Two-dimensional angle estimation method of random array in non-uniform noise scene

Abstract

The invention discloses a two-dimensional angle estimation method for a random array in a non-uniform noise scene, and the method comprises the steps: obtaining response signals collected by an EMVS array in random geometric distribution, and obtaining a covariance matrix of the response signals; removing the covariance influence of non-uniform noise in the covariance matrix to obtain a noise-free signal covariance tensor estimated value; the noise-free covariance matrix is recovered based on tensor filling, and a third-order PARAFAC tensor is obtained; and decomposing the third-order PARAFAC tensor based on a parallel factorization algorithm to obtain an azimuth angle and a polarization angle of the source signal. According to the method, the two-dimensional angle of the random array in the non-uniform noise scene is estimated based on tensor filling and parallel factorization, the two-dimensional direction-of-arrival estimation precision in the non-uniform noise environment can be improved while the aperture of the array is kept, and the defects in the aspects of noise suppression, calculation complexity and estimation precision in the prior art are overcome.

Description

Technical Field

[0001] The present invention relates to the technical field of array sensor direction finding, and in particular to a two-dimensional angle estimation method of a random array in a non-uniform noise scene. Background Art

[0002] Direction-of-arrival (DOA) estimation is a crucial technology in the fields of wireless communications, radar, sonar, etc. In the past few decades, DOA estimation has been widely studied and applied in the field of wireless communications, and a variety of classic DOA estimation algorithms have emerged. The current mainstream DOA estimation techniques include multiple signal classification algorithms, maximum likelihood estimation, matrix bundle method, rotational invariance technology (ESPRIT), and cumulant-based algorithms. Electromagnetic vector sensors (EMVS) have gradually become a research hotspot in the field of DOA estimation due to their ability to simultaneously sense electric and magnetic fields. However, in practical applications, complex noise environments (such as non-uniform noise) significantly affect the performance of these existing DOA estimation algorithms.

[0003] In order to cope with the challenge of non-uniform noise, researchers have proposed a variety of noise suppression methods. Among them, the denoising algorithm based on tensor filling can effectively solve the problem of non-uniform noise suppression and avoid the loss of array aperture. By removing the data affected by noise, tensor filling converts the noise-free signal recovery problem into a matrix or tensor filling problem, and finally uses algorithms such as ESPRIT for DOA estimation. However, these algorithms still have the problem of insufficient estimation accuracy under low signal-to-noise ratio (SNR) conditions, especially when data missing is serious. In addition, existing tensor decomposition algorithms, such as the singular value threshold (SVT) method, have high computational complexity, are sensitive to parameter settings, and lack robustness.

[0004] Therefore, the present invention proposes a two-dimensional angle estimation method for random arrays in non-uniform noise scenarios based on tensor padding and parallel factorization (PARAFAC), which can improve the two-dimensional wave direction estimation accuracy in non-uniform noise environments while maintaining the array aperture, so as to address the shortcomings of the prior art in noise suppression, computational complexity and estimation accuracy. Summary of the invention

[0005] The present invention provides a two-dimensional angle estimation method for a random array in a non-uniform noise scene, which is used to solve the technical problems of low accuracy, high calculation complexity and high sensitivity to algorithm parameters in the existing DOA estimation in a non-uniform noise scene.

[0006] In order to solve the above problems, the present invention provides a two-dimensional angle estimation method of a random array in a non-uniform noise scene, comprising:

[0007] Acquire response signals collected by an EMVS array with random geometric distribution, and obtain a covariance matrix of the response signals;

[0008] Removing the covariance effect of the non-uniform noise in the covariance matrix to obtain a noise-free signal covariance tensor estimate;

[0009] The noise-free covariance matrix is ​​restored based on tensor filling to obtain a third-order PARAFAC tensor;

[0010] The third-order PARAFAC tensor is decomposed based on a parallel factor decomposition algorithm to obtain the azimuth angle and polarization angle of the source signal.

[0011] Further, the covariance effect of the non-uniform noise in the covariance matrix is ​​removed to obtain a noise-free signal covariance tensor estimate, including:

[0012] The noise-free covariance tensor is expressed as:

[0013]

[0014] Among them, R z is the covariance matrix of the array response z(t) at time t, S Δ {·} is a sampling operator used to extract matrix elements within the coverage range of index Ω. R(m,n) is the (m,n)th item of R.

