Method for joint estimation of mutual coupling error and DOA based on energy valley-compressive sensing for MIMO radar

Abstract

The application discloses a kind of MIMO radar mutual coupling error and DOA joint estimation method based on energy valley-compressed sensing.The method is in the design framework of compressed sensing, for the problem that the array model of MIMO radar exists mutual coupling error and causes poor target angle recognition accuracy, by introducing different perturbation strategies in EVO algorithm and introducing weighted and subspace filtering operation in CS signal reconstruction process, improved EVO-CS algorithm is designed, not only can the algorithm obtain global optimal solution to the greatest extent, but also enhance the robustness of the algorithm under poor conditions such as low signal-to-noise ratio, widen the applicability of compressed sensing algorithm in MIMO radar, improve and improve the solving ability of compressed sensing algorithm in the realization of target angle positioning in MIMO radar scene.Example shows that the application can realize more accurate mutual coupling error coefficient and DOA estimation result, global optimization ability is stronger, the estimation accuracy is highest, effectively enhances the detection performance of MIMO radar system to identify space target.

Description

Technical Field

[0001] This invention relates to a technique for jointly estimating the mutual coupling error coefficient and DOA using an improved energy valley-compressed sensing method in MIMO radar, belonging to the field of radar array signal processing. Background Technology

[0002] As a popular new radar mode, Multiple Input Multiple Output (MIMO) radar utilizes multiple transmit and receive antennas to process target echo signals and has been widely used in various fields such as autonomous driving, life sign detection, and marine sonar. Compared to a single receive-only array, MIMO radar expands the virtual array aperture by leveraging the concept of shared arrays, achieving more accurate Direction of Arrival (DOA) estimation. However, traditional MIMO radar transmit and receive arrays typically use a uniform linear array structure. This dense array element layout causes severe mutual coupling effects and a limited aperture length, affecting subsequent target estimation results. Furthermore, an excessive number of physical array elements increases the system's hardware cost and processing complexity, hindering real-time processing in engineering. Therefore, combining MIMO radar with sparse transmit and receive arrays is of significant research importance for improving radar system performance.

[0003] To overcome the limitations of the Nyquist sampling theorem, compressed sensing (CS) theory emerged. It leverages the sparsity or compressibility of signals to achieve signal reconstruction and super-resolution parameter estimation using fewer or even single-shot signals. CS theory is not concerned with the sampled values ​​of the signal itself, but rather with the information contained within the signal, thus enabling signal acquisition at a rate far lower than that of the Nyquist sampling theorem. In MIMO radar applications, the received target signal is limited to only a few specific angles, with no signal incident in most angular directions across space; therefore, the target signal exhibits spatial sparsity. Consequently, achieving accurate target angle estimation using CS technology is of significant developmental importance.

[0004] When estimating the angle of a target echo signal, radar typically assumes that the array steering matrix is ​​unaffected. However, in practical applications, inter-element coupling effects are often unavoidable. Electromagnetic interactions between adjacent elements cause radiation pattern distortion, directly affecting antenna radiation characteristics and reducing angle estimation accuracy and algorithm stability. Therefore, designing an optimized algorithm that can not only accurately compensate for inter-element coupling error coefficients but also obtain accurate target angle estimates has become a critical problem that MIMO radar systems urgently need to solve.

