Uniform linear array two-dimensional direction of arrival and polarization parameter joint estimation method and system based on ESPRIT

Abstract

The invention relates to the technical field of array signal processing, in particular to a uniform linear array two-dimensional direction of arrival and polarization parameter joint estimation method and system based on ESPRIT, and the method comprises the steps: constructing a polarization sensitive array model; modeling a polarized signal: establishing an array receiving signal model, and deducing a receiving signal covariance matrix; signal subspace decomposition: carrying out characteristic decomposition on the covariance matrix, extracting a signal subspace and dividing the signal subspace into five types of subarrays; solving rotation invariance: deducing a closed-form solution of a pitch angle by utilizing a subarray phase relation, and calculating an azimuth angle through a phase difference ratio of three groups of subarrays; solving a polarization parameter: deducing a closed-form solution of the polarization parameter by combining the pitch angle and the azimuth angle, and averaging to eliminate an error; and signal parameter pairing: ensuring correct parameter pairing in the case of multiple information sources through a characteristic value matching mode. According to the method, under the condition that multi-dimensional search is not needed, high-precision and rapid joint estimation of the two-dimensional direction of arrival and the polarization parameters is achieved, the calculation complexity is remarkably reduced, and the real-time performance is improved.

Description

Technical Field

[0001] The present invention relates to the field of array signal processing technology, and in particular to a method and system for jointly estimating two-dimensional direction of arrival (DOA) and polarization parameters of a uniform linear array based on ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques), which is suitable for radar target tracking and electronic reconnaissance. Background Art

[0002] DOA estimation is a core issue in array signal processing. Traditional methods are mostly based on scalar arrays, which are difficult to deal with polarization interference and multipath effects in complex electromagnetic environments, resulting in reduced resolution and increased estimation errors. As a new array structure, polarization-sensitive arrays have strong spatial filtering capabilities and parameter estimation performance by fusing polarization information with spatial information. In previous studies, joint parameter estimation based on linear polarization-sensitive arrays can usually only achieve joint estimation of one-dimensional DOA and polarization parameters, while joint estimation of two-dimensional DOA and polarization parameters often requires relying on two-dimensional or planar array structures. However, traditional methods need to be expanded to two-dimensional arrays to achieve joint estimation of two-dimensional DOA and polarization parameters, which leads to a significant increase in array space and hardware costs. Linear arrays can solve this problem.

[0003] Existing linear array-based joint parameter estimation algorithms require multi-dimensional spectral peak search or iterative optimization, which is computationally intensive and has poor real-time performance. Although the RD-MUSIC algorithm is applicable to uniform linear arrays, it still requires a two-dimensional search, resulting in low computational efficiency. In addition, most methods only support one-dimensional DOA estimation or require special array topologies (such as L-shaped arrays), which are difficult to meet the needs of uniform linear arrays. Summary of the Invention

[0004] The present invention aims to solve the problems of existing technologies that rely on multi-dimensional spectral peak search or iterative optimization, have high computational complexity, and usually require a two-dimensional array structure, resulting in poor real-time performance and high hardware costs. The present invention proposes an ESPRIT-based uniform linear array two-dimensional direction of arrival and polarization parameter joint estimation method and system. Through signal subspace partitioning and closed-form solution, while avoiding the spectral peak search and iterative calculation of traditional methods, the high-precision and low-computational complexity joint estimation of the two-dimensional direction of arrival (pitch angle + azimuth angle) and polarization parameters is achieved, significantly improving real-time performance. The use of a uniform linear array reduces array space and hardware costs.

[0005] In order to achieve the above purpose, the technical solutions adopted are:

[0006] The present invention provides a method for jointly estimating two-dimensional direction of arrival and polarization parameters of a uniform linear array based on ESPRIT, comprising the following steps:

[0007] Step 1: Construct a polarization-sensitive array model: a uniform linear array consisting of L polarization-sensitive array elements is evenly distributed along the Z axis, and each polarization-sensitive array element contains three orthogonal dipoles;

[0008] Step 2: Polarization signal modeling: Define the elevation angle, azimuth angle, and polarization parameters of the incident signal, establish the array receive signal model, and derive the receive signal covariance matrix;

[0009] Step 3, signal subspace decomposition: perform eigendecomposition on the covariance matrix, extract the signal subspace and divide it into five types of submatrices;

[0010] Step 4: Solve the rotational invariance problem: Use the sub-array phase relationship to derive the closed-form solution for the elevation angle. Calculate the azimuth angle using the phase difference ratio of the three sub-arrays. Combined with the discriminant table, solve the azimuth quadrant ambiguity problem.

