Multi-cumulant matrix rotation invariant near-field COLD accurate model direction finding method

Abstract

The invention belongs to the technical field of array signal processing of a near-field source, and particularly relates to a near-field COLD accurate model direction finding method with a multi-cumulant matrix invariable in rotation. A uniform COLD array is utilized to construct a four-order cumulant matrix and cascade the four-order cumulant matrix to obtain a joint cumulant long matrix, a covariance matrix of the joint matrix is calculated and characteristic decomposition is carried out, spatial information and polarization information are successfully separated from a spatial polarization domain according to rotation invariance between signal subspaces, and the spatial information and the polarization information are acquired. And solving an azimuth angle, a distance parameter, a polarization auxiliary angle and a polarization phase difference parameter step by step by utilizing a least square method and a polarization vector relation. According to the method, the parameter estimation problem under the accurate model is considered, the amplitude attenuation of the signal on different array elements is considered, the information of all the array elements in the array can be effectively utilized, and the estimation accuracy is higher.

Description

Technical Field

[0001] The present invention belongs to the technical field of array signal processing of near-field sources, and more specifically, relates to a near-field COLD precise model direction finding method with multi-cumulant matrix rotation invariance. Background Art

[0002] Direction of Arrival (DOA) estimation is a major issue in the field of array signal processing, and it plays an important role in the research of wireless communications and radar. According to the distance classification of the information source to the reference array element, the information source can be divided into far-field source and near-field source. The far-field source is located in the far-field region, and the near-field source is located in the Fresnel region. Their wavefronts correspond to plane wavefronts and spherical wavefronts, respectively. Unlike the far-field source, the phase factor of the near-field source is a binary function of angle and distance, and due to the path loss of electromagnetic waves propagating in space, the signals received by different array elements from the same information source have amplitude attenuation.

[0003] In order to simplify the calculation of near-field source positioning, a large number of existing near-field DOA estimation algorithms use approximate models, but the accuracy of these algorithms will be affected by the approximate error. A large number of near-field algorithms have been proposed, but most of these algorithms are based on uniform linear arrays and cannot estimate the motion characteristics of electromagnetic wave vectors. Compared with ordinary arrays, the co-centered orthogonal loop and dipole (COLD) array can not only obtain the complex amplitude information of the signal, but also the polarization information of the electromagnetic signal. When the signal cannot be well resolved in the spatial domain, joint parameter estimation in the spatial and polarization domains can be performed. At the same time, these algorithms only consider providing closed-form solutions for parameter estimation and cannot effectively utilize the information of all array elements that can be provided in the array. Summary of the invention

[0004] In view of the above problems existing in the prior art, the present invention proposes a near-field COLD accurate model direction finding method with multi-cumulant matrix rotation invariance. The method estimates the spatial steering vector and polarization steering vector by using the rotation invariance between the fourth-order cumulant matrices of the array elements, estimates the position parameters by constructing a linear equation group, and estimates the polarization parameters by using the polarization vector information.

[0005] To achieve the above object, the present invention adopts the following technical solution:

[0006] The near-field COLD accurate model direction finding method with multi-cumulant matrix rotation invariance includes the following steps:

[0007] Step 1: Establish a near-field one-dimensional uniform COLD array model of an accurate propagation model, construct array element position information, and multiple narrowband near-field sources in space are incident on the array. According to the geometric propagation relationship of the accurate spherical wavefront, the spatial amplitude phase factor in the free space is obtained. The spatial amplitude phase factor constitutes a spatial domain steering vector, and the polarization vector is obtained. The steering vector is obtained through the spatial domain steering vector and the polarization vector. The spatial amplitude phase factor includes two-dimensional parameter information of azimuth and distance, and the polarization vector includes two-dimensional parameter information of polarization azimuth and polarization phase difference;

[0008] Step 2: Using the array element output data and array receiving data vector of the COLD array, first construct the fourth-order cumulant matrix of each array element, and then cascade to obtain the joint cumulant long matrix;

[0009] Step 3: Calculate the covariance matrix of the joint cumulant length matrix and perform eigendecomposition. Extract the signal subspace corresponding to the fourth-order cumulant of each array element in the order of index. By using the rotation invariance between the subspaces, the spatial amplitude phase factor can be separated to obtain the array manifold estimation value in the spatial domain.

[0010] Step 4: Further decompose the signal subspace corresponding to the fourth-order cumulant of each array element, and separate the polarization information from the signal subspace containing the spatial domain and polarization domain. The first half of the subspace corresponding to the fourth-order cumulant matrix of each array element is further cascaded to obtain the signal subspace E h , the second half of the subspace corresponding to the fourth-order cumulant matrix of each array element is further cascaded to obtain the signal subspace E v , according to the rotation invariance between subspaces, the matrix can be constructed By decomposing the features and extracting the eigenvalues, the polarization auxiliary angle estimation value and the polarization phase difference estimation value are obtained;

[0011] Step 5: According to the spatial array manifold matrix estimate, extract the spatial amplitude phase factor estimate and obtain the corresponding amplitude attenuation term. The matrix equations for azimuth and distance can be combined to obtain the rough estimate of azimuth and distance using the least squares method.

[0012] Step 6: Based on the rough estimates of azimuth and distance in step 5, the precise delay phase unambiguous rough estimates can be calculated. Based on the spatial array manifold matrix estimate, the spatial amplitude phase factor estimate can be obtained, and the corresponding delay phase term can be extracted. The precise delay phase unambiguous rough estimates are used to resolve the ambiguity, and the precise delay phase estimates can be obtained. By combining the matrix equations for azimuth and distance, the least squares method is used to obtain the precise azimuth estimate and the precise distance estimate.

