Parameter estimation method of near-field signal source under symmetric uniform linear array

Abstract

The application provides a parameter estimation method of a near-field signal source under a symmetric uniform linear array, comprising the following steps: receiving a signal of the near-field signal source by using a sensor array arranged according to the symmetric uniform linear array, and constructing a fourth-order cumulant matrix according to the received signal; performing singular value decomposition on the fourth-order cumulant matrix to obtain a left singular vector and a right singular vector, and the left singular vector spans a signal subspace and a noise subspace; the right singular vector spans the signal subspace and the noise subspace; using the signal subspace corresponding to the left singular vector and the rotation invariance characteristic, an ESPRIT-Like algorithm is used to estimate the angle of the near-field signal source, or using the signal subspace corresponding to the left singular vector and the rotation invariance characteristic and the orthogonal relationship between the noise subspace corresponding to the right singular vector and a direction vector to estimate the angle of the near-field signal source. The application can improve the resolution and estimation accuracy of the angle estimation of the near-field positioning algorithm under the condition of less calculation amount.

Description

Technical Field

[0001] This invention relates to near-field signal source localization, and more specifically to a method for estimating the parameters of near-field signal sources in a symmetrical uniform linear array. Background Technology

[0002] Source localization is an important research topic in the field of array signal processing, playing a crucial role in many areas such as underground detection, electronic communications, and aerospace. Source localization involves setting up a sensor array, constructing statistical quantities based on the electromagnetic waves received by the array, and then calculating these quantities to estimate the source parameters.

[0003] Traditional subspace-based algorithms or rotation-invariant-based algorithms can directly estimate the angle of arrival (AOA) of far-field signals. However, with the rise of indoor smart devices, far-field signal estimation algorithms are no longer sufficient to meet the needs of indoor device positioning, making research on near-field positioning algorithms more important.

[0004] In related technologies, the paper Simplified High-order DOA and Range Estimation with Linear Antenna Array[J].IEEE Communications Letters,2017,21(1):76-79 (hereinafter referred to as paper [1]) proposes a fast near-field localization algorithm based on cumulant matrix under uniform symmetric array. This algorithm can achieve effective estimation of near-field parameters when only one cumulant matrix is ​​constructed. However, since this algorithm only uses the right singular vector with less information content to estimate the angle, the resolution and estimation accuracy of the near-field angle are slightly poor. Paper CN111308416A proposes a parameter estimation method for near-field signals. It can only be applied to non-circular signals and cannot be applied to arbitrary signals. The dimension of the constructed fourth-order cumulant matrix is ​​also high, which results in high computational complexity during construction. The literature *Passive Localization of Mixed Near-Field and Far-Field Sources Using Two-stage MUSIC Algorithm* [J]. IEEE Transactions on Signal Processing, 2009, 58(1): 108-120 constructs two high-order cumulant matrices: one is a fourth-order cumulant matrix, and the other is a combination matrix of four fourth-order cumulants. The MUSIC method is then used to perform one-dimensional spectral peak search on both matrices to estimate the near-field angle and distance. The literature *Mixed-Order MUSIC Algorithm for Localization of Far-Field and Near-Field Sources* [J]. IEEE Signal Processing Letters, 2013, 20(4): 311-314 and *Localization of Mixed Far-Field and Near-Field Sources via Cumulant Matrix Reconstruction* [J]. IEEE Sensors Journal, 2018, PP: 1-1 both construct a fourth-order cumulant matrix and a second-order covariance matrix to estimate the parameters. These algorithms all construct two matrices for parameter estimation, and then use the ESPRIT method or the one-dimensional MUSIC method to estimate two near-field parameters on these two matrices respectively, constructing multiple cumulative matrices, which undoubtedly increases computational complexity. There are also many near-field source localization algorithms based on covariance matrices, but these algorithms have reduced resolution and estimation accuracy compared to fourth-order statistical methods. Summary of the Invention

[0005] To address the technical problems existing in the localization of near-field signal sources in the prior art, this invention provides a parameter estimation method for near-field signal sources under a symmetrical uniform linear array. The aim is to improve the resolution and estimation accuracy of angle estimation in near-field localization algorithms with less computation.

