Far and near field mixed source positioning method based on sparse reconstruction

Abstract

The invention discloses a far and near field mixed source positioning method based on sparse reconstruction, and relates to the far and near field mixed source positioning method based on sparse reconstruction. The invention belongs to the field of underwater acoustic detection. The problem that an existing far and near field mixed source positioning method based on sparse reconstruction cannot achieve high positioning precision and low calculation complexity at the same time is solved. The method comprises the following steps of: 1, initializing the current iteration number kappa to be equal to 1; 2, obtaining a covariance matrix according to array element receiving signals; 3, constructing a covariance vector far and near field mixed source sparse representation model and an initial far and near field mixed source dictionary set; 4, constructing a Bayesian hierarchical probability model; 5, updating signal power, precision and disturbance precision in the model; 6, updating the far and near field mixed source dictionary set; 7, judging whether an iteration stop condition is met or the maximum external iteration frequency is reached; if yes, outputting a far-field spatial spectrum estimation result, a near-field spatial spectrum estimation result and corresponding grid point estimation; otherwise, enabling kappa to be equal to kappa + 1 and returning to 5 until the condition is met.

Description

Technical Field

[0001] The invention relates to a far-field and near-field mixed source positioning method based on sparse reconstruction and belongs to the field of underwater acoustic detection. Background Art

[0002] Source localization is an extremely important research direction in array signal processing, and is widely used in radar, sonar, wireless communication and other fields. Traditional source localization methods are usually designed based on pure far-field or pure near-field models. However, in complex scenarios of practical applications, such as underwater noise source localization based on sonar arrays and indoor sound source localization based on microphone arrays, near-field sources and far-field sources exist simultaneously. It is difficult for traditional signal processing methods to effectively separate and locate far-field and near-field mixed sources. Existing subspace-based near-field and far-field mixed source localization algorithms usually assume that the near-field source is located in the Fresnel zone of the array, and separate the near-field source azimuth and distance parameters through the Fresnel approximation, which introduces model errors. In addition, in order to avoid phase ambiguity, these algorithms require that the array element spacing is not greater than 1 / 4 wavelength, and there is array aperture loss when estimating the far-field source azimuth. The existing near-field and far-field mixed source localization algorithm based on sparse Bayesian learning (FN-MSBL) constructs one-dimensional and two-dimensional overcomplete dictionaries for far-field plane waves and near-field spherical waves respectively, and uses sparse Bayesian learning to fit the array snapshot data to reconstruct the near-field and far-field spatial spectra. Although it overcomes the defects of subspace algorithms such as 1 / 4 wavelength array and low positioning accuracy, sparse Bayesian learning requires high-cost matrix inversion operations at each iteration, and the computational complexity is extremely high, which limits real-time applications. In practice, since the true source position cannot be completely on the sampling grid point, it is necessary to correct the off-grid error. At present, many one-dimensional off-grid methods have been proposed to improve the grid mismatch problem, but there are few methods for two-dimensional parameter off-grid of near-field sources. Summary of the invention

[0003] The purpose of the present invention is to solve the problem that the existing far-field and near-field mixed source methods based on sparse reconstruction cannot achieve a balance between high positioning accuracy and low computational complexity, and to propose a far-field and near-field mixed source positioning method based on sparse reconstruction.

[0004] A method for localizing a far-field and near-field mixed source based on sparse reconstruction. The specific process is as follows:

[0005] Step 1: Initialize the current number of iterations κ = 1;

[0006] Step 2: Obtain the covariance matrix based on the array element receiving signal;

[0007] Step 3: According to the covariance matrix, construct a covariance vector far-field and near-field mixed source sparse representation model and an initial far-field and near-field mixed source dictionary set;

[0008] Step 4: Based on the covariance vector far-field and near-field mixed source sparse representation model and the initial far-field and near-field mixed source dictionary set, construct a The Bayesian hierarchical probability model with the accuracy α and the perturbation accuracy β0;

[0009] Step 5: Update the signal power in the Bayesian hierarchical probability model through GAMP-VBI Accuracy α, disturbance accuracy β0;

[0010] Step 6: Update the signal power according to step 5 The accuracy α and perturbation accuracy β0 are used to update the near-field and far-field mixed source dictionary set through the gradient off-grid method;

[0011] Step 7: Determine whether the iteration stop condition is met or the maximum number of external iterations is reached;

[0012] If satisfied, the far-field spatial spectrum estimation result is output Near-field spatial spectrum estimation results and the corresponding grid point estimate

[0013] Otherwise, set κ = κ + 1 and return to step 5 until the iteration stop condition is met or the maximum number of external iterations is reached, and the far-field spatial spectrum estimation result is output. Near-field spatial spectrum estimation results and the corresponding grid point estimate

[0014] in, Estimate the angle corresponding to the vector for the far-field grid point; Estimate the angle corresponding to the vector for the near-field grid point; Estimate the distance corresponding to the vector for the near-field grid points.

[0015] The beneficial effects of the present invention are:

[0016] In order to reduce the computational complexity of the near-field and far-field mixed source positioning algorithm based on sparse reconstruction and correct the off-grid error of the near-field and far-field mixed source positioning, the present invention proposes a far-field and near-field mixed source fast positioning algorithm based on a unified sparse representation model of the near-field and far-field mixed sources in the covariance domain, using variational Bayesian inference and generalized approximate message passing to solve, and generalizes the gradient descent off-grid method to the near-field source two-dimensional parameter estimation, namely FN-GAMP-OGCVBI (GAMP-basedOff-grid Covariance-basedVBI for Far and Near-field Sources). The present invention effectively improves the computational efficiency and estimation accuracy of the algorithm and reduces the computational complexity.

[0017] The present invention proposes a method for fast positioning of near-field and far-field mixed sources based on sparse reconstruction. First, a sparse representation model of near-field and far-field mixed sources in the covariance domain and a Bayesian hierarchical probability model are constructed. The generalized approximate message passing-variational Bayesian inference (GAMP-VBI) is used to avoid matrix inversion operations in the solution, thereby achieving a significant reduction in computational complexity. Then, the gradient descent off-grid method is applied to update the grid point parameters, thereby reducing the positioning error caused by grid mismatch. Compared with the existing sparse Bayesian learning near-field and far-field mixed source positioning algorithm based on array element domain data, it has higher near-field and far-field source positioning accuracy and shorter calculation time. The present invention belongs to a method for fast positioning of near-field and far-field mixed sources, which can be applied to the field of passive sonar signal detection.

[0018] (1) The present invention extends the sparse representation model of far-field and near-field mixed sources to the covariance domain and utilizes the higher array signal-to-noise ratio gain of the covariance vector to improve the far-field DOA estimation performance when the number of snapshots is sufficient.

[0019] (2) The present invention compensates for the positioning error caused by grid mismatch through the gradient descent off-grid method.

[0020] (3) Compared with the existing far-field and near-field mixed source localization method based on sparse reconstruction, the present invention not only has higher resolution and positioning accuracy, but also significantly improves the computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a flow chart of the present invention;

[0022] FIG2( a ) is a far-field spatial spectrum diagram of the present invention and other algorithms;

[0023] FIG2( b ) is a local magnified view of the far-field spatial spectrum of the present invention and other algorithms;

[0024] Figure 3(a) is the near-field focusing spatial spectrum of the algorithm MVDR;

[0025] Figure 3(b) is the near-field spatial spectrum of the algorithm FN-OGMSBL;

[0026] Figure 3(c) is the near-field spatial spectrum of the algorithm FN-OGCVBI;

[0027] FIG3( d ) is a near-field spatial spectrum diagram of the present invention;

[0028] FIG4( a ) is a comparison diagram of the far-field source DOA estimation performance of the present invention and other algorithms as the signal-to-noise ratio changes;

[0029] FIG4( b ) is a comparison diagram of the near-field source angle estimation performance of the present invention and other algorithms as the interference-to-noise ratio changes;

[0030] FIG4( c ) is a comparison diagram of the near-field source distance estimation performance of the present invention and other algorithms as the interference-to-noise ratio changes;

[0031] FIG4( d ) is a comparison diagram of the calculation time of the present invention and other algorithms as the signal-to-noise ratio changes;

[0032] FIG5( a ) is a comparison diagram of the far-field source DOA estimation performance of the present invention and other algorithms as the number of snapshots changes;