[0011] Step 5: Polarization parameter solution: Combine the elevation angle and azimuth angle to derive the closed-form solution of the polarization parameter and take the average to eliminate the error.

[0012] Step 6: Signal parameter matching: Ensure that the parameters of multiple signal sources are correctly matched through eigenvalue matching.

[0013] According to the ESPRIT-based uniform linear array two-dimensional direction of arrival and polarization parameter joint estimation method of the present invention, further, in step 1, the array element spacing satisfies δ≤λ / 2, where λ is the operating wavelength.

[0014] According to the ESPRIT-based method for jointly estimating two-dimensional direction of arrival and polarization parameters of a uniform linear array of the present invention, further, step 3 extracts the signal subspace and divides it into five types of subarrays, specifically including:

[0015] Perform eigendecomposition on the covariance matrix R of the received signal to obtain the signal subspace E s and noise subspace E n , where E s It consists of the eigenvectors corresponding to the first K largest eigenvalues;

[0016] The array flow matrix A is divided into five sub-matrices. The first sub-matrix A q1 , the second sub-array A q2 The first 3 (L-1) rows and the last 3 (L-1) rows of the array flow matrix A are respectively composed of the third sub-matrix A x 、The fourth sub-array A y 、Fifth Sub-array A z They are respectively composed of dipole array flow patterns parallel to the X axis, Y axis and Z axis in the array flow pattern matrix A;

[0017] Through the linear relationship between the array manifold matrix A and the signal subspace E s of E s = AT, where T is a non-singular matrix, to determine the signal subspace E s of five types of sub-arrays E q1 、E q2 、E x 、E y 、E z .

[0018] According to the method for jointly estimating two-dimensional direction of arrival and polarization parameters of a uniform linear array based on ESPRIT of the present invention, further, the array manifold matrix A and each sub-array of A are column full-rank matrices.

[0019] According to the method for jointly estimating two-dimensional direction of arrival and polarization parameters of a uniform linear array based on ESPRIT of the present invention, further, in step 4, the closed-form solution of the elevation angle is calculated by the following formula:

[0020]

[0021] where q k is the phase factor of the array manifold matrix. [[ID=3�]]

[0022] According to the method for jointly estimating two-dimensional direction of arrival and polarization parameters of a uniform linear array based on ESPRIT of the present invention, further, in step 4, the closed-form solution of the azimuth angle is calculated by the following formula:

[0023]

[0024] where p k 、r k are both defined ratio factors, and Im represents the imaginary part of a complex number.

[0025] According to the method for jointly estimating two-dimensional direction of arrival and polarization parameters of a uniform linear array based on ESPRIT of the present invention, further, the discrimination method for azimuth quadrant ambiguity is based on the discriminant:

[0026]

[0027] If φ k < π and |Δ(φ k )| > |Δ(φ k + π)|, then the corrected azimuth angle is φ k = φ k + π; if φ k ≥ π and |Δ(φ k )| > |Δ(φ k + π)|, then the corrected azimuth angle is φ k = φk -π.

[0028] According to the ESPRIT-based method for jointly estimating two-dimensional direction of arrival and polarization parameters of a uniform linear array of the present invention, further, in step 5, the closed-form solution of the polarization parameter is calculated by the following formula:

[0029]

[0030] Among them, γ k1 , γ k2 ,η k1 ,η k2 Calculated by the following formulas:

[0031]

[0032] Among them, φ k is the azimuth of the signal, θ k is the signal’s elevation angle, γ k is the polarization amplitude angle of the signal, η k is the polarization phase angle of the signal.

[0033] According to the ESPRIT-based method for jointly estimating two-dimensional direction of arrival and polarization parameters of a uniform linear array of the present invention, further, in step 6, signal parameter pairing is achieved by:

[0034] calculate Get eigenvalues Matching Ψ1 eigenvalue q k2 and Ψ2 eigenvalue p k1 Minimum ratio error

[0035] calculate Get eigenvalues Matching Ψ2 eigenvalue p k1 and Ψ3 eigenvalue r k1 Minimum ratio error Where Ψ1 is the first sub-matrix E q1 With the second sub-matrix E q2 The rotation invariance relationship matrix between them, Ψ2 is the third sub-matrix E x With the fifth array E z The rotation invariance relationship matrix between them, Ψ3 is the fourth sub-matrix E y With the fifth array E z The rotation invariance relationship matrix between them.

