Near-field source positioning method based on covariance fitting

Abstract

The invention discloses a near field source positioning method based on covariance fitting. Calculating a spatial correlation function of an array element and constructing single-snapshot equivalent data by utilizing a symmetric characteristic of a uniform linear array, and eliminating signal correlation by utilizing spatial smoothing; performing convex optimization reconstruction on the smoothed covariance matrix based on a covariance fitting criterion, and recovering an idealized Toeplitz matrix structure; solving the reconstructed covariance matrix by adopting a rooting MUSIC algorithm, and resolving a near-field source angle parameter; and constructing a distance sensitive steering vector according to an angle estimation result, and establishing a distance polynomial equation by using noise subspace orthogonality to realize joint optimization estimation of the angle and the distance. Through the covariance matrix reconstruction and polynomial rooting technology, the estimation precision under the conditions of low signal-to-noise ratio and few snapshots is improved, the operand is reduced, meanwhile, the cumulative effect of angle errors to distance estimation is avoided, and efficient matching of near-field source positions is achieved in a complex scene.

Description

Technical Field

[0001] The present invention belongs to the field of sensor array signal processing technology in the field of signal and information processing, and specifically relates to a near-field source localization method based on covariance fitting. The method, for near-field narrowband signals received by a uniform linear array, achieves high-precision joint estimation of near-field source angle and distance by constructing a spatial correlation function, spatial smoothing decorrelation, and covariance matrix reconstruction technology in combination with a root-finding MUSIC algorithm. Background Art

[0002] Direction of Arrival (DOA) estimation is a core technology in array signal processing, with important applications in radar detection, acoustic positioning, wireless communications, and other scenarios. With the development of wireless and mobile communications, the number of target signal sources located within the Fresnel region has increased, making parameter estimation of near-field sources of great research significance. Compared with far-field sources, near-field source positioning requires simultaneous estimation of the incident angle and distance of the signal source, significantly increasing the technical challenges. Traditional near-field source positioning methods are mostly based on subspace algorithms for uniform linear arrays (such as MUSIC and ESPRIT). These methods primarily estimate the angle and distance of near-field sources by constructing two high-order cumulant matrices and applying the MUSIC or ESPRIT method to them for one- or two-dimensional spectral peak searches. However, their accuracy is limited by the search interval, resulting in high computational complexity and difficulty meeting real-time requirements.

[0003] To address the above problems, Li et al. proposed an algorithm for estimating the angle and distance of near-field sources by constructing a non-Hermitian high-order cumulant matrix and performing a singular value decomposition. This algorithm uses accumulated singular vectors and uses MUSIC to perform one-dimensional spectrum peak searches to estimate the angle and distance. Although this method reduces the computational complexity to a certain extent, it still requires two one-dimensional spectrum peak searches, which is still difficult to meet real-time requirements. Based on the covariance matrix algorithm, Jiang et al. proposed an algorithm based on the Root-MUSIC method to estimate distance parameters, replacing the one-dimensional spectrum peak search with polynomial root search. Although this algorithm reduces the computational complexity, its maximum number of resolvable sources is low, and the resolution and parameter estimation accuracy still need to be improved. This patent addresses the problems of needing to construct a high-order cumulant matrix, high computational complexity of spectrum peak search, and low resolution and estimation accuracy of the polynomial root search method. A near-field source localization method based on covariance fitting is proposed. This method achieves high-precision joint estimation of near-field source angle and distance by constructing a spatial correlation function, spatial smoothing decorrelation, and covariance matrix reconstruction technology, combined with the root-MUSIC algorithm. Summary of the Invention

[0004] In response to the shortcomings of existing near-field source positioning and estimation methods, this patent proposes a near-field source positioning method based on covariance fitting. This patented method first uses the received data of a uniform linear array as the basis, solves the spatial correlation function of the received data of every two array elements in a left-right symmetrical position, and arranges them in columns in a certain order. The column vectors are decorrelated to obtain a spatially smoothed covariance matrix. The reconstructed covariance matrix is ​​obtained by covariance fitting the matrix, and then the eigenvalue decomposition is performed on it to obtain a noise subspace. The principle of the root-finding MUSIC method is used to construct a polynomial based on the orthogonality of the noise subspace and the array flow matrix. The angle estimation value of the near-field source is obtained by performing angle conversion on the roots obtained by solving the polynomial. A distance-sensitive steering vector is constructed based on the angle estimation result, and a distance polynomial equation is established using the orthogonality of the noise subspace to achieve joint optimization estimation of angle and distance. This method uses the symmetric characteristics of the uniform linear array to construct a spatial correlation function, and combines the covariance fitting criterion to reconstruct the ideal matrix structure, significantly reducing the influence of noise and insufficient snapshot number. It further replaces the spectral peak search with polynomial root finding to achieve a closed-form solution for angle and distance, greatly reducing the computational complexity while improving accuracy, and has great application value in practical engineering.

