry about the reference array element and the array element spacing requires a quarter wavelength, thereby expanding the array aperture. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of the L-shaped COLD array accurate spherical wavefront model in the method of the present invention;

[0052] Figure 2 It is a three-dimensional joint scatter plot of the accurate estimated values 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, and the distances from each narrowband near-field source to the reference element in 500 Monte Carlo simulations;

[0053] Figure 3 It is a three-dimensional joint scatter plot of the estimated values of the polarization auxiliary angles and polarization phase differences of each narrowband near-field source in 500 Monte Carlo simulations. Specific implementation manner

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

[0055] A precise near-field polarization multi-parameter joint estimation method based on an L-shaped COLD array proposed by the present invention includes the following steps:

[0056] Step 1: As shown in Figure 1 , in a three-dimensional near-field source localization scenario, it is assumed that there are multiple narrowband near-field sources, and an L-shaped COLD array composed of a first linear array and a second linear array sharing the first COLD element is designed as a receiving array. The first linear array is deployed on the x-axis of the three-dimensional coordinate, the second linear array is deployed on the y-axis of the three-dimensional coordinate, and the shared first COLD element is deployed at the origin of the three-dimensional coordinate as a reference element to form an accurate spherical wavefront model of the L-shaped COLD array. After the receiving array receives the signals emitted by all narrowband near-field sources in the model, the expressions of the received signal vectors of the first linear array and the second linear array are obtained. Among them, the expressions of the received signal vectors of the first linear array and the second linear array both contain the spatial position parameters and polarization domain 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 includes M COLD elements, the second linear array includes N COLD elements, and the distance between two adjacent COLD elements in the first linear array and the second linear array is d. Among them, the receiving array includes a total of M + N - 1 COLD elements, M ≥ 3, N ≥ 3, and d = λ / 2, where λ represents the wavelength of the signal emitted by the narrowband near-field source.

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

[0059] Step 1.1: It is assumed that at time t, the receiving array receives the signals emitted by K narrowband near-field sources, and the spatial position parameters of the kth narrowband near-field source are set as and the polarization domain parameters are (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 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°].

[0060] Step 1.2: Denote the angle between the signal emitted by the k-th narrowband near-field source at time t incident on the reference element and the x-axis as α k , and denote the angle between the signal emitted by the k-th narrowband near-field source at time t incident on the reference element and the y-axis as β k ; then from the Figure 1 shown three-dimensional geometric relationship, θ k , can be mapped to α k and β k , that is, the relationship between θ k , and α k and β k can be determined,

[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 to the n-th COLD element of the second linear array respectively according to the trigonometric function relationship, and denote them as and where m = 1, 2, …, M, n = 1, 2, …, N, represents the distance from the m-th COLD element of the first linear array to the reference element, represents the distance from the n-th COLD element of the second linear array to the reference element,

[0062] Step 1.4: According to the propagation relationship of the exact spherical wavefront, the response of the signal emitted by the k-th narrowband near-field source at time t incident on the m-th COLD array element of the first linear array is converted into the amplitude-phase factor compared with that incident on the reference array element, and the response of the signal emitted by the k-th narrowband near-field source at time t incident on the n-th COLD array element of the second linear array is converted into the amplitude-phase factor compared with that incident on the reference array element, which are correspondingly denoted as and

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

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

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

[0066] where 12 represents the 2×1 all-ones vector. denotes the Kronecker product operator, denotes the Hadamard product operator, a p denotes the polarization state, 1 M denotes an all - one vector of size M×1, 1 N denotes an all - one vector of size N×1, v 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 denotes the angle between the signal emitted by the k - th narrow - band near - field source at time t incident on the m - th COLD element of the first linear array and the x - axis, β n,k denotes the angle between the signal emitted by the k - th narrow - band near - field source at time v incident on the n - th COLD element of the second linear array and the y - axis,