[0015] Furthermore, the noise-free covariance matrix is ​​restored based on tensor filling, including:

[0016] According to the tensor matrix filling principle, the optimization process of recovering the noise-free covariance tensor is expressed as:

[0017]

[0018] Among them, ||R|| * is the nuclear norm of the tensor R, ||[R] (n) || * is the matrix nuclear norm of the modulo-n expansion of the tensor R, α n is the weighting coefficient, α n is greater than 0 and satisfies The constant.

[0019] Furthermore, the optimization process of recovering the noise-free covariance tensor also includes:

[0020] by As The estimated value of n, transforming the optimization process into a constrained non-differentiable convex optimization problem:

[0021]

[0022] Determine and solve the objective function of the convex optimization problem based on variable separation technology;

[0023] The objective function of the convex optimization problem is:

[0024]

[0025] Among them, Ξ is a convex set, f 0 (R) is a smooth convex function, ||[R] (n) || * is the matrix nuclear norm of the modulo-n expansion of the tensor R.

[0026] Furthermore, determining and solving the objective function of the convex optimization problem based on the variable separation technology also includes:

[0027] The nuclear norm of the matrix || [R] (n) || * Smoothing: Introducing 4 dual variables and 4 variables Let f 0 (R) = 0, the objective function of the convex optimization problem is expressed as:

[0028]

[0029] Among them, ||·|| is the 2-norm of the matrix, <·> is the inner product operation, μ is a constant, is a convex function, ||·|| F represents the Frobenius norm;

[0030] The objective function is solved by an alternating iteration method to obtain an estimated value of the noise-free covariance tensor.

[0031] Furthermore, the noise-free covariance matrix is ​​restored based on tensor filling to obtain a third-order PARAFAC tensor, including:

[0032] R z Rearrange into a fourth-order tensor Symmetric Hermitian expansion of , stacked along the columns is the fourth-order tensor of noise;

[0033]

[0034] Noise Removal After that, the noise-free tensor Rearrange into a third-order PARAFAC tensor:

[0035]

[0036] Where V = A * ⊙B * R s , A * and B * denote the conjugate of A and B, ⊙ denotes the Khatri-Rao product, R s represents the covariance matrix of the source signal, is the spatial response matrix, is the polarization guiding matrix.

[0037] Further, the third-order PARAFAC tensor is decomposed based on a parallel factor decomposition algorithm, including:

[0038] Let X, Y and Z represent The modulo-1, modulo-2 and modulo-3 expansions are used to estimate Replace the theoretical values ​​X, Y, Z;

[0039] Through joint optimization Perform PARAFAC decomposition, and the decomposition objective function is expressed as follows:

[0040]

[0041] The decomposition objective function is solved by trilinear alternating least squares method, and the COMFAC algorithm is used to accelerate the convergence of the algorithm until the algorithm converges. and It is expressed as:

[0042]

[0043] in, Represent the estimated values ​​of A, B, and V after the (t-1)th iteration, Represents the pseudoinverse of a matrix.

[0044] Furthermore, the decomposition objective function is solved by using a trilinear alternating least squares method, which also includes:

[0045] When the factor matrix and When the Kruskal rank satisfies KR[A]+KR[B]+KR[V]≥2R+2, the PARAFAC decomposition is unique. and It is expressed as:

[0046]

[0047] Among them, KR[A], KR[B] and KR[V] are and Kruskal rank, R is a preset constant, Π is a permutation matrix; Ω n (n=1,2,3) are the corresponding scale fuzzy matrices, all of which are diagonal matrices, and Ω 1 Ω 2 Ω 3 =I; F n (n=1,2,3) is the error matrix.

