A decoupled estimation method for three-dimensional parameters of space-time near-field sources considering amplitude attenuation

Abstract

The invention relates to a three-dimensional parameter decoupling estimation of a space-time near-field source considering amplitude attenuation. The method comprises the following steps: firstly establishing a near-field signal model based on a cross array; two axes each include M arrays arranged uniformly and linearly; combining the space-time characteristics of array received data to increase the degree of freedom, constructing the received data of two uniform arrays as a fourth-order cumulant matrix C4(τ) associated with a time delay τ, and establishing virtual received data; converting the cumulant form into a contract form, then performing a vectorization operation to obtain #imgabs0#, calculating its covariance matrix, and then performing eigendecomposition to obtain a signal subspace and a noise subspace, constructing a spectrum peak search function of MUSIC, constructing two one-dimensional spectrum peak search estimators based on the rank loss principle to obtain two angles, and then obtaining a one-dimensional estimator for a distance parameter through the obtained angles; the method significantly reduces the computational complexity and has higher estimation accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of near-field signal source positioning, and in particular to a space-time near-field source three-dimensional parameter decoupling estimation method considering amplitude attenuation. Background Art

[0002] As an important research direction of signal source positioning, near-field signal source positioning is widely used in radar positioning, wireless communication and other fields. Since the time delay is a nonlinear function of the array element distance when the near-field source is incident on the array, Fresnel approximation processing is required, so the far-field positioning algorithm cannot be directly applied to the near-field source. For example, the two-dimensional MUSIC algorithm based on the near field extends the MUSIC algorithm in the far field to the near field, but it involves searching the global spatial domain, which is highly complex. In recent years, many scholars have reduced the complexity of the algorithm by reducing the multi-dimensional search to one-dimensional search, but most of these algorithms have problems with poor parameter estimation performance and array aperture loss; the conjugate symmetry of the received data and the autocorrelation of the signal can be used to construct an array with expanded aperture. In view of the fact that the spatial amplitude response of the array is different on different sensors due to the correlation between near-field propagation loss and distance, most existing algorithms ignore them by treating the distance-related amplitude attenuation as equal. In the three-dimensional estimation scenario, there is currently no near-field source algorithm that considers amplitude attenuation and utilizes space-time information. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a method for decoupling and estimating three-dimensional parameters of space-time near-field sources taking into account amplitude attenuation. The method uses space-time information to estimate azimuth, pitch angle and distance, has high estimation accuracy and low computational complexity.

[0004] The technical solution adopted by the present invention is a method for decoupling and estimating three-dimensional parameters of space-time near-field sources considering amplitude attenuation, the method comprising the following steps:

[0005] S1. Establish a near-field signal model based on a cross array. The near-field signal model consists of a uniform linear array located on the X-axis and a uniform linear array located on the Y-axis. The number of array elements on the two axes is equal, each of which is an array of M uniform linear arrangements. The symmetry centers of the two sub-arrays are located at the same point, and the reference sensor position corresponding to the symmetry center is used as the reference origin; the received data of the uniform linear array located on the X-axis and the uniform linear array located on the Y-axis are respectively expressed as:

[0006] Where K is the number of signal sources, p represents the a priori known path loss attenuation exponent value, represents the amplitude attenuation of the uniform linear array located on the X-axis, It represents the amplitude attenuation of the uniform linear array on the Y axis, usually p = 2, r0,k represents the distance from the kth signal source to the reference sensor, r m,k represents the distance from the kth signal source to the sensor at position (m,0), r n,k represents the distance from the kth signal source to the sensor at position (0,n), Ω1={-M x ,…,0,…,M x},Ω2={-M y ,…,0,…,M y},m∈Ω1,n∈Ω2, α k and β k represent the angles between the direction of the kth signal source and the X-axis and the Y-axis respectively, d represents the unit spacing of each subarray element, and λ represents the signal wavelength;

[0007] S2, define two arrays to receive data x m (t) and y n The fourth-order cumulant (t) at a delay of τ is:

[0008] Let p = -m, q = -n, M = M x =M y ,

[0009] M x =(N x -1) / 2,M y =(N y -1) / 2, where N x ,N y Respectively represent the number of array elements of the uniform linear array of the X-axis and Y-axis. After simplifying c4(m,n,p,q), we can get the fourth-order cumulant related to m,p,τ:

[0010] in, represents the kurtosis of the kth incident signal at a delay of τ;

[0011] S3. Based on C4(m,n,τ) obtained in step S2, convert it into a fourth-order cumulant matrix C4(τ) in the form of a contract containing all the information of the cross array: in,(·) H represents the conjugate transpose, A x =[a x (α1,r1),…,a x (α k ,r k ),…,a x (α K ,r K )], A y =[a y (β1,r1),…,a y (β k ,r k ),…,a y (β K ,r K )],

