A three-dimensional atomic norm based airborne MIMO radar STAP method

Abstract

The application discloses a three-dimensional atom norm-based airborne MIMO radar STAP method, which comprises the following steps: obtaining space-time snapshot data of L distance units; performing space-time snapshot data row sparse recovery by using an atom norm minimization method to obtain an estimated value of a clutter subspace; calculating an estimated value of a clutter plus noise covariance matrix of a to-be-detected distance unit; and calculating an adaptive weight vector of a space-time filter of the airborne MIMO radar. The application utilizes the inherent sparsity of a clutter space-time spectrum in an angle-Doppler domain, constructs a MIMO radar clutter signal sparse recovery model based on a three-dimensional continuous atom set according to a low-rank matrix recovery theory, avoids a dictionary mismatch problem in sparse recovery, realizes high-resolution estimation of the clutter space-time spectrum, and effectively improves the STAP clutter suppression performance of the airborne MIMO radar. The simulation experiment results show that the MIMO radar STAP processing performance of the application is better than that of an existing sparse recovery method based on a dictionary grid and a two-dimensional atom norm method in the case of dictionary mismatch.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, and in particular relates to a STAP (space-time adaptive processing) method for airborne MIMO (multiple-input multiple-output) radar based on three-dimensional atomic norm. Background Technology

[0002] Airborne MIMO radar employs waveform diversity technology, which, by creating more virtual signal processing channels in the spatial domain, achieves more system degrees of freedom (DOF) than single-input multiple-output (SIMO) radar, thus attracting widespread attention for moving target detection and parameter estimation. STAP technology effectively filters ground clutter through joint processing of spatial and temporal DOFs, but this technique relies on accurately estimating the clutter covariance matrix (CCM) of the range cell to be detected. According to the Reed-Mallett-Brennan (RMB) criterion, to achieve a signal-to-interference-plus-noise ratio (SNR) loss of less than 3 dB in CCM estimation, at least twice the number of independent and identically distributed (IID) samples is required. However, in real-world scenarios, the number of IID training samples used for CCM estimation is often insufficient due to non-uniform clutter environments and radar antenna array configurations. In MIMO radar, the increased system DOF also dramatically increases the required number of IID training samples. Therefore, how to accurately estimate CCM using a small number of IID training samples is a key challenge for STAP technology in airborne MIMO radar.

[0003] In recent years, sparse recovery techniques have rapidly developed in airborne SIMO radar STAP, and this technology has gradually expanded from SIMO radar to MIMO radar. Sparse recovery STAP utilizes the inherent sparsity of the clutter spectrum in the angle-Doppler domain to improve the accuracy of CCM estimation with single or small sample conditions. The dictionary grid partitioning is particularly crucial for sparse recovery techniques; however, current discrete dictionaries constructed using sparse recovery techniques still suffer from dictionary mismatch problems. Directly applying this technique to airborne MIMO radar STAP will degrade sparse recovery performance. Therefore, reducing the impact of dictionary mismatch on clutter suppression recovery performance has become a pressing technical problem for those skilled in the art. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to provide a STAP method for airborne MIMO radar based on the three-dimensional atomic norm.

[0005] To achieve the above objectives, the STAP method for airborne MIMO radar based on the three-dimensional atomic norm provided by this invention includes the following steps performed in sequence:

[0006] 1) Based on the geometric model of the uniform linear array of the airborne MIMO radar, and using the spatial transmission steering vector, spatial reception steering vector, and temporal steering vector, a set of clutter space-time steering vectors for the airborne MIMO radar is established, and then... Spatiotemporal snapshot data per distance unit ;

[0007] 2) Using the atomic norm minimization method to apply the above Spatiotemporal snapshot data per distance unit Sparse recovery is performed to obtain an estimate of the clutter subspace. ;

[0008] 3) Estimated values ​​for the above clutter subspace Eigenvalue decomposition is performed to obtain an estimate of the clutter covariance matrix. Then, the estimated value of the clutter plus noise covariance matrix of the range cell to be detected is calculated. ;

[0009] 4) Using the estimated value of the clutter plus noise covariance matrix of the above-mentioned range cell to be detected Calculate the adaptive weight vector of the airborne MIMO radar space-time filter. .

