A Tensor-Based Angle Estimation Method in Bistatic MIMO Radar

Abstract

The present invention relates to a tensor-based angle estimation method in bistatic MIMO radar, mainly solving the problem of target positioning in the case of multi-time-slot amplitude-phase errors in the antenna array. The implementation steps are as follows: 1) Construct a baseband received signal tensor model containing multi-time-slot amplitude-phase errors; 2) Use the singular value decomposition (SVD) algorithm to separate the baseband received signal in the ideal state from the baseband received signal containing multi-time-slot amplitude-phase errors; 3) Perform spatial smoothing and real-valued processing on the baseband received signal in the ideal state; 4) Use the HOSVD algorithm for the real-valued ideal baseband received signal to obtain the DOD and DOA of the target under the condition of amplitude-phase errors. The present invention can obtain the angle estimation of the target in the case of multi-time-slot amplitude-phase errors in the transmitting and receiving arrays, and the present invention does not involve iteration, reduces the complexity, and is applicable to both coherent and non-coherent target cases.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar target positioning, and particularly aims at a tensor-based angle estimation method in a bistatic MIMO radar. Background Art

[0002] Multiple-input multiple-output (MIMO) radar can make full use of the waveform diversity gain and spatial diversity gain of signals, and has greater advantages compared with traditional phased array radars. It greatly improves the performance of radar in terms of degrees of freedom, spatial resolution, and target detection. Bistatic MIMO radar can effectively estimate the direction of departure (DOD) and direction of arrival (DOA) of target waves by using the direction correlation between the transmitted and received array signals.

[0003] In recent years, many algorithms for angle estimation of bistatic MIMO radar have emerged. Among them, the classical ones include the multiple signal classification (MUSIC) algorithm, the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, and the propagator method (PM), etc. Later, in order to utilize the multi-dimensional structure of the received signals, the tensor-based parallel factor (PARAFAC) algorithm and the high-order singular value decomposition (HOSVD) algorithm were proposed. Although a tensor is a high-dimensional extension of vectors and matrices, it has a multi-dimensional structure unique to multi-dimensional data and has strong noise suppression ability. Therefore, it can further improve the accuracy of estimating targets. However, most of the current algorithms are applicable to ideal environments. For example, both the transmitting and receiving arrays are well-calibrated. However, the amplitude-phase error of the antenna array is a problem that cannot be ignored. The amplitude-phase error in the transmitting and receiving arrays will affect the angle estimation accuracy and thus affect the target positioning effect.

[0004] At present, many literatures have introduced how to correct the amplitude-phase error of traditional antenna arrays. Some literature has proposed the ESPRIT-like algorithm, which mainly estimates DOD and DOA by using the instrument sensor method (ISM). However, it requires eigenvalue decomposition, has a relatively large amount of calculation, and the angles cannot be automatically paired. Some literature has proposed an angle estimation algorithm that can eliminate the amplitude-phase error, which uses the fact that the steering vectors of any two different targets have the same amplitude-phase error to eliminate interference. However, this method does not consider the situation where the amplitude-phase error of the antenna array changes with time slots, and requires well-calibrated transmitting and receiving antennas. Summary of the Invention

[0005] Object of the Invention: Aiming at the deficiencies of the prior art, the present invention proposes a tensor-based angle estimation method in a bistatic MIMO radar in the case where the antenna array contains amplitude-phase errors in multiple time slots to obtain the specific position of the target.

[0006] Technical Solution: A tensor-based angle estimation method in the bistatic MIMO radar described in the present invention includes:

[0007] Construct a baseband received signal tensor model containing multi-slot amplitude and phase errors;

[0008] Using the Singular Value Decomposition (SVD) algorithm, separate the baseband received signal in the ideal state from the baseband received signal containing multi-slot amplitude and phase errors;

[0009] Perform spatial smoothing and real-valued processing on the baseband received signal in the ideal state;

[0010] The real-valued ideal baseband received signal uses the HOSVD algorithm to obtain the DOD and DOA of the target under the condition of amplitude and phase errors.

[0011] Furthermore, constructing a baseband received signal tensor model containing multi-slot amplitude and phase errors specifically includes:

[0012] Suppose there are M transmitting antennas and N receiving antennas with a uniform linear distribution in a bistatic MIMO radar system, and there are K targets in the range of interest. Then the baseband signal received by the system at the p-th slot (p ∈ {1, 2, …, P}) and the q-th pulse (q ∈ {1, 2, …, Q}) is:

[0013]

[0014] where and respectively represent the transmitting steering matrix and the receiving steering matrix containing amplitude and phase errors, and respectively represent the transmitting and receiving array steering matrices in the ideal state, and respectively represent the transmitting and receiving amplitude and phase error matrices in P slots, represents the signal feature matrix containing the target reflection coefficient and Doppler frequency shift, and diag(a) represents the diagonal matrix formed by the vector a, (·) T represents the transpose operation, is the waveform matrix where the transmitted signals are orthogonal to each other, and (1 / L)SS Η = I M , L is the number of samples in each pulse period, (·) Η represents the conjugate transpose operation, I M is the identity matrix of size M×M, W p,q represents additive white Gaussian noise, which follows a Gaussian distribution with a mean of 0 and a variance of σ 2 .