[0033] FIG5( b ) is a comparison diagram of the near-field source angle estimation performance of the present invention and other algorithms as the number of snapshots changes;

[0034] FIG5( c ) is a comparison diagram of the near-field source distance estimation performance of the present invention and other algorithms as the number of snapshots changes;

[0035] FIG5( d ) is a comparison diagram of the calculation time of the present invention and other algorithms as the number of snapshots changes;

[0036] Figure 6 This is a comparison chart of the success probability of far-field source resolution of the present invention and other algorithms versus angular interval. DETAILED DESCRIPTION

[0037] Specific implementation method 1: This implementation method is a method for positioning a far-field and near-field mixed source based on sparse reconstruction. The specific process is as follows:

[0038] Step 1: Initialize the current number of iterations κ = 1;

[0039] Step 2: Obtain the covariance matrix based on the array element receiving signal;

[0040] Step 3: According to the covariance matrix, construct a covariance vector far-field and near-field mixed source sparse representation model and an initial far-field and near-field mixed source dictionary set;

[0041] Step 4: Based on the covariance vector far-field and near-field mixed source sparse representation model and the initial far-field and near-field mixed source dictionary set, construct a The Bayesian hierarchical probability model with the accuracy α and the perturbation accuracy β0;

[0042] Step 5: Update the signal power in the Bayesian hierarchical probability model through GAMP-VBI Accuracy α, disturbance accuracy β0;

[0043] Step 6: Update the signal power according to step 5 The accuracy α and perturbation accuracy β0 are used to update the near-field and far-field mixed source dictionary set through the gradient off-grid method;

[0044] Step 7: Determine whether the iteration stop condition is met or the maximum number of external iterations is reached;

[0045] If satisfied, the far-field spatial spectrum estimation result is output Near-field spatial spectrum estimation results and the corresponding grid point estimate

[0046] Otherwise, set κ = κ + 1 and return to step 5 until the iteration stop condition is met or the maximum number of external iterations is reached, and the far-field spatial spectrum estimation result is output. Near-field spatial spectrum estimation results and the corresponding grid point estimate

[0047] in, Estimate the angle corresponding to the vector for the far-field grid point; Estimate the angle corresponding to the vector for the near-field grid point; Estimate the distance corresponding to the vector for the near-field grid points.

[0048] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that in step 2, the covariance matrix is ​​obtained according to the array element receiving signal; the specific process is:

[0049] Step 21: Consider that there are K1 narrowband far-field sources and K2 narrowband near-field sources incident on a symmetrical uniform linear array consisting of M array elements at the same time;

[0050] The near-field source is usually defined as being located at [0.62(D 3 / λ) 1 / 2 ,2D 2 / λ] in the Fresnel zone, the far-field source is located at a distance greater than 2D 2 / λ outside the Fresnel zone; D is the array aperture;

[0051] Among them, the array element spacing d = λ / 2, λ is the wavelength;

[0052] Assuming that the number of array elements M is an odd number, the central array element is the reference array element, and the received signal of the mth array element at time t is expressed as:

[0053]

[0054] Among them, x k (t) represents the signal envelope of the kth source received by the reference array element at time t, n m (t) represents the additive background noise received by the mth array element at time t, τ mk represents the delay difference between the kth signal source reaching the reference array element and the mth array element, r k represents the distance from the kth signal source to the reference array element, r mk Indicates the distance from the kth information source to the mth array element; m = 1, 2, ..., M;

[0055] If the kth source is a near-field source, the position of the kth source is defined in the polar coordinate system as (θ k ,r k ), the distance r from the kth source to the mth array element mk for:

[0056]

[0057] The time delay difference between the kth signal source of the near-field source and the reference array element and the mth array element satisfies

[0058] Where c is the speed of sound, θ k is the angle at which the kth signal source reaches the reference array element;

[0059] If the kth signal source is a far-field source, assume that the distance r from the kth signal source to the reference array element is k = +∞, the position of the kth source to the reference array element can be determined by the angle θ k The delay difference between the kth signal source reaching the reference array element and the mth array element is simplified to

[0060] Step 22: Define the array (a symmetrical uniform linear array consisting of M array elements) to receive the signal vector y(t) = [y1(t), ..., y M (t)] T , the far-field signal vector received by the reference array element at time t The near-field signal vector received by the reference array element at time t Background noise vector n(t) = [n1(t),...,n M (t)] T ;

[0061] The received signal of the array at time t is:

[0062]

[0063] Among them, y1(t) is the signal received by the first array element at time t, y M (t) is the signal received by the Mth array element at time t, x1(t) is the signal envelope of the first source received by the reference array element at time t, is the signal envelope of the K1th source received by the reference array element at time t, is the signal envelope of the K1+1th source received by the reference array element at time t, is the signal envelope of the K1+K2th source received by the reference array element at time t, n1(t) is the background noise received by the first array element, and n M (t) is the background noise received by the Mth array element;

[0064] is the far-field target array manifold, θ f is the angle set from the kth source in the far field to the reference array element, a f (θ1) is the steering vector of the first source in the far field, is the steering vector of the K1th source in the far field; T′ is the number of snapshots;

[0065] is the near-field target array manifold, θ n is the angle set from the near-field K2 sources to the reference array element, r n is the distance set from the near-field K2 signal sources to the reference array element, The angle is Distance is The near-field steering vector, The angle is Distance is The near-field steering vector of

[0066] in, is the angle at which the K1+1th signal source reaches the reference array element; is the angle at which the K1+K2th signal source reaches the reference array element; is the distance from the K1+1th signal source to the reference array element; is the distance from the K1+K2th signal source to the reference array element;

[0067] The expressions for the far-field and near-field steering vectors are:

[0068]

[0069]

[0070] Where j represents the imaginary unit, λ is the signal wavelength, and a f (θ k ) is the angle θ k The far-field steering vector, a n (θ k ,r k ) is the angle θ k , the distance is r k The near-field steering vector, r 1k is the distance from the kth information source to the first array element, r Mk is the distance from the kth information source to the Mth array element; θ k is the angle at which the kth signal source reaches the reference array element; r k is the distance from the kth signal source to the reference array element;

[0071] Step 23: Assume that each source signal is a statistically independent stationary Gaussian process, and the reference array element receives the signal x at time t k (t) has a mean of 0 and a variance of The complex Gaussian distribution of

[0072] Assume that the background noise received by each array element is n m (t) has a mean of 0 and a variance of σ 2 The complex Gaussian distribution of

[0073] Signal x k (t) and background noise n m (t) be independent of each other;

[0074] Based on the received signal y(t) of the array at time t, the theoretical covariance matrix R of the array output is obtained: y ; expressed as

[0075] R y =E{y(t)y H (t)}

[0076] =A f (θ f )diag(p)A f H (θ f )+A n (θ n ,r n )diag(η)A n H (θ n ,r n )+σ 2 I M ,

[0077] Where p is the far-field signal power vector, is the signal power of the first far-field source, is the signal power of the K1th far-field source;

[0078] η is the near-field signal power vector, is the signal power of the first near-field source, is the signal power of the K2th near-field source;

[0079] The superscript H indicates that conjugation is sought;

[0080] E{} is for expectation, I M is the M-dimensional identity matrix, and diag() is used to obtain the diagonal elements;

[0081] The covariance of the background noise n(t) in step 2 is σ 2 I M ; σ2 is the background noise n m The variance of (t);

[0082] Step 24: Considering the sparseness of the source position in space, the far-field angle range of 1 to 180° (including 1 and 180) is evenly divided into N1 grid points with a grid spacing of I1 to obtain a one-dimensional far-field grid point set

[0083] in, is the angle corresponding to the i-th element in the far-field grid point set, and i is the index of the i-th grid point in the N1 grids;

[0084] The “near field azimuth” is defined as the angle between the incident azimuth of the near field source signal and the array, and the “near field distance” is defined as the distance between the near field source and the reference array element.

[0085] The near-field azimuth is evenly divided into N2 grid points with a grid spacing of I2, and the near-field azimuth grid point set is obtained.

[0086] in, is the jth point in the near-field azimuth grid point set θ The angle corresponding to the element j θ is the jth grid in N2 θ The index of the grid points;

[0087] The near-field distance is evenly divided into N3 grid points with a grid spacing of I3, and the near-field distance grid point set is obtained.

