A Near-Field EMVS-MIMO Radar Parameter Estimation Method Based on an Accurate Model

Abstract

The present invention relates to a method for estimating parameters of a near-field EMVS-MIMO radar based on an accurate model, including: establishing a bistatic EMVS-MIMO radar system, and estimating the transmit angle, receive angle, transmit distance, receive distance, transmit polarization parameters and receive polarization parameters by using parallel factor decomposition and internal electromagnetic vector information. The whole process does not require spectral peak searching, has a low computational complexity, the estimated parameters can be automatically paired, there is no phase ambiguity problem, the accuracy is high, and it is applicable to geometric arrays with arbitrary element spacings in three-dimensional space.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and in particular to a method for estimating parameters of a near-field EMVS-MIMO radar based on an accurate model. Background Art

[0002] Parameter estimation of MIMO radar is a current research hotspot and difficulty. Compared with phased array radars, MIMO radars can achieve higher angular resolution, greater array degrees of freedom, and flexible transmit waveform design by utilizing mutually orthogonal waveform characteristics.

[0003] In recent years, in order to achieve joint parameter estimation of DOD and DOA in bistatic MIMO radars, many excellent algorithms have been proposed. Although the various algorithms proposed currently can achieve accurate positioning of target parameters in bistatic MIMO radars under different backgrounds, the transmit arrays and receive arrays used are all scalar uniform arrays or non-uniform arrays, and the target sources are mostly far-field sources. Compared with scalar arrays, electromagnetic vector sensor arrays can not only provide the angular information of targets, but also provide the polarization information of targets. Therefore, electromagnetic vector sensor arrays have higher target resolution and parameter estimation capabilities. In addition, when the target is located in the radiation near-field area of the MIMO radar, due to the non-linearity of the signal wavefront expression, if the far-field source direction-finding algorithm is directly applied, a large estimation deviation caused by model mismatch will occur; however, in the near-field scenario, there is currently no proposed MIMO radar multi-dimensional parameter estimation algorithm that utilizes polarization information. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for estimating parameters of a near-field EMVS-MIMO radar based on an accurate model, which can not only obtain the angular information and distance information of the target, but also obtain the polarization information of the target, while avoiding excessive computational complexity and an additional near-field multi-dimensional parameter pairing process, and the method is closer to the actual positioning scenario.

[0005] The technical solution adopted by the present invention is a method for estimating parameters of a near-field EMVS-MIMO radar based on an accurate model, and the method includes the following steps:

[0006] S1. Establish a system model of a bistatic MIMO radar based on EMVS, the transmit end of which is a transmit array composed of M EMVSs, and the receive end is a receive array composed of N EMVSs. The M EMVSs of the transmit array and the N EMVSs of the receive array are all distributed in three-dimensional space. Among them, the coordinates of the m-th EMVS of the transmit array and the n-th receive EMVS of the receive array are respectively expressed as (x t,m , y t,m , zt,m ), and (x r,n , y r,n , z r,n ), where m = 1, 2, …, M, n = 1, 2, …, N; Take the EMVS located at from the transmitting array as the reference element, and take the EMVS located at from the receiving array as the reference element;

[0007] S2. Set K near-field targets in three-dimensional space. The M EMVS of the transmitting array emit signals. After the signals are reflected by the K near-field targets, they are received by the receiving array. The positions of the K near-field targets are expressed as (θ t,k , θ r,k , φ t,k , φ r,k , r t,k , r r,k ), where θ t,k , φ t,k , r t,k respectively represent the elevation angle, azimuth angle of the near-field target relative to the transmitting array, and the distance from the transmitting array to the near-field target. θ r,k , φ r,k , r r,k respectively represent the elevation angle, azimuth angle of the near-field target relative to the receiving array, and the distance from the near-field target to the receiving array; The distances from the m-th element of the transmitting array to the k-th near-field target and from the k-th near-field target to the n-th element of the receiving array are obtained as follows:

[0008]

[0009]

[0010] where, r t,k = r t,0,k , r r,k = r r,0,k ;