[0005] Existing methods for estimating mutual coupling error coefficients and angles, such as beamforming algorithms, subspace algorithms, and deep learning algorithms, are all subject to their own limitations. Beamforming algorithms are simple but constrained by the Rayleigh limit, have low resolution, and cannot distinguish signal sources with similar angles; subspace algorithms have high resolution but are sensitive to model assumptions; deep learning algorithms are highly adaptable but dependent on data. In contrast, Cosmic Sensing (CS) leverages signal sparsity to achieve high-precision angle estimation while reducing hardware burden, making it an ideal choice for resource-constrained scenarios. However, within the CS framework, the design of the dictionary matrix and reconstruction algorithm has a crucial impact on the final signal recovery result. It not only needs to meet strict mathematical conditions but also needs to consider computational efficiency, hardware implementation, and noise resistance. A reasonable design can achieve efficient and robust signal recovery using a small amount of sampled data. Furthermore, the Orthogonal Matching Pursuit (OMP) algorithm is still limited in terms of computational efficiency, noise robustness, and grid dependence in DOA estimation. Therefore, this invention proposes a joint estimation method for mutual coupling error and DOA of MIMO radar based on Energy Valley Optimizer (EVO)-CS (EVO-CS). This method first designs a novel sparse transceiver array layout, and by formulating a joint optimization problem for mutual coupling error coefficient and DOA estimation, the improved EVO-CS method is used to obtain accurate mutual coupling error coefficient and signal angle under iterative cycles. Summary of the Invention

[0006] The purpose of this invention is to provide a novel method for jointly estimating mutual coupling error coefficients and DOA under MIMO radar. This method combines the EVO method and CS technology, and alternately estimates the mutual coupling error coefficients and signal angles in a cyclical iterative process to improve the error compensation capability and DOA estimation capability of the improved algorithm.

[0007] Technical solution: A joint estimation method for mutual coupling error and DOA of MIMO radar based on energy valley-compressed sensing. The implementation steps of this method include:

[0008] S1. Construct the array element arrangement of the MIMO radar's transmitting and receiving arrays. The array elements in the transmitting array are arranged according to a nested array model, and the receiving array adopts a relatively sparse uniform array.

[0009] S2. Based on the positions of the array elements of the transmitting and receiving arrays, model the steering vectors and steering matrices corresponding to the transmitting and receiving arrays respectively, thereby establishing a mathematical model of the target echo data received by the MIMO radar.

[0010] S3. Based on the positional relationship of each element in the transmission array, construct the mutual coupling error matrix corresponding to the transmission array, taking the mutual coupling error coefficient as the object.

[0011] S4. Determine the mathematical expression of the coupling coefficient based on the mutual coupling error matrix of the transmitting array;

[0012] S5. Construct array received data of MIMO radar under the influence of mutual coupling error;

[0013] S6. Construct the covariance matrix of the MIMO radar array received data;

[0014] S7. Using the vectorization operation of the matrix, obtain the virtual array received data corresponding to the virtual array formed by the MIMO radar;

[0015] S8. Design a dictionary matrix by utilizing the sparsity of the target signal in the spatial angular domain;

[0016] S9. Under the assumption of sparsity, construct a virtual array to receive data;

[0017] S10. Within the CS framework, construct a joint optimization problem for mutual coupling error coefficients and DOA estimation in a MIMO radar scenario, mathematically expressed as:

[0018]

[0019] In the formula, Indicates the mutual coupling error coefficient. Vectorization The vector after, Represents the autocorrelation matrix of the signal. This represents the coupling coefficient corresponding to the mutual coupling error of the transmit array. express Norm, express Norm, This represents the signal vector corresponding to the dictionary matrix. and They represent the first in the transmission array. and the Each array element position, It is a positive number. It is a dictionary matrix. It is the virtual received number corresponding to the virtual array of the MIMO radar. Indicates the maximum effective interval of mutual coupling error;

[0020] S11. Solve the joint optimization problem described in step S10 using the improved EVO-CS algorithm. This algorithm is based on the maximum number of iterations input and the coarsely estimated signal angle. The calculation of the output cross-coupling error estimation matrix and the signal DOA estimate involves the following calculation process:

[0021] 1) Calculate and estimate the mutual coupling error coefficients :fixed , This represents the maximum number of iterations, which simplifies the joint optimization problem and allows us to use an improved EVO algorithm to obtain the mutual coupling error coefficients.

[0022]

[0023] Construct a mutual coupling error coefficient matrix based on the estimated mutual coupling error coefficients. And compensate for the virtual received data of the MIMO radar. ;

[0024] 3) Estimate the signal angle Fixed mutual coupling error matrix The simplified joint optimization problem is as follows, and the improved WSOMP algorithm is used to solve it to obtain the estimated value of the target angle;

[0025]

[0026] 4) Update the virtual received data of the MIMO radar: .