[0088] in, is the jth point in the near-field distance grid point set r The distance corresponding to the element j r is the jth grid in N3 r The index of the point;

[0089] Therefore, the near-field space is discretized into a set of two-dimensional near-field grid points in the polar coordinate system: j θ =1,…,N2,j r =1,…N3;

[0090] The two-dimensional near-field grid point set is uniformly indexed by j

[0091] Among them, N n =N2×N3 is the total number of near-field grid points, j is N n The index of the jth point in the grid;

[0092] The theoretical covariance matrix R is output as an array yIt is expressed as the following overcomplete basis form:

[0093]

[0094] in, is the far-field target array manifold, is the far-field grid point set is the near-field target array manifold, is the near-field azimuth grid point set is the near-field distance grid point set

[0095] is the zero-filled expansion form of p in an overcomplete basis, is the spatial spectrum power corresponding to the first far-field grid point, is the spatial spectrum power corresponding to the N1th far-field grid point; the superscript T indicates the transposition;

[0096] is the zero-filled expansion of η in an overcomplete basis, is the spatial spectrum power corresponding to the first near-field grid point, For N n The spatial spectrum power corresponding to the near-field grid points;

[0097] The zero padding rule is

[0098]

[0099]

[0100] in, is the power of the kth source signal, is the angle corresponding to the jth element in the near-field grid point set, is the distance corresponding to the jth element in the near-field grid point set;

[0101] The actual covariance matrix estimate is estimated by the signal of a finite number of snapshots T′, that is,

[0102]

[0103] Among them, ΔR y is the estimation error of the covariance matrix, is the actual covariance matrix estimate, R y is the theoretical covariance matrix.

[0104] The other steps and parameters are the same as those in the first embodiment.

[0105] Specific implementation method three: This implementation method is different from specific implementation method one or two in that, in step three, a covariance vector far-field and near-field mixed source sparse representation model and an initial far-field and near-field mixed source dictionary set are constructed according to the covariance matrix;

[0106] The specific process is:

[0107] Step 31: Estimate the actual covariance matrix Vectorization:

[0108]

[0109] in, is the vectorized covariance matrix; vec(·) is the matrix vectorization operation; Δr is the disturbance vector;

[0110] and are the far-field overcomplete basis and the near-field overcomplete basis of the Khatri-Rao product form respectively. The specific expressions are:

[0111]

[0112]

[0113] in, is the Kronecker product symbol, (·) * denotes conjugation;

[0114] is the angle corresponding to the first element in the far-field grid point set, is the angle corresponding to the i-th element in the far-field grid point set, is the angle corresponding to the N1th element in the far-field grid point set;

[0115] The angle is The far-field steering vector, The angle is The far-field steering vector, The angle is The far-field steering vector of is a complex domain;

[0116] is the angle corresponding to the first element in the near-field grid point set, is the distance corresponding to the first element in the near-field grid point set, is the angle corresponding to the jth element in the near-field grid point set, is the distance of the jth element in the near-field grid point set, is the Nth point in the near-field grid point set nThe angle corresponding to the element is is the Nth point in the near-field grid point set n The distance corresponding to the elements, The angle is Distance is The near-field steering vector, The angle is Distance is The near-field steering vector, The angle is Distance is The near-field steering vector of

[0117] To jointly estimate the noise variance σ 2 ,make

[0118] in For an overcomplete basis dimension, the following unified sparse representation model for near and far fields is obtained:

[0119]

[0120] in, For an overcomplete dictionary; is the signal power;

[0121] Step 32: When the incident signal x k (t) When the complex Gaussian distribution is satisfied, the disturbance vector Δr obeys the asymptotic complex Gaussian distribution Δr~CN(0,W), where the estimated value of W is It is estimated by the covariance matrix, that is

[0122] because The off-diagonal elements of are non-zero, indicating There is a certain correlation between the various elements of , which will have a serious impact on the signal reconstruction performance, so consider Perform whitening operation to obtain the sparse representation model of the covariance vector after whitening:

[0123]

[0124] in, is the covariance vector after whitening operation, is the overcomplete dictionary after whitening operation, ε is the perturbation vector after whitening operation; CN() is the complex Gaussian distribution;

[0125] At this point, the covariance vector far-field and near-field mixed source sparse representation model has been constructed. That is the initial far-field and near-field mixed source dictionary set.

[0126] The other steps and parameters are the same as those in the first or second embodiment.

[0127] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that the step 4 constructs a signal power The Bayesian hierarchical probability model is based on the accuracy α of the perturbation vector ε and the accuracy β0 of the perturbation vector ε. The specific process is:

[0128] Step 41:

[0129] Assuming that the perturbation vector ε follows a complex Gaussian distribution with precision β0, then The likelihood function is

[0130] in, is the likelihood function, CN() is the complex Gaussian distribution, The dimension is M 2 The identity matrix of

[0131] Add a Gamma distribution hyper-prior with shape parameter c′ and rate parameter d′ to the precision β0 of the perturbation vector ε, that is, the prior distribution of β0 p(β0;c′,d′)=Gamma(β0|c′,d′);

[0132] Among them, p(β0;c′,d′) is the prior distribution of β0;

[0133] Assuming the signal power It obeys a zero-mean complex Gaussian distribution with precision α, that is The prior distribution of

[0134] To α n Add shape parameter a′ and rate parameter b n ′’s Gamma distribution super prior, that is, the prior distribution of α

[0135] Among them, p(α; a′, b′) is the prior distribution of α;

[0136] Step 42: Assume that the set of latent variables to be estimated is

[0137] Based on step 41 The likelihood function The prior distribution of The prior distribution of α p(α; a′, b′), the prior distribution of β0 p(β0; c′, d′) and the set of latent variables Θ, calculate the posterior distribution of Θ

[0138] The expression is:

[0139]

[0140] in, is the posterior distribution, for The prior probability of

[0141] At this point, the Bayesian hierarchical probability model is constructed (step 41 and step 42 together serve as the Bayesian hierarchical probability model).

[0142] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0143] Specific implementation method 5: This implementation method is different from any one of the specific implementation methods 1 to 4 in that the signal power is updated by GAMP-VBI in step 5. The accuracy α and disturbance accuracy β0 of ; the specific process is:

[0144] Step 51: Update signal power The specific method is:

[0145] 1) Set the tolerance threshold G ξ and the maximum number of iterations G l ;

[0146] 2) Initialization: Let

[0147] Among them, |·| 2 It means to square the matrix modulo the elements;

[0148] l represents the lth iteration of the GAMP algorithm, Indicates the GAMP algorithm for signal power The expected estimate of express The initial value of , s is the intermediate iteration parameter of the GAMP algorithm, s (0) represents the initial value of s, S represents the square of the modulus of the element in the overcomplete dictionary, represents the overcomplete dictionary after the whitening operation, Represents τ g The initial value of The accuracy parameter of

[0149] 3) Loop through the following steps

[0150]

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157]

[0158] Among them, μ p ,τ p ,s,τ s ,μ q ,τ q is the intermediate iteration parameter in the GAMP algorithm, The GAMP algorithm is used to obtain The approximate posterior expectation of g The GAMP algorithm is used to obtain The approximate posterior variance of ;

[0159] represents the lth iteration τ p The estimated value of represents the l-1th iteration τ p The estimated value of represents the lth iteration μ p The estimated value of represents the estimated value of g at the l-1th iteration, s (l-1) represents the estimated value of s at the l-1th iteration, s (l) represents the estimated value of s at the lth iteration, λ g represents the damping factor, represents a scalar output function, represents the covariance vector after the whitening operation obtained in step 3.2, β0 represents the perturbation accuracy parameter, represents the lth iteration τ s The estimated value of express The first derivative of represents the lth iteration τ q The estimated value of represents the lth iteration τ s The estimated value of represents the lth iteration μ q The estimated value of represents the overcomplete dictionary after the whitening operation obtained in step 3.2, Indicates the lth iteration The estimated value of represents a scalar input function, represents the lth iteration τ g The estimated value of express The first derivative of ; is the Hadamard product, and the damping factor ranges from λ g ∈(0,1] is used to improve the convergence of the GAMP algorithm;

[0160] Repeat 3) until the number of iterations l and the tolerance Satisfy the condition l≥G l or ξ≤G ξ Stop iteration when

[0161] || ||2 represents the two-norm;