[0006] This invention is achieved through the following technical solution:

[0007] Parameter estimation methods for near-field signal sources in symmetrical uniform linear arrays include:

[0008] A sensor array arranged in a symmetrical uniform linear array is used to receive signals from a near-field signal source, and a fourth-order cumulant matrix is ​​constructed based on the received signals.

[0009] Singular value decomposition is performed on the fourth-order cumulant matrix to obtain left singular vectors and right singular vectors. The left singular vectors span the signal subspace and the noise subspace; the right singular vectors also span the signal subspace and the noise subspace.

[0010] The angle of the near-field signal source can be estimated using the ESPRIT-Like algorithm by utilizing the rotation invariance of the signal subspace corresponding to the left singular vector, or by utilizing the rotation invariance of the signal subspace corresponding to the left singular vector and the orthogonality between the noise subspace corresponding to the right singular vector and the direction vector.

[0011] Preferably, the sensor array is a linear symmetric array with an element spacing of d and a number of elements of L = 2N+1, the number of near-field signal sources is K, and the signal wavelength of the near-field signal sources is λ. Then, the received signal of the sensor array at time t is expressed as x(t) = A. N s N (t)+n(t), where A N It is an array manifold, A N =[a(θ1,r1),...,a(θ k ,r k ),...,a(θ K ,r K )], θ k It is the angle of the k-th near-field signal source, r k It is the distance to the k-th near-field signal source, k = 1, 2, ..., K, s N It is the signal from K near-field signal sources, s N (t)=[s1(t),s2(t),...,s k (t),...,s K (t)] T s k (t) is the signal of the k-th near-field signal source, n(t) = [n -N(t),...,n0(t),…,n n (t),...,n N (t)] T n n (t) represents the Gaussian white noise experienced by the nth sensor element, and the steering vector.

[0012] Preferably, the constructed fourth-order cumulant matrix C1 is represented as:

[0013]

[0014] Where, the kth column of A1 is The kth column of A2 is

[0015] Where k = 1, 2, ..., K, K is the number of near-field signal sources, and 2N+1 is the number of array elements. θ k Let r be the angle of the k-th near-field signal source. k The distance to the k-th near-field signal source is given by d, where d is the element spacing, λ is the signal wavelength of the near-field signal source, j is the imaginary unit, and c is the distance to the k-th near-field signal source. k The fourth-order cumulant of the k-th near-field signal source is defined as follows:

[0016] Furthermore, singular value decomposition is performed on the fourth-order cumulant matrix, specifically:

[0017]

[0018] Where C1 is a fourth-order cumulant matrix, Σ s ∈R K×K and Σ f ∈R (L-K)×(L-K) It is a diagonal matrix, consisting of K large singular values ​​and LK small singular values, U s ∈C L×K and U f ∈C L×(L-K) These are the signal subspace and noise subspace spanned by the left singular vectors, respectively, V s ∈C L×K and V f ∈C L×(L-K) These are the signal subspace and the noise subspace spanned by the right singular vectors, respectively. The singular vectors of the signal subspace correspond to K large singular values, and the singular vectors of the noise subspace correspond to LK small singular values.

[0019] Where L = 2N + 1 is the number of array elements.

[0020] Furthermore, the angle of the near-field signal source is estimated by utilizing the rotation invariance property of the signal subspace corresponding to the left singular vector. Specifically, the estimated value of the angle of the near-field signal source is obtained by performing a peak search on the angle spectrum represented by equation (14).

[0021] p(θ) = [det(W) H JU s2 -W H Ψ(ω)U s1 )] -1 (14)

[0022] Where W is a 2N×N1 full-rank matrix, J is a 2N×2N commutative matrix, and Ψ(ω)=diag(e j2Nω ,e j2 (N-1)ω ,...,e j2(1-N)ω N1 is any integer greater than N and less than or equal to 2N, U s1 and U s2 For the signal subspace U corresponding to the left singular vector s The result is obtained by similar block segmentation, as shown in formula (12):

[0023]

[0024] Furthermore, the angle of the near-field signal source is estimated by utilizing the rotation invariance property of the signal subspace corresponding to the left singular vector and the orthogonality relationship between the noise subspace corresponding to the right singular vector and the direction vector. Specifically, the estimated value of the angle of the near-field signal source is obtained by performing a peak search on the angle spectrum represented by Equation (15).