[0005] A near-field source positioning method based on covariance fitting is applicable to a near-field source array having a uniform linear array structure. The near-field source model of the uniform linear array is symmetrical about the origin array element position. There are N array elements on the left and right of the origin array element position. The total number of array elements in the uniform linear array is L=2N+1, and the array element spacing between each array element is d. Taking the origin array element position as a reference point, the array element position set D in the uniform linear array is D=[-N,-N+1,…,-1,0,1,…,N-1,N]d={Ω1d,Ω2d,…,Ω L d|Ω1d<Ω2d<…<Ω L d}, where Ω l represents the index of the lth array element, Ω l =-N,-N+1,…,-1,0,1,…,N-1,N, l=1,2,…,L, characterized in that the near-field source positioning method includes the following steps:

[0006] Step 1: There are K uncorrelated near-field narrowband signal sources s k (t) is incident on the uniform linear array, k = 1, 2, ..., K, and the incident angle of each signal source is θ k , where θ k Indicates the kth signal source s k (t) The incident angle to the origin array element or the reference array element. Since the K signal sources are all near-field sources, it is necessary to estimate the distance from each signal source to the array when locating the position of the near-field source. The incident distance of each signal source is r k , where rk Indicates the kth signal source s k (t) is the distance between the reference array element and the far-field signal source. It is different from the plane wave before reaching the uniform linear array. The near-field signal source is a spherical wave before reaching the uniform linear array. Each signal source is located in the Fresnel region of the array aperture, that is, 0.62 (D 3 / λ) 1 / 2 ≤r k ≤2D 2 / λ, where D represents the array aperture of the uniform linear array, D = (L-1)d, d ≤ λ / 4, λ represents the signal wavelength, and at time t, the received data x of the lth element in the uniform linear array l (t) is specifically expressed as where n l (t) represents the additive white Gaussian noise of the lth array element, and the noise is uncorrelated with the incident signal; τ lk Indicates the kth signal source s k (t) The relative delay of the arrival at the lth array element relative to the arrival at the reference array element, τ lk The approximate formula is τ lk ≈γ k Ω l +φ k Ω l 2 , where γ k and φ k Specifically expressed as It can be obtained that at time t, the entire array of the uniform linear array receives data x(t)=As(t)+n(t), where represents the array flow matrix, represents the kth signal source steering vector, represents the overall signal vector at time t, represents the noise vector at time t, x(t)=[x1(t),x2(t),…,x L (t)] T , T represents the number of snapshots, and the multi-snapshot array of the uniform linear array receives data as, X = AS + N, where,

[0007] Step 2: Calculate the spatial correlation function of the data received by two array elements at left-right symmetrical positions in the uniform linear array in step 1, that is, select two array elements at Ω l d and Ω L-l+1 The array element at position d receives data and obtains its spatial correlation function

[0008]

[0009] where Ωl =-Ω L-l+1 , Indicates the kth signal source s k (t) power, Represents the noise power, δ() represents the Dirac function, and L spatial correlation functions are obtained. By arranging them in columns in a certain order, the column vector can be obtained. in

[0010] Represents a column vector with 1 in the middle and 0 in the rest of the positions. r is equivalent to the array receiving data of a single snapshot, A2 is equivalent to its array flow matrix, and p is equivalent to the signal data of a single snapshot.