[0010] In step 1), based on the geometric model of the uniform linear array of the airborne MIMO radar, and based on the spatial transmission steering vector, spatial reception steering vector, and temporal steering vector, a set of clutter space-time steering vectors for the airborne MIMO radar is established, thereby obtaining... Spatiotemporal snapshot data per distance unit The method is:

[0011] In the geometric model of a uniform linear array for airborne MIMO radar, the array consists of multiple array elements arranged along the length of the carrier platform, where the number of transmitting elements is... The spacing between the transmitting elements is The number of receiving array elements is The spacing between the receiving array elements is The flight speed of the carrier platform is The angle between the velocity direction and the array axis is the yaw angle. ,when When it is a frontal and side view array, when The image is not a frontal side view array; the height of the aircraft platform is... , , These are the azimuth and elevation angles corresponding to the clutter block, respectively; the operating wavelength of the airborne MIMO radar is... At a constant pulse frequency Emit within the coherent processing interval Each pulse; the airborne MIMO radar transmits orthogonal signals, and the received signals are separated by matched filtering at the receiving end. Each transmitting array element signal;

[0012] Define the spatial transmission steering vector for each clutter block. Spatial receiving steering vector and time-domain steering vector They are respectively:

[0013] (1);

[0014] (2);

[0015] (3);

[0016] set up For the first The pitch angle of each distance unit. For the first The azimuth angle of the clutter block, then the... Normalized spatial frequency of individual clutter blocks , No. Normalized Doppler frequency of each clutter block The set of clutter spacetime steering vectors for airborne MIMO radar can be written in Vandermonde vector form with respect to three-dimensional frequencies, i.e.:

[0017] (4);

[0018] in, Normalized spatial frequency of the transmission array for clutter blocks Normalized spatial frequency of the receiving array and normalized Doppler frequency The three-dimensional frequency composition, i.e. ;

[0019] No. The output of each distance unit after matched filtering Dimensional time-space snapshot data for:

[0020] (5);

[0021] In the formula, For the first Noise signal per distance cell, For the first The clutter signal of the nth range cell; where the nth Clutter signal per range cell The aforementioned set of airborne MIMO radar clutter spacetime steering vectors can be expressed as follows: The spatiotemporal signals of each clutter block are superimposed, that is:

[0022] (6);

[0023] In the formula, For the first The complex amplitude of a clutter block For Kronecker product;

[0024] Based on the above, Clutter signal per range cell After matched filtering Spatiotemporal snapshot data per distance unit It can be represented as:

[0025] (7);

[0026] in, for Clutter signal per unit distance, for Noise signal of each distance unit.

[0027] In step 2), the atomic norm minimization method is used to apply the above... Spatiotemporal snapshot data per distance unit Sparse recovery is performed to obtain an estimate of the clutter subspace. The method is:

[0028] Assume that the set of all clutter spacetime steering vectors on the continuous spacetime plane is a three-dimensional atom set. ,Right now:

[0029] (8);

[0030] Based on the above formula, we can obtain... Clutter signal per range cell of The norm is represented as:

[0031] (9);

[0032] In the formula, The number of atoms, i.e., the clutter rank; Clutter signal per range cell The atoms can be solved by solving the following equation This is obtained by minimizing the norm, i.e.:

[0033] (10);

[0034] in, Noise level; by It can be seen that, Clutter signal per range cell and clutter subspace It can be estimated by solving the rank minimization optimization problem, that is:

[0035] (11);

[0036] in, Let represent the rank of the matrix; this problem is NP-hard, but by convexly relaxing the rank constraint, equation (11) can be transformed into an atomic norm minimization problem, i.e.:

[0037] (12);

[0038] in, For trace operation, for The triple-block Toeplitz matrix, i.e.:

[0039] (13);

[0040] In the formula, for The block Toeplitz matrix, i.e.:

[0041] (14);

[0042] In the formula, for The Toeplitz matrix, i.e.:

[0043] (15);

[0044] The solution to the primal problem is obtained by solving the dual problem of equation (12), i.e.:

[0045] (16);

[0046] in, To perform the operation of taking the real part, for Clutter signal per range cell dual variables, , , , All are Gram matrices. It is a positive semidefinite Hermitian matrix with low rank and triple Toeplitz matrix structure properties. For half space, , The value can be:

[0047] (17);

[0048] The estimated value of the clutter subspace can be obtained by solving equation (16). and Estimated clutter signal per range cell .

