A three-dimensional parameter coarse and fine estimation method for spatio-temporal near-field sources based on second-order cross-correlation

Abstract

The present invention relates to a three-dimensional parameter rough and fine estimation method for near-field sources based on second-order cross-correlation, including: establishing a near-field signal model based on a cross array; constructing virtual received data r(m,n,τ) using the cross-correlation function of the signals received by the m-th sensor and the n-th sensor, and converting r(m,n,τ) into a time-delay cross-correlation matrix R(τ) containing information collected by all sensors in the cross array; obtaining estimated values #imgabs0# and #imgabs1# of the array manifold matrices A and B according to R(τ); extracting amplitude attenuation from #imgabs2# and #imgabs3#; constructing a coefficient matrix for the array x; directly obtaining estimated values #imgabs4# and #imgabs5# of the k-th incident signal according to the coefficient matrix of the array x; constructing a coefficient matrix for the array y to obtain an estimated value of #imgabs6#; the present invention adopts a cross array, and in the case of an accurate signal source-sensor spatial geometric relationship, without using the Fresnel approximation and considering the existence of amplitude attenuation, it can still accurately estimate the angle and distance of the signal, and these position parameters are associated with each signal source, without the need for an additional pairing process.

Description

Technical Field

[0001] The present invention relates to the technical field of near-field signal source positioning, and in particular to a coarse estimation method for three-dimensional parameters of space-time near-field sources based on second-order cross-correlation. Background Art

[0002] Near-field signal source localization, a key research area, has applications in numerous fields, including radar, mobile communications, and sonar. Since locating near-field sources requires estimating their angle and distance, and the spatial phase response of the signal is a nonlinear function of array element distance, many methods employ the Fresnel approximation, or Taylor expansion, to facilitate algorithm design. Furthermore, many near-field localization algorithms, such as cumulant-based three-dimensional localization algorithms, ignore the distance-dependent sensor propagation attenuation. This ignoring of propagation attenuation comes at the cost of model mismatch. In recent years, numerous three-dimensional near-field source localization methods have been proposed that account for propagation attenuation. These algorithms all employ the Fresnel approximation to simplify the spatial phase difference, but this also introduces systematic errors, which can degrade algorithm performance in practical applications. Furthermore, incorporating temporal information from the received data can improve algorithm estimation performance. However, most three-dimensional localization algorithms that exploit space-time characteristics are not based on an accurate spatial propagation model. Therefore, for the three-dimensional near-field source parameter estimation scenario, no near-field source localization methods that incorporate space-time information based on an accurate spatial propagation model have been proposed. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a coarse estimation method for three-dimensional parameters of space-time near-field sources based on second-order cross-correlation. This method combines space-time information with a third-order parallel factor (PARAFAC) data model constructed based on second-order cross-correlation to estimate the azimuth, pitch angle and distance of the near-field signal source, and its estimation accuracy is high.

[0004] The technical solution adopted by the present invention is a method for coarse and fine estimation of three-dimensional parameters of space-time near-field sources based on second-order cross-correlation, which includes the following steps:

[0005] S1. Establish a near-field signal model based on a cross array. The near-field signal model consists of two sub-arrays. The array x is a uniform linear array located on the x-axis, and the array y is a uniform linear array located on the y-axis. The number of array elements in array x and array y is equal. The sensor position corresponding to the symmetry center of array x and array y is the reference point of amplitude and phase. When there are K positions The uncorrelated narrowband near-field signal sources arrive at the two uniform linear arrays, where θ k , and r kThey are respectively the elevation angle, azimuth angle, and distance from the k-th signal source to the reference point; for the m-th sensor of array x and the n-th sensor of array y, the spatial amplitude-phase factors of the k-th signal source are respectively obtained and expressed as: where r m,k and r n,k respectively represent the distances from the k-th signal source to the sensors at positions (md, 0) and (0, nd), where m = -M x , …, 0, …, M x , n = -M y , …, 0, …, M y , d represents the element spacing of each array element, λ represents the signal wavelength, and respectively represent the amplitude attenuation of the k-th signal source corresponding to arrays x and y, α k and β k respectively represent the angles between the k-th signal source and the x-axis and y-axis; the signals received by arrays x and y are respectively expressed as: where A = [a(α1, r1),..., a(α k , r k ),..., a(α K , r K )] represents the (2M x + 1) × K-dimensional array manifold matrix of array x, represents the steering vector of the k-th signal source; B = [b(β1, r1),..., b(β k , r k ),..., b(β K , r K )] represents the array manifold matrix of array y, s(t) = [s1(t), …, s K (t)] T represents the K × 1-dimensional signal vector, w x (t) and w y (t) represent the corresponding additive noise vectors;