[0027] Furthermore, the specific design of step S1 includes:

[0028] The MIMO radar's transmitting array has a total of There are 1 array element, arranged in a nested array form, where subarray 1 has 100 elements. There are array elements, and the spacing between the array elements is... The position of each array element is described as follows: Subarray 2 has There are array elements, and the spacing between the array elements is... And the distance between the two subarrays is , The positions of the elements in the transmitting array are represented as follows: ;

[0029] The receiving array adopts a sparse, uniform array layout. There are array elements, and the spacing between the array elements is... Receiver array .

[0030] Furthermore, step S2 specifically includes the following processes:

[0031] Based on the steering matrix of the transmit and receive matrices, a mathematical model of the MIMO radar received data after matched filtering is established, as shown below:

[0032]

[0033] in, This represents the steering vector of the transmitting array. This represents the steering vector of the receiving array. The steering matrix of the joint array is represented. Represents a signal vector. Represents the noise vector. Indicates the number of incident signals. Indicates the Kronecker product. express KR product.

[0034] Furthermore, the mathematical expression of the mutual coupling error matrix in the transmit array in step S3 is as follows:

[0035]

[0036] in, This represents the mutual coupling error matrix corresponding to the transmit array, and its dimension is... ; This represents the operation of constructing a Toplitz matrix using vectors as rows and columns; Let represent the mutual coupling error coefficients, and satisfy . ; and They represent dimensions as follows: and A matrix of all zeros; The dimension is The identity matrix.

[0037] Furthermore, the coupling coefficient corresponding to the mutual coupling error of the transmit array determined in step S4 is:

[0038]

[0039] in, express F Norm; This indicates the operation of taking the diagonal elements of a matrix.

[0040] Furthermore, step S5, which constructs the array received data of the MIMO radar under the influence of mutual coupling error, is as follows:

[0041]

[0042] in, This represents the joint steering matrix affected by mutual coupling errors; This represents the joint steering vector affected by mutual coupling errors.

[0043] Furthermore, step S6 constructs the covariance matrix of the array received data of the MIMO radar as follows:

[0044]

[0045] in, Represents the autocorrelation matrix of the signal; Indicates noise power; The dimension is The identity matrix; This indicates an operation to calculate the expected value. This indicates the operation of finding the conjugate transpose.

[0046] Further, step S7 constructs the virtual received data corresponding to the virtual array of the MIMO radar:

[0047]

[0048] in, This represents the joint virtual array steering matrix affected by mutual coupling errors; This represents the steering vector of the joint virtual array affected by mutual coupling errors; Vectorization The vector after; Vectorization The vector after, Indicates the first A column vector with 1s at each position and all others being 0s; Indicates vectorization operation; This indicates a conjugate operation.

[0049] Furthermore, step S8 utilizes the sparsity of the target signal in the spatial angular domain to design the dictionary matrix as follows:

[0050]

[0051] in, Represents the column vectors of the dictionary matrix, and ; This represents the number of grid points used to divide the spatial domain by angle, and .

[0052] Furthermore, in step S9, under the assumption of sparsity, the ideal virtual array for receiving data is constructed as follows:

[0053]

[0054] in, Let represent the signal vector corresponding to the dictionary matrix, where it has a value only at the location of the actual signal and a value of 0 at other locations, exhibiting sparsity of . Its characteristics.

[0055] The beneficial effects are as follows: Compared with the prior art, the method described in this invention can accurately compensate for the mutual coupling error existing in the transmitting array, while achieving more accurate signal angle estimation and stronger identification capability for spatial incident signals. Secondly, its substantial features and significant effects also include:

[0056] (1) The sparse transceiver array constructed in this invention sparsely arranges the physical array elements in the transmitting and receiving arrays of the MIMO radar. Its array element arrangement method can use fewer transceiver physical array elements to achieve a virtual array with a longer virtual aperture and the fewest redundant array elements, effectively saving engineering costs and improving angular resolution.

