Sparse space-time adaptive processing method and device combined with amplitude-phase error correction

Abstract

The invention discloses a sparse space-time adaptive processing method and device combined with amplitude-phase error correction. The method comprises the following steps: constructing a clutter and noise signal model under an amplitude-phase error; according to clutter sparsity, using a minimum number of atoms to represent clutter signals without errors, and constructing an atomic norm minimization optimization problem to obtain an atomic norm minimization optimization model combining amplitude-phase errors and clutter subspaces; constraint is added to the atom norm minimization optimization model, and an augmented Lagrange expression of the atom norm minimization optimization model is obtained; initializing a part of parameters in the augmented Lagrange expression; iteratively updating a part of parameters in the newly added Guangdongian expression; according to an iteration updating result, calculating a clutter and noise covariance matrix without amplitude-phase error influence so as to update the clutter and noise covariance matrix; and obtaining a space-time adaptive processing weighted vector according to the updated clutter and noise covariance matrix. According to the invention, the purpose of clutter suppression can be efficiently realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a sparse space-time adaptive processing method and device for joint amplitude-phase error correction. Background Art

[0002] Space-time adaptive processing (STAP) is an effective technical means applied to moving target detection of space-based / spaceborne early warning radars. According to the space-time adaptive processing theory, STAP requires sufficient independent and identically distributed samples to estimate the clutter covariance matrix, and then calculates the weighting vector for clutter suppression.

[0003] In practical applications, due to the complex terrain distribution and the changing elevation, the clutter is non-uniform, resulting in a serious shortage of independent and identically distributed training samples and a decline in clutter suppression performance. The sparse STAP method expects to construct the clutter covariance matrix through the minimum number of space-time steering vectors to achieve clutter suppression under single / few samples, but there is a problem of grid mismatch. In order to fundamentally solve the grid mismatch problem, a gridless sparse STAP method has been proposed, but the existing methods cannot obtain robust clutter suppression performance in the absence of prior information on amplitude-phase errors, which limits the practical application of the gridless sparse STAP method.

[0004] Therefore, there is an urgent need to provide a space-time adaptive processing method to improve the above defects. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a sparse space-time adaptive processing method and device for joint amplitude-phase error correction. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] In the first aspect, the present invention provides a sparse space-time adaptive processing method for joint amplitude-phase error correction, including:

[0007] Construct a clutter plus noise signal model under amplitude-phase errors;

[0008] According to the clutter sparsity, represent the clutter signal without amplitude-phase errors using the minimum number of atoms, and construct an atomic norm minimization optimization problem; utilize the positive semi-definite block-Toeplitz structure of the clutter covariance matrix and the atomic norm relaxation to obtain an atomic norm minimization optimization model for joint amplitude-phase errors and the clutter subspace; add constraints to the atomic norm minimization optimization model to obtain the augmented Lagrangian expression of the atomic norm minimization optimization model;

[0009] Initialize some parameters in the augmented Lagrangian expression;

[0010] Iteratively update the ideal clutter data, ideal clutter subspace, Hermitian matrix, and decorrelation matrix in the augmented Lagrangian expression;

[0011] According to the iterative update results, calculate the clutter plus noise covariance matrix without the influence of amplitude-phase errors to update the clutter plus noise covariance matrix;

[0012] Obtain the space-time adaptive processing weight vector based on the updated clutter plus noise covariance matrix.

[0013] In a second aspect, the present invention also provides a sparse space-time adaptive processing device for joint amplitude-phase error correction, including:

[0014] A clutter plus noise signal model construction module for constructing a clutter plus noise signal model under amplitude-phase errors;

[0015] An optimization model construction module for representing the clutter signal without amplitude-phase errors using the minimum number of atoms according to clutter sparsity and constructing an atomic norm minimization optimization problem; utilizing the positive semi-definite block-Toeplitz structure of the clutter covariance matrix and atomic norm relaxation to obtain an atomic norm minimization optimization model for joint amplitude-phase errors and clutter subspace; adding constraints to the atomic norm minimization optimization model to obtain the augmented Lagrangian expression of the atomic norm minimization optimization model;

[0016] An initialization parameter module for initializing some parameters in the augmented Lagrangian expression;

[0017] A parameter iteration module for iteratively updating the ideal clutter data, ideal clutter subspace, Hermitian matrix, and decorrelation matrix in the augmented Lagrangian expression;

[0018] An update module for calculating the clutter plus noise covariance matrix without the influence of amplitude-phase errors according to the iterative update results to update the clutter plus noise covariance matrix;

[0019] A result acquisition module for obtaining the space-time adaptive processing weight vector based on the updated clutter plus noise covariance matrix.