[0006] S2. Construct virtual received data using the cross-correlation function of the signals received by the m-th sensor and the n-th sensor: where E{·} represents the statistical expectation function, represents the autocorrelation function of the k-th incident signal;

[0007] S3. Based on r(m,n,τ) obtained in step S2, convert it into a time-delay cross-correlation matrix R(τ) that contains information collected by all sensors in the cross array: R(τ) = AR s (τ)B H , where (·) T denotes conjugate transpose, (·) H denotes conjugate transpose, R s (τ) = diag[r s1 (τ), r s2 (τ), …, r sK (τ)];

[0008] S4. Perform a vectorization operation on the time-delay cross-correlation matrix R(τ) obtained in step S3 to get: where r s (τ) = vec(R s (τ)) = [r s1 (τ), r s2 (τ), …, r sk (τ)] T , represents the Khatri-Rao product, (·) * denotes conjugate;

[0009] S5. Uniformly sample the above-mentioned in the time domain with a sampling interval of τ l , τ l = T s , 2T s , …, LT s , to generate L pseudo-snapshot data: Stack them to generate a data matrix based on time delay which is expressed as: where

[0010] S6. Through trilinear decomposition of the data matrix obtained in step S5, obtain the estimated values of the array manifold matrices A and B and respectively extract the amplitude attenuation from the estimated values of the array manifold matrices and : and

[0011] S7. Construct a non-linear equation for the amplitude attenuation extracted in step S6:

[0012] S8. According to the non-linear equation obtained in step S7, construct a coefficient matrix for the array x: and D xk×E xk = F xk , where Using the least squares method, we get:

[0013] S9. Based on the coefficient matrix of the array x obtained in step S8, the and estimated values of the k-th incident signal can be directly obtained: Construct the coefficient matrix of the array y. From we get The estimated value of is: The rough estimated value of is the average of the estimated values of the array x and the array y:

[0014] S10. Obtain the unambiguous rough estimated phase factor:

[0015] S11. Extract the and phases in each steering vector: and Taking and as references, remove the phase ambiguities of the steering vectors and to obtain the unambiguous phase factor:

[0016] S12. Construct the non-linear equations related to the position parameters using the unambiguous phase factor obtained in step S11

[0017] S13. Represent the linear equations of the two sub-arrays in step S11 using the coefficient matrices respectively as:

[0018] α k , β k and the information matrix of r k is

[0019] S14. Finally, obtain the accurate estimates of the angle and distance parameters through the least squares method:

[0020] The beneficial effects of the present invention are as follows: the above-mentioned method for coarse estimation of three-dimensional parameters of space-time near-field sources based on second-order cross-correlation adopts a cross array. Based on the precise spatial geometric relationship between the signal source and the sensor, it takes into account the existence of amplitude attenuation without adopting the Fresnel approximation, and can still accurately estimate the angle and distance of the signal. These position parameters are associated with each signal source, and no additional pairing process is required. At the same time, in the parameter estimation process, the cross-correlation function and space-time characteristics of the signal are directly used to construct virtual received data. Compared with existing algorithms, the method of the present invention has better estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Schematic diagram of the structure of the three-dimensional near-field spatial propagation model based on the cross array in the present invention;

[0022] Figure 2 An α-angle resolution 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;

[0023] Figure 3 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;

[0024] Figure 4 1 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

[0025] The following examples are provided to verify the effectiveness and accuracy of the method for coarse estimation of three-dimensional parameters of space-time near-field sources based on second-order cross-correlation of the present invention.

[0026] The present invention relates to a method for coarse and fine estimation of three-dimensional parameters of space-time near-field sources based on second-order cross-correlation, the method comprising the following steps:

[0027] S1, such as Figure 1 As shown, a near-field signal model based on a cross array is established. The near-field signal model consists of array x and array y. The array x is a uniform linear array located on the x-axis, and the array y is a uniform linear array located on the y-axis. The number of array elements in array x and array y is equal. The sensor position corresponding to the symmetry center of array x and array y is the reference point of amplitude and phase. When there are K positions The uncorrelated narrowband near-field signal sources arrive at the two uniform linear arrays, where θ k , and r kThey are respectively the elevation angle, azimuth angle, and distance from the k-th signal source to the reference point; based on the accurate propagation model, for the m-th sensor of array x and the n-th sensor of array y, the spatial amplitude-phase factors of the k-th signal source are respectively obtained, which are expressed as: where r m,k and r n,k respectively represent the distances from the k-th signal source to the sensors at positions (md, 0) and (0, nd), where m = -M x , …, 0, …, M x , n = -M y , …, 0, …, M y , d represents the element spacing of each array element, λ represents the signal wavelength, and respectively represent the amplitude attenuation of the k-th signal source corresponding to arrays x and y, α k and β k respectively represent the angles between the k-th signal source and the x-axis and y-axis; the signals received by arrays x and y are respectively expressed as: where A = [a(α1, r1),..., a(α k , r k ),..., a(α K , r K )] represents the (2M x + 1) × K-dimensional array manifold matrix of array x, represents the steering vector of the k-th signal source; B = [b(β1, r1),..., b(β k , r k ),..., b(β K , r K )] represents the array manifold matrix of array y, s(t) = [s1(t), …, s K (t)] T represents the K × 1-dimensional signal vector, w x (t) and w y (t) represent the corresponding additive noise vectors;

[0028] S2. Construct virtual received data using the cross-correlation function of the received signals of the m-th sensor and the n-th sensor: where E{·} represents the statistical expectation function, represents the autocorrelation function of the k-th incident signal;

[0029] S3. Based on r(m,n,τ) obtained in step S2, convert it into a time-delay cross-correlation matrix R(τ) that contains information collected by all sensors in the cross array: R(τ) = AR s (τ)B H , where (·) T denotes conjugate transpose, (·) H denotes conjugate transpose, R s (τ) = diag[r s1 (τ), r s2 (τ), …, r sK (τ)];

[0030] S4. Perform a vectorization operation on the time-delay cross-correlation matrix R(τ) obtained in step S3 to get: where r s (τ) = vec(R s (τ)) = [r s1 (τ), r s2 (τ), …, r sk (τ)] T denotes the Khatri-Rao product, (·) * denotes conjugate;

[0031] S5. Uniformly sample the above-mentioned in the time domain with a sampling interval of τ l , τ l = T s , 2T s , …, LT s to generate L pseudo-snapshot data: Stack and generate a data matrix based on time delay which is expressed as: where

[0032] S6. Through trilinear decomposition of the data matrix obtained in step S5, obtain the estimated values of the array manifold matrices A and B and respectively extract the amplitude attenuation from the estimated values of the array manifold matrices and : and <s

[0033] S7. Construct a non-linear equation for the amplitude attenuation extracted in step S6:

[0034] S8. According to the non-linear equation obtained in step S7, construct a coefficient matrix for the array x: and D xk×E xk = F xk , where Using the least squares method, we get:

[0035] S9. According to the coefficient matrix of the array x obtained in step S8, the and estimated values of the k-th incident signal can be directly obtained: Construct the coefficient matrix of the array y. From we get The estimated value of is: The rough estimated value of is the average of the estimated values of the arrays x and y:

[0036] S10. Obtain the unambiguous rough estimated phase factor:

[0037] S11. Extract the and phases in each steering vector Taking and as references, remove the phase ambiguities of the steering vectors and to obtain the unambiguous phase factor:

[0038] S12. Construct the non-linear equation related to the position parameter using the unambiguous phase factor obtained in step S11

[0039] S13. Represent the linear equations of the two sub-arrays in step S11 with coefficient matrices respectively as: α k , β k and the information matrix of r k is

[0040] S14. Finally, obtain the accurate estimates of the angle and distance parameters through the least squares method:

[0041] To verify the effectiveness and accuracy of the method of the present invention, a simulation test is carried out on the method of the present invention as follows:

[0042] Two near-field signals that are spatio-temporally uncorrelated are set, and their angular and distance parameters are {60°, 80°, 1.15λ} and {50°, 75°, 1.2λ} respectively, and they are incident on the near-field signal model of a cross array. The near-field signal model of this cross array has 7 array elements on each of the X-axis and Y-axis, and there are 3 array elements corresponding to each side of each array, where λ represents the signal wavelength. It is set that the signal-to-noise ratio SNR varies from 0 dB to 30 dB, the number of snapshots is 1950, and the number of pseudo-snapshots is 50. The estimated root mean square error RMSE is as Figure 2 , Figure 3 and Figure 4 shown. From the figure, we can see that under the condition of the accurate spatial propagation model and considering the amplitude attenuation, the estimated parameters of the two near-field source signals can be correctly estimated and paired. Therefore, this algorithm is effective under near-field conditions, and when the signal-to-noise ratio increases, the estimation accuracy of the angle and distance steadily improves, and accurate parameter estimation can be achieved.