[0011] Step 3: Decorrelate the array received data r in step 2, and use the spatial smoothing method to achieve decorrelation of r by sacrificing part of the array aperture to avoid the influence of the correlation of r single snapshot data on the DOA estimation result. After spatial smoothing, the covariance matrix is ​​obtained in Equivalent to the received data of a sub-array in r, r p There are Q receiving data in total, P represents the number of sub-arrays into which r is divided, Q = L - P + 1;

[0012] Step 4: For the covariance matrix R in step 3 r Perform matrix reconstruction, because R after spatial smoothing r It is a full rank matrix and also a non-singular matrix. The covariance fitting method is adopted. The covariance fitting criterion adopted is in represents the covariance matrix under ideal conditions, which is a semi-positive Hermitian, Toeplitz matrix, that is, R = T(u), T(u) ≥ 0, where Represents the first column vector of T(u), and the equation of R is substituted into

[0013]

[0014] in is a complex matrix, which is solved by the CVX convex optimization toolbox, and finally the optimized covariance matrix T(u) is obtained. T(u) can be regarded as the ideal array element position [2Ω N+1 ,2Ω N+2 ,…,2Ω N+Q ] the covariance matrix of the array receiving data;

[0015] Step 5: Process T(u) in step 4 according to the principle of root-finding MUSIC method to obtain the near-field source angle estimate and perform eigenvalue decomposition on T(u) in represents the signal subspace, represents a diagonal matrix consisting of K larger eigenvalues, represents the noise subspace, represents a diagonal matrix consisting of (QK) small eigenvalues,

[0016] Step 6: Steering vector of the ideal array flow matrix corresponding to T(u) in step 5 make p(z)=[z 0 ,z 1 ,…,z Q-1 ] T , based on the orthogonality of the noise subspace and the array flow matrix, construct a polynomial about z Solve the polynomial f(z) and get the K roots with amplitudes closest to 1 right Perform angle conversion Get the corresponding K near-field source angle estimates

[0017] Step 7: Direct the signal source in step 1 to vector a(θ k ,r k ) is decomposed into another form a(θ k ,r k )=Φ4(γ k )a4(φ k ),in

[0018]

[0019] Step 8: Solve the covariance matrix of the original array received data x(t) in step 1, R x Perform eigenvalue decomposition, in represents the signal subspace, represents a diagonal matrix consisting of K large eigenvalues, represents the noise subspace, represents a diagonal matrix consisting of (LK) small eigenvalues;

[0020] Step 9: Estimate the near-field source angle obtained in step 6 Get γ k Estimated value of Φ4(γ k ) According to a4(φ k ) structure, let Build about z 2k Polynomial Solve the polynomial f(z) and find a root with a magnitude closest to 1 Should and or Corresponding to the same near-field source, according to the distance conversion formula right By performing distance conversion, we can get Matching near-field source distance estimates K Corresponding to K polynomials f2(z 2k ), we need to solve the polynomial f2(z 2k ) to get K The corresponding K

[0021] Compared with the prior art, the technical solution of the present invention has the following technical effects:

[0022] 1. This paper reconstructs an idealized Toeplitz covariance matrix through the covariance fitting criterion and combines it with spatial smoothing technology to eliminate signal correlation, significantly reducing the matrix mismatch problem under low signal-to-noise ratio and small number of snapshots, thereby improving the accuracy of the joint estimation of near-field source angle and distance;

[0023] 2. The present invention adopts the polynomial root-finding method to replace the traditional spectrum peak search. The proposed distance estimation method avoids the influence of the spectrum peak search interval on the distance estimation accuracy of other methods, has higher distance estimation accuracy, and significantly improves the real-time performance of the algorithm.

[0024] 3. The present invention constructs a joint optimization framework of angle and distance, and utilizes the orthogonality of the signal subspace reconstructed by the covariance matrix and the array flow matrix to achieve synchronous optimization of angle and distance parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is the structural diagram of the uniform linear array near-field source model of this patent;

[0026] Figure 2 This is the positioning estimation result of the patented signal processing method under four near-field sources;

[0027] Figure 3 The angle root mean square error change curve of each method under different SNR of the patented signal processing method;

[0028] Figure 4This is the change curve of the distance root mean square error of each method under different SNRs of the patented signal processing method;

[0029] Figure 5 The angle root mean square error change curve of each method under different fast numbers of the patented signal processing method;

[0030] Figure 6 This is the change curve of the distance root mean square error of each method under different snapshot numbers of the patented signal processing method. DETAILED DESCRIPTION

[0031] The present invention will now be further described with reference to the embodiments and accompanying drawings:

[0032] The first embodiment: Figure 1 The structure of the near-field source model of the uniform linear array used in the present invention is given. The total number of array elements in the uniform linear array is L = 9, N = 4, the spacing between the array elements is d = λ / 4, the array element position set of each array element is [-4, -3, -2, -1, 0, 1, 2, 3, 4] d, the entire uniform linear array is symmetrical about the central array element position, and there are K = 4 uncorrelated near-field narrowband signal sources incident on the uniform linear array, with an incident angle θ k and distance r k They are (-30°, 2λ), (-10°, 3.5λ), (20°, 5λ), and (40°, 6.5λ), respectively. The number of snapshots is T = 800, the signal-to-noise ratio (SNR) is 10 dB, the number of subarrays used for spatial smoothing is 5, and the number of array elements in each subarray is 5.

