A parameter estimation method for frequency-controlled array MIMO radar based on Bayesian tensor

Abstract

The present invention provides a method for estimating the parameters of a frequency-controlled array MIMO radar based on Bayesian tensors. Aiming at the target parameter estimation problem in a frequency-controlled array MIMO radar with array mutual coupling, the present invention first constructs the received signal of the frequency-controlled array MIMO radar containing unknown mutual coupling, DOA and distance information into a third-order complex-valued tensor model; secondly, the properties of the array mutual coupling are used to design a selection matrix to eliminate the influence of the array mutual coupling in the third-order complex-valued tensor received signal; then, the tensor model is optimized through real-valued and compressed operations to obtain a third-order real-valued compressed tensor to reduce the computational complexity of the tensor decomposition; finally, the Bayesian tensor decomposition is used to estimate the three factor matrices, thereby obtaining the target number, DOA and distance information. Therefore, the method proposed in the present invention can effectively eliminate the influence of array mutual coupling, realize high-precision parameter estimation when the number of targets is known or unknown, and has significant advantages in practical radar applications.

Description

Technical Field

[0001] The present invention relates to the technical field of radar parameter estimation, and in particular to a frequency-controlled array MIMO radar parameter estimation method based on Bayesian tensor. Background Art

[0002] In detection systems such as radar, sonar, and remote sensing, target parameter estimation is a core technology for obtaining critical information such as target angle and range. In recent years, frequency-steering array multiple-input, multiple-output (MIMO) radars have become a research hotspot due to their unique structural characteristics. These radars introduce small frequency offsets in the transmit array, allowing the echo signals to contain range-dependent phase signatures. By analyzing the phase variations in the received signals caused by frequency differences, joint angle-range estimation of targets can be achieved, effectively improving multi-target resolution and parameter estimation accuracy.

[0003] In recent years, a variety of parameter estimation algorithms have been proposed to address the joint range-angle estimation problem in frequency-steering array MIMO radars. These include the classic Multiple Signal Classification (MUSIC) algorithm, the rotational invariance technique (ESPRIT), and maximum likelihood estimation (AP-MLE), as well as methods based on tensor decomposition, such as high-order singular value decomposition (HOSVD) and parallel factorization (PARAFAC). These methods have demonstrated promising performance in achieving high-resolution target parameter estimation. However, existing methods generally rely on ideal or pre-calibrated array structures and fail to effectively account for the unknown mutual coupling effects present in radar antenna arrays. In frequency-steering array MIMO radars, array mutual coupling can cause pattern distortion, significantly reducing the accuracy of target parameter estimation.

[0004] Currently, research has focused on addressing the unknown mutual coupling effects in frequency-steering MIMO radar arrays. J. Zhu, S. Zhu, J. Xu, and L. Lan (Adaptive Detectors for FDA-MIMO Radar With Unknown Mutual Coupling [J]. IEEE Signal Process. Lett., vol. 30, pp. 1437-1441, 2023) investigated adaptive target detection in frequency-steering MIMO radars with mutual coupling. However, this approach did not estimate the target's angle or range. In their paper (Joint Range and Angle Estimation by FDA-MIMO Radar With Unknown MutualCoupling[J]. IEEE Trans. Aerosp. Electron. Syst., vol. 59, no. 4, pp. 3669-3683, 2023), L. Liu, H. Zhang, L. Lan, and J. -Y. Deng proposed a target parameter estimation algorithm for frequency-controlled array MIMO radar based on the MUSIC algorithm. This algorithm effectively eliminates the influence of array mutual coupling and achieves joint angle of arrival (DOA) and range estimation. However, this method does not fully utilize the multidimensional structure of the received signal, and the spectral peak search results in high computational complexity. Furthermore, existing methods often assume that the number of targets is known, which further limits their practical applications. Summary of the Invention

[0005] Purpose of the invention: In response to the shortcomings of the existing technology, the present invention proposes a frequency-controlled array MIMO radar parameter estimation method based on Bayesian tensor. This method fully exploits the multi-dimensional structural characteristics of the received signal through tensor modeling, effectively suppresses the influence of array mutual coupling with the help of selection matrix, and uses Bayesian tensor decomposition to achieve high-precision target parameter estimation when the number of targets is known or unknown.

