A High-Precision Joint Estimation Method for Multiple Parameters in Bistatic MIMO Radar

Abstract

The present invention relates to a high-precision multi-parameter joint estimation method in a multiple-input multiple-output (MIMO) radar system. It mainly solves the problem of target positioning in the case where the transmitting and receiving antenna arrays are not fully calibrated, that is, there are multi-slot gain and phase errors. The implementation steps are as follows: 1) Construct a baseband received signal model of angles and multi-slot gain and phase errors in the form of a multi-dimensional matrix; 2) Use the least squares Khatri-Rao factorization algorithm to obtain a mixed matrix containing angle information and a combined gain and phase error matrix; 3) For target angle estimation, an iterative algorithm combining spatial smoothing and real-valued processing is proposed; 4) Estimate the transmitting and receiving gain and phase errors in the first time slot to eliminate the scale ambiguity of the multi-slot combined gain and phase errors; 5) Use the least squares Khatri-Rao factorization algorithm to jointly estimate the multi-slot transmitting and receiving gain and phase errors. The present invention considers the situation where the transmitting and receiving antenna arrays have multi-slot gain and phase errors, can perform joint estimation of multiple parameters, and the proposed angle algorithm improves the positioning accuracy and is applicable to both coherent and non-coherent target cases.

Description

Technical Field

[0001] The present invention belongs to the technical field of bistatic MIMO radar positioning, and particularly relates to a high-precision multi-parameter joint estimation method in a bistatic MIMO radar. Background Art

[0002] As an emerging radar system, the main features of a multiple-input multiple-output (MIMO) radar are high spatial resolution and flexible waveform design, and large-scale independent antennas are used on both the transmitting and receiving arrays. Generally, MIMO radars can be divided into two types, namely distributed MIMO radars and centralized MIMO radars. The transmitting antenna array in a distributed MIMO radar is arranged sparsely, so the target position can be captured from different angles to form spatial diversity. A centralized MIMO radar is one in which the transmitting and receiving antennas are both concentrated and distributed in a small space, and the channel path characteristics of each antenna are similar. Coherent processing can be used to estimate the parameters of interest, and a narrow receiving beam can be generated at the receiving array to more accurately achieve target positioning. The bistatic MIMO radar studied in the present invention belongs to a centralized MIMO radar.

[0003] Estimating the direction of departure (DOD) and direction of arrival (DOA) of a positioning target is a relatively important issue in a bistatic MIMO radar, including techniques such as estimation of signal parameters via rotational invariance techniques (ESPRIT) based on two-dimensional matrices, multiple signal classification (MUSIC), etc., parallel factor (PARAFAC) decomposition and high-order singular value decomposition (HOSVD) based on multi-dimensional matrices. Compared with the estimation algorithms based on two-dimensional matrices, the estimation algorithms based on multi-dimensional matrices can better utilize the multi-dimensional structure of the received data, thereby improving the positioning accuracy and having a better positioning effect, especially in the case of low sampling and low signal-to-noise ratio (SNR). However, most of the algorithms mentioned above limit the angle estimation to an ideal scenario, such as no gain-phase errors in both the transmitting and receiving arrays. However, the gain-phase error is an important factor affecting the angle estimation performance of an actual radar system, that is, without calibrating the antenna array, the transmitting array and the receiving array will be coupled to each other, resulting in a serious degradation of the positioning accuracy.

[0004] In the case where the transmitting and receiving arrays contain gain-phase errors, a joint scheme for angle and gain-phase error estimation based on PARAFAC decomposition has been proposed in the literature. This scheme obtains the gain-phase error vector by using Lagrange multipliers, estimates the angle after eliminating the gain-phase error, and can achieve automatic pairing of angles. However, it will cause the accumulation of gain-phase errors and affect the angle estimation result. Some studies have shown that the gain-phase error can be estimated by using the relationship between any two different target steering vectors, and relatively good DOD and DOA can be obtained. However, this method is only suitable for the case where the antenna array contains single-slot gain-phase errors and requires at least two well-calibrated transmitting and receiving array elements. Summary of the Invention

[0005] Object of the Invention: In view of the deficiencies of the prior art, the present invention proposes a high-precision multi-parameter joint estimation method in a bistatic MIMO radar to achieve high-precision positioning of targets.

