CN117826076A - Near-field source three-dimensional parameter underdetermined estimation method based on space-time information combination - Google Patents
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Abstract
The invention discloses a near-field source three-dimensional parameter underdetermined estimation method based on space-time information combination, which is used for establishing a three-dimensional near-field signal source space propagation model based on an L-shaped array; calculating the fourth-order delay mutual accumulation amount of the data received by the m-th array element of the y array, the data received by the n-th array element of the x array, the data received by all the array elements of the x array and the data received by all the array elements of the y array, and obtaining a virtual received data matrix through two vectorization operations; extracting a noise subspace feature vector matrix based on covariance calculated by the virtual received data matrix; defining a pseudo power function, searching through a three-dimensional spectrum peak to obtain a plurality of maximum values of the pseudo power function, wherein the combination of function parameter values corresponding to each maximum value is the three-dimensional position parameter of a near-field signal source; the method has the advantages that the method has higher direction-finding precision and can realize underdetermined estimation of the near-field signal source.
Description
Technical Field
The invention relates to a near-field signal source positioning technology, in particular to a near-field source three-dimensional parameter underdetermined estimation method based on space-time information combination.
Background
The application of near field signal source positioning in the fields of radar, communication, radio detection and the like is expanding continuously. The traditional high-resolution direction finding algorithm is generally based on a far-field signal source plane wave model, when a signal source is positioned in a near-field region of an array, the phase difference of signals received by array elements is a nonlinear function related to the distance between the array elements, the far-field signal source positioning algorithm cannot be directly applied, fresnel approximation processing is required, and positioning accuracy is affected. For near field signal source positioning, amplitude attenuation related to distance exists on received data of the same signal by different array elements, and the estimation performance can be reduced even the requirement of direction finding precision cannot be met due to the fact that the amplitude attenuation is ignored. Most of the existing near-field signal source direction-finding algorithms either approximate the time delay or consider the amplitude attenuation as equal processing, the computational complexity of the algorithm is reduced but the direction-finding accuracy is limited. The amplitude attenuation is regarded as an equal processing, such as a classic subspace algorithm MUSIC algorithm, which directly carries out covariance calculation on the received data of the physical array elements, obtains a noise subspace through eigenvalue decomposition, and estimates the near-field signal source parameters by utilizing the orthogonal property of the signal subspace and the noise subspace, wherein the direction-finding precision is not ideal. Based on the virtual array element expansion and the improvement of algorithm estimation performance which can be performed by utilizing the time information of the received data, the invention provides a near-field source three-dimensional parameter underdetermined estimation method based on space-time information combination.
Disclosure of Invention
The invention aims to solve the technical problem of providing a near-field source three-dimensional parameter underdetermined estimation method based on space-time information combination, which is used for calculating four-order delay mutual accumulation by combining space-time information, performing virtual array element expansion through vectorization operation, calculating covariance of a virtual received data matrix, extracting a noise subspace characteristic vector matrix, and performing three-dimensional spectral peak search on a pseudo-power function by utilizing the orthogonal property of a signal subspace and a noise subspace to realize underdetermined estimation of the direction angle, pitch angle and distance between the pseudo-power function and a reference array element, and has high estimation precision.
The technical scheme adopted for solving the technical problems is as follows: a near-field source three-dimensional parameter underdetermined estimation method based on space-time information association is characterized by comprising the following steps:
step 1: establishing a three-dimensional near-field signal source space propagation model based on an L-shaped array: an array formed by N array elements is arranged on an x axis of a three-dimensional coordinate system to serve as an x array, an array formed by M array elements is arranged on a y axis of the three-dimensional coordinate system to serve as a y array, and the x array and the y array share an origin of the three-dimensional coordinate system to form an L-shaped array; the x array is a nested array and consists of two uniform linear arrays, wherein the number of array elements of one uniform linear array is L x And the array element distance is d, and the array element number of the other uniform linear array is N-L x And the array element spacing is (L) x +1) d; the y array is also a nested array and is also formed by two uniform linear arrays, wherein the number of array elements of one uniform linear array is L y And the array element distance is d, and the number of the array elements of the other uniform linear array is M-L y And the array element spacing is (L) y +1) d; by d xn Represents the position of the nth element of the x array, the nth E [1, L ] of the x array x ]The position of each array element is d xn N E [ L ] of = (n-1) d, x array x +1,N]The position of each array element is d xn ＝(n-L x )(L x +1) d-d; by d ym Represents the position of the m-th array element of the y array, the m-th E [1, L y ]The position of each array element is d ym M e [ L ] of = (m-1) d, y array y +1,M]The position of each array element is d ym ＝(m-L y )(L y +1) d-d; k near field signal sources are incident into the L-shaped array, and the kth near field signal source is arranged at a direction angle theta k And pitch angle phi k From the distance origin r k The coordinate position of the kth near-field signal source is denoted (r) k sinφ k cosθ k ,r k sinφ k sinθ k ,r k cosφ k )；
Wherein, N is more than 1, M is more than 1, the number of array elements of the L-shaped array is N+M-1, n=1, 2, …, N, m=1, 2, …, M,1 < L x ＜N，1＜L y < M, d is lambda/2, lambda is the signal wavelength, K is not less than 1, k=1, 2, …, K, θ k ∈(-180°,180°]，φ k ∈[0°,90°]，
Step 2: by r xn,k Representing the distance from the kth near field signal source to the nth array element of the x array, using r ym,k Representing the distance of the kth near field signal source to the mth element of the y-array, then, considering amplitude attenuation, calculating the amplitude phase factor of the signal sent by the kth near-field signal source received by the nth array element of the x array, and marking the amplitude phase factor as a xn (θ k ,φ k ,r k )，Similarly, the amplitude phase factor of the signal sent by the kth near-field signal source received by the mth array element of the y array is calculated and is marked as a ym (θ k ,φ k ,r k )，/>The data received by all the array elements of the x array are represented by x (t), the data received by all the array elements of the y array are represented by y (t), and x (t) =a x s(t)+n x (t)，y(t)＝A y s(t)+n y (t)；
Where g represents a known path loss attenuation index, e represents a natural constant, j represents an imaginary part,representing the attenuation of the signal sent by the kth near field signal source received by the nth array element of the x array relative to the signal sent by the kth near field signal source received by the reference array element, namely the array element at the origin, the attenuation of the signal sent by the kth near field signal source received by the nth array element of the x array is->Indicating that the nth element of the x array received the kth nearThe phase difference of the signal sent by the field signal source relative to the reference array element, namely the phase difference of the signal sent by the kth near field signal source received by the array element at the origin, namely +.>Representing the attenuation of the signal sent by the kth near field signal source received by the mth array element of the y array relative to the signal sent by the kth near field signal source received by the reference array element, namely the array element at the origin, and the attenuation is>Indicating the phase difference of the signal sent by the kth near field signal source received by the mth array element of the y array relative to the signal sent by the kth near field signal source received by the reference array element, namely the array element at the origin, wherein x (t) and y (t) are column vectors, t represents a time variable, A x Array flow pattern matrix representing x array, A x ＝[a x (θ 1 ,φ 1 ,r 1 ),a x (θ 2 ,φ 2 ,r 2 ),…,a x (θ K ,φ K ,r K )]，A x Is N x K, a x (θ k ,φ k ,r k )＝[a x1 (θ k ,φ k ,r k ),a x2 (θ k ,φ k ,r k ),…,a xN (θ k ,φ k ,r k )] T ，a x (θ k ,φ k ,r k ) Is N x 1, the superscript "T" denotes the transpose of the vector or matrix, s (T) denotes the near field signal source vector, s (T) = [ s ] 1 (t),s 2 (t),…,s K (t)] T The dimension of s (t) is Kx1, s k (t) represents the signal from the kth near field signal source, n x (t) represents an independent co-distributed additive noise vector added to the data received by all the array elements of the x array at time t, n x (t) dimension N.times.1, A y Array flow pattern matrix representing y array, A y ＝[a y (θ 1 ,φ 1 ,r 1 ),a y (θ 2 ,φ 2 ,r 2 ),…,a y (θ K ,φ K ,r K )]，A y Is M x K, a y (θ k ,φ k ,r k )＝[a y1 (θ k ,φ k ,r k ),a y2 (θ k ,φ k ,r k ),…,a yM (θ k ,φ k ,r k )] T ，a y (θ k ,φ k ,r k ) Is M x 1, n y (t) represents an independent co-distributed additive noise vector added to the data received by all elements of the y array at time t, n y (t) has dimension M×1;
step 3: based on x (t) and y (t) in the step 2, calculating the fourth-order delay mutual accumulation amount of the data received by the m-th array element of the y array, the data received by the n-th array element of the x array, the data received by all the array elements of the x array and the data received by all the array elements of the y array, and recording as C mn (τ)，