[0020] Advantages of the present invention:

[0021] A method and device for sparse space-time adaptive processing with joint amplitude-phase error correction provided by the present invention utilize the sparsity of clutter spatio-temporal distribution to establish an atomic norm minimization optimization model for joint amplitude-phase errors and clutter subspace, then perform parameter initialization, and then iteratively update the clutter signal subspace and amplitude-phase error decorrelation matrix. Finally, calculate the clutter plus noise covariance matrix without the influence of amplitude-phase errors according to the iterative update results, and further obtain the space-time adaptive processing weight vector to achieve the purpose of clutter suppression.

[0022] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0023] Figure 1 is a flowchart of a joint amplitude-phase error correction sparse space-time adaptive processing method provided by an embodiment of the present invention;

[0024] Fig. 2(a) is a graph showing the estimated deviation (%) of the amplitude error obtained by using the method provided by the embodiment of the present invention with the amplitude-phase error of 0.3 dB - 3° varying with the number of iterations;

[0025] Fig. 2(b) is a graph showing the estimated deviation (%) of the phase error obtained by using the method provided by the embodiment of the present invention with the amplitude-phase error of 0.3 dB - 3° varying with the number of iterations;

[0026] Fig. 2(c) is a graph showing the estimated deviation (%) of the amplitude error obtained by using the method provided by the embodiment of the present invention with the amplitude-phase error of 0.5 dB - 5° varying with the number of iterations;

[0027] Fig. 2(d) is a graph showing the estimated deviation (%) of the phase error obtained by using the method provided by the embodiment of the present invention with the amplitude-phase error of 0.5 dB - 5° varying with the number of iterations;

[0028] Fig. 3(a) is a comparison graph of the output signal-to-clutter-plus-noise ratio of the method provided by the embodiment of the present invention and the prior art method with the amplitude-phase error of 0.3 dB - 3°;

[0029] Fig. 3(b) is a comparison graph of the output signal-to-clutter-plus-noise ratio of the method provided by the embodiment of the present invention and the prior art method with the amplitude-phase error of 0.5 dB - 5°. Detailed Embodiments

[0030] The present invention will be further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0031] Please refer to Figure 1 , Figure 1 is a flowchart of a joint amplitude-phase error correction sparse space-time adaptive processing method provided by an embodiment of the present invention. A joint amplitude-phase error correction sparse space-time adaptive processing method provided by the present invention includes:

[0032] S101. Construct a clutter-plus-noise signal model under amplitude-phase error.

[0033] Specifically, in this embodiment, in post-Doppler processing, the signal of the to-be-detected Doppler channel can be modeled as Nc Superposition of echoes from individual scattering units. Considering the slow variation of the number of scattering units in L range gates adjacent to the unit to be detected, the clutter plus noise signal model is expressed as:

[0034]

[0035] where Γ AAPEs represents the decorrelation matrix under amplitude-phase errors, a(ω s,i ) represents the spatial steering vector without amplitude-phase errors, ω s,i represents the spatial frequency, μ i,l represents the echo amplitude of the i-th scattering unit in the l-th range gate, n represents the noise, and N c represents the number of independent scattering unit echoes;

[0036] The decorrelation matrix under amplitude-phase errors is expressed as:

[0037] Γ AAPEs = diag(θ);

[0038] where θ = [θ1,…,θ n ,…,θ N T represents the amplitude-phase error dependent on the angle, and θ n is the amplitude-phase error relative to the reference channel and is a complex number;

[0039] The spatial steering vector without amplitude-phase errors is expressed as:

[0040]

[0041] where d represents the element spacing of the radar array, represents the array spatial cone angle of the i-th scattering unit, N represents the number of channels, and λ represents the wavelength.

