Sparse dictionary correction space-time adaptive processing method based on sparse bayesian learning

Abstract

The present application relates to space-time adaptive processing clutter suppression field, especially to sparse dictionary correction space-time adaptive processing method based on sparse Bayesian learning, the present application constructs overcomplete dictionary by discrete spatial Doppler plane and restores sparse coefficient matrix through sparse Bayesian recovery; discrete overcomplete dictionary often exists off-network effect and is seriously affected by space and time decorrelation, correction matrix is introduced for overcomplete dictionary, the correction matrix can adaptively adjust overcomplete dictionary; by setting the contribution evaluation function of dictionary atom, the correction matrix is updated under the Bayesian framework, and the learning of the dictionary atom is indirectly realized; in the dictionary learning process, hidden variables often participate in the calculation, and the evidence factor maximum method is used to estimate the hidden variables; after the iteration is completed, the covariance matrix of the clutter is calculated, and the filter weight vector is used to suppress the clutter and detect the target.

Description

Technical Field

[0001] This invention relates to the field of spatiotemporal adaptive processing for clutter suppression, and more particularly to a spatiotemporal adaptive processing method for sparse dictionary correction based on sparse Bayesian learning. Background Technology

[0002] Space-Time Adaptive Processing (STAP) is a technique widely used in airborne radar systems for clutter suppression and target detection. Currently, many STAP researchers are dedicated to solving a core problem in the STAP algorithm: how to accurately estimate the clutter covariance matrix (CCM). Accurate CCM estimation is crucial for achieving effective clutter suppression with STAP.

[0003] According to the well-known Reed-Mallett-Brennan (RMB) criterion, to achieve a signal-to-clutter-to-noise ratio (SCNR) loss of less than 3 dB, the number of auxiliary samples required is at least twice the system's degrees of freedom. Due to limitations imposed by antenna array structure and complex clutter environments, traditional STAPs face challenges in obtaining sufficiently uniform training samples, leading to statistical mismatches in the CCM estimation of the target unit (CUT), thus compromising filtering accuracy. Therefore, improving the STAP output SCNR with limited samples has become a recent research hotspot.

[0004] To address the challenge of insufficient training samples, researchers have proposed several partially adaptive STAP methods. These methods include rank reduction (RR) algorithms, such as diagonal loading, principal component methods, parameter-adaptive matched filters, and multi-stage Wiener filters, which can reduce the required number of samples to twice the clutter rank. However, the performance of rank reduction methods is affected by the choice of rank parameter; choosing the wrong rank will reduce clutter suppression performance. In addition, there are dimensionality reduction algorithms, such as auxiliary channel processing methods, joint domain localization, and expansion factors, which can reduce the required number of samples to twice the degrees of freedom of the dimensionality reduction system. Optimal channel methods utilize the influence of angular Doppler channels on SCNR to adaptively select the optimal channel, but this increases computational complexity. Direct data domain methods use only the clutter data from the cutout for suppression without requiring auxiliary snapshot data, but this may reduce performance and cause aperture loss. Furthermore, knowledge-assisted algorithms can reduce the training sample requirement, but in practical applications, obtaining accurate prior knowledge of heterogeneous environments is costly and therefore not widely used.

[0005] Furthermore, sparse recovery (SR) theory has become another popular choice for solving this problem because it can reconstruct rapidly changing signals with high accuracy using very limited observation samples. SR theory has been widely applied in signal processing, image processing, computer vision, and pattern recognition. In radar applications, due to the sparsity of the echo power spectrum in the space-Doppler two-dimensional plane, the SR STAP method has a significant advantage in accurately recovering clutter profiles even with insufficient training samples, thus becoming a focus of STAP research.

[0006] In summary, the conventional STAP method based on the low-dimensional clutter subspace does not perform ideally. Therefore, it is of great significance to further improve the CCM estimation accuracy through the SR method while reducing the dependence on secondary data. Summary of the Invention

[0007] This invention addresses the problems of inaccurate clutter covariance matrix estimation and unsatisfactory clutter suppression in traditional SR-STAP methods, which are based on the assumption of no grid mismatch. It proposes a sparse dictionary correction spatiotemporal adaptive processing method based on sparse Bayesian learning. Under the influence of non-ideal factors such as clutter internal motion and array error, it can obtain superior performance that is highly competitive with existing methods by relying on only a few training samples.