[0057] (2) By dividing the spatial angle domain, this invention makes full use of the sparsity of the signal in space, and under the framework of compressed sensing, by designing the dictionary matrix and reconstruction algorithm in the MIMO radar scenario, it formulates the joint optimization problem of the array element mutual coupling error coefficient and the signal angle, breaks through the limitation of the Nyquist sampling rate, and greatly improves the resolution of the signal angle.

[0058] (3) In view of the shortcomings of the EVO algorithm, which is prone to getting trapped in local solutions and has weak search strength, the present invention embeds perturbation operations at different stages of its individual solution update to promote population diversity, effectively expand the degree of freedom of the solution space, and at the same time avoid the algorithm from getting trapped in local convergence, thereby increasing the probability of obtaining the global optimal solution.

[0059] (3) To address the RSOMP algorithm used by CS in the signal reconstruction process, residual weighting operation and subspace prior information are introduced. The subspace is dynamically estimated to improve the performance of the OMP algorithm. In the case of the disadvantage of being strongly affected by noise interference under low signal-to-noise ratio conditions, this invention introduces weighted and subspace filtering operation in the algorithm iteration process. The signal subspace projection matrix is ​​dynamically estimated to suppress noise components and fully preserve the low-dimensional subspace where the signal is located, which greatly improves the optimization performance of the OMP algorithm. Attached Figure Description

[0060] Figure 1 The layout of the transmitting and receiving arrays of the new MIMO radar;

[0061] Figure 2 Improved EVO-CS joint estimation flowchart of mutual coupling error coefficients and DOA;

[0062] Figure 3 Flowchart of the improved EVO algorithm;

[0063] Figure 4 Flowchart of the improved WSOMP algorithm. Detailed Implementation

[0064] To illustrate the technical solutions disclosed in this invention in detail, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0065] This invention provides a joint estimation method for mutual coupling error and DOA of MIMO radar based on EVO-CS. Referring to the accompanying drawings, the physical element layout block diagram of the transmit and receive arrays of the novel MIMO radar is as follows: Figure 1 As shown, the overall improved EVO-CS method operation flow is as follows: Figure 2 As shown, the improved EVO method operation flow is as follows: Figure 3 As shown, the operation flow of the improved Weighted Subspace OMP (WSOMP) algorithm is as follows: Figure 4 As shown. Specifically, the implementation of this method includes the following steps:

[0066] Step 1: Design the element arrangement of the MIMO radar's transmit and receive arrays. The elements in the MIMO radar's transmit array are arranged according to a nested array model, while the receive array uses a sparse, uniform array. This sparsely arranged transmit and receive array model effectively expands the virtual array aperture of the MIMO radar, minimizing the number of redundant elements and thus improving the array's angular resolution, significantly enhancing the radar system's angle measurement accuracy.

[0067] Design the element layout of the transmit and receive arrays for a MIMO radar. The transmit array of a MIMO radar contains a total of... There are 1 array element, arranged in a nested array form, where subarray 1 has 100 elements. There are array elements, and the spacing between the array elements is... The position of each array element can be described as Subarray 2 has There are array elements, and the spacing between the array elements is... And the distance between the two subarrays is , Then the positions of the elements of the transmitting array can be represented as The receiving array uses a sparse, uniform array layout, which has... There are array elements, and the spacing between the array elements is... , This sparsely arranged transceiver array model can generate the fewest redundant array elements, effectively expanding the virtual array aperture of the MIMO radar, thereby improving the array's angular resolution and greatly enhancing the radar system's angle measurement accuracy.

[0068] Step 2: Construct the array receive data for the MIMO radar. This is based on the positions of the elements in the transmitting array. Modeling the steering vector of the transmission array and guiding matrix Based on the positions of the array elements of the receiving array. Modeling the steering vector of the receiving array and guiding matrix Using the steering matrices of the transmit and receive arrays, a mathematical model is established for the MIMO radar received data after matched filtering, as shown below:

[0069]

[0070] in, The guiding matrix represents the joint array; Represents a signal vector; Represents a noise vector; Indicates the number of incident signals; Indicates the Kronecker product; This represents the KR product.