[0006] Technical solution: The method for estimating parameters of a frequency-controlled array MIMO radar based on Bayesian tensor described in the present invention includes:

[0007] The received signal of frequency-controlled array MIMO radar containing unknown mutual coupling, DOA and range information is constructed as a third-order complex-valued tensor model.

[0008] The array mutual coupling properties are used to design a selection matrix to eliminate the array mutual coupling effect in the third-order complex-valued tensor receiving signal.

[0009] The tensor model is optimized through real-valued and compressed operations to obtain a third-order real-valued compressed tensor to reduce the computational complexity of tensor decomposition;

[0010] Bayesian tensor decomposition is used to estimate three factor matrices to obtain target number, DOA and distance information;

[0011] Furthermore, the received signal of the frequency-controlled array MIMO radar containing unknown mutual coupling, DOA and range information is constructed as a third-order complex-valued tensor model, which specifically includes:

[0012] In a single-base frequency-controlled array MIMO radar, both the transmitting and receiving arrays are uniform linear arrays, respectively and Since there is a frequency increment in the transmitting array , so the The carrier frequency of the transmitting array element is ,in is the initial carrier frequency of the frequency-controlled array MIMO radar. Considering that the transmitting and receiving arrays are affected by unknown mutual coupling, and represents the unknown mutual coupling matrix of the transmit and receive arrays, where represents the Toeplitz matrix, and Indicates the The unknown mutual coupling coefficients of the transmitting and receiving array elements satisfy and , represents the complex domain. Assume that the frequency-controlled array MIMO radar contains pulses and simultaneously detect If there are no related goals, The DOA and distance of a target are expressed as and . Affected by the mutual coupling of the array and in the The received signal after matched filtering under pulses It can be expressed as:

[0013]

[0014] in, and represents the transmit and receive steering matrices affected by array mutual coupling, and represent the ideal transmitting and receiving steering matrices respectively, and Respectively and No. column vector, represents the signal feature matrix containing the target radar cross-section reflection coefficient and Doppler frequency shift, represents the matrix transpose operation, Indicated by No. A diagonal matrix consisting of row elements, The mean is 0 and the variance is Gaussian noise matrix.

[0015] use ,in Represents a matrix vectorization operation, and then along the pulse dimension conduct stacking to get the received signal ,Right now

[0016]

[0017] in, represents the Khatri-Rao product, is the noise matrix. Further, Can be seen as a PARAFAC model The matrix expansion form of

[0018]

[0019] in represents the third-order unit tensor, Represents a tensor - pattern matrix product, , is the noise tensor.

[0020] Furthermore, the properties of array mutual coupling are used to design a selection matrix to eliminate the array mutual coupling effect in the third-order complex-valued tensor received signal, specifically including:

[0021] use and The matrix properties of construct the selection matrix and , which can eliminate The unknown mutual coupling effects in and Respectively represent the dimension size and The all-zero matrix, and Respectively represent the dimension size and The unit array, and , and then get the third-order tensor ,Right now

[0022]

[0023] in and represents the transmitting and receiving steering matrices after eliminating unknown mutual coupling, where Column vector, i.e. and , respectively by and Before Line and In addition, Representation matrix and matrix The product of , diagonal matrix satisfy ,in represents the Hadamard product, , , and represents the scaling factor, represents the diagonalization operation, is the noise tensor.

[0024] Furthermore, the tensor model is optimized through real-valued and compressed operations to obtain a third-order real-valued compressed tensor to reduce the computational complexity of tensor decomposition. Specifically, the following steps are performed:

[0025] because ,in, represents the conjugate operation, the matrix and The column vectors are and The corresponding column vector elements constitute the central Hermitian vector, is a diagonal matrix containing DOA and distance information, combined with the tensor The conjugate tensor of , and get a new tensor for

[0026]

[0027] in, Representation matrix 、 、 and The product of is the transformed noise tensor, Indicates the dimension size is The subdiagonal of the commutative matrix is ​​1 and the rest of the elements are 0, the subscript .