[0042] S102. According to the clutter sparsity, use the minimum number of atoms to represent the clutter signal without amplitude-phase errors, and construct the atomic norm minimization optimization problem; utilize the positive semi-definite block-Toeplitz structure of the clutter covariance matrix and the atomic norm relaxation to obtain the atomic norm minimization optimization model for the joint amplitude-phase error and clutter subspace; add constraints to the atomic norm minimization optimization model to obtain the augmented Lagrangian expression of the atomic norm minimization optimization model.

[0043] Specifically, in this embodiment, the atomic norm minimization optimization problem is expressed as:

[0044]

[0045] ​Among them, X represents the echo data of the Doppler channel to be detected actually received by the radar under amplitude-phase error, Φ represents the overcomplete dictionary in the spatio-temporal two-dimensional plane, ||·|| F represents the matrix F norm, L represents the number of selected samples, and ε>0 represents the error tolerance.

[0046] In this embodiment, the atomic norm minimization optimization model combining amplitude-phase error and clutter subspace is expressed as:

[0047]

[0048] Among them, S c represents the ideal clutter data, T represents the ideal clutter subspace, min(·) represents the numerical minimization operation, tr(·) represents the trace of the matrix, Ω represents the auxiliary matrix, and ψ represents the Hermitian matrix.

[0049] In this embodiment, a convex constraint is added to the atomic norm minimization optimization model I represents the identity matrix, c represents an arbitrary constant, and the augmented Lagrangian expression of the atomic norm minimization optimization model is obtained:

[0050]

[0051] Among them, λ Φ >0 represents the regularization parameter, represents taking the real part, represents the Lagrange multiplier, represents the Lagrange multiplier matrix, ρ>0 represents the penalty parameter, <·> represents taking the sign after conjugate multiplication of the matrix, and the symbol (·) * represents the conjugate operation, and Ω represents the auxiliary matrix.

[0052] S103. Initialize some parameters in the augmented Lagrangian expression.

[0053] Specifically, in this embodiment, the decorrelation matrix Γ AAPEs under amplitude-phase error, the auxiliary matrix Ω, and the Lagrange multiplier matrix Π are initialized to the zero matrix, and the iteration times z, the error threshold ε of the iteration, and the maximum iteration times z max are initialized. Usually, the iteration times start from zero, that is, z = 0. The error threshold and the maximum iteration times can be selected according to the system operation resources and real-time requirements in practical applications. ε = 10 -2 , z max = 1000.

[0054] S104. Iteratively update the ideal clutter data, the ideal clutter subspace, the Hermitian matrix, and the decorrelation matrix in the augmented Lagrangian expression.

[0055] Specifically, in this embodiment, it specifically includes:

[0056] S1041. Take the partial derivatives of the ideal clutter data S, the ideal clutter subspace, and the Hermitian matrix ψ in the augmented Lagrangian expression to obtain the updated ideal clutter data, the updated ideal clutter subspace, and the updated Hermitian matrix ψ, which are expressed as: c , the ideal clutter subspace and the Hermitian matrix ψ to obtain the updated ideal clutter data updated ideal clutter subspace and the updated Hermitian matrix ψ z+1 , expressed as:

[0057]

[0058] where represents the pseudo-inverse, Ω ψ , and are obtained by decomposing the auxiliary matrix Ω, and Π ψ , and are obtained by decomposing the Lagrange multiplier matrix Π;

[0059] S1042. Take the partial derivative of the auxiliary matrix Ω in the augmented Lagrangian expression to obtain the updated auxiliary matrix Ω, which is expressed as: z+1 , expressed as:

[0060]

[0061] Perform eigenvalue decomposition on the updated auxiliary matrix, which is expressed as:

[0062]

[0063] where {v p} represents the set composed of the eigenvalues of the updated auxiliary matrix Ω z+1 , E Ω represents the matrix composed of eigenvectors, and V Ω represents the diagonal matrix composed of eigenvalues, p = 1, 2,..., N + L;

[0064] Set the negative eigenvalues in the set composed of eigenvalues to zero and reconstruct the updated auxiliary matrix, which is expressed as: , expressed as:

[0065]

