An Enhanced FDA-MIMO Dual-Mode Radar Cooperative Target Localization Method

Abstract

The present invention relates to an enhanced FDA-MIMO dual-mode radar cooperative target localization method, and the method includes the steps of: acquiring the final received signals of MIMO and FDA-MIMO dual-mode radars; calculating the signal subspace of the target signals; implementing DOA estimation of the target signals in the MIMO mode; calibrating the target phase matrix in different modes through subspace rotational invariance to obtain phase calibration information corresponding one-to-one to the target phase information; calculating a rough estimated value of DOD of the target in the MIMO mode, substituting it into the FDA-MIMO to estimate the distance information of the target, and finally jointly using the received data in the dual modes to achieve high-precision DOD estimation of the target. This localization method avoids the complex system design and the process of sub-array division and pairing in the existing solutions, and greatly reduces the complexity of target localization.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar positioning, and particularly relates to an enhanced FDA-MIMO dual-mode radar cooperative target positioning method. Background Art

[0002] Target positioning is an important research topic in both military and civilian fields. Bistatic radars adopt a separated transmitting and receiving antenna array architecture, and have higher survivability and detection advantages when facing the "four major threats": electronic interference, ultra-low altitude penetration, anti-radiation missiles, and stealth weapons. By placing the transmitting platform outside the enemy's attack range and using equipment such as aircraft as receiving platforms for reconnaissance on the battlefield, compared with traditional monostatic radars, the detection concealment and survivability are greatly enhanced. In modern military equipment, it is increasingly applied by more and more countries in radar systems such as vehicle-mounted, airborne, and land-based.

[0003] In the bistatic FDA-MIMO radar system, the direction of departure (DOD) of the target signal is usually different from the direction of arrival (DOA) of the target signal. The method of using the receiving steering vector to solve the range-angle coupling in monostatic radars is no longer applicable, resulting in more complex decoupling of range and angle in the transmitting steering vector in the bistatic scenario. Therefore, how to achieve range-angle decoupling in the bistatic FDA-MIMO system is the key problem for target positioning in the bistatic radar system.

[0004] Currently, the methods for solving the range-angle coupling problem in the transmitting steering vector of bistatic FDA-MIMO radars include: non-search target positioning methods, target positioning methods based on real subspace decomposition, space-time-frequency domain joint target positioning methods, etc. Non-search target positioning methods and target positioning methods based on real subspace decomposition need to divide the entire array into multiple sub-arrays and require an additional pairing process. The space-time-frequency domain joint target positioning method uses multiple mutually prime frequency increments to achieve the purpose of synthesizing multiple sub-arrays. The above methods will increase the complexity in the design of radar systems. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides an enhanced FDA-MIMO dual-mode radar cooperative target positioning method. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0006] An embodiment of the present invention provides an enhanced FDA-MIMO dual-mode radar cooperative target positioning method, including the steps of:

[0007] S1. Obtain the target echo data of several targets received by each receiving array element of the MIMO and FDA-MIMO dual-mode radars in the dual mode;

[0008] S2. At the radar receiving end, perform down-conversion and matched filtering on the target echo data in sequence to obtain the final received signal of the MIMO and FDA-MIMO dual-mode radar;

[0009] S3. Use the final received signal to obtain the data covariance matrix at the radar receiving end, and perform eigenvalue decomposition on the data covariance matrix to obtain the signal subspace of the target signal;

[0010] S4. Calculate the signal subspace of the MIMO mode and the signal subspace of the FDA-MIMO mode using the signal subspace, and transform the signal subspace of the MIMO mode and the signal subspace of the FDA-MIMO mode using the steering vector relationship of the MIMO and FDA-MIMO dual-mode radar to obtain the DOA estimation of the target signal;

[0011] S5. Match the signal subspace of the MIMO mode and the signal subspace of the FDA-MIMO mode using the signal subspace in the dual-mode, the rotational invariance of the array steering vector, and the characteristic matrix of the received signal of the dual-mode radar to obtain the phase calibration information corresponding one-to-one to the target phase information;

[0012] S6. Calculate the rough DOD estimation value of the target in the MIMO mode, then calculate the target distance estimation value in the FDA-MIMO mode in combination with the rough DOD estimation value and the phase calibration information, construct a distance compensation matrix, and jointly use the target distance estimation value and the transmit steering vectors of the MIMO mode and the FDA-MIMO mode to achieve the accurate DOD estimation of the target, and obtain the position information of the target under the dual-mode radar.

[0013] In an embodiment of the present invention, the target echo data is:

[0014] y n,l = y 1,n,l + y 2,n,l

[0015] where y 1,n,l represents the target echo generated by the MIMO mode, and y 2,n,l represents the target echo generated by the FDA-MIMO mode.

[0016] In an embodiment of the present invention, step S2 includes:

[0017] At the radar receiving end, perform down-conversion and matched filtering on the target echo data in sequence to obtain the echo signal of the MIMO mode and the echo signal of the FDA-MIMO mode:

[0018]

[0019]

[0020] Among them, ξ l represents the reflection coefficient of the target, f d,l = 2v l / λ 0 represents the Doppler shift of the l-th target in the MIMO radar, t represents time, τ′ 0,l = r l / c represents the propagation delay of the signal to the l-th target, f 0 represents the signal carrier frequency, c represents the speed of light, d represents the element spacing, m′ represents the m′-th transmitting element in the MIMO mode, m represents the m-th transmitting element in the FDA-MIMO mode, represents the transmitting angle of the l-th target, n represents the n-th receiving element, θ l represents the receiving angle of the l-th target, r l = r T,l + r R,l represents the propagation distance of the l-th target, r T,l and r R,l are the distances from the l-th target to the transmitter and the receiver respectively;

[0021] The first output combined signal of the n-th receiving element corresponding to the MIMO mode is obtained from the echo signal of the MIMO mode, and the second output combined signal of the n-th receiving element corresponding to the FDA-MIMO mode is obtained from the echo signal of the FDA-MIMO mode;

