Multi-cumulant matrix joint near-field direction finding method of accurate spherical wave model

Abstract

The invention discloses a multi-cumulant matrix joint near-field direction finding method of an accurate spherical wave model, and aims to improve the accuracy of near-field signal direction finding. The method comprises the following steps: establishing an accurate phase near-field source DOA model of a one-dimensional uniform linear array, and determining signal characteristics by using a spatial amplitude phase factor; an array manifold matrix is accurately estimated by constructing a cumulant matrix and a characteristic decomposition technology, so that the azimuth angle and the distance of the narrow-band near-field source are obtained; the method has the advantages that the precise spherical wave model under the uniform linear array is considered, the fourth-order cumulant matrixes of different array elements are calculated, the array manifold matrix is estimated by means of the rotation invariance principle, then the two-dimensional joint parameters of the narrow-band near-field source are estimated, the estimation precision is high, and better performance is achieved under the low signal-to-noise ratio.

Description

Technical Field

[0001] The invention relates to an array signal processing technology for a near-field source, and in particular to a multi-cumulant matrix combined near-field direction finding method of an accurate spherical wave model. Background Art

[0002] In the field of array signal processing, the Direction of Arrival (DOA) positioning problem is an important research direction, which has a wide range of applications in radar, sonar and other fields. In the positioning of far-field signal sources, the distance between the far-field signal source and the reference array element in the array is greater than the Fresnel zone, and the phase geometric propagation model of the signal is approximately a plane wave, while the wavefront of the near-field signal source is a spherical wave, resulting in a nonlinear phase difference relationship between the array elements, making the positioning of near-field signal sources more complicated than that of far-field signal sources.

[0003] Most of the existing near-field DOA algorithms use the Fresnel approximation, perform second-order Taylor expansion on the nonlinear phase, and ignore the influence of amplitude attenuation. Compared with the precise spherical wave model, this processing method will introduce non-random estimation errors. Near-field two-dimensional DOA algorithms that take amplitude attenuation into account have been proposed, such as the fourth-order cumulant MUSIC algorithm, but these algorithms still use the Fresnel approximation for the phase factor, which will still introduce systematic errors. At the same time, in the near-field scenario, the MUSIC algorithm needs to search for spectral peaks of azimuth and distance parameters, which has a high computational complexity. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a multi-cumulant matrix joint near-field direction finding method for an accurate spherical wave model, which considers the accurate spherical wave model under a uniform linear array, calculates the fourth-order cumulant matrix of different array elements, and estimates the array manifold matrix with the help of the rotational invariance principle, thereby realizing the estimation of the two-dimensional joint parameters of the narrowband near-field source, with high estimation accuracy and low algorithm complexity.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a multi-cumulant matrix combined near-field direction finding method of an accurate spherical wave model, characterized by comprising the following steps:

[0006] Step 1: Establish a precise phase near-field source DOA model of a one-dimensional uniform linear array. In the model, there is a one-dimensional uniform linear array and multiple incoherent narrowband near-field sources. Each narrowband near-field source incidents a signal onto the one-dimensional uniform linear array. The two-dimensional joint parameters of each narrowband near-field source, i.e., the azimuth angle of the narrowband near-field source and the distance to the reference array element in the one-dimensional uniform linear array, are used. The spatial amplitude phase factor of each narrowband near-field source reaching each array element in the one-dimensional uniform linear array is determined based on the precise spherical wave model. The spatial amplitude phase factor includes an amplitude attenuation term and a phase delay.

[0007] Step 2: For each array element in the one-dimensional uniform linear array, a fourth-order cumulant matrix of the array element is constructed according to the data scalars received by the array element from all narrowband near-field sources, the data scalars received by the reference array element from all narrowband near-field sources, and the data vectors received by the one-dimensional uniform linear array from all narrowband near-field sources, wherein the data scalars contain the spatial amplitude phase factors of all narrowband near-field sources reaching the corresponding array element, the data vectors contain the array manifold matrix, and the array manifold matrix is ​​composed of the spatial amplitude phase factors of all narrowband near-field sources reaching all array elements;

[0008] Step 3: Based on the fourth-order cumulant matrices of all array elements in the one-dimensional uniform linear array, a joint cumulant length matrix is ​​constructed; then, the signal subspace and the noise subspace are obtained by eigendecomposing the covariance matrix of the joint cumulant length matrix; then, the signal subspace corresponding to the fourth-order cumulant matrix of each array element is decomposed from the signal subspace; then, 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 is utilized, and the least squares criterion and eigendecomposition technique are applied to obtain the estimated value of the array manifold matrix;