[0162] 4) Output the number of iterations κ The estimated result of the approximate posterior distribution of is:

[0163]

[0164]

[0165] in, represents the number of iterations κ The estimated result of the approximate posterior distribution of , CN() represents the complex Gaussian distribution, μ represents The expected value of the approximate posterior distribution of The covariance of the approximate posterior distribution of , diag() means taking the diagonal elements;

[0166] Scalar functions and scalar function derivatives The specific form is:

[0167]

[0168]

[0169]

[0170]

[0171] Among them, I represents the identity matrix, α represents The accuracy parameter, express The first derivative of express The first derivative of ;

[0172] represents Hadamard division, represents a column vector whose elements are all 1;

[0173] Step 52: Update the accuracy parameter α; the specific method is:

[0174]

[0175] Among them, <·> q(·) It means calculating the expectation of the function in the angle brackets about the probability density q(·), and const means a constant;

[0176] q opt (α) represents the best approximate posterior distribution of α, express The prior distribution of , p(α; a′, b′) represents the prior distribution of α, express The approximate posterior distribution of ;

[0177] According to variational Bayesian inference, we get the approximate posterior

[0178] Among them, α n represents the nth element of α, The shape parameter is The rate parameter is Gamma distribution, represents the estimate of the shape parameter a′, a′ represents the shape parameter set in step 4.1, Indicates the rate parameter b n 'Estimation, b n ' represents the rate parameter set in step 4-1, express The nth element of represents the square of the two-norm; represents the intermediate variable, μ n is the nth element of μ, where μ represents the value obtained in step 5. The expectation of the approximate posterior distribution of * represents conjugation, Σ n,n is the nth row and nth column element of Σ;

[0179] Each element α of the precision parameter α under the number of iterations κ n The estimated result is

[0180] Step 53: Update the disturbance accuracy parameter β0; the specific update method is:

[0181]

[0182] Among them, <·> q(·) It means calculating the expectation of the function in the angle brackets about the probability density q(·), and const means a constant;

[0183] q opt (β0) represents the best approximate posterior distribution of β0, represents the likelihood function, p(β0; c′, d′) represents the prior distribution of β0;

[0184] According to variational Bayesian inference, we get the approximate posterior

[0185] in, tr(·) means finding the trace of the matrix;

[0186] The estimated result of β0 under the iteration number κ is

[0187] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0188] Specific implementation method 6: This implementation method is different from any one of the specific implementation methods 1 to 5 in that the signal power updated in step 6 according to step 5 The accuracy α and the disturbance accuracy β0 are used to update the near-field and far-field mixed source dictionary set through the gradient off-grid method; the specific process is:

[0189] Step 61: Order is the current far-field signal power estimate, is the current near-field signal power estimate, then the signal power estimate μ is divided into and

[0190] in, is a vector consisting of the 1st to N1th elements of μ, μ's N1+2 to N1+N n A vector consisting of elements; is the background noise power;

[0191] Similarly, Σ is divided into and

[0192] Where Σ is the signal covariance;

[0193] Σ p is the far-field signal covariance, is a matrix consisting of the elements of Σ located in rows 1 to N1 and columns 1 to N1;

[0194] Σ η is the near-field signal covariance, Σ is located between the N1+2th and N1+Nth n The row is located between N1+2 and N1+N. n The matrix consists of the elements of the columns; is the variance of the noise power in Σ;

[0195] Step 62: Let the current far-field one-dimensional and near-field two-dimensional grid point estimates be

[0196] Current far-field 1D grid point estimate and near-field 2D grid point estimation The corresponding grid point estimation vector expression is:

[0197]

[0198]

[0199]

[0200] in,

[0201] Estimate the angle corresponding to the vector at the far-field grid point, is the angle corresponding to the first element in the estimation vector of the far-field grid point, is the angle corresponding to the i-th element in the far-field grid point estimation vector, Estimate the angle corresponding to the N1th element in the vector for the far-field grid point;

[0202] is the angle corresponding to the estimated vector at the near-field grid point, is the angle corresponding to the first element in the near-field grid point estimation vector, is the angle corresponding to the jth element in the near-field grid point estimation vector, Estimate the Nth vector of the near-field grid point n The angle corresponding to the element is

[0203] Estimate the distance corresponding to the vector for the near-field grid point, Estimate the distance corresponding to the first element in the vector for the near-field grid point, is the distance corresponding to the jth element in the estimated vector for the near-field grid point, Estimate the Nth vector of the near-field grid point n The distance corresponding to each element;

[0204] Step 63: Based on the log-likelihood function Respectively and Taking partial derivatives, we get The partial derivative of The partial derivative of The partial derivative of

[0205] Step 64: Based on the near and far field grid points at the κth iteration as well as The partial derivative of The partial derivative of The partial derivative of Update the near and far field grid points at the κ+1th iteration

[0206] Step 65: Based on the near and far field grid points at the κ+1th iteration Update the dictionary set of far-field and near-field mixed sources at the κ+1th iteration

[0207] The other steps and parameters are the same as those in Specific Implementations 1 to 5.

[0208] Specific implementation method 7: This implementation method is different from specific implementation methods 1 to 6 in that the step 63 is based on the log-likelihood function Respectively and Taking partial derivatives, we get The partial derivative of The partial derivative of The partial derivative of The expression is:

[0209]

[0210]

[0211]

[0212] in, for The partial derivative of for The partial derivative of for Partial derivative of , real{} is the real part;

[0213] Q1 is a far-field overcomplete basis pair The partial derivative of Q2 is a near-field overcomplete basis pair The partial derivative of Q3 is a near-field overcomplete basis pair The partial derivative of

[0214] To estimate the The obtained far-field overcomplete basis is To estimate the The obtained near-field overcomplete basis;

[0215] Σ p is the far-field signal covariance, Σ p is the near-field signal covariance;

[0216] diag() is used to get the diagonal elements.

[0217] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0218] Specific implementation eight: This implementation differs from one of the specific implementations one to seven in that the step six four is based on the near and far field grid points at the k-th iteration. as well as The partial derivative of The partial derivative of The partial derivative of Update the near and far field grid points at the κ+1th iteration

[0219] The update formula is:

[0220]

[0221]

[0222]

[0223] in, is the one-dimensional grid point estimation vector of the far field at the κ+1th iteration, is the estimated vector of the near-field angle-dimensional grid points at the κ+1th iteration, is the estimated vector of the near-field distance dimension grid points at the κ+1th iteration, is the estimated vector of the far-field one-dimensional grid points at the κth iteration, is the estimated vector of the near-field angle-dimensional grid points at the κth iteration, is the estimated vector of the near-field distance dimension grid points at the κth iteration, For the κth iteration The partial derivative of For the κth iteration The partial derivative of For the κth iteration The partial derivative of

[0224] sign(·) is the sign function, ζ f , n|θ and n|r They are and Fixed step size for gradient descent.

[0225] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0226] Specific implementation method 9: This implementation method is different from the specific implementation methods 1 to 8 in that the step 65 is based on the near and far field grid points in the κ+1th iteration. Update the dictionary set of far-field and near-field mixed sources at the κ+1th iteration

[0227] The expression is:

[0228]

[0229]

[0230]

[0231] in, is the far-field overcomplete basis of the Khatri-Rao product form estimated at the κ+1th iteration, is the near-field overcomplete basis in the form of Khatri-Rao product estimated at the κ+1th iteration, I M is the M-dimensional identity matrix, vec{} is the vectorization operator;

[0232] is the estimated vector of the one-dimensional grid points in the far field at the κ+1th iteration The angle corresponding to the first element in , is the estimated vector of the one-dimensional grid points in the far field at the κ+1th iteration The angle corresponding to the i-th element in , is the estimated vector of the one-dimensional grid points in the far field at the κ+1th iteration The angle corresponding to the N1th element in ;

[0233] is the estimated vector of the near-field angle-dimensional grid points at the κ+1th iteration The angle corresponding to the first element in , is the estimated vector of the near-field angle-dimensional grid points at the κ+1th iteration The angle corresponding to the jth element in is, is the estimated vector of the near-field angle-dimensional grid points at the κ+1th iteration N n The angle corresponding to each element; is the estimated vector of the near-field distance dimension grid points at the κ+1th iteration The distance corresponding to the first element in , is the estimated vector of the near-field distance dimension grid points at the κ+1th iteration The distance corresponding to the jth element in , is the estimated vector of the near-field distance dimension grid points at the κ+1th iteration N n The distance corresponding to each element;

[0234] The angle is The far-field steering vector, The angle is The far-field steering vector, The angle is The far-field steering vector of

[0235] The angle is Distance is The near-field steering vector, The angle is Distance is The near-field steering vector, The angle is Distance is The near-field steering vector of

[0236] is the estimated value of the covariance W of the disturbance vector Δr in step 3.2.