[0066] where {v p} + represents setting the negative eigenvalues in {v p} to zero;

[0067] Substitute Γ AAPEs S c into the augmented Lagrangian expression.Transform it into a form related to the amplitude-phase error θ, expressed as:

[0068] Γ AAPEs S c =[Q1θ,…,,Q l θ,…Q L θ];

[0069] Among them,

[0070] S1043. Take the partial derivatives of θ and the Lagrange multiplier γ in the augmented Lagrangian expression to obtain the updated amplitude-phase error θ z+1 and the updated Lagrange multiplier γ z+1 , expressed as:

[0071]

[0072] Among them, Y represents a matrix, and the (n ,n p ,n l )-th element of the matrix

[0073]

[0074] vec(B)=[B(1,1),…,B(1,N),B(2,1),…,B(N,N)] T ;

[0075] Among them, vec(·) represents the matrix vectorization operation;

[0076] According to the updated θ z+1 , obtain the decorrelation matrix Γ AAPEs z+1 under the updated amplitude-phase error, expressed as:

[0077] Γ AAPEs z+1 =diag(θ z+1 );

[0078] According to the updated ideal clutter data the updated ideal clutter subspace T z+1 and the updated Hermitian matrix ψ z+1 , obtain the updated Lagrange multiplier matrix Π z+1 , expressed as:

[0079]

[0080] S1044. Update the iteration number z = z + 1, and repeat the update of the updated θ z+1 and the updated Lagrange multiplier γz+1 and the updated de-correlation matrix Γ under amplitude-phase error AAPEs z+1 and the updated Lagrange multiplier matrix Π z+1 until the estimation error of the clutter signal is less than the iterative error threshold ε, or the maximum number of iterations z is reached max , z ≤ z max .

[0081] S105. Calculate the clutter-plus-noise covariance matrix without the influence of amplitude-phase error according to the iterative update result to update the clutter-plus-noise covariance matrix.

[0082] Specifically, in this embodiment, perform eigen-decomposition on the updated ideal clutter subspace T z+1 to obtain:[[]]

[0083]

[0084] where E represents the matrix composed of eigenvectors, and V represents the diagonal matrix composed of eigenvalues;

[0085] Calibrate the amplitude-phase error and reconstruct the clutter-plus-noise covariance matrix R cn , which is expressed as:[[]]

[0086]

[0087] where S c (l) represents the l-th column of S c , and represents the noise energy.

[0088] S106. Obtain the space-time adaptive processing weight vector according to the updated clutter-plus-noise covariance matrix.

[0089] Specifically, in this embodiment, calculate the space-time adaptive processing weight vector w according to the reconstructed clutter-plus-noise covariance matrix R cn , which is expressed as:[[]]

[0090]

[0091] where s0 represents the space-time steering vector of the target.

[0092] In summary, the sparse space-time adaptive processing method with joint amplitude-phase error correction provided by the present invention combines the engineering processing flow of space-time adaptive processing, localizes clutter to the Doppler cells to be detected, establishes a post-Doppler space-time adaptive processing atomic norm minimization model including amplitude-phase errors, and utilizes the Toeplitz property of the clutter covariance matrix and atomic norm relaxation to transform the post-Doppler space-time adaptive processing under amplitude-phase error conditions into a joint optimization problem of clutter subspace estimation and channel amplitude-phase error correction, which can eliminate the influence of array amplitude-phase errors on sparse space-time adaptive processing. On this basis, the alternating direction multiplier framework is used to iteratively solve the clutter subspace while correcting the amplitude-phase errors between channels. Finally, the estimated clutter subspace matrix is eigen-decomposed, and then the clutter covariance matrix is reconstructed to obtain the space-time adaptive processing weighting vector, realizing robust clutter suppression in the presence of amplitude-phase errors. In addition, through Doppler localization processing, the present invention only sparsely reconstructs the clutter covariance matrix in the spatial channel dimension, effectively reducing the computational complexity compared with full-dimensional space-time adaptive processing, and has higher engineering application value.