[0009] Step 4: Based on the estimated value of the array manifold matrix, the spatial amplitude phase factor of each narrowband near-field source reaching each array element is obtained, and then the amplitude attenuation term of each narrowband near-field source reaching each array element is obtained; based on the amplitude attenuation term of each narrowband near-field source reaching each array element, the azimuth angle of each narrowband near-field source and the rough estimate of the distance to the reference array element are obtained;

[0010] Step 5: Based on the estimated value of the array manifold matrix, the spatial amplitude phase factor of each narrowband near-field source reaching each array element is obtained, and then the estimated value of the ambiguous phase delay of each narrowband near-field source reaching each array element is obtained; and based on the rough estimated value of the azimuth angle of each narrowband near-field source and the distance to the reference array element, a rough unambiguous estimated value of the phase delay of each narrowband near-field source reaching each array element is obtained; then, using the relationship between the estimated value of the ambiguous phase delay and the precise unambiguous estimated value of the phase delay, based on the estimated value of the ambiguous phase delay and the rough unambiguous estimated value of the phase delay, a precise unambiguous estimated value of the phase delay of each narrowband near-field source reaching each array element is obtained; and based on the precise unambiguous estimated value of the phase delay of each narrowband near-field source reaching each array element, a precise estimated value of the azimuth angle of each narrowband near-field source and the distance to the reference array element is obtained.

[0011] In step 1, the precise phase near-field source DOA model of the one-dimensional uniform linear array is established on a two-dimensional coordinate system; the one-dimensional uniform linear array is set on the x-axis of the two-dimensional coordinate system, the total number of array elements is L, the spacing between two adjacent array elements is d, the coordinate position of the i-th array element is ((i-1)d, 0), i=1, 2, ..., L, and the first array element is used as the reference array element; the number of narrowband near-field sources is K, and the two-dimensional joint parameter of the k-th narrowband near-field source is (θ k , r k ), k = 1, 2, ..., K, θ k represents the azimuth of the k-th narrowband near-field source, which is the angle between the signal incident direction of the k-th narrowband near-field source and the y-axis of the two-dimensional coordinate system, θ k ∈[-90°-90°], r k represents the distance from the kth narrowband near-field source to the reference array element; based on the precise spherical wave model, the spatial amplitude phase factor of the kth narrowband near-field source reaching the i-th array element is determined to be a i，k (θ k , r k ), Among them, r i，k represents the distance from the kth narrowband near-field source to the ith array element, e represents a natural constant, j is an imaginary number, λ represents the wavelength of the signal incident from a narrowband near-field source, γ i，k represents the amplitude attenuation term of the kth narrowband near-field source reaching the i-th array element, τ i，k represents the phase delay of the kth narrowband near-field source reaching the i-th array element,

[0012]

[0013] In step 2, the data scalar received by the i-th array element at time t from the K narrowband near-field sources is recorded as x i (t), Among them, s k (t) represents the signal incident from the kth narrowband near-field source at time t, w i (t) represents the noise on the i-th array element at time t; the data scalar received by the reference array element at time t from the K narrow-band near-field sources is x1(t); the data vector received by the one-dimensional uniform linear array from the K narrow-band near-field sources at time t is x(t), Among them, a k It represents the steering vector formed by the incident signal of the k-th narrowband near-field source onto the one-dimensional uniform linear array and the x-axis of the two-dimensional coordinate system. The superscript "T" indicates the transposition operation, w(t) indicates the zero-mean noise vector at time t, A represents the array manifold matrix, s(t) represents the signal vector at time t, Then according to x i (t), x1(t), and x(t), construct the fourth-order cumulant matrix C of the i-th array element i ,

[0014] , where cum(·) represents the cumulative calculation function, (·) * represents conjugation, (·) H represents the conjugate transpose, C i The element C with coordinates (m, n) i The calculation process of (m, n) is: Then C i The expression is rewritten into a compact form as follows: Among them, Φ i , C 4s are all diagonal matrices, diag[·] means to find the diagonal matrix, the diagonal elements represents the fourth-order cumulant of the signal incident by the k-th narrow-band near-field source, and m, n = 1, 2, ..., L, E{·} represents the mathematical expectation.