[0015] Vectorize Y p,q and stack it along the dimension of the time slot. Without considering noise, Yq :

[0016]

[0017] Among them, is the combined amplitude-phase error matrix, denotes the Kronecker product, and ⊙ denotes the Khatri-Rao product.

[0018] Vectorize Y q and stack it along the pulse dimension, we can get:

[0019]

[0020] Among them, Y = [vec(Y1), …, vec(Y q ), …, vec(Y Q ), where vec(·) represents the vectorization operation, and X T =(A⊙B)C T represents the baseband received signal after matched filtering in the ideal state, and it can be constructed as a third-order tensor

[0021] Furthermore, using the singular value decomposition (SVD) algorithm, the baseband received signal in the ideal state is separated from the baseband received signal with multi-slot amplitude-phase errors, specifically including:

[0022] For 's modulo-1 expansion matrix perform the pseudo-inverse operation to obtain the Khatri-Rao product form of the combined amplitude-phase error matrix and the ideal baseband received signal matrix, that is

[0023]

[0024] Among them represents the pseudo-inverse operation, and define the matrix F = X⊙Ψ PTR , and its f ∈ {1, 2, …, MN} columns, that is, F .f can be expressed as:

[0025]

[0026] Matrixize F .f and we can get

[0027]

[0028] The combined amplitude-phase error matrix Ψ PTR and the estimated value of the ideal baseband received signal matrix X can be obtained respectively by calculating The main left and right singular value vectors are obtained, i.e.,

[0029]

[0030] where (·) * denotes conjugation, and represent the first column elements of U (f) and V (f) respectively, and represents the first element of the eigenvalue matrix Σ( f ).

[0031] Furthermore, the baseband received signal in the ideal state is subjected to spatial smoothing and real-valued processing, specifically including:

[0032] Define the integer pair (M1, L1), and satisfy M1 + L1 = M + 1. At the same time, define the selection matrix where l ∈ {1, 2, …, L1}. Perform spatial smoothing on the received signal tensor in the ideal state, and the spatially smoothed third-order tensor can be obtained. Its three steering matrices are B and and represent the first M1 rows and the first L1 rows of the steering matrix A respectively.

[0033] To reduce the computational complexity of the algorithm, the present invention performs real-valued processing on the spatially smoothed tensor based on unitary transformation. Using the front and back smoothing technology, we can obtain:

[0034]

[0035] where represents the tensor and connected along the third dimension, and Γ N represents a swap matrix of size N×N, with all ones on its anti-diagonal and zeros elsewhere.

[0036] After adopting the front and back smoothing technology, the obtained tensor is a hermitian matrix, and it can be transformed into a real-valued tensor

[0037]

[0038] where is a unitary matrix.

[0039] Furthermore, the real-valued ideal baseband received signal uses the HOSVD algorithm to obtain the DOD and DOA of the target under the amplitude-phase error condition, specifically including:

[0040] Decompose the real-valued tensor using HOSVD to obtain the real-valued signal subspace:

[0041]

[0042] where, is the core tensor, and are real-valued unitary matrices, which are composed of the left singular vectors of the mode-i∈{1,2,3} matrix expansion of the tensor .

[0043] Since the tensor is full-rank, the tensor can be written in the form of "truncated HOSVD":

[0044]

[0045] where, is the core tensor, and are composed of the main left singular vectors of the mode-i matrix expansion of the tensor , and the expression of S s can be obtained:

[0046]

[0047] Define the real-valued signal subspace ε s :

[0048] ε s = S s × 1E s1 × 2E s2

[0049] Substitute S s into ε s , and find the mode-3 matrix expansion form of ε s , that is

[0050]

[0051] where, According to the real-valued shift-invariant property of ε s , γ1 and γ2 containing angle information are obtained through the least squares algorithm (LS):

[0052]

[0053] where, K B,1 and K B,2 take the real part and the imaginary part of respectively, KB,3 and K B,4 respectively take the real part and the imaginary part of, and is the selection matrix.

[0054] The estimated DOD and DOA of the k-th target, where k ∈ {1, 2, …, K}, are obtained by the following formula:

[0055]

[0056] where Re(·) represents the operation of taking the real part of a complex number, and Im(·) represents the operation of taking the imaginary part of a complex number.