[0022] The data of all receiving elements are combined to obtain a first echo data matrix and a second echo data matrix:

[0023] x 1 = η 1 A 1 s(t)

[0024] x 2 = η 2 A 2 s(t)

[0025] Among them, x 1 represents the first echo data matrix, x 2 represents the second echo data matrix, A 1 represents the steering vector matrix of the MIMO radar, A 2 represents the steering vector matrix of the FDA-MIMO radar, s(t) represents the transmitted signal of the radar;

[0026] The first echo data matrix and the second echo data matrix are combined to obtain the final received signal:

[0027]

[0028] Among them, n(t) represents Gaussian white noise, and A represents the steering vector matrix. represents the transmit steering vector of the i-th target in the MIMO mode. represents the transmit angle of the l-th target, L represents the total number of targets, and a r (θ i ) represents the receive steering vector of the l-th target. represents the transmit steering vector of the i-th target in the FDA-MIMO mode:

[0029]

[0030] It is expressed as:

[0031]

[0032] In an embodiment of the present invention, step S3 includes:

[0033] Obtain the data covariance matrix of the radar receiving end according to the final received signal:

[0034] R x = E{x(t)x H (t)} = R s + Q

[0035] Among them, is the covariance matrix of the target signal, is the covariance matrix of Gaussian white noise, x(t) represents the echo signal at the receiving end, and E represents the expected value operation;

[0036] Perform eigenvalue decomposition on the data covariance matrix to obtain the signal subspace of the target signal. Among them, the process of eigenvalue decomposition is:

[0037]

[0038] Among them, represents the signal subspace composed of the eigenvectors corresponding to L large eigenvalues, represents the noise subspace composed of the eigenvectors corresponding to the remaining MN - L small eigenvalues, is a diagonal matrix composed of L large eigenvalues, is a diagonal matrix composed of MN - L small eigenvalues.

[0039] In an embodiment of the present invention, step S4 includes:

[0040] Calculate the signal subspace of the MIMO mode and the signal subspace of the FDA-MIMO mode by using the said signal subspace respectively:

[0041] U sr1 = A r1 T

[0042] U sr2 = A r2 T

[0043] wherein, U sr1 represents the signal subspace of the MIMO mode, and U sr2 represents the signal subspace of the FDA-MIMO mode; A r1 represents the steering vector of the MIMO mode; A r2 represents the steering vector of the FDA-MIMO mode, T represents a non-singular matrix, I is an identity matrix, and 0 is a zero matrix;

[0044] Calculate the relationship of the steering vectors of the MIMO and FDA-MIMO dual-mode radar as:

[0045] A r2 = A r1 Φ r

[0046] wherein, Φ r is a first diagonal matrix of L×L dimension containing DOA information;

[0047]

[0048] Solve the diagonal elements of the first diagonal matrix from the signal subspace of the MIMO mode, the signal subspace of the FDA-MIMO mode, the relationship of the steering vectors, and the characteristic matrix of the received signal of the dual-mode radar, and obtain the DOA estimation of the target signal:

[0049]

[0050] wherein, represents the l-th diagonal element of the first diagonal matrix.

[0051] In an embodiment of the present invention, step S5 includes:

[0052] Calculate the signal subspace in the MIMO mode by using the signal subspace in the dual mode;

[0053] Combined with the signal subspace in the MIMO mode, calculate a second diagonal matrix containing DOD information by using the rotational invariance of the array steering vector:

[0054]

[0055] Calibrate the first diagonal matrix and the second diagonal matrix by using the characteristic matrix of the received signal of the dual-mode radar to obtain a first calibrated diagonal matrix and a second calibrated diagonal matrix:

[0056]

[0057]

[0058] Among them, represents the first calibrated diagonal matrix, Ψ r represents the similarity matrix of Φ r G r represents the characteristic matrix of the received signal of the dual-mode radar, HF represents the calibration matrix, H represents the scaling factor, F represents the column transformation matrix, T represents the non-singular matrix, Φ r represents the first diagonal matrix, represents the second calibrated diagonal matrix, Ψ 1,t represents the similarity matrix of Φ 1,t Φ 1,t represents the second diagonal matrix;

[0059] Calculate the signal subspace in the FDA-MIMO mode by using the signal subspace in the dual-mode;

[0060] Combined with the signal subspace in the FDA-MIMO mode, calculate a third diagonal matrix containing DOA information and distance information by using the rotational invariance of the array steering vector:

[0061]

[0062] Calibrate the third diagonal matrix by using the characteristic matrix of the received signal of the dual-mode radar to obtain a third calibrated diagonal matrix:

[0063]

[0064] Among them, represents the third calibrated diagonal matrix, Ψ 2,t represents the similarity matrix of Φ 2,t Φ 2,t represents the third diagonal matrix.

[0065] In an embodiment of the present invention, step S6 includes:

[0066] Estimate the DOD of the target in the MIMO mode from the phase information of the transmit steering vector to obtain a rough DOD estimate value:

[0067]

[0068] wherein, represents the l-th diagonal element of the second diagonal matrix;

[0069] Calculate the target distance estimation value in the FDA - MIMO mode by combining the rough DOD estimation value, the second calibration diagonal matrix, and the third calibration diagonal matrix:

[0070]

[0071] wherein, represents the DOD information of the target, and the rough estimation value obtained previously is used in actual calculation represents the l-th diagonal element of the third diagonal matrix;

[0072] Construct a distance compensation matrix using the target distance estimation value

[0073]

[0074] wherein, 1 N represents the N-dimensional identity matrix, represents the distance compensation coefficient, r represents the target distance estimation value,

[0075] Compensate the transmit steering vectors of the MIMO mode and the FDA - MIMO mode using the distance compensation matrix to obtain the compensated dual - mode radar steering vector matrix:

[0076]

[0077] wherein, represents the transmit steering vector of the compensated dual - mode radar, a r (θ l ) represents the receive steering vector of the dual - mode radar;

[0078] Implement the accurate DOD estimation of the target using the compensated dual - mode radar steering vector matrix to obtain the DOD estimation of the target in the dual - mode:

[0079]

[0080] wherein, represents the phase phase.

