Efficient Gridless Angle Estimation Method for Bistatic MIMO Radar in Planar Array

Abstract

The invention provides an efficient gridless angle estimation method for a bistatic MIMO radar under a planar array, which establishes a bistatic MIMO radar planar array structure; uses the established bistatic MIMO radar planar array structure to receive signals, and models the received signals x(t) collected by the receiver; constructs a matched filter, and acts on a received signal X within a pulse repetition interval, thereby establishing filtered array output data Y; constructs an atomic set to establish an atomic norm minimization optimization problem and solves it, and reconstructs a secondary Toeplitz matrix; obtains a receiving angle DOA and a transmitting angle DOD; the method does not require pre-estimation of angles, effectively avoids the array from being affected, can break through the limitation of grid division, obtains higher precision, has lower computational complexity, and has high computational efficiency for real-time positioning, and can be used for target positioning and target detection.

Description

Technical Field

[0001] The invention relates to an efficient gridless angle estimation method for a bistatic MIMO radar under a planar array, and belongs to the technical field of signal processing. Background Art

[0002] Direction-of-Arrival (DOA) estimation is an important research field in the field of array signal processing. Its basic principle is to use array antennas to receive spatial signals, and to analyze and effectively process the statistics of received signals through statistical signal processing technology and various optimization methods, so as to achieve array direction finding, that is, signal DOA estimation. Direction of arrival is also widely used in radar, seismic, sonar, voice and wireless communication.

[0003] The estimation of the direction of departure (DOD) and the direction of arrival (DOA) of bistatic MIMO radar has attracted extensive attention in academia. Among the existing methods:

[0004] 1) Subspace methods exploit the orthogonality between the signal subspace and the noise subspace, but their performance degrades severely under challenging conditions such as single snapshots;

[0005] 2) Most methods based on compressed sensing (CS) consider linear arrays and only recover part of the target's angle information. In the design process of the optimization problem, the spatial grid points of the signal's assumed arrival direction are pre-set, and it is assumed that the target angle is completely on the predefined grid, which causes an inherent model mismatch error. Therefore, it is crucial to obtain angle information in the continuous angle domain space.

[0006] Multiple-input multiple-output (MIMO) radar systems have attracted widespread attention due to their potential advantages over traditional phased array radars, but few people have considered bistatic MIMO radar systems, where both the transmitter and receiver are equipped with uniform planar arrays (UPAs). In bistatic MIMO radar systems using uniform planar arrays (UPAs), the 4-D angular space must be discretized using the CS method, so the sparse signal model has a large dimension, resulting in huge computational costs; it also faces the model mismatch problem that the CS method cannot avoid, and the modeling error cannot be avoided because DOA / DOD belongs to a continuous angular space.

[0007] In summary, in order to improve the estimation accuracy and performance and avoid the array being affected, a method that does not require angle estimation needs to be designed. At the same time, the burden of large computational workload needs to be alleviated. The above problems are issues that should be considered and solved in the angle estimation process of bistatic MIMO radar under planar array. Summary of the invention

[0008] The purpose of the present invention is to provide an efficient gridless angle estimation method for a bistatic MIMO radar under a planar array, so as to solve the problems in the prior art that the accuracy and performance of the existing estimation methods need to be improved and the amount of calculation is large.

[0009] The technical solution of the present invention is:

[0010] An efficient gridless angle estimation method for bistatic MIMO radar under planar array comprises the following steps:

[0011] S1. Establish a bistatic MIMO radar planar array structure;

[0012] S2, using the dual-base MIMO radar planar array structure established in step S1 to receive signals, and modeling the received signals x(t) collected by the receiver;

[0013] S3, construct a matched filter and apply it to the received signal X within a pulse repetition interval, thereby establishing the filtered array output data Y;

[0014] S4, construct an atomic set to establish an atomic norm minimization optimization problem and solve it, and reconstruct the secondary Toeplitz matrix;

[0015] S5. Perform gridless direction of arrival estimation according to the secondary Toeplitz matrix reconstructed in step S4 to obtain the receiving angle DOA and the transmitting angle DOD.

[0016] Furthermore, in step S1, a bistatic MIMO radar planar array structure is established. Specifically, the transmitter and receiver in the bistatic MIMO radar system are respectively equipped with a uniform planar array UPA, and the transmitter is equipped with a K t =N t ×M t antennas, where N t and M t Respectively represent the number of array elements corresponding to the x-axis and y-axis. The receiver is equipped with K r =N r ×M r antennas, of which N r and M r Respectively represent the number of array elements corresponding to the x-axis and y-axis to obtain the bistatic MIMO radar planar array structure.