[0015] The specific process of step 3 is as follows:

[0016] Step 3.1: Cascade the fourth-order cumulant matrices of L array elements in the order of array element indexes to construct a joint cumulant length matrix Q. Among them, Φ1 is the identity matrix I with dimension K×K K ;

[0017] Step 3.2: Calculate the covariance matrix R of Q, Then perform eigendecomposition on R to obtain the signal subspace U S and the noise subspace U N , the characteristic decomposition is: Among them, U S It is composed of eigenvectors corresponding to K large eigenvalues, U S The dimension is L 2 ×K,U N By L 2 -K eigenvalues ​​corresponding to the eigenvectors, U N The dimension is K 2 ×(L 2 -K),∑ S represents a diagonal matrix consisting of K large eigenvalues, Σ N Indicated by L 2 -A diagonal matrix consisting of K small eigenvalues;

[0018] Step 3.3: Subsume the signal subspace U S Decompose into L parts, namely in, Represents the fourth-order cumulant matrix C of the i-th array element i The corresponding signal subspace is The dimension is L×K;

[0019] Step 3.4: Using 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, the signal subspace corresponding to the fourth-order cumulant matrix of the i-th array element is transformed into The signal subspace corresponding to the fourth-order cumulant matrix of the reference array element The relationship between them is expressed as: in, represents a full rank matrix; then according to the least squares criterion, we solve for Ψ i , (·) + represents the pseudo-inverse of a matrix;

[0020] Step 3.5: Ψ i Perform eigendecomposition to obtain the diagonal matrix Φ i ; Then the diagonal matrix Φ i The diagonal elements of form a row vector;

[0021] Step 3.6: Substitute Φ1, Φ2, …, Φ obtained in step 3.5 L The row vectors spanned by the diagonal elements are concatenated in the order of the array element indices to obtain the estimated value of the array manifold matrix A.

[0022] It means to spread the diagonal elements of the matrix into row vectors. Represents γ i，k The estimated value of Represents τ i，k The estimated value of .

[0023] The specific process of step 4 is as follows:

[0024] Step 4.1: According to Get a i，k (θ k , r k ) Then Modulo operation, we get γ i，k Estimated value of Then Bring in In the equation, we get the unknown quantity: This leads to a system of equations containing L-1 equations: in, To pass Simplifying by algebraic operations, we get d i Indicates the distance between the ith array element and the reference array element, d i =(i-1)d, the unknown quantities in the equations are With r k sinθ k ;

[0025] Step 4.2: According to the system of equations, let the coefficient matrix Coefficient Matrix Unknown quantity vector Then, according to the least squares criterion, the unknown vector Δ is obtained. c，k Solution

[0026] Step 4.3: According to Get r k A rough estimate of and θ k A rough estimate of in, express The first element of express The second element of .

[0027] The specific process of step 5 is as follows:

[0028] Step 5.1: According to Get a i，k (θ k , r k ) Then By performing angle calculation, we can obtain the estimated value of the ambiguous phase delay of the kth narrowband near-field source reaching the i-th array element. Among them, angle(·) represents angle operation;

[0029] Step 5.2: Constructing the collection in, represents the set of positive integers, τ i，k Estimated value of

[0030] Step 5.3: According to r k A rough estimate of and θ k A rough estimate of Calculate τi，k A rough unambiguous estimate of in, To pass and Bring in The r obtained in i，k A rough estimate of

[0031] Step 5.4: S i Middle distance The nearest value is taken as τ i，k Estimated value of It is an accurate and unambiguous estimate;

[0032] Step 5.5: Bring in In the equation, we get the unknown quantity: This leads to a system of equations containing L-1 equations: in, To pass Simplifying by algebraic operations, we can get the unknown quantities in the system of equations as r k With r k sinθ k ;

[0033] Step 5.6: According to the system of equations, let the coefficient matrix Coefficient Matrix Unknown quantity vector Δ f，k =[r k , r k sinθ k ] T ; Then, according to the least squares criterion, the unknown vector Δ is obtained f，k Solution

[0034] Step 5.7: According to Get r k An accurate estimate of and θ k An accurate estimate of in, express The first element of express The second element of .

[0035] Compared with the prior art, the advantages of the present invention are:

[0036] The present invention considers a near-field source positioning method based on an accurate spherical wave model. This method uses the spatial amplitude phase factor under the accurate spherical wave model to avoid the systematic error introduced by the Fresnel approximation. First, the fourth-order cumulant matrix corresponding to each array element is constructed using the received data, and the joint cumulant length matrix is ​​obtained by cascading up and down according to the index order of the array element. Using the rotation invariance, this method can obtain an estimate of the array manifold matrix; using the least squares method to solve the matrix equations corresponding to the amplitude attenuation and phase delay respectively, the rough estimate and accurate estimate of the azimuth and distance parameters can be obtained, which has higher parameter estimation accuracy and can realize automatic pairing of azimuth and distance. In addition, this method does not require spectrum peak search and has low computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Schematic diagram of the precise phase near-field source DOA model of the one-dimensional uniform linear array established in the method of the present invention;

[0038] Figure 2 This is a scatter point matching effect diagram of the angle and distance parameters of three incoherent narrowband near-field sources estimated by the method of the present invention in a simulation experiment. DETAILED DESCRIPTION

[0039] The present invention is further described in detail below with reference to the accompanying drawings.