[0011] S3. After the receiving array receives the signal, the signal then passes through the matched filter at the receiving end, and the output of the matched filter is obtained; At time t, the output signal of the matched filter at the receiving end is x(t) = (D t D r )s(t) + n(t); where, s(t) = [s 1 (t), s 2 (t), …, s K (t)] T represents the reflection coefficient matrix, n(t) represents the additive white Gaussian noise, D t and D rRepresent the transmit array steering matrix and the receive array steering matrix, respectively, D t =[d t,1 ,d t,2 ,…,d t,K , D r =[d r,1 ,d r,2 ,…,d r,K where, where, τ t,m,k represents the propagation delay of the transmitted signal, τ r,n,k represents the propagation delay of the received signal, a m,t,k and a n,r,k represent the spatial responses of the EMVS of the transmit array and the spatial responses of the EMVS of the receive array, respectively, and can be expressed as:

[0012]

[0013]

[0014] where, v t,m,k (θ t,m,k ,φ t,m,k ) and v r,n,k (θ r,n,k ,φ r,n,k ) represent matrices related only to the direction parameters, g t,m,k and g r,n,k represent matrices related only to the polarization parameters;

[0015] S4. According to the output signal x(t) of the matched filter in step S3, calculate the covariance matrix of x(t), that is: R = E[x(t)x H (t)] = [D t D r R s [D t D r H +σ 2 I, where, represents the covariance matrix of the approaching target, represents the signal power of the k-th target, and I is an identity matrix;

[0016] S5. Rearrange the covariance matrix R of x(t) in step S4 into a fourth-order tensor form, that is: where, represents a fourth-order tensor operator, represents the tensor form of σ 2 I, D t×2 ​Denote D t in tensor form, D r×3 Denote D r in tensor form, Denote in tensor form, Denote D r as the conjugate matrix of D;

[0017] S6. Rearrange the fourth-order tensor obtained in step S5 into a third-order tensor That is: where represents a third-order tensor operator,

[0018] S7. Perform parallel factor decomposition on the third-order tensor in step S6 using the complex parallel factor algorithm to obtain the estimated values of the transmit array steering matrix D t and the receive array steering matrix D r as and and and satisfy the following two relationships: where Π is a column permutation matrix, Δ 1 , Δ 2 is a scale ambiguity matrix, N 1 , N 2 is an error matrix;

[0019] S8. Normalize and obtained in step S7, and construct two selection matrices after normalization: where, e m represents a 1×M row vector, whose m-th element is 1 and the rest are 0; e n represents a 1×N row vector, whose n-th element is 1 and the rest are 0; then use the two selection matrices to respectively select the l-th row to the l+6-th row of and the l-th row to the l+6-th row of , and write them as expressions respectively: H t,m The rotation invariant relationships between the i-th row of t,m and the j-th row of H r,n and between the i-th row of H r,n and the j-th row of where, i, j = 1, 2, 3, 4, 5, 6; H t,m (i, :) represents the i-th row of H t,m ​The i-th row of, H r,n (i,:) represents the i-th row of H r,n The i-th row of, H t,m (j,:) represents the j-th row of H t,m The j-th row of, H r,n (j,:) represents the j-th row of H r,n The j-th row; diag{·} represents the diagonalization operation;

[0020]

[0021] S9. According to step S8, obtain the estimated value of the electric field vector of the transmitting array and the estimated value of the magnetic field vector That is where represents the k-th element of in step S8 and represents the k-th element of in step S8. Similarly, obtain the estimated value of the electric field vector of the receiving array represents the k-th element of in step S8 and the estimated value of the magnetic field vector That is

[0022] S10. According to the estimated value of the Poynting vector obtained in step S9, obtain the estimated values of the Poynting vector of the k-th target at the m-th EMVS of the transmitting array and the Poynting vector of the k-th target at the n-th EMVS of the receiving array as follows:

[0023] where represents the vector cross product operation;

[0024] S11. According to the estimated value of the Poynting vector obtained in step S10, obtain the estimated values of the two-dimensional direction of departure (2D-DOD) of the k-th target with respect to the m-th element of the transmitting array and the two-dimensional direction of arrival (2D-DOA) of the k-th target with respect to the n-th element of the receiving array as follows:

[0025] S12. According to step S11, reconstruct the spatial response of the m-th element of the transmitting array with respect to the k-th target and the spatial response of the k-th target with respect to the n-th element of the receiving array That is After that, obtain the estimated values of g t,m,k and g r,n,k respectively and where, () + represents the pseudo-inverse operation on the matrix; from and​ The estimated values of the polarization parameters of the m-th element in the transmitting array with respect to the k-th target and the estimated values of the polarization parameters of the k-th target with respect to the n-th element in the receiving array can be obtained respectively, that is:

[0026] Then the estimated values of the two-dimensional transmitting polarization parameters (2D-TPA) and the two-dimensional receiving polarization parameters (2D-RPA) are:

[0027] S13. According to the geometric relationship of the system model of the bistatic MIMO radar based on EMVS, two linear equations related to the transmitting array and the receiving array are obtained respectively, that is Simplify the two linear equations. The coefficient matrices of the two simplified linear equations are F t,k and F r,k , and the constant term matrices are G t,k and G r,k , which are respectively expressed as:

[0028]

[0029] The terms related to the transmitting distance and the transmitting angle in the two simplified equations are expressed as: The terms related to the receiving distance and the receiving angle are expressed as: Combine the coefficient matrix F t,k , the coefficient matrix F r,k , the constant term matrix G t,k , the constant term matrix G r,k , the related term Θ t,k and the related term Θ r,k into an overall compact matrix, and the compact matrix is expressed as: where blkdiag{·} represents the block diagonalization operation; based on the compact matrix, the estimated value of Θ k can be obtained according to the least squares method as: Finally, the estimated values of the two-dimensional transmitting angle, the two-dimensional receiving angle, the transmitting distance and the receiving distance of the k-th target are respectively:

[0030]

[0031] The beneficial effects of the present invention are as follows: By adopting the above-mentioned near-field EMVS-MIMO radar parameter estimation method based on an accurate model, this method can obtain automatically paired near-field multi-dimensional parameters on the premise of a bistatic multiple-input multiple-output (MIMO) radar system based on electromagnetic vector sensors (EMVS) with arbitrarily configured spacings. By replacing traditional scalar sensors with electromagnetic vector sensors (EMVS), not only can the angle information and distance information of the target be obtained, but also the polarization information of the target can be obtained. In addition, the parallel factor decomposition method is used for parameter estimation, avoiding excessive computational complexity and an additional near-field multi-dimensional parameter pairing process; finally, the near-field EMVS-MIMO radar multi-dimensional parameter estimation method based on an accurate model is closer to the actual positioning scenario. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of the system model of the bistatic MIMO radar based on EMVS in the present invention;

[0033] Figure 2 It is an estimation diagram of the 2D-DOD of the near-field EMVS-MIMO radar obtained by using the method of the present invention in the example of the specific implementation manner of the present invention;

[0034] Figure 3 It is an estimation diagram of the 2D-DOA of the near-field EMVS-MIMO radar obtained by using the method of the present invention in the example of the specific implementation manner of the present invention;

[0035] Figure 4 It is an estimation diagram of the transmission distance and reception distance of the near-field EMVS-MIMO radar obtained by using the method of the present invention in the example of the specific implementation manner of the present invention;

[0036] Figure 5 It is an estimation diagram of the 2D-TPA of the near-field EMVS-MIMO radar obtained by using the method of the present invention in the example of the specific implementation manner of the present invention;

[0037] Figure 6 It is an estimation diagram of the 2D-RPA of the near-field EMVS-MIMO radar obtained by using the method of the present invention in the example of the specific implementation manner of the present invention. SPECIFIC IMPLEMENTATION MANNER

[0038] The following further describes the invention with reference to the accompanying drawings and in combination with specific implementation manners, so that those skilled in the art can implement it according to the text of the specification. The protection scope of the present invention is not limited to this specific implementation manner.