[0008] The technical solution of the present invention to solve the above-mentioned technical problems is as follows:

[0009] This invention provides a spatiotemporal adaptive processing method for sparse dictionary correction based on sparse Bayesian learning, comprising the following steps:

[0010] Step 100. Receive multi-channel radar echo signals and perform pulse compression. Preconstruct a space-time overcomplete dictionary for sparse recovery. Iteratively recover the sparse coefficient matrix from the pulse-compressed echo signals using sparse Bayesian learning.

[0011] Step 200. Based on the sparse coefficient matrix recovered through iteration, construct the calibration learning matrix of the overcomplete dictionary. By setting the contribution evaluation function of the dictionary atoms, perform parameter iterative learning on the calibration matrix of the overcomplete dictionary under the Bayesian framework to achieve effective updating of the dictionary atoms until the iteration termination condition is reached.

[0012] Step 300. Construct the final overcomplete dictionary using the learned correction matrix, estimate the clutter covariance matrix using the sparse coefficient matrix of the final overcomplete dictionary, calculate the optimal weight vector, and perform clutter suppression.

[0013] Further, step 100 includes:

[0014] Step 110. Construct an overcomplete dictionary D, wherein the overcomplete dictionary D comprises K dictionary atoms;

[0015] The entire Doppler plane is uniformly discretized into an overcomplete dictionary consisting of K dictionary atoms. Where d1, d2, ..., d K These are dictionary atoms, and the number of dictionary atoms is K = N. s ×N d =ρ s M×ρ d N, ρ s For spatial frequency, ρ d The resolution scale is the Doppler frequency, M is the number of antenna elements, and N is the number of pulses within the coherent processing interval.

[0016] Echo data Y = [y1, y2, ..., y] from L auxiliary range cells L ] represents a sparse linear combination of dictionary atoms:

[0017] Y = DA + N o ;

[0018] in, Let a1, a2, ..., a be the sparse coefficient matrix to be recovered. L Let y1, y2, ..., y be the sparse coefficients. L N is the echo vector; o This indicates additional error or noise, and L represents the number of auxiliary distance cells;

[0019] Assuming that the sparse coefficient matrix has a sparse solution, the sparse coefficient matrix A is described by the following approximation problem:

[0020]

[0021] Among them, ||·|| 2，0 Indicates mixing l 2,0 -norm, ||·|| F Let F-norm be denoted, and ξ be the error tolerance.

[0022] Step 120. Relying on the multi-observation vector model, relax l 2,0 - Norm yields:

[0023]

[0024] Among them, ||·|| 2，1 For l 2,1 Norm;

[0025] Assume noise N o Power is δ 2 Furthermore, it follows a zero-mean complex Gaussian distribution, yielding the likelihood function of the radar receiving array echo signal:

[0026]

[0027]

[0028] In the above formula, D represents an overcomplete dictionary; δ -2 p(Y|A; δ) represents the reciprocal of the noise power. 2 p(y) represents the likelihood function of matrix Y. l |a l ;δ 2 ) represents y l The likelihood function;

[0029] Let a be a sparse coefficient vector l Assume a zero-mean complex Gaussian prior, and assume a l If the sparse coefficient matrix A, with coefficients l = 1, 2, ..., L, are independent and identically distributed, then the prior distribution of A follows the following pattern:

[0030]

[0031]

[0032] Where Λ=diag(γ) represents a l The covariance matrix is ​​given by γ = [γ1, γ2, ..., γ]. K′ ], det(·) represents the determinant operation, p(A;Λ) represents the prior distribution of the sparse coefficient matrix A, p(a l ;Λ) represents the sparsity coefficient a l The prior distribution;

[0033] Combining the likelihood function and the prior distribution of A, the posterior distribution p(A|Y;Λ,σ) of A can be obtained by Bayes' criterion. 2 ):

[0034]

[0035] Where p(Y;Λ,σ) 2 () represents the normalization factor;

[0036] Normalization factor p(Y; Λ, σ) 2 ) is a fixed value and is ignored, p(A|Y;Λ,σ 2 ) follows a mean of μ A Covariance matrix Σ A The complex Gaussian distribution:

[0037]

[0038] Σ A =(δ -2 D H D+Λ-1 ) -1 ;

[0039] in,

[0040] Σ Y =δ 2 I+DΛD H ;

[0041] in, Assuming the identity matrix is ​​used, we introduce the Woodbury matrix identity to obtain...