[0093] Based on the same inventive concept, the present invention also provides a sparse space-time adaptive processing device with joint amplitude-phase error correction for implementing the sparse space-time adaptive processing method with joint amplitude-phase error correction provided in the above embodiments of the present invention. For the embodiments of the method, please refer to the above, which will not be elaborated herein. The device includes:

[0094] A clutter plus noise signal model construction module for constructing a clutter plus noise signal model under amplitude-phase error;

[0095] An optimization model construction module for representing the clutter signal without amplitude-phase error with the minimum number of atoms according to clutter sparsity and constructing an atomic norm minimization optimization problem; using the positive semi-definite block-Toeplitz structure of the clutter covariance matrix and atomic norm relaxation to obtain an atomic norm minimization optimization model jointly considering amplitude-phase error and clutter subspace; adding constraints to the atomic norm minimization optimization model to obtain an augmented Lagrangian expression of the atomic norm minimization optimization model;

[0096] An initialization parameter module for initializing some parameters in the augmented Lagrangian expression;

[0097] A parameter iteration module for iteratively updating the ideal clutter data, ideal clutter subspace, Hermitian matrix, and decorrelation matrix in the augmented Lagrangian expression;

[0098] An update module for calculating the clutter plus noise covariance matrix without the influence of amplitude-phase error according to the iterative update result to update the clutter plus noise covariance matrix;

[0099] A result acquisition module, configured to obtain a spatio-temporal adaptive processing weighting vector according to the updated clutter plus noise covariance matrix.

[0100] In an alternative embodiment of the present invention, the effect of the joint amplitude-phase error correction sparse spatio-temporal adaptive processing method provided in the above embodiment of the present invention is verified through a simulation experiment. Specifically:

[0101] I. Simulation conditions

[0102] In the simulation experiment of this embodiment, it is assumed that the detection system is a spaceborne bistatic radar. The orbital altitudes of the transmitting satellite and the receiving satellite are both 1000 km, the orbital inclinations are both 5°, the right ascensions of the ascending nodes are both 0°, the eccentricities are both 0°, the arguments of perigee are both 0°, and the true anomalies are 20° and 0° respectively. The radar operating wavelength is 0.23 m, the pulse repetition frequency is 2000 Hz, the CNR is 30 dB, the number of array channels is 6, the channel spacing is 0.9 m, and they are uniformly distributed.

[0103] II. Simulation content and result analysis

[0104] Simulation experiment 1: Examined the estimation of amplitude-phase errors (AAPEs) of the method of the present invention. In the method of the embodiment of the present invention, the constant c = 6, the penalty parameter ρ = 0.01, the de-correlation matrix Γ 0 = I N of the initial amplitude-phase error, the auxiliary matrix Ω 0 = 0 N×L of the initial amplitude-phase error, the Lagrange multiplier matrix Π 0 = 0 N×L of the initial amplitude-phase error, the number of iterations z = 0, the error threshold ε of the iteration = 0.01, and the maximum number of iterations z max = 1000.

[0105] Please refer to FIGS. 2(a), 2(b), 2(c) and 2(d). FIG. 2(a) is a curve graph of the estimation deviation (%) of the amplitude error obtained by using the method provided in the embodiment of the present invention when the amplitude-phase error is 0.3 dB - 3° versus the number of iterations. FIG. 2(b) is a curve graph of the estimation deviation (%) of the phase error obtained by using the method provided in the embodiment of the present invention when the amplitude-phase error is 0.3 dB - 3° versus the number of iterations. FIG. 2(c) is a curve graph of the estimation deviation (%) of the amplitude error obtained by using the method provided in the embodiment of the present invention when the amplitude-phase error is 0.5 dB - 5° versus the number of iterations. FIG. 2(d) is a curve graph of the estimation deviation (%) of the phase error obtained by using the method provided in the embodiment of the present invention when the amplitude-phase error is 0.5 dB - 5° versus the number of iterations. The calculation method of the estimation deviation δ is:

[0106]

[0107] Among them, is the estimated value, and x is the theoretical value. It can be seen that the method of the embodiment of the present invention can accurately estimate AAPEs.

[0108] Simulation experiment 2: By comparing the output signal-to-clutter-plus-noise ratio loss as the result of performance inspection, the output signal-to-clutter-plus-noise ratio loss is defined as follows:

[0109]

[0110] Among them, represents the target power, w represents the designed STAP weighting vector, R cn represents the estimated clutter-plus-noise covariance matrix, and s0 represents the target steering vector. The initial parameters adopt the test settings in Simulation experiment 1.