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

[0068] where, s k (t) denotes the signal emitted by the k - th narrow - band near - field source at time t, w x (t) denotes the zero - mean additive Gaussian white noise vector on the first linear array at time t, w x (t) is of dimension 2M×1, w y (t) denotes the zero - mean additive Gaussian white noise vector on the second linear array at time t, w y (t) is of dimension 2N×1, A x denotes the manifold matrix of the first linear array, A x =[a x，1 ,..., a x，K , A x is of dimension 2M×K, A y denotes the manifold matrix of the second linear array, A y =[a y，1 ,..., a y，K , A y is of dimension 2N×K, s(t) denotes 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 sub-array one and sub-array two, each containing the same number of COLD elements. Sub-array one consists of multiple consecutive COLD elements starting from the 1st COLD element of the first linear array, and sub-array two consists of multiple consecutive COLD elements starting from the last COLD element of the first linear array and moving forward. Similarly, divide the second linear array into sub-array three and sub-array four, each containing the same number of COLD elements. Sub-array three consists of multiple consecutive COLD elements starting from the 1st COLD element of the second linear array, and sub-array four consists of multiple consecutive COLD elements starting from the last COLD element of the second linear array and moving forward. Then, based on the received signal vector of the first linear array, obtain the received signal vectors of sub-array one and sub-array two respectively, and based on the received signal vector of the second linear array, obtain the received signal vectors of sub-array three and sub-array four respectively. Next, calculate the cross-covariance matrix between the received signal vector of sub-array one and the delayed received signal vector of sub-array two, and calculate the cross-covariance matrix between the received signal vector of sub-array three and the delayed received signal vector of sub-array four. Then, perform equally-spaced sampling on the vectors obtained after respectively vectorizing the two cross-covariance matrices to obtain the corresponding discrete data vectors in the delay domain. Finally, use the TALS theory to separately obtain the estimated values of the manifold matrix of sub-array one and the manifold matrix of sub-array two from the discrete data vectors in the delay domain corresponding to sub-array one and sub-array two, and use the TALS theory to separately obtain the estimated values of the manifold matrix of sub-array three and the manifold matrix of sub-array four from the discrete data vectors in the delay domain corresponding to sub-array three and sub-array four.

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

[0071] Further specified, in Step 2, the process of obtaining the estimated values of the manifold matrix of sub-array one and the manifold matrix of sub-array two respectively, and the estimated values of the manifold matrix of sub-array three and the manifold matrix of sub-array four respectively is as follows:

[0072] Step 2.1: Denote the received signal vectors of sub-array one and sub-array two as X1(t) and X2(t) respectively. Denote the received signal vectors of sub-array three and sub-array four as Y1(t) and Y2(t) respectively. Where The selection matrix representing sub-array one, The selection matrix representing sub-array two, I2 represents the 2×2 identity matrix, I M-1 represents the (M - 1)×(M - 1) identity matrix, 0 M-1，1 represents the zero vector of dimension (M - 1)×1, The selection matrix representing sub-array three, The selection matrix representing sub-array four, I N-1 represents the (N - 1)×(N - 1) identity matrix, 0 N-1，1 represents the zero vector of dimension (N - 1)×1, The manifold matrix representing sub-array one, The manifold matrix representing sub-array two, represents the zero-mean additive Gaussian white noise vector on sub-array one at time t, represents the zero-mean additive Gaussian white noise vector on sub-array two at time t, The manifold matrix representing sub-array three, The manifold matrix representing sub-array four, represents the zero-mean additive Gaussian white noise vector on sub-array three at time t, w y2 (t) represents the zero-mean additive Gaussian white noise vector on sub-array four at time t,

[0073] Step 2.2: Calculate the cross-covariance matrix of the received signal vector X1(t) of sub-array one and the received signal vector X2(t + τ) of sub-array 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 sub-array three and the received signal vector Y2(t + τ) of sub-array four after a delay of τ, denoted as R y (τ),

[0075] where, E[·] represents statistical expectation, (·) H represents the conjugate transpose operation, (·) * represents the conjugate operation, represents the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to sub-array one, Denote the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to sub-array two. s k (t + τ) represents the signal emitted by the k-th narrowband near-field source at time t + τ. Denote the zero-mean additive Gaussian white noise vector on sub-array two at time t + τ, R s (τ) is a diagonal matrix, R s (τ) = diag[r s，1 (τ), …, r s，k (τ), …, r s，K (τ)], diag[·] represents constructing a diagonal matrix. R w (τ) is a diagonal matrix, and its diagonal elements are σ 2 δ(τ), δ(·) represents the Dirac function, σ 2 represents the noise power. Denote the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to sub-array three. Denote the spatial polarization domain steering vector of the k-th narrowband near-field source with respect to sub-array four. Denote the zero-mean additive Gaussian white noise vector on sub-array four at time t + τ.