[0013] The technical solution is further optimized, and the step 1 is specifically as follows:

[0014] A near-field one-dimensional uniform COLD array model is established to accurately model the propagation of COLD elements. x axis, and the central array element is used as the reference array element and the coordinate origin. The total number of array elements is 2L+1, and the array element spacing is d, d=λ / 2, λ is the signal wavelength; Assume that there are K narrow-band near-field sources incident on the array in space, and the position parameter of the kth signal is (θ k , r k ), the polarization parameter is (γ k , η k ), r k is the distance from the kth signal source to the reference element of the array, θ k is the azimuth, that is, the angle θ between the incident direction of the kth signal source and the y-axis k ∈[-π / 2,π / 2],γ k is the polarization auxiliary angle γ of the kth signal source k ∈[0,π / 2],η k is the polarization phase difference η of the kth signal source k ∈[-π,π], the distance from the kth signal source to the lth array element is:

[0015]

[0016] Where l = -L, ..., 0, ..., L;

[0017] According to the geometric propagation relationship of the precise spherical wavefront, the spatial amplitude phase factor of the lth array element receiving the kth signal source is:

[0018]

[0019] b(θ k , r k )=[b -L，k , ..., b l，k , ..., b L，k ] T Represents the spatial steering vector of the kth signal source, whose dimension is (2L+1)×1, and the precise delay phase τ l，k , amplitude attenuation term ρ k，k ;

[0020] The polarization vector of the kth signal source is expressed as:

[0021]

[0022] The steering vector of the kth signal source is:

[0023]

[0024] in represents the Kronecker product, a(θ k , r k , γ k , η k ) has a dimension of 2(2L+1)×1;

[0025] The received data vector of the array at time t is x(t),

[0026]

[0027] The dimension of x(t) is 2(2L+1)×1, ⊙ represents the Khatri-Rao product, A=[a(θ1, r1, γ1, η1), ..., a(θ k , r k , γ k , η k ), ..., a(θ K , r K , γ K , η K )] is an array manifold matrix with dimension 2(2L+1)×K, B=[b(θ1,r1),...,b(θ k , r k ), ..., b(θ K , r K )] is the spatial array manifold matrix, G = [g(γ1,η1),...,g(γ k , η k ), ..., g(γ K , η K )] is the polarization domain array manifold matrix, whose dimension is 2×K, s(t)=[s1(t),...,s k (t), ..., s K (t)] T is a signal vector with dimension K×1, n(t) is a Gaussian white noise vector with dimension 2(2L+1)×1;

[0028] because The received data vector can be further expressed as:

[0029]

[0030] Where x1(t)=[x 1，-L (t), ..., x 1，0 (t), ..., x 1，L (t)] T is a vector consisting of the first 2L+1 elements of x(t), x2(t) = [x 2，-L (t), ..., x 2，0 (t), ..., x 2，L(t)] T is a vector consisting of the 2L+1 elements following x(t), a diagonal matrix Diagonal matrix P2 = diag[cosγ1, ..., cosγ k , ..., cosγ K ]; therefore, the steering vector can be rewritten as a(θ k , r k , γ k , η k )=[a 1，-L，k , ..., a 1,L,k， a 2，-L，k , ..., a 2,L,k ] T , and then we will use a k Instead of a(θ k , r k , γ k , η k ).

[0031] 8. The near-field COLD accurate model direction finding method with multi-cumulant matrix rotation invariance according to claim 2, characterized in that step 2 is specifically as follows:

[0032] Using the th array element output data and array received data vector, the fourth-order cumulant matrix C can be constructed l ,

[0033]

[0034] in,(·) * represents conjugation, (·) H represents the conjugate transpose. The fourth-order cumulant matrix C l It can be further expressed as C l =AΦ l C 4s A H , the dimension of the matrix is ​​2(2L+1)×2(2L+1), where the diagonal matrix Diagonal elements of a matrix represents the cumulative amount of the kth signal, the symbol cum(·) represents the calculated cumulative amount, and the diagonal matrix According to the construction method of the fourth-order cumulant matrix mentioned above, the fourth-order cumulant matrix corresponding to each array element can be obtained in a total of 2L+1, and the construction dimension is 2(2L+1) 2 ×2(2L+1) joint cumulant length matrix Q,

[0035]

[0036] Among them, Φ0 is the identity matrix.

[0037] This technical solution is further optimized, and the step 3 is specifically as follows:

[0038] Calculate the covariance matrix R of the joint cumulant length matrix Q, R = E{QQ H Its dimension is 2(2L+1) 2 ×2(2L+1) 2 , and then perform eigendecomposition on the matrix R, that is Among them, U s is the signal subspace composed of eigenvectors corresponding to K large eigenvalues, U N is 2(2L+1) 2 -The eigenvectors corresponding to the K small eigenvalues ​​constitute the noise subspace, ∑s is the diagonal matrix composed of K large eigenvalues, ∑ N is 2(2L+1) 2 -A diagonal matrix consisting of K small eigenvalues;

[0039] Signal subspace U s It can be decomposed into 2L+1 parts, the number of which corresponds to the number of array elements, that is,

[0040]

[0041] in From the signal subspace U s The 2(2L+1)L+1th row to the 2(2L+1)L+2(2L+1th row of is composed, which is represented as the signal subspace corresponding to the reference array element cumulant matrix;

[0042] Since the space spanned by the signal subspace is the same as the space spanned by the spatial array manifold matrix, and the signal subspace corresponding to the reference array element cumulant matrix and the signal subspace corresponding to each array element cumulant matrix satisfy rotation invariance, there exists a non-singular matrix So that the following relationship holds:

[0043]

[0044] So, the signal subspace Signal subspace corresponding to the reference array element The satisfying relationship between where ψ l =T -1 Φ l T, matrix ψ l Similar to the diagonal matrix Φ l , Φ l The diagonal elements of l According to the least squares method, the matrix ψ can be solved l ,