[0036] Furthermore, the present invention also provides an ESPRIT-based uniform linear array two-dimensional direction of arrival and polarization parameter joint estimation system, which is used to implement the above-mentioned ESPRIT-based uniform linear array two-dimensional direction of arrival and polarization parameter joint estimation method, including:

[0037] Polarization-sensitive array model building module for a uniform linear array consisting of L polarization-sensitive elements uniformly distributed along the Z axis, each polarization-sensitive element containing three orthogonal dipoles;

[0038] Polarization signal modeling module, used to define the elevation angle, azimuth angle, and polarization parameters of the incident signal, establish the array receiving signal model, and derive the received signal covariance matrix;

[0039] Signal subspace decomposition module, used to perform eigendecomposition on the covariance matrix, extract the signal subspace and divide it into five types of submatrices;

[0040] The rotation invariance solution module is used to derive the closed-form solution of the pitch angle using the phase relationship of the sub-arrays, calculate the azimuth angle by the phase difference ratio of the three groups of sub-arrays, and solve the azimuth quadrant ambiguity problem in combination with the discriminant table;

[0041] Polarization parameter solution module, used to combine the elevation angle and azimuth angle to derive the closed-form solution of the polarization parameters and take the average to eliminate the error;

[0042] The signal parameter matching module is used to ensure the correct matching of parameters when multiple sources are used through eigenvalue matching.

[0043] The beneficial effects achieved by adopting the above technical solution are:

[0044] This method constructs a polarization-sensitive uniform linear array model, divides the signal subspace extracted after eigendecomposition of the received signal covariance matrix into five subarray types, and uses the closed-form solution of subarray phase differences based on the principle of rotational invariance (ESPRIT) to obtain the elevation angle. The azimuth angle is calculated by the phase difference ratio of the three subarray groups, and finally, the polarization parameters are estimated in a closed-form through averaging. This technical approach avoids the multidimensional spectral peak search and iterative calculations required in traditional methods, significantly reducing computational complexity. The uniform linear array structure also saves array space and hardware costs. The closed-form solution significantly improves the algorithm's real-time performance, and eigenvalue matching is used to correctly pair the parameters of multiple signal sources. Simulations have shown that under different signal-to-noise ratios and snapshot numbers, the two-dimensional DOA estimation accuracy is superior to that of traditional algorithms, and the polarization parameter estimation accuracy is close to or equivalent, achieving both high efficiency and high precision. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings of the embodiments of the present invention. The drawings are only used to illustrate some embodiments of the present invention, but not to limit all embodiments of the present invention thereto.

[0046] Figure 1 1 is a flow chart of a method for jointly estimating two-dimensional direction of arrival and polarization parameters of a uniform linear array based on ESPRIT according to an embodiment of the present invention;

[0047] Figure 2 is a schematic diagram of a polarization-sensitive array model according to an embodiment of the present invention;

[0048] Figure 3 is an azimuth discrimination table according to an embodiment of the present invention;

[0049] Figure 4 is a multi-signal DOA estimation constellation diagram according to an embodiment of the present invention;

[0050] Figure 5 is a multi-signal polarization parameter estimation constellation diagram according to an embodiment of the present invention;

[0051] Figure 6 This is a comparison table of algorithm running times according to an embodiment of the present invention;

[0052] Figure 7 1 is a comparison chart of RMSE of DOA estimation under different signal-to-noise ratios according to an embodiment of the present invention;

[0053] Figure 8 1 is a comparison chart of RMSE of polarization parameter estimation under different signal-to-noise ratios according to an embodiment of the present invention;

[0054] Figure 9 1 is a comparison chart of RMSE of DOA estimation under different snapshot numbers in an embodiment of the present invention;

[0055] Figure 10 3 is a comparison chart of RMSE of polarization parameter estimation under different snapshot numbers according to an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The following will be combined with the accompanying drawings of specific embodiments of the present invention to clearly and completely describe the exemplary embodiments of the present invention. Unless otherwise defined, technical or scientific terms used in the present invention should be given the common meanings understood by people with ordinary skills in the relevant field.

[0057] This embodiment discloses a method for jointly estimating the two-dimensional direction of arrival and polarization parameters of a uniform linear array based on ESPRIT. Figure 1 As shown, it includes the following steps:

[0058] Step S101: Construct a polarization sensitive array model: The polarization sensitive array model is as follows: Figure 2 As shown in Figure 1, the array consists of L polarization-sensitive elements, each composed of three orthogonal dipoles, for a total of 3L elements. The center of each polarization-sensitive element is evenly distributed on the Z axis, with a spacing of δ between adjacent elements. The operating wavelength is λ. To avoid angular ambiguity, δ satisfies δ ≤ λ / 2.