[0237] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0238] Specific implementation method ten: This implementation method is different from any one of specific implementation methods one to nine in that in step seven, it is determined whether the iteration stop condition is satisfied or the maximum number of external iterations is reached;

[0239] If satisfied, the far-field spatial spectrum estimation result is output And the near-field spatial spectrum estimation results and the corresponding grid point estimate

[0240] Otherwise, let κ = κ + 1 and return to step 5. The far-field and near-field mixed source dictionary set in step 5 is Update to the value obtained in step 6 Until the iteration stop condition is met or the maximum number of external iterations is reached, the far-field spatial spectrum estimation result is output And the near-field spatial spectrum estimation results and the corresponding grid point estimate

[0241] in, Estimate the angle corresponding to the vector for the far-field grid point; Estimate the angle corresponding to the vector for the near-field grid point; Estimate the distance corresponding to the vector for the near-field grid point;

[0242] The specific process is:

[0243] Determine whether the iteration stop condition is met Or the maximum number of external iterations κ ≥ G is reached κ ;

[0244] If the iteration stop condition is met Or the maximum number of external iterations κ ≥ G is reached κ , then the iteration stops and the far-field spatial spectrum estimation result is output And the near-field spatial spectrum estimation results and the corresponding grid point estimates;

[0245] Among them G κ is the initial setting of the maximum number of external iterations, G τ is the initial tolerance threshold, α (κ) is the accuracy corresponding to the κth iteration, α (κ-1) is the accuracy corresponding to the κ+1th iteration;

[0246] Otherwise, set κ = κ + 1 and return to step 5 until the iteration stop condition is met or the maximum number of external iterations is reached, and the far-field spatial spectrum estimation result is output. And the near-field spatial spectrum estimation results and the corresponding grid point estimates.

[0247] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0248] The following examples are used to verify the beneficial effects of the present invention:

[0249] The performance simulation comparison is carried out on the minimum variance distortionless response (MVDR), the far-field and near-field mixed source off-grid positioning method FN-OGMSBL based on the array element domain SBL, the far-field and near-field mixed source positioning method FN-OGCVBI based on the covariance domain variational Bayesian inference (VBI), and the far-field and near-field mixed source fast positioning method based on the covariance GAMP-VBI (FN-GAMP-OGCVBI, the algorithm of the present invention). Consider a uniform symmetrical linear array with 11 array elements and an array element spacing of 0.5m (designed receiving signal frequency 1.5kHz). The algorithm parameters are set as follows: the far-field angle range [1~180] degrees is evenly divided into N1=90 grid points, and the grid spacing is I1=2°; the near-field angle is evenly divided into N2=36 grid points, and the grid spacing is I2=4°; the near-field distance is evenly divided into N3=10 grid points, and the grid spacing is I3=1 meter; the maximum number of external EM iterations G is set. q =200, tolerance τ = 10 -5 , the maximum number of iterations of the GAMP algorithm G l =5, tolerance ξ=10 -3All methods assume that the number of sources is known.

[0250] Simulation 1 compares the far-field and near-field spatial spectrum estimation results of each algorithm. Assume that there are 2 far-field sources and 2 near-field sources incident on the uniform linear array in space at the same time. The azimuths of the far-field sources are 60.4° and 70.8°, respectively, and the signal-to-noise ratio is 0dB. The positions of the near-field sources in the polar coordinate system are (43.8°, 3.5m) and (135.5°, 7.8m), the signal-to-noise ratio is 15dB, and the number of snapshots is 200. The far-field spatial spectrum of each algorithm is given in Figure 2. All algorithms can distinguish two far-field targets, among which the spectral peak of the MVDR far-field spatial spectrum is wider, and there is a spectral peak at the near-field azimuth; compared with FN-OGMSBL, FN-GAMP-OGCVBI has the highest accuracy and the sharpest spectral peak, indicating that the present invention has higher resolution and far-field direction finding accuracy. Figure 3(a), Figure 3(b), Figure 3(c) and Figure 3(d) are the near-field spatial spectra of MVDR focused beamforming, FN-OGMSBL, FN-OGCVBI and FN-GAMP-OGCVBI respectively. All algorithms can distinguish two near-field targets, among which MVDR has the highest background level; the near-field spatial spectrum of FN-OGMSBL has pseudo peaks due to inaccurate distance estimation; the near-field spatial spectrum of FN-GAMP-OGCVBI of the present invention has the clearest target, no obvious pseudo peaks, and has the highest near-field positioning accuracy.

[0251] Simulation 2 compares the statistical performance of each algorithm under different signal-to-noise ratios. Assume that there are two far-field sources and two near-field sources incident on the uniform linear array in space at the same time. The azimuths of the far-field sources are 92.2° and 100.6° respectively, and the signal-to-noise ratio varies from -15dB to 10dB. The positions of the near-field sources in the polar coordinate system are (66.4°, 7.2m) and (125.2°, 5.6m). The near-field sources are regarded as interference signals, and the signal-to-noise ratio is fixed at -15dB. The number of snapshots is fixed at 200, and the Monte Carlo simulation is performed 200 times. Figure 4(a) shows the RMSE changes of the far-field source DOA estimation of each algorithm with the change of signal-to-noise ratio, Figure 4(b) shows the RMSE changes of the near-field source azimuth estimation of different algorithms with the change of signal-to-noise ratio, and Figure 4(c) shows the RMSE changes of the near-field source distance estimation of different algorithms with the change of signal-to-noise ratio. Figure 4(d) shows the average calculation time of different algorithms with the change of signal-to-noise ratio. As can be seen from the figure, due to the first-order Taylor approximation error, the far-field and near-field positioning accuracy of FN-OGMSBL is unsatisfactory. FN-GAMP-OGCVBI significantly reduces the calculation time while maintaining a high positioning accuracy similar to that of FN-OGCVBI. The FN-GAMP-OGCVBI of the present invention has the highest far-field and near-field mixed source positioning accuracy, has significant advantages under various signal-to-noise ratios, and the average calculation time is only 19.02% of FN-OGMSBL and 8.79% of FN-OGCVBI. The above results demonstrate the advantages of the present invention in positioning accuracy and calculation efficiency.

[0252] Simulation 3 compares the statistical performance of each algorithm under different snapshot numbers. Assume that there are 2 far-field sources and 2 near-field sources incident on the uniform linear array in space at the same time. The azimuths of the far-field sources are 92.2° and 100.6° respectively, and the signal-to-noise ratio is fixed at 0dB. The positions of the near-field sources in the polar coordinate system are (66.4°, 7.2m) and (125.2°, 5.6m). The near-field sources are regarded as interference signals, and the signal-to-interference ratio is fixed at -15dB. The number of snapshots varies from 50 to 400, and the Monte Carlo simulation is performed 200 times. Figure 5(a) shows the RMSE of DOA estimation of far-field sources of different algorithms changing with the number of snapshots, Figure 5(b) shows the RMSE of angle estimation of near-field sources of different algorithms changing with the number of snapshots, and Figure 5(c) shows the RMSE of distance estimation of near-field sources of different algorithms changing with the number of snapshots. Figure 5(d) shows the average calculation time of different algorithms changing with the number of snapshots. As can be seen from the figure, the accuracy advantage of the far and near field source positioning of the FN-GAMP-OGCVBI of the present invention over the array domain algorithm FN-OGMSBL increases with the increase of the number of snapshots. This is because the covariance domain data improves the array output signal-to-noise ratio as the number of snapshots increases. The FN-GAMP-OGCVBI of the present invention has higher far and near field source positioning accuracy and lower calculation time when the number of snapshots is sufficient. The average calculation time under each number of snapshots is only 26.8% of that of FN-OGMSBL; while maintaining a high positioning accuracy similar to that of FN-OGCVBI, the calculation time is significantly reduced to 9.92% of that of FN-OGCVBI. The above results once again prove the advantages of the present invention in positioning accuracy and calculation efficiency.