[0111] Please refer to Fig. 3(a) and Fig. 3(b). Fig. 3(a) is a comparison diagram of the output signal-to-clutter-plus-noise ratio output by the method proposed in the embodiment of the present invention and the prior art method when the amplitude-phase error is 0.3dB - 3°. Fig. 3(b) is a comparison diagram of the output signal-to-clutter-plus-noise ratio output by the method proposed in the embodiment of the present invention and the prior art method when the amplitude-phase error is 0.5dB - 5°. Among them, the abscissa is the normalized Doppler frequency, the ordinate is the output signal-to-clutter-plus-noise ratio loss, and OPT represents the optimal STAP. It can be seen that the method JCE-ANM-STAP of the embodiment of the present invention is closer to the OPT curve than the prior art methods ANM-STAP, TNNR-STAP, and JCE-SR-STAP. Therefore, the method JCE-ANM-STAP of the present embodiment has better performance than the prior art methods ANM-STAP, TNNR-STAP, and JCE-SR-STAP.

[0112] Among them, ANM-STAP (Atomic norm minimization STAP) is the original atomic norm minimization STAP method, which does not consider the influence of AAPEs and directly solves the clutter plus noise covariance matrix based on the atomic norm minimization optimization model. TNNR-STAP (Truncated nuclear norm regularization STAP) is the truncated nuclear norm regularization method, which also does not consider the influence of AAPEs. Based on the atomic norm minimization optimization model, it performs truncated nuclear norm regularization on the optimization problem and then solves the clutter plus noise covariance matrix. JCE-SR-STAP (Joint calibration of the AAPEs and sparse recovery STAP) is a gridless sparse recovery method with joint AAPEs calibration, which considers the influence of AAPEs and iteratively updates the clutter plus noise covariance matrix and AAPEs on the discrete angle-Doppler grid.

[0113] Through experimental simulations, it can be proved that the method of the embodiment of the present invention can obtain the performance closest to OPT. By synthesizing the AAPEs estimation curves in FIGS. 2(a), 2(b), 2(c) and 2(d) and the output signal-to-clutter-plus-noise ratio loss curves in FIGS. 3(a) and 3(b), it can be concluded that: the method of the embodiment of the present invention can accurately estimate AAPEs at different AAPEs levels, effectively improving the performance of sparse STAP, and providing an effective solution for clutter suppression and target detection with single / few samples in the presence of AAPEs.

[0114] In summary, the gridless sparse space-time adaptive processing method with joint channel amplitude-phase error correction of the present invention overcomes the problem that the performance of the existing gridless sparse space-time adaptive processing method is seriously affected by amplitude-phase errors and can iteratively estimate the clutter subspace and amplitude-phase errors. This method improves the performance of gridless sparse space-time adaptive processing in the presence of amplitude-phase error effects.

[0115] It should be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variant are intended to cover non-exclusive inclusion, so that an article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the article or device comprising said element. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The orientation or positional relationship indicated by "upper", "lower", "left", "right", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the present invention.

[0116] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not have to be directed to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0117] The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A sparse space-time adaptive processing method for joint amplitude and phase error correction, characterized in that: include: Construct a clutter plus noise signal model under amplitude and phase errors; According to the clutter sparsity, the minimum number of atoms is used to represent the clutter signal without amplitude and phase errors, and the atomic norm minimization optimization problem is constructed; the semi-positive definite block-Toeplitz structure of the clutter covariance matrix and the atomic norm relaxation are used to obtain the atomic norm minimization optimization model of the joint amplitude and phase error and clutter subspace; constraints are added to the atomic norm minimization optimization model to obtain the augmented Lagrangian expression of the atomic norm minimization optimization model; Initializing some parameters in the augmented Lagrangian expression; Iteratively updating the ideal clutter data, the ideal clutter subspace, the Hermitian matrix and the decorrelation matrix in the augmented Lagrangian expression; According to the iterative update result, the clutter plus noise covariance matrix without the influence of amplitude and phase errors is calculated to update the clutter plus noise covariance matrix; According to the updated clutter plus noise covariance matrix, a space-time adaptive processing weight vector is obtained.