[0071] Step 3: Construct the mutual coupling error matrix in the transmit array, which is expressed as follows:

[0072]

[0073] in, This represents the mutual coupling error matrix corresponding to the transmit array, and its dimension is... ; This represents the operation of constructing a Toplitz matrix using vectors as rows and columns; Let represent the mutual coupling error coefficients, and satisfy . ; and They represent dimensions as follows: and A matrix of all zeros; The dimension is The identity matrix.

[0074] Step 4: Determine the coupling coefficient corresponding to the mutual coupling error of the transmit array:

[0075]

[0076] in, express F Norm; This indicates the operation of taking the diagonal elements of a matrix.

[0077] Step 5: Construct array received data for MIMO radar under the influence of mutual coupling errors:

[0078]

[0079] in, This represents the joint steering matrix affected by mutual coupling errors; This represents the joint steering vector affected by mutual coupling errors.

[0080] Step 6: Construct the covariance matrix of the array received data from the MIMO radar:

[0081]

[0082] in, Represents the autocorrelation matrix of the signal; Indicates noise power; The dimension is The identity matrix; This indicates an operation to calculate the expected value. This indicates the operation of finding the conjugate transpose.

[0083] Step 7: Construct virtual received data corresponding to the virtual array of the MIMO radar:

[0084]

[0085] in, This represents the joint virtual array steering matrix affected by mutual coupling errors; This represents the steering vector of the joint virtual array affected by mutual coupling errors; Vectorization The vector after; Vectorization The vector after, Indicates the first A column vector with 1s at each position and all others being 0s; Indicates vectorization operation; This indicates a conjugate operation.

[0086] Step 8: Utilize the sparsity of the target signal in the spatial angular domain to design the dictionary matrix:

[0087]

[0088] in, Represents the column vectors of the dictionary matrix, and ; This represents the number of grid points used to divide the spatial domain by angle, and .

[0089] Step 9: Under the assumption of sparsity, construct an ideal virtual array to receive data:

[0090]

[0091] in, Let represent the signal vector corresponding to the dictionary matrix, where it has a value only at the location of the actual signal and a value of 0 at other locations, exhibiting sparsity of . Its characteristics.

[0092] Step 10: Within the CS framework, construct a joint optimization problem for the mutual coupling error moment coefficients and DOA estimation under MIMO radar:

[0093]

[0094] in, Indicates the maximum effective interval of the mutual coupling error; and They represent the first in the transmission array. and the Each array element; express Norm; It represents a very small positive number.

[0095] Step 11: Solve the above optimization problem using the improved EVO-CS algorithm:

[0096] Improved EVO-CS algorithm

[0097] Input: Maximum number of iterations, coarsely estimated signal angle

[0098] Output: Mutual coupling error estimation matrix, signal DOA estimate

[0099]

[0100] While Maximum number of iterations (do)

[0101] ① Estimate the mutual coupling error coefficient :fixed The simplified joint optimization problem is as follows, and the improved EVO algorithm is used to solve it to obtain the mutual coupling error coefficient;

[0102]

[0103] ② Construct the mutual coupling error matrix using the estimated mutual coupling error coefficients from ①. And compensate for the virtual received data of the MIMO radar: ;

[0104] ③ Estimate signal angle Fixed mutual coupling error matrix The simplified joint optimization problem is as follows, and the improved WSOMP algorithm is used to solve it to obtain the estimated value of the target angle;

[0105]

[0106] ④ Update the virtual received data of the MIMO radar: ;

[0107] End

[0108] The operation steps of the improved EVO algorithm used in ① above can be described as follows:

[0109] Improved EVO algorithm

[0110] Input: Population size Maximum number of iterations

[0111] Output: The most stable individual particle

[0112] Determine the initial solution in the search space. (its dimension is the population size) (mutual coupling error coefficient length)

