An Improved 2D-DOA and Polarization Joint Estimation Method for Multipath Environments Based on Array Information

Abstract

This invention relates to the field of array signal processing technology, and provides a method for joint estimation of 2D-DOA and polarization in multipath environments based on array information improvement. The method includes a receiving antenna array consisting of parallel arrays, where each array element is composed of a complete electromagnetic vector sensor (EMVS). The transmitting array consists of a URA array geometry composed of EMVSs, with EMVS spacings of λ, where λ is the far-field signal wavelength, and λ is an integer greater than or equal to 1. The joint estimation of 2D-DOA and polarization using the above device includes the following steps: S1, rearranging the output data of the original model to construct a data model without rank deficiency; and performing eigenvalue decomposition on the covariance matrix of the rearranged data to obtain the signal subspace; S2, combining vector cross product and least squares techniques to obtain the joint estimation of 2D-DOA and polarization. This invention solves the rank deficiency problem caused by coherent sources by employing a matrix reconstruction method.

Description

Technical Field

[0001] This invention belongs to the technical field of array signal processing, and relates to a method for parameterizing multipath sources, particularly a 2D-DOA and polarization joint estimation method in a multipath environment based on polarization array information. Background Technology

[0002] Two-dimensional direction-of-arrival (2D-DOA) estimation is one of the main problems studied in array signal processing. Its main principle is to use a sensor array to spatially sample the incoming wave signal and estimate the angle by the phase difference between array elements. Currently, a large number of 2D-DOA estimation algorithms have emerged, such as the algorithm by Liu and Mendel (TH Liu, JM Mendel, "Azimuth and elevation direction finding using arbitrary array geometries," IEEE Transactions on Signal Processing, 1998, 46(7): 2061-2065.); the algorithm by Wu and Liao (Y.Wu, G.Liao, "A fast algorithm for 2-D direction-of-arrival estimation," Signal Processing, 2003, 83(8): 1827-1831.); and the algorithm by Xi and Liping (N.Xi, L.Liping, "A computationally efficient subspace algorithm for 2-D DOA estimation with L-shaped array," IEEE Signal Processing Letters, 2014, 21(8): 971-974.). However, the above algorithms generally only consider the application background of incoherent sources. In practical applications, the array received signal generally suffers from severe multipath effects, that is, the source signal is coherent. Coherent sources can cause rank deficiency in the received signal, which can lead to performance degradation or even failure of the algorithm.Some algorithms have addressed the multipath effect problem in 2D-DOA estimation. Typical solutions include spatial smoothing algorithms, such as Chen's algorithm (YMChen, "On spatial smoothing for two-dimensional direction-of-arrival estimation of coherent signals," IEEE Transactions on Signal Processing, 1997, 45(7): 1689-1696.); and covariance matrix reconstruction algorithms, such as Chen and Kwong's algorithm (FJChen, S.Kwong, "ESPRIT-like two-dimensional DOAestimation for coherent signals," IEEE Transactions on Aerospace and Electronic Systems, 2010, 46(3): 1477-1484.). However, these algorithms have certain drawbacks. Chen's scheme requires the array to be linear but also loses the effective aperture of the array; Kwong and Chen's scheme requires the array to be uniform.