2. The sparse space-time adaptive processing method for joint amplitude and phase error correction according to claim 1 is characterized in that: The clutter plus noise signal model It is expressed as: Among them, Γ AAPEs represents the decorrelation matrix under amplitude and phase errors, a(ω s,i ) represents the spatial steering vector when there is no amplitude or phase error, ω s,i represents the spatial frequency, μ i,l represents the echo amplitude of the ith scattering unit of the lth range gate, n represents the noise, N c Represents the number of independent scattering unit echoes; The decorrelation matrix under the amplitude and phase error is expressed as: C AAPEs =diag(θ); Where θ=[θ1,…,θ n ,…,θ N ] T represents the angle-dependent amplitude and phase error, θ n is the amplitude and phase error relative to the reference channel, which is a complex number; The spatial domain steering vector when there is no amplitude or phase error is expressed as: a(ω s,i )=[1,exp(jω s,i ),…,exp(j(N-1)ω s,i )] T ; Where d represents the element spacing of the radar array, represents the array spatial cone angle of the i-th scattering unit, N represents the number of channels, and λ represents the wavelength.

3. The sparse space-time adaptive processing method for joint amplitude and phase error correction according to claim 1, characterized in that: The atomic norm minimization optimization problem is expressed as: Among them, X represents the echo data of the Doppler channel to be detected actually received by the radar under the amplitude and phase errors, Φ represents the super-complete dictionary of the space-time two-dimensional plane, ||·|| F represents the norm of matrix F, L represents the number of selected samples, and ε>0 represents the error tolerance.

4. The sparse space-time adaptive processing method for joint amplitude and phase error correction according to claim 1, characterized in that: The atomic norm minimization optimization model of the joint amplitude-phase error and clutter subspace is expressed as: Among them, S c represents the ideal clutter data, represents the ideal clutter subspace, min(·) represents the numerical minimization operation, tr(·) represents the trace of the matrix, Ω represents the auxiliary matrix, and ψ represents the Hermitian matrix.

5. The sparse space-time adaptive processing method for joint amplitude and phase error correction according to claim 1, characterized in that: Adding convex constraints to the atomic norm minimization optimization model I represents the unit matrix, c represents an arbitrary constant, and the augmented Lagrangian expression of the atomic norm minimization optimization model is obtained: Among them, λ Φ >0 indicates the regularization parameter, represents the real part, represents the Lagrange multiplier, represents the Lagrange multiplier matrix, ρ>0 represents the penalty parameter, <·> represents the sign after conjugate multiplication of the matrices, and the symbol (·) * represents the conjugate operation, θ=[θ1,…,θ n ,…,θ N ] T Represents the angle-dependent amplitude and phase error.

6. The sparse space-time adaptive processing method for joint amplitude and phase error correction according to claim 1, characterized in that: Some parameters in the initialization augmented Lagrangian expression include: Initialize the decorrelation matrix Γ under amplitude and phase errors AAPEs , auxiliary matrix Ω, Lagrange multiplier matrix Π, initialization iteration number z, iteration error threshold ε, maximum iteration number z max .