[0017] Furthermore, in step S2, the dual-base MIMO radar planar array structure established in step S1 is used to receive the signal, and the received signal x(t) collected by the receiver is modeled, specifically,

[0018] S21, Suppose there are L from Θ1, Θ2, ..., Θ l,...,Θ L Direction far-field targets need to be located, where For the receiving array, define θ l and φ l are the angles between the lth target direction and the x-axis and y-axis relative to the receiver array, respectively. For the transmitting array, and ψ l are the angles between the lth target direction and the x-axis and y-axis relative to the transmitter array, respectively;

[0019] S22, using the bistatic MIMO radar planar array structure obtained in step S1, the transmitter transmits at a pulse repetition interval T PRI A pulse signal is sent to the target, and then the receiver receives the signal x(t), and the sent pulse waveforms are orthogonal to each other;

[0020] S23, the received signal x(t) collected by the receiver is modeled as:

[0021]

[0022] Among them, β l is the reflection coefficient of the lth target, s(t)=[s1(t),…,s L (t)] T is the transmitted signal, L is the number of targets, n(t) is the noise vector received by the receiving array, and a r (θ l ,φ l ) represent the steering vectors of the lth target at the transmitter and receiver respectively, expressed as: , where b n (m)=[1,e jπsin(m) ,…,e jπ(n-1)sin(m) ] T , n is {N t ,M t ,N r ,M r}, m is a set Θ l one,[·] T is the transpose operation, represents the Kronecker product.

[0023] Furthermore, in step S3, a matched filter is constructed and applied to a received signal within a pulse repetition interval, thereby establishing the filtered array output data Y, specifically,

[0024] S31. At the receiver, each antenna uses a high-resolution ADC to sample the received waveform and obtain the transmitter pulse repetition interval TPRI During the Q-long sampling data, in Indicates rounding down, T s is the sampling interval, then the received signal during a pulse is modeled as:

[0025]

[0026] Where X = [x(0), x(T s ),…,x((Q-1)T s )],A r =[a r (θ1,φ1),…,a r (θ L ,φ L )], Σ is a diagonal matrix with diagonal elements [β1,…,β L ] T ,S=[s(0),s(T s ),…,s((Q-1)T s )], because the rows of S are orthogonal, SS H =I L , I L is the L×L identity matrix, N is the noise matrix;

[0027] S32, Application S H As a matched filter, the array output data Y after filtering is established as:

[0028]

[0029] Where X is the received signal within a pulse repetition interval, S is the transmitted signal matrix, and A r and A t denote the matrices formed by the steering vectors of the receiver and transmitter, respectively, N is the noise matrix, [·] H represents the conjugate transpose operation,

[0030] Furthermore, in step S4, an atomic set is constructed to establish an atomic norm minimization optimization problem, specifically,

[0031] S41. Construct an atomic set based on the atomic norm theory and define the atomic set as:

[0032]

[0033] in, represents a complex set, and a r (θ, φ) represent the steering vectors of any target at the transmitter and receiver, respectively;

[0034] S42. Based on the atomic set defined in step S41, the atomic norm of the matrix Z is:

[0035]

[0036] Among them, c l Represents the coefficient, A l Belongs to atomic set represents the atomic norm of Z;

[0037] S43. According to the definition of atomic norm, the following atomic norm minimization problem is proposed:

[0038]

[0039] where η is the threshold constant, which depends on the noise; ||·|| F represents the Frobenius norm;

[0040] S44. Since the atomic norm minimization problem in step S43 cannot be solved in polynomial time, it is converted into a solvable semidefinite programming SDP problem:

[0041]

[0042] in, and is a secondary Toeplitz Hermitian matrix in which the target angle is encoded. tr[·] represents the trace operation. [·] ≥ 0 ensures that the reconstructed covariance matrix satisfies the semi-positive definite condition.

[0043] ,

[0044] t i (j) represents t i The j+Mth t elements, The elements r i (j) represents r i The j+Mth r elements, R r =(2N r -1)(2M r -1), Z H represents the conjugate transpose of the matrix Z, and Y is the filtered array output data;

[0045] S45. Solve the trace minimization problem obtained in step S44 using the CVX tool or the improved alternating direction multiplier method ADMM to obtain the optimal solution. and In this way, the reconstructed secondary Toeplitz matrix is ​​obtained and

[0046] Further, in step S45, the trace minimization problem obtained in step S44 is solved based on the improved alternating direction multiplier method ADMM, specifically,

[0047] S451, rewrite the optimization problem in step S44 into an optimization problem form that satisfies the ADMM algorithm:

[0048]

[0049] in, and is a secondary Toeplitz Hermitian matrix in which the target angle is encoded. tr[·] represents the trace operation. [·] ≥ 0 ensures that the reconstructed covariance matrix satisfies the semi-positive definite condition. Z H represents the conjugate transpose of the matrix Z, and Y is the filtered array output data;

[0050] S452, introduce the Lagrange multiplier matrix, and construct the augmented Lagrange function of the optimization problem in step S451:

[0051]

[0052] Where t and r represent the second-level Toeplitz matrix and Parameters, Y is the array output data after filtering, λ represents the penalty factor, ||·|| F represents the Frobenius norm, is the Lagrange multiplier matrix, U1, U2, U3 are the block matrices of U,

[0053] S453, the iterative update steps of the alternating direction multiplier method ADMM are:

[0054]

[0055] Among them, k and k+1 represent the number of iterations, t and r represent the secondary Toeplitz matrix and Parameters, Y is the array output data after filtering, Λ represents the multiplier matrix, λ represents the penalty factor,

[0056] S454, the iterative formula is implemented by applying the Toeplitz matrix trace operation derivative formula, and the corresponding parameters are derived to zero using the augmented Lagrange function, and the following parameter update criteria are obtained:

[0057]

[0058] Among them, k and k+1 represent the number of iterations, t and r represent the secondary Toeplitz matrix and Parameters, G t and G r is a diagonal matrix, The element g i =[g i (1-M r ),…,g i (0),…,g i (M r -1)], The element g i =[g i (1-M t ),…,g i (0),…,g i (M t -1)], Λ1 and Λ3 are block matrices of matrix Λ, and the specific relationship is U1, U2, and U3 are block matrices of U, and their specific relationship is λ represents the penalty factor, represents a zero vector, except that the middle element is 1, R r =(2N r -1)(2M r -1), express The adjoint operator of ;

[0059] S455, due to constraints That is, Z is projected onto a sphere with center Y and radius η, and the update formula of Z in step S454 is rewritten as:

[0060]

[0061] Among them, k and k+1 represent the number of iterations. Λ2 is the block matrix of matrix Λ, and the specific relationship is U2 is the block matrix of U, and the specific relationship is λ represents the penalty factor;

[0062] Under the constraint U≥0, the update criterion of U in step S453 is rewritten as:

[0063]

[0064] in, By This is achieved by setting all negative eigenvalues ​​of to zero;

[0065] S456: Obtain the optimal solution to the optimization problem in step S451 from steps S453 to S455 and In this way, the reconstructed secondary Toeplitz matrix is ​​obtained and

[0066] Further, in step S5, the gridless direction of arrival is estimated according to the secondary Toeplitz matrix reconstructed in step S4 to obtain the receiving angle DOA and the transmitting angle DOD, specifically:

[0067] S51, the secondary Toeplitz matrix obtained according to step S45 and It can be expressed as: in So is a diagonal matrix with diagonal elements, and They can be considered as ideal autocorrelation arrays of transmitter and receiver arrays respectively;

[0068] S52, in step S51 and Apply the matrix bundle plus pairing MaPP method to recover the information of L target angles The amount is Including angle of arrival and emission angle in, is {θ l ,φ l}, for and achieve the angle of arrival and emission angle Automatic pairing.

[0069] Further, in step S52, the arrival angle is achieved and emission angle Specifically, the pairing process of arrival angle DOD and launch angle DOA estimation is given as:

[0070] in,

[0071] l=1,...,L

[0072] in, is {θ l ,φ l}, i.e., the DOA of the target, for The estimated value of DOD is represents the steering vector of the lth estimated target at the receiver, It represents the steering vector of any estimated transmission angle DOD at the transmitter, and its specific form is: Among them, b n (m)=[1,e j πsin(m) ,…,e jπ(n-1)sin(m) ] T , n is {N t ,M t ,N r ,M r}, m is a set Θ l one, is the optimal solution of Z obtained in step S456, and L represents the target number.

[0073] The beneficial effects of the present invention are:

[0074] 1. This efficient gridless angle estimation method for bistatic MIMO radar under planar array does not require pre-estimation of angles, effectively avoids the influence of the array, ensures gridless direction of arrival estimation, thereby improving the degree of freedom and resolution of estimation, and reducing the computational complexity of estimation to a certain extent. This method can break through the limitations of grid division, overcome model mismatch errors, obtain higher accuracy, and obtain efficient direction of arrival estimation. At the same time, it has lower computational complexity and high computational efficiency of real-time positioning, and can be used for target positioning and target detection.

[0075] 2. The method of the present invention does not need to predefine spatial grid points during the design of the optimization problem, thereby realizing gridless direction of arrival estimation and ensuring the resolution of the direction of arrival estimation.

[0076] 3. An efficient gridless angle estimation method for dual-base MIMO radar under this planar array. The proposed atomic norm optimization problem establishes a solvable SDP problem, which is solved by the alternating direction multiplier method ADMM. It can obtain angle information in a non-discrete 4-D angle space, greatly reduce the amount of calculation, improve the computational efficiency of real-time positioning, and achieve efficient wave direction estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 It is a structural schematic diagram of an efficient gridless angle estimation method for a bistatic MIMO radar under a planar array according to an embodiment of the present invention.