[0049] In step 3), the estimated value of the above-mentioned clutter subspace Eigenvalue decomposition is performed to obtain an estimate of the clutter covariance matrix. Then, the estimated value of the clutter plus noise covariance matrix of the range cell to be detected is calculated. The method is:

[0050] Estimation of clutter subspace Eigenvalue decomposition is performed to obtain an estimate of the clutter covariance matrix. :

[0051] (18);

[0052] in, This represents eigenvalue decomposition; and subsequently, the estimated value of the clutter plus noise covariance matrix of the range cell to be detected. It can be represented as:

[0053] (19);

[0054] in, for unit vector, This represents noise power.

[0055] In step 4), the estimated value of the clutter plus noise covariance matrix of the aforementioned range cell to be detected is used. Calculate the adaptive weight vector of the airborne MIMO radar space-time filter. The method is:

[0056] Adaptive weight vector of airborne MIMO radar space-time filter It can be represented as:

[0057] (20);

[0058] in, The space-time guide vector of the distance cell to be detected.

[0059] The beneficial effects of this invention are:

[0060] This invention leverages the inherent sparsity of the clutter spatiotemporal spectrum in the angle-Doppler domain and constructs a sparse recovery model for MIMO radar clutter signals based on a three-dimensional continuous atom set according to low-rank matrix recovery theory. This avoids the dictionary mismatch problem in sparse recovery, achieves high-resolution estimation of the clutter spatiotemporal spectrum, and effectively improves the clutter suppression performance of airborne MIMO radar STAP. Furthermore, simulation results demonstrate that the method of this invention outperforms existing sparse recovery methods based on dictionary grids and two-dimensional atom norm methods in the presence of dictionary mismatch in MIMO radar STAP processing. Attached Figure Description

[0061] Figure 1 This is a geometric model of a uniform linear array for an airborne MIMO radar.

[0062] Figure 2 (a)-(f) represent dictionary mismatches (yaw angle) in the frontal and side-view arrays of the embodiments, respectively. The results of Capon spectrum estimation for clutter under the following conditions are: real clutter spectrum, FOCUSS method, SBL method, OGSBI method, ANM-2D method and the method of this invention.

[0063] Figure 3 (a)-(f) are the non-frontal side view arrays (yaw angles) in the embodiments, respectively. The results of clutter Capon spectrum estimation using the real clutter spectrum, FOCUSS method, SBL method, OGSBI method, ANM-2D method, and the method of this invention are presented.

[0064] Figure 4 In the embodiment, there is a dictionary mismatch in the frontal and side-view arrays (yaw angle). The signal-to-interference-plus-noise ratio (SIR) loss curve under the following conditions.

[0065] Figure 5 For the non-frontal side view array in the embodiment (yaw angle) The signal-to-interference-plus-noise ratio (SIR) loss curve under the following conditions. Detailed Implementation

[0066] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0067] The STAP method for airborne MIMO radar based on three-dimensional atomic norm provided by this invention includes the following steps performed in sequence:

[0068] 1) Based on the geometric model of the uniform linear array of the airborne MIMO radar, and using the spatial transmission steering vector, spatial reception steering vector, and temporal steering vector, a set of clutter space-time steering vectors for the airborne MIMO radar is established, and then... Spatiotemporal snapshot data per distance unit ;

[0069] exist Figure 1 The uniform linear array geometric model of the airborne MIMO radar shown consists of an array of multiple array elements arranged along the length of the carrier platform, where the number of transmitting elements is... The spacing between the transmitting elements is The number of receiving array elements is The spacing between the receiving array elements is The flight speed of the carrier platform is The angle between the velocity direction and the array axis is the yaw angle. ,when When it is a frontal and side view array, when The image is not a frontal side view array; the height of the aircraft platform is... , , These are the azimuth and elevation angles corresponding to the clutter block, respectively; the operating wavelength of the airborne MIMO radar is... At a constant pulse frequency Emit within the coherent processing interval Each pulse. The airborne MIMO radar transmits orthogonal signals, which are then separated at the receiver using matched filtering. Each transmitting array element sends a signal.