7. The sparse space-time adaptive processing method for joint amplitude and phase error correction according to claim 1, characterized in that: The iterative updating of the ideal clutter data, the ideal clutter subspace, the Hermitian matrix and the decorrelation matrix in the augmented Lagrangian expression includes: For the ideal clutter data S in the augmented Lagrangian expression c , ideal clutter subspace And the Hermitian matrix ψ is used to obtain the partial derivative to obtain the updated ideal clutter data Updated ideal clutter subspace and the updated Hermitian matrix ψ z+1 , expressed as: in, represents the pseudo-inverse, Ω ψ , and Decomposed from the auxiliary matrix Ω, Π ψ , and It is decomposed by the Lagrange multiplier matrix Π; The partial derivative of the auxiliary matrix Ω in the augmented Lagrangian expression is obtained to obtain the updated auxiliary matrix Ω z+1 , expressed as: The updated auxiliary matrix eigendecomposition is expressed as: Among them, {v p } represents the updated auxiliary matrix Ω z+1 The set of eigenvalues ​​of Ω represents the matrix composed of eigenvectors, V Ω represents the diagonal matrix composed of eigenvalues, p = 1, 2, ..., N + L; The negative eigenvalues ​​in the set of eigenvalues ​​are set to zero, and the updated auxiliary matrix is ​​reconstructed. It is expressed as: Among them, {v p } + Indicates that {v p }, the negative eigenvalues ​​in are set to zero; The Γ in the augmented Lagrangian expression is AAPEs S c Transformed into a form related to the amplitude and phase error θ, expressed as: C AAPEs S c =[Q1θ,…,,Q l θ,…Q L [i]; in, The amplitude-phase error θ and the Lagrange multiplier γ in the augmented Lagrangian expression are derived to obtain the updated amplitude-phase error θ z+1 and the updated Lagrange multiplier γ z+1 , expressed as: Where Y represents a matrix; The first (n p ,n l ) elements It is expressed as: vec(B)=[B(1,1),…,B(1,N),B(2,1),…,B(N,N)] T ; Among them, vec(·) represents the matrix vectorization operation; According to the updated θ z+1 , get the decorrelation matrix Γ under the updated amplitude and phase error AAPEs z+1 , expressed as: C AAPEs z+1 =diag(θ z+1 ); According to the updated ideal clutter data The updated ideal clutter subspace and the updated Hermitian matrix ψ z+1 , get the updated Lagrange multiplier matrix Π z+1 , expressed as: Update the number of iterations z = z + 1, and repeat the update of the updated θ z+1 , updated Lagrange multiplier γ z+1 , the decorrelation matrix Γ under the updated amplitude and phase error AAPEs z+1 and the updated Lagrange multiplier matrix Π z+1 , until the estimated error of the clutter signal is less than the iterative error threshold ε, Or the maximum number of iterations z is reached max , z≤z max .

8. The sparse space-time adaptive processing method for joint amplitude and phase error correction according to claim 1, characterized in that: The step of calculating the clutter plus noise covariance matrix without the influence of amplitude and phase errors according to the iterative update result to update the clutter plus noise covariance matrix includes: To update the ideal clutter subspace Performing feature decomposition, we get: Among them, E represents the matrix composed of eigenvectors, and V represents the diagonal matrix composed of eigenvalues; Correct the amplitude and phase errors and reconstruct the clutter plus noise covariance matrix R cn , expressed as: Among them, S c (l) indicates S c The lth column of represents the noise energy.

9. The sparse space-time adaptive processing method for joint amplitude and phase error correction according to claim 1, characterized in that: The step of obtaining a space-time adaptive processing weighting vector according to the updated clutter plus noise covariance matrix includes: According to the reconstructed clutter plus noise covariance matrix R cn , calculate the space-time adaptive processing weight vector w, expressed as: Where s0 represents the space-time steering vector of the target.

10. A sparse space-time adaptive processing device for joint amplitude and phase error correction, characterized in that: include: A clutter plus noise signal model building module is used to build a clutter plus noise signal model under amplitude and phase errors; The optimization model construction module is used to use the minimum number of atoms to represent the clutter signal without amplitude and phase errors according to the clutter sparsity, and to construct an atomic norm minimization optimization problem; using the semi-positive definite block-Toeplitz structure of the clutter covariance matrix and atomic norm relaxation, an atomic norm minimization optimization model of the joint amplitude and phase error and clutter subspace is obtained; adding constraints to the atomic norm minimization optimization model to obtain an augmented Lagrangian expression of the atomic norm minimization optimization model; Initialization parameter module, used to initialize some parameters in the augmented Lagrangian expression; A parameter iteration module, used for iteratively updating the ideal clutter data, the ideal clutter subspace, the Hermitian matrix and the decorrelation matrix in the augmented Lagrangian expression; An updating module, used for calculating the clutter plus noise covariance matrix without the influence of amplitude and phase errors according to the iterative updating result, so as to update the clutter plus noise covariance matrix; The result acquisition module is used to obtain the space-time adaptive processing weight vector according to the updated clutter plus noise covariance matrix.

Images