[0253] Simulation 4 compares the resolution performance of each algorithm for dual far-field target positions with different angle intervals in the presence of strong near-field interference sources. The two far-field sources are located at 60.3° and 60.3°+Δθ, respectively, where Δθ is the angle interval between the two far-field sources, and the signal-to-noise ratio is 0dB. The position of a near-field interference in the polar coordinate system is (50.4°, 6.7m), the signal-to-interference ratio is fixed at 15dB, the number of snapshots is fixed at 200, and the angle interval is The angle changes from 2° to 8°, and the Monte Carlo simulation is performed 200 times. Figure 6 The influence of different algorithms on the resolution probability of dual-target far-field sources with the angular separation of far-field sources under strong near-field interference is given. The resolution probability is defined as the estimated value in the simulation that satisfies the formula The ratio of the number of simulations to the total number of simulations. Figure 6 The results show that the FN-GAMP-OGCVBI of the present invention has the smallest resolvable far-field angular interval, and can resolve far-field dual-target signals with an angular interval of 4 degrees with a probability higher than 90% when the signal-to-noise ratio is 0 dB, which proves that the present invention effectively suppresses the influence of strong near-field interference on the accuracy of far-field source azimuth estimation, realizes far-field high-resolution azimuth estimation, and also proves the effectiveness of the off-grid method proposed in the present invention.

[0254] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for localizing mixed sources in far and near fields based on sparse reconstruction, characterized by: The specific process of the method is: Step 1: Initialize the current number of iterations κ = 1; Step 2: Obtain the covariance matrix based on the array element receiving signal; Step 3: According to the covariance matrix, construct a covariance vector far-field and near-field mixed source sparse representation model and an initial far-field and near-field mixed source dictionary set; Step 4: Based on the covariance vector far-field and near-field mixed source sparse representation model and the initial far-field and near-field mixed source dictionary set, construct a The Bayesian hierarchical probability model with the accuracy α and the perturbation accuracy β0; Step 5: Update the signal power in the Bayesian hierarchical probability model through GAMP-VBI Accuracy α, disturbance accuracy β0; Step 6: Update the signal power according to step 5 The accuracy α and perturbation accuracy β0 are used to update the near-field and far-field mixed source dictionary set through the gradient off-grid method; Step 7: Determine whether the iteration stop condition is met or the maximum number of external iterations is reached; If satisfied, the far-field spatial spectrum estimation result is output Near-field spatial spectrum estimation results and the corresponding grid point estimate Otherwise, set κ = κ + 1 and return to step 5 until the iteration stop condition is met or the maximum number of external iterations is reached, and the far-field spatial spectrum estimation result is output. Near-field spatial spectrum estimation results and the corresponding grid point estimate in, Estimate the angle corresponding to the vector for the far-field grid point; Estimate the angle corresponding to the vector for the near-field grid point; Estimate the distance corresponding to the vector for the near-field grid points.

2. The method for localizing a near-field mixed source based on sparse reconstruction according to claim 1, characterized in that: In the step 2, the covariance matrix is ​​obtained according to the array element receiving signal; the specific process is: Step 21: K1 narrowband far-field sources and K2 narrowband near-field sources are simultaneously incident on a symmetrical uniform linear array consisting of M array elements; Among them, the array element spacing d = λ / 2, λ is the wavelength; Assuming that the number of array elements M is an odd number, the central array element is the reference array element, and the received signal of the mth array element at time t is expressed as: Among them, x k (t) represents the signal envelope of the kth source received by the reference array element at time t, n m (t) represents the additive background noise received by the mth array element at time t, τ mk represents the delay difference between the kth signal source reaching the reference array element and the mth array element, r k represents the distance from the kth signal source to the reference array element, r mk Indicates the distance from the kth information source to the mth array element; m = 1, 2, ..., M; If the kth source is a near-field source, the position of the kth source is defined in the polar coordinate system as (θ k ,r k ), the distance r from the kth source to the mth array element mk for: The time delay difference between the kth signal source of the near-field source and the reference array element and the mth array element satisfies Where c is the speed of sound, θ k is the angle at which the kth signal source reaches the reference array element; If the kth signal source is a far-field source, assume that the distance between the kth signal source and the reference array element is r k = +∞, the position of the kth source to the reference array element can be determined by the angle θ k The delay difference between the kth signal source reaching the reference array element and the mth array element is simplified to Step 22: Define the array receiving signal vector y(t) = [y1(t),...,y M (t)] T , the far-field signal vector received by the reference array element at time t The near-field signal vector received by the reference array element at time t Background noise vector n(t) = [n1(t),...,n M (t)] T ; The received signal of the array at time t is: Among them, y1(t) is the signal received by the first array element at time t, y M (t) is the signal received by the Mth array element at time t, x1(t) is the signal envelope of the first source received by the reference array element at time t, is the signal envelope of the K1th source received by the reference array element at time t, is the signal envelope of the K1+1th source received by the reference array element at time t, is the signal envelope of the K1+K2th source received by the reference array element at time t, n1(t) is the background noise received by the first array element, and n M (t) is the background noise received by the Mth array element; is the far-field target array manifold, θ f is the angle set from the kth source in the far field to the reference array element, a f (θ1) is the steering vector of the first source in the far field, is the steering vector of the K1th source in the far field; T′ is the number of snapshots; is the near-field target array manifold, θ n is the angle set from the near-field K2 sources to the reference array element, r n is the distance set from the near-field K2 signal sources to the reference array element, The angle is Distance is The near-field steering vector, The angle is Distance is The near-field steering vector of in, is the angle at which the K1+1th signal source reaches the reference array element; is the angle at which the K1+K2th signal source reaches the reference array element; is the distance from the K1+1th signal source to the reference array element; is the distance from the K1+K2th signal source to the reference array element; The expressions for the far-field and near-field steering vectors are: Where j represents the imaginary unit, λ is the signal wavelength, and a f (θ k ) is the angle θ k The far-field steering vector, a n (θ k ,r k ) is the angle θ k , the distance is r k The near-field steering vector, r 1k is the distance from the kth information source to the first array element, r Mk is the distance from the kth information source to the Mth array element; θ k is the angle at which the kth signal source reaches the reference array element; r k is the distance from the kth signal source to the reference array element; Step 23: Assume that the reference array element receives the signal x at time t k (t) has a mean of 0 and a variance of The complex Gaussian distribution of Assume that the background noise received by each array element is n m (t) has a mean of 0 and a variance of σ 2 The complex Gaussian distribution of Signal x k (t) and background noise n m (t) be independent of each other; Based on the received signal y(t) of the array at time t, the theoretical covariance matrix R of the array output is obtained: y ; expressed as R y =E{y(t)y H (t)} =A f (i f )diag(p)A f H (i f )+A n (i n ,r n )diag(η)A n H (i n ,r n )+s 2 I M , Where p is the far-field signal power vector, is the signal power of the first far-field source, is the signal power of the K1th far-field source; η is the near-field signal power vector, is the signal power of the first near-field source, is the signal power of the K2th near-field source; The superscript H indicates that conjugation is sought; E{} is for expectation, I M is the M-dimensional identity matrix, and diag() is used to obtain the diagonal elements; The covariance of the background noise n(t) in step 2 is σ 2 I M ; σ 2 is the background noise n m The variance of (t); Step 24: Divide the far-field angle range 1 to 180° into N1 grid points evenly with a grid spacing of I1 to obtain a one-dimensional far-field grid point set in, is the angle corresponding to the i-th element in the far-field grid point set, and i is the index of the i-th grid point in the N1 grids; The near-field orientation is defined as the angle between the incident orientation of the near-field source signal and the array; The near-field distance is defined as the distance between the near-field signal source and the reference array element; The near-field azimuth is evenly divided into N2 grid points with a grid spacing of I2, and the near-field azimuth grid point set is obtained. in, is the jth point in the near-field azimuth grid point set θ The angle corresponding to the element j θ is the jth grid in N2 θ The index of the grid points; The near-field distance is evenly divided into N3 grid points with a grid spacing of I3, and the near-field distance grid point set is obtained. in, is the jth point in the near-field distance grid point set r The distance corresponding to the element j r is the jth grid in N3 r The index of the point; Therefore, the near-field space is discretized into a set of two-dimensional near-field grid points in the polar coordinate system: The two-dimensional near-field grid point set is uniformly indexed by j Among them, N n =N2×N3 is the total number of near-field grid points, j is N n The index of the jth point in the grid; The theoretical covariance matrix R is output as an array y It is expressed as the following overcomplete basis form: in, is the far-field target array manifold, is the far-field grid point set is the near-field target array manifold, is the near-field azimuth grid point set is the near-field distance grid point set is the zero-filled expansion form of p in an overcomplete basis, is the spatial spectrum power corresponding to the first far-field grid point, is the spatial spectrum power corresponding to the N1th far-field grid point; the superscript T indicates the transposition; is the zero-filled expansion of η in an overcomplete basis, is the spatial spectrum power corresponding to the first near-field grid point, For N n The spatial spectrum power corresponding to the near-field grid points; The zero padding rule is in, is the power of the kth source signal, is the angle corresponding to the jth element in the near-field grid point set, is the distance corresponding to the jth element in the near-field grid point set; The actual covariance matrix estimate is estimated by the signal of a finite number of snapshots T′, that is, Among them, ΔR y is the estimation error of the covariance matrix, is the actual covariance matrix estimate, R y is the theoretical covariance matrix.