[0076] Step 2.3: Vectorize R x (τ) to obtain the vector Furthermore, obtain Similarly, vectorize R y (τ) to obtain the vector Furthermore, obtain where, vec{·} represents the vectorization operation, ⊙ represents the Khatri-Rao product operator, ρ(τ) = [r s，1 (τ), …, r s，k (τ), …, r s，K (τ)] T .

[0077] Step 2.4: Perform equally-spaced sampling on to obtain the discrete data vector in the delay domain Similarly, perform equally-spaced sampling on to obtain the discrete data vector in the delay domain where, T s represents the pseudo-snapshot sampling interval, N p represents the number of pseudo-snapshots, Γ = [ρ(Ts ), ρ(2T s ), …, ρ(N p T s )]。

[0078] Step 2.5: and 's expressions satisfy the standard form of parallel factor analysis (PARAFAC). Using the TALS theory, separate from and to obtain their respective estimated values, denoted as and Similarly, using the TALS theory, separate from and to obtain their respective estimated values, denoted as and

[0079] Step 3: Obtain the horizontal and vertical direction components of the estimated value of the manifold matrix of sub - array one, and there is rotational invariance between the horizontal and vertical direction components; then solve for the solution of the diagonal matrix in the expression representing the rotational invariance property; and then extract the respective estimated values of the polarization domain parameters of each narrow - band near - field source from the solution of the diagonal matrix.

[0080] Further specified, the specific process of Step 3 is:

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

[0082] Step 3.2: Since and have a fixed amplitude - phase factor, so and have rotational invariance, there is: where Φ p is a diagonal matrix; then add perturbations to and respectively, and according to obtain Among them, denotes the perturbation of denotes the perturbation of

[0083] Step 3.3: Since and span the same subspace, let and has rank K, and let Then perform a generalized eigenvalue decomposition on to obtain where, denotes the diagonal matrix constructed from the eigenvalues, denotes the matrix constructed from the eigenvectors corresponding to the eigenvalues; then decompose into where, is four submatrices of the same dimension in has dimension 2K×2K, both have dimension K×K.

[0084] Step 3.4: Let Then determine according to to be orthogonal to ; then construct the optimization equation, described as: where, ||·|| F denotes the Frobenius norm, s.t. denotes "subject to...".

[0085] Step 3.5: Solve the optimization equation using the total least squares criterion to obtain the solution of Φ p denoted as and satisfies where, denotes the estimated value of γ k and denotes the estimated value of η k and

[0086] Step 3.6: Extract from and where, |·| denotes the modulus operation symbol, [·] k denotes the k-th element of the diagonal matrix, and angle(·) denotes the phase angle of the complex number.

[0087] Step 4: Obtain the horizontal and vertical direction components of the estimated values of the manifold matrices of Sub-array 2, Sub-array 3, and Sub-array 4 respectively; then normalize the horizontal and vertical direction components of the estimated values of the manifold matrices of Sub-array 1, Sub-array 2, Sub-array 3, and Sub-array 4 to the reference element respectively, so as to eliminate the influence of polarization components and obtain the spatial domain estimated values of the manifold matrices of Sub-array 1, Sub-array 2, Sub-array 3, and Sub-array 4 respectively.

[0088] It is further specified that the specific process of Step 4 is as follows:

[0089] Step 4.1: Obtain the estimated value of the manifold matrix of Sub-array 2 of the horizontal and vertical direction components, which are correspondingly denoted as and Similarly, obtain the estimated value of the manifold matrix of Sub-array 3 of the horizontal and vertical direction components, which are correspondingly denoted as and Obtain the estimated value of the manifold matrix of Sub-array 4 of the horizontal and vertical direction components, which are correspondingly denoted as and where J hy represents the horizontal direction selection matrix with respect to the second linear array, J vy represents the vertical direction selection matrix with respect to the second linear array,

[0090] Step 4.2: Obtain the spatial domain estimated values of the manifold matrices of Sub-array 1, Sub-array 2, Sub-array 3, and Sub-array 4 respectively, which are correspondingly denoted as where i = 1, 2, represents the horizontal direction component obtained after normalizing to the reference element, represents the vertical direction component obtained after normalizing to the reference element, represents the horizontal direction component obtained after normalizing to the reference element, represents the vertical direction component obtained after normalizing to the reference element.