Wherein C is mn The dimension of (τ) is NxM, τ represents the delay, cum {. Cndot. } is the cumulant operation, (. Cndot.) * Is a conjugate operation (.) H For conjugate transpose operation, y m (t) represents the data received by the m-th element of the y array, y m (t+τ) represents the data received by the m-th element of the y array after the delay τ, x n (t) represents the data received by the nth array element of the x array, x (t+τ) represents the data received by all array elements of the x array after time delay τ, s k (t + tau) represents the signal after the delay tau processing of the signal from the kth near field signal source,diag {.cndot }, represents converting a vector into a diagonal matrix with the vector as the main diagonal element, a ym (θ 1 ,φ 1 ,r 1 )、a ym (θ 2 ,φ 2 ,r 2 )、a ym (θ K ,φ K ,r K )Γ(τ)＝diag{γ 1 (τ),γ 2 (τ),…,γ K (τ)}，γ k (τ) represents the cumulative amount of the signal from the kth near field signal source and the signal after being time-delayed τ, +.>
Step 4: for C obtained in step 3 mn Vectorizing (tau) to obtain C mn The vectorization result of (τ) is denoted as c mn (τ)，
Wherein c mn The dimension of (τ) is (N×M) ×1, vec (. Cndot.) is vectorization, and the product of (Khatri) -Rao is performed, B represents a steering matrix,the dimension of B is (N×M) ×K, and the kth column of B is B k ，For the Kronecker product operation,
step 5: c based on step 4 mn (τ), M sequentially takes integer values from 1 to M, N sequentially takes integer values from 1 to N, and the matrix c (τ), c (τ) = [ c ] is obtained by arrangement 11 (τ),…,c 1N (τ),…,c 21 (τ),…,c MN (τ)]The method comprises the steps of carrying out a first treatment on the surface of the Then, c (τ) is expressed as c (τ) =bΓ (τ) B, based on the arrangement of the elements in c (τ) H ；
Wherein the dimension of c (τ) is (nxm) × (nxm);
step 6: c (tau) obtained in the step 5 is vectorized, and the vectorized result of c (tau) is taken as data received by the virtual array and is denoted as w (tau), w (tau) =vec (c (tau)) = (B) * ⊙B)γ(τ)＝Dγ(τ)；
Wherein w (τ) has a dimension of (N×M) 2 X1, D represents virtual guiding momentArray, d=b * The dimension of the pair of wires B and D is (N.times.M) 2 The K column of X K, D is D k ，γ(τ)＝[γ 1 (τ),γ 2 (τ),…,γ K (τ)] T ；
Step 7: taking τ=t based on w (τ) obtained in step 6 s ,2T s ,…,N p T s The virtual received data matrix W, w= [ W (T s ),w(2T s ),…,w(N p T s )]＝Dγ s ；
Wherein T is s Representing virtual sampling period, N p Representing the number of pseudo shots, N p The dimension of W is > 1 (N X M) 2 ×N p ，γ s ＝[γ(T s ),γ(2T s ),…,γ(N p T s )]；
Step 8: the covariance of W obtained in step 7 is calculated, denoted R,then pass throughCarrying out characteristic value decomposition on R to obtain all characteristic values; then sequencing all the characteristic values from small to large, and taking the front (N multiplied by M) 2 K eigenvalues, and the matrix formed by eigenvectors corresponding to the eigenvalues is used as a noise subspace eigenvector matrix E n ；
Wherein the dimension of R is (NxM) 2 ×(N×M) 2 R has rank of K, Λ ss ＝γ s γ s H ，E s Representing a signal subspace eigenvector matrix, Σ s Representing a diagonal matrix of signal subspace eigenvalues, E n Representing a noise subspace eigenvector matrix, Σ n Representing a diagonal matrix of noise subspace eigenvalues;
step 9: e based on step 8 n And uses the orthogonal property of signal subspace and noise subspace to determineThe pseudo-power function P (θ, Φ, r),then searching by using three-dimensional spectrum peak, and searching at interval (-180 deg., 180 deg.)]Searching for the value of theta in the interval [0 DEG, 90 DEG ]]The value of phi is searched internally and is within the interval +.>The value of r is searched internally, K maximum values exist in P (theta, phi and r), and the combination of the value of theta, the value of phi and the value of r corresponding to the kth maximum value is the three-dimensional position parameter of the kth near-field signal source;
wherein θ represents a direction angle variable, φ represents a pitch angle variable, r represents a distance variable from an origin,a x (θ, φ, r) is a x (θ k ,φ k ,r k ) θ in (a) k ,φ k ,r k Correspondingly replace theta, phi, r, a y (θ, φ, r) is a y (θ k ,φ k ,r k ) θ in (a) k ,φ k ,r k The corresponding substitution is theta, phi and r.
Compared with the prior art, the invention has the advantages that:
the method comprises the steps of adopting an L-shaped array, calculating data received by an m-th array element of a y array, data received by an n-th array element of an x array, four-order delay mutual accumulation amounts of data received by all array elements of the x array and data received by all array elements of the y array, obtaining a virtual received data matrix through two vectorization operations, calculating covariance of the virtual received data matrix, carrying out eigenvalue decomposition to extract a noise subspace eigenvector matrix, and carrying out three-dimensional spectral peak search of a pseudo-power function to obtain three-dimensional position parameters of a near-field signal source. Compared with the method for directly using physical array element to receive data for estimation, the method has higher direction-finding precision and can realize underdetermined estimation of the near-field signal source after the virtual array element is expanded.
Drawings
FIG. 1 is a schematic diagram of a three-dimensional near-field signal source space propagation model based on an L-shaped array established by the method of the invention;
FIG. 2 is a resolved view of the direction angle of a near field signal source obtained by the method of the present invention;
FIG. 3 is a resolution of the pitch angle of a near field signal source obtained using the method of the present invention;
fig. 4 is a graph of the estimation result of the three-dimensional position parameter of the near-field signal source obtained by the method of the invention.
Detailed Description
The invention is described in further detail below with reference to the embodiments of the drawings.