[0012] S4, perform vectorization operation on the contract form C4(τ) obtained in step S3 to obtain: in, represents the Khatri-Rao product, A x and A y is the array flow matrix of the two subarrays, (·) * denotes conjugation;

[0013] S5. In the time domain Perform uniform sampling with a sampling interval of τ l (τ l =T s ,2T s ,…,LT s ), thus generating L pseudo snapshot data The pseudo snapshot matrix generated by superposition of L pseudo snapshot data is expressed as:

[0014] C s =[c s (T s ),c s (2T s ),…,c s (LT s )], we can get: in,

[0015] According to the relationship between Khatri-Rao product and Kronecker product, we can get: Among them, (α k ,β k ,r k ) is the angle and distance of the kth signal, represents the Kronecker product;

[0016] S6. Get the pseudo snapshot matrix The covariance matrix of is: in, is the matrix C s The covariance matrix of is the noise power, I is the unit matrix;

[0017] S7. Covariance matrix Performing feature decomposition yields: Among them, N x N y ×K matrix U s and N x N y ×(N x N y -K) Matrix U n denote the signal subspace and the noise subspace respectively, and the K×K matrix Σ s and (N x N y -K)×(N x N y -K) matrix Σ n denote the eigenvalues ​​of the matrices corresponding to the signal subspace and the noise subspace, respectively, and The eigenvalues ​​of

[0018] S8. Construct a spectrum peak search function of MUSIC according to the signal subspace and noise subspace of step S7: in,(·) H represents the conjugate transpose, U s and U n denote the signal subspace and the noise subspace respectively, represents the steering vector;

[0019] S9. According to According to the symmetry of the array structure, the Y-axis corresponds to the steering vector a of the subarray. y (β,r) is expressed as: Further get a x The decomposition formula of (α,r) is: x (α,r)=ζ x (α)υ x (α,r);

[0020] S10, according to a x The decomposition of (α, r) and the properties of the Kronecker product give us The expansion of is:

[0021]

[0022] S11, based on the rank loss principle, according to the step S10 obtained The expansion of is used to construct a one-dimensional estimator about the angle β: in

[0023] S12, the step S10 The expansion of is further expanded into:

[0024] Then construct an estimator for the angle α: in The one-dimensional estimator of angle β obtained in step S11 is Substitute the estimator for the angle α into In the figure, the angle α can be obtained by searching the one-dimensional spectrum peak;

[0025] S13. Finally, the estimated parameters and Substituting into the MUSIC spectrum peak search function, we get a one-dimensional estimator for the distance parameter r:

[0026] The beneficial effects of the present invention are as follows: the above-mentioned three-dimensional parameter decoupling estimation method for space-time near-field sources taking into account amplitude attenuation adopts a uniformly symmetrical cross-cross symmetrical array, which can still accurately estimate the position parameters of the signal while taking into account amplitude attenuation, and the parameters can be automatically matched. At the same time, in the parameter estimation process, the three-dimensional parameter search is decoupled into three one-dimensional parameter estimators by utilizing the symmetry of the array structure, which significantly reduces the computational complexity. Compared with the existing algorithms, the method of the present invention has better estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a structural schematic diagram of a near-field signal model based on a cross array in the present invention;

[0028] Figure 2 It is an α angle resolution diagram of a near-field signal obtained by using the method of the present invention in an example of a specific embodiment of the present invention;

[0029] Figure 3 It is a β-angle resolution diagram of a near-field signal obtained by using the method of the present invention in an example of a specific embodiment of the present invention;

[0030] Figure 4 This is a distance-resolved image of a near-field signal obtained by using the method of the present invention in an example of a specific embodiment of the present invention. DETAILED DESCRIPTION

[0031] The invention will be further described below with reference to the accompanying drawings and in combination with specific implementations, so that those skilled in the art can implement the invention with reference to the description. The protection scope of the invention is not limited to the specific implementations.

[0032] The present invention relates to a method for decoupling and estimating three-dimensional parameters of space-time near-field sources considering amplitude attenuation, the method comprising the following steps:

[0033] S1. Establish a near-field signal model based on a cross array. The near-field signal model consists of a uniform linear array located on the X-axis and a uniform linear array located on the Y-axis. The number of array elements on the two axes is equal, each of which is an array of M uniform linear arrangements. The symmetry centers of the two sub-arrays are located at the same point, and the reference sensor position corresponding to the symmetry center is used as the reference origin; the received data of the uniform linear array located on the X-axis and the uniform linear array located on the Y-axis are respectively expressed as:

[0034] Where K is the number of signal sources, p represents the a priori known path loss attenuation exponent value, represents the amplitude attenuation of the uniform linear array located on the X-axis, It represents the amplitude attenuation of the uniform linear array on the Y axis, usually p = 2, r 0,k represents the distance from the kth signal source to the reference sensor, r m,k represents the distance from the kth signal source to the sensor at position (m,0), r n,k represents the distance from the kth signal source to the sensor at position (0,n), Ω1={-M x ,…,0,…,M x},Ω2={-M y ,…,0,…,M y},m∈Ω1,n∈Ω2, α k and β k represents the angles between the direction of the kth signal source and the x-axis and y-axis respectively, d represents the unit spacing of each subarray element, λ represents the signal wavelength, and by observing the geometric structure of the array, α k and β k Can be and Associated with azimuth and elevation angles; In order to make full use of the spatial and temporal two-dimensional characteristics of the received data and because the cumulant is insensitive to Gaussian noise, it can improve the estimation performance of source positioning, define two arrays to receive data x m (t) and y n The fourth-order cumulant (t) at a delay of τ is:

[0035] S2. Let p = -m, q = -n, M = M x =M y , M x =(N x -1) / 2,M y =(N y -1) / 2,N x ,N y Respectively represent the number of uniform linear array elements on the X-axis and Y-axis, then after simplification, the fourth-order cumulant related to m, p, τ can be obtained: in, represents the kurtosis of the kth incident signal at a delay of τ;

[0036] S3. Based on C4(m,n,τ) obtained in step S2, convert it into a fourth-order cumulant matrix C4(τ) in the form of a contract containing all the information of the cross array: in,(·) H represents the conjugate transpose, A x =[a x (α1,r1),…,a x (α k ,r k ),…,a x (α K ,r K )], A y =[a y (β1,r1),…,a y (β k ,r k ),…,a y (β K ,r K )],

[0037] S4, perform vectorization operation on the contract form C4(τ) obtained in step S3 to obtain: in, represents the Khatri-Rao product, A x and A y is the array flow matrix of the two subarrays, (·) * denotes conjugation;

[0038] S5. In the time domain Perform uniform sampling with a sampling interval of τ l (τ l =T s ,2T s ,…,LT s ), thus generating L pseudo snapshot data The pseudo snapshot matrix generated by superposition of L pseudo snapshot data is expressed as: C s =[c s (T s ),c s (2T s ),…,c s (LT s )], we can get: in, According to the relationship between Khatri-Rao product and Kronecker product, we can get Among them (α k ,β k, r k ) is the angle and distance of the kth signal, represents the Kronecker product;

[0039] S6. Calculate the pseudo snapshot matrix The covariance matrix of is: in, is the matrix C s The covariance matrix of is the noise power, I is the unit matrix;

[0040] S7. Covariance matrix Performing feature decomposition yields: Among them, N x N y ×K matrix U s and N x N y ×(N x N y -K) Matrix U n denote the signal subspace and the noise subspace respectively, and the K×K matrix Σ s and (N x N y -K)×(N x N y -K) matrix Σ n are the eigenvalues ​​of the matrices corresponding to the signal subspace and the noise subspace, respectively, and The eigenvalues ​​of

[0041] S8. Construct a spectrum peak search function of MUSIC according to the signal subspace and noise subspace of step S7: in(·) H represents the conjugate transpose, U s and U n denote the signal subspace and the noise subspace respectively, is the guiding vector;

[0042] S9. According to According to the symmetry of the array structure, the y-axis corresponds to the steering vector a of the subarray. y (β,r) can be expressed as: Further get a x The decomposition formula of (α,r) is: x (α,r)=ζ x (α)υ x (α,r);

[0043] S10, according to a x The decomposition of (α, r) and the properties of the Kronecker product give us The expansion of is:

[0044]

[0045] S11. Based on the rank loss principle, The expansion of is used to construct a one-dimensional estimator about the angle β: in

[0046] S12, the step S10 The expansion of is further expanded into:

[0047] Therefore, the estimator for the angle α is constructed: in The one-dimensional estimator of angle β obtained in step S11 is Substitute the estimator for the angle α into In the figure, the angle α can be obtained by searching the one-dimensional spectrum peak;

[0048] S13. Finally, the estimated parameters and Substituting into the MUSIC spectrum peak search function, we get a one-dimensional estimator for the distance parameter r:

[0049] The following examples are provided to verify the effectiveness and accuracy of the three-dimensional parameter decoupling estimation method of the space-time near-field source considering amplitude attenuation of the present invention.

[0050] There are two near-field signals that are space-time uncorrelated, with angle and distance parameters of {30°, 60°, 0.7λ} and {85°, 150°, 0.3λ}, incident on a cross-symmetric array. The array has 5 elements on the X-axis and 5 elements on the Y-axis, and each subarray has 2 elements on one side. λ represents the signal wavelength. The signal-to-noise ratio (SNR) is set to 30dB, the number of snapshots is 1000, and the number of pseudo snapshots is 50. The results are shown in Figure 1. Figure 2 , Figure 3 and Figure 4 As shown in the figure, we can see that the estimated parameters of the two near-field source signals can be correctly estimated and paired under the condition of amplitude attenuation. Therefore, the algorithm is effective under near-field conditions, and the angle estimation is accurate to two decimal places, and the distance estimation is accurate to four decimal places, which can achieve accurate parameter estimation.