[0042] Σ A =Λ-ΛD H (δ 2 I+DΛD H ) -1 DΛ;

[0043]

[0044] Step 130. When the hyperparameters Λ and δ 2 Given that A is the maximum a posteriori estimate of A, the posterior mean is:

[0045]

[0046] The expectation-maximization iterative method is used to calculate the elements of the unknown hyperparameter Λ and δ. 2 Make an estimate:

[0047]

[0048]

[0049] in, This indicates an update to the diagonal elements of Λ in this iteration. This indicates the update of the diagonal elements of Λ in the previous iteration. This indicates the update of noise power in this iteration.

[0050] Further, step 200 includes:

[0051] Constructing the correction matrix Where p1, p2, ..., p K Represents the correction vector;

[0052] Based on the constructed correction matrix, the sparse recovery formula can be rewritten as follows:

[0053] X=(P⊙D)A+N o ;

[0054] Within the Bayesian framework, assume p kThe prior probabilities of k = 1, 2, ..., K follow a complex Gaussian distribution with zero mean, that is... Among them B k =diag(β) k ), β k =[β k,1 ,β k,2 ,...,β k,MN ], among which, B k For p k The covariance matrix, β k For B k The diagonal element, β k,MN Represents vector β k The last element, there are MN elements in total;

[0055] but:

[0056]

[0057] In the above formula, p(p k ; B k ) represents p k The probability distribution.

[0058] Furthermore, step 200 also includes:

[0059] Set dictionary atoms d for the correction matrix k Contribution evaluation function E k :

[0060] E k =(p k ⊙d k )A[k,:]+N k =(p k ⊙d k )A[k,:]+Y-(P⊙D)A;

[0061] in, random column vector e k,l Represents the correction vector p k The contribution to the l-th distance cell, A[k,:] is the k-th row vector of the sparse coefficient matrix, N k For E k The noise and error terms included;

[0062] Within the sparse Bayesian framework, assuming N k Power is λ k And it follows a complex Gaussian distribution with zero mean, i.e. Among them, I MN Let λ represent an identity matrix of size MN×MN. k ∈λ=[λ1,λ1,...,λ K′[] represents the variance coefficient of the noise, and we assume that the contribution evaluation function E k The column vectors are independent, so the contribution evaluation function E k The likelihood function is expressed as:

[0063]

[0064]

[0065] Wherein, p(E) k |p k ;λ k E represents the contribution evaluation function. k The likelihood function, p(e k,l |p k ;λ k ) represents e k,l The likelihood function, where A(k,l) is the element in the k-th row and l-th column of the sparse coefficients A;

[0066] p k The posterior probability density p(p k |E k ; B k ,λ) is represented as:

[0067]

[0068] In addition, p(p k |E k ; B k ,λ k It follows a complex Gaussian distribution:

[0069]

[0070] And the mean μ k The covariance matrix Σ k for:

[0071]

[0072]

[0073] in,[·] * To represent the conjugate operation, if the hidden variable λ k and [β] k,1 ,β k,2 ,...,β k,MN If ] is known, then atom p k The maximum posterior probability estimate is the posterior mean μ. k ;

[0074] Estimating hidden variables during the iteration process using evidence factor maximization;

[0075]

[0076]

[0077] Among them, intermediate variables

[0078] The iteration termination condition is:

[0079]

[0080] Where Y is the observation matrix P old and P new Let D represent the correction matrices obtained in the previous iteration and the current iteration, respectively. Let D be the sparse recovery dictionary and A be the sparse coefficient matrix. F Let F be the norm, ⊙ be the Hadamard product, and χ be the iteration termination threshold.

[0081] Furthermore, step 300 specifically includes:

[0082] Step 310. Construct the final overcomplete dictionary P⊙D using the learned calibration matrix;

[0083] Step 320. Using the final overcomplete dictionary P⊙D, estimate the clutter covariance matrix to obtain:

[0084]

[0085] in, Let Π represent the clutter covariance matrix, and let Π represent the intermediate variable composed of sparse coefficients, expressed as:

[0086] Compared with the prior art, the present invention has the following technical effects:

[0087] (1) This invention preconstructs a spatiotemporally overcomplete dictionary and uses sparse Bayesian learning to iteratively solve the sparse coefficient matrix of the pulse-compressed echo signal. To address the grid mismatch defect in sparse STAP, a dictionary atom contribution evaluation function is constructed and an overcomplete dictionary correction matrix is ​​introduced. Under the Bayesian framework, the overcomplete dictionary atoms are corrected and fitted to reduce the negative impact of overcomplete dictionary mismatch and non-ideal factors. The overcomplete dictionary obtained is used to reconstruct the echo signal, thereby improving the CCM estimation accuracy of the original sparse Bayesian method and improving the filtering performance.