[0091] Step 5: According to the spatial domain estimation values of the manifold matrices of Sub-array 1 and Sub-array 2 respectively, obtain the parametric closed-form solutions of the distances from each narrowband near-field source to the reference element, and the parametric closed-form solutions of the angles between the signals emitted by each narrowband near-field source incident on the reference element and the x-axis; according to the spatial domain estimation values of the manifold matrices of Sub-array 3 and Sub-array 4 respectively, obtain the parametric closed-form solutions of the distances from each narrowband near-field source to the reference element, and the parametric closed-form solutions of the angles between the signals emitted by each narrowband near-field source incident on the reference element and the y-axis; then take the average value of the two parametric closed-form solutions of the distances from each narrowband near-field source to the reference element as the rough estimation value, and according to the relationship between the angle between the signal emitted by each narrowband near-field source incident on the reference element and the x-axis and the elevation angle and azimuth angle of each narrowband near-field source, as well as the relationship between the angle between the signal emitted by each narrowband near-field source incident on the reference element and the y-axis and the elevation angle and azimuth angle of each narrowband near-field source, obtain the rough estimation values of the elevation angle and azimuth angle of each narrowband near-field source respectively.

[0092] Further specified, the specific process of Step 5 is as follows:

[0093] Step 5.1: For the phase ambiguity problem of the L-shaped COLD array with a COLD element interval of λ / 2, the manifold matrices of the separated sub-arrays each contain a set of unambiguous delay phases. Use and in the unambiguous delay phases for parametric rough estimation. For the reference element is the first COLD element in Sub-array 1, the second row element of the reference element is the second COLD element in Sub-array 2, the second row element of corresponds to the response of the third COLD element in the manifold matrix of the first linear array, so there is also no phase ambiguity. Extract an unambiguous delay phase estimation value from the second row and k-th column element of and denote it as and express as Extract an unambiguous delay phase estimation value from the second row and k-th column element of and denote it as and express where represents the second row and k-th column element of i = 1, 2, k represents the estimation value of r represents the estimation value of represents Estimated value.

[0094] Step 5.2: Establish and in relation to r k and α k respectively, with the relational expressions as follows: Then solve the relational expressions to obtain the closed-form parameter solutions for r k and α k respectively, denoted as and

[0095] Step 5.3: Extract a delayed phase estimated value from the element in the second row and k-th column of , denoted as and represent as Extract a delayed phase estimated value from the element in the second row and k-th column of , denoted as and represent as where represents the element in the second row and k-th column of , i = 1, 2, represents the estimated value of and represents the estimated value of

[0096] Step 5.4: Establish and in relation to r k and β k respectively, with the relational expressions as follows: Then solve the relational expressions to obtain the closed-form parameter solutions for r k and β k respectively, denoted as and

[0097] Step 5.5: Calculate to obtain the rough estimated value of r k Substitute and into and respectively to obtain the rough estimated values of θ k and respectively, denoted as and

[0098] Step 6: Obtain the corresponding accurate estimates based on the rough estimates of the distances from each narrowband near-field source to the reference element, and the rough estimates of the elevation angle and azimuth angle of each narrowband near-field source. Here, obtaining the accurate estimates is directly achieved using existing technologies.

[0099] To further illustrate the feasibility and effectiveness of the method of the present invention, simulation experiments are conducted on the method of the present invention.

[0100] It is assumed that there are three incoherent narrowband near-field sources incident on an L-shaped COLD array in three-dimensional space, the signal-to-noise ratio parameter is 25 dB, and 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 domain parameters of the three narrowband near-field sources are (10°, 20°), (35°, -40°), and (45°, 30°) respectively. The number of elements on the x-axis is M = 7, the number of 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 taken as N p = 50.

[0101] Figure 2 A three-dimensional joint scatter plot of the angles between the signals emitted by each narrowband near-field source incident on the reference element and the x-axis, the angles with the y-axis, and the accurate estimates of the distances from each narrowband near-field source to the reference element under 500 Monte Carlo simulations is given. Figure 3 A three-dimensional joint scatter plot of the estimated values of the polarization auxiliary angles and polarization phase differences of each narrowband near-field source under 500 Monte Carlo simulations is given. The simulation results show that the estimation accuracy of the spatial position parameters and polarization domain parameters of the narrowband near-field sources obtained by the method of the present invention is relatively high and can be automatically paired.