[0006] Technical Solution: A high-precision multi-parameter joint estimation method in a bistatic MIMO radar according to the present invention includes:

[0007] Construct a baseband received signal model of angles and multi-slot gain-phase errors in the form of a multi-dimensional matrix;

[0008] Use the least squares Khatri-Rao factorization algorithm to obtain a mixing matrix containing angle information and a combined gain-phase error matrix;

[0009] For target angle estimation, an iterative algorithm combining spatial smoothing and real-valued processing is proposed;

[0010] Estimate the transmitting and receiving gain-phase errors in the first slot to eliminate the scale ambiguity of the multi-slot combined gain-phase error;

[0011] Use the least squares Khatri-Rao factorization algorithm to jointly estimate the multi-slot transmitting and receiving gain-phase errors.

[0012] Further, constructing a baseband received signal model of angles and multi-slot gain-phase errors in the form of a multi-dimensional matrix specifically includes:

[0013] The present invention considers a bistatic MIMO radar system with M transmitting antennas and N receiving antennas. Both the transmitting and receiving antenna arrays are uniform linear arrays (ULA). It is assumed that both the transmitting and receiving antenna arrays contain multi-slot gain-phase errors. The baseband signal received by the system at the q-th pulse in the p-th slot, where p ∈ {1, 2,..., P} and q ∈ {1, 2,..., Q}, is constructed. That is

[0014]

[0015] Among them, is an orthogonal waveform matrix and satisfies (1 / L)SS Η = I M , is the identity matrix, (·) Η represents conjugate transpose, L represents the number of sampling points per pulse, and respectively represent the multi-slot receiving gain phase error matrix and the receiving steering matrix, and respectively represent the multi-slot transmitting gain phase error matrix and the transmitting steering matrix, represents the signal feature matrix containing the target reflection coefficient and Doppler frequency shift, D i (A) represents the diagonal matrix formed by the i-th row of matrix A, A ∈ {Γ PR , Γ PT , B}, (·) Τ represents transpose, represents the corresponding additive white Gaussian noise.

[0016] X p,q After multiple vectorizations and stackings, it can be constructed into a three-dimensional matrix model That is

[0017]

[0018] Among them, is the identity tensor, is the combined gain phase error matrix, is the mixing matrix containing angle information, which can form a three-dimensional matrix ⊙ and respectively represent the Khatri-Rao product and the Kronecker product.

[0019] Construct the modulus-1 matrix expansion form of the three-dimensional matrix :

[0020]

[0021] Furthermore, using the least squares Khatri-Rao factorization algorithm, the mixing matrix containing angle information and the combined gain phase error matrix are obtained, specifically including:

[0022] For using the pseudo-inverse and transpose operations, H⊙Γ PTR is obtained, and the r-th column of H⊙Γ PTR with r ∈ {1, 2, …, MN} is matrixized to obtain According to the property of Khatri-Rao factorization, it is known that Gr is a rank-1 matrix, that is

[0023]

[0024] where represents the outer product.

[0025] According to the properties of the rank-1 matrix, the mixed estimation matrix containing angle information and the combined gain phase error estimation matrix can be obtained through the left singular value matrix U r and the right singular value matrix V (r) in the SVD of G (r) That is

[0026]

[0027] where and represent the first column elements of U (r) and V (r) respectively, represents the first element of the eigenvalue matrix Σ (r) , (·) * represents the conjugate.

[0028] Furthermore, for target angle estimation, an iterative algorithm combining spatial smoothing and real-valued processing is proposed, specifically including:

[0029] Apply spatial smoothing operation to the three-dimensional matrix containing angle information to obtain the spatially smoothed three-dimensional matrix

[0030]

[0031] where L1 is the number of subarrays, and M sub is the number of array elements contained in each subarray, satisfying M sub = M - L1 + 1, and represent taking the first M T rows and the first L1 rows of the transmit steering matrix A sub respectively, and A R , and are three steering matrices.

[0032] Construct a new three-dimensional matrix That is

[0033]

[0034] ​Among them, Π N is a swap matrix, with elements on its anti-diagonal being 1 and the rest being 0.

[0035] Apply pre- and post-smoothing operations to to obtain the central Hermitian three-dimensional matrix Perform a unitary transformation to obtain a real-valued three-dimensional matrix

[0036] For perform a trilinear alternating least squares (TALS) decomposition, that is, represent the solution of the real-valued estimated steering matrix as three least squares (LS) problems, namely

[0037]

[0038]

[0039]

[0040] Among them, and respectively represent 's modulus-1, modulus-2, and modulus-3 expansion matrices, and are respectively 's three real-valued steering matrices, ||·|| F represents the Frobenius norm.

[0041] The TALS algorithm iteratively updates the estimates of the three steering matrices, namely

[0042]

[0043]

[0044]

[0045] Among them, and are respectively and 's estimates, represents the pseudo-inverse.