[0081] In an embodiment of the present invention, the position information of the target under the dual - mode radar includes the DOA estimation of the target signal, the target distance estimation value, and the DOD estimation of the target in the dual - mode.

[0082] Compared with the prior art, the beneficial effects of the present invention:

[0083] The positioning method of the present invention combines the radar received data in the dual-mode, calibrates the target phase matrix in different modes through the subspace rotational invariance, then realizes the DOA estimation of the target in the MIMO mode and calculates the rough DOD estimation value of the target, substitutes it into the FDA-MIMO to estimate the target distance information without additional decoupling operations, and finally combines the received data in the dual-mode to realize the high-precision DOD estimation of the target. Without the subarray division and pairing process, the positioning function of the target is realized through the transformation of the target phase matrix in different modes. The complex system design and the subarray division and pairing process in the existing solutions are avoided in the whole method process, greatly reducing the complexity of target positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 FIG. is a schematic flow chart of an enhanced FDA-MIMO dual-mode radar cooperative target positioning method provided by an embodiment of the present invention;

[0085] Figure 2 FIG. is a comparison diagram of the DOA estimation value of the target signal obtained in 50 simulation experiments and the target true parameters by the target positioning method of the embodiment of the present invention;

[0086] Figure 3 FIG. is a comparison diagram of the DOD estimation value of the target signal obtained in 50 simulation experiments and the target true parameters by the target positioning method of the embodiment of the present invention;

[0087] Figure 4 FIG. is a comparison diagram of the distance estimation value of the target signal obtained in 50 simulation experiments and the target true parameters by the target positioning method of the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0088] The following further describes the present invention in detail with specific embodiments, but the embodiments of the present invention are not limited thereto.

[0089] Embodiment 1

[0090] Please refer to Figure 1 , Figure 1 FIG. is a schematic flow chart of an enhanced FDA-MIMO dual-mode radar cooperative target positioning method provided by an embodiment of the present invention.

[0091] This embodiment proposes an enhanced target positioning method based on the MIMO and FDA-MIMO dual-mode bistatic radar systems, which can realize the target positioning function under the dual-mode radar system. The method specifically includes the steps:

[0092] S1. Obtain the target echo data of several targets received by each receiving array element of the MIMO and FDA-MIMO dual-mode radars in the dual-mode.

[0093] Specifically, consider the MIMO and FDA-MIMO dual-mode radar signal models. The number of transmitting array elements in the MIMO mode is M1, and the number of transmitting array elements in the FDA-MIMO mode is M2. Then, the radar transmitting signals in the MIMO mode and the FDA-MIMO mode can be expressed as follows:

[0094]

[0095]

[0096] where denotes the pulse function, φ 1,m' (t) and φ 2,m (t) represent the transmitting reference signals in the MIMO mode and the FDA-MIMO mode, respectively. T p is the pulse width, f m = f 0 + (m - 1)Δf is the frequency of the transmitting signal of the m-th element of the FDA-MIMO radar, f 0 is the signal carrier frequency, Δf is the frequency offset between adjacent elements. Usually, Δf << f 0 , m' represents the m'-th element of the MIMO radar mode, M 1 represents the number of transmitting array elements of the MIMO radar, M 2 represents the number of transmitting array elements of the FDA-MIMO radar, and t represents time.

[0097] Consider an equally spaced uniform linear array. The element spacing d t in the MIMO mode, the element spacing d r in the FDA-MIMO mode, and the receiving element spacing d are all d t = d r = d = λ max / 2, where λ max is the maximum wavelength, and there is no phase ambiguity at this time. Assume that there are L uncorrelated targets in space, and the distances, DODs, and DOAs are Then, the target echo data received by the n-th receiving element from the l-th target is:

[0098] y n,l = y 1,n,l + y 2,n,l (3)

[0099] where y 1,n,l represents the target echo generated by the MIMO mode, and y 2,n,l represents the target echo generated by the FDA-MIMO mode. y 1,n,l and y 2,n,l can be expressed as follows:

[0100]

[0101]

[0102] Among them, ξ l represents the reflection coefficient of the target, t represents time, and τ 0 represents the propagation delay of the reference array element signal, and f d,l = 2v l / λ 0 and f d,m,l = 2v l / λ m respectively represent the Doppler frequency shifts of the l-th target in the MIMO mode and the FDA-MIMO mode. When Δf << f, the two can be considered equal; τ 1,m',l and τ 2,m,l respectively represent the propagation delays of the transmitted signals in the MIMO mode and the FDA-MIMO mode reaching the l-th target, is the propagation delay of the echo signal of the l-th target reaching the receiving end, r T,l and r R,l respectively represent the distances from the l-th target to the transmitting end and the receiving end, d t represents the transmitting array element spacing, represents the transmitting angle of the l-th target, d r represents the receiving array element spacing, and θ l represents the receiving angle of the l-th target.

[0103] S2. At the radar receiving end, the target echo data is sequentially down-converted and matched filtered to obtain the final received signals of the MIMO and FDA-MIMO dual-mode radar. Specifically, it includes:

[0104] S21. At the radar receiving end, the target echo data is sequentially down-converted and matched filtered to obtain the echo signals of the MIMO mode and the echo signals of the FDA-MIMO mode:

[0105]

[0106]

[0107] Among them, ξ l represents the reflection coefficient of the target, f d,l = 2v l / λ 0 represents the Doppler frequency shift of the l-th target in the MIMO radar, t represents time, and τ′ 0,l = r l / c represents the propagation delay of the signal to the l-th target, and f 0\(f_0\) represents the signal carrier frequency, \(c\) represents the speed of light, \(d\) represents the array element spacing, and \(m'\) represents the \(m'\)-th array element in the MIMO radar mode. \(\theta_{tl}\) represents the transmission angle of the \(l\)-th target, \(n\) represents the \(n\)-th receiving array element, and \(\theta\) l \(\varphi_{rl}\) represents the reception angle of the \(l\)-th target, and \(r\) l \(r = r\) T,l \(+ r\) R,l \(r_{l}\) represents the propagation distance of the \(l\)-th target, and \(r\) T,l and \(r\) R,l are the distances from the \(l\)-th target to the transmitter and the receiver, respectively.