[0033] The above conditions are used to locate near-field sources. The specific implementation process is as follows:

[0034] Step 1: There are K uncorrelated near-field narrowband signal sources s k (t) is incident on the uniform linear array, k = 1, 2, ..., K, and the incident angle of each signal source is θ k , where θ k Indicates the kth signal source s k (t) The incident angle to the origin array element or the reference array element. Since the K signal sources are all near-field sources, it is necessary to estimate the distance from each signal source to the array when locating the position of the near-field source. The incident distance of each signal source is r k , where r k Indicates the kth signal source s k (t) is the distance between the reference array element and the far-field signal source. It is different from the plane wave before reaching the uniform linear array. The near-field signal source is a spherical wave before reaching the uniform linear array. Each signal source is located in the Fresnel region of the array aperture, that is, 0.62 (D 3 / λ) 1 / 2 ≤r k ≤2D2 / λ, where D represents the array aperture of the uniform linear array, D = (L-1)d, d ≤ λ / 4, λ represents the signal wavelength, and at time t, the received data x of the lth element in the uniform linear array l (t) is specifically expressed as where n l (t) represents the additive white Gaussian noise of the lth array element, and the noise is uncorrelated with the incident signal; τ lk Indicates the kth signal source s k (t) The relative delay of the arrival at the lth array element relative to the arrival at the reference array element, τ lk The approximate formula is τ lk ≈γ k Ω l +φ k Ω l 2 , where γ k and φ k Specifically expressed as It can be obtained that at time t, the entire array of the uniform linear array receives data x(t)=As(t)+n(t), where represents the array flow matrix, represents the kth signal source steering vector, represents the overall signal vector at time t, represents the noise vector at time t, x(t)=[x1(t),x2(t),…,x L (t)] T , T represents the number of snapshots, and the multi-snapshot array of the uniform linear array receives data as, X = AS + N, where,

[0035] Step 2: Calculate the spatial correlation function of the data received by two array elements at left-right symmetrical positions in the uniform linear array in step 1, that is, select two array elements at Ω l d and Ω L-l+1 The array element at position d receives data and obtains its spatial correlation function

[0036]

[0037] where Ω l =-Ω L-l+1 , Indicates the kth signal source s k (t) power, Represents the noise power, δ(·) represents the Dirac function, and L spatial correlation functions are obtained. By arranging them in columns in a certain order, the column vector can be obtained. in Represents a column vector with 1 in the middle and 0 in the rest of the positions. r is equivalent to the array receiving data of a single snapshot, A2 is equivalent to its array flow matrix, and p is equivalent to the signal data of a single snapshot.

[0038] Step 3: Decorrelate the array received data r in step 2, and use the spatial smoothing method to achieve decorrelation of r by sacrificing part of the array aperture to avoid the influence of the correlation of r single snapshot data on the DOA estimation result. After spatial smoothing, the covariance matrix is ​​obtained in Equivalent to the received data of a sub-array in r, r p There are Q receiving data in total, P represents the number of sub-arrays into which r is divided, Q = L - P + 1;

[0039] Step 4: For the covariance matrix R in step 3 r Perform matrix reconstruction, because R after spatial smoothing r It is a full rank matrix and also a non-singular matrix. The covariance fitting method is adopted. The covariance fitting criterion adopted is in represents the covariance matrix under ideal conditions, which is a semi-positive Hermitian, Toeplitz matrix, that is, R = T(u), T(u) ≥ 0, where Represents the first column vector of T(u), and the equation of R is substituted into

[0040]

[0041] in is a complex matrix, which is solved by the CVX convex optimization toolbox, and finally the optimized covariance matrix T(u) is obtained. T(u) can be regarded as the ideal array element position [2Ω N+1 ,2Ω N+2 ,…,2Ω N+Q ] the covariance matrix of the array receiving data;