The invention provides a near-field source three-dimensional parameter underdetermined estimation method based on space-time information combination, which comprises the following steps:
step 1: as shown in fig. 1, a three-dimensional near-field signal source space propagation model based on an L-type array is established: an array formed by N array elements is arranged on an x axis of a three-dimensional coordinate system to serve as an x array, an array formed by M array elements is arranged on a y axis of the three-dimensional coordinate system to serve as a y array, and the x array and the y array share an origin of the three-dimensional coordinate system to form an L-shaped array; the x array is a nested array and consists of two uniform linear arrays, wherein the number of array elements of one uniform linear array is L x And the array element distance is d, and the array element number of the other uniform linear array is N-L x And the array element spacing is (L) x +1) d; the y array is also a nested array and is also formed by two uniform linear arrays, wherein the number of array elements of one uniform linear array is L y And the array element distance is d, and the number of the array elements of the other uniform linear array is M-L y And the array element spacing is (L) y +1) d; by d xn Represents the position of the nth element of the x array, the nth E [1, L ] of the x array x ]The position of each array element is d xn N E [ L ] of = (n-1) d, x array x +1,N]The position of each array element is d xn ＝(n-L x )(L x +1)d-d；By d ym Represents the position of the m-th array element of the y array, the m-th E [1, L y ]The position of each array element is d ym M e [ L ] of = (m-1) d, y array y +1,M]The position of each array element is d ym ＝(m-L y )(L y +1) d-d; k near field signal sources are incident into the L-shaped array, and the kth near field signal source is arranged at a direction angle theta k And pitch angle phi k From the distance origin r k The coordinate position of the kth near-field signal source is denoted (r) k sinφ k cosθ k ,r k sinφ k sinθ k ,r k cosφ k ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein, N is more than 1, M is more than 1, the number of array elements of the L-shaped array is N+M-1, n=1, 2, …, N, m=1, 2, …, M,1 < L x ＜N，1＜L y < M, d is lambda/2, lambda is the signal wavelength, K is not less than 1, k=1, 2, …, K, θ k ∈(-180°,180°]，φ k ∈[0°,90°]，
Step 2: by r xn,k Representing the distance from the kth near field signal source to the nth array element of the x array, using r ym,k Representing the distance from the kth near field signal source to the mth array element of the y array, which is obtained from the geometrical relationship Then, considering amplitude attenuation, calculating the amplitude phase factor of the signal sent by the kth near-field signal source received by the nth array element of the x array, and marking the amplitude phase factor asSimilarly, the amplitude phase factor of the signal sent by the kth near-field signal source received by the mth array element of the y array is calculated and is marked as a ym (θ k ,φ k ,r k )，The data received by all the array elements of the x array are represented by x (t), the data received by all the array elements of the y array are represented by y (t), and x (t) =a x s(t)+n x (t)，y(t)＝A y s(t)+n y (t); where g represents a known path loss attenuation index, in this embodiment g=2, e represents a natural constant, e=2.71 …, j represents an imaginary part, and +.>Representing the attenuation of the signal sent by the kth near field signal source received by the nth array element of the x array relative to the signal sent by the kth near field signal source received by the reference array element, namely the array element at the origin, the attenuation of the signal sent by the kth near field signal source received by the nth array element of the x array is->Indicating the phase difference of the signal sent by the kth near field signal source received by the nth array element of the x array relative to the signal sent by the kth near field signal source received by the reference array element, namely the array element at the origin, and the phase difference is>Representing the attenuation of the signal sent by the kth near field signal source received by the mth array element of the y array relative to the signal sent by the kth near field signal source received by the reference array element, namely the array element at the origin,indicating the phase difference of the signal sent by the kth near field signal source received by the mth array element of the y array relative to the signal sent by the kth near field signal source received by the reference array element, namely the array element at the origin, wherein x (t) and y (t) are column vectors, t represents a time variable, A x Array flow pattern matrix representing x array, A x ＝[a x (θ 1 ,φ 1 ,r 1 ),a x (θ 2 ,φ 2 ,r 2 ),…,a x (θ K ,φ K ,r K )]，A x Is N x K, a x (θ k ,φ k ,r k )＝[a x1 (θ k ,φ k ,r k ),a x2 (θ k ,φ k ,r k ),…,a xN (θ k ,φ k ,r k )] T ，a x (θ k ,φ k ,r k ) Is N x 1, a x (θ 1 ,φ 1 ,r 1 )、a x (θ 2 ,φ 2 ,r 2 )、a x (θ K ,φ K ,r K ) Through a x (θ k ,φ k ,r k )＝[a x1 (θ k ,φ k ,r k ),a x2 (θ k ,φ k ,r k ),…,a xN (θ k ,φ k ,r k )] T Acquisition, a x1 (θ k ,φ k ,r k )、a x2 (θ k ,φ k ,r k )、a xN (θ k ,φ k ,r k ) By->The acquisition, superscript "T" denotes the transpose of the vector or matrix, s (T) denotes the near field signal source vector, s (T) = [ s ] 1 (t),s 2 (t),…,s K (t)] T The dimension of s (t) is Kx1, s k (t) represents the signal from the kth near field signal source, s 1 (t) represents the 1 st near field signal source, s 2 (t) represents the 2 nd near field signal source, s K (t) represents the Kth near field signal source, n x (t) represents an independent co-distributed additive noise vector added to the data received by all the array elements of the x array at time t, n x (t) dimension N.times.1, A y Array flow pattern matrix representing y array, A y ＝[a y (θ 1 ,φ 1 ,r 1 ),a y (θ 2 ,φ 2 ,r 2 ),…,a y (θ K ,φ K ,r K )]，A y Is M x K, a y (θ k ,φ k ,r k )＝[a y1 (θ k ,φ k ,r k ),a y2 (θ k ,φ k ,r k ),…,a yM (θ k ,φ k ,r k )] T ，a y (θ k ,φ k ,r k ) Is M x 1, a y (θ 1 ,φ 1 ,r 1 )、a y (θ 2 ,φ 2 ,r 2 )、a y (θ K ,φ K ,r K ) Through a y (θ k ,φ k ,r k )＝[a y1 (θ k ,φ k ,r k ),a y2 (θ k ,φ k ,r k ),…,a yM (θ k ,φ k ,r k )] T Acquisition, a y1 (θ k ,φ k ,r k )、a y2 (θ k ,φ k ,r k )、a yM (θ k ,φ k ,r k ) By passing throughAcquisition, n y (t) represents an independent co-distributed additive noise vector added to the data received by all elements of the y array at time t, n y The dimension of (t) is Mx 1.