Claims

1. An accurate near-field polarization multi-parameter joint estimation method based on L-shaped COLD array, characterized in that The following steps are involved: Step 1: In a three-dimensional near-field source positioning scenario, it is assumed that there are multiple narrow-band near-field sources, and an L-shaped COLD array consisting of a first linear array and a second linear array sharing the first COLD array element is designed as a receiving array, and the first linear array is deployed on the axis of the three-dimensional coordinates, and the second linear array is deployed on the axis of the three-dimensional coordinates, and the shared first COLD array element is deployed at the origin of the three-dimensional coordinates as a reference array element, forming an L-shaped COLD array precise spherical wavefront model. In the model, after the receiving array receives the signals emitted by all narrow-band near-field sources, the expressions of the received signal vectors of the first linear array and the second linear array are obtained, wherein the expressions of the received signal vectors of the first linear array and the second linear array each contain the spatial position parameters and polarization domain parameters of each narrow-band near-field source, and the spatial position parameters of each narrow-band near-field source include the distance from each narrow-band near-field source to the reference array element, and the elevation angle and azimuth angle of each narrow-band near-field source; Step 2: Divide the first linear array into sub-array 1 and sub-array 2 containing the same number of COLD elements, where sub-array 1 consists of a plurality of consecutive COLD elements starting from the first COLD element of the first linear array, and sub-array 2 consists of a plurality of consecutive COLD elements starting from the last COLD element of the first linear array; similarly, divide the second linear array into sub-array 3 and sub-array 4 containing the same number of COLD elements, where sub-array 3 consists of a plurality of consecutive COLD elements starting from the first COLD element of the second linear array, and sub-array 4 consists of a plurality of consecutive COLD elements starting from the last COLD element of the second linear array; then, according to the received signal vector of the first linear array, obtain the received signal vectors of sub-array 1 and sub-array 2, and according to the received signal vector of the second linear array, obtain the received signal vectors of sub-array 1 and sub-array 2 respectively, and obtain the received signal vectors of sub-array 1 and sub-array 2 respectively, and obtain the received signal vectors of sub-array 1 and sub-array 2 respectively, and obtain the received signal vectors of sub-array 1 and sub-array 2 respectively, and obtain the received signal vectors of sub-array 1 and sub-array 2 respectively according to the received signal vector of the second linear array. Receive signal vectors, obtain the received signal vectors of subarray three and subarray four respectively; then calculate the cross-covariance matrix between the received signal vector of subarray one and the received signal vector of subarray two after delay, and calculate the cross-covariance matrix between the received signal vector of subarray three and the received signal vector of subarray four after delay; then perform equal-interval sampling on the vectors obtained after vectorization of the two cross-covariance matrices respectively, and obtain the corresponding delay domain discrete data vectors; finally, use TALS theory to separate the estimated values ​​of the manifold matrix of subarray one and the manifold matrix of subarray two from the delay domain discrete data vectors corresponding to subarray one and subarray two, and use TALS theory to separate the estimated values ​​of the manifold matrix of subarray three and the manifold matrix of subarray four from the delay domain discrete data vectors corresponding to subarray three and subarray four; Step 3: Obtain the horizontal and vertical components of the estimated value of the manifold matrix of subarray 1, and 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 characteristic; and then extract the estimated values ​​of the polarization domain parameters of each narrowband near-field source from the solution of the diagonal matrix; Step 4: Obtain the horizontal component and the vertical component of the estimated value of the manifold matrix of each of the sub-array 2, the sub-array 3, and the sub-array 4 respectively; then normalize the horizontal component and the vertical component of the estimated value of the manifold matrix of each of the sub-array 1, the sub-array 2, the sub-array 3, and the sub-array 4 to the reference array element respectively, and obtain the spatial domain estimated value of the manifold matrix of each of the sub-array 1, the sub-array 2, the sub-array 3, and the sub-array 4; Step 5: According to the spatial domain estimation values ​​of the manifold matrices of subarrays 1 and 2, the parameter closed-form solution of the distance from each narrowband near-field source to the reference array element and the parameter closed-form solution of the angle between the signal emitted by each narrowband near-field source and the reference array element and the x-axis are obtained; according to the spatial domain estimation values ​​of the manifold matrices of subarrays 3 and 4, the parameter closed-form solution of the distance from each narrowband near-field source to the reference array element and the parameter closed-form solution of the angle between the signal emitted by each narrowband near-field source and the reference array element and the y-axis are obtained. A closed-form solution is obtained; then the average value of the two-parameter closed-form solutions of the distance from each narrow-band near-field source to the reference array element is taken as a rough estimate, and according to the relationship between the angle of the signal emitted by each narrow-band near-field source incident on the reference array element with the x-axis and the elevation angle and azimuth angle of each narrow-band near-field source, and the relationship between the angle of the signal emitted by each narrow-band near-field source incident on the reference array element with the y-axis and the elevation angle and azimuth angle of each narrow-band near-field source, a rough estimate of the elevation angle and azimuth angle of each narrow-band near-field source is obtained; Step 6: Obtain corresponding precise estimation values ​​according to the rough estimation value of the distance from each narrowband near-field source to the reference array element and the rough estimation values ​​of the elevation angle and azimuth angle of each narrowband near-field source.