[0108] S22. Obtain the first output combined signal of the \(n\)-th receiving array element corresponding to the MIMO mode from the echo signal of the MIMO mode, and obtain the second output combined signal of the \(n\)-th receiving array element corresponding to the FDA - MIMO mode from the echo signal of the FDA - MIMO mode.

[0109] Since \(\Delta f\) is very small, the phase difference of the signal propagation of the FDA - MIMO radar and the MIMO radar for the \(l\)-th target signal can be expressed by Therefore, the first output combined signal of the \(n\)-th receiving array element corresponding to the MIMO mode can be obtained from the echo signal of the MIMO mode, and the second output combined signal of the \(n\)-th receiving array element corresponding to the FDA - MIMO mode can be obtained from the echo signal of the FDA - MIMO mode. The first output combined signal and the second output combined signal are:

[0110]

[0111]

[0112] where \(\lambda\) 0 represents the signal wavelength, and \(\Delta f\) represents the signal frequency offset between adjacent array elements.

[0113] S23. Combine the data of all receiving array elements to obtain the first echo data matrix and the second echo data matrix.

[0114] Specifically, by combining the data of all \(N\) receiving array elements, the first echo data matrix of the MIMO radar and the second echo data matrix of the FDA - MIMO radar can be obtained, which are respectively expressed as:

[0115] \(\mathbf{x}\) 1 \(=\eta\) 1 \(\mathbf{A}\) 1 \(\mathbf{s}(t)\) (10)

[0116] \(\mathbf{x}\) 2 \(=\eta\) 2 \(\mathbf{A}\) 2 \(\mathbf{s}(t)\) (11)

[0117] Among them, A 1 represents the steering vector matrix of the MIMO radar, and A 2 represents the steering vector matrix of the FDA-MIMO radar, and s(t) represents the radar transmission signal.

[0118] S24. Combine the first echo data matrix and the second echo data matrix to obtain the final received signal of the MIMO and FDA-MIMO dual-mode radar:

[0119]

[0120] Among them, n(t) represents Gaussian white noise, and A represents the steering vector matrix, represents the transmission steering vector of the i-th target in the MIMO mode, represents the transmission angle of the i-th target, L represents the total number of targets, and a r (θ i ) represents the reception steering vector of the i-th target, represents the transmission steering vector of the i-th target in the FDA-MIMO mode.

[0121] The steering vector matrix A can be expressed as:

[0122]

[0123] Among them, can be expressed as:

[0124]

[0125] S3. Use the final received signal to obtain the data covariance matrix at the radar receiving end, and perform eigenvalue decomposition on the data covariance matrix to obtain the signal subspace of the target signal. Specifically, it includes:

[0126] S31. Obtain the data covariance matrix at the radar receiving end according to the final received signal.

[0127] According to the final received signal, that is, formula (12), the data covariance matrix at the radar receiving end is obtained as:

[0128] R x = E{x(t)x H (t)} = R s + Q (15)

[0129] Among them, is the covariance matrix of the target signal, is the covariance matrix of Gaussian white noise, \(x(t)\) represents the received data of the dual-mode radar, and \(E\) represents the expectation operation. In the actual application scenario, due to the limited number of sampling snapshots, generally use to estimate the data covariance matrix, where \(J\) is the number of sampling snapshots.

[0130] S32. Perform eigenvalue decomposition on the data covariance matrix to obtain the signal subspace \(U\) of the target signal s .

[0131] Specifically, performing eigenvalue decomposition on the data covariance matrix can obtain:

[0132]

[0133] where, represents the signal subspace composed of the eigenvectors corresponding to \(L\) large eigenvalues, represents the noise subspace composed of the eigenvectors corresponding to the remaining \(MN - L\) small eigenvalues, is a diagonal matrix composed of \(L\) large eigenvalues, is a diagonal matrix composed of \(MN - L\) small eigenvalues.

[0134] S4. Calculate the signal subspace of the MIMO mode and the signal subspace of the FDA - MIMO mode using the signal subspace, and perform transformation on the signal subspace of the MIMO mode and the signal subspace of the FDA - MIMO mode using the steering vector relationship of the MIMO and FDA - MIMO dual - mode radar to obtain the DOA estimation of the target signal. Specifically include:

[0135] S41. Calculate the signal subspace of the MIMO mode and the signal subspace of the FDA - MIMO mode respectively using the signal subspace.

[0136] First, define two data matrices as and which can be expressed as:

[0137]

[0138] where \(I\) is the identity matrix and \(0\) is the zero matrix.

[0139] According to the subspace theory, the signal subspace of the target signal in formula (16) can be expressed as:

[0140] U s = A^T (18)

[0141] where \(T\) is a non - singular matrix. Substituting formula (18) into formula (17) can obtain the signal subspace of the MIMO mode and the signal subspace of the FDA - MIMO mode:

[0142]

[0143] Among them, U sr1 represents the signal subspace of the MIMO mode, and U sr2 represents the signal subspace of the FDA-MIMO mode. A r1 represents the steering vector of the MIMO mode. A r2 represents the steering vector of the FDA-MIMO mode.

[0144] S42. Calculate the relationship between the steering vectors of the MIMO and FDA-MIMO dual-mode radar.