[0025] p(θ) = [det(W) H JU s2 -W H Ψ(ω)U s1 )×(a1 H (θ)V f V f H a1(θ))] -1 (15)

[0026] Where W is a 2N×N1 full-rank matrix, J is a 2N×2N commutative matrix, and Ψ(ω)=diag(e j2Nω ,e j2 (N-1)ω ,...,e j2(1-N)ω N1 is any integer greater than N and less than or equal to 2N, U s1 and U s2 For the signal subspace U corresponding to the left singular vector s The result is obtained by similar block segmentation, as shown in formula (12):

[0027]

[0028] Preferably, it also includes estimating the distance to the near-field signal source.

[0029] Furthermore, estimating the distance to the near-field signal source specifically involves using the MUSIC method to estimate the distance to the near-field signal source based on the estimated angle of the near-field signal source and the left singular vector.

[0030] Furthermore, it also includes: estimating the distance of the near-field signal source, specifically: performing a peak search on the angle spectrum represented by equation (16), and the peak position corresponds to the estimated value of the distance of the near-field signal source;

[0031]

[0032] in, This is the angle estimate of the near-field signal source.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] This invention constructs only a fourth-order cumulant matrix. After singular value decomposition of a non-Hermitian symmetric fourth-order cumulant matrix, the left singular vector, the right singular vector, and the corresponding signal subspace and noise subspace are obtained. Next, Method 1 first uses the signal subspace spanned by the left singular vector corresponding to the large singular value, and uses the rotation invariant property of its signal subspace to estimate the near-field angle (angle of the near-field signal source) using the ESPRIT-Like algorithm. Method 2, based on Method 1, combines the orthogonality between the noise subspace spanned by the right singular vector corresponding to the small singular value and the direction vector to estimate the near-field angle. Compared with the traditional high-order cumulant method, this invention only constructs a fourth-order cumulant matrix and performs a singular value decomposition on it to estimate the near-field parameters, reducing the amount of computation. Moreover, compared with the existing fast near-field positioning technology (Reference [1]), the cumulant matrix and its left singular vector in this invention contain richer information, improving the resolution and estimation accuracy of the angle.

[0035] Furthermore, after estimating the near-field angle, the noise subspace spanned by the left singular vector corresponding to the small singular value is orthogonal to the direction vector, that is, the near-field distance (distance to the near-field signal source) is estimated using the MUSIC algorithm. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of a near-field signal source model.

[0037] Figure 2 A schematic diagram for resolving angular spectra.

[0038] Figure 3 This is a schematic diagram illustrating how resolution changes with signal-to-noise ratio.

[0039] Figure 4 This is a schematic diagram illustrating how parameter estimation accuracy changes with signal-to-noise ratio.

[0040] Figure 5 This is a schematic diagram illustrating how the accuracy of parameter estimation changes with snapshots. Detailed Implementation

[0041] To further understand the present invention, the present invention will be described below with reference to embodiments. These descriptions are only for further explaining the features and advantages of the present invention and are not intended to limit the claims of the present invention.

[0042] This invention discloses a parameter estimation method for a near-field signal source under a symmetric uniform linear array, comprising two approaches. First, a fourth-order non-Hermitian cumulant matrix is ​​constructed using the signals received by the sensor array. Singular value decomposition is then performed on this matrix to obtain a left singular vector and a right singular vector. The spaces spanned by the singular vectors corresponding to large and small singular values ​​are the signal subspace and the noise subspace, respectively. Approach one first estimates the angle of the near-field signal source using the rotation-invariant property of the signal subspace corresponding to the left singular vector. Approach two, building upon Approach one, simultaneously estimates the near-field angle using the orthogonality between the noise subspace corresponding to the right singular vector and the direction vector. Both methods then substitute the estimated angle into the steering vector of the near-field signal source, utilizing the orthogonality between the steering vector and the noise subspace corresponding to the left singular vector to estimate the distance to the near-field signal source.