[0045]

[0046] in(·) + Represents the pseudo-inverse of the matrix. l Performing eigendecomposition, we can get the diagonal matrix Φ l ;

[0047] Then, the diagonal matrix Φ is obtained by eigendecomposition l The diagonal elements are formed into row vectors and concatenated in the order of the position index of the corresponding array elements to obtain the spatial array manifold matrix estimate

[0048]

[0049] Among them, diag -1 (·) represents the diagonal elements of the matrix are stretched into row vectors, and the spatial domain guide vector estimate

[0050] This technical solution is further optimized, and the step 4 is specifically as follows:

[0051] Since the matrix A = G⊙B, the fourth-order cumulant matrix C l Can be decomposed into:

[0052]

[0053] So the signal subspace can be further decomposed into:

[0054]

[0055] in The signal subspace The first 2L+1 row vectors are composed of The signal subspace The last 2L+1 row vectors are formed;

[0056] Extract from signal subspace Construct signal subspace E h ,

[0057]

[0058] Extract from signal subspace Construct signal subspace E v ,

[0059]

[0060] According to the rotation invariance between the signal subspace corresponding to the fourth-order cumulant matrix of different array elements and the signal subspace corresponding to the fourth-order cumulant matrix of the reference array element, it can be known that

[0061]

[0062] According to the matrix and matrix Computable Matrix E h and E v Substitute into the above formula and further simplify it to get in Substituting the diagonal matrices P1 and P2 into the above formula, we can calculate the matrix:

[0063]

[0064] Because, P = TDT -1 , the matrix D is similar to the diagonal matrix P, and the diagonal elements of the matrix P are the eigenvalues ​​of the matrix D. Therefore, the eigendecomposition of the matrix D can obtain the estimate of the diagonal matrix P Therefore, the polarization auxiliary angle estimate of the kth signal can be obtained: Polarization phase difference estimate of the kth signal in Represents a diagonal matrix The kth diagonal element.

[0065] This technical solution is further optimized, and the step 5 is specifically as follows:

[0066] Due to the amplitude attenuation term ρ l，k for,

[0067]

[0068] After expanding and simplifying the above formula, we can get:

[0069]

[0070] Where d1=ld represents the distance between the lth array element and the reference array element; the estimated spatial amplitude phase factor obtained in step 3 is By performing a modulo operation, we can get an estimate of the amplitude attenuation term where abs(·) represents the modulo operation; the estimated value Substituting into the above formula, we can get the equation relationship of the unknown quantity

[0071]

[0072] In addition to the reference array element, the above equations can be listed as 2L items, and the equation group is as follows:

[0073]

[0074] The two unknown quantities in the equations are With r k sinθ k ; From the equation system, we can get the coefficient matrix,

[0075]

[0076] And the unknown vector is

[0077] Using the least squares method, we can get the unknown vector The solution is,

[0078]

[0079] The expressions for the distance estimate and the azimuth estimate are:

[0080]

[0081] in represents the first element of the unknown vector, Represents the second element of the unknown vector.

[0082] This technical solution is further optimized, and the step 6 is specifically as follows:

[0083] The spatial amplitude phase factor estimate obtained in step 3 is taken into account for angle calculation to obtain the delayed phase estimate Where angle(·) represents the angle operation. It is worth noting that the delay phase obtained by this operation is the principal value of the angle, not the actual delay phase, that is, the phase is ambiguous. With the exact delay phase τ in step 1 l，k The accurate delay phase estimate of There is an integer multiple relationship of 2πn, and the set can be constructed Used for deambiguation, accurate delay phase estimation is the set S l Elements of

[0084] Using the distance estimate obtained in step 5 and the angle estimate A rough estimate of the delayed phase without ambiguity can be constructed

[0085]

[0086] in Accurate delay phase estimate is the set S l Unambiguous rough estimate of the intermediate and delayed phase The value with the smallest deviation, that is,

[0087]

[0088] To simplify the calculation, we now obtain the accurate delay phase estimate obtained from the above formula: After normalization by 2π / λ, the result is recorded as

[0089]

[0090] Delayed Items The angle and distance parameters from the source satisfy the relationship:

[0091]

[0092] By algebraic operations, we can list r k ,θ k and The relationship is:

[0093]

[0094] The obtained accurate and unambiguous estimate Substituting into the above formula, we can get the equation relationship:

[0095]

[0096] In addition to the reference array element, the above equations can be listed as 2L items, and the equation group can be obtained:

[0097]

[0098] The two unknown quantities in the equations are r k With r k sinθ k ; The coefficient matrix can be listed from the above formula,

[0099]

[0100] The unknown vector is Δ f，k =[r k , r k sinθ k ] T ; According to the least squares criterion, the solution of the unknown vector is for,

[0101]

[0102] The expressions for the precise estimated values ​​of the azimuth angle and the distance are:

[0103]

[0104] in represents the first element of the unknown vector, Represents the second element of the unknown vector.

[0105] Different from the prior art, the above technical solution has the following beneficial effects:

[0106] The present invention solves the problem of near-field source positioning based on an accurate geometric propagation model, uses a one-dimensional uniform COLD array to receive data signals, constructs an array element polarization joint cumulant length matrix, and uses the least squares method to solve the matrix equation to estimate the position parameters, effectively utilizing all array element information that can be provided in the array, and has higher parameter estimation accuracy. Compared with a uniform linear array, this method can not only estimate the spatial domain parameters of the signal source, but also jointly estimate the polarization auxiliary angle and polarization phase difference parameters of the signal source, and has higher resolution. In addition, the present invention is based on an accurate model and uses an accurate spatial amplitude phase factor. Compared with the Fresnel approximation, this method will not introduce systematic errors and has higher estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 A schematic diagram of the structure of a one-dimensional uniform COLD array and a near-field precise geometric propagation model used in the present invention;

[0108] Figure 2 It is a scatter point matching result diagram of the spatial domain parameters estimated by the present invention in a specific implementation mode;

[0109] Figure 3 This is a diagram of scatter point matching results of polarization domain parameters estimated by the present invention in a specific implementation manner. DETAILED DESCRIPTION

[0110] In order to explain the technical content, structural features, achieved objectives and effects of the technical solution in detail, the following is a detailed description in conjunction with specific embodiments and accompanying drawings.