Claims

1. A three-dimensional parameter rough and fine estimation method for near-field sources in space-time based on second-order cross-correlation, characterized in that: The method comprises the following steps: S1. Establish a near-field signal model based on a cross-shaped array. The near-field signal model consists of two sub-arrays. The array x is a uniform linear array located on the x-axis, and the array y is a uniform linear array located on the y-axis. The number of array elements of array x and array y is equal, and the sensor position corresponding to the symmetry center of array x and array y is the reference point for amplitude and phase. When there are K uncorrelated narrowband near-field signal sources at positions arrive at the two uniform linear arrays, where θ k , and r k are the elevation angle, azimuth angle, and distance of the k-th signal source to the reference point, respectively. For the m-th sensor of array x and the n-th sensor of array y, the spatial amplitude-phase factors of the k-th signal source are obtained respectively, which are expressed as: where r m,k and r n,k represent the distances from the k-th signal source to the sensors at positions (md, 0) and (0, nd) respectively, where m = -M x , …, 0, …, M x , n = -M y , …, 0, …, M y , d represents the element spacing of each array, λ represents the signal wavelength, and represent the amplitude attenuations corresponding to the k-th signal source for arrays x and y respectively. α k and β k respectively represent the angles between the k-th signal source and the x-axis and y-axis; the signals received by array x and array y are respectively expressed as: Among them, A = [a(α1, r1),..., a(α k , r k ),..., a(α K , r K )] represents the (2M x + 1)×K dimensional array manifold matrix of the array x, represents the steering vector of the k-th signal source; B = [b(β1,r1),...,b(β k ,r k ),...,b(β K ,r K )] represents the array manifold matrix of the array y, s(t) = [s1(t), …, s K (t)] T represents a K×1 dimensional signal vector, w x (t) and w y (t) represent the corresponding additive noise vectors; S2. Construct virtual received data by using the cross-correlation function of the signals received by the m-th sensor and the n-th sensor: where E{·} represents the statistical expectation function, represents the autocorrelation function of the k-th incident signal; S3. Based on \(r(m,n,\tau)\) obtained in step S2, transform it into a time-delay cross-correlation matrix \(R(\tau)\) that contains information collected by all sensors in the cross array: \(R(\tau)=AR s (\tau)B H , where \((\cdot) T \) represents conjugate transpose, \((\cdot) H \) represents conjugate transpose, \(R s (\tau)=\text{diag}[r s1 (\tau),r s2 (\tau),\cdots,r sK (\tau)]; S4. Perform a vectorization operation on the time-delay cross-correlation matrix \(R(\tau)\) obtained in step S3 to obtain: where \(r\) s (\(\tau\)) = vec(\(R\) s (\(\tau\))) = [\(r\) s1 (\(\tau\)), \(r\) s2 (\(\tau\)), …, \(r\) sk (\(\tau\))] T , ⊙ represents the Khatri-Rao product, and (·) * represents the conjugate; S5. Uniformly sample the following in the time domain with a sampling interval of τ l , where τ l = T s , 2T s , …, LT s , to generate L pseudo-snapshot data: Stack and generate a data matrix based on time delay which is expressed as: where S6. Through the data matrix obtained in step S5 perform trilinear decomposition to obtain the estimated values of the array manifold matrices A and B and Extract the amplitude attenuation from the estimated values of the array manifold matrices and respectively: and S7. Construct a non-linear equation for the amplitude attenuation extracted in step S6: S8. According to the non-linear equation obtained in step S7, construct a coefficient matrix for the array x: and D xk ×E xk = F xk , where Using the least squares method, we get: S9. Obtain directly the and estimated value of the k-th incident signal: Construct the coefficient matrix of array y, and from obtain The estimated value of is: The rough estimated value of is the average of the estimated values of array x and array y: S10. Obtain a non-blurred rough estimation phase factor: S11. Extract the phases of and in each steering vector: as well as Take and as references, remove the phase ambiguities of the steering vectors and to obtain the ambiguity-free phase factors: S12. Construct the non - ambiguous phase factor obtained in step S11 into a non - linear equation related to the position parameter S13. Express the linear equations for the two sub-arrays in step S11 as coefficient matrices respectively: α k , β k and r k The information matrix of S14. Finally, precise estimates of the angle and distance parameters are obtained by the least squares method:

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