[0042] Step 5: Process T(u) in step 4 according to the principle of root-finding MUSIC method to obtain the near-field source angle estimate and perform eigenvalue decomposition on T(u) in represents the signal subspace, represents a diagonal matrix consisting of K larger eigenvalues, represents the noise subspace, represents a diagonal matrix consisting of (QK) small eigenvalues;

[0043] Step 6: The steering vector of the array flow matrix in the ideal case corresponding to T(u) in step 5 is make p(z)=[z 0 ,z 1 ,…,z Q-1 ] T , based on the orthogonality of the noise subspace and the array flow matrix, construct a polynomial about z Solve the polynomial f(z) and get the K roots with amplitudes closest to 1 right Perform angle conversion Get the corresponding K near-field source angle estimates

[0044] Step 7: Direct the signal source in step 1 to vector a(θ k ,r k ) is decomposed into another form a(θ k ,r k )=Φ4(γ k )a4(φ k ),in

[0045]

[0046] Step 8: Solve the covariance matrix of the original array received data x(t) in step 1, R x Perform eigenvalue decomposition, in represents the signal subspace, represents a diagonal matrix consisting of K large eigenvalues, represents the noise subspace, represents a diagonal matrix consisting of (LK) small eigenvalues;

[0047] Step 9: Estimate the near-field source angle obtained in step 6 Get γ k Estimated value of Φ4(γ k ) According to a4(φ k ) structure, let Build about z 2k Polynomial Solve the polynomial f(z) and find a root with a magnitude closest to 1 Should and or Corresponding to the same near-field source, according to the distance conversion formula right By performing distance conversion, we can get Matching near-field source distance estimates K Corresponding to K polynomials f2(z 2k ), we need to solve the polynomial f2(z 2k ) to get K The corresponding K

[0048] The method of the present invention based on the above conditions is simulated by MATLAB simulation software and its CVX convex optimization toolbox, and the near-field source location estimation results of the method of the present invention are as follows: Figure 2 As shown. Figure 2 The experimental results show that under the conditions of this example, the method proposed in this paper can realize both near-field source angle estimation and near-field source distance estimation, and the maximum number of estimable signal sources can reach the number of sub-array elements minus 1, that is, the maximum number of estimable signal sources is 4. This is because when estimating the near-field source angle, the method proposed in this paper decorrelates the covariance matrix, resulting in the dimension of the covariance matrix finally used for angle estimation being the number of sub-array elements, because the maximum number of estimable signal sources can only be the dimension of the covariance matrix minus 1.

[0049] Second embodiment: The relationship between the angle root mean square error and the signal-to-noise ratio and the relationship between the distance root mean square error and the signal-to-noise ratio of the signal processing method of this patent are studied respectively, and the effect diagram obtained is as follows Figure 3 、 Figure 4 As shown in FIG, the change curves of the dimension-reduced MUSIC algorithm, the accumulative positioning method, and the overlapping subarray positioning method under different signal-to-noise ratios are also given. The application conditions of the method of the present invention are as follows:

[0050] The method of the present invention is based on a uniform linear array, the array structure of which is as follows: Figure 1 As shown, there are K=2 uncorrelated near-field narrowband signal sources incident on the uniform linear array, with an incident angle θ k and distance r k The angles are (20°, 5λ) and (50°, 2λ), T = 500, SNR starts from -10dB and increases to 15dB in steps of 5dB. W = 500 Monte Carlo simulation experiments are performed each time at different SNRs. The number of subarrays is 5, and the number of array elements in each subarray is also 5. The simulation is performed using MATLAB software.

[0051] analyze Figure 3It can be seen that the angle root mean square error of the method of this patent and the angle root mean square error of the comparison method will gradually decrease with the increase of the signal-to-noise ratio. At a lower SNR, the angle root mean square error of the method proposed in this paper is the smallest, slightly smaller than the angle root mean square error of the positioning method based on overlapping subarrays, and much smaller than the angle root mean square error of the dimensionality reduction MUSIC method and the positioning method based on accumulative measurement; at a higher SNR, the angle root mean square errors of the four methods are very close; the near-field source angle estimation accuracy of the four methods gradually increases with the increase of SNR. At a lower SNR, the angle estimation accuracy of the method proposed in this paper is the largest, close to the angle estimation accuracy of the positioning method based on overlapping subarrays, and much larger than the other two methods; at a higher SNR, the angle estimation accuracy of the four methods are close to each other. From the overall effect, the angle estimation result obtained by the method of this patent is the best.