3. The method for localizing a far-field and near-field mixed source based on sparse reconstruction according to claim 2, characterized in that: In the step 3, a covariance vector near-field mixed source sparse representation model and an initial near-field mixed source dictionary set are constructed according to the covariance matrix; the specific process is: Step 31: Estimate the actual covariance matrix Vectorization: in, is the vectorized covariance matrix; vec(·) is the matrix vectorization operation; Δr is the disturbance vector; and are the far-field overcomplete basis and the near-field overcomplete basis of the Khatri-Rao product form respectively. The specific expressions are: in, is the Kronecker product symbol, (·) * denotes conjugation; is the angle corresponding to the first element in the far-field grid point set, is the angle corresponding to the i-th element in the far-field grid point set, is the angle corresponding to the N1th element in the far-field grid point set; The angle is The far-field steering vector, The angle is The far-field steering vector, The angle is The far-field steering vector of is a complex domain; is the angle corresponding to the first element in the near-field grid point set, is the distance corresponding to the first element in the near-field grid point set, is the angle corresponding to the jth element in the near-field grid point set, is the distance of the jth element in the near-field grid point set, is the Nth point in the near-field grid point set n The angle corresponding to the element is is the Nth point in the near-field grid point set n The distance corresponding to the elements, The angle is Distance is The near-field steering vector, The angle is Distance is The near-field steering vector, The angle is Distance is The near-field steering vector of make in For an overcomplete basis dimension, the following unified sparse representation model for near and far fields is obtained: in, For an overcomplete dictionary; is the signal power; Step 32: When the incident signal x k (t) When the complex Gaussian distribution is satisfied, the disturbance vector Δr obeys the asymptotic complex Gaussian distribution Δr~CN(0,W), where the estimated value of W is It is estimated by the covariance matrix, that is right Perform whitening operation to obtain the sparse representation model of the covariance vector after whitening: in, is the covariance vector after whitening operation, is the overcomplete dictionary after whitening operation, ε is the perturbation vector after whitening operation; CN() is the complex Gaussian distribution; At this point, the covariance vector far-field and near-field mixed source sparse representation model has been constructed. That is the initial far-field and near-field mixed source dictionary set.

4. The method for localizing a near-field mixed source based on sparse reconstruction according to claim 3 is characterized in that: The step 4 constructs a signal power The Bayesian hierarchical probability model is based on the accuracy α of the perturbation vector ε and the accuracy β0 of the perturbation vector ε. The specific process is: Step 41: Assuming that the perturbation vector ε follows a complex Gaussian distribution with precision β0, then The likelihood function is in, is the likelihood function, CN() is the complex Gaussian distribution, The dimension is M 2 The identity matrix of Add a Gamma distribution hyper-prior with shape parameter c′ and rate parameter d′ to the precision β0 of the perturbation vector ε, that is, the prior distribution of β0 p(β0;c′,d′)=Gamma(β0|c′,d′); Among them, p(β0;c′,d′) is the prior distribution of β0; Assuming the signal power It obeys a zero-mean complex Gaussian distribution with precision α, that is The prior distribution of To α n Add shape parameter a′ and rate parameter b n ′’s Gamma distribution super prior, that is, the prior distribution of α Among them, p(α; a′, b′) is the prior distribution of α; Step 42: Assume that the set of latent variables to be estimated is Based on step 41 The likelihood function The prior distribution of The prior distribution of α p(α; a′, b′), the prior distribution of β0 p(β0; c′, d′) and the set of latent variables Θ, calculate the posterior distribution of Θ The expression is: in, is the posterior distribution, for The prior probability of At this point, the Bayesian hierarchical probability model is constructed.