[0078] Figure 2 FIG. 4 is a schematic diagram illustrating a planar array constituting a bistatic MIMO radar in an embodiment.

[0079] Figure 3 It is a schematic diagram comparing the mean square error of the estimation performance of the efficient gridless angle estimation method of the bistatic MIMO radar under the planar array of the embodiment and the existing method.

[0080] Figure 4 It is a schematic diagram comparing the running time of the efficient gridless angle estimation method of the bistatic MIMO radar under the planar array of the embodiment and the existing method.

[0081] Figure 5 It is a schematic diagram illustrating the mean square error of the estimation performance of the efficient gridless angle estimation method for bistatic MIMO radar under planar array in an embodiment with different numbers of array elements.

[0082] Figure 6 It is a schematic diagram illustrating the running time of the estimation performance of different array element numbers of the efficient gridless angle estimation method for bistatic MIMO radar under planar array in an embodiment. DETAILED DESCRIPTION

[0083] The preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0084] Example

[0085] An efficient gridless angle estimation method for bistatic MIMO radar with planar arrays, such as Figure 1 , including the following steps,

[0086] S1. Establish a bistatic MIMO radar planar array structure: In step S1, establish a bistatic MIMO radar planar array structure, specifically, the transmitter and receiver in the bistatic MIMO radar system are respectively equipped with uniform planar arrays UPA, and the distances between them are relatively far. Select a set of integers N t 、M t 、N r 、M r ,like Figure 2 , the transmitter is equipped with K t =N t ×M t antennas, where N t and M t Respectively represent the number of array elements corresponding to the x-axis and y-axis. The receiver is equipped with K r =N r ×Mr antennas, of which N r and M r Respectively represent the number of array elements corresponding to the x-axis and y-axis to obtain the bistatic MIMO radar planar array structure.

[0087] S2, using the dual-base MIMO radar planar array structure established in step S1 to receive signals, and modeling the received signal x(t) collected by the receiver, specifically,

[0088] S21, Suppose there are L from Θ1, Θ2, ..., Θ l ,...,Θ L Direction far-field targets need to be located, where For the receiving array, define θ l and φ l are the angles between the lth target direction and the x-axis and y-axis relative to the receiver array, respectively. For the transmitting array, and ψ l are the angles between the lth target direction and the x-axis and y-axis relative to the transmitter array, respectively;

[0089] S22, using the bistatic MIMO radar planar array structure obtained in step S1, the transmitter transmits at a pulse repetition interval T PRI A pulse signal is sent to the target, and then the receiver receives the signal x(t), and the sent pulse waveforms are orthogonal to each other;

[0090] S23, the received signal x(t) collected by the receiver is modeled as:

[0091]

[0092] Among them, β l is the reflection coefficient of the lth target, s(t)=[s1(t),…,s L (t)] T is the transmitted signal, L represents the number of targets, n(t) is the noise vector received by the receiving array, and a r (θ l ,φ l ) represent the steering vectors of the lth target at the transmitter and receiver respectively, expressed as: Among them, b n (m)=[1,e jπsin(m) ,…,e jπ(n-1)sin(m) ] T , n represents {N t ,M t ,N r ,M r}, m represents the set Θ l one,[·] T represents the transpose operation, represents the Kronecker product.

[0093] S3, construct a matched filter and apply it to the received signal within a pulse repetition interval, thereby establishing the filtered array output data Y, specifically,

[0094] S31. At the receiver, each antenna uses a high-resolution ADC to sample the received waveform and obtain T PRI During the Q-long sampling data, Among them, T PRI represents the transmitter pulse repetition interval, Indicates rounding down, T s is the sampling interval, then the received signal during a pulse is modeled as:

[0095]

[0096] Where X = [x(0), x(T s ),…,x((Q-1)T s )],A r =[a r (θ1,φ1),…,a r (θ L ,φ L )], Σ is a diagonal matrix with diagonal elements [β1,…,β L ] T ,S=[s(0),s(T s ),…,s((Q-1)T s )], because the rows of S are orthogonal, SS H =I L , I L is the L×L identity matrix, N is the noise matrix;

[0097] S32, Application S H As a matched filter, the array output data Y after filtering is established as:

[0098]

[0099] Where X is the received signal within a pulse repetition interval, S is the transmitted signal matrix, and A r and A t denote the matrices formed by the steering vectors of the receiver and transmitter, respectively, N is the noise matrix, [·] H represents the conjugate transpose operation,

[0100] S4, construct an atomic set to establish an atomic norm minimization optimization problem and solve it, and reconstruct the secondary Toeplitz matrix;

[0101] S41. Construct an atomic set based on the atomic norm theory and define the atomic set as:

[0102]

[0103] in, represents a complex set, and a r (θ, φ) represent the steering vectors of any target at the transmitter and receiver, respectively;