[0040] The present invention proposes a multi-cumulant matrix combined near-field direction finding method for an accurate spherical wave model, which comprises the following steps:

[0041] Step 1: Establish a precise phase near-field source DOA (Direction of Arrival) model of a one-dimensional uniform linear array (ULA). In this model, there is a one-dimensional uniform linear array and multiple incoherent narrowband near-field sources. Each narrowband near-field source incidents a signal onto the one-dimensional uniform linear array. The two-dimensional joint parameters of each narrowband near-field source, namely the azimuth angle of the narrowband near-field source and the distance to the reference array element in the one-dimensional uniform linear array, are used to determine the spatial amplitude phase factor of each narrowband near-field source reaching each array element in the one-dimensional uniform linear array based on the precise spherical wave model. The spatial amplitude phase factor includes an amplitude attenuation term and a phase delay.

[0042] Specifically, in step 1, Figure 1As shown, the precise phase near-field source DOA model of the one-dimensional uniform linear array is established on a two-dimensional coordinate system; the one-dimensional uniform linear array is set on the x-axis of the two-dimensional coordinate system, the total number of array elements is L, in this embodiment, L=9, the spacing between two adjacent array elements is d, d=λ / 2, λ represents the wavelength of the signal incident from the narrow-band near-field source, the coordinate position of the i-th array element is ((i-1)d, 0), i=1, 2, ..., L, and the first array element is used as the reference array element; the number of narrow-band near-field sources is K, in this embodiment, K=3, and the two-dimensional joint parameter of the k-th narrow-band near-field source is (θ k , r k ), k = 1, 2, ..., K, θ k represents the azimuth of the k-th narrowband near-field source, which is the angle between the signal incident direction of the k-th narrowband near-field source and the y-axis of the two-dimensional coordinate system, θ k ∈[-90° 90°], r k represents the distance from the kth narrowband near-field source to the reference array element; based on the precise spatial geometric propagation relationship, i.e., the precise spherical wave model, the spatial amplitude phase factor of the kth narrowband near-field source reaching the ith array element is determined to be a i，k (θ k , r k ), Among them, r i，k represents the distance from the kth narrowband near-field source to the ith array element, e represents a natural constant, e = 2.71828, j is an imaginary number, λ represents the wavelength of the signal incident from the narrowband near-field source, γ i,k represents the amplitude attenuation term of the kth narrowband near-field source reaching the i-th array element, τ i,k represents the phase delay of the kth narrowband near-field source reaching the i-th array element,

[0043] Step 2: For each array element in the one-dimensional uniform linear array, a fourth-order cumulant matrix of the array element is constructed according to the data scalars received by the array element from all narrowband near-field sources, the data scalars received by the reference array element from all narrowband near-field sources, and the data vectors received by the one-dimensional uniform linear array from all narrowband near-field sources, wherein the data scalars contain the spatial amplitude phase factors of all narrowband near-field sources reaching the corresponding array element, the data vectors contain the array manifold matrix, and the array manifold matrix is ​​composed of the spatial amplitude phase factors of all narrowband near-field sources reaching all array elements.

[0044] Specifically, in step 2, the data scalar received by the i-th array element at time t from the K narrowband near-field sources is recorded as x i (t), Among them, s k(t) represents the signal incident from the kth narrowband near-field source at time t, w i (t) represents the noise on the i-th array element at time t; the data scalar received by the reference array element at time t from the K narrow-band near-field sources is x1(t); the data vector received by the one-dimensional uniform linear array from the K narrow-band near-field sources at time t is x(t), Among them, a k It represents the steering vector formed by the incident signal of the k-th narrowband near-field source onto the one-dimensional uniform linear array and the x-axis of the two-dimensional coordinate system. The superscript "T" indicates the transposition operation, w(t) indicates the zero-mean noise vector at time t, A represents the array manifold matrix, s(t) represents the signal vector at time t, Then according to x i (t), x1(t), and x(t), construct the fourth-order cumulant matrix C of the i-th array element i ,

[0045] , where cum(·) represents the cumulative calculation function, (·) * represents conjugation, (·) H represents the conjugate transpose, C i The element C with coordinates (m, n) i The calculation process of (m, n) is: Then C i The expression is rewritten into a compact form as follows: Among them, Φ i , C 4s are all diagonal matrices, diag[·] means to find the diagonal matrix, the diagonal elements represents the fourth-order cumulant of the signal incident by the k-th narrow-band near-field source, and m, n = 1, 2, ..., L, E{·} represents the mathematical expectation.