[0039] The present invention relates to a near-field EMVS-MIMO radar parameter estimation method based on an accurate model, and this method includes the following steps:

[0040] S1. Establish a system model of a bistatic MIMO radar based on electromagnetic vector sensors (EMVS). The transmitting end is a transmitting array composed of M EMVS, and the receiving end is a receiving array composed of N EMVS. The M EMVS of the transmitting array and the N EMVS of the receiving array are all distributed in three-dimensional space. Among them, the coordinates of the m-th EMVS of the transmitting array and the n-th receiving EMVS of the receiving array are respectively expressed as (x t,m , y t,m , z t,m ) and (x r,n , y r,n , z r,n ), where m = 1, 2, …, M, n = 1, 2, …, N; Take the EMVS located at in the transmitting array as the reference element, and take the EMVS located at in the receiving array as the reference element;

[0041] S2. Set K near-field targets in three-dimensional space. The M EMVS of the transmitting array transmit signals. After the signals are reflected by the K near-field targets, they are received by the receiving array. The positions of the K near-field targets are expressed as (θ t,k , θ r,k , φ t,k , φ r,k , r t,k , r r,k ), where θ t,k , φ t,k , r t,k respectively represent the elevation angle, azimuth angle of the near-field target relative to the transmitting array, and the distance from the transmitting array to the near-field target, and θ r,k , φ r,k , r r,k respectively represent the elevation angle, azimuth angle of the near-field target relative to the receiving array, and the distance from the near-field target to the receiving array; Obtain the distances from the m-th element of the transmitting array to the k-th near-field target and from the k-th near-field target to the n-th element of the receiving array as follows:

[0042]

[0043]

[0044] Among them, r t,k = r t,0,k , r r,k = r r,0,k ;

[0045] S3. After the receiving array receives the signal, the signal then passes through the matching filter at the receiving end and is output by the matching filter; At time t, the output signal of the matching filter at the receiving end is x(t) = (D tD r )s(t)+n(t); where s(t)=[s 1 (t), s 2 (t), …, s K (t)] T represents the reflection coefficient matrix, n(t) represents additive white Gaussian noise, D t and D r respectively represent the transmit array steering matrix and the receive array steering matrix, D t =[d t,1 , d t,2 , …, d t,K , D r =[d r,1 , d r,2 , …, d r,K where, where τ t,m,k represents the propagation delay of the transmitted signal, τ r,n,k represents the propagation delay of the received signal, a m,t,k and a n,r,k respectively represent the spatial responses of the EMVS of the transmit array and the spatial responses of the EMVS of the receive array, and can be respectively expressed as:

[0046]

[0047]

[0048] v t,m,k (θ t,m,k , φ t,m,k ), v r,n,k (θ r,n,k , φ r,n,k ) represents a matrix related only to the direction parameters, g t,m,k , g r,n,k represent matrices related only to the polarization parameters; since the polarization parameters of different targets with respect to the transmit / receive array elements are approximately equal, i.e., γ t,1,k =γ t,2,k =…=γ t,M,k =γ t,k , η t,1,k =η t,2,k =…=η t,M,k =η t,k ; γ r,1,k =γ r,2,k =…=γ r,N,k =γ r,k , η r,1,k =η r,2,k =…=ηr,N,k = η r,k ;

[0049] S4. Calculate the covariance matrix of x(t) based on the output signal x(t) of the matched filter in step S3, i.e.:

[0050] R = E[x(t)x H (t)] = [D t D r R s [D t D r H + σ 2 I, where represents the covariance matrix of the approaching target, represents the signal power of the k-th target. I is a diagonal matrix;

[0051] S5. Rearrange the covariance matrix R of x(t) in step S4 into a fourth-order tensor form, i.e.:

[0052] where represents a fourth-order tensor operator, represents the tensor form of σ 2 I, D t×2 represents the tensor form of D t of D r×3 represents the tensor form of D r of D represents (D t conjugate matrix of) tensor form, represents the conjugate matrix of D r ;

[0053] S6. Let Rearrange the fourth-order tensor obtained in step S5 into a third-order tensor i.e.: where represents a third-order tensor operator,

[0054] S7. Perform parallel factor (PARAFAC) decomposition on the third-order tensor in step S6 using the complex parallel factor (COMFAC) algorithm to obtain the estimated values of the transmit array steering matrix D t and the receive array steering matrix D r and and and and satisfy the following two relationships:​ Among them, Π is a column permutation matrix, and Δ 1 , Δ 2 is a scale ambiguity matrix, and N 1 , N 2 is an error matrix;