[0145] The relationship between the steering vectors of the MIMO and FDA-MIMO dual-mode radar can be obtained through Equation (19) as follows:

[0146] A r2 = A r1 Φ r (20)

[0147] Among them, Φ r is a first diagonal matrix of L×L dimension containing DOA information, expressed as:

[0148]

[0149] S43. Solve the diagonal elements of the first diagonal matrix from the signal subspace of the MIMO mode, the signal subspace of the FDA-MIMO mode, the relationship between the steering vectors, and the characteristic matrix of the received signal of the dual-mode radar to obtain the DOA estimation of the target signal.

[0150] Specifically, by combining the signal subspace of the MIMO mode, the signal subspace of the FDA-MIMO mode, and the relationship between the steering vectors, that is, by combining Equation (19) and Equation (20), we can obtain:

[0151]

[0152] It can be known that Ψ r and Φ r are similar matrices. Therefore, the diagonal elements of Φ r are the matrix eigenvalues of Ψ r . Therefore, by performing eigenvalue decomposition on the matrix Ψ r , we can obtain:

[0153]

[0154] Among them, is obtained from Ψ rThe diagonal matrix composed of the L eigenvalues of G r is the matrix composed of the corresponding eigenvectors. Thus, the DOA estimation of the target signal can be obtained as:

[0155]

[0156] where represents the matrix Ψ r the l-th eigenvalue.

[0157] S5. Match the signal subspace of the MIMO mode and the signal subspace of the FDA-MIMO mode by using the signal subspace in the dual mode, the rotational invariance of the array steering vector, and the characteristic matrix of the dual-mode radar received signal, and obtain the phase calibration information corresponding to the target phase information. Specifically, it includes:

[0158] S51. Calculate the signal subspace in the MIMO mode by using the signal subspace in the dual mode.

[0159] Specifically, according to formula (18), the relationship between the radar signal subspace in the single mode and the radar signal subspace in the dual mode can be obtained for the signal subspace of the target signal as:

[0160]

[0161] where U 1,s = A 1 T, U 1,s = A 1 T.

[0162] Therefore, the signal subspace in the MIMO mode can be calculated according to the signal subspace in the dual mode and is expressed as:

[0163]

[0164] Here, considering that η 1 is a constant in the single mode, it is ignored.

[0165] S52. Combine the signal subspace in the MIMO mode and use the rotational invariance of the array steering vector to calculate the second diagonal matrix containing the DOD information.

[0166] Specifically, two data matrices are defined in the same way as and expressed as:

[0167]

[0168] According to the rotational invariance of the array steering vector matrix, there is:

[0169] A1,t2 = A 1,t1 Φ 1,t (28)

[0170] Among them, Φ 1,t is the second diagonal matrix containing DOD information, expressed as:

[0171]

[0172] S53. Calibrate the first diagonal matrix and the second diagonal matrix using the characteristic matrix of the received signal of the dual-mode radar to obtain a first calibrated diagonal matrix and a second calibrated diagonal matrix.

[0173] Specifically, combining formulas (25)-(29) gives:

[0174]

[0175] Actually, the DOD of the target can be estimated by performing eigenvalue decomposition on the matrix Ψ 1,t However, since it cannot be guaranteed that the DOD estimated by formula (30) and the DOA estimated by formula (23) correspond to the same target, at this time, the decoupling of distance and angle in the FDA-MIMO mode cannot be guaranteed. Therefore, next, the characteristic matrix of the received signal of the dual-mode radar is used to simultaneously match the signal subspaces corresponding to the MIMO radar and the FDA-MIMO radar, as follows:

[0176] According to formulas (22) and (23), it is easy to verify that G r and T -1 are both matrices composed of the eigenvectors of Ψ r Therefore, they have the following relationship:

[0177] G r = T -1 HF (31)

[0178] Among them, H and F represent the scale factor and the column transformation matrix respectively. Substituting formulas (22) and (31) into (23), we can get:

[0179]

[0180] Among them, represents the first calibrated diagonal matrix, Ψ r represents the similar matrix of Φ r G r represents the characteristic matrix of the received signal of the dual-mode radar, HF represents the calibration matrix, H represents the scale factor, F represents the column transformation matrix, T represents a non-singular matrix, and Φ r represents the first diagonal matrix.

[0181] Next, define a matrix Then, by combining formulas (30) and (31), we can obtain:

[0182]

[0183] From formulas (32) and (33), it can be seen that matrix Φ r and matrix Φ 1,t are obtained by the same column transformation from the column transformation of matrix HF, and both are diagonal matrices. Therefore, the targets corresponding to the diagonal elements of the two must be the same. In this way, by simply selecting the same diagonal index elements in matrix Φ r and matrix Φ 1,t , the DOA and DOD estimations of the target can be achieved simultaneously. Before that, it is necessary to calibrate the subspace data of the FDA-MIMO radar to ensure that the DOD, DOA, and distance of the target signal satisfy one-to-one correspondence.

[0184] S54. Calculate the signal subspace in the FDA-MIMO mode using the signal subspace in the dual mode.

[0185] By analogy with formula (26), the signal subspace in the FDA-MIMO mode can be calculated as follows:

[0186]

[0187] S55. Combine the signal subspace in the FDA-MIMO mode and use the rotational invariance of the array steering vector to calculate the third diagonal matrix containing DOA information and distance information.

[0188] Similarly, define two data matrices as and Expressed as:

[0189]

[0190] Further derivation gives:

[0191] A 2,t2 = A 2,t1 Φ 2,t (36)

[0192] where Φ 2,t is the third diagonal matrix containing DOA information and distance information, expressed as:

[0193]

[0194] S56. Calibrate the third diagonal matrix using the eigenmatrix of the received signal of the dual-mode radar to obtain a third calibrated diagonal matrix.

[0195] By combining formulas (25) and (35), we can obtain:

[0196]

[0197] Obviously, the diagonal elements of Φ 2,t can be obtained by performing eigenvalue decomposition on the matrix Ψ 2,t . However, due to the range-angle coupling in the transmit steering vector of the FDA-MIMO radar, that is, the coupling between the target range and DOD, it is impossible to directly calculate the target range information. Although the corresponding DOD information in the MIMO radar mode can be estimated through formula (33) above, since it cannot be guaranteed that the DOD estimation in the MIMO mode and the DOD estimation in the FDA-MIMO mode correspond to the same target, the range and DOD coupling problem in the FDA-MIMO cannot still be solved through the DOD estimation in the MIMO radar.