[0059] Step S102, polarization signal modeling: defining the elevation angle, azimuth angle and polarization parameters of the incident signal, and establishing an array receiving signal model.

[0060] Assume that there are K far-field narrowband continuous wave signals incident on the array, and the angle information and polarization information of the kth signal are (θ k ,φ k ) and (γ k ,η k ),θ k ∈[0,π / 2) is the pitch angle of the signal; φ k ∈(-π,π) is the azimuth of the signal, γ k ∈[0,π / 2) is the polarization amplitude angle of the signal, η k ∈[0,2π) is the polarization phase angle of the signal, where k satisfies k≤L-1; according to the geometric relationship, for a given array element, after coordinate transformation, the electromagnetic wave receiving vector can be expressed as:

[0061] E=E(-cosγsinφ+sinγcosθcosφ·e jη )e x

[0062] +E(cosγcosφ+sinγcosθsinγ·e jη )e y

[0063] +E(-sinγsinθ·e jη )e z

[0064] Define the spatial phase factor according to the different positions of the array elements Assume n i (t) is a random noise with a Gaussian distribution and a mean of zero. The signal vector received by the i-th (i=1, 2, …, L) array element is:

[0065]

[0066] in:

[0067]

[0068] Where ω is the signal frequency, is the initial phase of the signal, and the subsequent E k The value of is 1.

[0069] Let z(t), s(t) and n(t) be column vectors containing the received signal, incident signal and noise respectively, that is:

[0070] z(t)=[z1(t)z2(t)…z L(t)] Τ

[0071] s(t)=[s1(t)s2(t)[s K (t)] Τ

[0072] n(t)=[n1(t)n2(t)…n L (t)] Τ

[0073] in,(·) T represents the transpose. The received signal vector is expressed as:

[0074] z(t)=As(t)+n(t)

[0075] A=[a1 a2…a K ] is a 3L×K array flow matrix, where And suppose a k is linearly independent. To ensure the feasibility of the algorithm, A is required to be a matrix with full column rank, thus excluding some degenerate cases. Assuming that the array samples the incident signal at N different times, the goal of the algorithm is to obtain parameter estimates from the sampled signals.

[0076] Step S103: Derivation of the covariance matrix of the received signal based on the received signal. Assuming that the number of incident signals is known, the covariance matrix of the received signal is obtained:

[0077] R=E{z(t)z Η (t)}

[0078] =AR s A Η +R n

[0079] =R0+σ 2 I

[0080] Where R s =E{s(t)s H (t)};σ 2 is the variance of Gaussian white noise, I is the identity matrix, and E(·) represents the expectation.

[0081] Step S104, signal subspace decomposition: perform eigendecomposition on the covariance matrix to obtain the signal subspace E s and noise subspace E n . Solving from the idea of ​​characteristic root solution, the covariance matrix R can be written as:

[0082]

[0083] In the covariance matrix of the array, λ1+σ2 ≥λ2+σ 2 ≥…≥λ K +σ 2 >σ 2 =…=σ 2 are the eigenvalues ​​of R, e1,e2,…,e K ,e K+1 ,…,e 3L is the corresponding eigenvector, and the eigenvalues ​​are arranged in descending order. The first K large eigenvalues ​​correspond to the signal, and the rest correspond to noise. s ,Λ n are all diagonal matrices, and U is the eigenvector matrix. It can be proved that:

[0084] span(E s )=span(A)

[0085] Among them, E s =[e1 e2…e K ] is the eigenvector corresponding to the first K largest eigenvalues, and span(·) represents the spanned subspace. According to subspace theory, the signal subspace is the same as the column space of the array flow matrix A, that is, there exists a non-singular matrix T such that:

[0086] E s =AT

[0087] Split the array flow matrix A, assuming A q1 and A q2 are all 3(L-1)×K matrices, and are composed of the first 3(L-1) rows and the last 3(L-1) rows of A respectively; assuming A x 、A y and A z Each is an L×K matrix, consisting of 3i-2 (i = 1, 2, …, L) rows, 3i-1 (i = 1, 2, …, L) rows, and 3i (i = 1, 2, …, L) rows of A, respectively. This means they are composed of dipole array flow patterns parallel to the X, Y, and Z axes, respectively. L represents the number of array elements, and K represents the number of signal sources. The array flow pattern matrix A is required to be full column rank, and each subarray is also a full column rank matrix.