[0046] Step 3: Based on the fourth-order cumulant matrices of all array elements in the one-dimensional uniform linear array, a joint cumulant length matrix is ​​constructed; then, the signal subspace and noise subspace are obtained by eigendecomposing the covariance matrix of the joint cumulant length matrix; then, the signal subspace corresponding to the fourth-order cumulant matrix of each array element is decomposed from the signal subspace; and then, the rotational invariance between the signal subspace corresponding to the fourth-order cumulant matrices of different array elements and the signal subspace corresponding to the fourth-order cumulant matrix of the reference array element is utilized, and the least squares criterion and eigendecomposition technique are applied to obtain the estimated value of the array manifold matrix.

[0047] Further defined, the specific process of step 3 is:

[0048] Step 3.1: L The fourth-order cumulant matrices of the array elements are cascaded up and down according to the index order of the array elements to construct the joint cumulant length matrix Q. Among them, Φ1 is the identity matrix I with dimension K×K K .

[0049] Step 3.2: Calculate the covariance matrix R of Q, Then perform eigendecomposition on R to obtain the signal subspace U S and the noise subspace U N , the characteristic decomposition is: Among them, the characteristic decomposition of R can get L 2 eigenvalues, arrange all eigenvalues ​​in order from large to small, with the first K eigenvalues ​​as large eigenvalues ​​and the last L eigenvalues ​​as small. 2 -K eigenvalues ​​as small eigenvalues, U S It is composed of eigenvectors corresponding to K large eigenvalues, U S The dimension is L 2 ×K,U N By L 2 -K eigenvalues ​​corresponding to the eigenvectors, U N The dimension is L 2 ×(L 2 -K),∑ S represents a diagonal matrix consisting of K large eigenvalues, ∑ N Indicated by L 2 -A diagonal matrix consisting of K small eigenvalues.

[0050] Step 3.3: Subsume the signal subspace U S Decompose into L parts, namely in, Represents the fourth-order cumulant matrix C of the i-th array element i The corresponding signal subspace is The dimension is L×K.

[0051] Step 3.4: Use 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, and because the fourth-order cumulant matrix C of the i-th array element i The corresponding signal subspace The space spanned by the array manifold matrix A is the same space, so there exists a full-rank matrix The signal subspace satisfies the relationship Therefore, the signal subspace corresponding to the fourth-order cumulant matrix of the i-th array element is The signal subspace corresponding to the fourth-order cumulant matrix of the reference array element The relationship between them is expressed as: in, represents a full rank matrix; then according to the least squares criterion, we solve for Ψ i , (·) + Represents the pseudoinverse of a matrix.

[0052] Step 3.5: Due to Therefore, i Similar to the diagonal matrix Φ i , Φ i The diagonal elements of i The eigenvalue of Ψ i Perform eigendecomposition to obtain the diagonal matrix Φ i ; Then the diagonal matrix Φ i The diagonal elements of form a row vector.

[0053] Step 3.6: Substitute Φ1, Φ2, …, Φ obtained in step 3.5 L The row vectors spanned by the diagonal elements are concatenated in the order of the array element indices to obtain the estimated value of the array manifold matrix A.

[0054] It means to spread the diagonal elements of the matrix into row vectors. Represents γ i，k The estimated value of Represents τ i，k The estimated value of .

[0055] Step 4: Based on the estimated value of the array manifold matrix, the spatial amplitude phase factor of each narrowband near-field source reaching each array element is obtained, and then the amplitude attenuation term of each narrowband near-field source reaching each array element is obtained; based on the amplitude attenuation term of each narrowband near-field source reaching each array element, a rough estimate of the azimuth angle of each narrowband near-field source and the distance to the reference array element is obtained.

[0056] Further defined, the specific process of step 4 is:

[0057] Step 4.1: According to Get a i，k (θ k , r k ) Then Modulo operation, we get γ i，k Estimated value of Then Bring in In the equation, we get the unknown quantity: This leads to a system of equations containing L-1 equations: in, To pass Simplifying by algebraic operations, we get d i Indicates the distance between the ith array element and the reference array element, d i =(i-1)d, the unknown quantities in the equations are With r k sinθ k .

[0058] Step 4.2: According to the system of equations, let the coefficient matrix Coefficient Matrix Unknown quantity vector Then, according to the least squares criterion, the unknown vector Δ is obtained. c，k Solution

[0059] Step 4.3: According to Get r k A rough estimate of and θ k A rough estimate of in, express The first element of express The second element of .