Claims

1. A method for decoupling and estimating three-dimensional parameters of space-time near-field sources considering amplitude attenuation, characterized by: S1. Establish a near-field signal model based on a cross array. The near-field signal model consists of a uniform linear array located on the X-axis and a uniform linear array located on the Y-axis. The number of array elements on the two axes is equal, each of which is an array of M uniform linear arrangements. The symmetry centers of the two sub-arrays are located at the same point, and the reference sensor position corresponding to the symmetry center is used as the reference origin; the received data of the uniform linear array located on the X-axis and the uniform linear array located on the Y-axis are respectively expressed as: Where K is the number of signal sources, p represents the a priori known path loss attenuation exponent value, represents the amplitude attenuation of the uniform linear array located on the X-axis, represents the amplitude attenuation of the uniform linear array on the Y axis, r 0,k represents the distance from the kth signal source to the reference sensor, r m,k represents the distance from the kth signal source to the sensor at position (m,0), r n,k represents the distance from the kth signal source to the sensor at position (0,n), Ω1={-M x ,…,0,…,M x },Ω2={-M y ,…,0,…,M y },m∈Ω1,n∈Ω2, α k and β k represent the angles between the direction of the kth signal source and the X-axis and the Y-axis respectively, d represents the unit spacing of each subarray element, and λ represents the signal wavelength; S2, define two arrays to receive data x m (t) and y n The fourth-order cumulant (t) at a delay of τ is: Let p = -m, q = -n, M = M x =M y , M x =(N x -1) / 2,M y =(N y -1) / 2, where N x ,N y Respectively represent the number of array elements of the uniform linear array of the X-axis and Y-axis. After simplifying c4(m,n,p,q), we can get the fourth-order cumulant related to m,p,τ: in, represents the kurtosis of the kth incident signal at a delay of τ; S3. Based on C4(m,n,τ) obtained in step S2, convert it into a fourth-order cumulant matrix C4(τ) in the form of a contract containing all the information of the cross array: in,(·) H represents the conjugate transpose, S4, perform vectorization operation on the contract form C4(τ) obtained in step S3 to obtain: in, represents the Khatri-Rao product, A x and A y is the array flow matrix of the two subarrays, (·) · denotes conjugation; S5. In the time domain Perform uniform sampling with a sampling interval of τ l (τ l =T s ,2T s ,…,LT s ), thus generating L pseudo snapshot data The pseudo snapshot matrix generated by superposition of L pseudo snapshot data is expressed as: C s =[c s (T s ),c s (2T s ),…,c s (LT s )], we can get: in, According to the relationship between Khatri-Rao product and Kronecker product, we can get: Among them, (α k ,β k ,r k ) is the angle and distance of the kth signal, represents the Kronecker product; S6. Get the pseudo snapshot matrix The covariance matrix of is: in, is the matrix C s The covariance matrix of is the noise power, I is the unit matrix; S7. Covariance matrix Performing feature decomposition yields: Among them, N x N y ×K matrix U s and N x N y ×(N x N y -K) Matrix U n denote the signal subspace and the noise subspace respectively, and the K×K matrix Σ s and (N x N y -K)×(N x N y -K) matrix Σ n denote the eigenvalues ​​of the matrices corresponding to the signal subspace and the noise subspace, respectively, and The eigenvalues ​​of S8. Construct a spectrum peak search function of MUSIC according to the signal subspace and noise subspace of step S7: in,(·) H represents the conjugate transpose, U s and U n denote the signal subspace and the noise subspace respectively, represents the steering vector; S9. According to According to the symmetry of the array structure, the Y-axis corresponds to the steering vector a of the subarray. y (β,r) is expressed as: Further get a x The decomposition formula of (α,r) is: x (α,r)=ζ x (α)υ x (α,r); S10, according to a x The decomposition of (α, r) and the properties of the Kronecker product give us The expansion of is: S11, based on the rank loss principle, according to the step S10 obtained The expansion of is used to construct a one-dimensional estimator about the angle β: in S12, the step S10 The expansion of is further expanded into: Then construct an estimator for the angle α: in The one-dimensional estimator of angle β obtained in step S11 is Substitute the estimator for the angle α into In , the angle α is obtained by searching the one-dimensional spectrum peak; S13. Finally, the estimated parameters and Substituting into the MUSIC spectrum peak search function, we get a one-dimensional estimator for the distance parameter r:

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