[0088] By E s =AT can get the signal subspace E s Five types of sub-arrays E q1 、E q2 、E x 、E y 、E z .

[0089] Step S105: Rotational invariance solution: The closed-form solution for the elevation angle is derived using the subarray phase relationship. The azimuth angle is calculated using the phase difference ratios of the three subarrays. The azimuth angle quadrant ambiguity is resolved using a discriminant table. The ESPRIT principle is used to achieve two-dimensional DOA parameter solution.

[0090] (1) Solve the pitch angle

[0091] According to the rotation invariance, we can get the equation:

[0092] E q1 =A q1 T

[0093] E q2 =A q2 T

[0094] in

[0095] E q2 =E q1 Ψ1

[0096] A q2 =A q1 Φ1

[0097] Where, Φ1=diag[q1 q2…q K ], Φ1 and Ψ1 have the same eigenvalues, and the expression of Ψ1 is:

[0098]

[0099] in represents the pseudo-inverse, so the pitch angle θ of the signal k The expression is:

[0100]

[0101] Due to the pitch angle There is no quadrant ambiguity problem.

[0102] (2) Solve the azimuth

[0103] In order to solve φ k , first define the ratio p k With r k :

[0104]

[0105] Similar to the above pitch angle solution process, the following equation can be obtained:

[0106] E x =A x T

[0107] Ey = A y T

[0108] E z = A z T

[0109] where

[0110] E x = E z Ψ2

[0111] A x = A z Φ2

[0112] E y = E z Ψ3

[0113] A y = A z Φ3

[0114] Similarly, the expressions Φ2 = diag[p1 p2…p K , Φ3 = diag[r1 r2…r K , and the expressions for Ψ2 and Ψ3 are:

[0115]

[0116] Based on the characteristics of p k and r k , we can obtain:

[0117]

[0118] Therefore, the azimuth angle of the signal is:

[0119]

[0120] Since the result range of the arctangent function tan -1 is but the actual azimuth angle range is (-π, π), there is a quadrant ambiguity. To ensure the correct solution, it is necessary to verify φ k using a discriminant As Figure 3 [[ID=�0]] shown, if φ k < π and |Δ(φ k )| > |Δ(φ k + π)|, then the corrected azimuth angle is φ k = φ k + π; if φ k ≥ π and |Δ(φ<00001?49>)| > |Δ(φ k + π)|, then the corrected azimuth angle is φk =φ k -π.

[0121] Step S106, polarization parameter solution: Combine the elevation angle and the azimuth angle to derive a closed-form solution for the polarization parameter, and take the average to eliminate the error.

[0122] In order to obtain the polarization parameter information of the signal, the algorithm continues to calculate the polarization parameter of the signal. k and r k Processing is performed by the above step S105 k The expression of can be obtained:

[0123]

[0124] therefore,

[0125]

[0126] By r k The expression of can be obtained:

[0127]

[0128] therefore

[0129]

[0130] Averaging the two expressions of the polarization parameters, the final result is as follows:

[0131]

[0132] because There is no quadrant ambiguity problem in the process of solving polarization parameters.

[0133] Step S107: Signal parameter matching: ensuring correct parameter matching for multiple signal sources through eigenvalue matching.

[0134] For multiple incident signals, it is necessary to determine the eigenvalue groupings for Ψ1, Ψ2, and Ψ3. Specifically, it is necessary to determine which eigenvalues ​​of Ψ1 correspond to the eigenvalues ​​of Ψ2 and which correspond to the eigenvalues ​​of Ψ3. Because the MUSIC spectral search method is computationally intensive, this approach employs an alternative eigenvalue pairing method. To correctly pair the eigenvalues ​​of the three matrices, Ψ1 can be paired with Ψ2 first, and then Ψ2 with Ψ3.

[0135]

[0136] Where, 12 The eigenvalue of corresponds to the ratio of the eigenvalue of Ψ2 to the eigenvalue of Ψ1. Therefore, for k = 1, 2…K, The value of corresponds to the eigenvalue p of Ψ2 k1 and the eigenvalue q of Ψ1 k2 All sets of ratios with The pairing with the smallest difference is:

[0137]

[0138] Similarly, pair Ψ2 with Ψ3:

[0139]

[0140] Get Collection

[0141]

[0142] in For 23 The eigenvalue of .