[0046] Utilize the rotational invariance of the steering matrix to restore the relevant information of the target angle, namely

[0047]

[0048] where K A,1 、K A,2 、K A,3 and K A,4is the rotation matrix, denotes taking the k-th column element of, where k ∈ {1, 2, …, K}, denotes taking the k-th column element of.

[0049] The DOD and DOA of the k-th estimated target are obtained by the following formula:

[0050]

[0051] Furthermore, estimate the transmit and receive gain-phase errors in the first time slot to eliminate the scale ambiguity of the multi-time slot combined gain-phase error, specifically including:

[0052] Utilize the orthogonality of the transmission waveform S to construct the baseband received signal Y with gain-phase errors in the first time slot 1,q :

[0053]

[0054] where and respectively represent the diagonal matrices composed of the gain-phase errors of the transmit and receive arrays in the first time slot, m and n are the well-calibrated number of array elements added at the transmitter and receiver ends in the first time slot, and diag(·) represents the diagonalization operation.

[0055] Let A TT = D1(Γ PT )A T , A RR = D1(Γ PR )A R , vectorize and stack Y 1,q to obtain the three-dimensional matrix model of the received signal Y 1,q That is i.e.,

[0056]

[0057] Perform TALS decomposition on to obtain the three estimated steering matrices of and

[0058] Since the gain-phase errors included in the steering vectors of different targets are the same, taking the receive steering vector as an example, randomly select two different target steering vectors in the receive steering matrix, i.e., target i, j ∈ {1, 2, …, K}, and i ≠ j, and construct the following formula:

[0059] ​

[0060] where. / represents element-wise division at the corresponding positions, and.× represents element-wise multiplication at the corresponding positions.

[0061] The received gain error vector of the first time slot estimation is:

[0062]

[0063] Using the obtained The same method can be used to obtain the transmitted gain error vector of the first time slot estimation

[0064] Find the well-calibrated steering vector in the receiving array That is

[0065]

[0066] Take the phase using the phase(·) function to get That is

[0067]

[0068] For Using the LS algorithm, the least squares solution ω k , the DOA of the k-th target is obtained through the following formula:

[0069]

[0070] where represents the second element of the vector . Similarly, the DOD is obtained.

[0071] Use the phase(·) function to find the phase of the received steering vector of the k-th target and the phase of the well-calibrated received steering vector and the phase of

[0072] The received phase error of the first time slot estimation of the k-th target can be obtained by taking the difference. Similarly, the transmitted phase error of the first time slot estimation is obtained

[0073] Furthermore, the least squares Khatri-Rao factorization algorithm is used to jointly estimate the multi-time slot transmitted and received gain phase errors, specifically including:

[0074] Transpose Γ PTR to get Take its p-th column where p ∈ {1, 2,..., P}, that is Matrixizing it gives

[0075] Using SVD, that is the estimated values of the multi-slot transmit gain phase error matrix Γ PT and the receive gain phase error matrix Γ PR can be obtained respectively, that is

[0076]

[0077] where and represent the first column elements of U (p) and V (p) respectively, represents the first element of the eigenvalue matrix Σ (p) respectively.

[0078] Beneficial effects: Compared with the prior art, its main advantages are as follows: The present invention can estimate the angles of targets and the existing multi-slot gain phase errors in a bistatic MIMO radar. The proposed angle decomposition method can obtain higher positioning accuracy through spatial smoothing and unitary transformation processing based on forward and backward smoothing. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 is the flowchart of the angle and multi-slot gain phase error estimation for the bistatic MIMO radar of the present invention;

[0080] Figure 2 is the schematic diagram of the target positioning structure of the bistatic MIMO radar of the present invention;

[0081] Figure 3 is the comparison diagram of the root mean square error (RMSE) performance of the angle estimation between the present invention and the existing MUSIC method and the existing unitary HOSVD method in the case of two coherent targets among three targets;

[0082] Figure 4 is the comparison diagram of the RMSE performance of the angle estimation between the present invention and the existing PARAFAC method in the case of non-coherent targets;

[0083] Figure 5 is the comparison diagram of the RMSE performance of the multi-slot transmit gain phase error with different numbers of well-calibrated array elements in the first slot transmit array in the case of non-coherent targets;

[0084] Figure 6 is the comparison diagram of the RMSE performance of the multi-slot receive gain phase error with different numbers of well-calibrated array elements in the first slot receive array in the case of non-coherent targets. DETAILED DESCRIPTION OF THE INVENTION

[0085] To make the features and advantages of the present invention more obvious and understandable, the present invention will be described in detail below with reference to the accompanying drawings.