[0104] S42. Based on the atomic set defined in step S41, the atomic norm of the matrix Z is:

[0105]

[0106] Among them, c l Represents the coefficient, A l Belongs to atomic set represents the atomic norm of Z;

[0107] S43. According to the definition of atomic norm, the following atomic norm minimization problem is proposed:

[0108]

[0109] S44. Since the atomic norm minimization problem in step S43 cannot be solved in polynomial time, it is converted into a solvable semidefinite programming SDP problem:

[0110]

[0111] in, and is a two-level Toeplitz Hermitian matrix in which the target angle is encoded. tr[·] represents the trace operation, and [·] ≥ 0 ensures that the reconstructed covariance matrix satisfies the semi-positive definite condition.

[0112]

[0113] t i (j) represents t i The j+Mth t elements, The elements r i (j) represents r i The j+Mth r elements, Rr =(2N r -1)(2M r -1), Z H represents the conjugate transpose of the matrix Z, and Y is the filtered array output data;

[0114] S45. Solve the trace minimization problem obtained in step S44 using the CVX tool or the improved alternating direction multiplier method ADMM to obtain the optimal solution. and In this way, the reconstructed secondary Toeplitz matrix is ​​obtained and

[0115] In step S45, the trace minimization problem obtained in step S44 is solved based on the improved alternating direction multiplier method ADMM, specifically,

[0116] S451, rewrite the optimization problem of step S44 into an optimization problem form that satisfies the ADMM algorithm:

[0117]

[0118] in, and is a secondary Toeplitz Hermitian matrix in which the target angle is encoded. tr[·] represents the trace operation. [·] ≥ 0 ensures that the reconstructed covariance matrix satisfies the semi-positive definite condition. Z H represents the conjugate transpose of the matrix Z, and Y is the filtered array output data;

[0119] S452, introduce the Lagrange multiplier matrix, and construct the augmented Lagrange function of the optimization problem in step S451:

[0120]

[0121] Where t and r represent the second-level Toeplitz matrix and Parameters, Y is the array output data after filtering, λ represents the penalty factor, ||·|| F represents the Frobenius norm. is the Lagrange multiplier matrix, U1, U2, U3 are the block matrices of U,

[0122] S453, the iterative update steps of the alternating direction multiplier method ADMM are:

[0123]

[0124] Among them, k and k+1 represent the number of iterations, t and r represent the secondary Toeplitz matrix and Parameters, Y is the array output data after filtering, Λ represents the multiplier matrix, λ represents the penalty factor,

[0125] S454, apply the Toeplitz matrix trace operation related derivative formula to realize the iterative formula, and use the augmented Lagrange function to differentiate the corresponding parameters to zero, and obtain the following parameter update criteria:

[0126]

[0127] Among them, k and k+1 represent the number of iterations, t and r represent the secondary Toeplitz matrix and Parameters, G t and G r is a diagonal matrix, The element g i =[g i (1-M r ),…,g i (0),…,g i (M r -1)], The element g i =[g i (1-M t ),…,g i (0),…,g i (M t -1)], Λ1 and Λ3 are block matrices of matrix Λ, and the specific relationship is U1, U2, and U3 are block matrices of U, and their specific relationship is λ represents the penalty factor, represents a zero vector, except that the middle element is 1, R r =(2N r -1)(2M r -1), express The adjoint operator of ;

[0128] S455, due to constraints That is, Z is projected onto a sphere with center Y and radius η, and the update formula of Z in step S454 is rewritten as:

[0129]

[0130] Among them, k and k+1 represent the number of iterations. Λ2 is the block matrix of matrix Λ, and the specific relationship is U2 is the block matrix of U, and the specific relationship is λ represents the penalty factor;

[0131] Under the constraint U≥0, the update criterion of U in step S453 is rewritten as:

[0132]

[0133] in, By This is achieved by setting all negative eigenvalues ​​of to zero;

[0134] S456: Obtain the optimal solution to the optimization problem in step S451 from steps S453 to S455 and In this way, the reconstructed secondary Toeplitz matrix is ​​obtained and

[0135] S5, perform gridless direction of arrival estimation based on the secondary Toeplitz matrix reconstructed in step S4 to obtain the receiving angle DOA and the transmitting angle DOD. Specifically,

[0136] S51, the secondary Toeplitz matrix obtained according to step S45 and It can be expressed as: in So is a diagonal matrix with diagonal elements, and They can be considered as ideal autocorrelation arrays of transmitter and receiver arrays respectively;

[0137] S52, in step S51 and Apply the matrix bundle plus pairing MaPP method to recover the information of L target angles The amount is Including angle of arrival and emission angle in, is {θ l ,φ l}, for and achieve the angle of arrival and emission angle Automatic pairing.