[0048] Furthermore, the third-order PARAFAC tensor is decomposed based on a parallel factor decomposition algorithm to obtain the azimuth angle of the source signal, including:

[0049] make represent The kth column of represents the k'th column of B, but

[0050]

[0051] in, Represents Ω 2 The kth diagonal element of and represent The electric response vector and magnetic response vector of ;

[0052] Direction cosine p is obtained by cross-producting the normalized vector k' The estimated value of k' The estimated value of is calculated as:

[0053]

[0054] in, and Direction cosines The electromagnetic intensity in three dimensions, and represent The electric response vector and magnetic response vector of ;

[0055] According to a k The phase vector h k For the p k The estimated value of Perform refined recovery:

[0056] Assume h kIndicates a k The phase vector, h k =Γp k ,

[0057] Use the least squares method to recover p k :

[0058]

[0059]

[0060] The refined restored direction cosine estimate is:

[0061]

[0062] where phase{·} represents the phase in radians, is a real-valued integer vector, represents the phase vector estimate, represents the unbiased phase vector estimate after phase compensation,

[0063] The 2D-DOA azimuth angle is estimated as:

[0064]

[0065] in, Represents the elevation angle, represents the azimuth, and Respectively The first and second elements of .

[0066] Furthermore, the third-order PARAFAC tensor is decomposed based on a parallel factor decomposition algorithm to obtain the polarization angle of the source signal, including:

[0067] according to according to Get the matrix D k , denoted as for The estimate, but

[0068]

[0069] in, express The estimate, Indicates no effect on g k' Scalar of phase, ζ k represents the auxiliary polarization angle, η represents the polarization angle, and Respectively The first and second elements of , |·| means taking the absolute value.

[0070] Compared with the prior art, the beneficial effects of the present invention include: the method of the present invention can effectively handle complex noise environments by removing the influence of non-uniform noise in the covariance matrix, and can maintain good performance even in high noise or severe interference conditions, significantly improve the signal-to-noise ratio of the signal, and have good noise resistance; through PARAFAC tensor decomposition, it can utilize implicit information in multidimensional data to improve the positioning accuracy of the signal source, so that reliable angle estimation can be obtained even under low signal-to-noise ratio conditions with weak signals; in addition, the method has no strict requirements on the array geometry, allows the use of randomly distributed arrays, can be flexibly configured according to specific application requirements, and can adapt to any array structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 A schematic diagram of a flow chart of a two-dimensional angle estimation method for a random array in a non-uniform noise scenario provided by the present invention;

[0072] Figure 2 A schematic diagram of random geometric distribution of the receiving array provided by the present invention;

[0073] Figure 3 A scatter plot of simulation results of the far-field TEM signal provided by the present invention acting on the EMVS array of the receiving signal in the presence of a non-uniform noise background;

[0074] Figure 4 A schematic diagram of a curve showing a change in the average root mean square error (RMSE) of the two-dimensional DOA estimation provided by the present invention relative to the signal-to-noise ratio (SNR). DETAILED DESCRIPTION

[0075] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0076] This embodiment provides a two-dimensional angle estimation method for a random array in a non-uniform noise scenario, such as Figure 1 As shown, Figure 1 is a flow chart of a two-dimensional angle estimation method for a random array in the non-uniform noise scenario, the method comprising:

[0077] Step S101: Acquire response signals collected by an EMVS array with random geometric distribution to obtain a covariance matrix of the response signals;

[0078] Step S102: removing the covariance influence of the non-uniform noise in the covariance matrix to obtain a noise-free signal covariance tensor estimate;

[0079] Step S103: restoring the noise-free covariance matrix based on tensor filling to obtain a third-order PARAFAC tensor;

[0080] Step S104: Decomposing the third-order PARAFAC tensor based on a parallel factor decomposition algorithm to obtain an azimuth angle and a polarization angle of a source signal;

[0081] The two-dimensional angle estimation method of a random array in a non-uniform noise scenario provided in this embodiment can effectively handle complex noise environments by removing the influence of non-uniform noise in the covariance matrix, and can maintain good performance even in high noise or severe interference conditions, significantly improve the signal-to-noise ratio of the signal, and have good noise resistance. Through PARAFAC tensor decomposition, the implicit information in the multi-dimensional data can be utilized to improve the positioning accuracy of the signal source, so that reliable angle estimation can be obtained even under low signal-to-noise ratio conditions with weak signals. In addition, the method has no strict requirements on the array geometry, allows the use of randomly distributed arrays, can be flexibly configured according to specific application requirements, and can adapt to any array structure.