2. The accurate near-field polarization multi-parameter joint estimation method based on the L-type COLD array according to claim 1 is characterized in that In step 1, the first linear array includes M COLD array elements, the second linear array includes N COLD array elements, and the spacing between two adjacent COLD array 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.

3. The accurate near-field polarization multi-parameter joint estimation method based on the L-shaped COLD array according to claim 2 is characterized in that In step 1, the process of obtaining the expressions of the received signal vectors of the first linear array and the second linear array is as follows: Step 1.1: Set the signals received by the receiving array at time t from K narrowband near-field sources, and set the spatial position parameters of the k-th narrowband near-field source as and the polarization domain parameters as (γ k , η k ), where 1 < K < min(M, N), min(·) is the minimum value 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°]; Step 1.2: Let the angle between the signal emitted by the kth narrowband near-field source at time t and the x-axis incident on the reference array element be α k , the angle between the signal emitted by the kth narrowband near-field source at time t and the y-axis is recorded as β k ; Then confirm With α k and β k relationship, Step 1.3: Obtain the distance from the kth narrowband near-field source to the mth COLD element of the first linear array and the distance from the nth COLD element of the second linear array, which are recorded as and Wherein, m = 1, 2, ..., M, n = 1, 2, ..., N, represents the distance from the mth COLD element of the first line array to the reference element, Indicates the distance from the nth COLD array element of the second linear array to the reference array element; Step 1.4: According to the propagation relationship of the precise spherical wavefront, the response of the signal emitted by the k-th narrowband near-field source at the m-th COLD element of the first linear array at time t is converted into the amplitude phase factor compared with the amplitude phase factor incident on the reference element, and the response of the signal emitted by the k-th narrowband near-field source at time t is converted into the amplitude phase factor compared with the amplitude phase factor incident on the reference element, which are recorded as and Where p represents the path loss exponent, e is a natural constant, and j is an imaginary number. It represents the amplitude attenuation of the signal emitted by the k-th narrowband near-field source incident on the m-th COLD element of the first linear array relative to the reference element at time t, It represents the amplitude attenuation of the signal emitted by the k-th narrowband near-field source incident on the n-th COLD element of the second linear array relative to the reference element at time t, ψ m，k It represents the delayed phase of the signal emitted by the k-th narrowband near-field source at time t and incident on the m-th COLD element of the first linear array relative to the reference element, θ n，k It represents the delayed phase of the signal emitted by the k-th narrowband near-field source at time t and incident on the n-th COLD array element of the second linear array relative to the reference array element; Step 1.5: Obtain the spatial steering vector of the k-th narrowband near-field source about the first linear array and the spatial steering vector of the k-th narrowband near-field source about the second linear array, which are denoted as a sx (α k , r k ) and a sy (β k , r k ), in,(·) T Represents 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, which are denoted as a x，k and a y,k , Among them, 12 represents a 2×1 all-1 vector, represents the Kroneckerproduct operator, represents the Hadamard product operator, a p represents the polarization state, 1 M represents an M×1 vector of all 1s, 1 N represents the full l vector of N×1, V 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 represents the angle between the x-axis and the signal emitted by the k-th narrowband near-field source incident on the m-th COLD element of the first linear array at time t, β n，k It represents the angle between the signal emitted by the k-th narrowband near-field source at time t and the y-axis when it is incident on the n-th COLD element of the second linear array. 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, which are recorded as X(t) and Y(t) respectively. Among them, s k (t) represents the signal emitted by the kth narrowband near-field source at time t, w x (t) represents the additive Gaussian white noise vector with zero mean on the first line array at time t, w y (t) represents the additive white Gaussian noise vector with zero mean on the second line array at time t, A x represents the manifold matrix of the first line array, A x =[a x，1 , ..., a x，K ], A y represents the manifold matrix of the second linear array, A 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 accurate near-field polarization multi-parameter joint estimation method based on the L-shaped COLD array according to claim 3 is characterized in that In step 2, subarray 1 is composed of the first M-1 COLD elements of the first linear array, and subarray 2 is composed of the last M-1 COLD elements of the first linear array; subarray 3 is composed of the first N-1 COLD elements of the second linear array, and subarray 4 is composed of the last N-1 COLD elements of the second linear array.