[0138] In step S52, the arrival angle is achieved and emission angle Specifically, the pairing process of arrival angle DOD and launch angle DOA estimation is given as:

[0139] in,

[0140] l=1,...,L

[0141] in, is {θ l ,φ l}, that is, the target’s arrival angle DOA, for The estimated value of the target launch angle DOD is represents the steering vector of the lth estimated target at the receiver, represents the steering vector at the transmitter for any estimated transmission angle DOD, [·] H is the conjugate transpose operation, [·] * is a conjugate operation, the specific form is: Among them, b n (m)=[1,e j πsin(m) ,…,e jπ(n-1)sin(m) ] T , n is {N t ,M t ,N r ,M r}, m is a set Θ l one, is the optimal solution of Z obtained in step S456, and L represents the target number.

[0142] This efficient gridless angle estimation method for bistatic MIMO radar under planar array does not require pre-estimation of angles, effectively avoids the influence of the array, ensures gridless DOA estimation, thereby improving the degree of freedom and resolution of estimation, and reducing the computational complexity of estimation to a certain extent. This method can break through the limitations of grid division, overcome model mismatch errors, obtain higher accuracy, and obtain efficient DOA estimation, while having lower computational complexity, and can be used for target positioning and target detection.

[0143] This efficient gridless angle estimation method for bistatic MIMO radar under planar array uses the ANM method to estimate the angle of bistatic MIMO radar with uniform planar array UPA, overcoming the shortcomings of the CS-based method. Compared with the ANM method based on uniform linear array ULA, the array is expanded to a planar array, and the target angle is expanded from 2-D space to 4-D space, enabling the radar to detect the full angle information of the target.

[0144] This efficient gridless angle estimation method for bistatic MIMO radar under planar array, a bistatic MIMO radar system equipped with UPA, obtains angle information without discretizing 4-D angle space, establishes a solvable SDP using ANM technology, avoids the modeling error of CS method, and uses gridless method to estimate the direction of arrival in continuous domain.

[0145] In order to accelerate the calculation, this efficient gridless angle estimation method for bistatic MIMO radar under planar array is derived by an iterative algorithm based on ADMM to achieve efficient and low-complexity array direction finding, and finally realizes efficient gridless angle estimation of bistatic MIMO radar under planar array. This method uses the alternating direction multiplier method ADMM to solve, overcomes the problem of low efficiency of large-scale array real-time positioning calculation, can obtain angle information in a non-discrete 4-D angle space, greatly reduce the amount of calculation, and achieve efficient wave direction estimation.

[0146] The effect of the efficient gridless angle estimation method of the bistatic MIMO radar under the planar array of the embodiment is further described below in conjunction with a simulation example.

[0147] Simulation experiment 1: Assume that there are two targets to be located and use 4×4 UPA for transmission and reception. 400 Monte Carlo runs were performed. The simulation results are shown in the figure below. Figure 3 As shown in Figure 2, due to the grid effect, the RMSEs of the three grid methods, MUSIC, OMP, and L1SVD, are all saturated ( Figure 3 The dashed line in the middle represents the lower limit of the gridding), and it can be seen that the CVX-based method 2D-DANM and the ADMM-based method 2D-DANM-ADMM proposed in the embodiment can break through this lower limit and decrease with the increase of the signal-to-noise ratio. Figure 4 It is shown that compared with the CVX-based method 2D-DANM, the implementation of the ADMM-based method 2D-DANM-ADMM can greatly reduce the running time, especially the running time of the ADMM-based method 2D-DANM-ADMM can be close to OMP.

[0148] Simulation experiment 2: Assuming that two targets are to be located, the size of the UPA varies from 3×3 to 5×5. In each Monte Carlo run, the size of the UPAs of the transmitter and receiver are the same. The simulation results are shown in Figure 5 As shown in Figure 2, the RMSEs of MUSIC, OMP, and L1SVD are all bounded by the grid interval. The CVX-based method 2D-DANM and the ADMM-based method 2D-DANM-ADMM proposed in the embodiment can break through this limitation and obtain better estimation accuracy in larger arrays. Simulation Results Figure 6 The running time is shown, and it can be seen that increasing the array size will increase the amount of calculation, but the CVX-based method 2D-DANM and the ADMM-based method 2D-DANM-ADMM of the embodiment still have high computational efficiency.

[0149] This efficient gridless angle estimation method for dual-base MIMO radar under planar array fully discovers the full angle information of the target, overcomes the grid effect, and uses the atomic norm minimization optimization method to establish a gridless model of the dual-base planar array. The angle estimation is obtained without discretizing the 4-D angle space, which increases the accuracy of the wave direction estimation. This efficient gridless angle estimation method for dual-base MIMO radar under planar array reduces the high computational complexity of large-scale arrays by adopting an alternating direction multiplier, which reflects economy and efficiency.