[0070] Define the spatial transmission steering vector for each clutter block. Spatial receiving steering vector and time-domain steering vector They are respectively:

[0071] (1);

[0072] (2);

[0073] (3);

[0074] set up For the first The pitch angle of each distance unit. For the first The azimuth angle of the clutter block, then the... Normalized spatial frequency of individual clutter blocks , No. Normalized Doppler frequency of each clutter block The set of clutter spacetime steering vectors for airborne MIMO radar can be written in Vandermonde vector form with respect to three-dimensional frequencies, i.e.:

[0075] (4);

[0076] in, Normalized spatial frequency of the transmission array for clutter blocks Normalized spatial frequency of the receiving array and normalized Doppler frequency The three-dimensional frequency composition, i.e. ;

[0077] No. The output of each distance unit after matched filtering Dimensional time-space snapshot data for:

[0078] (5);

[0079] In the formula, For the first Noise signal per distance cell, For the first The clutter signal of the nth range cell; where the nth Clutter signal per range cell The aforementioned set of airborne MIMO radar clutter spacetime steering vectors can be expressed as follows: The spatiotemporal signals of each clutter block are superimposed, that is:

[0080] (6);

[0081] In the formula, For the first The complex amplitude of a clutter block For Kronecker product;

[0082] Based on the above, Clutter signal per range cell After matched filtering Spatiotemporal snapshot data per distance unit It can be represented as:

[0083] (7);

[0084] in, for Clutter signal per unit distance, for Noise signal of each distance unit.

[0085] 2) Using the atomic norm minimization method to apply the above Spatiotemporal snapshot data per distance unit Sparse recovery is performed to obtain an estimate of the clutter subspace. ;

[0086] Assume that the set of all clutter spacetime steering vectors on the continuous spacetime plane is a three-dimensional atom set. ,Right now:

[0087] (8);

[0088] Based on the above formula, we can obtain... Clutter signal per range cell of The norm is represented as:

[0089] (9);

[0090] In the formula, The number of atoms, i.e., the clutter rank; Clutter signal per range cell The atoms can be solved by solving the following equation This is obtained by minimizing the norm, i.e.:

[0091] (10);

[0092] in, Noise level; by It can be seen that, Clutter signal per range cell and clutter subspace It can be estimated by solving the rank minimization optimization problem, that is:

[0093] (11);

[0094] in, Let represent the rank of the matrix; this problem is NP-hard, but by convexly relaxing the rank constraint, equation (11) can be transformed into an atomic norm minimization problem, i.e.:

[0095] (12);

[0096] in, For trace operation, for The triple-block Toeplitz matrix, i.e.:

[0097] (13);

[0098] In the formula, for The block Toeplitz matrix, i.e.:

[0099] (14);

[0100] In the formula, for The Toeplitz matrix, i.e.:

[0101] (15);

[0102] The solution to the primal problem is obtained by solving the dual problem of equation (12), i.e.:

[0103] (16);

[0104] in, To perform the operation of taking the real part, for Clutter signal per range cell dual variables, , , , All are Gram matrices. It is a positive semidefinite Hermitian matrix with low rank and triple Toeplitz matrix structure properties. For half space, , The value can be:

[0105] (17);

[0106] The estimated value of the clutter subspace can be obtained by solving equation (16). and Estimated clutter signal per range cell .

[0107] 3) Estimated values ​​for the above clutter subspace Eigenvalue decomposition is performed to obtain an estimate of the clutter covariance matrix. Then, the estimated value of the clutter plus noise covariance matrix of the range cell to be detected is calculated. ;

[0108] Estimation of clutter subspace Eigenvalue decomposition is performed to obtain an estimate of the clutter covariance matrix. :

[0109] (18);

[0110] in, This represents eigenvalue decomposition; and subsequently, the estimated value of the clutter plus noise covariance matrix of the range cell to be detected. It can be represented as:

[0111] (19);

[0112] in, for unit vector, This represents noise power.