5. The accurate near-field polarization multi-parameter joint estimation method based on the L-shaped COLD array according to claim 4 is characterized in that In step 2, the process of obtaining the estimated values ​​of the manifold matrix of sub-array 1 and the manifold matrix of sub-array 2, and the estimated values ​​of the manifold matrix of sub-array 3 and the manifold matrix of sub-array 4 is as follows: Step 2.1: The received signal vector of subarray 1 and the received signal vector of subarray 2 are recorded as X1(t) and X2(t) respectively. The received signal vector of subarray three and the received signal vector of subarray four are denoted as Y1(t) and Y2(t) respectively. in, represents the selection matrix of sub-matrix 1, represents the selection matrix of sub-matrix 2, I2 represents the identity matrix with a dimension of 2×2, I M-1 represents the identity matrix of dimension (M-1)×(M-1), 0 M-1，1 represents a zero vector of dimension (M-1)×1, represents the selection matrix of sub-matrix three, represents the selection matrix of sub-matrix four, I N-1 represents the identity matrix of dimension (N-1)×(N-1), 0 N-1，1 represents a zero vector of dimension (N-1)×1, represents the manifold matrix of submatrix one, represents the manifold matrix of submatrix 2, represents the additive Gaussian white noise vector with zero mean on sub-matrix 1 at time t, represents the additive Gaussian white noise vector with zero mean on sub-matrix 2 at time t, represents the manifold matrix of submatrix three, represents the manifold matrix of submatrix four, represents the additive Gaussian white noise vector with zero mean on the three sub-matrices at time t, represents the additive Gaussian white noise vector with zero mean on the four sub-matrices at time t, Step 2.2: Calculate the cross-covariance matrix of the received signal vector X1(t) of subarray 1 and the received signal vector X2(t+τ) of subarray 2 after the delay 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 the delay τ, denoted as R y (τ), Among them, E[·] represents the statistical expectation, (·) H represents the conjugate transpose operation, (·) * represents the conjugate operation, represents the spatial and polarization domain steering vector of the kth narrowband near-field source with respect to subarray 1, represents the spatial and polarization domain steering vector of the kth narrowband near-field source with respect to subarray 2, s k (t+τ) represents the signal emitted by the kth narrowband near-field source at time t+τ, represents the additive Gaussian white noise vector with zero mean on sub-matrix 2 at time t+τ, R s (τ) is a diagonal matrix, R s (τ) = diag[r s，1 (τ),…,r s，k (τ),…,r s，K (τ)], diag[·] means constructing a diagonal matrix, R w (τ) is a diagonal matrix whose diagonal elements are σ 2 δ(τ), δ(·) represents the Dirac function, σ 2 represents the noise power, represents the spatial and polarization domain steering vector of the k-th narrowband near-field source with respect to subarray three, represents the spatial and polarization domain steering vector of the kth narrowband near-field source about subarray 4, represents the additive white Gaussian noise vector with zero mean on the four sub-matrices at time t+τ; Step 2.3: R x (τ) is vectorized to obtain the vector Then get Similarly, for R y (τ) is vectorized to obtain the vector Then get Where vec{·> represents a vectorized operation, ⊙ represents the Khatri-Rao product operator, ρ(τ)=[r s，1 (τ),…,r s，k (τ),…,r s，K (τ)] T ; Step 2.4: Perform equal-interval sampling to obtain a discrete data vector in the delay domain Likewise, Perform equal-interval sampling to obtain a discrete data vector in the delay domain Among them, T s represents the pseudo-snapshot sampling interval, N p represents the number of pseudo snapshots, Γ=[ρ(T s ), ρ(2T s ),…,ρ(N p T s )]; Step 2.5: Apply TALS theory to Separated from and The respective estimated values ​​are recorded as and Similarly, using TALS theory from Separated from and The respective estimated values ​​are recorded as and 6. The accurate near-field polarization multi-parameter joint estimation method based on the L-shaped COLD array according to claim 5 is characterized in that The specific process of step 3 is as follows: Step 3.1: Get the estimated value of the manifold matrix of submatrix 1 The horizontal and vertical components of and Among them, J hx represents the horizontal selection matrix about the first line array, J vx represents the vertical selection matrix about the first line array, Both e1 and e2 are row vectors of dimension 1×2, the first element of e1 is 1 and the rest are 0, the second element of e2 is 1 and the rest are 0; Step 3.2: and There is rotation invariance between them, we have: Among them, φ p is a diagonal matrix; then and Add disturbances to each, according to get in, express The disturbance, express of disturbance; Step 3.3: Order and The rank of is K, and let Then Perform generalized eigendecomposition and obtain in, represents the diagonal matrix constructed from eigenvalues, Represents the matrix constructed by the eigenvectors corresponding to the eigenvalues; then Decompose into in, for Four sub-matrices of the same dimension in ; Step 3.4: Order Then according to Sure and Orthogonal; reconstruct the optimization equation, described as: Among them, ||·|| F represents the Frobenius norm; Step 3.5: Solve the optimization equation using the total least squares criterion to obtain Φ p The solution is denoted as and satisfy in, Represents γ k The estimated value of Represents η k An estimated value of Step 3.6: From Extracted from and Among them, |·| represents the modulus operator, [·] k It means taking the kth element of the diagonal matrix, and angle(·) means taking the phase angle of the complex number.