[0043] The present invention provides a method for estimating near-field signal source parameters under a symmetrical uniform linear array, which specifically includes the following steps:

[0044] 1) Construct a fourth-order non-Hermitian cumulant matrix C1 and perform singular value decomposition on it.

[0045] The present invention constructs as follows Figure 1 The near-field signal source model is shown. The array is a linear symmetric array with an element spacing of d and a number of elements of L = 2N+1. The signal source consists of K independent near-field signals with a wavelength of λ. The received signal of the array can then be expressed as x(t) = [x -N (t),x -N+1 (t),…,x n (t),…,x N-1 (t),x N (t)] T , where x n (t) represents the signal at the nth array element, where n = 1, 2, ..., N, and can be specifically represented as... j is the imaginary unit, where s k (t) represents the signal of the k-th near-field source, k = 1, 2, ..., K, nn (t) represents the Gaussian white noise received by the nth array element, τ lk It is the phase difference between the k-th near-field signal source at the l-th array element and its phase at the 0th array element. θ k It is the angle of the k-th near-field signal source, r k This is the distance to the k-th near-field signal source. The distance to the near-field signal source must satisfy the Fresnel region condition 0.62(D). 3 / λ) 1 / 2 <r k <2D 2 / λ, D=(L-1)d / λ, where D is the array aperture, then in Then at time t, the array signal x(t) = A N s N (t)+n(t), where A N It is an array manifold, A N =[a(θ1,r1),...,a(θ k ,r k ),...,a(θ K ,r K )], s N It is the signal from K near-field signal sources, s N (t)=[s1(t),s2(t),...,s k (t),...,s K (t)] T s k (t) is the signal of the k-th near-field signal source, n(t) = [n -N (t),...,n0(t),…,n n (t),...,n N (t)] T , guide vector

[0046] Therefore, the fourth-order cumulant matrix C1 can be constructed according to the following formula.

[0047]

[0048] in

[0049]

[0050] Here, m, n, p, q are the parameters used to define the cum function.

[0051] make:

[0052]

[0053] in, m, n ∈ [-N, N]. Therefore, according to the definition, C1 can be written as:

[0054]

[0055] Where, the kth column of A1 is The kth column of A2 is

[0056] The singular value decomposition of C1 yields:

[0057]

[0058] Where, Σ s ∈R K×K and Σ f ∈R (L-K)×(L-K) It is a diagonal matrix, consisting of K large singular values ​​and LK remaining small singular values, U s ∈C L×K and U f ∈C L×(L-K) V is the signal subspace and noise subspace spanned by the left singular vectors, respectively. s ∈C L×K and V f ∈C L×(L-K) It consists of a signal subspace and a noise subspace spanned by right singular vectors, respectively. The singular vectors of the signal subspace correspond to K large singular values, and the singular vectors of the noise subspace correspond to LK small singular values.

[0059] 2) Estimate the angle using the signal subspace spanned by the left singular vector.

[0060] The method of this invention divides a pair of array manifolds A2 into blocks, with the following:

[0061]

[0062] in:

[0063]

[0064]

[0065] Where N1 is any integer greater than N and less than or equal to 2N, and J is a commutative matrix of 2N×2N dimensions:

[0066]

[0067] as well as:

[0068]

[0069]

[0070] Where M represents the upper and lower bounds.

[0071] For the signal subspace U corresponding to the left singular vector s By performing similarity segmentation, we have:

[0072]

[0073] Based on the ESPRIT-Like method, the diagonal matrix containing the source angle but excluding the source distance is constructed as follows:

[0074] Ψ(ω)=diag(e j2Nω ,e j2(N-1)ω ,...,e j2(1-N)ω (13)

[0075] When Ψ(ω)=D(ω) m When ) can be satisfied, matrix JU s2 -Ψ(ω)U s1 The m-th column is 0, and the determinant of the matrix is ​​0. Therefore, the estimated angle of the near-field signal source can be obtained by searching for the spectral peaks of the angle spectrum represented by the following formula.

[0076] p(θ) = [det(W) H JU s2 -W H Ψ(ω)U s1 )] -1 (14)

[0077] Where W is a full-rank matrix with dimensions 2N×N1.