[0003] Electromagnetic vector sensors (EMVS), as a novel type of sensor, represent a new branch of array signal processing. EMVS senses incoming wave signals through mutually orthogonal dipoles and magnetic rings. A single EMVS can sense not only the 2D-DOA information of the incoming wave but also its polarization characteristics. Compared to arrays composed of traditional scalar sensors, EMVS arrays theoretically possess significant advantages, manifested in higher resolution, stronger anti-interference capabilities, more stable detection capabilities, and polarization multiple access capabilities. Therefore, they have attracted widespread attention from academic and engineering communities both domestically and internationally. 2D-DOA and polarization estimation have correspondingly become one of the hot topics in current research on electromagnetic vector sensor arrays. After nearly 30 years of development, a large number of excellent estimation algorithms have emerged, including parameter estimation algorithms based on rotation invariant techniques (Estimation Method of Signal Parameters via Rotational, ESPRIT), such as Ren and Ma's (S. Ren, X. Ma, "2-D unitary ESPRIT-like direction-of-arrival (DOA) estimation for coherent signals with a uniform rectangular array," Sensors, 2013, 13(4): 4272-4288.); and parallel factor (PARAFAC) algorithms, such as Ahmed and Xiaofei's (T. Ahmed, Z. Xiaofei, "Rectangular array of electromagnetic vector sensors: tensor modeling / decomposition and DOA-polarisation estimation," IET Signal Processing, 2019, 13(7): 689-699.).In addition, some algorithms have already addressed the coherent source problem in EMVS arrays, such as spatial smoothing algorithms (Xu and Liu, “Simultaneous Estimation of Direction of Arrival and Polarization Parameters of Coherent Signal Sources in Electromagnetic Vector Sensor Arrays: Spatial Smoothing Method,” Journal of Communications, 05(2004):28-38.); polarization smoothing algorithms (Rahamim and Tabrikian, “Source localization using vector sensor array in a multipath environment,” IEEE Transactions on Signal Processing, 2004, 52(11):3096-3103.); and polarization difference smoothing algorithms (He and Jiang, “Polarization difference smoothing for direction finding of coherent signals,” IEEE Transactions on Aerospace and Electronic Systems, 2004, 52(11):3096-3103.). Systems, 2010, 46(1):469-480., etc. However, Xu's algorithm is limited by the uniform linear shape of the array, and the accuracy of the algorithm is limited by the array aperture; Rahamim's algorithm cannot estimate the polarization state because it smooths the polarization information; He's algorithm also cannot estimate the polarization state because it performs subtraction on the polarization information. Considering the shortcomings of the above algorithms, there is an urgent need for an improved new method to overcome the deficiencies in algorithm accuracy, complexity, and array element spacing. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a joint estimation method for 2D-DOA and polarization in a multipath environment based on array information, which is suitable for parallel array manifolds, can solve the rank deficiency problem caused by coherent sources, and uses a URA array scenario close to that used in actual engineering. It combines spatial rotation invariance and vector cross product techniques to obtain joint estimation of 2D-DOA and polarization.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by this invention is: a 2D-DOA and polarization joint estimation method based on array information improvement in multipath environments, including a receiving antenna with an array manifold consisting of parallel arrays, each array element consisting of a complete electromagnetic vector sensor (EMVS), and a transmitting array consisting of M×N EMVS forming a URA array geometry, with EMVS spacing d. x =D x λ / 2, d y =D y λ / 2, where λ is the wavelength of the far-field signal, D x and D y It is an integer greater than or equal to 1;

[0006] The joint estimation of 2D-DOA and polarization using the above-mentioned apparatus includes the following steps:

[0007] S1. Rearrange the output data of the original model to construct a data model without rank deficiency: and perform eigenvalue decomposition on the covariance matrix of the rearranged data to obtain the signal subspace;

[0008] S2. Combine vector cross product and least squares techniques to obtain 2D-DOA and polarization joint estimates.

[0009] In the preferred embodiment, step S1 includes the following steps:

[0010] S11. Rearrange the output data of the original model to form a new model;

[0011] Let M and N (M and N are integers) represent the number of rows and columns of the receiving array EMVS, let λ represent the signal wavelength, and let d x =D x λ / 2 and d y =D y λ / 2 represents the row element spacing and column element spacing, respectively, and D x and D y Let θ be an integer greater than or equal to 1; the number of far-field signals in the receiving array element is represented by K (K is a positive integer), let θ k φ k γ k η k Let be the elevation angle, azimuth angle, auxiliary polarization angle, and polarization phase difference of the k-th (k = 1, 2, ..., K) signal source relative to the receiving array, respectively. The output formula of the receiving array is:

[0012]