[0150] The above is only a preferred embodiment of the present invention, and does not limit the present invention in any form. Although the present invention has been discussed above with a preferred embodiment, it is not used to limit the present invention. Any technician familiar with the profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. An efficient gridless angle estimation method for bistatic MIMO radar in a planar array, characterized by: The following steps are included: S1. Establish a bistatic MIMO radar planar array structure. Specifically, the transmitter and receiver in the bistatic MIMO radar system are equipped with a uniform planar array UPA, and the transmitter is equipped with a K t =N t ×M t antennas, where N t and M t Respectively represent the number of array elements corresponding to the x-axis and y-axis. The receiver is equipped with K r =N r ×M r antennas, of which N r and M r Denote the number of array elements corresponding to the x-axis and the y-axis respectively, to obtain the bistatic MIMO radar planar array structure; S2, using the dual-base MIMO radar planar array structure established in step S1 to receive signals, and modeling the received signal x(t) collected by the receiver; specifically, S21, Suppose there are L from Θ1, Θ2, ..., Θ l ,...,Θ L Direction far-field targets need to be located, where For the receiving array, define θ l and φ l are the angles between the lth target direction and the x-axis and y-axis relative to the receiver array, respectively. For the transmitting array, and ψ l are the angles between the lth target direction and the x-axis and y-axis relative to the transmitter array, respectively; S22, using the bistatic MIMO radar planar array structure obtained in step S1, the transmitter transmits at a pulse repetition interval T PRI A pulse signal is sent to the target, and then the receiver receives the signal x(t), and the sent pulse waveforms are orthogonal to each other; S23, the received signal x(t) collected by the receiver is modeled as: Among them, β l is the reflection coefficient of the lth target, s(t)=[s1(t),…,s L (t)] T is the transmitted signal, L is the number of targets, n(t) is the noise vector received by the receiving array, and a r (θ l ,φ l ) represent the steering vectors of the lth target at the transmitter and receiver respectively, expressed as: Among them, b n (m)=[1,e jπsin(m) ,…,e jπ(n-1)sin(m) ] T , n is {N t ,M t ,N r ,M r }, m is a set Θ l one,[·] T is the transpose operation, represents the Kronecker product; S3, construct a matched filter and apply it to the received signal X within a pulse repetition interval, thereby establishing the filtered array output data Y; S4, construct an atomic set to establish an atomic norm minimization optimization problem and solve it, and reconstruct the secondary Toeplitz matrix; S5. Perform gridless direction of arrival estimation according to the secondary Toeplitz matrix reconstructed in step S4 to obtain the receiving angle DOA and the transmitting angle DOD.