[0060] Step 5: Based on the estimated value of the array manifold matrix, the spatial amplitude phase factor of each narrowband near-field source reaching each array element is obtained, and then the estimated value of the ambiguous phase delay of each narrowband near-field source reaching each array element is obtained; and based on the rough estimated value of the azimuth angle of each narrowband near-field source and the distance to the reference array element, a rough unambiguous estimated value of the phase delay of each narrowband near-field source reaching each array element is obtained; then, using the relationship between the estimated value of the ambiguous phase delay and the precise unambiguous estimated value of the phase delay, based on the estimated value of the ambiguous phase delay and the rough unambiguous estimated value of the phase delay, a precise unambiguous estimated value of the phase delay of each narrowband near-field source reaching each array element is obtained; and based on the precise unambiguous estimated value of the phase delay of each narrowband near-field source reaching each array element, a precise estimated value of the azimuth angle of each narrowband near-field source and the distance to the reference array element is obtained.

[0061] Further defined, the specific process of step 5 is:

[0062] Step 5.1: According to Get a i，k (θ k , r k ) Then By performing angle calculation, we can obtain the estimated value of the ambiguous phase delay of the kth narrowband near-field source reaching the i-th array element. Here, angle(·) represents angle operation.

[0063] Step 5.2: Due to is the principal value of the argument, and There is ambiguity and it is related to τ i，k Estimated value of exist The integer multiple relationship, so the set can be constructed in, represents the set of positive integers, τ i，k Estimated value of

[0064] Step 5.3: According to r k A rough estimate of and θ k A rough estimate of Calculate τ i，k A rough unambiguous estimate of in, To pass and Bring in The r obtained in i，k A rough estimate of .

[0065] Step 5.4: S i Middle distance The nearest value is taken as τ i，k Estimated value of is an accurate and unambiguous estimate.

[0066] Step 5.5: Bring in In the equation, we get the unknown quantity: This leads to a system of equations containing L-1 equations: in, To pass Simplifying by algebraic operations, we can get the unknown quantities in the system of equations as r k With r k sinθ k .

[0067] Step 5.6: According to the system of equations, let the coefficient matrix Coefficient Matrix Unknown quantity vector Δ f，k =[r k , r k sinθ k ]T ; Then, according to the least squares criterion, the unknown vector Δ is obtained f，k Solution

[0068] Step 5.7: According to Get r k An accurate estimate of and θ k An accurate estimate of in, express The first element of express The second element of .

[0069] In order to verify the effectiveness and accuracy of the method of the present invention, a simulation test is now carried out on the method of the present invention. The specific parameters and results of the simulation are as follows:

[0070] In the simulation experiment, it is assumed that there are three incoherent narrowband near-field sources in space, which are incident on a one-dimensional uniform linear array with a total number of elements L = 9, and the element spacing is d = λ / 2, λ = 1. The two-dimensional joint parameters of each narrowband near-field source are: (-20°, 5λ), (-25°, 5.5λ) and (30°, 6λ). The number of snapshots N = 1000, and the signal-to-noise ratio is 20dB.

[0071] Figure 2 The scatter matching diagram of the angle parameters and distance parameters of three narrow-band near-field sources estimated by the method of the present invention is given. Figure 2 It can be seen that the method of the present invention has good estimation performance when estimating the position parameters of the near-field source, and the angle parameter and the distance parameter can be automatically paired. The error of the angle parameter is within 1°, and the error of the distance parameter is within 0.1λ. Therefore, the method of the present invention can realize the estimation of the two-dimensional parameters of the near-field source, and has good performance.