[0111] The present invention proposes a near-field COLD accurate model direction finding method with multi-cumulant matrix rotation invariance, and the specific steps are as follows:

[0112] Step 1: Establish a near-field one-dimensional uniform COLD array model of the precise propagation model, construct the array element position information, and multiple narrowband near-field sources in space are incident on the array. According to the geometric propagation relationship of the precise spherical wavefront, the spatial amplitude phase factor in the free space is obtained. The spatial amplitude phase factor constitutes the spatial domain steering vector, and the polarization vector is obtained. The steering vector is obtained through the spatial domain steering vector and the polarization vector. The spatial amplitude phase factor includes two-dimensional parameter information of azimuth and distance, and the polarization vector includes two-dimensional parameter information of polarization azimuth and polarization phase difference.

[0113] See also Figure 1 As shown, it is a schematic diagram of the precise spherical wavefront geometric propagation model and the COLD array structure. This embodiment establishes a near-field one-dimensional uniform COLD array model of the precise propagation model. The array uniformly places the COLD array elements on the x-axis, and uses the central array element as the reference array element and the coordinate origin. The total number of array elements is 2L+1, and the array element spacing is d, d=λ / 2 (λ is the signal wavelength). Assume that there are K narrowband near-field sources incident on the array in space, and the position parameter of the kth signal is (θ k , r k ), the polarization parameter is (γ k , η k ), r k is the distance from the kth signal source to the reference element of the array, θ k is the azimuth, that is, the angle θ between the incident direction of the kth signal source and the y-axis k ∈[-π / 2,π / 2],γ k is the polarization auxiliary angle γ of the kth signal source k ∈[0,π / 2],η k is the polarization phase difference η of the kth signal source k ∈[-π,π], the distance from the kth signal source to the lth array element is:

[0114]

[0115] Among them, l = -L,…,0,…,L.

[0116] According to the geometric propagation relationship of the precise spherical wavefront, the spatial amplitude phase factor of the lth array element receiving the kth signal source is:

[0117]

[0118] b(θ k , r k )=[b -L，k , ..., b l，k , ..., b L,k ] TRepresents the spatial steering vector of the kth signal source, whose dimension is (2L+1)×1, and the precise delay phase τ l，k , amplitude attenuation term ρ k，k .

[0119] The polarization vector of the kth signal source is expressed as:

[0120]

[0121] The steering vector of the kth signal source is:

[0122]

[0123] in represents the Kronecker product, a(θ k , r k , γ k , η k ) has a dimension of 2(2L+1)×1.

[0124] The received data vector of the array at time t is x(t),

[0125]

[0126] The dimension of x(t) is 2(2L+1)×1, ⊙ represents the Khatri-Rao product, A=[a(θ1, r1, γ1, η1), ..., a(θ k , r k , γ k , η k ), ..., a(θ K , r K , γ k , η K )] is an array manifold matrix with dimension 2(2L+1)×K, B=[b(θ1,r1),...,b(θ k , r k ), ..., b(θ K , r K )] is the spatial array manifold matrix, G = [g(γ1,η1),...,g(γ k , η k ), ..., g(γ K , η K )] is the polarization domain array manifold matrix, whose dimension is 2×K, s(t)=[s1(t),...,s k (t), ..., s K (t)] T is a signal vector with dimension K×1, and n(t) is a Gaussian white noise vector with dimension 2(2L+1)×1.

[0127] because The received data vector can be further expressed as:

[0128]

[0129] Where x1(t)=[x 1，-L (t), ..., x 1，0 (t), ..., x 1，L (t)] T is a vector consisting of the first 2L+1 elements of x(t), x2(t) = [x 2，-L (t), ..., x 2，0 (t), ..., x 2，L (t)] T is a vector consisting of the 2L+1 elements following x(t), a diagonal matrix Diagonal matrix P2 = diag[cosγ1, ..., cosγ k , ..., cosγ K ]. Therefore, the steering vector can be rewritten as a(θ k , r k , γ k , η k )=[a 1，-L，k , ..., a 1，L，k , a 2，-L，k , ..., a 2，L,k ] T For ease of writing, we will use a k Instead of a(θ k , r k , γ k , η k ).

[0130] Step 2: Using the array element output data and array receiving data vector of the COLD array, first construct the fourth-order cumulant matrix of each array element, and then cascade to obtain the joint cumulant long matrix.

[0131] Using the th array element output data and array received data vector, the fourth-order cumulant matrix C can be constructed l ,

[0132]

[0133] in,(.) * represents conjugation, (·) H represents the conjugate transpose. The fourth-order cumulant matrix C l It can be further expressed as C l =AΦ l C 4s A H, the dimension of the matrix is ​​2(2L+1)×2(2L+1), where the diagonal matrix Diagonal elements of a matrix represents the cumulative amount of the kth signal, the symbol cum(·) represents the calculated cumulative amount, and the diagonal matrix According to the construction method of the fourth-order cumulant matrix mentioned above, the fourth-order cumulant matrix corresponding to each array element can be obtained in a total of 2L+1, and the construction dimension is 2(2L+1) 2 ×2(2L+1) joint cumulant length matrix Q,

[0134]

[0135] Among them, Φ0 is the identity matrix.