[0088] (2) This invention can accurately obtain the estimation of the clutter covariance matrix and effectively reduce the influence of grid mismatch and non-ideal factors in sparse STAP. Compared with the existing spatiotemporal adaptive processing method based on clutter low-dimensional subspace and sparse recovery, this invention can significantly improve the estimation accuracy of clutter covariance matrix and clutter suppression performance under the condition of insufficient training samples. This invention is applicable to airborne non-frontal side-look scenarios in highly heterogeneous environments. Attached Figure Description

[0089] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0090] Figure 1 This is a block diagram illustrating the principle of the sparse dictionary correction spatiotemporal adaptive processing method based on sparse Bayesian learning in this invention.

[0091] Figure 2 The Capon spectrum of clutter in the comparison method is shown when the array offset angle is 30 degrees.

[0092] Figure 3 The clutter Capon spectrum of the method of the present invention when the array deviation angle is 30 degrees;

[0093] Figure 4 The Capon spectrum of clutter in the comparison method is given when the array offset angle is 60 degrees.

[0094] Figure 5 The clutter Capon spectrum of the proposed method is shown when the array offset angle is 60 degrees.

[0095] Figure 6 A comparison chart of signal-to-noise ratio loss when the array offset angle is 30 degrees;

[0096] Figure 7 This is a comparison chart showing the signal-to-noise ratio loss when the array offset angle is 60 degrees. Detailed Implementation

[0097] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the specific implementation methods, structures, features, and effects of the technical solutions proposed according to the present invention are described in detail below with reference to the accompanying drawings and preferred embodiments. Specific features, structures, or characteristics in one or more embodiments may be combined in any suitable form. Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0098] This invention addresses the problems of inaccurate clutter covariance matrix estimation and unsatisfactory clutter suppression in traditional SR-STAP methods, which are based on the assumption of no grid mismatch. It proposes a sparse dictionary correction spatiotemporal adaptive processing method based on sparse Bayesian learning. Under the influence of non-ideal factors such as clutter internal motion and array errors, this method can achieve superior performance compared to existing methods, relying only on a small number of training samples.

[0099] In one embodiment of the present invention, a sparse dictionary correction spatiotemporal adaptive processing method based on sparse Bayesian learning is provided, comprising the following steps:

[0100] Step 100. Receive multi-channel radar echo signals and perform pulse compression. Preconstruct a space-time overcomplete dictionary for sparse recovery. Iteratively recover the sparse coefficient matrix from the pulse-compressed echo signals using sparse Bayesian learning.

[0101] Step 200. Based on the sparse coefficient matrix recovered through iteration, construct the calibration learning matrix of the overcomplete dictionary. By setting the contribution evaluation function of the dictionary atoms, perform parameter iterative learning on the calibration matrix of the overcomplete dictionary under the Bayesian framework to achieve effective updating of the dictionary atoms until the iteration termination condition is reached.

[0102] Step 300. Construct the final overcomplete dictionary using the learned correction matrix, estimate the clutter covariance matrix using the sparse coefficient matrix of the final overcomplete dictionary, calculate the optimal weight vector, and perform clutter suppression.

[0103] The following is a detailed explanation of each of the above steps:

[0104] Step 100. Receive multi-channel radar echo signals and perform pulse compression. Preconstruct a space-time overcomplete dictionary for sparse recovery. Iteratively recover the sparse coefficient matrix from the pulse-compressed echo signals using sparse Bayesian learning.

[0105] This step involves discretizing the spatial Doppler plane, constructing an overcomplete dictionary, and recovering the sparse coefficient matrix using sparse Bayesian methods. Specifically, this step may include the following sub-steps:

[0106] Step 110. Construct an overcomplete dictionary D, wherein the overcomplete dictionary D comprises K dictionary atoms.