[0113] 4) Using the estimated value of the clutter plus noise covariance matrix of the above-mentioned range cell to be detected Calculate the adaptive weight vector of the airborne MIMO radar space-time filter. .

[0114] Adaptive weight vector of airborne MIMO radar space-time filter It can be represented as:

[0115] (20);

[0116] in, The space-time guide vector of the distance cell to be detected.

[0117] To verify the STAP method for airborne MIMO radar based on the three-dimensional atomic norm provided by this invention, the inventors conducted the following experiment:

[0118] The experimental parameters were set as follows: height of the carrier platform. Flight speed of the carrier platform Number of launch array elements Number of receiving array elements coherent pulse number Pulse repetition frequency The operating wavelength of airborne MIMO radar Spacing between launch array elements Receiver element spacing clutter block count noise ratio The OGSBI method has a mesh resolution of 0.02, and the iteration termination condition is... The maximum number of iterations is 2000. The mesh discretization coefficients for the FOCUSS and SBL methods are... The regularization parameter of the FOCUSS method is ,use Norm, the initial value of the regularization parameter in the SBL method is The hyperparameter pruning threshold is The maximum number of iterations for the FOCUSS and SBL methods are 800 and 2000, respectively. To analyze the clutter spectrum estimation performance of the five methods under grid mismatch conditions, the airborne MIMO radar array is configured as a front-side looking array (yaw angle...). ) and non-horizontal look-ahead array (yaw angle) Two methods are used: Capon spectrum (minimum variance spectrum) to describe the clutter spectrum. The Capon spectrum is a high-resolution spectrum used for analyzing clutter spectra. The Capon spectrum is defined as follows: .

[0119] Experiment 1: Figure 2 There is a dictionary mismatch (yaw angle) in the frontal and side-view arrays. The figure shows that the clutter spectrum estimated by the FOCUSS and SBL methods is significantly broadened and has low resolution. This is because both methods are based on a fixed discrete dictionary. During dictionary construction, the clutter ridge slope cannot be accurately obtained, and the clutter ridge lines and discretized grid points cannot be perfectly aligned, leading to dictionary mismatch. The estimation results can only fall on the pre-defined discrete grid points, and the density of the dictionary grid affects the estimation performance. The OGSBI method dynamically solves the dictionary mismatch error, and its estimation results are better than the FOCUSS and SBL methods; however, the error introduced by model approximation limits its performance improvement. While the two-dimensional ANM method avoids the dictionary mismatch problem caused by constructing a discrete dictionary in the gridded method, the loss of system degrees of freedom limits its estimation accuracy. The method of this invention makes full use of the system's degrees of freedom. Its estimated clutter spectrum is concentrated near the real clutter ridge and is very close to the real clutter spectrum. This verifies that the clutter spectrum estimation performance of the method of this invention is better than the sparse recovery method based on dictionary grid and the two-dimensional ANM method when there is dictionary mismatch in the front-side view array.

[0120] Experiment 2: Figure 3 For non-horizontal side view array (yaw angle) Capon spectrum estimation of clutter under the non-frontal side-view array condition. As can be seen from the figure, under the non-frontal side-view array condition, the clutter spectrum estimated by the FOCUSS method, SBL method, and OGSBI method is more blurred and has a more serious broadening due to dictionary mismatch. This is because the clutter ridges are distributed along an ellipse under the non-frontal side-view array condition, and there is a significant offset between the clutter ridges and the discretized grid points. Only a small number of discrete grid points are completely aligned with the clutter ridges, making the dictionary mismatch problem more serious. Although the two-dimensional ANM method is not affected by the dictionary mismatch problem, the loss of system degrees of freedom limits its estimation performance improvement. However, the method of the present invention can still obtain a relatively clear clutter spectrum without significant broadening, which verifies that the clutter spectrum estimation performance of the present invention under the non-frontal side-view array condition is better than the sparse recovery method based on dictionary grid and the two-dimensional ANM method.