7. The accurate near-field polarization multi-parameter joint estimation method based on the L-shaped COLD array according to claim 6 is characterized in that The specific process of step 4 is as follows: Step 4.1: Get the estimated value of the manifold matrix of submatrix 2 The horizontal and vertical components of and Similarly, get the estimated value of the manifold matrix of submatrix three The horizontal and vertical components of and Get an estimate of the manifold matrix for submatrix four The horizontal and vertical components of and Among them, J hy represents the horizontal selection matrix about the second line array, J vy represents the vertical selection matrix about the second line array, Step 4.2: Obtain the spatial domain estimation value of the manifold matrix of each of sub-arrays 1, 2, 3, and 4, which is recorded as 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 element, 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 accurate near-field polarization multi-parameter joint estimation method based on the L-shaped COLD array according to claim 7 is characterized in that The specific process of step 5 is as follows: Step 5.1: From An unambiguous delayed phase estimate is extracted from the 2nd row and kth column element of and will Expressed as from An unambiguous delayed phase estimate is extracted from the 2nd row and kth column element of and will Expressed as in, express The element in the 2nd row and the kth column of , i=1,2, Represents r k The estimated value of express The estimated value of express An estimated value of Step 5.2: Establish and Respectively with r k and a k The relationship is as follows: Solve the relationship again and get r k and a k The closed-form solutions of their respective parameters are recorded as and Step 5.3: From Extract a delayed phase estimate from the 2nd row and kth column element of and will Expressed as from Extract a delayed phase estimate from the 2nd row and kth column element of and will Expressed as in, express The element in the 2nd row and the kth column of , i=1,2, express The estimated value of express An estimated value of Step 5.4: Establish and Respectively with r k and β k The relationship is as follows: Solve the relationship again and get r k and β k The closed-form solutions of their respective parameters are recorded as and Step 5.5: Calculation Get r k A rough estimate of Will and Substitute and In the k and Their respective rough estimates are recorded as and

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