[0107] The clutter is sparse across the entire spatial Doppler plane, which is uniformly discretized into an overcomplete dictionary consisting of K dictionary atoms. Where d1, d2, ..., d K These are dictionary atoms, and the number of dictionary atoms is K = N. s ×N d =ρs M×ρ d N, ρ s For spatial frequency, ρ d Where M is the resolution scale for the Doppler frequency, M is the number of antenna array elements, and N is the number of pulses within the coherent processing interval.

[0108] Echo data Y = [y1, y2, ..., y] from L auxiliary range cells L ] can be represented as a sparse linear combination of dictionary atoms:

[0109] Y = DA + N o ;

[0110] in, Let a1, a2, ..., a be the sparse coefficient matrix to be recovered. L Let y1, y2, ..., y be the sparse vector to be recovered. L N is the echo vector; o This indicates additional error or noise, and L represents the number of auxiliary distance cells.

[0111] Assuming that the sparse coefficient matrix has a sparse solution, the sparse coefficient matrix A is described by the following approximation problem:

[0112]

[0113] Among them, ||·|| 2，0 Indicates mixing l 2,0 -norm, ||·|| F Let F denote the F-norm and ξ be the error tolerance. Although the above problem is known to be NP-hard, it is relatively easy to approximate using various techniques such as greedy algorithms and relaxation methods.

[0114] Step 120. Relying on the multi-observation vector model, relax l 2,0 - Norm yields:

[0115]

[0116] Among them, ||·|| 2，1 For l 2,1 Norm.

[0117] The multi-observation vector model is defined as Y containing multiple observation vectors, meaning Y consists of multiple column vectors, each representing the echo space-time steering vector of a reference cell.

[0118] Assume the noise power is δ 2 Furthermore, since it follows a zero-mean complex Gaussian distribution, the likelihood function of the radar receiving array echo signal can be obtained:

[0119]

[0120]

[0121] In the above formula, D represents an overcomplete dictionary; δ -2 p(Y|A; δ) represents the reciprocal of the noise power. 2 p(y) represents the likelihood function of matrix Y. l |a l ;δ 2 ) represents y l The likelihood function.

[0122] Let a be a sparse coefficient vector l Assume a zero-mean complex Gaussian prior, and assume a l If the sparse coefficient matrix A, with coefficients l = 1, 2, ..., L, are independent and identically distributed, then the prior distribution of A follows the following pattern:

[0123]

[0124]

[0125] Where Λ=diag(γ) represents a l The covariance matrix is ​​given by γ = [γ1, γ2, ..., γ]. K′ ], det(·) represents the determinant operation, p(A;Λ) represents the prior distribution of the sparse coefficient matrix A, p(a l ;Λ) represents the sparsity coefficient a l The prior distribution of .

[0126] Combining the likelihood function and the prior distribution of A, the posterior distribution p(A|Y;Λ,σ) of A can be obtained by Bayes' criterion. 2 ):

[0127]

[0128] Where p(Y;Λ,σ) 2 ) represents the normalization factor.

[0129] Normalization factor p(Y; Λ, σ) 2 If ) is a fixed value and is ignored, then p(A|Y;Λ,σ) 2 ) follows a mean of μ A Covariance matrix Σ A The complex Gaussian distribution:

[0130]

[0131] Σ A =(δ -2 D H D+Λ -1 )-1 ;

[0132] in,

[0133] Σ Y =δ 2 I+DΛD H ;

[0134] in, Assuming the identity matrix is ​​used, we introduce the Woodbury matrix identity to obtain...

[0135] Σ A =Λ-ΛD H (δ 2 I+DΛD H ) -1 DΛ;

[0136]

[0137] Step 130. When the hyperparameters Λ and δ 2 When A is known, the maximum a posteriori estimate of A is the posterior mean.

[0138]

[0139] The expectation-maximization iterative method is used to calculate the elements of the unknown hyperparameter Λ and δ. 2 Make an estimate:

[0140]

[0141]

[0142] in, This indicates an update to the diagonal elements of Λ in this iteration. This indicates the update of the diagonal elements of Λ in the previous iteration. This indicates the update of noise power in this iteration.

[0143] In addition, an iteration cutoff threshold τ needs to be set. When the cutoff condition is less than τ, the iteration stops and the iteration result is output.

[0144]

[0145] Where, γ old For the hyperparameter estimation of the previous iteration, γ new This is the hyperparameter estimation for this iteration.