[0086] Figure 2 It is a schematic diagram of the target positioning structure of a bistatic MIMO radar. As shown in Figure 2 the bistatic MIMO radar positioning system shown, where the number of transmitting antennas is M, the number of receiving antennas is N, the transmitting array antennas transmit mutually orthogonal signals, and positioning is achieved by estimating the DOD and DOA of the target.

[0087] Embodiment 1

[0088] Please refer to Figure 3 , Figure 3 which is a comparison chart of the RMSE performance of angle estimation between the proposed method and the existing MUSIC method and the existing unitary HOSVD method when there are two coherent targets among three targets in the present invention. The system parameters are: K = 3, P = 4, Q = 100, and the attenuation coefficients of the last two coherent targets are ε = [0.9e j1.1π , 0.8e j0.75π . As the SNR increases, the RMSE performance of angle estimation of the proposed method is better than that of the existing MUSIC method and the existing unitary HOSVD method because the proposed method applies spatial smoothing and unitary transformation processing based on forward and backward smoothing, thereby increasing the number of sampling points of the system and improving the performance of angle estimation.

[0089] Embodiment 2

[0090] Please refer to Figure 4 , Figure 4 which is a comparison chart of the RMSE performance of angle estimation between the proposed method and the existing PARAFAC method in the case of non-coherent targets in the present invention. The system parameters are: M = 8, N = 6, L1 = 3, M sub = 6, P = 4, m = n = 2. Figure 4 It shows that the proposed method is better than the existing PARAFAC method in terms of angle estimation performance because the proposed method can use all array elements for angle measurement, thereby improving the angle measurement accuracy, while the existing PARAFAC method can only use the first two well-calibrated array elements for angle measurement, and there will be obvious errors in the estimated angles.

[0091] Embodiment 3

[0092] Please refer to Figure 5 , Figure 5 which is a comparison chart of the RMSE performance of the gain phase error of multi-slot transmission in the case of non-coherent targets in the present invention when the number of well-calibrated array elements in the transmitting array of the first slot is different. The system parameters are: M = 8, N = 6, K = 3, L1 = 3, M sub= 6, Q = 100, P = 6. Figure 5 It shows that as the number m of well-calibrated array elements in the transmitting array in the first time slot increases, the performance of the estimated multi-time-slot transmitting gain phase error of the proposed method becomes better and better. This is because the increase in m will make the estimated transmitting gain phase error in the first time slot more accurate, which can better eliminate the scale ambiguity of the multi-time-slot combined gain phase error and improve the estimation accuracy of the multi-time-slot transmitting gain phase error.

[0093] Embodiment 4

[0094] Please refer to Figure 6 , Figure 6 which is a comparison graph of the RMSE performance of the multi-time-slot receiving gain phase error when the number of well-calibrated array elements in the receiving array in the first time slot is different in the case of non-coherent targets for the present invention. System parameters are: M = 8, N = 6, K = 3, L1 = 3, M sub = 6, Q = 100, P = 6. Figure 6 It shows that as the number n of well-calibrated array elements in the receiving array in the first time slot increases, the performance of the estimated multi-time-slot receiving array gain phase error of the proposed method becomes better. As n increases, the estimated receiving array gain phase error in the first time slot is more accurate, so the estimated multi-time-slot receiving gain phase error will be better.

[0095] In summary, the present invention is applicable to the joint estimation of angles and multi-time-slot gain phase errors in a bistatic MIMO radar system. Through the least squares Khatri-Rao factorization algorithm, a hybrid matrix containing angle information and a combined gain phase error matrix can be obtained simultaneously. The iterative algorithm using spatial smoothing and real-valued processing can obtain high-precision DOD and DOA, and at the same time, the multi-time-slot transmitting gain phase error and receiving gain phase error can be accurately estimated.

[0096] The description of the above embodiments is only to help understand the method and its main idea of the present invention. The content of this specification cannot be used to limit the scope of the rights of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.