Step 3: based on x (t) and y (t) in the step 2, calculating the fourth-order delay mutual accumulation amount of the data received by the m-th array element of the y array, the data received by the n-th array element of the x array, the data received by all the array elements of the x array and the data received by all the array elements of the y array, and recording as C mn (τ)，
The method comprises the steps of carrying out a first treatment on the surface of the Wherein C is mn The dimension of (τ) is NxM, τ represents the delay, cum {. Cndot. } is the cumulant operation, (. Cndot.) * Is a conjugate operation (.) H For conjugate transpose operation, y m (t) represents the data received by the m-th element of the y array, y m (t+τ) represents the data received by the m-th element of the y array after the delay τ, x n (t) represents the data received by the nth element of the x array, and x (t+τ) represents the delay of all elements of the x arrayData received after τ, s k (t + tau) represents the signal after the delay tau processing of the signal from the kth near field signal source,diag {.cndot }, represents converting a vector into a diagonal matrix with the vector as the main diagonal element, a ym (θ 1 ,φ 1 ,r 1 )、a ym (θ 2 ,φ 2 ,r 2 )、a ym (θ K ,φ K ,r K ) By->Acquisition, a xn (θ 1 ,φ 1 ,r 1 )、a xn (θ 2 ,φ 2 ,r 2 )、a xn (θ K ,φ K ,r K ) By->Acquisition, Γ (τ) =diag { γ 1 (τ),γ 2 (τ),…,γ K (τ)}，γ k (τ) represents the cumulative amount of the signal from the kth near field signal source and the signal after being time-delayed τ, +.>γ 1 (τ)、γ 2 (τ)、γ K (tau) passing throughAnd (5) obtaining.
Step 4: for C obtained in step 3 mn Vectorizing (tau) to obtain C mn The vectorization result of (τ) is denoted as c mn (τ)，Wherein c mn The dimension of (τ) is (N×M) ×1, vec (. Cndot.) is vectorization, by Khatri-Rao product, B is a steering matrix, and +.>The dimension of B is (N×M) ×K, and the kth column of B is B k ，/>For the Kronecker product operation,
step 5: c based on step 4 mn (τ), M sequentially takes integer values from 1 to M, N sequentially takes integer values from 1 to N, and the matrix c (τ), c (τ) = [ c ] is obtained by arrangement 11 (τ),…,c 1N (τ),…,c 21 (τ),…,c MN (τ)]The method comprises the steps of carrying out a first treatment on the surface of the Then, c (τ) is expressed as c (τ) =bΓ (τ) B, based on the arrangement of the elements in c (τ) H The method comprises the steps of carrying out a first treatment on the surface of the Wherein the dimension of c (τ) is (NxM) × (NxM), c 11 (τ)、c 1N (τ)、c 21 (τ)、c MN (tau) passing throughAnd (5) obtaining.
Step 6: c (tau) obtained in the step 5 is vectorized, and the vectorized result of c (tau) is taken as data received by the virtual array and is denoted as w (tau), w (tau) =vec (c (tau)) = (B) * As follows, "-B) gamma (τ) =Dγ (τ); wherein w (τ) has a dimension of (N×M) 2 X 1, D denotes a virtual steering matrix, d=b * The dimension of the pair of wires B and D is (N.times.M) 2 The K column of X K, D is D k ，γ(τ)＝[γ 1 (τ),γ 2 (τ),…,γ K (τ)] T 。
Step 7: taking τ=t based on w (τ) obtained in step 6 s ,2T s ,…,N p T s The virtual received data matrix W, w= [ W (T s ),w(2T s ),…,w(N p T s )]＝Dγ s The method comprises the steps of carrying out a first treatment on the surface of the Wherein T is s Representing virtual sampling period, N p Representing the number of pseudo shots,np > 1, W is of dimension (NxM) 2 ×N p Compared with x (T) and y (T), the virtual array element number corresponding to W is greatly improved, and W (T) s )、w(2T s )、w(N p T s ) Let w (τ) =vec (c (τ))= (B * As indicated by B) gamma (τ) =Dγ (τ) acquisition, γ s ＝[γ(T s ),γ(2T s ),…,γ(N p T s )]，γ(T s )、γ(2T s )、γ(N p T s ) By γ (τ) = [ γ ] 1 (τ),γ 2 (τ),…,γ K (τ)] T And (5) obtaining.