[0052] analyze Figure 5 It can be seen that the distance root mean square error of the patented method and the angle root mean square error of the comparison method will gradually decrease with the increase of the signal-to-noise ratio, and under the same SNR, the distance root mean square error of the method proposed in this paper is the smallest; the near-field source distance estimation accuracy of the four methods gradually increases with the increase of SNR. Under the same SNR, the distance estimation accuracy of the method proposed in this paper is the largest. From the overall effect, the distance estimation method proposed by the patented method has higher distance estimation accuracy.

[0053] The third embodiment: The relationship between the angle root mean square error and the signal-to-noise ratio and the relationship between the distance root mean square error and the number of snapshots of the signal processing method of the patent are studied respectively. The effect diagram obtained is as follows Figure 5 、 Figure 6 As shown in the figure, the change curves of the dimension-reduced MUSIC algorithm, the accumulative positioning method, and the overlapping subarray positioning method under different snapshot numbers are also given. The application conditions of the method of the present invention are as follows:

[0054] The method of the present invention is based on a uniform linear array, the array structure of which is as follows: Figure 1 As shown, there are K=2 uncorrelated near-field narrowband signal sources incident on the uniform linear array, with an incident angle θ k and distance r k The angles are (20°, 5λ) and (50°, 2λ), T = 500, SNR starts from -10dB and increases to 15dB in steps of 5dB. W = 500 Monte Carlo simulation experiments are performed each time at different SNRs. The number of subarrays is 5, and the number of array elements in each subarray is also 5. The simulation is performed using MATLAB software.

[0055] analyze Figure 5It can be seen that as the number of snapshots increases, the angle root mean square error of the four methods gradually decreases, and under the same number of snapshots, the angle root mean square error of the method proposed in this patent is the smallest; the near-field source angle estimation accuracy of the four methods gradually increases with the increase of the number of snapshots, and under the same number of snapshots, the angle estimation accuracy of the method proposed in this patent is the largest.

[0056] analyze Figure 6 It can be seen that as the number of snapshots increases, the root mean square error of the distance of the four methods gradually decreases, and under the same number of snapshots, the root mean square error of the distance of the method proposed in this patent is the smallest; the near-field source distance estimation accuracy of the four methods gradually increases with the increase of the number of snapshots, and under the same number of snapshots, the distance estimation accuracy of the method proposed in this article is the highest.

[0057] The specific examples described in this patent are merely illustrative of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the specific examples described without departing from the present invention or exceeding the scope of the claims.