[0078] In Method 2 of this invention, it is noted that the array manifold A1 is determined only by the angle, and its column vector a1(θ) k The noise subspace V corresponding to the right singular vector obtained after the singular value decomposition of the cumulant matrix will be... f Since the near-field angle is orthogonal, it can be estimated by combining this orthogonality with equation (14) in method one. Therefore, by performing a spectral peak search on the following equation, the estimated value of the near-field signal source angle can be obtained.

[0079] p(θ) = [det(W) H JU s2 -W H Ψ(ω)U s1 )×(a1 H (θ)V f V f H a1(θ))] -1 (15)

[0080] Where θ is the near-field signal source angle to be estimated, a1(θ)=[e -j2ω(-N) ,...,1,...,e -j2ωN ] T .

[0081] This invention selects to use the signal subspace corresponding to the left singular vector for angle estimation, making full use of array information and improving the accuracy of angle estimation.

[0082] 3) Estimate the distance to the left singular vector using the MUSIC method.

[0083] The near-field angle estimate obtained in step 2) Substitute a2(θ) k ,r k By performing a spectral peak search on the following formula, the position of the spectral peak corresponds to the estimated value of the near-field distance.

[0084]

[0085] Where r is the distance to the near-field signal source to be estimated.

[0086] This invention obtains the angle and distance parameters of the near-field source from the array received signal, and completes the positioning estimation.

[0087] Example 1

[0088] See Figure 2 Assume a linear symmetric array has 9 elements, and the spacing between the elements is... When the positions of the near-field signal sources are (-2°, λ) and (2°, 1.5λ), and the signal-to-noise ratio is 4dB, the angle spectrum resolution of the angle estimation algorithm of the method of the present invention, which uses the left singular vector and the existing fast near-field positioning technology (reference [1]) which uses the right singular vector, is compared with that of the angle estimation algorithm of the method of the present invention, which simultaneously uses the left and right singular vectors. Then see Figure 3 We statistically analyzed 100 Monte Carlo experiments, with the signal-to-noise ratio varying from -6dB to 8dB, and compared the resolution curves of the three experiments with the change in signal-to-noise ratio.

[0089] See Figure 4 Assume a linear symmetric array has 13 elements, and the spacing between the elements is... With 500 snapshots, 100 Monte Carlo simulations, and a signal-to-noise ratio (SNR) that changes from 0 dB to 10 dB, the angle estimation RMSE curve of Method 1 of this invention using the left singular vector to estimate the angle is compared with that of the existing fast near-field positioning technology (reference [1]) using the right singular vector to estimate the angle, or the angle estimation RMSE curve of Method 2 of this invention using both left and right singular vectors to estimate the angle is compared with that of the SNR.

[0090]

[0091] In the formula, K is the number of near-field signal sources, and B is the number of experiments. This is the estimated direction of arrival (DOA) of the k-th near-field signal source in the b-th snapshot.

[0092] See Figure 5 The setup of the array and near-field signal source is as follows: Figure 4 Under the conditions that the signal-to-noise ratio is 4dB, the number of Monte Carlo operations is 100, and the number of snapshots changes from 500 to 2000, the first method of the present invention uses the left singular vector to estimate the angle and the near-field signal source fast positioning method (reference [1]) uses the right singular vector to estimate the angle, or the second method of the present invention uses both left and right singular vectors to estimate the angle, and the angle estimation RMSE curve changes with the number of snapshots.

[0093] Depend on Figure 2 It can be seen that under this condition, the method of the first method in this invention can obtain two obvious spectral peaks on the angle spectrum by using the left singular vector of the fourth-order cumulant matrix and the ESPRIT-Like method. However, the method of using the right singular vector in the fast positioning algorithm (reference [1]) can no longer distinguish the two spectral peaks. At the same time, the two spectral peaks obtained by the method of the second method in this invention using the left and right singular vectors are also more obvious than those obtained by the fast positioning algorithm (reference [1]). Figure 3 The trend of resolution variation with signal-to-noise ratio under 100 experiments also confirms that Method 1 and Method 2 of the present invention can obtain higher angular resolution of the fast positioning algorithm (reference [1]) under various signal-to-noise ratios by using the left singular vector.