[0057] Beneficial effects: Compared with the prior art, its main advantages are as follows: The present invention can perform angle estimation of targets in the case of multi-slot amplitude and phase errors in the transmitting and receiving antenna arrays of a bistatic MIMO radar. The proposed angle decomposition method based on HOSVD reduces the computational complexity of the algorithm through spatial smoothing and real-valued processing, and improves the accuracy of target positioning. Description of the Drawings

[0058] Figure 1 is the flowchart of angle estimation of the present invention;

[0059] Figure 2 is the schematic structural diagram of target positioning of the bistatic MIMO radar of the present invention;

[0060] Figure 3 is the performance graph of the root mean square error (RMSE) of angle estimation of the proposed method, the existing MUSIC method, and the existing real-valued ESPRIT method varying with the signal-to-noise ratio (SNR) in the case of three coherent targets of the present invention;

[0061] Figure 4 is the performance graph of the RMSE of angle estimation of the proposed method, the existing MUSIC method, and the existing real-valued ESPRIT method varying with the number of pulses Q in the case of non-coherent targets of the present invention;

[0062] Figure 5 is the performance graph of the normalized mean square error (NMSE) of the combined amplitude and phase error estimated by the proposed method and the existing PARAFAC method varying with SNR in the case of non-coherent targets of the present invention. Detailed Embodiments

[0063] 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.

[0064] Figure 2 is the schematic structural diagram of target positioning of the bistatic MIMO radar, as Figure 2The bistatic MIMO radar positioning system shown has M transmitting array elements and N receiving array elements. There are K targets within the range of interest. The direction of departure (DOD) and direction of arrival (DOA) of the targets are estimated to obtain the positions of the targets.

[0065] Implementation Example 1

[0066] Please refer to Figure 3 , Figure 3 , which gives the performance graphs of the root mean square error (RMSE) of angle estimation of the proposed method, the existing MUSIC method, and the existing real-valued ESPRIT method versus SNR in the case of three coherent targets. It is set that the number of targets K = 3, the number of time slots P = 4, the number of pulses Q = 100, and the attenuation coefficients of the three coherent targets are ε = [0.9e j1.1π , 0.8e j0.75π , 0.85e j0.95π . Figure 3 It shows that as the SNR increases, the RMSE performance of angle estimation of the proposed method is significantly better than that of the existing MUSIC method and the existing real-valued ESPRIT method. Since the proposed method applies spatial smoothing and real-valued processing, it is beneficial to the decoherence of targets, and the real-valued processing increases the number of sampling points, which can improve the angle estimation accuracy. Although the existing real-valued ESPRIT method also performs real-valued processing and obtains partial decorrelation ability, when the number of coherent targets exceeds two, the existing real-valued ESPRIT method shows a large performance loss.

[0067] Implementation Example 2

[0068] Please refer to Figure 4 , Figure 4 , which gives the performance graphs of the angle estimation RMSE of the proposed method, the existing MUSIC method, and the existing real-valued ESPRIT method versus Q in the case of three coherent targets. Considering the case where the SNR is 10 dB, K = 3, P = 4, and ε = [0.9e j1.1π , 0.8e j0.75π , 0.85e j0.95π . Figure 4 It shows that as the number of snapshots Q increases, the angle estimation performance of the proposed method improves. This is because the increase in the number of samples of the proposed method improves the angle measurement accuracy, while the existing MUSIC method and the existing real-valued ESPRIT method perform poorly in the case of three coherent targets, and increasing Q has little effect.

[0069] Implementation Example 3

[0070] Please refer to Figure 5 , Figure 5The performance diagram of the NMSE of the combined amplitude and phase error estimated by the proposed method and the existing PARAFAC method with respect to SNR is given in the case of incoherent targets. Set M = 8, N = 6, K = 4, L1 = 3, M1 = 6, P = 4, Q = 400. Figure 5 It shows that in the case where the transmitting and receiving arrays contain multi-slot amplitude and phase errors, the combined amplitude and phase error estimated by the proposed method is more accurate. This is because the proposed method can separate the combined amplitude and phase error matrix from the baseband received signal containing multi-slot amplitude and phase errors by using the SVD algorithm. Therefore, a more accurate amplitude and phase error estimation can be obtained. The phase error estimation of the existing PARAFAC method is carried out on the basis of angle estimation, which will affect the overall performance of the algorithm in estimating the amplitude and phase error.

[0071] In summary, the present invention is applicable to the angle estimation of the positioning target of a bistatic MIMO radar in the case where the transmitting and receiving antenna arrays contain multi-slot amplitude and phase errors. By using the SVD algorithm, the baseband received signal in the ideal state is separated from the baseband received signal containing amplitude and phase errors. The HOSVD algorithm with spatial smoothing and real-valued processing makes the estimated DOD and DOA have high accuracy and reduces the computational complexity.