[0113] Evaluation of the objective function value of the particle

[0114]

[0115] While Maximum number of iterations

[0116] Determine the enrichment limit EB for particles

[0117] Identify the most stable particle in the population

[0118] For

[0119] Determine the first enrichment level of individual particles and stable level

[0120] If

[0121] Determine the stability limits of particles

[0122] If

[0123] produce Alpha Index I and II

[0124] For

[0125]

[0126] End For

[0127] produce Gamma Index I and II

[0128] Determine the neighborhood particles

[0129] For

[0130]

[0131] End For

[0132] Else if

[0133] Determine the central particle

[0134]

[0135] Determine the neighborhood particles

[0136]

[0137] End If

[0138] Else if

[0139] Determining the most stable particle and the most unstable particles

[0140]

[0141] End If

[0142] End For

[0143] End While

[0144] The operation steps of the improved WSOMP algorithm used in ② above can be described as follows:

[0145] Improved WSOMP algorithm

[0146] Input: Received data Perception Matrix Number of signals

[0147] Output: Reconstructed data

[0148] Initialization: Residual index set Reconstructing the atomic set

[0149]

[0150] While

[0151] ① Residual weighting: Calculate weights based on residuals. .

[0152] ② Subspace filtering: for Perform singular value decomposition to obtain the principal eigenvectors. And calculate the projection matrix of the signal subspace based on the principal eigenvectors. .

[0153] ③ Atom selection: Calculating residuals With dictionary Projection between each column ,choose Maximum value of elements And record its index position in the dictionary. .

[0154] ④ Update the index set and rebuild the atom set: according to and Update the index set and rebuild the atom set.

[0155] ⑤ Use the least squares method to find an approximate solution: .

[0156] ⑥ Update residuals: .

[0157] End While

[0158] The specific embodiments of the present invention have been described in detail above. It should be understood that certain details are not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims without affecting the essence of the present invention.

Claims

1. A joint estimation method for MIMO radar mutual coupling error and DOA based on energy valley-compressed sensing, characterized in that, The implementation steps of this method include: S1. Construct the array element arrangement of the MIMO radar's transmitting and receiving arrays. The array elements in the transmitting array are arranged according to a nested array model, and the receiving array adopts a relatively sparse uniform array. S2. Based on the positions of the array elements of the transmitting and receiving arrays, model the steering vectors and steering matrices corresponding to the transmitting and receiving arrays respectively, thereby establishing a mathematical model of the target echo data received by the MIMO radar. S3. Based on the positional relationship of each element in the transmission array, construct the mutual coupling error matrix corresponding to the transmission array, taking the mutual coupling error coefficient as the object. S4. Determine the mathematical expression of the coupling coefficient based on the mutual coupling error matrix of the transmitting array; S5. Construct array received data of MIMO radar under the influence of mutual coupling error; S6. Construct the covariance matrix of the MIMO radar array received data; S7. Using the vectorization operation of the matrix, obtain the virtual array received data corresponding to the virtual array formed by the MIMO radar; S8. Design a dictionary matrix by utilizing the sparsity of the target signal in the spatial angular domain; S9. Under the assumption of sparsity, construct a virtual array to receive data; S10. Within the CS framework, construct a joint optimization problem for mutual coupling error coefficients and DOA estimation in a MIMO radar scenario, mathematically expressed as: In the formula, Indicates the mutual coupling error coefficient. Vectorization The vector after, Represents the autocorrelation matrix of the signal. This represents the coupling coefficient corresponding to the mutual coupling error of the transmit array. express Norm, express Norm, This represents the signal vector corresponding to the dictionary matrix. and They represent the first in the transmission array. and the Each array element position, It is a positive number. It is a dictionary matrix. It is the virtual receive vector corresponding to the virtual array of the MIMO radar. Indicates the maximum effective interval of mutual coupling error; S11. Solve the joint optimization problem described in step S10 using the improved EVO-CS algorithm. This algorithm is based on the maximum number of iterations input and the coarsely estimated signal angle. The calculation of the output cross-coupling error estimation matrix and the signal DOA estimate involves the following calculation process: 1) Calculate and estimate the mutual coupling error coefficients :fixed , This represents the number of iterations, which simplifies the joint optimization problem and allows us to use an improved EVO algorithm to obtain the mutual coupling error coefficients. Construct a mutual coupling error coefficient matrix based on the estimated mutual coupling error coefficients. And compensate for the virtual received data of the MIMO radar. ; 3) Estimate the signal angle Fixed mutual coupling error matrix The simplified joint optimization problem is as follows, and the improved WSOMP algorithm is used to solve it to obtain the estimated value of the target angle; 4) Update the virtual received data of the MIMO radar: .