Claims

1. A multi-cumulant matrix joint near-field direction finding method based on an accurate spherical wave model, characterized in that The following steps are involved: Step 1: Establish a precise phase near-field source DOA model of a one-dimensional uniform linear array. In the model, there is a one-dimensional uniform linear array and multiple incoherent narrowband near-field sources. Each narrowband near-field source incidents a signal onto the one-dimensional uniform linear array. The two-dimensional joint parameters of each narrowband near-field source, i.e., the azimuth angle of the narrowband near-field source and the distance to the reference array element in the one-dimensional uniform linear array, are used. The spatial amplitude phase factor of each narrowband near-field source reaching each array element in the one-dimensional uniform linear array is determined based on the precise spherical wave model. The spatial amplitude phase factor includes an amplitude attenuation term and a phase delay. Step 2: For each array element in the one-dimensional uniform linear array, a fourth-order cumulant matrix of the array element is constructed according to the data scalars received by the array element from all narrowband near-field sources, the data scalars received by the reference array element from all narrowband near-field sources, and the data vectors received by the one-dimensional uniform linear array from all narrowband near-field sources, wherein the data scalars contain the spatial amplitude phase factors of all narrowband near-field sources reaching the corresponding array element, the data vectors contain the array manifold matrix, and the array manifold matrix is ​​composed of the spatial amplitude phase factors of all narrowband near-field sources reaching all array elements; Step 3: Based on the fourth-order cumulant matrices of all array elements in the one-dimensional uniform linear array, a joint cumulant length matrix is ​​constructed; then, the signal subspace and the noise subspace are obtained by eigendecomposing the covariance matrix of the joint cumulant length matrix; then, the signal subspace corresponding to the fourth-order cumulant matrix of each array element is decomposed from the signal subspace; then, 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 is utilized, and the least squares criterion and eigendecomposition technique are applied to obtain the estimated value of the array manifold matrix; Step 4: Based on the estimated value of the array manifold matrix, the spatial amplitude phase factor of each narrowband near-field source reaching each array element is obtained, and then the amplitude attenuation term of each narrowband near-field source reaching each array element is obtained; based on the amplitude attenuation term of each narrowband near-field source reaching each array element, the azimuth angle of each narrowband near-field source and the rough estimate of the distance to the reference array element are obtained; Step 5: Based on the estimated value of the array manifold matrix, the spatial amplitude phase factor of each narrowband near-field source reaching each array element is obtained, and then the estimated value of the ambiguous phase delay of each narrowband near-field source reaching each array element is obtained; and based on the rough estimated value of the azimuth angle of each narrowband near-field source and the distance to the reference array element, a rough unambiguous estimated value of the phase delay of each narrowband near-field source reaching each array element is obtained; then, using the relationship between the estimated value of the ambiguous phase delay and the precise unambiguous estimated value of the phase delay, based on the estimated value of the ambiguous phase delay and the rough unambiguous estimated value of the phase delay, a precise unambiguous estimated value of the phase delay of each narrowband near-field source reaching each array element is obtained; and based on the precise unambiguous estimated value of the phase delay of each narrowband near-field source reaching each array element, a precise estimated value of the azimuth angle of each narrowband near-field source and the distance to the reference array element is obtained.

2. The multi-cumulant matrix combined near-field direction finding method of the accurate spherical wave model according to claim 1 is characterized in that In the step 1, the precise phase near-field source DOA model of the one-dimensional uniform linear array is established on a two-dimensional coordinate system; the one-dimensional uniform linear array is arranged on the x-axis of the two-dimensional coordinate system, the total number of array elements is L, the spacing between two adjacent array elements is d, the coordinate position of the i-th array element is ((i-1)d, 0), i=1, 2, ..., L, and the first array element is used as a reference array element; The number of narrowband near-field sources is K, and the two-dimensional joint parameter of the kth narrowband near-field source is (θ k , r k ), k = 1, 2, ..., K, θ k represents the azimuth of the k-th narrowband near-field source, which is the angle between the signal incident direction of the k-th narrowband near-field source and the y-axis of the two-dimensional coordinate system, θ k ∈[-90° 90°], r k represents the distance from the kth narrowband near-field source to the reference array element; based on the precise spherical wave model, the spatial amplitude phase factor of the kth narrowband near-field source reaching the i-th array element is determined to be a i，k (θ k , r k ), Among them, r i，k represents the distance from the kth narrowband near-field source to the ith array element, e represents a natural constant, j is an imaginary number, λ represents the wavelength of the signal incident from a narrowband near-field source, γ i，k represents the amplitude attenuation term of the kth narrowband near-field source reaching the i-th array element, τ i,k represents the phase delay of the kth narrowband near-field source reaching the i-th array element, 3. The multi-cumulant matrix combined near-field direction finding method of the accurate spherical wave model according to claim 2 is characterized in that In step 2, the data scalar received by the i-th array element at time t from the K narrowband near-field sources is recorded as x i (t), Among them, s k (t) represents the signal incident from the kth narrowband near-field source at time t, w i (t) represents the noise on the i-th array element at time t; the data scalar received by the reference array element at time t from the K narrow-band near-field sources is x1(t); the data vector received by the one-dimensional uniform linear array from the K narrow-band near-field sources at time t is x(t), Among them, a k It represents the steering vector formed by the incident signal of the k-th narrowband near-field source onto the one-dimensional uniform linear array and the x-axis of the two-dimensional coordinate system. The superscript "T" indicates the transposition operation, w(t) indicates the zero-mean noise vector at time t, A represents the array manifold matrix, s(t) represents the signal vector at time t, Then according to x i (t), x1(t), and x(t), construct the fourth-order cumulant matrix C of the i-th array element i , ， Where cum(·) represents the cumulative calculation function, (·) * represents conjugation, (·) H represents the conjugate transpose, C i The element C with coordinates (m, n) i The calculation process of (m, n) is: Then C i The expression is rewritten into a compact form as follows: Among them, Φ i , C 4s are all diagonal matrices, diag[·] means to find the diagonal matrix, the diagonal elements represents the fourth-order cumulant of the signal incident by the k-th narrow-band near-field source, m, n = 1, 2, ..., L, E{·} represents the mathematical expectation.