[0146] Step 200. Based on the sparse coefficient matrix recovered through iteration, construct the calibration learning matrix of the overcomplete dictionary. By setting the contribution evaluation function of the dictionary atoms, perform parameter iterative learning on the calibration matrix of the overcomplete dictionary under the Bayesian framework to achieve effective updating of the dictionary atoms until the iteration termination condition is reached.

[0147] Discrete overcomplete dictionaries often suffer from off-network effects and are severely affected by decorrelation in the spatial and temporal domains. A correction matrix is ​​introduced to address the overcomplete dictionary, which can adaptively adjust the dictionary. By setting a contribution evaluation function for dictionary atoms, the correction matrix is ​​updated within a Bayesian framework, indirectly achieving the learning of dictionary atoms. Latent variables often participate in the dictionary learning process; therefore, the evidence factor maximization method is used to estimate the latent variables.

[0148] In some embodiments, this step may include the following steps:

[0149] Step 210. Construct an overcomplete dictionary and introduce a correction matrix;

[0150] The overcomplete dictionary D still has limited data recovery capabilities in different clutter environments. An ideal overcomplete dictionary can adapt to different heterogeneous application scenarios. Dictionary atoms obtained through learning can adapt to unknown parameter variables in actual radar echo data and have a stronger representation ability for decorrelation factors. The dictionary learning model provides adaptability by modifying the matrix and often shows better performance than a fixed dictionary.

[0151] Constructing the correction matrix Where p1, p2, ..., p K Represents the correction vector;

[0152] Based on the constructed correction matrix, the sparse recovery formula can be rewritten as follows:

[0153] X=(P⊙D)A+N o ;

[0154] Within the Bayesian framework, assume p k The prior probabilities of k = 1, 2, ..., K follow a complex Gaussian distribution with zero mean, that is... Among them B k =diag(β) k ), β k =[β k,1 ,β k,2 ,...,β k,MN ], among which, among which, B k For p k The covariance matrix, β k For B k The diagonal element, β k,MNRepresents vector β k The last element, there are MN elements in total;

[0155] but:

[0156]

[0157] In the above formula, p(p k ; B k ) represents p k The probability distribution.

[0158] Step 220. Set the contribution evaluation function of the dictionary atoms for the correction matrix and update the correction matrix within the Bayesian framework.

[0159] Set dictionary atoms d for the correction matrix k Contribution evaluation function E k :

[0160] E k =(p k ⊙d k )A[k,:]+N k =(p k ⊙d k )A[k,:]+Y-(P⊙D)A;

[0161] in, random column vector e k,l Represents the correction vector p k The contribution to the l-th distance cell, A[k,:] is the k-th row vector of the sparse coefficient matrix, N k For E k It includes noise and error terms.

[0162] Within the sparse Bayesian framework, assuming N k Power is λ k And it follows a complex Gaussian distribution with zero mean, i.e. Among them, I MN Let λ represent an identity matrix of size MN×MN. k ∈λ=[λ1,λ1,...,λ K′ [] represents the variance coefficient of the noise, and we assume that the contribution evaluation function E k The column vectors are independent, so the contribution evaluation function E k The likelihood function can be expressed as:

[0163]

[0164]

[0165] Wherein, p(E) k |pk ;λ k E represents the contribution evaluation function. k The likelihood function, p(e k,l |p k ;λ k ) represents e k,l The likelihood function is given by A(k,l), where A(k,l) is the element in the k-th row and l-th column of the sparse coefficients A.

[0166] p k The posterior probability density p(p k |E k ; B k ,λ) can be expressed as:

[0167]

[0168] In addition, p(p k |E k ; B k ,λ k It follows a complex Gaussian distribution:

[0169]

[0170] And the mean μ k The covariance matrix Σ k for:

[0171]

[0172]

[0173] in,[·] * This represents the conjugate operation, if the hidden variable λ k and [β] k,1 ,β k,2 ,...,β k,MN If ] is known, then atom p k The maximum posterior probability estimate is the posterior mean μ. k .

[0174] Step 230. Estimate the hidden variables during the iteration process using evidence factor maximization;

[0175]

[0176]

[0177] Among them, intermediate variables

[0178] The iteration termination condition is:

[0179]

[0180] Where, Y is the observation matrix P old and P new Let D represent the correction matrices obtained in the previous iteration and the current iteration, respectively. Let D be the sparse recovery dictionary and A be the sparse coefficient matrix. F Let F be the norm, ⊙ be the Hadamard product, and χ be the iteration termination threshold.