2. The efficient gridless angle estimation method for bistatic MIMO radar under planar array as claimed in claim 1, characterized in that: In step S3, a matched filter is constructed and applied to a received signal within a pulse repetition interval, thereby establishing the filtered array output data Y, specifically, S31. At the receiver, each antenna uses a high-resolution ADC to sample the received waveform and obtain the transmitter pulse repetition interval T PRI During the Q-long sampling data, in Indicates rounding down, T s is the sampling interval, then the received signal during a pulse is modeled as: Where X = [x(0), x(T s ),…,x((Q-1)T s )],A r =[a r (θ1,φ1),…,a r (θ L ,φ L )], Σ is a diagonal matrix with diagonal elements [β1,…,β L ] T ,S=[s(0),s(T s ),…,s((Q-1)T s )], because the rows of S are orthogonal, SS H =I L , I L is the L×L identity matrix, N is the noise matrix; S32, Application S H As a matched filter, the array output data Y after filtering is established as: Where X is the received signal within a pulse repetition interval, S is the transmitted signal matrix, and A r and A t denote the matrices formed by the steering vectors of the receiver and transmitter, respectively, N is the noise matrix, [·] H represents the conjugate transpose operation, 3. The efficient gridless angle estimation method for bistatic MIMO radar under planar array as claimed in claim 2, characterized in that: In step S4, an atom set is constructed to establish an atom norm minimization optimization problem, specifically, S41. Construct an atomic set based on the atomic norm theory and define the atomic set as: in, represents a complex set, and a r (θ, φ) represent the steering vectors of any target at the transmitter and receiver, respectively; S42. Based on the atomic set defined in step S41, the atomic norm of the matrix Z is: Among them, c l Represents the coefficient, A l Belongs to atomic set represents the atomic norm of Z; S43. According to the definition of atomic norm, the following atomic norm minimization problem is proposed: where η is the threshold constant, which depends on the noise; ||·|| F represents the Frobenius norm; S44. Since the atomic norm minimization problem in step S43 cannot be solved in polynomial time, it is converted into a solvable semidefinite programming SDP problem: in, and is a secondary Toeplitz Hermitian matrix in which the target angle is encoded. tr[·] represents the trace operation. [·] ≥ 0 ensures that the reconstructed covariance matrix satisfies the semi-positive definite condition. , t i (j) represents t i The j+Mth t elements, , where the elements r i (j) represents r i The j+Mth r elements, R r =(2N r -1)(2M r -1), Z H represents the conjugate transpose of the matrix Z, and Y is the filtered array output data; S45. Solve the trace minimization problem obtained in step S44 using the CVX tool or the improved alternating direction multiplier method ADMM to obtain the optimal solution. and In this way, the reconstructed secondary Toeplitz matrix is ​​obtained and 4. The efficient gridless angle estimation method for bistatic MIMO radar under planar array as claimed in claim 3, characterized in that: In step S45, the trace minimization problem obtained in step S44 is solved based on the improved alternating direction multiplier method ADMM, specifically, S451, rewrite the optimization problem in step S44 into an optimization problem form that satisfies the ADMM algorithm: in, and is a secondary Toeplitz Hermitian matrix in which the target angle is encoded. tr[·] represents the trace operation. [·] ≥ 0 ensures that the reconstructed covariance matrix satisfies the semi-positive definite condition. Z H represents the conjugate transpose of the matrix Z, and Y is the filtered array output data; S452, introduce the Lagrange multiplier matrix, and construct the augmented Lagrange function of the optimization problem in step S451: Where t and r represent the second-level Toeplitz matrix and Parameters, Y is the array output data after filtering, λ represents the penalty factor, ||·|| F represents the Frobenius norm, is the Lagrange multiplier matrix, U1, U2, U3 are the block matrices of U, S453, the iterative update steps of the alternating direction multiplier method ADMM are: Among them, k and k+1 represent the number of iterations, t and r represent the secondary Toeplitz matrix and Parameters, Y is the array output data after filtering, Λ represents the multiplier matrix, λ represents the penalty factor, S454, the iterative formula is implemented by applying the Toeplitz matrix trace operation derivative formula, and the corresponding parameters are derived to zero using the augmented Lagrange function, and the following parameter update criteria are obtained: Among them, k and k+1 represent the number of iterations, t and r represent the secondary Toeplitz matrix and Parameters, G t and G r is a diagonal matrix, The element g i =[g i (1-M r ),…,g i (0),…,g i (M r -1)], The element g i =[g i (1-M t ),…,g i (0),…,g i (M t -1)], Λ1 and Λ3 are block matrices of matrix Λ, and the specific relationship is U1, U2, and U3 are block matrices of U, and their specific relationship is λ represents the penalty factor, represents a zero vector, except that the middle element is 1, R r =(2N r -1)(2M r -1), express The adjoint operator of ; S455, due to constraints That is, Z is projected onto a sphere with center Y and radius η, and the update formula of Z in step S454 is rewritten as: Among them, k and k+1 represent the number of iterations. Λ2 is the block matrix of matrix Λ, and the specific relationship is U2 is the block matrix of U, and the specific relationship is λ represents the penalty factor; Under the constraint U≥0, the update criterion of U in step S453 is rewritten as: in, By This is achieved by setting all negative eigenvalues ​​of to zero; S456: Obtain the optimal solution to the optimization problem in step S451 from steps S453 to S455 and In this way, the reconstructed secondary Toeplitz matrix is ​​obtained and 5. The efficient gridless angle estimation method for bistatic MIMO radar under planar array as claimed in claim 3 or 4, characterized in that: In step S5, the gridless direction of arrival is estimated according to the secondary Toeplitz matrix reconstructed in step S4 to obtain the receiving angle DOA and the transmitting angle DOD, specifically: S51, the secondary Toeplitz matrix obtained according to step S45 and It is expressed as: in So is a diagonal matrix with diagonal elements, and are considered as ideal autocorrelation arrays of transmitter array and receiver array respectively; S52, in step S51 and Apply the matrix bundle plus pairing MaPP method to recover the information of L target angles The amount is Including angle of arrival and emission angle in, is {θ l ,φ l }, for and achieve the angle of arrival and emission angle Automatic pairing.

6. The efficient gridless angle estimation method for bistatic MIMO radar under planar array as claimed in claim 5, characterized in that: In step S52, the arrival angle is achieved and emission angle Specifically, the pairing process of arrival angle DOD and launch angle DOA estimation is given as: in, l＝1,...,L in, is {θ l ,φ l }, that is, the target’s arrival angle DOA, for The estimated value of the target launch angle DOD is represents the steering vector of the lth estimated target at the receiver, represents the steering vector at the transmitter for any estimated transmission angle DOD, [·] H is the conjugate transpose operation, [·] * is a conjugate operation, the specific form is: Among them, b n (m)=[1,e jπsin(m) ,…,e jπ(n-1)sin(m) ] T , n is {N t ,M t ,N r ,M r }, m is a set Θ l one, is the optimal solution of Z obtained in step S456, and L represents the target number.

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