[0055] S8. Normalize the and obtained in step S7, and construct two selection matrices after normalization: Among them, e m represents a 1×M dimensional row vector, whose m-th element is 1 and the rest are 0; e n represents a 1×N dimensional row vector, whose n-th element is 1 and the rest are 0; then use the two selection matrices to respectively select the and from the l-th row to the l + 6-th row, and write it as an expression: H t,m 's i-th row and H t,m 's j-th row, and H r,n 's i-th row and H r,n 's j-th row respectively have the following rotation invariant relationships: Among them, i, j = 1, 2, 3, 4, 5, 6; H t,m (i, :) represents the i-th row of H t,m , H r,n (i, :) represents the i-th row of H r,n , H t,m (j, :) represents the j-th row of H t,m , H r,n (j, :) represents the j-th row of H r,n ; diag{·} represents the diagonalization operation;

[0056]

[0057] S9. Obtain the estimated value of the electric field vector of the transmitting array and the estimated value of the magnetic field vector, that is Among them, represents the k-th element of in step S8, represents the k-th element of in step S8. Similarly, obtain the estimated value of the electric field vector of the receiving array and the estimated value of the magnetic field vector, that is

[0058] S10. According to step S99, further calculate the estimated values of the Poynting vector of the k-th target at the m-th EMVS of the transmitting array and the Poynting vector of the k-th target at the n-th EMVS of the receiving array as follows: Where, represents the vector cross product operation;

[0059] S11. According to the estimated values of the Poynting vector obtained in step S10, obtain the estimated values of the two-dimensional direction of departure (2D-DOD) of the k-th target with respect to the m-th element in the transmitting array and the two-dimensional direction of arrival (2D-DOA) of the k-th target with respect to the n-th element in the receiving array as follows:

[0060]

[0061] S12. According to step S11, reconstruct the spatial response of the m-th element in the transmitting array with respect to the k-th target and the spatial response of the k-th target with respect to the n-th element in the receiving array That is After that, obtain the estimated values of g t,m,k and g r,n,k respectively. and Where, () + represents the pseudo-inverse operation on the matrix; from the estimated values and the estimated values of the polarization parameters of the m-th element in the transmitting array with respect to the k-th target and the estimated values of the polarization parameters of the k-th target with respect to the n-th element in the receiving array can be obtained respectively, that is: Then the estimated values of the two-dimensional transmit polarization parameter (2D-TPA) and the two-dimensional receive polarization parameter (2D-RPA) are:

[0062] S13. According to the geometric relationship of the system model of the bistatic MIMO radar based on EMVS, two linear equations related to the transmitting array and the receiving array are obtained respectively, that is Simplify the two linear equations, and the simplified results of the two equations can be obtained as:

[0063]

[0064] The coefficient matrices F t,k , F r,k and the constant term matrices G t,k , G r,k are respectively expressed as:

[0065]

[0066] The relevant terms related to the transmission distance and transmission angle in the two simplified equations are expressed as: The relevant terms related to the reception distance and reception angle are expressed as: The coefficient matrix F t,k 、the coefficient matrix F r,k 、the constant term matrix G t,k 、the constant term matrix G r,k 、the relevant term Θ t,k and the relevant term Θ r,k are integrated into a single overall compact matrix, and the compact matrix is expressed as: In the formula, blkdiag{·} represents the block diagonalization operation; based on the obtained compact matrix expression, the estimated value of Θ k is: Finally, the estimated values of the two-dimensional transmission angle, two-dimensional reception angle, transmission distance, and reception distance of the k-th target are respectively:

[0067]

[0068] The above method uses parallel factor decomposition and the internal information of electromagnetic vectors to estimate the transmission angle, reception angle, transmission distance, reception distance, transmission polarization parameter, and reception polarization parameter. The entire process does not require spectral peak search, has low computational complexity, the estimated parameters can be automatically paired, there is no phase ambiguity problem, high accuracy, and it is applicable to geometric arrays with arbitrary element spacings in three-dimensional space.