[0136] Step 3: Calculate the covariance matrix of the joint cumulant K matrix and perform eigendecomposition. Extract the signal subspace corresponding to the fourth-order cumulant of each array element in the order of index. By using the rotational invariance between the subspaces, the spatial amplitude phase factors can be separated to obtain the array manifold estimation value in the spatial domain.

[0137] Calculate the covariance matrix R of the joint cumulant length matrix Q, R = E{QQ H Its dimension is 2(2L+1) 2 ×2(2L+1) 2 , and then perform eigendecomposition on the matrix R, that is Among them, U s is the signal subspace composed of eigenvectors corresponding to K large eigenvalues, U N is 2(2L+1) 2 The eigenvectors corresponding to -K small eigenvalues ​​constitute the noise subspace, ∑ s is a diagonal matrix consisting of K large eigenvalues, ∑ N is 2(2L+1) 2 -A diagonal matrix consisting of K small eigenvalues.

[0138] Signal subspace U s It can be decomposed into 2L+1 parts, the number of which corresponds to the number of array elements, that is,

[0139]

[0140] in From the signal subspace U s The 2(2L+1)L+1th row to the 2(2L+1)L+2(2L+1th row of is composed, which is represented as the signal subspace corresponding to the reference array element cumulant matrix.

[0141] Since the space spanned by the signal subspace is the same as the space spanned by the spatial array manifold matrix, and the signal subspace corresponding to the reference array element cumulant matrix and the signal subspace corresponding to each array element cumulant matrix satisfy rotation invariance, there exists a non-singular matrix So that the following relationship holds:

[0142]

[0143] So, the signal subspace Signal subspace corresponding to the reference array element The satisfying relationship between where ψ l =T -1 Φ l T, matrix ψ l Similar to the diagonal matrix Φ l , Φ l The diagonal elements of l According to the least squares method, the matrix ψ can be solved l ,

[0144]

[0145] in(·) + Represents the pseudo-inverse of the matrix. l Performing eigendecomposition, we can get the diagonal matrix Φ l .

[0146] Then, the diagonal matrix Φ is obtained by eigendecomposition l The diagonal elements are formed into row vectors and concatenated in the order of the position index of the corresponding array elements to obtain the spatial array manifold matrix estimate

[0147]

[0148] Among them, diag -1 (·) represents the diagonal elements of the matrix are stretched into row vectors, and the spatial domain guide vector estimate

[0149] Step 4: Further decompose the signal subspace corresponding to the fourth-order cumulant of each array element, and separate the polarization information from the signal subspace containing the spatial domain and polarization domain. The first half of the subspace corresponding to the fourth-order cumulant matrix of each array element is further cascaded to obtain the signal subspace E h , the second half of the subspace corresponding to the fourth-order cumulant matrix of each array element is further cascaded to obtain the signal subspace E v , according to the rotation invariance between subspaces, the matrix can be constructed By decomposing the features and extracting the eigenvalues, the polarization auxiliary angle estimation value and the polarization phase difference estimation value are obtained.

[0150] Since the matrix A = G⊙B, the fourth-order cumulant matrix C l Can be decomposed into:

[0151]

[0152] So the signal subspace can be further decomposed into:

[0153]

[0154] in The signal subspace The first 2L+1 row vectors are composed of The signal subspace The last 2L+1 row vectors are formed.

[0155] Extract from signal subspace Construct signal subspace E h ,

[0156]

[0157] Extract from signal subspace Construct signal subspace E v ,

[0158]

[0159] According to the rotation invariance between the signal subspace corresponding to the fourth-order cumulant matrix of different array elements and the signal subspace corresponding to the fourth-order cumulant matrix of the reference array element, it can be known that

[0160]

[0161] According to the matrix and matrix Computable Matrix E h and E v Substitute into the above formula and further simplify it to get in Substituting the diagonal matrices P1 and P2 into the above formula, we can calculate the matrix:

[0162]

[0163] Because, P = TDT -1 , the matrix D is similar to the diagonal matrix P, and the diagonal elements of the matrix P are the eigenvalues ​​of the matrix D. Therefore, the eigendecomposition of the matrix D can obtain the estimate of the diagonal matrix P Therefore, the polarization auxiliary angle estimate of the kth signal can be obtained: Polarization phase difference estimate of the kth signal in Represents a diagonal matrix The kth diagonal element.

[0164] Step 5: Based on the spatial array manifold matrix estimate, extract the spatial amplitude phase factor estimate and obtain the corresponding amplitude attenuation term. The matrix equations for azimuth and distance can be combined to obtain a rough estimate of azimuth and distance using the least squares method.

[0165] Due to the amplitude attenuation term ρ k，k for,

[0166]

[0167] After expanding and simplifying the above formula, we can get:

[0168]

[0169] Where d1=ld represents the distance between the lth array element and the reference array element. By performing a modulo operation, we can get an estimate of the amplitude attenuation term Where abs(·) represents the modulo operation. Substituting into the above formula, we can get the equation relationship of the unknown quantity:

[0170]

[0171] In addition to the reference array element, the above equations can be listed as 2L items, and the equation group is as follows:

[0172]

[0173] The two unknown quantities in the equations are With r k sinθ k . From the equations, we can get the coefficient matrix,

[0174]

[0175] And the unknown vector is

[0176] Using the least squares method, we can get the unknown vector The solution is,

[0177]

[0178] The expressions for the distance estimate and the azimuth estimate are:

[0179]

[0180] in represents the first element of the unknown vector, Represents the second element of the unknown vector.