Claims

1. A near-field source localization method based on covariance fitting, the method is applicable to a near-field source array having a uniform linear array structure, wherein the near-field source model of the uniform linear array is symmetrical about the origin array element position, there are N array elements to the left and right of the origin array element position, the total number of array elements in the uniform linear array is L = 2N + 1, the array element spacing between each array element is d, and the origin array element position is used as the reference point. Then, the array element position set D in the uniform linear array is D = {Ω1d,Ω2d,…,Ω L d|Ω1d<Ω2d<…<Ω L d}, where Ω l represents the index of the lth array element, Ω l =-N,-N+1,…,-1,0,1,…,N-1,N, l=1,2,…,L, characterized in that: The near-field source localization method includes the following steps: Step 1: There are K uncorrelated near-field narrowband signal sources s k (t) is incident on the uniform linear array, k = 1, 2, ..., K, and the incident angle of each signal source is θ k , where θ k Indicates the kth signal source s k (t) The incident angle to the origin array element or the reference array element. Since the K signal sources are all near-field sources, it is necessary to estimate the distance from each signal source to the array when locating the position of the near-field source. The incident distance of each signal source is r k , where r k Indicates the kth signal source s k (t) is the distance between the reference array element and the far-field signal source. It is different from the plane wave before reaching the uniform linear array. The near-field signal source is a spherical wave before reaching the uniform linear array. Each signal source is located in the Fresnel region of the array aperture, that is, 0.62 (D 3 / λ) 1 / 2 ≤r k ≤2D 2 / λ, where D represents the array aperture of the uniform linear array, D = (L-1)d, d ≤ λ / 4, λ represents the signal wavelength, and at time t, the received data x of the lth element in the uniform linear array l (t) is specifically expressed as where n l (t) represents the additive white Gaussian noise of the lth array element, and the noise is uncorrelated with the incident signal; τ lk Indicates the kth signal source s k (t) The relative delay of the arrival at the lth array element relative to the arrival at the reference array element, τ lk The approximate formula is τ lk ≈γ k Ω l +φ k Ω l 2 , where γ k and φ k Specifically expressed as It can be obtained that at time t, the entire array of the uniform linear array receives data x(t)=As(t)+n(t), where represents the array flow matrix, represents the kth signal source steering vector, represents the overall signal vector at time t, represents the noise vector at time t, x(t)=[x1(t),x2(t),…,x L (t)] T , T represents the number of snapshots, and the multi-snapshot array of the uniform linear array receives data as, X = AS + N, where, Step 2: Calculate the spatial correlation function of the data received by two array elements at left-right symmetrical positions in the uniform linear array in step 1, that is, select two array elements at Ω l d and Ω L-l+1 The array element at position d receives data and obtains its spatial correlation function where Ω l =-Ω L-l+1 , Indicates the kth signal source s k (t) power, Represents the noise power, δ(·) represents the Dirac function, and L spatial correlation functions are obtained. By arranging them in columns in a certain order, the column vector can be obtained. in Represents a column vector with 1 in the middle and 0 in the rest of the positions. r is equivalent to the array receiving data of a single snapshot, A2 is equivalent to its array flow matrix, and p is equivalent to the signal data of a single snapshot. Step 3: Decorrelate the array received data r in step 2, and use the spatial smoothing method to achieve decorrelation of r by sacrificing part of the array aperture to avoid the influence of the correlation of r single snapshot data on the DOA estimation result. After spatial smoothing, the covariance matrix is ​​obtained in Equivalent to the received data of a sub-array in r, r p There are Q receiving data in total, P represents the number of sub-arrays into which r is divided, Q = L - P + 1; Step 4: For the covariance matrix R in step 3 r Perform matrix reconstruction, because R after spatial smoothing r It is a full rank matrix and also a non-singular matrix. The covariance fitting method is adopted. The covariance fitting criterion adopted is in represents the covariance matrix under ideal conditions, which is a semi-positive Hermitian, Toeplitz matrix, that is, R = T(u), T(u) ≥ 0, where Represents the first column vector of T(u), and the equation of R is substituted into in is a complex matrix, which is solved by the CVX convex optimization toolbox, and finally the optimized covariance matrix T(u) is obtained. T(u) can be regarded as the ideal array element position [2Ω N+1 ,2Ω N+2 ,…,2Ω N+Q ] the covariance matrix of the array receiving data; Step 5: Process T(u) in step 4 according to the principle of root-finding MUSIC method to obtain the near-field source angle estimate and perform eigenvalue decomposition on T(u) in represents the signal subspace, represents a diagonal matrix consisting of K larger eigenvalues, represents the noise subspace, represents a diagonal matrix consisting of (QK) small eigenvalues; Step 6: The steering vector of the array flow matrix in the ideal case corresponding to T(u) in step 5 is make p(z)=[z 0 ,z 1 ,…,z Q-1 ] T , based on the orthogonality of the noise subspace and the array flow matrix, construct a polynomial about z Solve the polynomial f(z) and get the K roots with amplitudes closest to 1 right Perform angle conversion Get the corresponding K near-field source angle estimates Step 7: Direct the signal source in step 1 to vector a(θ k ,r k ) is decomposed into another form a(θ k ,r k )=Φ4(γ k )a4(φ k ),in Step 8: Solve the covariance matrix of the original array received data x(t) in step 1, R x Perform eigenvalue decomposition, in represents the signal subspace, represents a diagonal matrix consisting of K large eigenvalues, represents the noise subspace, represents a diagonal matrix consisting of (LK) small eigenvalues; Step 9: Estimate the near-field source angle obtained in step 6 Get γ k Estimated value of Φ4(γ k ) According to a4(φ k ) structure, let Build about z 2k Polynomial Solve the polynomial f(z) and find a root with a magnitude closest to 1 Should and or Corresponding to the same near-field source, according to the distance conversion formula right By performing distance conversion, we can get Matching near-field source distance estimates K Corresponding to K polynomials f2(z 2k ), we need to solve the polynomial f2(z 2k ) to get K The corresponding K

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