[0013] In the above formula, Indicates the Kronecker product. Represents the KhatriRao product. and These are the spatial response vectors of the receiving array to the k-th signal, representing the x-axis and y-axis, respectively. For the corresponding polarization response vector, s k Let A be the complex envelope of the k-th signal; x =[a x,1 ,a x,2 ,…,a x,K ] T A y =[a y,1 ,a y,2 ,…,a y,K ] T , For noise samples; the superscript T indicates transpose; define u k =sinθ k cosφ k v k =sinθ k sinφ k The formulas for the response vectors are as follows:

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] Definition B y =A y ⊙B, The model constructed after rearranging the received output Y is as follows:

[0020] X = B y (S T ⊙A x ) T +N z (3)

[0021] In the formula, X is the rearranged data matrix. This represents the noise corresponding to the rearranged data.

[0022] In the preferred embodiment, step S1 further includes the following step:

[0023] S12. Perform eigenvalue decomposition on the constructed new model to obtain the signal subspace;

[0024] The corresponding covariance matrix R of X is:

[0025] R = B y (S T ⊙A x ) T (S T ⊙A x B y +R Nz (4)

[0026] Next, eigenvalue decomposition is performed on the covariance matrix R to obtain the signal subspace E. s Because of B y Full rank rules:

[0027] E s =B y T(5)

[0028] In the formula, T is a full-rank matrix with a certain dimension of K×K.

[0029] In the preferred embodiment, step S2 includes the following steps:

[0030] S21. Construct the polarization selectivity matrix and estimate the rotation-invariant polarization factor, defining... In the formula: I N I represents an N×N identity matrix. 6,q Representing the q-th row of I6 with dimension 1×6, we get:

[0031] J q E S T -1 =J1E S T -1 D (q,1) (6)

[0032] Where the superscript -1 denotes the inverse of the matrix and the polarization domain rotation invariant factor. structure calculate

[0033]

[0034] The superscript * indicates the conjugate operation. The above formula yields... That is, u k v k The estimated value, ▲ represents the vector cross product operation;

[0035] S22. Obtain the joint estimation of the source's 2D-DOA and polarization. The 2D-DOA estimation is:

[0036]

[0037] The polarization estimate is:

[0038]

[0039]

[0040]

[0041] In the formula express The q-th element in the array, || represents the modulo operation, and angle[] represents the principal angle value.

[0042] This invention provides a joint 2D-DOA and polarization estimation method for multipath environments based on array information, applicable to parallel array manifolds. It addresses the rank deficiency problem caused by coherent sources through matrix reconstruction. This method not only provides high-resolution 2D-DOA estimation of coherent sources but also provides polarization characteristics of the source signals. This invention shows particularly good performance against coherent sources, i.e., multipath backgrounds. The algorithm is also applicable to array structures with arbitrary element spacing. Attached Figure Description

[0043] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0044] Figure 1 This is a schematic diagram of the receiving array of the present invention.

[0045] Figure 2 These are scatter plots of the 2D-DOA and polarization estimation of the estimator proposed in this invention.

[0046] Figure 3 This is a schematic diagram comparing the average RMSE of 2D-DOA estimation as a function of the number of samplings.

[0047] Figure 4 This is a schematic diagram comparing the average RMSE of 2D-DOA estimation as SNR changes.

[0048] Figure 5 This is a schematic diagram comparing the average RMSE of 2D-DOA estimates as the correlation coefficient changes.

[0049] Figure 6 This is a schematic diagram comparing the average RMSE of 2D-DOA estimation as the element spacing changes. Detailed Implementation

[0050] Example 1:

[0051] Signal model: Let M and N (M and N are integers) represent the number of rows and columns of the receiving array EMVS, let λ represent the signal wavelength, and let d x =D x λ / 2 and d y=D y λ / 2 represents the row element spacing and column element spacing, respectively, and D x and D y For integers greater than or equal to 1, the positions of the receiving array elements are assumed as follows: Figure 1 As shown; let K (K is a positive integer) represent the number of far-field signals, and let θ k φ k γ k η k These are the elevation angle, azimuth angle, auxiliary polarization angle, and polarization phase difference (θ) of the k-th (k = 1, 2, ..., K) source relative to the receiving array. k ,φ k This is also known as the 2D-DOA of the source. The receiver array output is represented as:

[0052]

[0053] in, ⊙ represents the Kronecker product, and ⊙ represents the KhatriRao product. and These are the spatial response vectors of the receiving array along the x-axis and y-axis to the k-th signal, respectively. It is the corresponding polarization response vector, s k Let A be the complex envelope of the k-th signal; x =[a x,1 ,a x,2 ,…,a x,K ] T A y =[a y,1 ,a y,2 ,…,a y,K ] T , It is a noise sample. Define u k =sinθ k cosφ k v k =sinθ k sinφ k The specific forms of the above response vectors are as follows:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] The algorithm proposed in this invention (low-rank recovery) defines B y =A y ⊙B, The matrix data in expression (1) is vectorized to obtain a new set of data. Its specific form is as follows:

[0060]

[0061] Here, vec() represents vectorizing the data, where 1 is a K-row, 1-column vector of all 1s. This is the corresponding noise. Furthermore, let's... Further analysis:

[0062] Z = [z1, z2, ..., z L ] T +N' expression (4a)

[0063]

[0064] Z consists of L smaller blocks, each containing 6 × M × N elements. An operator `unvec()` is defined, with the following function:

[0065] unvec(z l ) = B y (s l ⊙A x ) T Expression (5)

[0066] That is, z l If we take every 6N elements from top to bottom of this column vector as a column, then the result of unvec(Z) is as follows:

[0067]

[0068] This means taking the column vector Z, which contains 6×M×N×L elements, and dividing it into columns of 6N elements each, and arranging them sequentially until the end, resulting in a total of M×L columns. In the formula, This is the corresponding noise after the data has been rearranged. (S) T ⊙A x ) T It is a full-rank matrix, and the proof is as follows:

[0069] Let c i c j They are (S) T ⊙A x ) T Two different columns, namely

[0070]

[0071]

[0072] but

[0073]

[0074] Because A x Any two distinct columns are linearly independent, therefore thereby Therefore (S) T ⊙A x ) T For any two columns that are linearly independent, as long as M ≥ K (assuming a fully correlated signal), we can obtain the rank((S)). T ⊙A x ) T X = K. This solves the problem of rank loss in the array output data covariance caused by signal correlation, achieving the goal of restoring the rank. The corresponding covariance matrix R of X is:

[0075]

[0076] Eigenvalue decomposition of the covariance matrix R yields the signal subspace E. S In the above formula, since B... y For a full rank, the following relationship holds:

[0077] E s =B y T expression (10)

[0078] In the formula, T is a full-rank matrix with a certain dimension of K×K.

[0079] 2D-DOA and polarization joint estimation:

[0080] For a complete EMVS, its polarization response vector satisfies:

[0081]

[0082] In the above formula, ▲ represents the vector cross product, and the superscript * represents conjugate. Because

[0083]

[0084] in, b k (q) represents b k The q-th element in the array (q = 1, 2, ..., 6). Since...

[0085]

[0086] Considering ||b k(1)|| 2 Let it be a constant. but:

[0087]

[0088] The key to obtaining 2D-DOA estimates is estimation.

[0089] definition In the formula I N I represents an N×N identity matrix. 6,q Let q be the q-th row of dimension I6, which is 1×6. We get:

[0090] J q E S T -1 =J1E S T -1 D (q,1) Expression (15)

[0091] Where the polarization domain rotation invariant factor Further transformation of expression (15) yields:

[0092]

[0093] In the above formula, T represents E. S After eigenvalue decomposition, the column combinations of the corresponding eigenvectors for each eigenvalue are obtained. Then, using... By replacing T and sequentially calculating the left-hand side (q = 2, 3, ..., 6) of expression (16), we can obtain D. (q,1) The estimate is that its k-th diagonal element corresponds to The estimated value is denoted as Then you can construct calculate:

[0094]

[0095] The above formula is obtained That is, u k v k The estimated value is shown in ▲, which represents the vector cross product operation.