5. The method for localizing a far-field and near-field mixed source based on sparse reconstruction according to claim 4, characterized in that: In step 5, the signal power is updated by GAMP-VBI The accuracy α and disturbance accuracy β0 of ; the specific process is: Step 51: Update signal power The specific method is: 1) Set the tolerance threshold G ξ and the maximum number of iterations G l ; 2) Initialization: let l = 1, s (0) =0, Among them, |·| 2 It means to square the matrix modulo the elements; l represents the lth iteration of the GAMP algorithm, Indicates the GAMP algorithm for signal power The expected estimate of express The initial value of , s is the intermediate iteration parameter of the GAMP algorithm, s (0) represents the initial value of s, S represents the square of the modulus of the element in the overcomplete dictionary, represents the overcomplete dictionary after the whitening operation, Represents τ g The initial value of The accuracy parameter of 3) Loop through the following steps Among them, μ p ,τ p ,s,τ s ,μ q ,τ q is the intermediate iteration parameter in the GAMP algorithm, The GAMP algorithm is used to obtain The approximate posterior expectation of g The GAMP algorithm is used to obtain The approximate posterior variance of ; represents the lth iteration τ p The estimated value of represents the l-1th iteration τ p The estimated value of represents the lth iteration μ p The estimated value of represents the estimated value of g at the l-1th iteration, s (l-1) represents the estimated value of s at the l-1th iteration, s (l) represents the estimated value of s at the lth iteration, λ g represents the damping factor, represents a scalar output function, represents the covariance vector after the whitening operation obtained in step 3.2, β0 represents the perturbation accuracy parameter, represents the lth iteration τ s The estimated value of express The first derivative of represents the lth iteration τ q The estimated value of represents the lth iteration τ s The estimated value of represents the lth iteration μ q The estimated value of represents the overcomplete dictionary after the whitening operation obtained in step 3.2, Indicates the lth iteration The estimated value of represents a scalar input function, represents the lth iteration τ g The estimated value of express The first derivative of ; is the Hadamard product, and the damping factor ranges from λ g ∈(0,1]; Repeat 3) until the number of iterations l and the tolerance Satisfy the condition l≥G l or ξ≤G ξ Stop iteration when || ||2 represents the two-norm; 4) Output the number of iterations κ The estimated result of the approximate posterior distribution of is: in, represents the number of iterations κ The estimated result of the approximate posterior distribution of , CN() represents the complex Gaussian distribution, μ represents The expected value of the approximate posterior distribution of The covariance of the approximate posterior distribution of , diag() means taking the diagonal elements; Scalar functions and scalar function derivatives The specific form is: Among them, I represents the identity matrix, α represents The accuracy parameter, express The first derivative of express The first derivative of ; represents Hadamard division, represents a column vector whose elements are all 1; Step 52: Update the accuracy parameter α; the specific method is: Among them, <·> q(·) It means calculating the expectation of the function in the angle brackets about the probability density q(·), and const means a constant; q opt (α) represents the best approximate posterior distribution of α, express The prior distribution of , p(α; a′, b′) represents the prior distribution of α, express The approximate posterior distribution of ; Get the approximate posterior Among them, α n represents the nth element of α, The shape parameter is The rate parameter is Gamma distribution, represents the estimate of the shape parameter a′, a′ represents the shape parameter set in step 4.1, Indicates the rate parameter b n 'Estimation, b n ' represents the rate parameter set in step 4-1, express The nth element of represents the square of the two-norm; represents the intermediate variable, μ n is the nth element of μ, where μ represents the value obtained in step 5. The expectation of the approximate posterior distribution of * represents conjugation, Σ n,n is the nth row and nth column element of Σ; Each element α of the precision parameter α under the number of iterations κ n The estimated result is Step 53: Update the disturbance accuracy parameter β0; the specific update method is: Among them, <·> q(·) It means calculating the expectation of the function in the angle brackets about the probability density q(·), and const means a constant; q opt (β0) represents the best approximate posterior distribution of β0, represents the likelihood function, p(β0; c′, d′) represents the prior distribution of β0; Get the approximate posterior in, tr(·) means finding the trace of the matrix; The estimated result of β0 under the iteration number κ is 6. The method for localizing a far-field and near-field mixed source based on sparse reconstruction according to claim 5, characterized in that: In step 6, the signal power updated according to step 5 The accuracy α and the disturbance accuracy β0 are used to update the near-field and far-field mixed source dictionary set through the gradient off-grid method; the specific process is: Step 61: Order is the current far-field signal power estimate, is the current near-field signal power estimate, then the signal power estimate μ is divided into and in, is a vector consisting of the 1st to N1th elements of μ, The N1+2 to N1+Nth n A vector consisting of elements; is the background noise power; Similarly, Σ is divided into and Where Σ is the signal covariance; Σ p is the far-field signal covariance, is a matrix consisting of the elements of Σ located in rows 1 to N1 and columns 1 to N1; Σ η is the near-field signal covariance, Σ is located between the N1+2th and N1+Nth n The row is located between N1+2 and N1+N. n The matrix consists of the elements of the columns; is the variance of the noise power in Σ; Step 62: Let the current far-field one-dimensional and near-field two-dimensional grid point estimates be and Current far-field 1D grid point estimate and near-field 2D grid point estimation The corresponding grid point estimation vector expression is: in, Estimate the angle corresponding to the vector at the far-field grid point, is the angle corresponding to the first element in the estimation vector of the far-field grid point, is the angle corresponding to the i-th element in the far-field grid point estimation vector, Estimate the angle corresponding to the N1th element in the vector for the far-field grid point; is the angle corresponding to the estimated vector at the near-field grid point, is the angle corresponding to the first element in the near-field grid point estimation vector, is the angle corresponding to the jth element in the near-field grid point estimation vector, Estimate the Nth vector of the near-field grid point n The angle corresponding to the element is Estimate the distance corresponding to the vector for the near-field grid point, Estimate the distance corresponding to the first element in the vector for the near-field grid point, is the distance corresponding to the jth element in the estimated vector for the near-field grid point, Estimate the Nth vector of the near-field grid point n The distance corresponding to each element; Step 63: Based on the log-likelihood function Respectively and Taking partial derivatives, we get The partial derivative of The partial derivative of The partial derivative of Step 64: Based on the near and far field grid points at the κth iteration as well as The partial derivative of The partial derivative of The partial derivative of Update the near and far field grid points at the κ+1th iteration Step 65: Based on the near and far field grid points at the κ+1th iteration Update the dictionary set of far-field and near-field mixed sources at the κ+1th iteration 7. The method for localizing a far-field and near-field mixed source based on sparse reconstruction according to claim 6, characterized in that: In step 63, based on the log-likelihood function Respectively and Taking partial derivatives, we get The partial derivative of The partial derivative of The partial derivative of The expression is: in, for The partial derivative of for The partial derivative of for Partial derivative of , real{} is the real part; Q1 is a far-field overcomplete basis pair The partial derivative of Q2 is a near-field overcomplete basis pair The partial derivative of Q3 is a near-field overcomplete basis pair The partial derivative of To estimate the The obtained far-field overcomplete basis is To estimate the The obtained near-field overcomplete basis; Σ p is the far-field signal covariance, Σ p is the near-field signal covariance; diag() is used to get the diagonal elements.

8. The method for localizing a far-field and near-field mixed source based on sparse reconstruction according to claim 7, characterized in that: In step 64, based on the near and far field grid points in the κth iteration as well as The partial derivative of The partial derivative of The partial derivative of Update the near and far field grid points at the κ+1th iteration The update formula is: in, is the one-dimensional grid point estimation vector of the far field at the κ+1th iteration, is the estimated vector of the near-field angle-dimensional grid points at the κ+1th iteration, is the estimated vector of the near-field distance dimension grid points at the κ+1th iteration, is the estimated vector of the far-field one-dimensional grid points at the κth iteration, is the estimated vector of the near-field angle-dimensional grid points at the κth iteration, is the estimated vector of the near-field distance dimension grid points at the κth iteration, For the κth iteration The partial derivative of For the κth iteration The partial derivative of For the κth iteration The partial derivative of sign(·) is the sign function, ζ f , n|θ and n|r They are and Fixed step size for gradient descent.

9. The method for localizing a near-field mixed source based on sparse reconstruction according to claim 8, characterized in that: In step 65, based on the near and far field grid points in the κ+1th iteration Update the dictionary set of far-field and near-field mixed sources at the κ+1th iteration The expression is: in, is the far-field overcomplete basis of the Khatri-Rao product form estimated at the κ+1th iteration, is the near-field overcomplete basis in the form of Khatri-Rao product estimated at the κ+1th iteration, I M is the M-dimensional identity matrix, vec{} is the vectorization operator; is the estimated vector of the one-dimensional grid points in the far field at the κ+1th iteration The angle corresponding to the first element in , is the estimated vector of the one-dimensional grid points in the far field at the κ+1th iteration The angle corresponding to the i-th element in , is the estimated vector of the one-dimensional grid points in the far field at the κ+1th iteration The angle corresponding to the N1th element in ; is the estimated vector of the near-field angle-dimensional grid points at the κ+1th iteration The angle corresponding to the first element in , is the estimated vector of the near-field angle-dimensional grid points at the κ+1th iteration The angle corresponding to the jth element in is, is the estimated vector of the near-field angle-dimensional grid points at the κ+1th iteration N n The angle corresponding to each element; is the estimated vector of the near-field distance dimension grid points at the κ+1th iteration The distance corresponding to the first element in , is the estimated vector of the near-field distance dimension grid points at the κ+1th iteration The distance corresponding to the jth element in , is the estimated vector of the near-field distance dimension grid points at the κ+1th iteration N n The distance corresponding to each element; The angle is The far-field steering vector, The angle is The far-field steering vector, The angle is The far-field steering vector of The angle is Distance is The near-field steering vector, The angle is Distance is The near-field steering vector, The angle is Distance is The near-field steering vector of is the estimated value of the covariance W of the disturbance vector Δr in step 3.

2.

10. The method for localizing a near-field mixed source based on sparse reconstruction according to claim 9, characterized in that: In the step 7, it is determined whether the iteration stop condition is met or the maximum number of external iterations is reached; If satisfied, the far-field spatial spectrum estimation result is output And the near-field spatial spectrum estimation results and the corresponding grid point estimate Otherwise, let κ = κ + 1 and return to step 5. The far-field and near-field mixed source dictionary set in step 5 is Update to the value obtained in step 6 Until the iteration stop condition is met or the maximum number of external iterations is reached, the far-field spatial spectrum estimation result is output And the near-field spatial spectrum estimation results and the corresponding grid point estimate in, Estimate the angle corresponding to the vector for the far-field grid point; Estimate the angle corresponding to the vector for the near-field grid point; Estimate the distance corresponding to the vector for the near-field grid point; The specific process is: Determine whether the iteration stop condition ||α is met (κ) -α (κ-1) ||2 / ||α (κ-1) ||2≤G τ Or the maximum number of external iterations κ ≥ G is reached κ ; If the iteration stop condition ||α is met (κ) -α (κ-1) ||2 / ||α (κ-1) ||2≤G τ Or the maximum number of external iterations κ ≥ G is reached κ , then the iteration stops and the far-field spatial spectrum estimation result is output And the near-field spatial spectrum estimation results and the corresponding grid point estimates; Among them G κ To set the maximum number of external iterations, G τ is the initial tolerance threshold, α (κ) is the accuracy corresponding to the κth iteration, α (κ-1) is the accuracy corresponding to the κ+1th iteration; Otherwise, set κ = κ + 1 and return to step 5 until the iteration stop condition is met or the maximum number of external iterations is reached, and the far-field spatial spectrum estimation result is output. And the near-field spatial spectrum estimation results and the corresponding grid point estimates.

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