[0121] Experiment 3: This experiment uses the signal-to-interference-plus-noise ratio (SIN) loss. The evaluation index, SINR loss, serves as a measure of the clutter suppression performance of the five methods. Defined as the ratio of the SINR of the space-time filter output to the SINR of the output with only white noise, i.e.: ,in The target signal is guided by a vector. Figure 4 There is a dictionary mismatch for the frontal side-view array (yaw angle). The signal-to-interference-plus-noise ratio (SIR) loss curve under the following conditions. Figure 5 Non-horizontal side view array (yaw angle) The signal-to-interference-plus-noise ratio (SIR) loss curves under the given conditions. Each curve in the SIR loss section was obtained from 100 Monte Carlo simulations. Figure 4 As can be seen, for the front-side view array, the FOCUSS, SBL, and OGSBI methods suffer from dictionary mismatch due to insufficient grid points in the constructed discrete dictionary to align with the clutter ridges, resulting in widening of the notch in the main clutter region. In contrast, the method of this invention and the two-dimensional ANM method do not exhibit significant widening in the main clutter region, but the SINR loss curve obtained by the method of this invention is closest to the SINR loss curve of the optimal filter. Figure 5 As can be seen, for non-frontal side-view arrays, due to the more severe dictionary mismatch problem, the clutter subspace estimated by the FOCUSS method, SBL method, and OGSBI method deviates significantly from the real clutter subspace, resulting in severe widening of the notch in the main clutter region. In contrast, the method of this invention and the two-dimensional ANM method can still form a relatively narrow null in this region. However, the SINR loss curve in other regions is closer to the SINR loss curve of the optimal filter than the two-dimensional ANM method, demonstrating better clutter suppression performance and slow-moving target detection capability.

[0122] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A three-dimensional atomic norm based airborne MIMO radar STAP method, characterized in that: The STAP method for airborne MIMO radar based on the three-dimensional atomic norm includes the following steps performed in sequence: 1) Based on the geometric model of the uniform linear array of the airborne MIMO radar, and using the spatial transmission steering vector, spatial reception steering vector, and temporal steering vector, a set of clutter space-time steering vectors for the airborne MIMO radar is established, and then... Spatial-temporal snapshot data per distance unit ; 2) Using the atomic norm minimization method to apply the above Spatial-temporal snapshot data per distance unit Sparse recovery is performed to obtain an estimate of the clutter subspace. ; 3) Estimated values ​​for the above clutter subspace Eigenvalue decomposition is performed to obtain an estimate of the clutter covariance matrix. Then, the estimated value of the clutter plus noise covariance matrix of the range cell to be detected is calculated. ; 4) Using the estimated value of the clutter plus noise covariance matrix of the above-mentioned range cell to be detected Calculate the adaptive weight vector of the airborne MIMO radar space-time filter. ; In step 2), the atomic norm minimization method is used to apply the above... Spatial-temporal snapshot data per distance unit Sparse recovery is performed to obtain an estimate of the clutter subspace. The method is: Assume that the set of all clutter spacetime steering vectors on the continuous spacetime plane is a three-dimensional atom set. ,Right now: （8）； in, Normalized spatial frequency of the transmission array for clutter blocks Normalized spatial frequency of the receiving array and normalized Doppler frequency The three-dimensional frequency composition, i.e. ; This is the set of airborne MIMO radar clutter spacetime steering vectors; Based on the above formula, we can obtain... Clutter signal per range cell of The norm is represented as: （9）； In the formula, The number of atoms, i.e., the clutter rank; Clutter signal per range cell The atoms can be solved by solving the following equation This is obtained by minimizing the norm, i.e.: （10）； in, Noise level; by It can be seen that, Clutter signal per range cell and clutter subspace It can be estimated by solving the rank minimization optimization problem, that is: （11）； in, Let represent the rank of the matrix; this problem is NP-hard, but by convexly relaxing the rank constraint, equation (11) can be transformed into an atomic norm minimization problem, i.e.: （12）； in, For trace operation, for The triple-block Toeplitz matrix, i.e.: （13）； In the formula, , ,for The block Toeplitz matrix, i.e.: （14）； In the formula, , ,for The Toeplitz matrix, i.e.: （15）； The solution to the primal problem is obtained by solving the dual problem of equation (12), i.e.: （16）； in, To perform the operation of taking the real part, for Clutter signal per range cell dual variables, , , , All are Gram matrices. It is a positive semidefinite Hermitian matrix with low rank and triple Toeplitz matrix structure properties. For half space, , The value can be: （17）； The estimated value of the clutter subspace can be obtained by solving equation (16). and Estimated clutter signal per range cell .