[0028] Utilization nature , the tensor Re-expressed as ,in Representation matrix 、 and The product of , so the complex-valued central Hermitian tensor can be obtained by smoothing the front and back ,in Represents the concatenation operation of two tensors in the third dimension.

[0029] Then, the unitary transformation operation is used to transform Transformed into a third-order real-valued tensor ,Right now

[0030]

[0031] in, 、 and are three real-valued factor matrices, represents the matrix conjugate transpose operation, Representation matrix and The row stacking result is represents the field of real numbers, is the noise tensor, Denotes a unitary matrix whose subscript is an odd number satisfying , when the subscript is an even number, ,Right now

[0032]

[0033] in is a positive integer, is the imaginary unit, Indicates the dimension size is The unit array, represents an all-0 matrix, Indicates the dimension size is A commutative matrix with 1s on the subdiagonal and 0s on the rest of the diagonal.

[0034] On the basis of obtaining the real-valued tensor, the approximate HOSVD technique is used to convert Compress to obtain a real-valued compressed tensor ,Right now

[0035]

[0036] in 、 and is an orthogonal matrix, which is composed of three-order tensors The three mode matrices are expanded and singular value decomposition is performed to obtain the previous 、 and Left singular value vectors. Vectorize it and use the properties of Khatri-Rao product to get

[0037]

[0038] in, represents the Kronecker product, , and represents the compressed real-valued factor matrix, and can be equivalently expressed as:

[0039]

[0040] in is the compressed noise tensor.

[0041] Furthermore, Bayesian tensor decomposition is used to estimate three factor matrices to obtain target number, DOA, and distance information, including:

[0042] First, establish a tensor probability model and define The likelihood function is

[0043]

[0044] in, Indicates proportional to the sign, represents the exponential operation, represents the Frobenius norm, is the Kruskal operator, represents the noise accuracy term, whose prior distribution is modeled as a hyperparameter The gamma distribution of

[0045]

[0046] in represents the gamma function.

[0047] Factor Matrix The prior distribution of is modeled as a generalized hyperbolic distribution with a hierarchical structure, i.e.

[0048]

[0049] in, Representing a tensor The maximum rank of express No. column vector, represents a Gaussian distribution, Indicates the dimension size is The all-zero vector, Indicates the dimension size is The unit array, express and In addition, represents the latent factor, which is modeled as a hyperparameter The generalized inverse Gaussian distribution of

[0050]

[0051] in, represents the Bessel function of the second kind.

[0052] Defining unknown parameter sets ,calculate and The joint distribution of

[0053]

[0054] Using Bayesian thinking to calculate The posterior distribution of

[0055]

[0056] Due to direct calculation It is highly complex, so variational Bayesian inference is used to find a posterior distribution , making and The Kullback-Leibler (KL) divergence between is the smallest, that is,

[0057]

[0058] in, express and The KL divergence value between , Indicates that the distribution The mathematical expectation under is a constant.

[0059] Then, the KL divergence minimization problem is transformed into The maximization problem is .

[0060] Based on the mean field theory, , we can get The optimal solution for

[0061]

[0062] in, Indicates except outside The mathematical expectation of the distribution of other variables in . Furthermore, 、 and The optimal form of 、 and , then through Solve in sequence. Through iteration, the convergence threshold is reached, and then we get The estimated value of .

[0063] During the iteration process, the latent factors The mean of the -1 power, that is , will be continuously updated. Since the factor matrix sparsity of the prior choice, in A value will cause The corresponding The column elements are 0. The tensor rank is obtained by enumerating the non-zero columns in each factor matrix, that is, determining the target number .

[0064] In obtaining the real-valued factor matrix After that, we first need to recover the complex-valued factor matrix ,Right now

[0065]

[0066] Then from Calculate the phase containing parameter information and , further solve Estimated value of ,Right now

[0067]

[0068] in, and Respectively and No. column vector, represents the wavelength, represents the speed of light, is the distance between adjacent array elements, and are the sine and inverse sine functions, respectively.