Step 8: the covariance of W obtained in step 7 is calculated, denoted R,then pass throughCarrying out characteristic value decomposition on R to obtain all characteristic values; then sequencing all the characteristic values from small to large, and taking the front (N multiplied by M) 2 K eigenvalues, and the matrix formed by eigenvectors corresponding to the eigenvalues is used as a noise subspace eigenvector matrix E n The method comprises the steps of carrying out a first treatment on the surface of the Wherein the dimension of R is (NxM) 2 ×(N×M) 2 R has rank of K, Λ ss ＝γ s γ s H ，E s Representing a signal subspace eigenvector matrix, Σ s Representing a diagonal matrix of signal subspace eigenvalues, E n Representing a noise subspace eigenvector matrix, Σ n Representing a diagonal matrix of noise subspace eigenvalues.
Step 9: e based on step 8 n And defines a pseudo power function P (theta, phi, r) by utilizing the orthogonal property of the signal subspace and the noise subspace,then searching by using three-dimensional spectrum peak, and searching at interval (-180 deg., 180 deg.)]Searching for the value of theta in the interval [0 DEG, 90 DEG ]]The value of phi is searched internally and is within the interval +.>The value of r is searched internally, K maximum values exist in P (theta, phi and r), and the combination of the value of theta, the value of phi and the value of r corresponding to the kth maximum value is the three-dimensional position parameter of the kth near-field signal source; wherein θ represents a direction angle variable, φ represents a pitch angle variable, r represents a distance variable from the origin, +.>a x (θ, φ, r) is a x (θ k ,φ k ,r k ) θ in (a) k ,φ k ,r k Correspondingly replace theta, phi, r, a y (θ, φ, r) is a y (θ k ,φ k ,r k ) θ in (a) k ,φ k ,r k The corresponding substitution is theta, phi and r.
In order to verify the effectiveness and accuracy of the method, the method is subjected to simulation test, and the method is concretely as follows:
the method comprises the steps of setting 4 uncorrelated near field signal sources, wherein the direction angle, pitch angle and distance between the uncorrelated near field signal sources and a reference array element (namely an origin) are respectively { -142 degrees, 10 degrees, 2 lambda }, { -47 degrees, 35 degrees, 7 lambda }, {48 degrees, 60 degrees, 12 lambda }, {143 degrees, 85 degrees and 17 lambda }, wherein lambda is a signal wavelength, the lambda is incident on a three-dimensional near field signal source space propagation model based on an L-shaped array, 2 array elements are respectively arranged on an x axis and a y axis of the model, the array elements are shared at the origin, the total array element number is 3, and the array element distance d=lambda/2 is taken as lambda=1. The signal-to-noise ratio SNR is set to 60dB, the number of snapshots is 1050, and the number of pseudo snapshots is 50.
The method is used for estimating the three-dimensional position parameters (direction angle, pitch angle and distance between the near-field signal source and the reference array element). Fig. 2 shows a resolved view of the direction angle of the near field signal source, the abscissa being the direction angle variable and the ordinate being the pseudo-power function value expressed in dB, it can be seen from fig. 2 that 4 maxima occur at the direction angle value at which the near field signal source is located, in agreement with theory. Fig. 3 shows a resolution of the pitch angle of the near field signal source, the abscissa is the pitch angle variable, and the ordinate is the pseudo-power function value expressed in dB, and it can be seen from fig. 3 that 4 maxima also appear at the pitch angle value where the near field signal source is located, consistent with theory. Fig. 4 shows an estimated result diagram of three-dimensional position parameters of the near-field signal source, wherein three-dimensional coordinates respectively represent a direction angle, a pitch angle and a distance from a reference array element, and an estimated value and a set value are compared, and as can be seen from fig. 4, the near-field signal source can be accurately distinguished under the condition that the number of the near-field signal sources is larger than the number of the array elements. Therefore, the method can realize underdetermined estimation and can achieve higher parameter estimation precision.