2. The STAP method for airborne MIMO radar based on three-dimensional atomic norm according to claim 1, characterized in that: In step 1), based on the geometric model of the uniform linear array of the airborne MIMO radar, and based on the spatial transmission steering vector, spatial reception steering vector, and temporal steering vector, a set of clutter space-time steering vectors for the airborne MIMO radar is established, thereby obtaining... Spatial-temporal snapshot data per distance unit The method is: In the geometric model of a uniform linear array for airborne MIMO radar, the array consists of multiple array elements arranged along the length of the carrier platform, where the number of transmitting elements is... The spacing between the transmitting array elements is The number of receiving array elements is The spacing between the receiving array elements is The flight speed of the carrier platform is The angle between the velocity direction and the array axis is the yaw angle. ,when When it is a frontal and side view array, when The time is a non-frontal side view array, and the height of the aircraft platform is , , These are the azimuth and elevation angles corresponding to the clutter block, respectively; the operating wavelength of the airborne MIMO radar is... At a constant pulse frequency Emit within the coherent processing interval Each pulse; the airborne MIMO radar transmits orthogonal signals, and the received signals are separated by matched filtering at the receiving end. Each transmitting array element signal; Define the spatial transmission steering vector for each clutter block. Spatial receiving steering vector and time-domain steering vector They are respectively: （1）； （2）； （3）； set up For the first The pitch angle of each distance unit. For the first The azimuth angle of the clutter block, then the... Normalized spatial frequency of individual clutter blocks , No. Normalized Doppler frequency of each clutter block The set of clutter spacetime steering vectors for airborne MIMO radar can be written in Vandermonde vector form with respect to three-dimensional frequencies, i.e.: （4）； in, Normalized spatial frequency of the transmission array for clutter blocks Normalized spatial frequency of the receiving array and normalized Doppler frequency The three-dimensional frequency composition, i.e. ; No. The output of each distance unit after matched filtering Dimensional time-space snapshot data for: （5）； In the formula, For the first Noise signal of each distance cell, For the first The clutter signal of the nth range cell; where the nth Clutter signal per range cell The aforementioned set of airborne MIMO radar clutter spacetime steering vectors can be expressed as follows: The spatiotemporal signals of each clutter block are superimposed, that is: （6）； In the formula, For the first The complex amplitude of a clutter block For Kronecker product; Based on the above, Clutter signal per range cell After matched filtering Spatial-temporal snapshot data per distance unit It can be represented as: （7）； in, for Clutter signal per range cell, for Noise signal of each distance unit.

3. The STAP method for airborne MIMO radar based on three-dimensional atomic norm according to claim 2, characterized in that: In step 3), the estimated value of the above-mentioned clutter subspace Eigenvalue decomposition is performed to obtain an estimate of the clutter covariance matrix. Then, the estimated value of the clutter plus noise covariance matrix of the range cell to be detected is calculated. The method is: Estimates of clutter subspace Eigenvalue decomposition is performed to obtain an estimate of the clutter covariance matrix. : （18）； in, This represents eigenvalue decomposition; and subsequently, the estimated value of the clutter plus noise covariance matrix of the range cell to be detected. It can be represented as: （19）； in, for unit vector, This represents noise power.

4. The STAP method for airborne MIMO radar based on three-dimensional atomic norm according to claim 3, characterized in that: In step 4), the estimated value of the clutter plus noise covariance matrix of the aforementioned range cell to be detected is used. Calculate the adaptive weight vector of the airborne MIMO radar space-time filter. The method is: Adaptive weight vector of airborne MIMO radar space-time filter It can be represented as: （20）； in, The space-time guide vector of the distance cell to be detected.

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