[0181] Step 300. Construct the final overcomplete dictionary using the learned correction matrix, estimate the clutter covariance matrix using the sparse coefficient matrix of the final overcomplete dictionary, calculate the optimal weight vector, and perform clutter suppression.

[0182] This step may include the following sub-steps:

[0183] Step 310. Construct the final overcomplete dictionary P⊙D using the learned calibration matrix;

[0184] Step 320. Using the final overcomplete dictionary P⊙D, estimate the clutter covariance matrix to obtain:

[0185]

[0186] in, Let Π represent the clutter covariance matrix, and let Π represent the intermediate variable composed of sparse coefficients.

[0187] The performance of the proposed method is evaluated using the final clutter Capon spectrum and SCNR loss. The clutter Capon spectrum is calculated as follows:

[0188]

[0189] in, x l N′ represents the space-time steering vector of the l-th distance unit, and M′ represents the number of power points discrete in the space frequency. The larger the preset values ​​of N′ and M′, the higher the accuracy of the power spectrum, but the computational complexity increases accordingly.

[0190] The results are as follows Figures 2 to 5 As shown, in order to illustrate the superiority of the proposed method, it is compared with the conventional STAP algorithm based on sparse Bayesian learning. It can be found that the proposed method significantly reduces clutter spread compared with the comparison method under different array deviation angles. It can match clutter ridges well under conditions with non-ideal factors. It can perform matching learning for the spatial and temporal decorrelation factors of the actual observation scene. There are almost no false peaks, and the fitting of clutter is more concentrated and smooth.

[0191] Furthermore, SCNR loss SCNR loss The calculation method is as follows:

[0192]

[0193] Where, δ 2 ω is the noise power, ω is the filter weight vector calculated using the estimated CCM, and s is the space-time steering vector of the desired target.

[0194] The results are as follows Figures 6 to 7 As shown, under different array deviation angles, it can be found that the present invention can obtain the filtering effect closest to the optimal STAP using only 5 training samples. This is because the present invention can better fit the nonlinear clutter ridge shape, reduce the off-grid effect caused by the non-frontal side-view array placement, and reduce the influence of non-ideal factors. Therefore, the present invention has a wider range of practical applications.

[0195] In summary, the method in this embodiment discretizes the spatial Doppler plane, constructs an overcomplete dictionary, and recovers the sparse coefficient matrix using sparse Bayesian methods. Discrete overcomplete dictionaries often suffer from off-network effects and are severely affected by decorrelation in the spatial and temporal domains. Therefore, a correction matrix is ​​introduced to the overcomplete dictionary, enabling adaptive adjustment. By setting contribution evaluation metrics for dictionary atoms, the correction matrix is ​​updated within the Bayesian framework, indirectly achieving the learning of dictionary atoms. Since latent variables often participate in the dictionary learning process, the evidence factor maximization method is used to estimate these latent variables. After iteration, the covariance matrix of clutter and the filter weight vector are calculated to suppress clutter and detect targets, significantly improving the signal-to-clutter-to-noise ratio in highly heterogeneous environments.

[0196] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A sparse dictionary correction spatiotemporal adaptive processing method based on sparse Bayesian learning, characterized in that, Includes the following steps: Step 100. Receive multi-channel radar echo signals and perform pulse compression. Preconstruct a space-time overcomplete dictionary for sparse recovery. Iteratively recover the sparse coefficient matrix from the pulse-compressed echo signals using sparse Bayesian learning. Step 200. Based on the sparse coefficient matrix recovered through iteration, construct the calibration learning matrix of the overcomplete dictionary. By setting the contribution evaluation function of the dictionary atoms, perform parameter iterative learning on the calibration matrix of the overcomplete dictionary under the Bayesian framework to achieve effective updating of the dictionary atoms until the iteration termination condition is reached. Step 300. Construct the final overcomplete dictionary using the learned correction matrix, estimate the clutter covariance matrix using the sparse coefficient matrix of the final overcomplete dictionary, calculate the optimal weight vector, and perform clutter suppression.