[0198] To solve this problem, use the eigenmatrix G r of the received signal in the dual mode to calibrate Ψ 2,t in the FDA-MIMO mode. First, define a matrix expressed as:

[0199]

[0200] Substitute formulas (31) and (38) to obtain the third calibrated diagonal matrix:

[0201]

[0202] where, represents the third calibrated diagonal matrix, Ψ 2,t represents the similarity matrix of Φ 2,t , and Φ 2,t represents the third diagonal matrix.

[0203] It can be seen from formulas (32), (33), and (40) that the diagonal matrices Φ r , Φ 1,t and Φ 2,t corresponding to the dual-mode radar, MIMO radar, and FDA-MIMO radar can be transformed into and forms respectively through the calibration matrix HF. After calibration, and The included target phase information is in one-to-one correspondence. At this time, the target DOD and range coupling problems in the FDA-MIMO radar can be solved by the target DOD estimation obtained by the MIMO radar.

[0204] S6. Calculate the rough DOD estimation value of the target in the MIMO mode, then combine the rough DOD estimation value and the phase calibration information to calculate the target range estimation value in the FDA-MIMO mode, and construct a range compensation matrix. Combine the target range estimation value and the transmit steering vectors of the MIMO mode and the FDA-MIMO mode to achieve the accurate DOD estimation of the target, and obtain the position information of the target under the dual-mode radar. Specifically, it includes:

[0205] S61. Estimate the DOD of the target in the MIMO mode from the phase information of the transmit steering vector to obtain the rough DOD estimation value:

[0206]

[0207] Where, represents the l-th diagonal element of the second diagonal matrix;

[0208] S62. Combine the rough DOD estimation value, the second calibration diagonal matrix, and the third calibration diagonal matrix to calculate the target range estimation value in the FDA-MIMO mode.

[0209] According to formulas (33) and (40), it can be known that the matrices and correspond to the same target at the same diagonal index. Therefore, the phase term in the MIMO radar mode corresponds to the term in the FDA-MIMO radar mode. Considering the phase ambiguity in the transmit steering vector of the FDA-MIMO radar, the discriminant is given as follows:

[0210]

[0211] It is easy to verify that when , k = 0; when , k = 1. Furthermore, the target range estimation value in the FDA-MIMO mode can be calculated as:

[0212]

[0213] Where, represents the transmit angle of the l-th target, and the rough estimation value is used instead in actual calculation, represents the l-th eigenvalue of the matrix

[0214] ​S63. Accurately estimate the direction of departure (DOD) of the target.

[0215] S631. Construct a distance compensation matrix using the estimated target distance value.

[0216] First, define the matrix Expressed as:

[0217]

[0218] where U 2,s and G r are given by formulas (34) and (23) respectively. Combining formulas (25) and (31), the above formula (44) can be further written as:

[0219]

[0220] Subsequently, construct a distance compensation matrix using the estimated target distance value The compensation matrix can be expressed as:

[0221]

[0222] where, 1 N represents the N-dimensional identity matrix, r represents the estimated target distance value, represents the distance compensation coefficient,

[0223]

[0224] S632. Compensate the transmit steering vectors of the MIMO mode and the FDA-MIMO mode using the distance compensation matrix to obtain the compensated dual-mode radar steering vector matrix.

[0225] The compensated can be expressed as:

[0226]

[0227] where, represents the inner product of matrix elements. Obviously, after compensation, the distance phase term in the transmit steering vector of the FDA-MIMO radar is eliminated. By analogy with the FDA-MIMO radar, the matrix of the MIMO radar can be obtained Expressed as:

[0228]

[0229] Superimpose the MIMO radar and FDA-MIMO radar matrices to obtain:

[0230]

[0231] Among them, A′ is the steering vector matrix after dual-mode radar data compensation. Similarly, the steering vector matrix after FDA-MIMO radar compensation can be obtained as:

[0232]

[0233] in, It can be expressed as:

[0234]

[0235] Therefore, the emission steering vector of the dual-mode radar can be expressed as:

[0236]

[0237] Considering the phase difference between MIMO radar and FDA-MIMO radar is Therefore, the transmission steering vector of the dual-mode radar can be further written as:

[0238]

[0239] The final compensated dual-mode radar steering vector matrix A′ is:

[0240]

[0241] in, represents the transmission steering vector of the dual-mode radar after compensation, a r (θ l ) represents the receive steering vector.

[0242] S633: Use the compensated dual-mode radar guidance vector matrix to achieve accurate DOD estimation of the target, and obtain the DOD estimation of the target in the dual mode.

[0243] Define two matrices as and Respectively expressed as:

[0244]

[0245] Obviously the matrix and satisfy:

[0246]

[0247] where Φ t is a diagonal matrix, expressed as:

[0248]

[0249] By combining formula (50) and formula (56), we can get:

[0250]

[0251] According to formula (59), it can be known that matrix Φ t and are similar matrices and both are diagonal matrices. Therefore, the diagonal elements of matrix can be directly used to achieve the DOD estimation of the target. At the same time, since the matrix calibration work has been completed before, the DOD of the target in the dual-mode can be expressed as:

[0252]

[0253] In summary, the position information of the target under the dual-mode radar includes the DOA estimation of the target signal, the target distance estimation value, and the DOD estimation of the target in the dual-mode, which is expressed as:

[0254]

[0255] The positioning method of this embodiment combines the radar received data in the dual-mode, calibrates the target phase matrix in different modes through the subspace rotational invariance, then realizes the DOA estimation of the target in the MIMO mode and calculates the rough DOD estimation value of the target, substitutes it into the FDA-MIMO without additional decoupling operation to estimate the target distance information, and finally combines the received data in the dual-mode to achieve the high-precision DOD estimation of the target. Without the subarray division and pairing process, the positioning function of the target is realized through the transformation of the target phase matrix in different modes. The complex system design and the subarray division and pairing process in the existing scheme are avoided in the whole method process, which greatly reduces the complexity of target positioning.