[0181] Step 6: Based on the rough estimates of azimuth and distance in step 5, the precise delay phase unambiguous rough estimates can be calculated. Based on the spatial array manifold matrix estimate, the spatial amplitude phase factor estimate can be obtained, and the corresponding delay phase term can be extracted. The precise delay phase unambiguous rough estimates are used to resolve the ambiguity, and the precise delay phase estimates can be obtained. By combining the matrix equations for azimuth and distance, the least squares method is used to obtain the precise azimuth estimate and the precise distance estimate.

[0182] The spatial amplitude phase factor estimate obtained in step 3 is taken into account for angle calculation to obtain the delayed phase estimate Where angle(·) represents the angle operation. It is worth noting that the delayed phase obtained by this operation is the main value of the argument, not the actual delayed phase, that is, the phase is ambiguous. With the exact delay phase τ in step 1 l，k The accurate delay phase estimate of There is an integer multiple relationship of 2πn, and the set can be constructed Used for deambiguation, accurate delay phase estimation is the set S l elements.

[0183] Using the distance estimate obtained in step 5 and the angle estimate A rough estimate of the delayed phase without ambiguity can be constructed

[0184]

[0185] in Accurate delay phase estimate is the set S l Unambiguous rough estimate of the intermediate and delayed phase The value with the smallest deviation, that is,

[0186]

[0187] To simplify the calculation, we now obtain the accurate delay phase estimate obtained from the above formula: After normalization by 2π / λ, the result is recorded as

[0188]

[0189] Delayed Items The angle and distance parameters from the source satisfy the relationship:

[0190]

[0191] By algebraic operations, we can list r k ,θ k and The relationship is:

[0192]

[0193] The obtained accurate and unambiguous estimate Substituting into the above formula, we can get the equation relationship:

[0194]

[0195] In addition to the reference array element, the above equations can be listed as 2L items, and the equation group can be obtained:

[0196]

[0197] The two unknown quantities in the equations are r k With r k sinθ k The coefficient matrix can be listed from the above formula:

[0198]

[0199] The unknown vector is Δ f，k =[r k , r k sinθ k ] T According to the least squares criterion, the solution of the unknown vector is for,

[0200]

[0201] The expressions for the precise estimated values ​​of the azimuth angle and the distance are:

[0202]

[0203] in represents the first element of the unknown vector, Represents the second element of the unknown vector.

[0204] The following examples are provided to verify the effectiveness and accuracy of the near-field COLD precise model direction finding method with multi-cumulant matrix rotation invariance of the present invention.

[0205] In order to verify the effectiveness of the method of the present invention in near-field DOA parameter estimation, a simulation test is now carried out on the algorithm steps, and the specific parameters of the simulation are as follows:

[0206] The simulation of the present invention assumes that there are two incoherent narrowband near-field signal sources in space, which are incident on a uniform array with a total of 9 array elements. The central array element of the array is used as the reference array element, and the array element spacing is d=λ / 2, λ=1. The incident angle, distance, polarization auxiliary angle and polarization phase difference parameters are: (-10°, 5λ, 20°, -20°) and (30°, 6λ, 60°, 90°), respectively, the number of snapshots N=1000, and the signal-to-noise ratio is 20dB. Figure 2 and Figure 3 As shown, there are spatial domain parameter scatter point matching result diagram and polarization domain parameter scatter point matching result diagram respectively. Figures 2 to 3 The scatter matching diagram of azimuth and distance, polarization auxiliary angle and polarization phase difference of the present invention is given. It can be seen from the figure that the root mean square error of azimuth and distance parameters and polarization auxiliary angle and polarization phase difference also has a high accuracy when the signal-to-noise ratio is 0dB, and with the increase of signal-to-noise ratio, the estimation precision synchronization is improved, and the algorithm performance is good.

[0207] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that the process, method, article or terminal device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or terminal device. In the absence of further restrictions, the elements defined by the sentence "include..." or "comprise..." do not exclude the existence of other elements in the process, method, article or terminal device including the elements. In addition, in this article, "greater than", "less than", "exceed" and the like are understood to exclude the number itself; "above", "below", "within" and the like are understood to include the number itself.

[0208] Although the above embodiments have been described, once those skilled in the art know the basic creative concepts, they can make additional changes and modifications to these embodiments. Therefore, the above description is only an embodiment of the present invention and does not limit the patent protection scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the specification and drawings of the present invention, or directly or indirectly used in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A near-field COLD accurate model direction finding method with multi-cumulant matrix rotation invariance, characterized in that: The following steps are involved: Step 1: Establish a near-field one-dimensional uniform COLD array model of an accurate propagation model, construct array element position information, and multiple narrowband near-field sources in space are incident on the array. According to the geometric propagation relationship of the accurate spherical wavefront, the spatial amplitude phase factor in the free space is obtained. The spatial amplitude phase factor constitutes a spatial domain steering vector, and the polarization vector is obtained. The steering vector is obtained through the spatial domain steering vector and the polarization vector. The spatial amplitude phase factor includes two-dimensional parameter information of azimuth and distance, and the polarization vector includes two-dimensional parameter information of polarization azimuth and polarization phase difference; Step 2: Using the array element output data and array receiving data vector of the COLD array, first construct the fourth-order cumulant matrix of each array element, and then cascade to obtain the joint cumulant long matrix; Step 3: Calculate the covariance matrix of the joint cumulant length matrix and perform eigendecomposition. Extract the signal subspace corresponding to the fourth-order cumulant of each array element in the order of index. By using the rotation invariance between the subspaces, the spatial amplitude phase factor can be separated to obtain the array manifold estimation value in the spatial domain. Step 4: Further decompose the signal subspace corresponding to the fourth-order cumulant of each array element, and separate the polarization information from the signal subspace containing the spatial domain and polarization domain; further cascade the first half of the subspace corresponding to the fourth-order cumulant matrix of each array element to obtain the signal subspace E h , the second half of the subspace corresponding to the fourth-order cumulant matrix of each array element is further cascaded to obtain the signal subspace E v , according to the rotation invariance between subspaces, the matrix can be constructed By decomposing the features and extracting the eigenvalues, the polarization auxiliary angle estimation value and the polarization phase difference estimation value are obtained; Step 5: According to the spatial array manifold matrix estimate, extract the spatial amplitude phase factor estimate and obtain the corresponding amplitude attenuation term. The matrix equations for azimuth and distance can be combined to obtain the rough estimate of azimuth and distance using the least squares method. Step 6: Based on the rough estimates of azimuth and distance in step 5, the rough estimate of accurate delayed phase without ambiguity can be calculated; based on the estimated value of the spatial array manifold matrix, the estimated value of the spatial amplitude phase factor can be obtained, and the corresponding delayed phase term can be extracted. The delayed phase term of the spatial array manifold matrix estimate can be extracted, and the accurate delayed phase unambiguous rough estimate can be used to deambiguate to obtain the accurate delayed phase estimate. By combining the matrix equations for azimuth and distance and using the least squares method, the accurate azimuth estimate and the accurate distance estimate can be obtained.