[0096] The 2D-DOA estimate is:

[0097]

[0098] And because

[0099] b k =Q k h k Expression (19)

[0100] available:

[0101]

[0102]

[0103] Therefore, the polarization estimate is:

[0104]

[0105] In the formula express The q-th element in the array, || represents the modulo operation, and angle[] represents the principal angle value.

[0106] Example 2:

[0107] To verify the effectiveness of the present invention framework, the Monte Carlo method was used to evaluate the estimation performance. Here, an M×N URA receiver array is defined, where each element is a complete co-located EMVS. The element spacing is d. x and d y Let λ be the wavelength of the electromagnetic wave signal (the reciprocal of its frequency), L be the number of samples, and α be the correlation coefficient. Assume K = 3 far-field signals with parameters θ = (40°, 10°, 60°), φ = (-15°, 45°, 20°), γ = (12°, 39°, 63°), and η = (33°, 47°, -21°). Furthermore, assume L samples have been collected. The results of each simulation plot depend on 200 independent trials. In the simulation, the signal-to-noise ratio (SNR) is defined as SNR = 10lg(||YN||). 2 / ||N|| 2 Y and N are both data matrices in expression (1). Performance is evaluated using root mean square error (RMSE). It is worth noting that the algorithm simulation uses an autoregressive process to model the intensity of relevant information sources, and the correlation coefficient matrix is ​​defined as:

[0108]

[0109]

[0110] In the formula, α∈[0,1] is the correlation coefficient. This form of correlation is closer to the actual situation and is more practical.

[0111] First, the scatter plot results of the 2D-DOA and polarization joint estimation of the proposed coherence estimator are obtained from... Figure 2 Given that M = 6, N = 6, SNR = 20 dB, L = 1, d x =d y=λ / 2, α = 1. It can be clearly seen that all parameters are correctly estimated and automatically paired. The results show that the proposed framework scheme can provide closed-form solutions for source 2D-DOA and polarization estimation.

[0112] Secondly Figure 3 The paper presents the average RMSE performance of 2D-DOA estimation of the source under different sampling numbers, where M=6, N=6, SNR=18dB, and d x =d y =λ / 2, α = 1. To highlight the reliability of the present invention, this scheme is compared with the Spatial-Smoothing algorithm (Xu Yougen, Liu Zhiwen, “Simultaneous estimation of direction of arrival and polarization parameters of coherent signal source of electromagnetic vector sensor array: spatial smoothing method,” Journal of Communications. 05(2004):28-38.), ESPRIT-Like algorithm (F.Wen, J.Shi, Z.Zhang. “Closed-form estimation algorithm for EMVS-MIMO radar with arbitrary sensor geometry,” Signal Process., 2021, 186, 108117.), Polarization-Smoothing algorithm (D.Rahamim, J.Tabrikian, R.Shavit. “Source localization using vector sensor array in a multipath environment,” IEEE Transactions on Signal Processing, 2004, 52(11):3096-3103.) and the Cramé-Rao boundary (labeled CRB) of URA. It is worth noting that all algorithms provide better RMSE performance as the number of samples increases. However, the RMSE of the method proposed in this invention is higher than all the compared algorithms, especially when the number of samples is small (e.g., L < 10), which indicates that the proposed solution is more practical.