[0069] Beneficial Effects: Compared with existing technologies, the present invention's main advantages are: using tensor modeling, it can fully utilize the multidimensional structure of the received signal of a frequency-controlled array MIMO radar. By designing a selection matrix, it can effectively eliminate the influence of array mutual coupling. The proposed Bayesian tensor decomposition method can achieve accurate DOA and range estimation in both known and unknown target situations. The advantages and methods of the present invention can be further understood through the following detailed description and accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 This is a flow chart of a frequency-controlled array MIMO radar parameter estimation method based on Bayesian tensor of the present invention;

[0071] Figure 2 This is a schematic diagram of the structure of a frequency-controlled array MIMO radar with array mutual coupling according to the present invention;

[0072] Figure 3 The performance diagram of the relationship between the root mean square error (RMSE) and signal-to-noise ratio (SNR) of DOA estimation of the present invention and the existing dimensionality reduction MUSIC method, the existing ESPRIT method and the existing unitary HOSVD method under the condition of known target number is shown;

[0073] Figure 4 This is a performance diagram of the relationship between RMSE and SNR of distance estimation of the present invention and the existing dimensionality reduction MUSIC method, the existing ESPRIT method and the existing unitary HOSVD method under the condition of known target number;

[0074] Figure 5 This is a performance diagram of the relationship between RMSE and SNR of DOA estimation under multiple different unknown target numbers and pulse numbers of the present invention;

[0075] Figure 6 This is a performance diagram of the relationship between RMSE and SNR of distance estimation under multiple different numbers of unknown targets and pulses of the present invention. DETAILED DESCRIPTION

[0076] In order to make the features and advantages of the present invention more obvious and easy to understand, preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0077] Figure 2 FIG. 1 is a schematic diagram of the structure of the frequency-controlled array MIMO radar under the condition of array mutual coupling of the present invention, as shown in FIG. Figure 2 The frequency-controlled MIMO radar array shown contains The number of transmitting array elements, The number of receiving array elements, among which there are unknown mutual coupling problems in the transmitting array and the receiving array, and there are For each target, the transmitting array transmits mutually orthogonal signals, and the DOA and distance of the target are extracted by analyzing the echo signals after matched filtering.

[0078] Implementation Example 1

[0079] See Figure 3 and Figure 4 The two figures show the relationship between the RMSE and SNR of the DOA and distance estimation of the present invention, the existing dimensionality reduction MUSIC method, the existing ESPRIT method, and the existing unitary HOSVD method under the condition of a known number of targets. The system parameters are: 、 、 、 、 、 , the SNR varies from -10dB to 20dB in 5dB intervals. It can be seen that the proposed method and existing methods can effectively eliminate the influence of array mutual coupling in frequency-steering array MIMO radars, and the RMSE of DOA and range estimation for both the proposed method and existing methods gradually decreases with increasing SNR. Furthermore, the proposed method consistently outperforms existing methods in DOA and range estimation. This is due to the proposed method's use of tensor modeling, tensor real-valuedization, and iterative Bayesian tensor decomposition to obtain more accurate factor matrix estimates, resulting in superior DOA and range estimation performance in frequency-steering array MIMO radars with array mutual coupling.

[0080] Implementation Example 2

[0081] See Figure 5 and Figure 6 , these two figures are the performance diagrams of the relationship between DOA and distance estimation RMSE and SNR under different unknown target numbers and pulse numbers of the present invention. 、 、 、 、 、 , SNR varies from -10dB to 20dB with an interval of 5dB. They show that the proposed method can detect different unknown target numbers. The DOA and distance of the target are accurately estimated, thus relaxing the prior requirement of the number of known targets. It will increase the difficulty of achieving accurate parameter estimation by the proposed method, but by increasing the number of pulses The estimation accuracy of DOA and distance can be effectively improved, which shows that the proposed method can be adapted to practical scenarios with multiple unknown targets.

[0082] In summary, the present invention considers a frequency-controlled array MIMO radar parameter estimation method based on Bayesian tensor. Through tensor modeling, the multidimensional structure of the received signal can be fully utilized, and the array mutual coupling effect can be effectively eliminated by using the selection matrix. Based on the proposed Bayesian tensor decomposition method, high-precision estimation of the DOA and distance of the target can be achieved when the number of targets is known or unknown.

[0083] The above embodiments are only for the purpose of helping to understand the method and main idea of ​​the present invention. The contents of this specification cannot be used to limit the scope of the present invention. Therefore, the scope of protection of the present invention shall be subject to the appended claims.