Claims

1. A high-precision joint estimation method for multiple parameters in bistatic MIMO radar, characterized in that The method includes: Construct a baseband received signal model for the angle and multi-time slot gain phase error in the form of a multi-dimensional matrix, specifically including: setting and represent the transmit and receive steering matrices respectively, and represent the multi-time slot transmit and receive gain phase error matrices respectively, represents the signal feature matrix, is the orthogonal waveform matrix, and construct a three-dimensional matrix model of the baseband received signal as where is the identity tensor, is the combined gain phase error matrix, is the mixing matrix containing angle information, which can form a three-dimensional matrix ⊙ and represent the Khatri-Rao product and the Kronecker product respectively, (·) Τ represents the transpose; Using the least squares Khatri-Rao factorization algorithm, a mixing matrix containing angle information and a combined gain phase error matrix are obtained, specifically including: For Using the pseudo-inverse and transpose operations, obtain \(H\odot\Gamma\) PTR , and vectorize the \(r\in\{1,2,\ldots,MN\}\)-th column of \(H\odot\Gamma\) PTR to obtain According to the properties of Khatri-Rao factorization, it can be known that \(G\) r is a rank-1 matrix, that is Among them represents the outer product. According to the properties of rank-1 matrices, the mixing matrix H containing angle information and the combined gain phase error matrix Γ PTR can be obtained through r the left singular value matrix U (r) and the right singular value matrix V (r) in the SVD of G, that is Among them, and respectively represent the first column elements of U (r) and V (r) , represents the first element of the eigenvalue matrix Σ (r) , (·) * represents conjugation; For target angle estimation, an iterative algorithm combining spatial smoothing and real-valued processing is proposed, specifically including: a three-dimensional matrix containing angle information Apply spatial smoothing operation to obtain a spatially smoothed three-dimensional matrix Among them, L1 is the number of sub-arrays, and M sub is the number of array elements included in each sub-array, satisfying M sub = M - L1 + 1, and respectively represent taking the first M sub rows and the first L1 rows of the transmit steering matrix, and define a new three-dimensional matrix Among them, ∏ N is a switching matrix, with elements on its anti-diagonal being 1 and the rest being 0. By using the front and back smoothing operations, a central Hermitian three-dimensional matrix is derived. Using a unitary matrix, a real-valued three-dimensional matrix is obtained. With the help of the TALS algorithm for decomposition, an estimated steering matrix and can be obtained. By using the rotational invariance of the steering matrix to restore the relevant information of the target angle, φ t,k and φ r,k are obtained: where K A,1 , K A,2 , K A,3 and K A,4 are rotation matrices, denotes taking the k-th column element with k ∈ {1, 2, …, K}, denotes taking the k-th column element, denotes the pseudo-inverse. Finally, the DOD and DOA of the k-th target are obtained through the following formula: Estimate the transmit and receive gain phase errors of the first time slot to eliminate the scale ambiguity of the multi-time slot combined gain phase error, specifically including: constructing a three-dimensional matrix of the baseband received signal containing gain phase errors in the first time slot Among them, D1(Γ PT ) and D1(Γ PR ) respectively represent the diagonal matrices composed of the gain-phase errors of the transmitting and receiving arrays in the first time slot. The number of well-calibrated array elements m and n are added to the transmitting and receiving ends in the first time slot, and the estimated steering matrices of A RR , A TT and B are obtained by using the TALS algorithm and In the case of a single time slot, since the gain-phase errors included in the steering vectors of different targets are the same, two different target steering vectors can be randomly selected from the receiving steering matrix, that is, the targets i, e ∈ {1, 2, …, K}, and i ≠ e, and the following equations are respectively constructed: where. / represents element-wise division at the corresponding positions, and.× represents element-wise multiplication at the corresponding positions. Since and have the same phase and different amplitudes, the received gain error vector for the first time slot estimation can be obtained according to the following formula: In the same way, the transmit gain error vector of the first time slot estimation can be obtained Since the accurately calibrated array elements are respectively included in the transmit and receive arrays, the accurately calibrated array elements can be used for DOD and DOA estimation. The well-calibrated array elements are expressed as: Take phase, i.e., By using the LS algorithm, the DOA of the k-th target is obtained, and the receiving steering vector is obtained by using the phase(·) function respectively and the well-calibrated receiving steering vector phase and At this time, the estimated receiving phase error in the first time slot can be estimated by the difference between the two phases. Similarly, the estimated transmitting phase error in the first time slot can be obtained Jointly estimate the multi-slot transmit and receive gain phase errors using the least squares Khatri-Rao factorization algorithm, specifically including: Let Γ PTR be transposed to get Take its p-th column where p ∈ {1, 2, …, P}, that is Matrixize it to obtain Using SVD, that is where (·) Η denotes the conjugate transpose, and the estimated values of the multi-slot transmit gain phase error matrix Γ PT and the receive gain phase error matrix Γ PR can be obtained respectively, that is Among them, and respectively represent the first column elements of U (p) and V (p) , and represents the first element of the eigenvalue matrix Σ (p) .

Images