[0069] The following provides examples to verify the effectiveness and accuracy of an EMVS-MIMO radar multi-dimensional parameter estimation method based on an accurate model according to the present invention.

[0070] Assume M = N = 6, d t = d r = λ / 4, L = 1000; it is set that there are two near-field targets in the near-field space of the MIMO radar, and their (θ t,k , θ r,k , φ t,k , φ r,k , r t,k , r r,k , γ t,k , γ r,k , η t,k , η r,k ) are respectively:

[0071] (60°, 50°, 30°, 20°, 10, 8, 10°, 30°, 30°, 20°), (30°, 60°, 20°, 50°, 12, 15, 45°, 80°, 60°, 50°).

[0072] Assume that the signal-to-noise ratio SNR of two near-field targets is 10 dB, and 10 Monte Carlo simulation experiments are carried out. The parameter estimation results of the near-field targets are as follows Figure 2 and Figure 3 , from Figure 2 and Figure 3 it can be shown that: This algorithm can correctly identify two target sources, and the parameters can be automatically paired with high estimation accuracy.

Claims

1. A near-field EMVS-MIMO radar parameter estimation method based on an accurate model, characterized in that: This method includes the following steps: S1. Establish a system model of a bistatic MIMO radar based on EMVS. The transmitting end is a transmitting array composed of M EMVS, and the receiving end is a receiving array composed of N EMVS. The M EMVS of the transmitting array and the N EMVS of the receiving array are all distributed in three-dimensional space. Among them, the coordinates of the m-th EMVS of the transmitting array and the n-th receiving EMVS of the receiving array are respectively expressed as (x t,m , y t,m , z t,m ) and (x r,n , y r,n , z r,n ), where m = 1, 2, …, M and n = 1, 2, …, N; Take the EMVS located at from the transmitting array as the reference element, and take the EMVS located at from the receiving array as the reference element; S2. Set K near-field targets in three-dimensional space. The M EMVS of the transmitting array transmit signals. After the signals are reflected by the K near-field targets, they are received by the receiving array. The positions of the K near-field targets are expressed as (θ t,k , θ r,k , φ t,k , φ r,k , r t,k , r r,k ), where θ t,k , φ t,k , r t,k respectively represent the elevation angle, azimuth angle of the near-field target relative to the transmitting array, and the distance from the transmitting array to the near-field target, and θ r,k , φ r,k , r r,k respectively represent the elevation angle, azimuth angle of the near-field target relative to the receiving array, and the distance from the near-field target to the nth element of the receiving array; the distances from the mth element of the transmitting array to the kth near-field target and from the kth near-field target to the nth element of the receiving array are obtained as follows: where r t,k = r t,0,k , r r,k = r r,0,k ; S3. After the receiving array receives the signal, the signal then passes through the matched filter at the receiving end and is output by the matched filter. At time t, the output signal of the matched filter at the receiving end is x(t) = (D t D r ) s(t) + n(t); where, s(t) = [s 1 (t), s 2 (t), …, s K (t)] T represents the reflection coefficient matrix, represents the additive white Gaussian noise, D t and D r represent the transmitting array steering matrix and the receiving array steering matrix, respectively, D t = [d t,1 , d t,2 , …, d t,K , D r = [d r,1 , d r,2 , …, d r,K where, Among them, τ t,m,k represents the propagation delay of the transmitted signal, τ r,n,k represents the propagation delay of the received signal, a m,t,k and a n,r,k respectively represent the spatial responses of the EMVS of the transmitting array and the spatial responses of the EMVS of the receiving array, and can be respectively expressed as: Among them, v t,m,k (θ t,m,k , φ t,m,k ) and v r,n,k (θ r,n,k , φ r,n,k ) represent matrices that are only related to the direction parameters, and g t,m,k and g r,n,k represent matrices that are only related to the polarization parameters; S4. Calculate the covariance matrix of x(t) based on the output signal x(t) of the matched filter in step S3, i.e.: R = E[x(t)x H (t)] = [D t D r R s [D t D r H + σ 2 I, where represents the covariance matrix of the approaching target, represents the signal power of the k-th target, and I is an identity matrix;​ S5. Rearrange the covariance matrix R of x(t) in step S4 into a fourth-order tensor form, i.e.: where represents a fourth-order tensor operator, represents the tensor form of σ 2 I, D t×2 represents the tensor form of D t and D r×3 represents the tensor form of D r . The tensor form of represents . The tensor form of represents D r . The conjugate matrix of S6. Rearrange the fourth-order tensor obtained in step S5 into a third-order tensor again That is where represents a third-order tensor operator S7. For the third-order tensor in step S6 perform parallel factor decomposition using the complex parallel factor algorithm to obtain the estimated values of the emission array steering matrix D t and the receiving array steering matrix D r ; and and and satisfy the following two relationships: where Π is a column permutation matrix, Δ 1 , Δ 2 is a scale ambiguity matrix, N 1 , N 2 is an error matrix; S8. Normalize the results obtained in step S7 and to construct two selection matrices after normalization: where, e m represents a 1×M row vector, whose m-th element is 1 and the rest are 0; e n represents a 1×N row vector, whose n-th element is 1 and the rest are 0; then use the two selection matrices to respectively select the rows from the l-th row to the (l + 6)-th row of and the rows from the l-th row to the (l + 6)-th row of H t,m The i-th row of t,m and the j-th row of H r,n The i-th row of H r,n and the j-th row of There are rotation invariant relationships respectively as follows: where i, j = 1, 2, 3, 4, 5, 6; H t,m (i, :) represents the i-th row of H t,m ; H r,n (i, :) represents the i-th row of H r,n ; H t,m (j, :) represents the j-th row of H t,m ; H r,n (j, :) represents the j-th row of H r,n ; diag{·} represents the diagonalization operation; S9. According to step S8, obtain the estimated value of the electric field vector of the transmitting array and the estimated value of the magnetic field vector That is where represents the k-th element of in step S8, represents the k-th element of in step S8. Similarly, obtain the estimated value of the electric field vector of the receiving array and the estimated value of the magnetic field vector That is S10. According to step S9, further obtain the estimated values of the Poynting vector at the m-th EMVS of the transmitting array for the k-th target and the Poynting vector at the n-th EMVS of the receiving array for the k-th target as: Among them, represents the vector cross product operation; S11. According to the estimated values of the Poynting vector obtained in step S10, obtain the estimated values of the two-dimensional transmission angle of the k-th target with respect to the m-th element in the transmitting array and the two-dimensional reception angle of the k-th target with respect to the n-th element in the receiving array as: S12. According to step S11, reconstruct the spatial response of the m-th element in the transmitting array with respect to the k-th target and the spatial response of the k-th target with respect to the n-th element in the receiving array That is After that, the estimated values of g t,m,k and g r,n,k are obtained respectively and where, () + represents the pseudo-inverse operation on the matrix; from and the estimated values of the polarization parameters of the m-th element in the transmitting array with respect to the k-th target and the estimated values of the polarization parameters of the k-th target with respect to the n-th element in the receiving array can be obtained respectively, that is: Then the estimated values of the two-dimensional transmit polarization parameters and the two-dimensional receive polarization parameters are as follows: S13. According to the geometric relationship of the system model of the bistatic MIMO radar based on EMVS, two linear equations related to the transmitting array and the receiving array are obtained respectively, namely Simplify the two linear equations. After simplification, the coefficient matrices of the two linear equations are F t,k and F r,k , and the constant term matrices are G t,k and G r,k , which are respectively expressed as: The relevant terms related to the emission distance and emission angle in the two simplified equations are expressed as: The relevant terms related to the reception distance and reception angle are expressed as: The coefficient matrix F t,k 、the coefficient matrix F r,k 、the constant term matrix G t,k 、the constant term matrix G r,k 、the relevant term Θ t,k and the relevant term Θ r,k are combined into an overall compact matrix, and the compact matrix is expressed as: where blkdiag{·} represents the block diagonalization operation; based on the said compact matrix, the estimated value of Θ k is: Finally, the estimated values of the two-dimensional emission angle, two-dimensional reception angle, emission distance, and reception distance of the k-th target are respectively:

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