2. The joint estimation method for MIMO radar mutual coupling error and DOA according to claim 1, characterized in that, Step S1 specifically includes the following design: The MIMO radar's transmitting array has a total of There are 1 array element, arranged in a nested array form, where subarray 1 has 100 elements. There are array elements, and the spacing between the array elements is... The position of each array element is described as follows: Subarray 2 has There are array elements, and the spacing between the array elements is... And the distance between the two subarrays is , The positions of the elements in the transmitting array are represented as follows: ; The receiving array adopts a sparse, uniform array layout. There are array elements, and the spacing between the array elements is... The receiving array is represented as .

3. The joint estimation method for MIMO radar mutual coupling error and DOA according to claim 2, characterized in that, Step S2 specifically includes the following processes: Based on the steering matrix of the transmit and receive matrices, a mathematical model of the MIMO radar received data after matched filtering is established, as shown below: in, This represents the steering vector of the transmitting array. This represents the steering vector of the receiving array. The guiding matrix of the joint array is represented. Represents a signal vector. Represents the noise vector. Indicates the number of incident signals. Indicates the Kronecker product. express KR product.

4. The joint estimation method for MIMO radar mutual coupling error and DOA according to claim 3, characterized in that, The coupling coefficient corresponding to the mutual coupling error of the transmit array determined in step S4 is: in, express F Norm; This represents the operation of taking the diagonal elements of a matrix. This represents the mutual coupling error matrix in the transmit array.

5. The joint estimation method for MIMO radar mutual coupling error and DOA according to claim 4, characterized in that, Step S5 constructs the array received data of the MIMO radar under the influence of mutual coupling error: in, This represents the joint steering matrix affected by mutual coupling errors; This represents the joint steering vector affected by mutual coupling errors.

6. The joint estimation method for MIMO radar mutual coupling error and DOA according to claim 5, characterized in that, Step S6 constructs the covariance matrix of the array received data of the MIMO radar as follows: in, Represents the autocorrelation matrix of the signal; Indicates noise power; The dimension is The identity matrix; This indicates an operation to calculate the expected value. This indicates the operation of finding the conjugate transpose.

7. The joint estimation method for MIMO radar mutual coupling error and DOA according to claim 6, characterized in that, Step S7: Construct virtual received data corresponding to the virtual array of the MIMO radar: in, This represents the joint virtual array steering matrix affected by mutual coupling errors; This represents the steering vector of the joint virtual array affected by mutual coupling errors; Vectorization The vector after; Vectorization The vector after, Indicates the first A column vector with 1s at each position and all others being 0s; Indicates vectorization operation; This indicates a conjugate operation.

8. The joint estimation method for MIMO radar mutual coupling error and DOA according to claim 7, characterized in that, Step S8 utilizes the sparsity of the target signal in the spatial angular domain to design the dictionary matrix as follows: in, Represents the column vectors of the dictionary matrix, and ; This represents the number of grid points used to divide the spatial domain by angle, and .

9. The joint estimation method for MIMO radar mutual coupling error and DOA according to claim 8, characterized in that, Step S9, under the assumption of sparsity, constructs an ideal virtual array to receive data as follows: in, Let represent the signal vector corresponding to the dictionary matrix, where it has a value only at the location of the actual signal and a value of 0 at other locations, exhibiting sparsity of . Its characteristics.

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