[0256] The following further illustrates the effect of the present invention in combination with simulation experiments.

[0257] To evaluate the performance of this method, consider that the spacing between the uniform linear array, the dual-mode radar transmitting array element and the receiving array element is In the simulation, four target position information are set as (-20°, -38°, 5000m), (-16°, -10°, 5800m), (10°, 16°, 7000m) and (30°, 45°, 9000m) respectively, and the other simulation parameters are shown in Table 1.

[0258] Table 1 Simulation parameter table of MIMO and FDA-MIMO dual-mode bistatic radar

[0259] Parameter Parameter value Parameter Parameter value Number of MIMO radar array elements 8 <![CDATA[Carrier frequency f 0 > 10 GHz Number of FDA-MIMO radar array elements 8 Frequency offset Δf 15 KHz Number of receiving array elements 8 Number of sampling snapshots J 300

[0260] Please refer to Figure 2 、 Figure 3 and Figure 4 , Figure 2The comparison chart of the DOA estimated value of the target signal obtained in 50 simulation experiments and the target true parameters for the target positioning method of the embodiment of the present invention. Figure 3 The comparison chart of the DOD estimated value of the target signal obtained in 50 simulation experiments and the target true parameters for the target positioning method of the embodiment of the present invention. Figure 4 The comparison chart of the distance estimated value of the target signal obtained in 50 simulation experiments and the target true parameters for the target positioning method of the embodiment of the present invention.

[0261] From Figure 2 it can be seen that for the 4 set targets, the target positioning method of this embodiment shows stable estimation performance for the DOA of the target, which is basically consistent with the target true parameters. Similarly, for the simulation Figure 3 , it can be seen that the target positioning method of this embodiment also shows excellent performance in the DOD estimation of the target, which is basically equal to the true DOD of the target. The simulation Figure 4 gives the comparison of the target positioning method of this embodiment with the target true parameters during distance estimation. It can be seen that although there is a certain range of fluctuations in the target distance obtained during the estimation process, generally the target distance values estimated in each experiment are basically consistent with the true parameters. In summary, the target positioning method of this embodiment can effectively achieve high-precision parameter estimation of the target in the dual-mode FDA-MIMO radar.

[0262] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should all be regarded as belonging to the protection scope of the present invention.

Claims

1. An enhanced FDA-MIMO dual-mode radar cooperative target localization method, characterized in that, it includes the steps: S1. Obtain the target echo data of several targets received by each receiving element of the MIMO and FDA-MIMO dual-mode radar in the dual mode; S2. Perform down-conversion and matched filtering on the target echo data in sequence at the radar receiving end to obtain the final received signals of the MIMO and FDA-MIMO dual-mode radar; S3. Use the final received signals to obtain the data covariance matrix at the radar receiving end, and perform eigenvalue decomposition on the data covariance matrix to obtain the signal subspace of the target signal; S4. Use the signal subspace to calculate the signal subspace of the MIMO mode and the signal subspace of the FDA-MIMO mode, and use the steering vector relationship of the MIMO and FDA-MIMO dual-mode radar to transform the signal subspace of the MIMO mode and the signal subspace of the FDA-MIMO mode to obtain the DOA estimation of the target signal; S5. Match the signal subspace of the MIMO mode and the signal subspace of the FDA-MIMO mode by using the signal subspace in the dual mode, the rotational invariance of the array steering vector, and the characteristic matrix of the received signals of the dual-mode radar to obtain the phase calibration information corresponding one-to-one to the target phase information; S6. Calculate the rough DOD estimation value of the target in the MIMO mode, then combine the rough DOD estimation value and the phase calibration information to calculate the target distance estimation value in the FDA-MIMO mode, and construct a distance compensation matrix, and jointly use the target distance estimation value and the transmit steering vectors of the MIMO mode and the FDA-MIMO mode to achieve the accurate DOD estimation of the target, and obtain the position information of the target under the dual-mode radar.

2. The enhanced FDA-MIMO dual-mode radar cooperative target localization method according to claim 1, characterized in that, the target echo data is: y n,l = y 1,n,l + y 2,n,l Among them, y 1,n,l represents the target echo generated by the MIMO mode, and y 2,n,l represents the target echo generated by the FDA-MIMO mode.

3. The enhanced FDA-MIMO dual-mode radar cooperative target localization method according to claim 1, characterized in that, step S2 includes: Perform down-conversion and matched filtering on the target echo data in sequence at the radar receiving end to obtain the echo signal of the MIMO mode and the echo signal of the FDA-MIMO mode: Among them, ξ l represents the reflection coefficient of the target, f d,l = 2v l / λ 0 represents the Doppler shift of the l-th target in the MIMO radar, t represents time, τ′ 0,l = r l / c represents the propagation delay of the signal to the l-th target, f 0 represents the signal carrier frequency, c represents the speed of light, d represents the element spacing, m′ represents the m′-th transmitting element in the MIMO mode, m represents the m-th transmitting element in the FDA-MIMO mode, represents the emission angle of the l-th target, n represents the n-th receiving element, θ l represents the reception angle of the l-th target, r l = r T,l + r R,l represents the propagation distance of the l-th target, r T,l and r R,l are the distances from the l-th target to the transmitter and the receiver respectively; Obtain the first output combined signal of the nth receiving element corresponding to the MIMO mode from the echo signal of the MIMO mode, and obtain the second output combined signal of the nth receiving element corresponding to the FDA-MIMO mode from the echo signal of the FDA-MIMO mode; Combine the data of all receiving elements to obtain the first echo data matrix and the second echo data matrix: x 1 = η 1 A 1 s(t) x 2 = η 2 A 2 s(t) where x 1 represents the first echo data matrix, and x 2 represents the second echo data matrix, A 1 represents the steering vector matrix of the MIMO radar, and A 2 represents the steering vector matrix of the FDA-MIMO radar, and s(t) represents the transmitted signal of the radar; Combine the first echo data matrix and the second echo data matrix to obtain the final received signal: where \(n(t)\) represents Gaussian white noise, and \(A\) represents the steering vector matrix, which represents the transmit steering vector of the \(i\)-th target in the MIMO mode, where \(\theta_{l}\) represents the transmit angle of the \(l\)-th target, \(L\) represents the total number of targets, and \(a\) r (\(\theta_{l}\) i ) represents the receive steering vector of the \(l\)-th target, which represents the transmit steering vector of the \(i\)-th target in the FDA-MIMO mode: Expressed as:

4. The enhanced FDA-MIMO dual-mode radar cooperative target localization method according to claim 1, characterized in that, step S3 includes: Obtain the data covariance matrix at the radar receiving end according to the final received signal: R x = E{x(t)x H (t)} = R s + Q Among them, is the covariance matrix of the target signal, is the covariance matrix of Gaussian white noise, x(t) represents the received echo signal, and E represents the expected value operation; Perform eigenvalue decomposition on the data covariance matrix to obtain the signal subspace of the target signal, where the process of eigenvalue decomposition is as follows: Among them, represents the signal subspace composed of the eigenvectors corresponding to the L large eigenvalues, represents the noise subspace composed of the eigenvectors corresponding to the remaining MN - L small eigenvalues, is a diagonal matrix composed of L large eigenvalues, is a diagonal matrix composed of MN - L small eigenvalues.

5. The enhanced FDA-MIMO dual-mode radar cooperative target localization method according to claim 1, characterized in that, step S4 includes: Calculate the signal subspace of the MIMO mode and the signal subspace of the FDA-MIMO mode respectively using the signal subspace: U sr1 = A r1 T U sr2 = A r2 T Among them, U sr1 represents the signal subspace of the MIMO mode, and U sr2 represents the signal subspace of the FDA-MIMO mode. A r1 represents the steering vector of the MIMO mode. A r2 represents the steering vector of the FDA-MIMO mode, T represents a non-singular matrix, I is the identity matrix, and 0 is the zero matrix; Calculate the steering vector relationship of the MIMO and FDA-MIMO dual-mode radars as: A r2 = A r1 Φ r where, Φ r is the first diagonal matrix of L×L dimension containing DOA information; Solve for the diagonal elements of the first diagonal matrix from the signal subspace of the MIMO mode, the signal subspace of the FDA-MIMO mode, the steering vector relationship, and the characteristic matrix of the received signal of the dual-mode radar to obtain the DOA estimate of the target signal: Among them, represents the l-th diagonal element of the first diagonal matrix.

6. The enhanced FDA-MIMO dual-mode radar cooperative target localization method according to claim 5, characterized in that, step S5 includes: Calculate the signal subspace in the MIMO mode using the signal subspace in the dual mode; Combine the signal subspace in the MIMO mode and use the rotational invariance of the array steering vector to calculate the second diagonal matrix containing DOD information: Calibrate the first diagonal matrix and the second diagonal matrix using the characteristic matrix of the received signal of the dual-mode radar to obtain the first calibrated diagonal matrix and the second calibrated diagonal matrix: Among them, represents the first calibration diagonal matrix, Ψ r represents the similarity matrix of Φ r G represents the characteristic matrix of the dual-mode radar received signal, HF represents the calibration matrix, H represents the scale factor, F represents the column transformation matrix, T represents the non-singular matrix, and Φ r represents the first diagonal matrix, r represents the second calibration diagonal matrix, Ψ 1,t 1,t represents the similarity matrix of Φ 1,t 1,t represents the second diagonal matrix;​ Calculate the signal subspace in the FDA-MIMO mode using the signal subspace in the dual mode; Combine the signal subspace in the FDA-MIMO mode and use the rotational invariance of the array steering vector to calculate the third diagonal matrix containing DOA information and distance information: Calibrate the third diagonal matrix using the characteristic matrix of the received signal of the dual-mode radar to obtain the third calibrated diagonal matrix: Among them, represents the third calibration diagonal matrix, Ψ 2,t represents the similarity matrix of Φ 2,t , and Φ 2,t represents the third diagonal matrix.

7. The enhanced FDA-MIMO dual-mode radar cooperative target localization method according to claim 6, characterized in that, step S6 includes: Estimate the DOD of the target in the MIMO mode from the phase information of the transmit steering vector to obtain a rough DOD estimate value: Among them, represents the l-th diagonal element of the second diagonal matrix; Combine the rough DOD estimate value, the second calibrated diagonal matrix, and the third calibrated diagonal matrix to calculate the target distance estimate value in the FDA-MIMO mode: Among them, represents the DOD information of the target, and the rough estimated value obtained from the previous estimation is used in actual calculation represents the l-th diagonal element of the third diagonal matrix; Construct a distance compensation matrix using the target distance estimation value Among them, 1 N represents an N-dimensional identity matrix, represents a distance compensation coefficient, r represents an estimated target distance value, Compensate the transmit steering vectors of the MIMO mode and the FDA-MIMO mode using the distance compensation matrix to obtain a compensated dual-mode radar steering vector matrix: Among them, represents the transmit steering vector of the compensated dual-mode radar, and a r (θ l ) represents the receive steering vector of the dual-mode radar; Use the compensated dual-mode radar steering vector matrix to achieve accurate DOD estimation of the target and obtain the DOD estimate of the target in the dual mode: Among them, represents the phase.

8. The enhanced FDA-MIMO dual-mode radar cooperative target localization method according to claim 7, characterized in that, The position information of the target under the dual-mode radar includes the DOA estimate of the target signal, the target distance estimate value, and the DOD estimate of the target in the dual mode.

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