[0082] Specifically, in step S101, consider that there are K far-field narrow-band planar transverse electromagnetic wave (TEM) signals in a space filled with a homogeneous isotropic medium, which are received by an array consisting of M EMVS units. The geometric distribution of the array is random, such as Figure 2 As shown. If the coordinates of the mth EMVS are P m =[x m ,y m ,z m ] T , the first element is fixed at the origin as the reference P 1 =[0,0,0] T , then the array response at time t is:

[0083]

[0084] In formula (1), Represents the source signal vector at time t; is the array receiving noise; C=A⊙B, is the spatial response matrix, is the polarization steering matrix, λ represents the carrier wavelength; b k is defined as follows:

[0085]

[0086] In formula (2), Represents the elevation angle, represents the azimuth, ζ k represents the auxiliary polarization angle, and η represents the polarization angle.

[0087] Furthermore, assuming that the noise satisfies a Gaussian distribution with a mean of zero and a covariance of H, the noise can be expressed as:

[0088] E{n(t 1 ,τ)n H (t 2 ,τ)}=Hδ(t 1 -t 2 ),(3)

[0089] In formula (3), E{·} represents the mathematical expectation; δ(·) represents the unit impulse function, (·) H Represents the Hermitian transpose.

[0090] It should be noted that the noise considered in this application is additive and unrelated to the source signal. Therefore, the covariance matrix of z(t) is given by:

[0091]

[0092] In formula (4), R s =E{s(t)s H (t)} and R n =E{n(t) H n(t)} represent the covariance matrix of the source signal and the covariance matrix of the noise respectively.

[0093] Since the source signals are uncorrelated with each other, R s =diag([λ 1 ,λ 2 ,…,λ K ]), diag{·} represents the construction of a diagonal matrix, λ k is the power of the kth source signal.

[0094] In practical applications, when there are L snapshots available, R z It can be estimated as follows:

[0095]

[0096] In formula (5), z H (t) represents the conjugate transpose of z(t).

[0097] As a preferred embodiment, in step S102, first define a set Δ record R n Index of non-zero elements in:

[0098] Δ={(n,n)|n=1,2,…,6M}, (6)

[0099] Define a sampling operator S Δ {·}, which extracts the matrix elements in the range covered by index Ω:

[0100]

[0101] Where R(m,n) represents the (m,n)th item of R and satisfies

[0102]

[0103] From formula (4), we can see that R n is a diagonal matrix, so R n =S Δ {R n}.

[0104] The covariance matrix of uniform noise is eliminated to construct a noise-free covariance tensor

[0105]

[0106] In formula (9), R z represents the covariance matrix of the array response z(t), Represents the noise-free covariance tensor.

[0107] For the noise-free covariance tensor The optimization process is as follows:

[0108]

[0109] In formula (10), ||R|| * Represents the nuclear norm of the tensor R, the nuclear norm ||R|| * It is defined as the weighted sum of the modulo-n expansion of the tensor R, that is:

[0110]

[0111] In formula (11), ||R|| * is the matrix nuclear norm of the modulo-n expansion, α n is the weighting coefficient, which is greater than 0 and satisfies The constant.

[0112] In a specific embodiment, for The estimated value of the preset fitting error coefficient β n, then the optimization in formula (11) can also be transformed into a constrained optimization problem:

[0113]

[0114] The optimization problem of formula (12) is a non-differentiable convex optimization problem. As a specific embodiment, the convex optimization here can be solved by using the variable separation technology. Specifically:

[0115] By smoothing the above optimization problem, the optimization objective function is:

[0116]

[0117] In formula (13), Ξ is a convex set; f 0 (R) is a smooth convex function.

[0118] In some embodiments, since the matrix nuclear norm ||[R] (n) || * Non-smooth, so it is necessary to ||[R] (n) || * Smoothing treatment.

[0119] Here we first explain the principle of the selected smoothing process: for a matrix X, its dual form is:

[0120]

[0121] In formula (14), ||·|| represents the 2-norm of the matrix; <·> is the inner product operation, then the smooth form of g(X) is:

[0122]

[0123] In formula (15), d μ (Y) is a convex function; μ is a constant, ||·‖ F represents the Frobenius norm.