[0113] Furthermore, the performance of the present invention was compared under three different conditions, namely (1) different algorithms under different signal-to-noise ratios (M=6, N=6, L=500, d x =d y =λ / 2, α=1); (2) Correlation intensity of different signals (M=6, N=6, L=500, SNR=2dB, d x =d y =λ / 2); (3) Different element spacing (M=6, N=6, SNR=18dB, L=500, α=1 and d is taken in this experiment)x =d y =d), In order to obtain high-resolution 2D-DOA estimation when the element spacing is significantly greater than half a wavelength, this invention utilizes the rotation-invariant factor in the spatial domain to obtain accurate results. For details, please refer to Wong and Zoltowski (KTWong,MD Zoltowski, "High accuracy 2D angle estimation with extended aperturevector sensor arrays," 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings. IEEE, 1996, 5: 2789-2792.). The results are shown in the figure below. Figure 4 It can be seen that all algorithms provide better RMSE performance as SNR increases. However, the RMSE of the method proposed in this invention is higher than all the compared algorithms, indicating that the proposed solution provides more accurate estimation performance. Figure 5 It can be seen that the algorithm proposed in this invention outperforms existing solutions under conditions of high signal correlation strength, i.e., a large α. From Figure 6 It can be seen that the algorithm proposed in this invention is superior to existing solutions when the element spacing is less than or greater than half a wavelength.

[0114] This invention proposes a joint 2D-DOA and polarization estimation algorithm based on matrix rearrangement in a multipath context. The algorithm first rearranges the matrix data output from the receiving array to obtain new matrix data. Then, it uses eigenvalue decomposition to obtain an estimate of the signal subspace, and utilizes the rotation-invariant property of the array's polarization domain to obtain the 2D-DOA and joint estimate. The proposed algorithm achieves parameter estimation with low computational complexity, moderate accuracy, and automatic pairing.

[0115] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The embodiments and features described in these embodiments can be arbitrarily combined without conflict. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for joint estimation of 2D-DOA and polarization in multipath environments based on array information improvement, characterized by: The receiving antenna, consisting of a parallel array of elements, includes an array manifold where each element is a complete electromagnetic vector sensor; the transmitting array consists of... The URA array geometry is composed of several electromagnetic vector sensors, with the spacing between the electromagnetic vector sensors being as follows: , ,in For far-field signal wavelength, and It is an integer greater than or equal to 1; use and This indicates the number of rows and columns of the receiving array electromagnetic vector sensor. , For integers, use Indicates the number of far-field signals. Let be a positive integer. , , , The first indivual, Given the elevation angle, azimuth angle, auxiliary polarization angle, and polarization phase difference of the signal source relative to the receiving array, the output of the receiving array is: （1）； In the above formula, Indicates the Kronecker product. Represents the KhatriRao product. and , respectively shaft and The receiving array of the axis to the first The spatial response vector of a signal. For the corresponding polarization response vector, For the first The complex envelope of a signal; , superscript T Indicates transpose; , For noise samples, define , The formulas for the response vectors are as follows: （2a）； （2b）； （2c）； （2d）； （2e）； The joint estimation of 2D-DOA and polarization includes the following steps: S1. The output data of the original model is rearranged to form a data model without rank deficit, and eigenvalue decomposition based on the covariance matrix is ​​performed to obtain the signal subspace. Step S1 includes the following steps: S11. Rearrange the output data of the original model to form a new model; （3）； In the formula, For rearranged data, , This represents the noise corresponding to the rearranged data. S12. Perform eigenvalue decomposition on the constructed new model to obtain the signal subspace; The corresponding covariance matrix for: （4）； Next, the covariance matrix Perform eigenvalue decomposition to obtain the signal subspace. ,because If the rank is full, then: （5）； In the formula For a certain dimension A full-rank matrix; S2. Using vector cross product and least squares techniques, 2D-DOA and polarization joint estimates are obtained from the signal subspace of S1. Step S2 includes the following steps: S21. Construct the polarization selectivity matrix and estimate the rotation-invariant polarization factor, defining... In the formula: The dimension is The identity matrix, The dimension is of The Okay, we get: （6）； Where the superscript -1 denotes the inverse of the matrix and the polarization domain rotation invariant factor. ,structure , ,calculate: （7）； Among them, superscript This represents the conjugate operation; obtained through formula 7. , Indicates to , The estimated value, This is a vector cross product operation; S22. Obtain the joint 2D-DOA and polarization estimates of the source. The 2D-DOA estimate is: （8）； The polarization estimate is: （9a）； （9b）； （9c）； In the formula express The first in One element, For modulo operation, This indicates that the principal angle value is taken.

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