4. The multi-cumulant matrix combined near-field direction finding method of the accurate spherical wave model according to claim 3 is characterized in that The specific process of step 3 is as follows: Step 3.1: Cascade the fourth-order cumulant matrices of L array elements in the order of array element indexes to construct a joint cumulant length matrix Q. Among them, Φ1 is the identity matrix I with dimension K×K K ; Step 3.2: Calculate the covariance matrix R of Q, Then perform eigendecomposition on R to obtain the signal subspace U S and the noise subspace U N , the characteristic decomposition is: Among them, U S It is composed of eigenvectors corresponding to K large eigenvalues, U S The dimension is L 2 ×K,U N By L 2 -K eigenvalues ​​corresponding to the eigenvectors, U N The dimension is L 2 ×(L 2 =K), ∑s represents a diagonal matrix consisting of K large eigenvalues, ∑ N Indicated by L 2 -A diagonal matrix consisting of K small eigenvalues; Step 3.3: Subsume the signal subspace U S Decompose into L parts, namely in, Represents the fourth-order cumulant matrix C of the i-th array element i The corresponding signal subspace is The dimension is L×K; Step 3.4: Using 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, the signal subspace corresponding to the fourth-order cumulant matrix of the i-th array element is transformed into The signal subspace corresponding to the fourth-order cumulant matrix of the reference array element The relationship between them is expressed as: in, represents a full rank matrix; then according to the least squares criterion, we solve for Ψ i , (·) + represents the pseudo-inverse of a matrix; Step 3.5: Ψ i Perform eigendecomposition to obtain the diagonal matrix Φ i ; Then the diagonal matrix Φ i The diagonal elements of form a row vector; Step 3.6: Substitute Φ1, Φ2, …, Φ obtained in step 3.5 L The row vectors spanned by the diagonal elements are concatenated in the order of the array element indices to obtain the estimated value of the array manifold matrix A. diag -1 (·) means to expand the diagonal elements of the matrix into row vectors, Represents γ i，k The estimated value of Represents τ i，k The estimated value of .

5. The multi-cumulant matrix combined near-field direction finding method of the accurate spherical wave model according to claim 4 is characterized in that The specific process of step 4 is as follows: Step 4.1: According to Get a i，k (θ k , r k ) Then Modulo operation, we get γ i，k Estimated value of Then Bring in In the equation, we get the unknown quantity: This leads to a system of equations containing L-1 equations: in, To pass Simplifying by algebraic operations, we get d i Indicates the distance between the ith array element and the reference array element, d i =(i-1)d, the unknown quantities in the equations are With r k sinθ k ; Step 4.2: According to the system of equations, let the coefficient matrix Coefficient Matrix Unknown Quantity Vector Then, according to the least squares criterion, the unknown vector Δ is obtained. c，k Solution Step 4.3: According to Get r k A rough estimate of and θ k A rough estimate of in, express The first element of express The second element of .

6. The multi-cumulant matrix combined near-field direction finding method of the accurate spherical wave model according to claim 5 is characterized in that The specific process of step 5 is as follows: Step 5.1: According to Get a i，k (θ k , r k ) Then By performing angle calculation, we can obtain the estimated value of the ambiguous phase delay of the kth narrowband near-field source reaching the i-th array element. Among them, angle(·) represents angle operation; Step 5.2: Constructing the collection in, represents the set of positive integers, τ i，k Estimated value of Step 5.3: According to r k A rough estimate of and θ k A rough estimate of Calculate τ i，k A rough unambiguous estimate of in, To pass and Bring in The r obtained in i，k A rough estimate of Step 5.4: S i Middle distance The nearest value is taken as τ i，k Estimated value of is an accurate and unambiguous estimate. Step 5.5: Bring in In the equation, we get the unknown quantity: This leads to a system of equations containing L-1 equations: in, To pass Simplifying by algebraic operations, we can get the unknown quantities in the system of equations as r k With r k sinθ k ; Step 5.6: According to the system of equations, let the coefficient matrix Coefficient Matrix Unknown quantity vector Δ f，k =[r k , r k sinθ k ] T ; Then, according to the least squares criterion, the unknown vector Δ is obtained f,k Solution Step 5.7: According to Get r k An accurate estimate of and θ k An accurate estimate of in, express The first element of express The second element of .

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