[0124] Therefore, by introducing four dual variables and 4 variables The matrix nuclear norm ‖[R] in equation (13) can be (n) || * It is expressed as:

[0125]

[0126] In formula (16), f μ (R) is smooth, so ||[R] (n) || * It is differentiable. Let f0 (R)=0. For the tensor filling problem in this embodiment, an optimization strategy can be adopted:

[0127]

[0128] The solution to the optimization problem in formula (17) can be quickly completed by using the alternating iteration method, and then the noise-free covariance tensor R can be obtained s Estimated value of

[0129] As a preferred embodiment, in step S103, the noise-free covariance matrix is ​​restored based on tensor filling to obtain a third-order PARAFAC tensor, including:

[0130] R z Can be rearranged into a fourth-order tensor The (m,p,n,q)th element is represented as:

[0131]

[0132] In formula (18), m,n∈{1,2,…,M}, p,q∈{1,2,…,6}, z m,p (t) is the 6(m-1)+pth element of z(t), z n,q (t) has the same meaning as above, (·) * Represents conjugation.

[0133] In fact, R z Can be seen as The symmetric Hermitian expansion of Transform the subscript indices of the first two dimensions, shrink the first and second subscript indices, and then stack the second two indices along the row to obtain:

[0134]

[0135] It can be seen from formula (19) that is a fourth-order PARAFAC tensor, represented as:

[0136]

[0137] After noise reduction The influence of becomes a noise-free tensor Eliminate the noise tensor It can then be rearranged into a third-order PARAFAC tensor:

[0138]

[0139] In formula (21), V = A * ⊙B * R s , A * and B * denote the conjugate of A and B, ⊙ denotes the Khatri-Rao product, R s represents the covariance matrix of the source signal, is the spatial response matrix, is the polarization guiding matrix.

[0140] Let X, Y and Z represent The module-1, module-2 and module-3 expansions of The modulo-1 and modulo-2 expansions of are as follows:

[0141]

[0142] Use estimated value Substituting the theoretical values ​​X, Y, Z, then PARAFAC decomposition can be done through joint optimization:

[0143]

[0144] This optimization problem is generally solved using the trilinear alternating least squares (TALS) method, which is also the basis for the decomposition of the third-order PARAFAC model.

[0145] Here we explain the principle of TALS: Assuming that any two of A, B and V are known, fix the two factors and use the least squares (LS) to estimate the unknown matrix. Alternately fit the three LS problems in equation (24) until the algorithm converges.

[0146] For example, in the tth iteration (t = 1, 2, ..., T), given B and V, then It can be obtained by:

[0147]

[0148] in, Represent the estimated values ​​of A, B, and V after the (t-1)th iteration, Represents the pseudoinverse of a matrix.

[0149] Since the alternating least squares algorithm is sensitive to initial values, this application uses the COMFAC algorithm to accelerate the convergence of the algorithm, that is, first compress the third-order PARAFAC model, then iterate the algorithm on the compressed low-dimensional tensor, and finally restore the obtained solution to the original high-dimensional tensor space. When the PARAFAC decomposition is completed, you can get and

[0150] Furthermore, the PARAFAC decomposition of a tensor is often unique if the factor matrix and The Kruskal rank satisfies:

[0151] KR[A]+KR[B]+KR[V]≥2R+2, (28)

[0152] Then the above PARAFAC decomposition is unique, but the obtained factor matrix has column ambiguity and scale ambiguity, which can be expressed as:

[0153]

[0154] Among them, KR[A], KR[B] and KR[V] are and Kruskal rank, R is a preset constant, Π is a permutation matrix; Ω n (n=1,2,3) are the corresponding scale fuzzy matrices, all of which are diagonal matrices, and Ω 1 Ω 2 Ω 3 =I; F n (n=1,2,3) is the error matrix.