Claims (1)
1. A near-field source three-dimensional parameter underdetermined estimation method based on space-time information association is characterized by comprising the following steps:
step 1: establishing a three-dimensional near-field signal source space propagation model based on an L-shaped array: an array formed by N array elements is arranged on an x axis of a three-dimensional coordinate system to serve as an x array, an array formed by M array elements is arranged on a y axis of the three-dimensional coordinate system to serve as a y array, and the x array and the y array share an origin of the three-dimensional coordinate system to form an L-shaped array; the x array is a nested array and consists of two uniform linear arrays, wherein the number of array elements of one uniform linear array is L x And the array element distance is d, and the array element number of the other uniform linear array is N-L x And the array element spacing is (L) x +1) d; the y array is also a nested array and is also formed by two uniform linear arrays, wherein the number of array elements of one uniform linear array is L y And the array element distance is d, and the number of the array elements of the other uniform linear array is M-L y And the array element spacing is (L) y +1) d; by d xn Represents the position of the nth element of the x array, the nth E [1, L ] of the x array x ]The position of each array element is d xn N E [ L ] of = (n-1) d, x array x +1,N]The position of each array element is d xn ＝(n-L x )(L x +1) d-d; by d ym Represents the position of the m-th array element of the y array, the m-th E [1, L y ]The position of each array element is d ym M e [ L ] of = (m-1) d, y array y +1,M]The position of each array element is d ym ＝(m-L y )(L y +1) d-d; k near field signal sources are incident into the L-shaped arrayk near field signal sources are at a direction angle theta k And pitch angle phi k From the distance origin r k The coordinate position of the kth near-field signal source is denoted (r) k sinφ k cosθ k ,r k sinφ k sinθ k ,r k cosφ k )；
Wherein, N is more than 1, M is more than 1, the number of array elements of the L-shaped array is N+M-1, n=1, 2, …, N, m=1, 2, …, M,1 < L x ＜N，1＜L y < M, d is lambda/2, lambda is the signal wavelength, K is not less than 1, k=1, 2, …, K, θ k ∈(-180°,180°]，φ k ∈[0°,90°]，
Step 2: by r xn,k Representing the distance from the kth near field signal source to the nth array element of the x array, using r ym,k Representing the distance of the kth near field signal source to the mth element of the y-array, then, considering amplitude attenuation, calculating the amplitude phase factor of the signal sent by the kth near-field signal source received by the nth array element of the x array, and marking the amplitude phase factor as a xn (θ k ,φ k ,r k )，Similarly, the amplitude phase factor of the signal sent by the kth near-field signal source received by the mth array element of the y array is calculated and is marked as a ym (θ k ,φ k ,r k )，/>The data received by all the array elements of the x array are represented by x (t), the data received by all the array elements of the y array are represented by y (t), and x (t) =a x s(t)+n x (t)，y(t)＝A y s(t)+n y (t)；
Where g represents a known path loss attenuation index, e represents a natural constant, j represents an imaginary part,representing the attenuation of the signal sent by the kth near field signal source received by the nth array element of the x array relative to the signal sent by the kth near field signal source received by the reference array element, namely the array element at the origin, the attenuation of the signal sent by the kth near field signal source received by the nth array element of the x array is->Indicating the phase difference of the signal sent by the kth near field signal source received by the nth array element of the x array relative to the signal sent by the kth near field signal source received by the reference array element, namely the array element at the origin, and the phase difference is>Representing the attenuation of the signal sent by the kth near field signal source received by the mth array element of the y array relative to the signal sent by the kth near field signal source received by the reference array element, namely the array element at the origin, and the attenuation is>Indicating the phase difference of the signal sent by the kth near field signal source received by the mth array element of the y array relative to the signal sent by the kth near field signal source received by the reference array element, namely the array element at the origin, wherein x (t) and y (t) are column vectors, t represents a time variable, A x Array flow pattern matrix representing x array, A x ＝[a x (θ 1 ,φ 1 ,r 1 ),a x (θ 2 ,φ 2 ,r 2 ),…,a x (θ K ,φ K ,r K )]，A x Is N x K, a x (θ k ,φ k ,r k )＝[a x1 (θ k ,φ k ,r k ),a x2 (θ k ,φ k ,r k ),…,a xN (θ k ,φ k ,r k )] T ，a x (θ k ,φ k ,r k ) Is N x 1, the superscript "T" denotes the transpose of the vector or matrix, s (T) denotes the near field signal source vector, s (T) = [ s ] 1 (t),s 2 (t),…,s K (t)] T The dimension of s (t) is Kx1, s k (t) represents the signal from the kth near field signal source, n x (t) represents an independent co-distributed additive noise vector added to the data received by all the array elements of the x array at time t, n x (t) dimension N.times.1, A y Array flow pattern matrix representing y array, A y ＝[a y (θ 1 ,φ 1 ,r 1 ),a y (θ 2 ,φ 2 ,r 2 ),…,a y (θ K ,φ K ,r K )]，A y Is M x K, a y (θ k ,φ k ,r k )＝[a y1 (θ k ,φ k ,r k ),a y2 (θ k ,φ k ,r k ),…,a yM (θ k ,φ k ,r k )] T ，a y (θ k ,φ k ,r k ) Is M x 1, n y (t) represents an independent co-distributed additive noise vector added to the data received by all elements of the y array at time t, n y (t) has dimension M×1;