[0094] Depend on Figure 4 and Figure 5 It can be seen that the estimation accuracy of these three methods increases with the increase of signal-to-noise ratio and snapshot. The method of the first and second methods of this invention, which uses the left singular vector, always has a higher angle estimation accuracy than the fast positioning method (reference [1]). This is because the left singular vector contains more information of the array signal, and the second method, which also uses the right singular vector, can have a higher angle estimation accuracy than the first method even with an increase in computation.

[0095] In summary, the estimation method of this invention has smaller errors, higher resolution, and higher accuracy compared to other algorithms.

Claims

1. A parameter estimation method for a near-field signal source under a symmetrical uniform linear array, characterized in that, include: A sensor array arranged in a symmetrical uniform linear array is used to receive signals from a near-field signal source, and a fourth-order cumulant matrix is ​​constructed based on the received signals. The constructed fourth-order cumulant matrix Represented as: (4) in, The Listed as , The Listed as , ; in, =1,2,…,K, where K is the number of near-field signal sources. The number of array elements , , For the first The angle of a near-field signal source It is the first The distance to a near-field signal source For the spacing between array elements, The signal wavelength of the near-field signal source. j The imaginary unit, For the first k The fourth-order cumulant of a near-field signal source is defined as follows: ; Singular value decomposition is performed on the fourth-order cumulant matrix to obtain left singular vectors and right singular vectors. The left singular vectors span the signal subspace and the noise subspace; the right singular vectors also span the signal subspace and the noise subspace. Singular value decomposition is performed on a fourth-order cumulant matrix, specifically as follows: (5) in, It is a fourth-order cumulant matrix. and It is a diagonal matrix, and its constituent elements are as follows: Large singular values ​​and A small singular value and These are the signal subspace and noise subspace spanned by the left singular vectors, respectively. and These are the signal subspace and noise subspace spanned by right singular vectors, respectively. The singular vectors of the signal subspace correspond to... The large singular values ​​correspond to the singular vectors in the noise subspace. A small singular value; in, The number of array elements; The angle of the near-field signal source can be estimated by using the rotation invariance property of the signal subspace corresponding to the left singular vector and the ESPRIT-Like algorithm. Alternatively, the angle of the near-field signal source can be estimated by using the rotation invariance property of the signal subspace corresponding to the left singular vector and the orthogonality relationship between the noise subspace corresponding to the right singular vector and the direction vector. The angle of the near-field signal source is estimated by utilizing the rotation invariance property of the signal subspace corresponding to the left singular vector. Specifically, the estimated value of the angle of the near-field signal source is obtained by performing a peak search on the angle spectrum represented by Equation (14). (14) in, for A full-rank matrix of dimension 1 for A commutative matrix of dimension 1 , greater than N And less than or equal to 2 N any integer, and For the signal subspace corresponding to the left singular vector The result is obtained by similar block segmentation, as shown in formula (12): (12) The angle of the near-field signal source is estimated by utilizing the rotation invariance property of the signal subspace corresponding to the left singular vector and the orthogonality relationship between the noise subspace corresponding to the right singular vector and the direction vector. Specifically, the estimated value of the angle of the near-field signal source is obtained by performing a peak search on the angle spectrum represented by Equation (15). (15)。 2. The parameter estimation method for a near-field signal source under a symmetrical uniform linear array according to claim 1, characterized in that, Also includes: Estimate the distance to the near-field signal source.

3. The parameter estimation method for a near-field signal source under a symmetrical uniform linear array according to claim 2, characterized in that, The specific method for estimating the distance to the near-field signal source is as follows: based on the estimated angle of the near-field signal source, the distance to the near-field signal source is estimated using the MUSIC method on the left singular vector.

4. The parameter estimation method for a near-field signal source under a symmetrical uniform linear array according to claim 1, characterized in that, Also includes: To estimate the distance to the near-field signal source, specifically: perform a peak search on the angle spectrum represented by equation (16), and the position of the peak corresponds to the estimated distance to the near-field signal source; (16) in, This is the angle estimate of the near-field signal source.

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