[0155] As a preferred embodiment, in step S104, the third-order PARAFAC tensor is decomposed based on a parallel factor decomposition algorithm to obtain the azimuth angle of the source signal, including:

[0156] make represent The kth column of , then according to the second equation in formula (29):

[0157]

[0158] In formula (30), Represents Ω 2 The kth diagonal element of 2,k Represents F 2 The kth column of

[0159] represent The kth column of Due to the scale blur effect, represents the k'th column of B but can be rewritten as:

[0160]

[0161] From the normalized Poynting vector principle, we can know that the direction cosines can be estimated by normalized vector cross product. Therefore, the direction cosine vector p k' The estimated value of can be obtained by the following formula:

[0162]

[0163] In formula (32), and represent The electric response vector and magnetic response vector of and There is no blur.

[0164] However, due to The spatial structure of the array is not included, resulting in a very low estimated resolution. This can be further improved by the following method to obtain a refined direction cosine vector. Specifically:

[0165] Focus on the spatial response vector a k , let h k Indicates a k The phase vector can be written as:

[0166]

[0167] h k =Γp k , (34)

[0168] in, From formula (34), we can see that p k It can be restored by the least squares method, that is:

[0169]

[0170] In reality, h k This can be obtained:

[0171]

[0172] In equation (36), phase{·} represents the phase in radians, and the output range of the phase function is (π,π]. However, in a sparse array structure, the phase difference between two adjacent array elements may be greater than 2π. When the phase exceeds the basic range, the function cannot be processed correctly, resulting in phase ambiguity. Therefore, the periodicity of the array phase can be described as:

[0173]

[0174] In formula (37), is a real-valued integer vector, as long as υ is estimatedk , you can

[0175] Get h k The true phase of and The resolution of the directional cosines is low, but they are free of ambiguity and are close to the true direction cosines.

[0176] Therefore, (32) can be used to estimate υ k :

[0177]

[0178] At the same time, the phase vector estimate can be obtained

[0179]

[0180] In formula (39), express The kth column of . Then, υ k It can be estimated as follows:

[0181]

[0182] In formula (40), round{·} means rounding to the nearest integer.

[0183] Then, the phase is compensated:

[0184]

[0185] The refined direction cosines are estimated as:

[0186]

[0187] Finally, the 2D-DOA can be estimated by calculation:

[0188]

[0189] in, Represents the elevation angle, represents the azimuth, and Respectively The first and second elements of .

[0190] According to formula b k =D k g k , the polarization steering vector is formed by generating a matrix that depends only on the direction and a vector that depends only on the polarization parameters:

[0191]

[0192] Therefore, after estimating the 2D–DOA pair After that, the direction-related matrix D can be restored k (Recorded as ):

[0193]

[0194] in, represent The estimate, It is a scalar and does not affect g k' So, η k′ and k′ The estimated value of can be obtained as follows:

[0195]

[0196] in, express The estimate, Indicates no effect on g k' Scalar of phase, ζ k represents the auxiliary polarization angle, η represents the polarization angle, and Respectively The first and second elements of , |·| means taking the absolute value.

[0197] In order to verify the usefulness of the solution of the present invention, a specific example is given below. Consider an EMVS receiving array consisting of M = 4 array elements and L = 200 available measurement values. Next, assume that there are K = 3 far-field TEM signals acting on the EMVS array of the receiving signal in the presence of a non-uniform noise background.

[0198] The parameters are set as: ζ=[12°,39°,63°] T , η=[13°,47°,-21°] T , the signal-to-noise ratio is SNR=20, each estimation result is based on 500 independent experiments, and the simulation result scatter plot is shown in the attached figure. Figure 3 shown.

[0199] Keeping the above parameters unchanged, in order to make a fair comparison with existing methods, such as Figure 4 As shown, we will propose the algorithm ( Figure 4The method of this application is marked as Proposed) and the estimation accuracy is compared with the representative matrix decomposition algorithms ESPRIT algorithm, ESPRIT-Like algorithm, IESPRIT method, the representative tensor decomposition algorithm MPARAFAC method, and the curves corresponding to CRB for coprime arrays (marked as "CRB-C") and CRB for L-type arrays (marked as "CRB-L").