2. The near-field COLD accurate model direction finding method with multi-cumulant matrix rotation invariance as claimed in claim 1 is characterized in that: The step 1 is specifically as follows: A near-field one-dimensional uniform COLD array model of an accurate propagation model is established. The COLD array elements are evenly placed on the x-axis, and the central array element is used as the reference array element and the coordinate origin. The total number of array elements is 2L+1, and the array element spacing is d, d=λ / 2, where λ is the signal wavelength. Assuming that there are K narrowband near-field sources incident on the array in space, the position parameter of the kth signal is (θ k , r k ), the polarization parameter is (γ k , η k ), r k is the distance from the kth signal source to the reference element of the array, θ k is the azimuth, that is, the angle θ between the incident direction of the kth signal source and the y-axis k ∈[-π / 2,π / 2],γ k is the polarization auxiliary angle γ of the kth signal source k ∈[0,π / 2],η k is the polarization phase difference η of the kth signal source k ∈[-π,π], the distance from the kth signal source to the lth array element is: Where l = -L, ..., 0, ..., L; According to the geometric propagation relationship of the precise spherical wavefront, the spatial amplitude phase factor of the lth array element receiving the lth signal source is: b(θ k , r k )=[b -L , k , ..., b l，k , ..., b L，k ] T Represents the spatial steering vector of the kth signal source, whose dimension is (2L+1)×1 and the precise delay phase is π l，k , amplitude attenuation term ρ l，k ; The polarization vector of the kth signal source is expressed as: The steering vector of the kth signal source is: in represents the Kronecker product, a(θ k , r k , γ k , η k ) has a dimension of 2(2L+1)×1; The received data vector of the array at time t is x(t), The dimension of x(t) is 2(2L+1)×1, ⊙ represents the Khatri-Rao product, A=[a(θ1, r1, γ1, η1), ..., a(θ k , r k , γ k , η k ), ..., a(θ K , r K , γ K , η K )] is an array manifold matrix with dimension 2(2L+1)×K, B=b[θ1,r1),...,b(θ k , r k ), ..., b(θ K , r K )] is the spatial array manifold matrix, G = [g(γ1,η1),...,g(γ k , η k ), ..., g(γ K , η K )] is the polarization domain array manifold matrix, whose dimension is 2×K, s(t)=[s1(t),...,s k (t), ..., s K (t)] T is a signal vector with dimension K×1, n(t) is a Gaussian white noise vector with dimension 2(2L+1)×1; because The received data vector can be further expressed as: Where x1(t)=[x 1，-L (t), ..., x 1，0 (t), ..., x 1，L x2(t)=[x(t)] is a vector consisting of the first 2L+1 elements of x(t), x2(t)=[x 2，-L (t), ..., x 2，0 (t), ..., x 2，L (t)] T is a vector consisting of the 2L+1 elements following x(t), a diagonal matrix Diagonal matrix P2 = diag[cosγ1, ..., cosγ k , ..., cosγ K ]; therefore, the steering vector can be rewritten as a(θ k , r k , γ k , η k )=[a 1，-L，k , ..., a 1，L，k , a 2，-L，k , ..., a 2，L，k ] T , and then we will use a k Instead of a(θ k , r k , γ k , η k ).

3. The near-field COLD accurate model direction finding method with multi-cumulant matrix rotation invariance as claimed in claim 2, characterized in that: The step 2 is specifically as follows: Using the lth array element output data and the array received data vector, the fourth-order cumulant matrix C can be constructed: l , in,(·) * represents conjugation, (·) H represents the conjugate transpose; the fourth-order cumulant matrix C l It can be further expressed as C l =AΦ l C 4s A H , the dimension of the matrix is ​​2(2L+1)×2(2L+1), where the diagonal matrix Diagonal elements of a matrix represents the cumulative amount of the kth signal, the symbol cum(·) represents the calculated cumulative amount, and the diagonal matrix According to the construction method of the fourth-order cumulant matrix mentioned above, the fourth-order cumulant matrix corresponding to each array element can be obtained in a total of 2L+1, and the construction dimension is 2(2L+1) 2 ×2(2L+1) joint cumulant length matrix Q, Among them, Φ0 is the identity matrix.