[0143] Just A, A q1 , A q2 , A x , A y and A z It is a full-rank matrix, and this method can jointly estimate the direction information and polarization information of the signal.

[0144] According to the algorithm flow, the amount of computation is mainly reflected in the maximum amount of computation of constructing the covariance matrix, eigenvalue decomposition, three generalized inverse operations, three complex multiplication operations, three eigenvalue decomposition calculations and two parameter pairings. The amount of computation of other linear operations is negligible. Therefore, the total amount of computation of this algorithm is O{(10L-4)K 2 +3K 3 +9NL 2 +27L 3 The RD-MUSIC algorithm mainly involves the process of constructing the covariance matrix, eigenvalue decomposition and two binary searches. Therefore, the computational complexity of RD-MUSIC is O{9NL 2 +27L 3 +(9L 2 +3L)n 2}, where n is the number of search points. Since the number of search points is large and the estimation accuracy is affected by the search step size, the computational complexity of this algorithm is much smaller than that of the RD-MUSIC algorithm.

[0145] Corresponding to the above method, this embodiment further discloses an ESPRIT-based uniform linear array two-dimensional direction of arrival and polarization parameter joint estimation system, comprising:

[0146] Polarization-sensitive array model building module for a uniform linear array consisting of L polarization-sensitive elements uniformly distributed along the Z axis, each polarization-sensitive element containing three orthogonal dipoles.

[0147] The polarization signal modeling module is used to define the elevation angle, azimuth angle, and polarization parameters of the incident signal, establish the array receiving signal model, and derive the received signal covariance matrix.

[0148] The signal subspace decomposition module is used to perform eigendecomposition on the covariance matrix, extract the signal subspace and divide it into five types of submatrices.

[0149] The rotation invariance solving module is used to derive the closed-form solution of the pitch angle by using the phase relationship of the sub-arrays, calculate the azimuth angle by the phase difference ratio of the three groups of sub-arrays, and solve the azimuth quadrant ambiguity problem in combination with the discriminant table.

[0150] The polarization parameter solution module is used to combine the elevation angle and azimuth angle to derive the closed-form solution of the polarization parameters and take the average to eliminate the error.

[0151] The signal parameter matching module is used to ensure the correct matching of parameters when multiple sources are used through eigenvalue matching.

[0152] To verify the effectiveness of this solution, the following is further explained with the help of simulation experimental data:

[0153] The array is arranged as follows Figure 2 As shown, the linear polarization sensitive array is distributed along the Z axis, with 8 array elements. Each array element contains three dipoles, and the array element spacing is half a wavelength. The incident signal is a far-field narrowband signal, and the signals are independent of each other. The noise is Gaussian white noise, and the signal and noise are independent of each other. In order to verify the effectiveness of the algorithm and the performance of parameter pairing, it is assumed that three signals are incident on the polarization sensitive array, and the pitch angles of the signals are θ = (10°, 20°, 60°); the azimuth angles of the signals are φ = (60°, 150°, -30°); the polarization amplitude angles of the signals are γ = (50°, 20°, 30°); and the polarization phase angles of the signals are η = (110°, 60°, 150°). The number of snapshots is 5000, the signal-to-noise ratio is SNR = 20dB, and the number of Monte Carlo experiments is 100. Reference Figure 4 and Figure 5 ,It can be seen that the algorithm can correctly estimate the two-dimensional DOA and polarization parameters of the three incident signals, and the pairing is correct.

[0154] In order to verify the computational complexity advantage of this scheme over the RD-MUSIC algorithm, and to more intuitively see the comparison of the two algorithms in terms of running time, refer to Figure 6The table compares the runtime of the two algorithms as the number of array elements varies. This assumes three signal sources, a 1° search interval for the RD-MUSIC algorithm, and other experimental conditions remain unchanged. The runtime is the average of 100 Monte Carlo experiments. This demonstrates that the complexity of this approach is significantly lower than that of the RD-MUSIC algorithm. This is because all other variables are significantly smaller than the number of search points n. Furthermore, the estimation accuracy of RD-MUSIC depends on the size of n.