Claims

1. A frequency-controlled array MIMO radar parameter estimation method based on Bayesian tensor, characterized in that The method includes: The received signal of a frequency-steering array MIMO radar containing unknown mutual coupling, DOA, and range information is constructed as a third-order complex-valued tensor model. Specifically, a single-base frequency-steering array MIMO radar affected by array mutual coupling is considered. The transmitting array and the receiving array contain M and N array elements, respectively. Both are uniform linear arrays. The number of targets is K. The DOA and range of the k-th target are expressed as φ k and d k , the unknown mutual coupling matrices of the transmitting and receiving arrays are and where toeplitz(·) represents the Toeplitz matrix, and are the unknown mutual coupling coefficients of the l-th transmitting and receiving elements, L<M / 2 and L<N / 2, respectively. In the complex domain, there is a frequency increment Δf between the transmitting elements of the frequency-controlled array MIMO radar, and the carrier frequency of the m={1,2,…,M}th transmitting element is f m =f0+(m-1)Δf, where f0 is the initial carrier frequency. There are Q pulses in a coherent processing interval of the frequency-controlled array MIMO radar. The received signal after matched filtering under the influence of array mutual coupling and the q={1,2,…,Q}th pulse is for in, and represents the transmit and receive steering matrices affected by array mutual coupling, b T (φ k ,d k ) and b R (φ k ) represent the matrix B T and B R The kth column vector of represents the signal characteristic matrix containing the target radar cross-section reflection coefficient and Doppler frequency shift, (·) T represents the matrix transpose operation, D q (Ξ) represents the diagonal matrix consisting of the q-th row elements of Ξ, Indicates that the mean is 0 and the variance is σ 2 Gaussian noise matrix, Y q Vectorize to get Where vec(·) represents the matrix vectorization operation, let y q Stack Q times along the pulse dimension, and we get It satisfies the tensor The matrix expansion form of , and for in, represents the third-order unit tensor, × n represents the n-mode matrix product of tensors, n∈{1,2,3}, is the noise tensor; The array mutual coupling properties are used to design a selection matrix to eliminate the array mutual coupling effect in the third-order complex-valued tensor receiving signal. The tensor model is optimized through real-valued and compressed operations to obtain a third-order real-valued compressed tensor to reduce the computational complexity of tensor decomposition; Bayesian tensor decomposition is used to estimate three factor matrices to obtain the target number, DOA and distance information.

2. The method for frequency-controlled array MIMO radar parameter estimation based on Bayesian tensor according to claim 1, characterized in that: The array mutual coupling properties are used to design a selection matrix to eliminate the array mutual coupling effect in the third-order complex-valued tensor receiving signal, specifically including: using the unknown mutual coupling matrix Ω of the transmitting and receiving arrays T and Ω R The matrix properties of construct the selection matrix and to eliminate The unknown mutual coupling effect is and Respectively represent the dimension size and The all-zero matrix, and Respectively represent the dimension size and The unit array, and Then we get the third-order tensor for in and represents the transmit and receive steering matrix after eliminating array mutual coupling, whose kth column vector is {1, 2, ..., K}, that is, and By b T (φ k ,d k ) and b R (φ k ) Line and Row elements are composed of Denotes the product of matrix Ξ and matrix Γ, and the diagonal matrix Γ satisfies in represents the Hadamard product, and represents the scaling factor, diag(·) represents the diagonalization operation, is the noise tensor.