4. The near-field COLD accurate model direction finding method with multi-cumulant matrix rotation invariance as claimed in claim 3 is characterized in that: The step 3 is as follows: Calculate the covariance matrix R of the joint cumulant length matrix Q, R = E{QQ H Its dimension is 2(2L+1) 2 ×2(2L+1) 2 , and then perform eigendecomposition on the matrix R, that is Among them, U s is the signal subspace composed of eigenvectors corresponding to K large eigenvalues, U N is 2(2L+1) 2 The eigenvectors corresponding to -K small eigenvalues ​​constitute the noise subspace, Σ s is a diagonal matrix consisting of K large eigenvalues, ∑ N is 2(2L+1) 2 -A diagonal matrix consisting of K small eigenvalues; Signal subspace U s It can be decomposed into 2L+1 parts, the number of which corresponds to the number of array elements, that is, in From the signal subspace U s The 2(L+1)L+1th row to the 2(2L+1)L+2(2L+1)th row of is composed, which is represented as the signal subspace corresponding to the reference array element cumulant matrix; Since the space spanned by the signal subspace is the same as the space spanned by the spatial array manifold matrix, and the signal subspace corresponding to the reference array element cumulant matrix and the signal subspace corresponding to each array element cumulant matrix satisfy rotation invariance, there exists a non-singular matrix So that the following relationship holds: So, the signal subspace Signal subspace corresponding to the reference array element The satisfying relationship between Among them Ψ l =T -1 Φ l T, matrix Ψ l Similar to the diagonal matrix Φ l , Φ l The diagonal elements of l According to the least squares method, the matrix Ψ can be solved l , in(·) + Represents the pseudo-inverse of the matrix, and the matrix Ψ l Performing eigendecomposition, we can get the diagonal matrix Φ l ; Then, the diagonal matrix Φ is obtained by eigendecomposition l The diagonal elements are formed into row vectors and concatenated in the order of the position index of the corresponding array elements to obtain the spatial array manifold matrix estimate Among them, diag -1 (·) represents the diagonal elements of the matrix are stretched into row vectors, and the spatial domain guide vector estimate 5. The near-field COLD accurate model direction finding method with multi-cumulant matrix rotation invariance as claimed in claim 4 is characterized in that: The step 4 is specifically as follows: Since the matrix A = G⊙B, the fourth-order cumulant matrix C l Can be decomposed into: So the signal subspace can be further decomposed into: in The signal subspace The first 2L+1 row vectors are composed of The signal subspace The last 2L+1 row vectors are formed; Extract from signal subspace Construct signal subspace E h , Extract from signal subspace Construct signal subspace E v , According to the rotation invariance between the signal subspace corresponding to the fourth-order cumulant matrix of different array elements and the signal subspace corresponding to the fourth-order cumulant matrix of the reference array element, it can be known that According to the matrix and matrix Computable Matrix E h and E v Substitute into the above formula and further simplify it to get in Substituting the diagonal matrices P1 and P2 into the above formula, we can calculate the matrix: Because, P = TDT -1 , the matrix D is similar to the diagonal matrix P, and the diagonal elements of the matrix P are the eigenvalues ​​of the matrix D. Therefore, the eigendecomposition of the matrix D can obtain the estimate of the diagonal matrix P Therefore, the polarization auxiliary angle estimate of the kth signal can be obtained: Polarization phase difference estimate of the kth signal in Represents a diagonal matrix The kth diagonal element.

6. The near-field COLD accurate model direction finding method with multi-cumulant matrix rotation invariance as claimed in claim 5, characterized in that: The step 5 is specifically as follows: Due to the amplitude attenuation term ρ l，k for, After expanding and simplifying the above formula, we can get: where d l =ld represents the distance between the lth array element and the reference array element; the estimated value of the spatial amplitude phase factor obtained in step 3 is By performing a modulo operation, we can get an estimate of the amplitude attenuation term where abs(·) represents the modulo operation; the estimated value Substituting into the above formula, we can get the equation relationship of the unknown quantity In addition to the reference array element, the above equations can be listed as 2L items, and the equation group is as follows: The two unknown quantities in the equations are With r k sinθ k ; From the equation system, we can get the coefficient matrix, And the unknown vector is Using the least squares method, we can get the unknown vector The solution is, The expressions for the distance estimate and the azimuth estimate are: in represents the first element of the unknown vector, Represents the second element of the unknown vector.

7. The near-field COLD accurate model direction finding method with multi-cumulant matrix rotation invariance as claimed in claim 6, characterized in that: The step 6 is specifically as follows: The spatial amplitude phase factor estimate obtained in step 3 is taken into account for angle calculation to obtain the delayed phase estimate Where angle(·) represents the angle operation. It is worth noting that the delay phase obtained by this operation is the principal value of the angle, not the actual delay phase, that is, the phase is ambiguous. With the exact delay phase τ in step 1 l，k The accurate delay phase estimate of There is an integer multiple relationship of 2πn, and the set can be constructed Used for deambiguation, accurate delay phase estimation is the set S l Elements of Using the distance estimate obtained in step 5 and the angle estimate A rough estimate of the delayed phase without ambiguity can be constructed in Accurate delay phase estimate is the set S l Unambiguous rough estimate of the intermediate and delayed phase The value with the smallest deviation, that is, To simplify the calculation, we now obtain the accurate delay phase estimate obtained from the above formula: After normalization by 2π / λ, the result is recorded as Delayed Items The angle and distance parameters from the source satisfy the relationship: By algebraic operations, we can list r k ,θ k and The relationship is: The obtained accurate and unambiguous estimate Substituting into the above formula, we can get the equation relationship: In addition to the reference array element, the above equations can be listed as 2L items, and the equation group can be obtained: The two unknown quantities in the equations are r k With r k sinθ k ; The coefficient matrix can be listed from the above formula, The unknown vector is Δ f，k =[r k , r k sinθ k ] T ; According to the least squares criterion, the solution of the unknown vector is for, The expressions for the precise estimated values ​​of the azimuth angle and the distance are: in represents the first element of the unknown vector, Represents the second element of the unknown vector.

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