[0155] In order to verify the effect of signal-to-noise ratio on the algorithm, it is assumed that an incident signal with parameters (θ k ,φ k ,γ k ,η k )=(10°,70°,20°,60°), the signal-to-noise ratio range is 0:20dB, and it increases by 2dB every time. The number of snapshots is 5000, and the number of Monte Carlo experiments is 500. The method of the present invention is compared with the RD-MUSIC algorithm, and the number of antennas, array element spacing and other simulation conditions of the two algorithms are kept the same. The search step size of the RD-MUSIC algorithm is set to 0.1°, and the parameter estimation accuracy is measured using the root mean square error (RMSE). The experimental results are referenced. Figure 7 and Figure 8 ,It can be seen that the DOA estimation accuracy of this scheme is better than that of the RD-MUSIC algorithm, and the ,polarization parameter estimation accuracy is slightly lower at 0:10dB, while the estimation ,accuracies of the two algorithms are comparable when 10dB and above.

[0156] In order to verify the effect of the number of snapshots on the algorithm of this scheme, the number of signals and the DOA and polarization parameters of the signals are kept unchanged, the signal-to-noise ratio is set to 20dB, the number of snapshots is set to 50:5000, and the number of Monte Carlo experiments is 500. By comparing the RMSE of the RD-MUSIC algorithm and the algorithm of this scheme, Figure 9 and Figure 10 , a similar conclusion can be drawn. When the search step size of the RD-MUSIC algorithm is 0.1°, the DOA estimation accuracy of the proposed algorithm is better than that of the RD-MUSIC algorithm. The estimation accuracy of the polarization amplitude angle is superior when the snapshot number is 500:4000. In other cases, the RD-MUSIC algorithm has higher accuracy. Although the polarization phase angle estimation accuracy is inferior to that of the RD-MUSIC algorithm, the difference between the two algorithms is very small, and the performance is basically the same.

[0157] The above experimental results further demonstrate the superiority of this scheme in the joint estimation of DOA and polarization parameters of linear arrays, which reduces the computational cost while maintaining high-precision parameter estimation.

[0158] It should be noted that the terms "first," "second," and "third" are used solely to distinguish between objects in the description and do not necessarily define a specific order or priority. For example, the names "first sub-array" and "second sub-array" are used solely to distinguish between different sub-arrays during sub-array division and do not restrict their functions or computational order. Those skilled in the art will understand that such terms can be interchanged or redefined in appropriate scenarios to achieve the technical objectives of the present invention.

[0159] Finally, it should be noted that the above-described embodiments are only specific implementation methods of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the above-described embodiments, those skilled in the art should understand that any person skilled in the art can modify or easily conceive of changes to the technical solutions described in the above-described embodiments within the technical scope disclosed by the present invention, or replace some of the technical features therein with equivalents. Such modifications, changes, or replacements do not deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A method for jointly estimating two-dimensional direction of arrival and polarization parameters of a uniform linear array based on ESPRIT, characterized in that: The following steps are involved: Step 1: Construct a polarization-sensitive array model: a uniform linear array consisting of L polarization-sensitive array elements is evenly distributed along the Z axis, and each polarization-sensitive array element contains three orthogonal dipoles; Step 2: Polarization signal modeling: Define the elevation angle, azimuth angle, and polarization parameters of the incident signal, establish the array receive signal model, and derive the receive signal covariance matrix; Step 3, signal subspace decomposition: perform eigendecomposition on the covariance matrix, extract the signal subspace and divide it into five types of submatrices; Step 4: Solve the rotational invariance problem: Use the sub-array phase relationship to derive the closed-form solution for the elevation angle. Calculate the azimuth angle using the phase difference ratio of the three sub-arrays. Combined with the discriminant table, solve the azimuth quadrant ambiguity problem. Step 5: Polarization parameter solution: Combine the elevation angle and azimuth angle to derive the closed-form solution of the polarization parameter and take the average to eliminate the error. Step 6: Signal parameter matching: Ensure that the parameters of multiple signal sources are correctly matched through eigenvalue matching.

2. The ESPRIT-based method for joint estimation of two-dimensional direction of arrival and polarization parameters of a uniform linear array according to claim 1, characterized in that: In step 1, the array element spacing satisfies δ≤λ / 2, where λ is the operating wavelength.