[0072] 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 tensor-based angle estimation method in bistatic MIMO radar, characterized in that The method includes: Construct a baseband received signal tensor model containing multi-slot amplitude and phase errors, specifically including: assuming that there are M transmitting antennas and N receiving antennas with a uniform linear distribution in a bistatic MIMO radar system, and there are K targets within the range of interest. and respectively represent the transmitting steering matrix and the receiving steering matrix containing amplitude and phase errors. and respectively represent the transmitting and receiving array steering matrices in the ideal state. and respectively represent the amplitude and phase error matrices of the transmitting and receiving arrays in P time slots. represents the signal feature matrix containing target reflection coefficients and Doppler frequency shifts. is the waveform matrix where the transmitted signals are orthogonal to each other, and (1 / L)SS Η = I M , where (·) Η represents the conjugate transpose operation, L is the number of samples in each pulse period, and I M is the identity matrix of size M×M. The baseband signal received by the system at the p-th time slot (p ∈ {1, 2, …, P}) and the q-th pulse (q ∈ {1, 2, …, Q}) is Among them, diag(a) represents a diagonal matrix formed by the vector a, W p,q represents additive white Gaussian noise, which follows a Gaussian distribution with a mean of 0 and a variance of σ 2 . Vectorize Y p,q and stack it along the time slot dimension. Without considering noise, we can obtain Among them, is the combined amplitude-phase error matrix, denotes the Kronecker product, ⊙ denotes the Khatri-Rao product. Vectorizing Y q and stacking it along the pulse dimension, we can obtain Among them, Y = [vec(Y1), …, vec(Y q ), …, vec(Y Q ), and vec(·) represents the vectorization operation. X Τ = (A ⊙ B)C Τ represents the baseband received signal after matched filtering in the ideal state; Using the singular value decomposition (SVD) algorithm, the baseband received signal in the ideal state is separated from the baseband received signal containing multi-slot amplitude-phase errors, specifically including: For the modulo-1 expansion matrix of perform a pseudo-inverse operation to obtain the Khatri-Rao product form of the combined amplitude-phase error matrix and the ideal baseband received signal matrix, that is, X⊙Ψ PTR , define the matrix F = X⊙Ψ PTR , take its f-th column F where f ∈ {1, 2, …, MN} .f , and matrixize F .f to obtain that is Among them, the combined amplitude-phase error matrix Ψ PTR and the estimated value of the ideal baseband received signal matrix X can be obtained by calculating the main left singular value and right singular value vectors respectively, that is Among them, (·) * represents conjugation, and respectively represent the first column elements of U (f) and V (f) ; the first element of the eigenvalue matrix Σ is represented by (f) ; Spatial smoothing and real-valued processing are performed on the baseband received signal in the ideal state, specifically including: defining an integer pair (M1, L1) that satisfies M1 + L1 = M + 1, and simultaneously defining a selection matrix where l ∈ {1, 2, …, L1}, and performing spatial smoothing on the received signal tensor in the ideal state, to obtain a spatially smoothed third-order tensor whose three steering matrices are respectively B and and respectively represent the first M1 rows and the first L1 rows of the steering matrix A. By performing real-valued processing on the spatially smoothed tensor using the front and back smoothing techniques, we can obtain Among them, ∪3 represents the concatenation of two tensors along the third dimension, Γ N represents a commutation matrix of size N×N, with elements on its anti-diagonal being 1 and the rest being 0. Using unitary transformation, is transformed into a real-valued tensor That is wherein is a unitary matrix; The actualized ideal baseband received signal uses the HOSVD algorithm to obtain the DOD and DOA of the target under the amplitude-phase error conditions, specifically including: Since the tensor is full rank, the tensor can be written in the form of "truncated HOSVD" as Among them, is the nuclear tensor, and are unitary matrices composed of the main left singular vectors expanded from the modulus - i ∈ {1, 2, 3} matrices of the tensor Define the real - valued tensor signal subspace as ε s = S s × 1E s1 × 2E s2 Substitute S s into ε s , and then the modulo-3 matrix expansion form of ε s is obtained as Among them, matrices γ1 and γ2 containing angle information are obtained through the least squares algorithm (LS), that is where, K B,1 and K B,2 respectively take the real and imaginary parts of, K B,3 and K B,4 respectively take the real and imaginary parts of, and are selection matrices, represents the pseudo-inverse operation, and the estimated DOD and DOA of the k-th target with k ∈ {1, 2, …, K} are obtained by the following formula Wherein, Re(·) represents the operation of taking the real part of a complex number, and Im(·) represents the operation of taking the imaginary part of a complex number.

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