[0200] Among them, ESPRIT-Like, IESPRIT, and are all tested under sparse L-type array geometry. 1 =2 and M 2 =3, ESPRIT uses a half-wavelength spacing ULA (Uniform Linear Array), the total number of array elements is M = M 1 ×M 2 The MPARAFAC method uses an M 1 =2 and M 2 =3 one-dimensional coprime array for testing, and the average root mean square error (RMSE) of the two-dimensional DOA estimation relative to the signal-to-noise ratio (SNR) is plotted as follows: Figure 4 shown.

[0201] pass Figure 4 The results show that the algorithm proposed in the present invention has high accuracy and shows excellent performance under low signal-to-noise ratio conditions.

[0202] The present invention provides a two-dimensional angle estimation method for a random array in a non-uniform noise scene. First, a random EMVS array is set, signal data z(t) is collected, and covariance is performed to obtain a data covariance matrix R. z ; Secondly, remove the elements in the covariance tensor affected by the noise covariance to suppress the non-uniform noise and obtain the noise-free signal covariance tensor estimate Again, the noise-free covariance matrix is ​​restored using the tensor filling technique to obtain the third-order PARAFAC tensor Finally, the azimuth and polarization angles are obtained using a parallel factorization algorithm.

[0203] By removing the influence of non-uniform noise in the covariance matrix, it can effectively handle complex noise environments, maintain good performance even in high noise or severe interference, significantly improve the signal-to-noise ratio, and have good noise resistance; through PARAFAC tensor decomposition, it can make full use of the implicit information in multi-dimensional data, improve the positioning accuracy of the signal source, and obtain reliable angle estimation even under low signal-to-noise ratio conditions with weak signals; in addition, this method has no strict requirements on the geometry of the array, allows the use of randomly distributed arrays, can be flexibly configured according to specific application requirements, and can adapt to any array structure. The present invention solves the technical problems of low accuracy, high computational complexity, and high sensitivity to algorithm parameters in existing DOA estimation in non-uniform noise scenarios.

[0204] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A two-dimensional angle estimation method for a random array in a non-uniform noise scene, characterized in that: include; Acquire response signals collected by an EMVS array with random geometric distribution, and obtain a covariance matrix of the response signals; Removing the covariance effect of the non-uniform noise in the covariance matrix to obtain a noise-free signal covariance tensor estimate; The noise-free covariance matrix is ​​restored based on tensor filling to obtain a third-order PARAFAC tensor; The third-order PARAFAC tensor is decomposed based on a parallel factor decomposition algorithm to obtain the azimuth angle and polarization angle of the source signal.

2. The two-dimensional angle estimation method of a random array in a non-uniform noise scene according to claim 1, characterized in that: Removing the covariance effect of the non-uniform noise in the covariance matrix to obtain a noise-free signal covariance tensor estimate includes: The noise-free covariance tensor is expressed as: Among them, R z is the covariance matrix of the array response z(t) at time t, S Δ {·} is a sampling operator used to extract matrix elements within the coverage range of index Ω. in: R(m,n) is the (m,n)th item of R.

3. The two-dimensional angle estimation method of a random array in a non-uniform noise scene according to claim 2, characterized in that: The noise-free covariance matrix is ​​restored based on tensor filling, including: According to the tensor matrix filling principle, the optimization process of recovering the noise-free covariance tensor is expressed as: Among them, ||R|| * is the nuclear norm of the tensor R, ||[R] (n) || * is the matrix nuclear norm of the modulo-n expansion of the tensor R, α n is the weighting coefficient, α n is greater than 0 and satisfies The constant.

4. The two-dimensional angle estimation method of a random array in a non-uniform noise scene according to claim 3, characterized in that: The optimization process of recovering the noise-free covariance tensor also includes: by As The estimated value of n , transforming the optimization process into a constrained non-differentiable convex optimization problem: Determine and solve the objective function of the convex optimization problem based on variable separation technology; The objective function of the convex optimization problem is: where Ξ is a convex set, f0(R) is a smooth convex function, ||[R] (n) || * is the matrix nuclear norm of the modulo-n expansion of the tensor R.