3. The ESPRIT-based method for joint estimation of two-dimensional direction of arrival and polarization parameters of a uniform linear array according to claim 1, characterized in that: In step 3, the signal subspace is extracted and divided into five types of sub-matrices, including: Perform eigendecomposition on the covariance matrix R of the received signal to obtain the signal subspace E s and noise subspace E n , where E s It consists of the eigenvectors corresponding to the first K largest eigenvalues; The array flow matrix A is divided into five sub-matrices. The first sub-matrix A q1 , the second sub-array A q2 The first 3 (L-1) rows and the last 3 (L-1) rows of the array flow matrix A are respectively composed of the third sub-matrix A x 、The fourth sub-array A y 、Fifth Sub-array A z They are respectively composed of dipole array flow patterns parallel to the X axis, Y axis and Z axis in the array flow pattern matrix A; Through the array flow matrix A and the signal subspace E s The linear relationship E s =AT, where T is a non-singular matrix, determining the signal subspace E s Five types of sub-arrays E q1 、E q2 、E x 、E y 、E z .

4. The ESPRIT-based method for joint estimation of two-dimensional direction of arrival and polarization parameters of a uniform linear array according to claim 3, characterized in that: The array flow matrix A and each sub-matrix of A are column-full rank matrices.

5. The ESPRIT-based method for joint estimation of two-dimensional direction of arrival and polarization parameters of a uniform linear array according to claim 1, characterized in that: In step 4, the closed-form solution for the pitch angle is calculated using the following formula: Among them, q k is the phase factor of the array flow matrix.

6. The ESPRIT-based method for joint estimation of two-dimensional direction of arrival and polarization parameters of a uniform linear array according to claim 1, characterized in that: In step 4, the closed-form solution for the azimuth angle is calculated using the following formula: Among them, p k 、r k are defined ratio factors, and Im represents the imaginary part of the complex number.

7. The ESPRIT-based method for joint estimation of two-dimensional direction of arrival and polarization parameters of a uniform linear array according to claim 6, characterized in that: The method for determining azimuth quadrant ambiguity is based on the discriminant: If φ k <π and |Δ(φ k )| > |Δ(φ k + π)|, then the corrected azimuth angle is φ k = φ k + π; if φ k ≥ π and |Δ(φ k )| > |Δ(φ k + π)|, then the corrected azimuth angle is φ k = φ k - π.

8. The ESPRIT-based method for joint estimation of two-dimensional direction of arrival and polarization parameters of a uniform linear array according to claim 1, characterized in that: In step 5, the closed-form solution of the polarization parameter is calculated using the following formula: Among them, γ k1 , γ k2 ,η k1 ,η k2 Calculated by the following formulas: Among them, φ k is the azimuth of the signal, θ k is the signal’s elevation angle, γ k is the polarization amplitude angle of the signal, η k is the polarization phase angle of the signal.

9. The ESPRIT-based method for joint estimation of two-dimensional direction of arrival and polarization parameters of a uniform linear array according to claim 3, characterized in that: In step 6, signal parameter pairing is achieved in the following way: calculate Get eigenvalues Matching Ψ1 eigenvalue q k2 and Ψ2 eigenvalue p k1 Minimum ratio error calculate Get eigenvalues Matching Ψ2 eigenvalue p k1 and Ψ3 eigenvalue r k1 Minimum ratio error Where Ψ1 is the first sub-matrix E q1 With the second sub-matrix E q2 The rotation invariance relationship matrix between them, Ψ2 is the third sub-matrix E x With the fifth array E z The rotation invariance relationship matrix between them, Ψ3 is the fourth sub-matrix E y With the fifth array E z The rotation invariance relationship matrix between them.

10. A uniform linear array two-dimensional direction of arrival and polarization parameter joint estimation system based on ESPRIT, characterized by: The method for jointly estimating two-dimensional direction of arrival and polarization parameters of a uniform linear array based on ESPRIT according to any one of claims 1 to 9 comprises: Polarization-sensitive array model building module for a uniform linear array consisting of L polarization-sensitive elements uniformly distributed along the Z axis, each polarization-sensitive element containing three orthogonal dipoles; Polarization signal modeling module, used to define the elevation angle, azimuth angle, and polarization parameters of the incident signal, establish the array receiving signal model, and derive the received signal covariance matrix; Signal subspace decomposition module, used to perform eigendecomposition on the covariance matrix, extract the signal subspace and divide it into five types of submatrices; The rotation invariance solution module is used to derive the closed-form solution of the pitch angle using the phase relationship of the sub-arrays, calculate the azimuth angle by the phase difference ratio of the three groups of sub-arrays, and solve the azimuth quadrant ambiguity problem in combination with the discriminant table; Polarization parameter solution module, used to combine the elevation angle and azimuth angle to derive the closed-form solution of the polarization parameters and take the average to eliminate the error; The signal parameter matching module is used to ensure the correct matching of parameters when multiple sources are used through eigenvalue matching.

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