3. The method for frequency-controlled array MIMO radar parameter estimation based on Bayesian tensor according to claim 2, characterized in that: The tensor model is optimized by real-valued and compressed operations to obtain a third-order real-valued compressed tensor to reduce the computational complexity of tensor decomposition. Specifically, the following are used: and tensors The conjugate tensor of Get a new tensor for where ⊙ represents the Khatri-Rao product, (·) * represents the conjugation operation, and The column vectors are and The corresponding column vector elements constitute the central Hermitian vector, Π Q Ξ * Γ * Φ * Represents the matrix π Q ,Ξ * , Γ * and Φ * The product of is a diagonal matrix containing DOA and distance information, is the transformed noise tensor, Π ε represents a commutative matrix of dimension ε×ε with the subdiagonal being 1 and the rest being 0. In addition, the use of properties The tensor Re-expressed as Where ΞΓΦ represents the product of matrices Ξ, Γ, and Φ, and the complex-valued central Hermitian tensor is obtained by forward and backward smoothing operations Where ∪3 represents the connection operation of two tensors in the third dimension, and the unitary transformation operation is used to convert Transformed into a third-order real-valued tensor Right now in, and are three real-valued factor matrices, (·) H represents the matrix conjugate transpose operation, Denote matrices ΞΓΦ and Π Q Ξ * Γ * Φ * The row stacking result is represents the field of real numbers, is the noise tensor, Ψ represents the unitary matrix, and its subscript is an odd number satisfying Ψ 2α+1 , when the subscript is an even number, it satisfies Ψ 2α ,Right now Where α is a positive integer, j is an imaginary unit, I α represents the unit matrix of dimension α×α, 0 represents the matrix of all zeros, π α Represents a commutative matrix with dimension α×α, whose subdiagonal elements are 1 and the rest are 0. We further use the approximate HOSVD technique to convert Compress to obtain a real-valued compressed tensor Right now in and is an orthogonal matrix, which is composed of three-order tensors After the three pattern matrices are expanded, singular value decomposition is performed to obtain the first R1, R2 and R3 left singular value vectors. Vectorize it and use the properties of Khatri-Rao product to get in, represents the Kronecker product, and represents the compressed real-valued factor matrix, and then is represented as: in is the compressed noise tensor.

4. The method for frequency-controlled array MIMO radar parameter estimation based on Bayesian tensor according to claim 3, characterized in that: Bayesian tensor decomposition is used to estimate three factor matrices to obtain target number, DOA and distance information. Specifically, the tensor probability model is first established, and the definition The likelihood function is Among them, ∝ means proportional to the sign, exp(·) represents the exponential operation, ||·|| F represents the Frobenius norm, is the Kruskal operator, τ=σ -2 represents the noise accuracy term, whose prior distribution is modeled as a hyperparameter is {a 0 ,b 0 } is the gamma distribution, that is Where ga(·) represents the gamma function, the factor matrix The prior distribution of is modeled as a generalized hyperbolic distribution with a hierarchical structure, i.e. Among them, R represents a tensor The maximum rank, R ≥ K, Indicates A (n) The rth column vector of represents a Gaussian distribution, represents a full 0 vector of dimension (R1+R2+R3)×1, represents the unit matrix of dimension (R1+R2+R3)×(R1+R2+R3), Indicates s r and The product of s r represents the latent factor, which is modeled as a hyperparameter The generalized inverse Gaussian distribution of Where Bessel(·) represents the Bessel function of the second kind, and defines the unknown parameter set calculate and The joint distribution of Using Bayesian thinking to calculate The posterior distribution of Then use variational Bayesian inference to find a posterior distribution Make and The Kullback-Leibler (KL) divergence between is the smallest, that is, in, express and The KL divergence value between Indicates that the distribution The mathematical expectation under is a constant, and the KL divergence minimization problem is transformed into The maximization problem is Based on the mean field theory, get The optimal solution for in, Indicates except outside The mathematical expectation of the distribution of other variables in , and further, s r and the optimal form of τ, namely and Then through Solve in sequence and solve by iteration to reach the convergence threshold The estimated value of During the iteration process, the latent factor s r The mean of the -1 power, that is Will be continuously updated, since the factor matrix sparsity of the prior choice, The (RK) values ​​in The corresponding (RK) column elements are 0, and the tensor rank is obtained by enumerating the non-zero columns in each factor matrix, that is, determining the target number K, and obtaining the real-valued factor matrix After that, we first need to recover the complex-valued factor matrix and Then from The phase containing parameter information is obtained from {P T ,P R }, and then extract {φ k ,d k Estimated value of Right now in, and Respectively represent P T and P R The kth column vector, λ represents the wavelength, c represents the speed of light, r T =r R =λ2 is the spacing between adjacent array elements, sin(·) and arcsin(·) are sine and arcsine functions respectively.

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