2. The sparse dictionary correction spatiotemporal adaptive processing method based on sparse Bayesian learning according to claim 1, characterized in that, Step 100 includes: Step 110. Construct an overcomplete dictionary The overcomplete dictionary include One dictionary atom; The entire Doppler plane is uniformly discretized into... K An overcomplete dictionary composed of dictionary atoms ,in, For dictionary atoms, the number of dictionary atoms , For spatial frequency, The resolution scale is the Doppler frequency. This refers to the number of antenna array elements. The number of pulses within the coherent processing interval; Echo data from each auxiliary range cell Represented as a sparse linear combination of dictionary atoms: ； in, Let be the sparse coefficient matrix to be recovered. The sparsity coefficient is . Echo vector; This indicates additional error or noise. Indicates the number of auxiliary distance units; Assume that the sparse coefficient matrix has a sparse solution. The problem can be described by the following approximation: ； in, Indicates mixing -norm, Describing the F-norm, This is the tolerance for error; Step 120. Relaxation based on the multi-observation vector model. - Norm yields: ； in, for Norm; Assuming noise Power is Furthermore, it follows a zero-mean complex Gaussian distribution, yielding the likelihood function of the radar receiving array echo signal: ； ； In the above formula, This indicates an overcomplete dictionary; Represents the reciprocal of noise power. Representation matrix The likelihood function, express The likelihood function; sparse coefficient vector Assume a zero-mean complex Gaussian prior, and assume If the coefficients are independent and identically distributed, then the sparse coefficient matrix... The prior distribution follows: ； ； in, express The covariance matrix has , Represents determinant operations, Represents the sparse coefficient matrix The prior distribution, Represents the sparsity coefficient The prior distribution; Combining likelihood function and The prior distribution can be obtained using Bayes' criterion. posterior distribution : ； in, Indicates the normalization factor; Normalization factor Set it to a fixed value and ignore it. Follow the mean covariance matrix The complex Gaussian distribution: ； ； in, ； in, Assuming the identity matrix is ​​used, we introduce the Woodbury matrix identity to obtain... ； ； Step 130. When hyperparameters and When known, The maximum a posteriori estimate is the posterior mean: ； Using the expectation-maximization iterative method for unknown hyperparameters elements and Make an estimate: ； ； in, This indicates that in this iteration... Update diagonal elements This indicates that in the previous iteration... Update diagonal elements This indicates the update of noise power in this iteration.

3. The sparse dictionary correction spatiotemporal adaptive processing method based on sparse Bayesian learning according to claim 2, characterized in that, Step 200 includes: Constructing the correction matrix ,in, Represents the correction vector; Within the Bayesian framework, it is assumed that... The prior probability follows a complex Gaussian distribution with zero mean, that is... ,in , ,in, for The covariance matrix, for diagonal elements, Representing vectors The last element, total indivual; but: ； In the above formula, express The probability distribution.

4. The sparse dictionary correction spatiotemporal adaptive processing method based on sparse Bayesian learning according to claim 3, characterized in that, Step 200 also includes: Set dictionary atoms for the correction matrix Contribution evaluation function E k : ； in, random column vectors Represents the correction vector For the The contribution of each distance cell, The sparse coefficient matrix is ​​the first row vectors for The noise and error terms included; Within the sparse Bayesian framework, it is assumed that Power is And it follows a complex Gaussian distribution with zero mean, i.e. ,in, I MN Indicates the size is The identity matrix, This represents the variance coefficient of the noise, and we also assume a contribution evaluation function. The column vectors are independent, so the contribution evaluation function... The likelihood function is expressed as: in, Function representing contribution evaluation The likelihood function, express The likelihood function, Sparsity coefficient The Middle Line 1 Column elements; posterior probability density Represented as: ； also, It follows a complex Gaussian distribution: ； And mean Covariance Matrix for: in, This indicates the conjugate operation, if the variable is hidden. and If it is known, then the atom The maximum posterior probability estimate is the posterior mean. ; Estimating hidden variables during the iteration process using evidence factor maximization; ； ； Among them, intermediate variables , ; The iteration termination condition is: ； in, Observation matrix and These represent the correction matrices obtained in the previous iteration and the current iteration, respectively. For sparse recovery dictionaries, It is a sparse coefficient matrix. Denotes the F-norm, For Hadama accumulation, This is the iteration termination threshold.

5. The sparse dictionary correction spatiotemporal adaptive processing method based on sparse Bayesian learning according to claim 4, characterized in that, Step 300 specifically includes: Step 310. Construct the final overcomplete dictionary using the learned calibration matrix. ; Step 320. Utilize the final overcomplete dictionary The clutter covariance matrix was estimated to be: ； in, Represents the clutter covariance matrix. The intermediate variable representing the sparse coefficients is denoted as: .

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