5. The two-dimensional angle estimation method of a random array in a non-uniform noise scene according to claim 4, characterized in that: Determining and solving the objective function of the convex optimization problem based on the variable separation technology also includes: The nuclear norm of the matrix || [R] (n) || * Smoothing: Introducing 4 dual variables and 4 variables Let f0(R) = 0, the objective function of the convex optimization problem is expressed as: Among them, ||·|| is the 2-norm of the matrix, <·> is the inner product operation, μ is a constant, is a convex function, ||·|| F represents the Frobenius norm; The objective function is solved by an alternating iteration method to obtain an estimated value of the noise-free covariance tensor.

6. The two-dimensional angle estimation method of a random array in a non-uniform noise scene according to claim 2, characterized in that: The noise-free covariance matrix is ​​restored based on tensor filling to obtain a third-order PARAFAC tensor, including: R z Rearrange into a fourth-order tensor Symmetric Hermitian expansion of , stacked along the columns is the fourth-order tensor of noise; Noise Removal After that, the noise-free tensor Rearrange into a third-order PARAFAC tensor: Where V = A * ⊙B * R s , A * and B * denote the conjugate of A and B, ⊙ denotes the Khatri-Rao product, R s represents the covariance matrix of the source signal, is the spatial response matrix, is the polarization guiding matrix.

7. The two-dimensional angle estimation method of a random array in a non-uniform noise scene according to claim 6, characterized in that: Decomposing the third-order PARAFAC tensor based on a parallel factor decomposition algorithm includes: Let X, Y and Z represent The modulo-1, modulo-2 and modulo-3 expansions are used to estimate Replace the theoretical values ​​X, Y, Z; Through joint optimization Perform PARAFAC decomposition, and the decomposition objective function is expressed as follows: The decomposition objective function is solved by trilinear alternating least squares method, and the COMFAC algorithm is used to accelerate the convergence of the algorithm until the algorithm converges. and It is expressed as: in, Represent the estimated values ​​of A, B, and V after the (t-1)th iteration, Represents the pseudoinverse of a matrix.

8. The two-dimensional angle estimation method of a random array in a non-uniform noise scene according to claim 7, characterized in that: The decomposition objective function is solved by using a trilinear alternating least squares method, and further comprising: When the factor matrix and When the Kruskal rank satisfies KR[A]+KR[B]+KR[V]≥2R+2, the PARAFAC decomposition is unique. and It is expressed as: Among them, KR[A], KR[B] and KR[V] are and Kruskal rank, R is a preset constant, Π is a permutation matrix; Ω n (n=1,2,3) are the corresponding scale fuzzy matrices, all of which are diagonal matrices, and Ω1Ω2Ω3=I; F n (n=1,2,3) is the error matrix.

9. The two-dimensional angle estimation method of a random array in a non-uniform noise scene according to claim 7, characterized in that: The third-order PARAFAC tensor is decomposed based on a parallel factor decomposition algorithm to obtain the azimuth angle of the source signal, including: make represent The kth column of represents the k'th column of B, but in, represents the kth diagonal element of Ω2, and represent The electric response vector and magnetic response vector of ; Direction cosine p is obtained by cross-producting the normalized vector k 'Estimated value, p k The estimated value of ' is calculated as: in, and Direction cosines The electromagnetic intensity in three dimensions, and represent The electric response vector and magnetic response vector of ; According to a k The phase vector h k For the p k' Estimated value of Perform refined recovery: Assume h k Indicates a k The phase vector, h k =Γp k , Use the least squares method to recover p k : The refined recovered direction cosine estimate is: where phase{·} represents the phase in radians, is a real-valued integer vector, represents the phase vector estimate, represents the unbiased phase vector estimate after phase compensation, The 2D-DOA azimuth angle is estimated as: in, represents the elevation angle, θ k represents the azimuth, and Respectively The first and second elements of .

10. The two-dimensional angle estimation method of a random array in a non-uniform noise scene according to claim 9, characterized in that: The third-order PARAFAC tensor is decomposed based on a parallel factor decomposition algorithm to obtain the polarization angle of the source signal, including: according to according to Get the matrix D k , denoted as for The estimate, but in, express The estimate, Indicates no effect on g k' Scalar of phase, ζ k represents the auxiliary polarization angle, η represents the polarization angle, and Respectively The first and second elements of , |·| means taking the absolute value.

Images