step 3: based on x (t) and y (t) in the step 2, calculating the fourth-order delay mutual accumulation amount of the data received by the m-th array element of the y array, the data received by the n-th array element of the x array, the data received by all the array elements of the x array and the data received by all the array elements of the y array, and recording as C mn (τ)，
Wherein C is mn The dimension of (τ) is NxM, τ represents the delay, cum {. Cndot. } is the cumulant operation, (. Cndot.) * Is a conjugate operation (.) H For conjugate transpose operation, y m (t) represents the mth array element of the y arrayReceived data, y m (t+τ) represents the data received by the m-th element of the y array after the delay τ, x n (t) represents the data received by the nth array element of the x array, x (t+τ) represents the data received by all array elements of the x array after time delay τ, s k (t + tau) represents the signal after the delay tau processing of the signal from the kth near field signal source,diag {.cndot }, represents converting a vector into a diagonal matrix with the vector as the main diagonal element, a ym (θ 1 ,φ 1 ,r 1 )、a ym (θ 2 ,φ 2 ,r 2 )、a ym (θ K ,φ K ,r K )Γ(τ)＝diag{γ 1 (τ),γ 2 (τ),…,γ K (τ)}，γ k (τ) represents the cumulative amount of the signal from the kth near field signal source and the signal after being time-delayed τ, +.>
Step 4: for C obtained in step 3 mn Vectorizing (tau) to obtain C mn The vectorization result of (τ) is denoted as c mn (τ)，
Wherein c mn The dimension of (τ) is (N×M) ×1, vec (. Cndot.) is vectorization, and the product of (Khatri) -Rao is performed, B represents a steering matrix,the dimension of B is (N×M) ×K, and the kth column of B is B k ， For the Kronecker product operation,
step 5: c based on step 4 mn (τ), M sequentially takes integer values from 1 to M, N sequentially takes integer values from 1 to N, and the matrix c (τ), c (τ) = [ c ] is obtained by arrangement 11 (τ),…,c 1N (τ),…,c 21 (τ),…,c MN (τ)]The method comprises the steps of carrying out a first treatment on the surface of the Then, c (τ) is expressed as c (τ) =bΓ (τ) B, based on the arrangement of the elements in c (τ) H ；
Wherein the dimension of c (τ) is (nxm) × (nxm);
step 6: c (tau) obtained in the step 5 is vectorized, and the vectorized result of c (tau) is taken as data received by the virtual array and is denoted as w (tau), w (tau) =vec (c (tau)) = (B) * ⊙B)γ(τ)＝Dγ(τ)；
Wherein w (τ) has a dimension of (N×M) 2 X 1, D denotes a virtual steering matrix, d=b * The dimension of the pair of wires B and D is (N.times.M) 2 The K column of X K, D is D k ，γ(τ)＝[γ 1 (τ),γ 2 (τ),…,γ K (τ)] T ；
Step 7: taking τ=t based on w (τ) obtained in step 6 s ,2T s ,…,N p T s The virtual received data matrix W, w= [ W (T s ),w(2T s ),…,w(N p T s )]＝Dγ s ；
Wherein T is s Representing virtual sampling period, N p Representing the number of pseudo shots, N p The dimension of W is > 1 (N X M) 2 ×N p ，γ s ＝[γ(T s ),γ(2T s ),…,γ(N p T s )]；
Step 8: the covariance of W obtained in step 7 is calculated, denoted R,then pass throughCarrying out characteristic value decomposition on R to obtain all characteristic values; then sequencing all the characteristic values from small to large, and taking the front (N multiplied by M) 2 K eigenvalues, and the matrix formed by eigenvectors corresponding to the eigenvalues is used as a noise subspace eigenvector matrix E n ；
Wherein the dimension of R is (NxM) 2 ×(N×M) 2 R has rank of K, Λ ss ＝γ s γ s H ，E s Representing a signal subspace eigenvector matrix, Σ s Representing a diagonal matrix of signal subspace eigenvalues, E n Representing a noise subspace eigenvector matrix, Σ n Representing a diagonal matrix of noise subspace eigenvalues;
step 9: e based on step 8 n And defines a pseudo power function P (theta, phi, r) by utilizing the orthogonal property of the signal subspace and the noise subspace,then searching by using three-dimensional spectrum peak, and searching at interval (-180 deg., 180 deg.)]Searching for the value of theta in the interval [0 DEG, 90 DEG ]]The value of phi is searched internally and is within the interval +.>The value of r is searched internally, K maximum values exist in P (theta, phi and r), and the combination of the value of theta, the value of phi and the value of r corresponding to the kth maximum value is the three-dimensional position parameter of the kth near-field signal source;
wherein θ represents a direction angle variable, φ represents a pitch angle variable, r represents a distance variable from an origin,a x (θ, φ, r) is a x (θ k ,φ k ,r k ) θ in (a) k ,φ k ,r k Correspondingly replaced by theta, phi,r，a y (θ, φ, r) is a y (θ k ,φ k ,r k ) θ in (a) k ,φ k ,r k The corresponding substitution is theta, phi and r.
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